Wind Science and Engineering: Origins, Developments, Fundamentals and Advancements [1st ed.] 978-3-030-18814-6;978-3-030-18815-3

Table of contents :
Front Matter ....Pages i-xv
Introduction (Giovanni Solari)....Pages 1-4
Front Matter ....Pages 5-5
The Wind in Antiquity (Giovanni Solari)....Pages 7-84
Front Matter ....Pages 85-85
The Wind and the New Science (Giovanni Solari)....Pages 87-167
The New Culture of the Wind and Its Effects (Giovanni Solari)....Pages 169-271
Front Matter ....Pages 273-273
Scientific Progress and Its Impact on Wind (Giovanni Solari)....Pages 275-324
Wind Meteorology, Micrometeorology and Climatology (Giovanni Solari)....Pages 325-440
Wind and Aerodynamics (Giovanni Solari)....Pages 441-558
Wind, Environment and Territory (Giovanni Solari)....Pages 559-654
Wind Actions and Effects on Structures (Giovanni Solari)....Pages 655-801
Wind Hazard, Vulnerability and Risk (Giovanni Solari)....Pages 803-837
Front Matter ....Pages 839-839
Advancements in Wind Science and Engineering (Giovanni Solari)....Pages 841-924
Back Matter ....Pages 925-944

Citation preview

Springer Tracts in Civil Engineering

Giovanni Solari

Wind Science and Engineering Origins, Developments, Fundamentals and Advancements

Springer Tracts in Civil Engineering Series Editors Giovanni Solari, Wind Engineering and Structural Dynamics Research Group, University of Genoa, Genova, Italy Sheng-Hong Chen, School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China Marco di Prisco, Politecnico di Milano, Milano, Italy Ioannis Vayas, Institute of Steel Structures, National Technical University of Athens, Athens, Greece

Springer Tracts in Civil Engineering (STCE) publishes the latest developments in Civil Engineering—quickly, informally and in top quality. The series scope includes monographs, professional books, graduate textbooks and edited volumes, as well as outstanding PhD theses. Its goal is to cover all the main branches of civil engineering, both theoretical and applied, including: • • • • • • • • • • • • • •

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Giovanni Solari

Wind Science and Engineering Origins, Developments, Fundamentals and Advancements

123

Prof. Giovanni Solari Department of Civil, Chemical and Environmental Engineering Polytechnic School University of Genoa Genoa, Italy

ISSN 2366-259X ISSN 2366-2603 (electronic) Springer Tracts in Civil Engineering ISBN 978-3-030-18814-6 ISBN 978-3-030-18815-3 (eBook) https://doi.org/10.1007/978-3-030-18815-3 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To my Family

Preface

I have been studying the wind and its effects on construction, environment and territory for over 40 years. In the course of these years, I have mainly carried out research on wind engineering, trying to keep as broad a vision as possible; this research has led me to publish many scientific papers in international journals. In parallel, starting from wind and structural engineering, I have studied and followed, mainly for passion, the aspects more properly related to the evolution of knowledge, culture and science; I have written a limited number of papers in this field, but I have given many talks at universities, academies and cultural associations of all kinds. For a long time, I have considered these two visions distinct, as if the first were my job and the second a hobby that allowed me to fly higher, to overcome the analytical, numerical, experimental and technological conception of scientific research, projecting myself into a wider and more charming world. Under this point of view, I have often lived two parallel lives. Until I started to think, it was a pity and a limitation to keep two such visions distinct because, if integrated together, they could offer mutual insights and interpretations able to raise both. From this stems the conception and writing of a book that tries to translate and harmonise these two visions through a historical reconstruction and a synthetic perspective of distant worlds that pursue and attract one another: on the one hand, the wind as a source of life and comfort and as a cause of injury and death; on the other hand, the wind as a focal topic of scientific and humanistic cultures, exceptionally branched into microworlds at different scales, which over the centuries have been ignored or inspired by each other. In this spirit, the book goes through scientific sections full of equations, sections dominated by technological issues described by means of technical drawings, sections where the history of the development of the wind science and technology prevails in a discursive form, narrative sections that collect often curious facts and discoveries related to wind, sections with a humanistic and sometimes philosophical matrix. Everything is intertwined and joined in order to recognise and provide the links, motivations and intersections that have given rise to the Wind Science and Engineering. vii

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Preface

The result is a complex and articulated text that alternates easy and hopefully pleasant passages with demanding parts, searching for a viewpoint wider than the usual scientific approach, which is often aiming to investigate ever more deeply and in detail increasingly circumscribed problems. During this process, I have found it fascinating to research into ancient thinkers’ speculations which are the core of scientific theories. I have met great human stories behind great scientific discoveries. I have understood how the most sophisticated equipment is often the evolution of bizarre instrumentations. I have reached the awareness that several fundamental equations are the result of endless coarse attempts, that many basic concepts were born independently by sectors that have long been ignored each other, and that great ideas attributed to famous scientists were actually developed or conceived by others who have not been lucky enough to be recognized for their own merits. I have also found it fascinating to study and try to communicate the concept that what was developed in our own field is often the result of visions accrued at a larger scale. Or it was already known in areas which, if studied in depth, would have avoided rediscovering already known aspects or would have enabled us to start from knowledge bases from which it would have been possible to reach higher levels. Just towards the end of this work, I realized it gave me the opportunity of making a long journey through time and space, and above all through my life, which made me rediscover the texts where I studied, the people I attended along my career or I wanted to know, the difficulty of getting into sectors little known or unknown, the curiosity to understand and the fear of making mistakes, the effort to seek, the joy of finding and the suffering of failing. As the publication of this book draws near, I feel the concern for the judgement of those who will read individual chapters, or even worse individual sections, with a specific knowledge of their topics greater than that of the author. I ask them to get into the whole of the wind science and engineering, or at least to recognise the effort made to treat this matter altogether, without resorting to the simplest collection of contributions from different specialists with different and uneven views and approaches. Perhaps, ideas and reflections on the vast spaces that still exist towards the creation of a truly interdisciplinary view of the wind can emerge just out of the shortcomings exhibited by the author in the treatment of individual parts, deliberately not entrusted to the review of experts. Now, I just have to thank those who contributed directly and indirectly to this book, hoping not to forget anyone. I thank the University of Genova, the Polytechnic School (formerly the Faculty of Engineering) and the Department of Civil, Chemical and Environmental Engineering (DICCA, formerly DICAT, DISEG and ISC), who put me in the position to express myself as much as I could and to do what I aspired to. I thank Margherita Capelletti, and before her Sonia Russo, who assisted me in the drafting of the text, Promoest, Susanna Marrella and Carlo Lagomarsino, who edited the translation and the revision of my writings, Rita Soffientino, who provided me with

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hard-to-find books and papers, Springer and Pier Paolo Riva, who accepted and implemented this editorial proposal. Any error remains my sole responsibility. I thank all the students who have followed my lessons, my many graduates, doctoral scholars, postdoc researchers and visiting scientists, in particular Stefano Brusco, Ileana Calotescu, Federico Canepa, Michela Damele, Luca Roncallo, Stefano Torre, Andi Xhelaj, Shi Zhang and Josip Zuzul. I thank my friends and colleagues who over the years have been part of the WinDyn Research Group, primarily Giuseppe Piccardo, with whom I shared a life of friendship and work, then Maria Pia Repetto and Massimiliano Burlando, with and thanks to whom, I crowned the dream of an Advanced Grant of the European Research Council for the THUNDERR Project. Its support for this book is acknowledged. I thank all those with whom I spent wonderful hours at conferences, universities and institutions all over the world; by virtue of the personal relationships I established with them, wherever I was, in space and time, I felt surrounded by friends and part of a large family. Among them, I express special thanks to my great friends and outstanding colleagues Ahsan Kareem and Yukio Tamura, with whom I shared the most significant moments of my career and of my personal life. I thank Genova and Liguria, where I was born and lived, to which I am deeply attached. From the beauty and familiarity of my lands, I have always drawn peace and inspiration. Finally, I thank my whole Family for what I received from them and to them I dedicate this book. I am grateful to my wife Simonetta for the beautiful moments we spent together. I entrust my commitment to the memory of my sons Davide and Matteo. Genoa, Italy

Giovanni Solari

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Part I 2

Origins: From the Dawn of History to the Renaissance . . . . . . . . . . . .

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The Wind and the New Science . . . . . . . . . . . . . . . . . . . . 3.1 Speculation and Experience . . . . . . . . . . . . . . . . . . . . 3.2 Atmospheric Physics and Measurements . . . . . . . . . . 3.3 Mathematics and Automated Computation . . . . . . . . . 3.4 Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Mechanics in the Sixteenth and Seventeenth Centuries 3.6 The Coming of Fluid Dynamics . . . . . . . . . . . . . . . . . 3.7 Thermodynamics and Steam Machines . . . . . . . . . . . .

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The Wind in Antiquity . . . . . . . . . . . 2.1 The Wind in Mythology . . . . . . 2.2 Speculation and Observation . . . 2.3 Science and Experience . . . . . . . 2.4 Astrology and Meteorology . . . . 2.5 Sailing Ships . . . . . . . . . . . . . . 2.6 Wings and Kites . . . . . . . . . . . . 2.7 The First Windmills . . . . . . . . . 2.8 Climate and Architecture . . . . . . 2.9 Structural Damage and Collapse 2.10 Leonardo da Vinci . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . .

Part II 3

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Developments: From the Renaissance to the End of the Nineteenth Century

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3.8 The Kinetic Theory of Gases . 3.9 Structural Mechanics . . . . . . . 3.10 Music, Sound and Vibration . References . . . . . . . . . . . . . . . . . . . 4

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The New Culture of the Wind and Its Effects . . . . . . . . . . . . 4.1 The First Meteorology Studies . . . . . . . . . . . . . . . . . . . . 4.2 The Resistance of Bodies in Fluids . . . . . . . . . . . . . . . . 4.3 Wind Intensity Scales . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Sail Propulsion and Sailing . . . . . . . . . . . . . . . . . . . . . . 4.5 Flight Experiences and Scientific Research . . . . . . . . . . . 4.6 The Diffusion of Windmills . . . . . . . . . . . . . . . . . . . . . . 4.7 The Structures of the Industrial Revolution . . . . . . . . . . . 4.8 Cable-Supported Bridges in the Nineteenth Century . . . . 4.9 The Girder and Truss Bridges of the Nineteenth Century References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Part III

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Fundamentals: From the Late Nineteenth Century to the Mid-Twentieth Century

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Scientific Progress and Its Impact on Wind . 5.1 Fluid Mechanics . . . . . . . . . . . . . . . . . . 5.2 Probability and Random Processes . . . . . 5.3 The Advent of the Electronic Computer . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Wind Meteorology, Micrometeorology and Climatology . 6.1 Ground-Level Measurements . . . . . . . . . . . . . . . . . . 6.2 Upper Air and Remote Measurements . . . . . . . . . . . 6.3 Meteorology and Weather Forecasts . . . . . . . . . . . . . 6.4 Wind Classification . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Micrometeorology . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 The Theory of Turbulence . . . . . . . . . . . . . . . . . . . . 6.7 Wind in the Atmospheric Boundary Layer . . . . . . . . 6.8 Wind Climatology . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Wind 7.1 7.2 7.3 7.4 7.5

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and Aerodynamics . . . . . . . . . . . . . . . . . . . . Advancements in Experimental Aerodynamics The First Wind Tunnels . . . . . . . . . . . . . . . . Boundary Layer Wind Tunnels . . . . . . . . . . . The New Horizons of Aeronautics . . . . . . . . . Aerodynamics of Sailing . . . . . . . . . . . . . . . .

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7.6 Aerodynamics of Road Vehicles . . . . . . . . . . . . . . . . . . . . . . . 524 7.7 Aerodynamics of Trains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 8

Wind, Environment and Territory . . . . . . . . . . 8.1 From Windmills to Wind Turbines . . . . . . 8.2 The Atmospheric Diffusion of Pollutants . . 8.3 Soil Erosion and Transport . . . . . . . . . . . . 8.4 Snow Drift . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Windbreaks, Shelterbelts and Crops . . . . . . 8.6 Bioclimatic City Planning and Architecture References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Wind Actions and Effects on Structures . . . . . 9.1 The Evolution of Suspension Bridges . . . . 9.2 The Evolution of Towers and Skyscrapers 9.3 Wind Actions and Effects on Structures . . 9.4 Design Wind Speed . . . . . . . . . . . . . . . . 9.5 Building Aerodynamics . . . . . . . . . . . . . . 9.6 Dynamic Response to Turbulent Wind . . . 9.7 Vortex Shedding . . . . . . . . . . . . . . . . . . . 9.8 Galloping . . . . . . . . . . . . . . . . . . . . . . . . 9.9 Flutter . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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10 Wind Hazard, Vulnerability and Risk 10.1 Tropical Cyclones . . . . . . . . . . . . 10.2 Tornadoes and Thunderstorms . . . References . . . . . . . . . . . . . . . . . . . . . . Part IV

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Advancements: From the Mid-Twentieth Century to the Third Millennium

11 Advancements in Wind Science and Engineering 11.1 Wind Effects on Buildings and Structures . . . 11.2 The Birth of Wind Engineering . . . . . . . . . . 11.3 Towards Wind Science and Engineering . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925

About the Author

Giovanni Solari is a professor of Structural and Wind Engineering at the University of Genoa, senior adviser at the Beijing Jiaotong University, guest professor at the University of Western Ontario, Canada, and formerly at the Universidad de la República, Uruguay, honorary professor at the Shijiazhuang Tiedao University and at the South Central University, Changsha, China, and honorary doctor honoris causa at the Technical University of Civil Engineering, Bucharest. He was awarded the Scanlan Medal 2017 (EMI-ASCE), the Reese Research Prize 2014 (SEI-ASCE), the Flachsbart Medal 2013 (WTG), the Davenport Medal 2011 (IAWE) and the Cermak Medal 2006 (EMI-ASCE). He was a president of the International Association for Wind Engineering (IAWE), founding co-editor of Wind and Structures, series editor of Springer Tracts in Civil Engineering, scientific responsible of the European Projects “Wind and Ports” and “Wind, Ports and Sea”. The European Research Council awarded him an Advanced Grant 2016 for the THUNDERR Project. He is a member of the Liguria Academy of Science and Letters and author of nearly 400 papers, almost 150 of which appeared in peer-reviewed journals. He carried out the wind loading and response analysis of several signature structures, including the Leaning Tower of Pisa, the Messina Strait Bridge and the Brancusi Endless Column. He currently serves as the designated president of the Italian Institute of Welding.

xv

Chapter 1

Introduction

Abstract This chapter provides an overview of the four periods in which knowledge of the wind and mankind’s ability to exploit its beneficial aspects and protect itself from the harmful ones develops. In the first period, from the dawn of history to the Renaissance, the origins of wind knowledge were manifested through varied and disjoint contributions. In the second period, from the Renaissance to the end of the nineteenth century, the new form of knowledge based on experience, science, produced substantial evolutions in the culture of the wind and its effects. In the third period, from the late nineteenth to the mid-twentieth century, the foundations of the individual disciplines destined to give life to wind engineering were born and the first links between different sectors were manifested. In the fourth and last period, from the mid-twentieth century to the third millennium, the many strands of the wind culture show substantial advancements that first lead to the foundation of wind engineering and then to the enlarged view of wind science and engineering.

Few natural phenomena are as ethereal, indefinable and mysterious as the wind. Few natural phenomena produce so visible, tangible and varied effects as the wind does. Few natural phenomena, throughout the centuries, have been the object of speculation, observations, experiences and research as abundant as those carried out on the wind. These aspects are mostly due to the rare property of dualism possessed by the wind: the wind is evil when it destroys buildings and anthropogenic areas, producing more fatalities and damage than any other natural event; when it whips men, houses and settlements with air that is either too cold or too hot; when it makes urban spaces uncomfortable; when it destroys crops and exposes transport to risks; when it erodes the soil to the point of making whole lands deserts; when it drifts snow, burying buildings and roads; and when it is a tool for air pollution and for aggression on our monumental heritage. On the other hand, the wind is good because, as the engine of atmospheric motions, life on Earth would not exist without it. The wind is good when it powers windmills and wind turbines, producing clean renewable energy; when it favours the circulation of fresh air inside buildings or along the arteries of the urban fabric; when it offers breath to the populations that live in deserts or on lands dried up

© Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_1

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1 Introduction

by the sun; when it disperses the emissions of pollutant sources away from populated areas; and when it carries smog clouds away from heated urban islands. The evolution of knowledge of the wind and mankind’s ability to exploit its beneficial aspects and protect itself from the harmful ones has developed through four periods [1]. The first period, from the dawn of history to the Renaissance (Chap. 2), was dominated first by a mythological vision, then by a speculative approach in part inspired by observation and finally by the beginnings of a scientific method based on experience. The first weather forecasts appeared, partly dictated by astrological practice. Man used the energy of the wind to sail, to support the flying of kites and to drive the blades of the first windmills. He also developed the first experiences aiming at guaranteeing his settlements and homes a bioclimatic environment, so as to improve living conditions. He noted, however, usually with feelings of resignation and inevitability, the destruction caused by windstorms. In the second period, from the Renaissance to the end of the nineteenth century, a form of knowledge based on experience developed, science, supplanting the role of speculation and observation. The wind availed itself of this progress drawing on concepts and principles from the basic disciplines that were born and developed in this period, especially in physics, mathematics and probability theory, mechanics, fluid dynamics and thermodynamics, structural mechanics and vibration (Chap. 3). Thanks to these disciplines and the progress made in the field of navigation and flight, meteorological knowledge was accrued, a new culture arose on the resistance of bodies immersed in the wind, and the exploitation of wind energy progressed; man also became aware of the risks faced by the boldest constructions seeing their collapse, due to the wind, especially of many bridges that were the pride of the engineering of this time (Chap. 4). In the third period, from the late nineteenth to the mid-twentieth century, the maturation of the basic disciplines is completed, especially fluid mechanics and probability theory, from which wind science draws; it is also worth noting the advent of the computer and its fundamental link with meteorological forecasts (Chap. 5). At the same time, new lines of research were developed concerning meteorology, aerodynamics, wind actions and effects on environment and construction, wind hazard, vulnerability and risk. Knowledge of the wind phenomena took maximum impetus from the progress of ground instruments and remote monitoring, from the evolution of meteorology and from the advent of micrometeorology, the theory of turbulence and climatology (Chap. 6). Aerodynamics made enormous progress in the experimental field thanks to the dissemination of full-scale measurements and above all of wind tunnels; this greatly contributed to the new culture that pervaded the fields of aeronautics, shipping, and road and rail transport (Chap. 7). Environmental wind actions and effects were fertile fields of study with regard to wind turbines, supplanting the old mills, the atmospheric dispersion of pollutants, soil erosion and snowdrift, the protection of crops, the urban and architectural design inspired by bioclimatic principles (Chap. 8). The study of wind actions and effects on buildings was strengthened by the realisation of long and light bridges, tall and slender towers and skyscrapers, and, more generally, a new generation of structures increasingly susceptible to wind loading; a new

1 Introduction

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culture also matured of the static, dynamic and aeroelastic wind actions on structures (Chap. 9). Thanks to new knowledge in the fields of meteorology and construction, man understood that wind-induced disasters can be contrasted and mitigated by manifold interventions to which he devoted efforts and enthusiasm (Chap. 10). In the fourth and last period, from the mid-twentieth century to the third millennium, the many strands of wind culture, until then generally cultivated as independent subjects, have come to be configured according to an autonomous and uniform scientific framework (Chap. 11). In 1961, Alan Garnett Davenport (1932–2009) laid the foundations of this transition, creating the namesake chain [2]: it links together the fundamentals of wind, aerodynamics and mechanics, originating the first unitary procedure to analyse wind actions and effects on structures; this gave rise to four international conferences on this subject, from 1963 to 1975, outlining the stages of the first phase of the new course. During the last of these conferences, the community involved took note of the new form of knowledge. In the meanwhile, it realised that this view was narrow and restrictive. Hence, the will arose to establish a wider scientific community that deals, in its entirety, with the various issues related to wind actions and effects not only on constructions but also on environment and territory. This remark gave rise to the advent of Wind Engineering, defined by Jack Edward Cermak (1922–2012) in 1975 as “the rational treatment of the interactions between wind in the atmospheric boundary layer and man and his works on the surface of earth”. With it, the International Association for Wind Engineering was also born, aimed at co-ordinating the activities of this new sector, and a series of six namesake conferences, from 1979 to 1999, outlining the stages of the second phase of the new course. In the last of these conferences, the conviction and the awareness matured that the role of the wind was now crucial to many areas of science and technology and the number of those studying and working in this sector, increasingly wide and varied, had become absolutely huge. Hence, the idea and the will arose to give the association born just 24 years before a more modern and efficient organisation, which is able to play a stronger and more proactive role with regard to the needs of society and humanity towards the wind. In this new perspective, the awareness is essential that the wind is the cause of about 75% of the damage and deaths caused by nature on the Earth every year. The conferences that took place in the following years offered testimony of the third phase of the new course, pointing out such a broad and complex framework as to make “Wind engineering” an almost reductive definition. Hence, a wider viewpoint has been emerging that goes beyond the engineering world and projects this discipline into a higher and more general scenario well-embraced by the new definition “Wind science and engineering”. This is also the title of the present book.

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References 1. Cermak JE (1975) Applications of fluid mechanics to wind engineering—a freeman scholar lecture. J Fluid Eng ASME 97:9–38 2. Davenport AG (1961) The application of statistical concepts to the wind loading of structures. Proc Inst Civ Eng 19:449–472

Part I

Origins: From the Dawn of History to the Renaissance

Chapter 2

The Wind in Antiquity

Abstract This chapter addresses the will of men, which took place in the period that goes from the beginning of history to the Renaissance, to know the wind, to exploit its beneficial aspects and to protect themselves from its harmful effects. Accordingly, it describes a mythological view that emphasises the dualism between the wind as a source of life and as a means of death, the advent of a naturalistic speculation inspired by observation and the first scientific concepts, prodromes of experience, mainly focused on mathematical, mechanical and astronomical problems, as well as the innate interest of man for weather knowledge and forecasting. At the same time, it describes the first man’s attempts to exploit the wind power as an energy source, equipping boats with sails, using atmospheric currents to support kites, taking advantage of wind power to operate mill blades for multiple forms of work. In the same spirit of profound dualism, the development of architectural principles inspired by local climate is described as well as the mechanical role of wind actions and effects on buildings. The chapter ends dealing with the outstanding interest of Leonardo da Vinci towards wind and his studies on fluid and solid mechanics, meteorological instrumentation, aerodynamics and human flight.

The period that goes from the beginnings of history to the Renaissance was dominated by the will of man to know the wind, to exploit its beneficial aspects and protect themselves from its harmful effects. At first, man related to the culture of wind by elaborating a mythological view that emphasised the dualism between the wind as a source of life and the wind as a means of death (Sect. 2.1). Later, with the advent of Greek civilisation, a naturalistic speculation was born inspired by observation (Sect. 2.2). At the same time, although at a sporadic level, the first scientific concepts and prodromes of experience, mainly related to mathematical, mechanical and astronomical problems established themselves (Sect. 2.3). From the background of this reality, the innate interest of man emerged for weather knowledge and forecasting: it found answers in two disciplines, meteorology and astrology, destined to attract and repel throughout history (Sect. 2.4). At the same time, man learnt to exploit the wind power as an energy source, equipping his boats with sails (Sect. 2.5). Later, he began to hover in the sky using © Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_2

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just as unlikely as dangerous wings or exploited atmospheric currents to support his kites (Sect. 2.6). Lastly, he used wind power to operate mill blades for multiple forms of work (Sect. 2.7). In any case, he understood that the wind, so generous in vital potential, frequently and suddenly can change into a fierce enemy. In the same spirit of profound dualism between the wind that is good and the wind that is bad, man has tried to improve his living conditions by blocking the path to the coldest winds or creating pleasant streams of air where the heat is more oppressive; in this way, he has developed, from ancient times, architectural and urban principles inspired by the local climate (Sect. 2.8). On the other hand, he has observed, generally with a sense of resignation and ineluctability, the destruction caused to the territory by windstorms; he has also sought to understand the mechanical role of wind actions on buildings, delaying the study of remedies to guard against their consequences (Sect. 2.9). With the advent of the Renaissance, the world was pervaded by a fervour of activity and innovation that affected all fields of knowledge, including that of the wind. Leonardo da Vinci anticipated and inspired this transformation, providing extraordinary contributions to many scientific areas including fluid and solid mechanics, meteorological instrumentation, aerodynamics and human flight (Sect. 2.10). Some of his ideas still retain unchanged relevance to today’s world. There emerged a picture of a reality where the study of wind struggled to take on clear contours and autonomy of thought and discussion. The culture of this phenomenon remained an integral and in some cases hidden part of broader and more general themes. These themes cannot be ignored, if we want to capture and highlight the first moments in which the relationship between man and wind manifested itself at its embryonic level.

2.1 The Wind in Mythology Ancient peoples regarded natural phenomena as direct or indirect manifestations of divine power. The wind, in its many manifestations, was of all the natural phenomena, the one which probably captured the imagination of man more and inspired him to combinations and allegories related to religious ideas and to the concept of genesis. In many primitive societies and cultures, the wind was personified and divinised by appearances that reproduced its prerogatives [1, 2]. One of the most fascinating aspects of the wind mythology was that peoples of every place and age autonomously matured similar beliefs and striking coincidences around such an intangible and immaterial phenomenon. Many of the oldest myths made the wind rise from holes or caves hidden in the ground or in the sky. The Bakitara of Uganda believed in the existence of four holes in the sacred hill of Kahola, the home of the winds, from which they flew. Yukon Inuit narrated of a wooden doll made by a couple without children; it acquired life and reached the hem of the world, where it found a hole in the sky covered with skin; it cut through it, and released the wind with a herd of caribou. The Iroquois believed that

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the winds were held captive by Gaoh in the cave of a mountain called Kahola, “the house of the winds”. Similarly, Batek Negrito of Malaysia argued that the winds were kept in a cave of Batu Balok and carried out by ropes pulled by Gobar, the Supreme Being. Sarawak’s Dusus believed in the existence of Kinorohingan, a blacksmith who forged the seven parts of each man’s soul; when they wore out, he turned them into twisted winds and kept them in a cave. The Maori of New Zealand told the legend of Mani, a hero who captured the winds to confine them to caves. In the Cook Islands, the wind was enclosed in the sky, represented by a pumpkin dotted with holes closed by stoppers that were placed or raised, depending on circumstances, by the “great priest”. In the Hawaii, “the perennial wind pumpkin” was guarded by “kahuna”, who handed down the names and secrets of the winds from fathers to sons. In Polynesia, it was believed that there were holes on the horizon through which Raka, the god of the winds, and his sons blew out. At the beginning of the first millennium BC, a rich mythology flourished in Greece. Aeolus, son of Poseidon, god of the sea, was the guardian of winds that he kept chained in a cave of the Island of Eolia. Legend has it that, as time went by, he lost control of them. So, when Odysseus arrived with his crew, he closed them in a bag of ox skin and released them with satisfaction. His sailors opened it believing that the sack contained a treasure and was overwhelmed by the impetus of the freed winds. The sack that enclosed the winds was a cornerstone of many other myths and ancient legends. In the Chinese tradition, the wind god is Feng Po, an old man with a white beard and a blue cap; he had a yellow sack called “the mother of the winds”; orienting the opening of the sack, he determined their direction. Fujin, the Japanese wind demon, was depicted as a horrible being who pulled the winds from a bag carried over his shoulder; their intensity depended on the opening of the mouth of this bag. Caves, pumpkins and sacks were clear symbols of a maternal womb from which the wind flows to come to light. In this regard, there was a deep bond with other myths where the wind was associated with the life that was born. The Sermat people in Indonesia believed that only the sky was originally inhabited; from the sky, along a palm tree that is still venerated, descended a woman made pregnant by the south wind as she slept; all the people of our planet are her descendants. The Sulawesi people believed that they came from a girl who was made pregnant by Western winds. Hiawatha, the Algonquin hero, was born after his mother Wenonah received the visit of an astute wind. The ancient Finns told us that the virgin Ilmater, mother of the witch Vainamoinen, was inseminated by the east wind. The goddess Hera conceived Hephaestus, one of the gods, after inhaling an errant wind. The Babylonian goddess Tiamat was born when her mother’s womb was filled with furious winds. The Arunta women in Australia hid themselves in their huts when the storm came from the north; it brought the seeds of the devil, responsible for twins being born. The vision of the wind that brings life was linked to two other very common images in the mythology of the wind: birds and creation. The Harpies of Greek mythology—Aello (storm), Celaeno (obscure, with reference to storm clouds), Podarge (quickest) and Ocypete (she who flies fast)—were demonic beings with the head, the chest and the arms of a woman, the rest of the body of a bird of prey; in the

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Fig. 2.1 a Hung Kong [3]; b Enlil

Greek popular belief, they carried divine revenge in the form of storms. Taiwanese people considered Hung Kong, a bird with monstrous wings, the cause of typhoons scourging the China Sea (Fig. 2.1a). In the Norwegian myth, Hraesvelgr was an eagle that devours corpses; sat on the edge of the world and distributed the wind by beating its wings. Similarly, New Mexico’s Indians told of a crow that flew over the sea and brought it to life thanks to the wind caused by its wings. The Inuit on the shores of the Bering Sea worshiped Tulukauguk, the father crow and creator of the world. Brama, the creator, freed himself in the air on the back of Hamsa, the duck that personified the wind. According to the Melanesians, the world at the beginning was chaos; it remained so until Tabuerik, the god-bird, pounded over the turmoil and gave it a full form of thanks to the wind produced by beating his wings. The Aztecs of Mexico honoured the god of the Quetzalcoatl wind; his son Ehecatonatiuh allegorically represented the second historical age of mankind, the one destroyed by the wind; the gods then transformed men into monkeys to help them cling to the branches of trees, avoiding being grabbed by storms. A relationship between wind and man emerged based on a dualism between good and evil [1, 3]. In the early days of the Assyrian Babylonian civilisation, around 3000 BC, Enlil was worshipped as the god of hurricanes (Fig. 2.1b); from 2000 BC, he was replaced by Teshup, god of lightning and storms and wind-maker; he was also honoured as the God of the wind’s beneficial rainfall, an indispensable element for crops. Rudra, the Hindu god of the storms, is cited in the Vedas, the four sacred texts of Indian tradition; he is described as a god sometimes benevolent sometimes destructive, the divine healer and at the same time the demon who kills men and animals. For the Hurons and Iroquois of Canada, the Lord of the Winds was the father of Ioskeha, the creator, and of Tawiscara, the evil power. Amon, ancient Egyptian god of wind and fertility, with the passing of time took on the role of the king of the

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gods; later, he acquired the qualities of Ra, the god of sun and spring of life, taking the name Amon-Ra. At Uxmal, temple of the Maya culture, storms were depicted with sigma, double sigma and swastika symbols, representing the devastating power of nature; yet they were coupled with the phallus and snake, typical emblems of fertility and life; it was symptomatic that Mexico saw in the hurricane an essential source of irrigation for its sun-scorched lands (Sect. 10.1). The role of the wind is still characterised, even in modern terms, by the same dualism between good and evil. The wind is good when it fills the sails of boats, when it feeds mills producing energy, when it favours fresh air circulation inside homes or along the arteries of the urban fabric, when it takes away the fumes of polluting sources or brings the rain to the most arid areas. The wind is bad when it lashes men, houses and settlements with freezing or too hot air, when it devastates crops and makes transport dangerous, when it erodes soil or builds snow drifts, when it becomes a source of pollution, when it damages or even destroys buildings and territory. This dualism does not comprise an ancient myth, which was to play an important role in the development of scientific knowledge in the twentieth century: the Aeolian harp [1, 2]. It is to be found in some of the oldest tales, not as a musical instrument in the strict sense, but as a magical item or concept, inspired and brought to life by the wind. Its sound is described as being soporific and lulling, or ethereal and spectral, adding to the mysterious aura surrounding the harp. The Jewish tradition has it that, at night King David hung the harp over his bed, so that he could be soothed by the sounds of the wind. Aeolus is the divine harpist, under calm, balmy conditions. During the monsoon, the first kite builders (Sect. 2.6) created sound orchestras over the villages of Malaysia. In England, during the Middle Ages, the Archbishop of Canterbury Saint Dunstan (925–988) reinstated the dictates of monastic life, making use of the sound of harps strummed by wind, raising suspicions of witchcraft. Athanasius Kircher (1602–1680) described the Aeolian harp he realised in Misurgia universalis, sive ars magna dissoni et consoni1 (1650). It comprised a rectangular box in which 12 catgut strings of various thicknesses were tensioned (Fig. 2.2). More than two centuries had to pass before Strouhal, Reynolds and Karman provided a scientific explanation of the physical phenomenon that causes the harp’s cords to vibrate (Sect. 5.1).

2.2 Speculation and Observation Philosophy, which in Greek means “love for wisdom”, is the study of the general principles common to the various disciplines of wisdom and knowledge. According to the philosophers of ancient Greece, to whom foundation of this discipline is normally attributed at around 600 BC, it is the totality of all the sciences. Interpreting the terms 1 A description of the harp is contained in Liber IX, Magia Phonotactica, Machinamentum X, Aliam Machinam harmonicam Automatam concinnare, quae nullo rotarum, follium, vel Cilindri phonotactici ministerio, sed solo vento & aerte perpetuum quondam harmoniosum sonum excitet.

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Fig. 2.2 Athanasius Kircher’s Aeolian harp (from Misurgia universalis)

science and philosophy in a modern key, the science of the Greeks is what is now called philosophy. The first Greek philosophers, the Presocratics, developed a cosmogonic and cosmological conception where nature, and therefore wind, played a central role. Using observation, the mythological interpretation was flanked and progressively overcome by the speculative vision [4–11]. With rare exceptions, the experience was absent. The Ionian School, along the coasts of Asia Minor, was the first Greek philosophical school. Founded by Thales, it included, among its exponents, Anaximandros and Anaximenes. Thales of Miletos (about 624–546 BC), considered by tradition one of the seven sages, was the first philosopher who tried to explain the world and cosmos according to the principles of nature, rather than as a consequence of divine forces. He argued that water, or humidity, is the “principle of all and has created everything”. He rejected the existence of void. He supported the concept, albeit at the embryonic level, that man lives at the bottom of a sort of ocean formed by the atmosphere [9]. He also promoted the idea that the study of nature requires direct observations [5]. He is considered the founder of geometry (Sect. 2.3). Anaximandros of Miletos (about 611–547 BC) was the author of On nature, a work in which he claims that everything is born from “ápeiron”, the infinite, ingenerated, indestructible and indefinite principle. It was associated with the concept of water as a generator principle and that of fire, which, by joining with solid bodies, made them liquid, and joining with liquid elements transformed them into air [11]. Within this vision, that represents the first speculation on the origin of the wind, it was described as a movement of air masses produced by forces associated, in some way, to the sun [6]. Thanks to this statement, Anaximandros preceded by over two millennia some basic concepts of modern meteorology [9]. He was also the first to argue that the earth is in the centre of the universe. Unlike Anaximandros, Anaximenes of Miletos (about 586–528 BC) stated that the air is the primordial principle from which “everything comes, everything returns”; thanks to its perennial motion, it penetrates everywhere and constitutes the universal

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bond of nature. From air, the four basic elements of life are formed: air itself, fire, water and earth; water and earth originate from the air through condensation, fire forms due to rarefaction. He noted also that air cools moving upward due to the progressive reduction of intensity of sunlight reflected from the earth’s surface [7]. The second Greek philosophical school was the Pythagorean School founded by Pythagoras of Samos (around 570–495 BC) in Crotone around 530 BC. By attributing to mathematics the role of the principal form of knowledge, and by interpreting the number as the principle of proportion and perfect harmony of the universe (Sect. 2.3), he identified five regular solids: cube, octahedron, tetrahedron, icosahedron and dodecahedron. The first four depicted the elements that form matter, in the order earth, water, fire and air; in turn, they derived from the combination of pairs of four basic qualities: cold, hot, wet and dry (for example, water is cold and humid; fire is hot and dry). The fifth solid was identified with ether. On such bases, Pythagoras argued that the study of “mundanae” figures was equivalent to the analysis of the five elementary particles.2 The Pythagorean School also offered remarkable contributions to astronomy and music. Philolaus of Croton (born around 430 BC) laid the foundations of heliocentric theory proposing a cosmological model that denied geocentricism. Aristarchus of Samos (about 310–250 BC) conceived the Earth as a rotating sphere, with other planets, around a central fire. Animated by these principles, Pythagoreans explained the order of the universe as a musical harmony of heavenly bodies that produced sounds; separated by intervals corresponding to the harmonic lengths of sound strings (Sect. 2.3), they formed the harmony of the spheres. They also introduced the concept, persisting in medieval times that geometry, arithmetic, music and astronomy constitute the “quadrivium” of education. Parallel to the Pythagorean School, two philosophical orientations developed in Hellas and Magna Graecia that dealt with the problem of origin in an opposing way. The first of these, the Eleatic School, was born in Elea in Magna Graecia thanks to Xenophanes of Colophon (about 565–470 BC). Doubting every affirmation, he professed the negation of science. This doctrine was to have devastating consequences on the development of thought and knowledge. His most important pupil, Parmenides (born around 540 BC), wrote On nature, a work where he stated that the absolute and original being cannot be identified either with matter or with a concept that has immediate relations with the sensitive world, being an “immobile and eternal one”. He also extended the concepts of uniqueness and immutability to earthly things, denying the existence of not being and of its real manifestations such as movement, becoming, void and nothingness. Zeno of Elea (about 492–425 BC), the principal follower of Parmenides, founded dialectics, which is the art of arguing. To uphold the principles of his master, he refuted the concepts of continuity and movement making use, among other things, of Achille’s famous paradoxes of the tortoise and of the arrow pointed in the direction of the tree. He instilled a lively aversion to science in the young Socrates. 2 Orientals

argue that five-element theory (“pentchatouan”) was born in India thanks to Kanada. From this conception, comes the atomistic theory.

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Opposed to this doctrine was the orientation founded by Heraclitus of Ephesus (about 536–470 BC). In his work On nature, he manifested contempt for the materialistic theories of Anaximandros and Anaximenes, arguing that reality is a “becoming” that stems from a generating fire in continuous transformation, a kind of material soul of which everything is made and to which everything returns. Around this thought, various philosophical lines developed that counteract the movement to immobility. Empedocles of Agrigentum (around 482–423 BC) explained the reasons for the movement by asserting that the four elements of Anaximenes—air, water, earth and fire—are the origin of all beings. He also worked on Pythagorean ideas by establishing a parallelism with the most general concepts of solid, liquid, gaseous and “more rarefied than gaseous”. Continuously agitated, these elements combine in the universe in different proportions, under the influence of two opposing divine powers: love, or attraction, that tends to unite them, and hatred, or repulsion, that tends to divide them. Within this conception, Empedocles provided a justification for the material texture of the wind; discussing the subject in an aura of mysticism and allegory, he also professed to be able to dominate the forces of nature. For this reason, he was called the “tamer of the winds”. Closer to the spirit of Heraclitus was the thought of Democritus of Abdera (about 460–370 BC), the founder of atomism. A disciple of Leucippus of Miletos (about 450–370 BC) but soon more famous than his master, he interpreted the universe and the wind, as a set of infinite indivisible and impenetrable particles, atoms, all equal in their quality but different in weight and size; they move continuously in the void and, colliding, aggregate and disintegrate, forming matter. The wind picks up when many atoms concentrate in a small space; it calms when large portions of space contain few atoms. According to Democritus, everything is material, including soul, and is regulated by forces acting mechanically. Partially, similar concepts were developed by Anaxagoras of Clazomenae (about 499–428 BC). He argued that the universe is made up of infinite particles, “omeomeríe” or “seeds” of equal weight and size but of different quality; they are grouped by a sorting mind called “Nous” or”intellect”. According to Anaxagoras, heat determines ascent of the air. He also understood that the air is warm near the ground and cold in the upper air. Clouds are formed when hot air, rising, comes into contact with the coldest air. In the fifth century BC, in the face of the problem of origin, Greek thought was then faced with two alternative solutions. One imagined reality as absolute, immutable and eternal. The other saw it pervaded by an energy that pushed it to become continuous. From this contrast, the Sophist movement was born, namely the dialectical development of philosophy inspired by practical purposes. The greatest exponents were Gorgias of Lentini (about 485–380 BC), in the Eleatic spirit, and Protagoras of Abdera (about 480–411 BC) in the line of Heraclitus. Socrates (470/469–399 BC), animated by a deep concept of absolute justice, reacted to Sophist thought by challenging the search for the useful to the benefit of the universal and eternal truth. Deeply influenced by Zeno, he denied the role of science in speculative problems and claimed that its use should be limited to

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practical issues. He conveyed this form of aversion, at least in part, to Plato and Aristotle, conditioning the evolution of scientific thought for many centuries. Plato (428/427–348/347 BC), the disciple favoured by Socrates, animated the thought of the master of religious afflatus, posing it in a sphere of sublime values; he formulated the doctrine of ideas, according to which there are two worlds, one superior and spiritual, immutable and eternal, the other inferior and material, changing and temporary. Between the spiritual world and the material world, he placed the soul, which participated in the essence of the first and in the materiality of the second. In Athens, Plato founded the “Akademia”, where he promoted mathematics, astronomy, natural sciences and humanities. Like Thales, he proclaimed the importance of observation. He loved the Pythagorean bent for mathematics. More than the study of nature, he dedicated himself to physics and metaphysics. Aristotle (384–322 BC), Plato’s principal student, developed a partially different vision from that of his master. While Plato loved ideas, Aristotle loved facts.3 While Plato was a speculative mathematician, Aristotle was a contemplative naturalist scientist [5]. Founder of the Peripatetic School, also called Lyceum, he gave life to a new doctrine that spanned vast horizons (Sect. 2.3), embracing the learning of his time. In this way, he realised a system of ideas that were to remain, for the whole of the Middle Ages and beyond, the official conception of the world, considered insurmountable and blindly accepted. Aristotle shared the two basic principles of Plato’s theory, calling the immaterial world “form” and the material world “matter”. Unlike Plato, the two worlds were not independent but necessary for each other. Moreover, while Plato fixed the order of the universe, inspired by a mythology full of charm, Aristotle solved the problem by establishing a rigorous cosmology. According to Aristotle, the universe was divided into two concentric worlds: one celestial or supernatural the other terrestrial or sublunar. The celestial world was made up of ether, an incorruptible element called the fifth essence; it was composed of eight concentric balls to which the stars and planets belong; the last of them, the closest to earth is the moon. The terrestrial world was identified with our planet, the immobile centre of the universe, the site of continuous transformation of generation and destruction. Aristotle dealt with these concepts in On the heavens, where he argued that earth’s transformations are caused by the opposing principles of heat and cold, humidity and dryness; acting in pairs, they produce the four fundamental elements: fire, air, water and earth; the first two tend to ascend, the others tend to fall. Aristotle considered heat, emanation of fire, a quality or an accident that brought together homogeneous substances and decreased or separated heterogeneous ones. Outside the universe, beyond the last sky, there was God, “motionless motor” and “thought of thought”. Aristotle tackled the topic of wind in Meteorologica, the discourse on celestial phenomena. It is the first meteorological treatise and consists of four books [10]. The first summarises the previous works on natural sciences, defines the object and 3 Someone

described Aristotle as a proponent of the experimental method for his sentence: “Experience must give its own matter to be elaborated and converted into general principles; logic is not the instrument that must provide the form of science.”

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the extension of meteorology, distinguishes the four elements of nature, describes comets, wind, rain, clouds, rivers, springs, dew, hail and climate and dwells on the previous misconceptions. In the second book, Aristotle formulates the general theory of wind by saying that “from the warming of the earth by the sun a nonsimple exhalation is necessarily generated, but rather of two types: one more like vapour, the other is more like the breath”: the humid exhalation is at the base of the formation mechanism of clouds, rain, snow, springs, rivers, dew and frost; the dry exhalation, highly flammable, produces comets, falling stars, winds, earthquakes, lightning strikes, whirlwinds and typhoons [3]. In the same book, he introduced a classification and definition of winds depending on their oncoming direction. He also proved the non-existence of empty space (the famous theory of “horror vacui”, “nature abhors the void”) that was to be a brake on the progress of knowledge for almost two millennia. In his third book, Aristotle formulated a theory of thunder and lightning, placing these phenomena in relation to fire, whirlwinds and typhoons. In his fourth book, he deepened the theory of the four elements, separating the active ones, heat and cold, from the passive ones, dryness and humidity. Inspired by observation, Aristotle also refined the classification of the winds according to their origin in a peripatetic treatise, Ventorum situs et appellationes, where he identified twelve principal winds associated with as many directions4 (Fig. 2.3) [12]: Thraskias and Argestes bring calm; Argestes and Euros, initially associated with a dry climate, cause a progressive increase in humidity; Meses and Boreas are cold winds; Notos, Zephyros and Euros are warm winds; Kaikias and Lips make the sky cloudy; the wind does not blow from the south-southwest [7]. He applied these concepts to formulate a number of urban principles of great interest (Sect. 2.8). Theophrastus of Eresus (371–286 BC) was a pupil of Aristotle famous for his meteorological predictions (Sect. 2.4), and the author of a treatise, On winds, where he affirmed the existence of various types of winds, each accompanied by peculiar forces and conditions. He defined Greek winds, characterised by recurrence and cyclic forms, monsoons; among them, there were the twenty Etesian winds; they blow from the north in summer, for a definite number of days, ceasing in the evening, never happening at night. He also argued that air movement is caused by snow melting. With Aristotle, the intense creative movement of Greek philosophy ended. The philosophical schools that developed after him reflected the sense of bitterness pervading the spirits and reflected the rampant dejection in the Greek–Roman world; so, they called upon previous experience, to come to conceptions that help overcome the daily drama of existence. It is a strange fact that the behaviour of the beaten population, the Greeks, spread to the victors, the Romans. They shied away from the abstract speculations of Plato and Aristotle to follow new philosophies more adherent to practical life. 4 Throughout

the classical era, there were two wind roses in the Mediterranean, one referring to twelve directions, the other to eight. According to some researchers, the wind rose of twelve winds originated from the Mesopotamian Zodiac, namely of 12 signs. Moving the Zodiac from heaven to earth organises the territory in the image of heaven, attracting the favour of gods. It is possible that Aristotle was influenced by this conception.

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Fig. 2.3 Aristotle’s wind rose [12]

On the basis of this assumption, the Romans developed four lines of thought: epicureanism, stoicism, scepticism and eclecticism. Epicureanism, founded by Epicurus of Samos (341–270 BC) and spread to Rome by Titus Lucretius Carus (98–54 BC), resumed the atomic doctrine of Leucippus and Democritus, arguing that the universe lives on the unstoppable motion of atoms which aggregate and disintegrate, giving rise to an infinite succession of worlds and composite materials; in the De rerum natura (60 BC) Lucretius stated that heat is a fluid substance emitted by burning bodies, he noted that sound takes some time to pass from source to the receiver and identified the energy source of the tornado in the electric forces present in the air (Sect. 10.2). Stoicism, founded by Zeno of Citium (334–262 BC) in the footsteps of Heraclitus, and advocated by Emperor Marcus Aurelius (121–180 AD), dealt with the world as a great living organism with a body of water and earth and a soul, or “pneuma”, of air and fire. Scepticism, founded by Pyrrho of Elis (360–270 BC), criticised previous philosophies, arguing that man cannot reach the truth because of the subjectivism of his state of mind. Eclecticism, of which Cicero (106–43 BC) was the greatest exponent, was the typical Roman philosophical orientation, collected the principles of the various philosophies, aligning them with the “common sense” possessed by all men. Against this background, the naturalistic and speculative interest in the wind, born in ancient Greece, continued with the Romans thanks to Virgil, Ovid, Seneca and Pliny the Elder. Their writings offered a clear testimony of a still deeply rooted mythological vision. Publius Vergilius Maro (70–19 BC) recounted some stories of Homer (IX–VIII century BC) in the Odissey, presenting the Harpies (Sect. 2.1) as creatures heralding storms. In Georgics, he dealt with weather forecasts (Sect. 2.4). In Aeneid, he provided numerous descriptions of the Mediterranean winds, highlighting a nomenclature often different from the Greek one.

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The masterpiece of Publius Ovidius Naso (43 BC–17 AD), Metamorphoses, consists of 15 books that narrate the transformations from original chaos to the divinisation of Caesar (100–44 BC) through about 200 fairy tales from which the legend of Daedalus and Icarus (Sect. 2.6) stands out. In this poem, Ovid reordered Greek and Roman myths, exhibiting them in a widely renewed narrative form. Most of the wind representations in medieval and Renaissance art, in Elizabethan and Romantic literature, and in modern thought, are still anchored to his descriptions. Lucius Annaeus Seneca (2–65 AD) was the author of Naturales quaestiones, a four-volume treatise inspired by the Greek opera [7]. The first three volumes were dedicated to rainbows, dawn, thunder, lightning and wind. The fourth dealt with clouds, rain, dew, hail, frost, snow and ice. Seneca also explored astronomy, earthquakes and comets, interposing moral reflections and lively stories. He had cleared the concept that temperature decreases as the height increases. Pliny the Elder (23–79 AD) was the greatest representative of Roman scientific excellence in the imperial age. He wrote the first encyclopaedia of natural sciences, Naturalis historia, a reference document on science in the ancient world. The work, in 37 volumes, contains a synthesis of over 2000 works by Greek and Latin authors centred on nature and largely on the wind. This provides a vision where mythology and observation coexist. On the one hand, Pliny interpreted genesis explaining that there are “certain caverns and holes that generate winds continuously and without rest” (Sect. 2.1). On the other hand, he came to describe the complex circulatory phenomena that occur in the Mediterranean area referring, unlike Aristotle, to a rose of eight winds: Septentrio (N), Aquilo (NE), Subsolanus (E), Volturnus (SE), Auster (S), Africus (SO), Favonius) and Corus (NO). With the advent of the vulgar era, two new philosophical orientations emerged: Neoplatonism and Christianity. Neoplatonism, established by the Greek Plotinus (204–270), spread to Rome from 245 AD, when Plotinus himself founded a school that introduced two profound innovations: the conception of a supreme truth that unlike the Aristotelian divinity was unthinkable and unrecognisable by reason, and the affirmation of a form of non-rational knowledge. Christianity developed through two successive periods, Patristic (first–eighth century) and Scholastic (ninth–fourteenth century), which ferried humanity from Aristotelian truth to Galilean reason. Patristics pursued a dual objective: to fix the peculiar elements of Christianity and to establish a path of reconciliation between Christian philosophy and pagan philosophy. Saint Augustine (354–430), the most creative figure of the early period of Patristics, recognised the contribution of Neoplatonism to Christianity in the Confessions (397), where he noted the deep influence exerted by this philosophical school on his religious thought. With the spread of these doctrines, the influence of the great pagan thinkers—Aristotle, Lucretius and Pliny—began to decline, and the interpretation of atmospheric phenomena returned to ethics and theology. The discovery and dissemination of passages as “the Lord struts in the whirlwind and in the storm”, from the first chapter of the Book of Nahum, stifled what remained of the ancient naturalist philosophy. Isidore of Seville and Bede the Venerable partially moved away from this conception. Isidore of Seville (560–636) was the author of a monumental work in 20

2.2 Speculation and Observation

19

volumes, Etymologiarum sive originum libri XX, in which he included most of the human learning of the time; it contains reflections on astrology (Sect. 2.4). Bede the Venerable (674–735) was an English Benedictine monk, living in Northumbria, renowned for his vast culture in the field of science,5 music, medicine and literature; De natura rerum, a work composed between 690 and 730, was a paraphrase of the Plinian paraphrasing of Aristotle, filtered through the naturalist theology of Isidore of Seville [9]; De temporum ratione refers to atmosphere and climatology, arguing that the wind is moving air, not an exhalation of the earth as per Aristotelian dictates [8]. With the advent of the Middle Ages, Christianity pervaded the Europe unified by Charlemagne (742–814) and the need for translating teaching into more rational forms was felt. Scholasticism, classically divided into three periods, was the philosophical movement that fused the profane doctrines of ancient philosophers and the sacred wisdom of Christianity into a single system of thought; with this aim it re-elaborated the philosophical theories of the past, especially that of Aristotle, to rationally illustrate and legitimise Christian revelation and theology, mainly inspired by Saint Augustine. This attitude favoured the systematisation of knowledge with respect to the acquisition of new methods of investigation. Among the most authoritative representatives of the first period of Scholasticism Peter Abelard of Bath (1079–1142), who returned to composing treatises on natural phenomena after a long silence on the subject, and Hugh of Saint Victor (about 1096–1141), also famous for his scientific vision (Sect. 2.3) deserve a particular mention. The second period of Scholasticism, extending to the resurgence of Aristotelian philosophy, was deeply influenced by the work of some Arab philosophers including Avicenna (Abu Ali al-Husayn Ibn Sina, 980–1037) and Averroes (Muhammad ibn Ahmad Muhammad ibn Rushd, 1126–1198), famous for commentaries on the works of Aristotle and for his attempt to restore the most authentic thought, freeing it from neoplatonising readings. Among the European thinkers of this period who were able to leave an indelible imprint of scientific nature (Sects. 2.3 and 2.4), Albertus Magnus (1207–1280) and Roger Bacon (1210–1294) emerged, along with Saint Thomas Aquinas6 (1225–1274). In the third and final period of Scholasticism, the contributions of Scotland’s John Duns Scotus (1270–1308) and of the Englishman William of Ockham (1280–1349) stand out. The first prepared the ground for the separation of philosophical and scientific culture, drawing a clear demarcation between discerned knowledge, God’s grace, and rational knowledge, a natural process of the human mind striving to perceive objects. The second used his famous razor to open the way to empiricism (Sect. 2.3), marking the decadence of medieval Scholasticism. 5 Bede the Venerable introduced the term “calculator” to indicate a man dedicated to the calculation

of time. Thomas Aquinas, one of the most important philosophers and theologians of the Middle Ages, was the author of Summa theologica (1269). Alongside a discovery of the difference in weight of hot air and cold air, there is also the statement that wind and storms are acts of the devil.

6 Saint

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Finally, it is worth mentioning a literary passage of 1563; it offers testimony to the evolution of human thought that, after almost two millennia of wandering, returns to its origins. Inspired by Aristotle, William Fulke (1538–1589) [2] defined the wind as a “white and dry exhalation, brought high in the air by the sun’s power”. At the same time, he paraphrased Pliny, saying that “there are large and wonderful crevices, caves or cracks in the globe of the earth in which the air (…) cannot conform to being nailed there, it finds a small hole there and in the surrounding area, as if it were a mouth to escape from”. When Galileo Galilei (1564–1642) (Sect. 3.1) abandoned Aristotelian doctrine as a scientific conception, unlimited horizons were to open up for science. By contrast, humanity was to plunge into a deep identity crisis.

2.3 Science and Experience Parallel to the development of speculative thinking, which blossomed in the ancient Hellas and returned to its origins through complex evolution (Sect. 2.2), the first scientific concepts were stated, mainly related to mathematical, mechanical and astronomical problems [4, 13, 14]. Furthermore, even though embryonic and sporadic, the first inklings of the transformation of observation into experience emerged. Such manifestations, though still far from the direct study of the wind, were the germs and precursors of the great advances that were to take place from the seventeenth century (Chap. 3). It is clear that the demarcation line between science and speculation and between experience and observation was, at this time, quite evanescent and questionable. The role of scientist and philosopher was often the prerogative of the same person; the justification of the first scientific concepts was often based on predominantly speculative reasoning; in an era devoid of tools, the meaning of the word “experience” was necessarily reductive compared to the present one. According to tradition, Thales (about 624–546 BC) covered the dual role of the one who initiated Greek philosophy (Sect. 2.2) and introduced geometry into Europe. He is attributed with the homonymous theorem on the set of parallel lines cut by two transversal lines, a cornerstone of modern Euclidean geometry. According to Pythagoras (570–495 BC), “all things are numbers”, and numbers are the principle of the proportion and perfect harmony of the universe; therefore, he attributed mathematics the role of the main form of knowledge. In this field, Pythagoras enunciated his famous theorem, he separated even numbers from the odd, he discovered prime and irrational numbers and he introduced the regular solids attributing them with a speculative meaning (Sect. 2.2). Pythagoras was also the first to support the utility of cultivating science and the importance of experiments in the study of mechanical phenomena. He carried out

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Fig. 2.4 Experiments carried out by Pythagoras [16]

famous experiments on string vibration and sound emission.7 He determined what lengths the strings needed to have to make, other conditions being the same, the different notes of the musical scale; likewise, he determined, the length being the same, what weights should strike a vertically placed string to achieve the same range of sounds. Thanks to these experiments (Fig. 2.4) [15–17], he understood that sound originates from the vibrations produced by the impact of the sound body on the air mass and that the range of sounds depends on the variety of sound waves and on the mass of the vibrating body. Empedocles (about 482–423 BC) acquired the experimental method from the Pythagorean School. He applied it to show that air is a body substance separated from the vacuum. For this, he used a conic jar perforated at the base and at the top; he pushed the base of the jar into the water and held the hole at the top clamped; he noted that the liquid entered the vessel only by opening the upper hole and allowing the air to go out. Finally, he overturned the jar full of liquid in the air and saw that water did not come out if the hole in the base is closed; in this way, he showed that air produces on the water a push from the bottom up. Democritus (about 460–370 BC) introduced the embryo of the causation principle, asserting that nothing happens without a cause. He also anticipated principles of 7 Interest in vibrations was born with the discovery of the first musical instruments (Sect. 3.10). Music

aroused great interest, from 4000 BC, with the Chinese, the Hindu, the Japanese, and probably the Egyptians. From 3000 BC, the first strings, especially harps, appeared on the walls of Egyptian tombs; one of these, housed in the British Museum, comes from Ur and dates back to 2600 BC. Our current musical concepts come from the Greek civilisation, where musicians and philosophers studied the laws of sound production to improve instruments.

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infinitesimal calculus, determining the volume of pyramids and cones as the sum of an infinite number of sections with infinitely thin thickness. Aristotle (384–322 BC) played a crucial role also in mechanics. He wrote an eight-volume treatise, Physics, destined to open boundless horizons of study and discussion: the first six books dealt with predominantly philosophical themes; the seventh and eighth investigate the causes and essence of the movement. Once again, concepts were formulated, especially the causation principle, which delayed scientific progress; born in a spirit where rotating motion played a dominant role on the straight one, the assertion that “everything that is moved is necessarily moved by something else” constituted an obstacle to the conception of the law of inertia.8 However, two great insights were outlined: the first stated the principle of contiguity, by virtue of which there was a need for immediate contact between the motor and the mobile, the second introduced the first glimpse of the principle of virtual works. Equally, important concepts are reported in On the heavens, where Aristotle stated that “the continuum can be defined as a quantity which is divisible in parts which in turn are infinitely divisible. A line is a quantity divisible in one direction. A quantity divisible in three directions is a body. The divisible quantities are continuous”. He also asserted that a moving body in a fluid encounters a resistance [14]. Aristotle also had an interest in sound and music. In Physics, he formulated some relatively correct hypotheses on sound generation and propagation. In the last book of Politics, he emphasised the importance of musical education, highlighting its ethical qualities superior to those of any other artistic expression. This line of thought was followed by Aristoxenus of Taranto (fourth century BC), a Greek philosopher and Peripatetic pupil of Aristotle, known for his studies of music. Unlike Pythagoras, who evaluated the notes on mathematical bases, and in the style of his master, Aristoxenus judged the sounds by ear. He was also the author of the first musical works, including the The harmonics, in three volumes, and the Elements of rhythm, of which only a fragment has survived. Euclid (about 325–265 BC), probably trained in Athens at the Platonic Academy around 300 BC, founded in Alexandria in Egypt a school of mathematics. His masterpiece, Elements, is a treatise in thirteen books regarding geometry, proportions, number properties and incommensurable quantities. Fruit of the systematic application of the deductive method, it is still the basis of the Euclidean geometry. In addition to absolutely fundamental contributions, Euclid ventured into some unlucky reflections in the mechanical field. He observed in particular that the fall speed of a body is greater the rarer the medium in which it occurs is. By not taking measures, he extrapolated that concept to the point that the falling velocity of a body in a vacuum is infinite. Since that is clearly impossible, he concluded that vacuum cannot exist [11]. Even Euclid was the author of a treatise, Introduction to harmony, about the physical nature of sound.

8 Aristotle

explained the motion of a falling body stating that, after leaving its own motor, the movement is maintained by the medium in which it moved.

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Archimedes (287–212 BC), the most important student of Euclid, had an essential role in the history of science. His contributions range from mathematics to the statics of fluids and solids, up to the invention of mechanical devices. In the field of mathematics, Archimedes studies on areas and volumes anticipated fundamental theorems of modern geometry. Among these were the determination of the surface of the sphere and the relationship between the length of the circumference and the diameter of the circle. In determining the area of a circle, after Democritus, a new infinitesimal calculus was displayed; applying the method of exhaustion, the area of a circle is calculated as the limit area of an inscribed polygon with a progressively larger number of sides. In the field of fluid statics, Archimedes drew up a treatise, De insidentibus aquae, where he formulated the homonymous principle that a body immersed in a fluid is subjected to a direct upward thrust applied to the centre of gravity of the body, of intensity equal to the weight of the volume of the displaced fluid. In the same treatise, he reinforced Aristotle’s thinking by claiming that a fluid, whether it is a gas or a liquid, is a continuous substance and as such can be treated in mathematical form; he also understood the concept of pressure, arguing that any point on the surface of a body immersed in a fluid is subjected to a force due to the fluid itself; he also stated that each portion of fluid bears the weight of the entire column above. Finally, Archimedes seemed to understand, albeit vaguely, that a fluid at rest is set in motion by a pressure difference. The main results obtained by Archimedes in solid statics are contained in On the equilibrium of planes or of their centres of gravity, a work of clear scientific setting far from the Aristotelian vision. Archimedes introduced eight postulates, of experimental origin, of which four inherent to the lever and four related to the centre of gravity of flat figures; from these numerous theorems derive, relying on pure mathematical proofs. In this way, he was a forerunner of the axiomatic setting of many modern theories. Finally, Archimedes is attributed to the invention of the composite pulley and feeder, or Archimedes screw, used for lifting water (Sect. 2.7). Hipparchus of Nicaea (about 190–120 BC), the most important ancient Greek astronomer, was the first to put the succession of seasons down to variations in the distance between earth and the sun and to provide a measure of the year with an approximation that is still acceptable. He introduced the use of geographic coordinates called latitude and longitude. He compiled a table of circle chords considered the basis of modern trigonometry. Claudius Ptolemy (about 100–178 AD), astronomer and Greek mathematician, carried out most of the observations at the base of his theories at the temple of Canopus, near Alexandria in Egypt. His fundamental treatise, Almagesto (originally Megalé mathematiké sýtaxis, or syntax of mathematics), is a monumental collection of 13 books which present the features of a geocentric universe and systematise many previous philosophical and astronomical contributions, in particular the work of Hipparchus. His astronomical conception was to be almost uncontested for about fourteenth centuries (Sect. 3.1).

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Fig. 2.5 Ptolemy’s geographical map

In the geographic and cartographic field, Ptolemy published Geography, where he used the concepts of latitude and longitude introduced by Hipparchus to create a famous map of the world, as known at its own time, with the illustration of the 12 dominant winds (Fig. 2.5); he built that map by first tackling, in mathematical terms, the problem of globe projection on a plane surface. In the same work, he also provided a classification of climates. Ptolemy’s interests also ranged in music and light, where he drew up two treatises entitled Harmonics and Optics, and in astrology (Sect. 2.4). At the same time when Pythagoras Hipparchus and Ptolemy were making essential contributions to future scientific development, Alexandria in Egypt came to the fore with a school focussed on creating ingenious mechanical devices. Its leading players included Ctesibius, Heron, Philo and Pappus. Ctesibius (third century BC) is credited with the invention of the water winch, hydraulic pump, and the first hydro-mechanical clock in the second half of the third century BC. He also managed to compress air and used this principle for launching small projectiles. Heron of Alexandria (first century BC) wrote Pneumatics (about 62 BC) and Automata, in which he illustrated the concepts behind and the construction of pressurised devices that use compressed or heated air to drive cylinders and connecting rods, to activate propellers and toothed wheels, syphons, and valves; standout items among these are the organ activated by a windmill (Sect. 2.7), the “aeolipile”, the

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Fig. 2.6 Heron: a Aeolipile; b device for throwing open the temple doors

fountain, and the device that threw open the temple doors. The aeolipile was a type of prototype steam engine; it was made up of a sphere that was kept rotating due to the action of the steam that was contained inside it and that came out with some force via two little pipes diametrically opposite one another (Fig. 2.6a). The fountain made use of atmospheric pressure to create a vertical water jet. Figure 2.6b shows the device for throwing open the temple doors: the fire burning on the altar heats up the air in the container below; this expands and forces the water to move, via a syphon, into a tank supported by chains; the weight of the water makes the tank move downwards, pulling on the chains, which open the doors; this process is reversed when the fire goes out. Heron’s fame is also due to the formula for determining the area of a triangle as a function of the length of its sides. Philo of Byzantium (born around 15–10 BC) described an experiment in which air, heated in a vessel, moved to a tank full of water, causing vortex bubbles. By taking up some of Heron’s ideas, he also made the first prototype of a thermoscope (Sect. 3.2). Pappus, an Egyptian mathematician of the fourth century AD, is considered to be the founder of trigonometry, along with Hipparchus and Ptolemy. In his Collection, he dealt with the problem of movement and the equilibrium of heavy body on an inclined surface, providing a wrong solution. Edoardo Benvenuto (1940–1998) described what happened with the coming of the Middle Ages [13]. This event “witnessed an initial approach to specific physical and especially mechanical problems, but in a singularly indirect and hidden manner, to the extent of adding legitimacy to the somewhat common public opinion that there was no experimental attention given to the prevailing interests of scientists,

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until the great change that occurred in the seventeenth century. This opinion is partly true: medieval physics revolved around Aristotle’s texts, conforming to the same exegetic line that governed speculative actions of any theologian, that is, anyone who turned his curiosity to discovering new objects or things that could be perceived from experience, but still tied to repeated reading of the sacred text”. The Middle Ages also changed the concept that technical activity was subordinate to speculation, giving the sciences, and especially the mechanical arts, an essential role in the formation of culture. In this context, the study of medicine, chemistry, and astronomy, carried out in the Benedictine monasteries took on a crucial role, with the first infiltration of Greek and Arab knowledge into western Christianity. This was done mainly by disseminating famous texts including Euclid’s Elements, translated from Arabic to Latin around 1120, as well as an array of technical and scientific information, via thirteenth-century encyclopaedias, which are still a precious resource for outlining the knowledge of the times. Hugh of Saint Victor (1096–1141), a French theologian and philosopher, offered a classification of knowledge, broken down into theoretical (including theology, mathematics, physics and music), practical (ethical), and mechanical sciences and discourse (rhetoric and dialectics). He wrote Didascalion, a compendium of knowledge at the time, extolling a utilitarian view of science. It established an analogy with the ancient “trivium” (grammar, dialectics and rhetoric) and the “quadrivium” (arithmetic, geometry, astronomy, music), and maintained that mechanics is “the science in which one learns the methods for making things”. Albertus Magnus (Albert von Bollstadt, 1207–1280) was a German philosopher and theologian, known as the “Doctor universalis” due to his encyclopaedic erudition; in accordance with the rules of the Dominican order to which he belonged, he crossed a large part of Europe on foot. This allowed him to acquire a vast array of knowledge about nature and environment, on which he wrote De coelo et mundo and Libri IV Meteorum. In the former, he showed that he understood that the air has weight and has the “capacity to lift”. “If we take air in its natural state, we cannot but see that it makes a full wineskin heavier than when it is empty (deflated). If, in addition, it is thin enough, when a man blows the flame of a candle with his own breath, the wineskin rises to the middle of the room, whereas if he blows near a torch, it can also reach the ceiling”. It was due to this concept, which predated the flights of the Montgolfier brothers (Sect. 4.5) by five centuries, that Albertus Magnus is seen as a forerunner of aerostatics [18]. The Franciscan monk, Roger Bacon (1214–1292), an English philosopher, theologian and scientist, called “Doctor mirabilis” due to his versatility, disagreed with the Aristotelian line of thought, maintaining that one had to approach science using experiments based on observing physical phenomena: “Sine experentia nihil sufficienter sciri potest”. He also understood the need to study mathematics as an educational exercise and as a basis for other sciences. Opus maius, an encyclopaedic treatise written between 1266 and 1278 and Compendium studii theologiae (1292), a work written in prison after he was condemned for magic and heresy (1278), show Bacon’s extraordinary far-sightedness. Along with curious reflections on the efficacy of the philosopher’s stone, he showed his conviction that air could support bodies

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just as water is able to keep ships afloat. About two centuries before Leonardo da Vinci (Sect. 2.10), he maintained that “one can make machines to fly, built so that a man standing in the centre of the machine, can manoeuvre it, using some device that allows artfully built wings to beat the air, like the birds do when in flight”. He also maintained that there was a sea route via the West to the Indies, which could be covered in a few days with a favourable wind. The German Jordanus Nemorarius (Jordanus de Nemore, 1225–1260), an author of fundamental texts on arithmetic, algebra, geometry and statics played a leading role in the scientific culture of the thirteenth century. In the mathematics field, he was one of the first to use letters in place of numbers and also discovered second degree equations. In the statics sector, he wrote Elemanta Jordani super demonstrationem ponderis, Liber de ponderibus and Liber Jordani de ratione ponderis. In the first, he established seven axioms, from which nine theorems were derived, including the embryo of the principle of virtual works. In the second, he highlighted the concept of moment. In the third, he formulated important laws on the inclined plane. Pietro d’Abano (about 1250–1315), an Italian physician and philosopher, wrote Conciliator differentiarum quae inter philosophos et medicos versantur, a work in which he dealt with the influence the stars have on events in the world and man’s decisions. In that same work, he stated that mechanics forms the basis and presupposition for other sciences, and, since all phenomena follow lines established beforehand, the world is governed by mathematical laws. In addition to these general principles, he also maintained that there is an altitude above which air is not disturbed by the movements of the lower strata (Sect. 6.5). Cecco d’Ascoli (about 1269–1327), an Italian poet and scientist, who was burnt at the stake for heresy, wrote Acerba, an encyclopaedia of science, in which he also covered studies, observations and experiences carried out personally. He stated that an echo is the reflection of sound waves, that summer heat haze or mirages are caused by the air beating up, and that thunder and lightning are different manifestations of the same physical phenomenon (Sect. 6.4). The English theologian William of Ockham (1280–1349) made an essential contribution to the principle of causality. Applying his famous “razor”, in terms of which “Entia non sunt multiplicanda praeter necessitate”, he maintained that scientific explanations must be based on theories backed up by experience. This principle denies Aristotle’s distinction between natural movement, caused by the shape of the body, and violent movement, which calls for the constant nearness of an engine that drives it. Instead, Ockham maintained that a moving body moves because it is moving and does not require an engine separate from the mobile object: in this way, he pointed to the first glimmer of the law of inertia. Jean Buridan (1290–1358) wrote Quaestiones octavi libri physicorum, in which he set about expelling Aristotle’s abstractions from physics. He especially studied “the property a moving object has to keep movement going within itself” [13]. By reiterating some concepts introduced by John of Alexandria (Filipone, sixth century AD) and Saint Thomas Aquinas (1225–1274), he refuted the theory that air transmits movement, using a boat as an example: it continues to move, even when the wind stops blowing, in which case, air, in fact, has a braking action. He also formulated

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an alternative theory: “As soon as a driving force moves a moving object, it gives it a certain impetus, proportionate to the speed applied and the quantity of material the body moved. This impetus or surge, keeps the movement going until the air resistance and gravity, which counteract the movement, overcome it” [13]. These insights make Buridan a forerunner of the concept of momentum, perfected by Galilei (Sect. 3.1) and Descartes (Sect. 3.5), and, at least in part, the concept of living force, attributed to Leibniz (Sect. 3.5). Albert of Saxony (1316–1390) reiterated and corrected Aristotle’s theories, maintaining and developing the experimental method. He formulated the first theory of gravity, in which he maintained that the Earth’s centre of gravity is at its centre, to which all bodies tend to move, as their natural movement. In his Acutissimae quaestiones, he showed his conviction that the earth is round. Nicolas Oresme (1325–1382) owes his fame to genial insights into the fields of astronomy, in which he maintained the rotation of the earth and heliocentrism, of physics, in which he was ahead of some discoveries by Galilei related to gravitational falls (Sect. 3.1), and of mathematics, where he was a precursor of analytical geometry (Sect. 3.3). He developed extraordinary principles in this sector, albeit at an embryonic level, on representing space using diagrams related to systems of orthogonal axes; he also introduced the concept of a fourth dimension, associated with evolution over time.

2.4 Astrology and Meteorology Meteorology is the science that studies the earth’s atmosphere and its properties. One branch of this, weather forecasting, deals with the evolution of the atmosphere over time. From the earliest times, this issue has been an interest at the heart of mankind, who sees the far-reaching link between its own existence and the weather conditions, very often putting this link at a divine and supernatural level. Equally often, this link involved another discipline, astrology, aimed at studying the relationships in place between the movements of the stars and events on earth. The joint study of astrology and meteorology, especially in relation to weather forecasting, has therefore very ancient roots and reflects the evolutions of beliefs and skills of peoples during various historical times [19]. Astrology began in Central Asia, probably in Chaldea, around 5000 BC. From there, it spread to Mesopotamia, where the annual cycle of the seasons was defined by astronomical and meteorological observations, and to Egypt, where forecasting times of abundance and drought for the waters of the Nile were based on the periodic appearance of stars that belong to particular constellations. Later on, it reached Ancient Greece, and the Maya, Indian and Chinese peoples, who made extensive use of astrology to prepare the first calendars, and established rudimentary correlations between astral and earth cycles, especially as regards evolution and recurrence over time, and all phenomena related to nature in general.

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With the passing of time, man came to appreciate the limits to the knowledge related to the annual cycle of seasons and was filled with a desire to forecast weather events in the short term. With this goal in mind, they began to notice that certain types of weather often follow precise phenomena. This gave rise to phenomenonbased meteorology, which produced autonomous, varied rules, according to where they were applied. It especially took root among farmers and seafarers, for whom weather forecasts played a vital role. As a result, weather predictions, proverbs and sayings have come about, dealing with signs believed to indicate upcoming weather conditions. Some are based on superstitions and mythology, while others reflect empirical meteorological wisdom, based on the actual observation of natural phenomena. Initially, this knowledge came from oral traditions or ancient people, before being added to in each generation. They appeared in literary form from 3000 BC when writing was invented. The epic Babylonian poems from 2000 BC include vivid descriptions of creation and genesis, along with accounts of extraordinary weather phenomena; above all, the Epic of Gilgamesh was one thousand years ahead of the story of the Great Flood in the Old Testament, referring to a violent storm along with hurricanes, torrential rain and disastrous flooding. In India, attempts to forecast the arrival of the summer monsoon were based on signs that date back to ancient times. In 1000 BC, the Chinese who lived along the banks of the Yangtze River forecasted the onset of seasons and weather developments, based on stars. Numerous clay tablets found to show that the Babylonians engaged in weather forecasting from the seventh century BC, based on the movements of planets and celestial cycles. This situation changed partly when the Greek civilisation appeared and Aristotelian speculation on natural phenomena developed (Sect. 2.2). This stimulated curiosity among common people in weather forecasting, giving rise to widespread interest, documented by calendars, or parapegmata, put up in the city’s public buildings; they recorded the weather events throughout the year, and sometimes provided rudimentary forecasts. Teophrastus of Eresus (371–286 BC), one of Aristotle’s students, is known for his Book of signs, a treatise that divides the main astronomical signs into two categories: he put those associated with the appearance or disappearance of stars and other celestial phenomena in one group, while the other group summarises signs associated with the behaviour of animals. More specifically, he described 80 signs for rain, 45 for wind, 50 for storms, 24 for good weather, and 7 for long-term weather conditions. Of the 45 signs that indicate wind, many are fanciful and picturesque—the howling of wolves, dogs that roll on the ground, ducks that flap their wings, and the appearance of very bright falling stars in the sky—while others are ingenuous [6, 12]. Aratus of Soli (about 320–240 BC), a Greek poet from the Hellenist era, and follower of Zeno of Citium (334–262 BC), is the author of a hexameter poem, Phainomena, based on stoic philosophical theory. The first part deals with celestial realm and constellations, while the second deals with weather forecasting based on astrology. Thanks to the Latin translation by Publius Terentius Varro Atacinus (about 82–35 BC), Cicero (106–43 BC) and Rufius Festus Avienius (fourth century BC),

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Fig. 2.7 Tower of the Winds: a elevation [3]; b demi-gods on the façade [19]

Aratus’s poem was enormously successful through to the humanistic age; some claim that it was the most widely known work in the whole of Hellenism. The Tower of the Winds (Fig. 2.7a), an octagonal structure built by Andronikos Kyrrhestes in Athens on the Acropolis, between the first and second century BC, bears witness to the first connection between wind and weather, based on sound empirical principles [20]. There is a bronze weathervane on the roof, depicting the effigy of Triton; this is believed to be the first instrument for measuring weather phenomena.9 As it aligns itself with the direction of the wind, the weathervane points to one of the eight demi-gods sculpted on the façade (Fig. 2.7b). Each bears the name of a wind—Boreas (N), Kaikias (NE), Apeliotes (E), Euros (SE), Notos (S), Lips (SW), Zephyros (W), Skiron (NW)—and personifies a specific weather condition [21]. Depending on whether the violent aspect of a storm or the beneficial effects on the weather and cultures, the image tends to resemble a monster or a god. Interest in meteorology continued with the Romans, who started the tradition of writing encyclopaedias on natural sciences (Sect. 2.2). The best known of these, Naturalis historia, was written by Pliny the Elder (23–79) and contains numerous references to the evolution of the weather. Some years before, Publius Maro Vergilius (Virgil, 70–19 BC), had dealt with the problem of weather forecasting in Georgics, providing some indications on the importance of changes in the weather and seasons, in relation to crops. 9 Having

visited the Acropolis, Marcus Vitruvius Pollio (70–23 BC) provided a precise description of the Tower of the Winds. This showed interest in the wind vane, evidently an instrument unknown to the Romans.

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Ptolemy (about 100–178 BC), the famous Greek astronomer and mathematician (Sect. 2.3), wrote Tetrabiblos, in which he tried to provide a scientific basis for astrology. It contains a summary of the main meteorological signs and, for the entire Middle Ages, was the reference for weather forecasts. Despite the decline of the Roman Empire and the dawn of the Middle Ages not favouring the furthering of knowledge, interest in meteorology and the tendency to forecast weather did not wane. Isidore of Seville (560–636) tackled these problems, for example, in Etymologiarum sive originum libri XX, in which he criticised astrology as a divining art. However, he did recognise a physical link between stars and weather conditions, going into extensive discussions on this topic. Interest in the relationship between astrology and meteorology increased after the death of Mohammed (570–632), when Greek, Roman, Persian, and Indian cultures were reassessed, blended, and added to by a new generation of Muslim philosophers and students that flourished from the eighth to the eleventh century. During this period, Islam became the centre of the civilised world. The Arabs began studying meteorology through astronomical observations, giving rise to vast interest in a pseudo-science known as astrometeorology [19, 21]. It gained a great following and aroused enormous interest because, unlike phenomenological meteorology that provided short-term weather interpretations, astrometeorology promoted the hope that it was possible to forecast the weather in the long-term. The Spanish astrologers of Toledo formulated one of the first and most famous astrological prophecies in his Letter of Toledo addressed to Pope Clement III in 1185. There they predicted that in September the following year, the joint movements of various planets would cause winds able to destroy almost all structures; it would also bring with it great famines and many other disasters. The people were so terrified by this prophecy that the construction of underground refuges spread; this preceded by almost one thousand years a now normal tendency on all areas of the world afflicted by tornadoes (Sect. 10.2). The complete lack of foundation for Toledo’s prediction did not suffice to deter interest and trust on this new discipline that had numerous contributions added to it, especially in the thirteenth century [21]. Standouts among these were De impressionibus aeris seu de prognosticatione (1235–1253) by Roberto Grossatesta (1168–1253), a treatise on weather forecasting based on astrological principles, the signs of the zodiac, and the planets, Iudicium particulare by Bartholomew of Parma (thirteenth–fourteenth century), Repertorium prognosticon de mutatione aeris (1338) by Firmino da Bellavalle, and Summa iudicalis de accidentibus mundi (1338–1379) by John of Eschenden. Nicolas Oresme (1325–1382) was one of the few who contested and criticised astrometeorology, stating that weather forecasting would only become possible once the physical laws of meteorology were understood. These concepts were too farsighted for an age still dominated by Aristotelian theories and the divinisation of atmospheric phenomena. Many of the attempts to interpret them as natural causes and to explain them in terms of physical laws therefore clashed with the church’s opinion and often resulted in violent conflicts between science and religion.

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However, astrometeorology did provide undoubted advantages. In order to prove its validity, the practice spread of doing meteorological observations and recording them, at least initially, at the edges of astrological tables and almanacs. The aim was to compare forecasts with reality and to establish adequate statistical correlations between astronomical phenomena and the weather; in fact, this trend resulted in recording and storing enormous amounts of information on weather and climate. This situation evolved in the first half of the fourteenth century, when these astrological notes gradually reduced in number, and observations became frequent, continuous and organised. The best interpretation of this transition was provided by the English clergyman, William Merle (?–1347), who recorded the weather conditions for Oxford every day from January 1337 to January 1344 in Consideraciones temperiei. He also wrote a treatise on weather forecasting, De prognosticatione, in which he both revived and summarised the theories of Aristotle, Virgil, Pliny the Elder and Ptolemy, and dealt with ancient popular British traditions. The favour towards astrometeorology revived towards the end of the Middle Ages. At this time, literature known as prognostic became fashionable, made up of very brief works written mainly in Latin. They contained detailed weather forecasts covering a year, prepared according to classical astrological rules. These spread on the back of the arrival and spreading of the printing press. In Europe alone, in the sixteenth century, more than 3000 were published, prepared by about 600 different forecasters. One of these, Pronostico o vero iudicio generale composto per lo eccellente messer Hyeronimo Cardano phisico milanese, dal 1534 insino al 1550, con molti capitoli eccellenti, was published in Venice in 1534, seemingly by Gerolamo Cardano (1501–1576), a famous mathematician and student of the probability theory (Sects. 3.3 and 3.4). This work contains a preamble, followed by 19 chapters dealing with various problems, including war, the pontificate, and famines. In chapter III, which deals with studying air and astrometeorology, Cardano gave particular importance to the appearance of comets that bring famines, droughts, storms with lightning, earthquakes, and other disasters. Chapter IV, dealing with weather forecasts, gives specific dates to the physical phenomena dealt with: “From 6 July to 9 August 1534, there will be great drought, on 25 August 1537, there will be cloudy weather and rough, and on 21 June 1540, heavy rain, strong winds, and so on”; however, he failed to indicate the locations affected. During the same period, the astrological forecasts prepared for certain years or periods of the year were accompanied by the formulation of general rules that applied to weather forecasting for any period. The best-known example of this new trend is Die bauern-praktik, a popular compendium of farmworkers’ practices, published in Germany in 1508 and subsequently translated into the major European languages. This practice was still so strong in the sixteenth and seventeenth centuries that laws were promulgated in France, prohibiting the use of astrological almanacs for disseminating prophecies on a political basis. The British almanacs, monopolised by the Universities and the Stationer’s Company, fell under the jurisdiction of the Archbishop of Canterbury. Astrological forecasts even enjoyed the favour of illustrious students like Tycho Brahe (1546–1601) and Johannes Kepler (1571–1630) (Sect. 3.1).

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Not even the advent of scientific meteorology was able to suppress interest in astrological forecasts; rather, these became even stronger in the eighteenth and nineteenth centuries (Sect. 4.1).

2.5 Sailing Ships Man learnt to make use of wind energy by equipping his ships with sails [22, 23]. Many believe that the first rudimentary sailing ships appeared on the Indian and Chinese seas around 5000 BC. Some maintain that sailing ships originated in the Middle East, where the storms are less violent than in other countries, and winds are more regular and predictable. Yet others claim that the Egyptian civilisation originated from people who came from Mesopotamia or India by sea, using sails as early as 6000 BC. There are also some who are convinced that the use of sail power originated in ancient times in the South Pacific, where the natives used this means of getting from one island to another. The first documented information relates to a sail made of palm leaves. It is depicted on a predynastic Egyptian vase, probably attributable to the period between 4000 and 3000 BC. From the same period (about 3500 BC), there is a clay model of a Sumerian vessel found in Eridu, in the Mesopotamian basin between the Tigris and the Euphrates; it shows a housing for the mast on the centreline, displaced towards the bow, with holes for the cables that supported it. From 3000 BC on, the Egyptians used sailing vessels first to tackle the waters of the Nile, then the Mediterranean, the Red Sea, the Indian Ocean and the Persian Gulf [1]. A predynastic rock carving found in the Nubia Region dates back to this period. It depicts a trapezoidal sail hanging from the mast of a vessel made of rushes [5]. Information on sailing vessels became more precise during the reign of the Pharaoh Snefru (about 2650 BC), when a scribe described equipment that had been so perfected and efficient, that it was possible to equip a fleet of 40 ships for a voyage as far as the ports of Lebanon and back. Later, under the Pharaoh Sahure (about 2480 BC), the Egyptian voyages to Syria became legendary; they show that sailing into the wind was done using oar power, whereas sailing with the wind was done by hoisting a two-legged mast with high, narrow sails (Fig. 2.8a). A bass-relief at Deir el-Gebrawi shows that the transition from high, narrow sails, to sails that were wider than they were high, came about 2300 BC. At this time, the vessels did not have a loadbearing structure, and this function was entrusted to the planking; they had an elegant, gondola-like shape, with ends that sloped somewhat at both the bow and the stern. During the reign of Queen Hatshepsut (1520–1483 BC) a fleet of five Egyptian ships reached the Land of Punt, to load luxury goods. It is located beyond the Red Sea, on the northern coast of what is now Somalia, or even further south, beyond the easternmost point in Africa. It is said that, knowing the seasonal directions of the monsoon, it was possible to do the outward and return voyage using sail power; this is an important indication of the progress in the art of seamanship and knowledge of

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Fig. 2.8 a Egyptian ship at the time of Sahure; b merchant Phoenician ship (eighth century BC) [22]

the wind. Some bass-reliefs from the period show the new equipment; the sail can now be adjusted to suit the direction of the wind, by means of a boom; the mast is no longer two-legged, but a single mast. Meanwhile, positioned at the crossroads of Egyptian, Mesopotamian, Lebanese, and Greek trade, between 2000 and 1450 BC, Crete became the centre of the Aegean civilisation, and the first maritime power in history. It played the role of guarding shipping, which already at that time was plagued by piracy, by some populations from the Middle East. A Minoan fresco from the fourteenth century BC shows the entry to the port of Santorini, with an Egyptian vessel in the centre, with its ends raised; to the right one sees the bow of an Aegean ship, characterised by the ram on the front, a typical attack element. This represents the main innovation introduced by Hellenist seamen, compared to the Egyptian vessels. Having conquered Crete, the Greeks acquired the Minoan seafaring art and took over the commercial and military position previously possessed by the island. Some descriptions by Homer (ninth–eighth century BC) in the Odyssey, give a vivid picture of the ships of his time. Hesiod (eighth century BC) wrote Works and days, a poem in which he dispensed advice on the best way to sail, taking the actions of the malevolent gods of the atmosphere into account. At the same time as the Greeks were affirming their naval power, the Phoenicians were developing a formidable propensity for merchant shipping. Using ships similar to those used by the Greeks, they pushed along the Mediterranean coastlines, passing the Pillars of Hercules, and reaching Britain. In Histories, Herodotus (484–425 BC) recounted circumnavigation of Africa by a Phoenician fleet, during the reign of the Pharaoh Necho (610–594 BC); during the three-year expedition, the fleet went down the Red Sea to the Indian Ocean, and then re-entered the Mediterranean via the Pillars of Hercules. Thanks to the Phoenicians, the use of sail power became a real art [1], especially as a result of an extraordinary knowledge of the strength, direction and humidity of the wind at all places and in all seasons of the year. On Phoenician warships, the sail, normally made of linen, was an additional system to the use of oars; in order to reduce their area when the wind was too strong, the lower portions were drawn

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Fig. 2.9 Roman Corvus on a sail ship

upwards, using a system similar to that of the Venetians. Merchant ships (Fig. 2.8b), on the other hand, used sails as their main means of propulsion. The yard, about 12 m high, was used to hoist a rectangular sail of about 60 m2 ; with a favourable wind, the ship reached a speed of five knots. From the second century BC, the Mediterranean was plied by Roman fleets. While keeping the model of Greek and Phoenician ships almost unaltered, the Romans developed sail-powered seamanship techniques, especially for military purposes (Fig. 2.9). Besides the typical large mainsail, the second sail appeared on Roman ships, supported by what was called a jigger mast, more towards the bow; this made it possible to bring the hull around quickly, to one side or the other. From the first century BC, the third mast appeared in the stern, the mizzen mast. Finally, sails appeared with a yard hinged at the base, or triangular sails, in order to increase the ship’s speed. These and other innovations made it possible for Roman ships to go from Lazio to Tunisia, and from Sicily to Egypt, at an average speed of nearly six knots. Lucan (39–65 AD) described the imposing form of a Roman grain ship, about 50 m long, with a crew the size of an army; numerous relics remain of these and similar vessels. These show the almost perfect knowledge of the Mediterranean winds, documented by Pliny the Elder (23–79 AD), and some shortcomings in terms of structure: the large size sail transmits very strong forces on the hull, often incompatible with the materials used; this posed numerous problems for the Romans, in terms of governing the ship and its capacity to take on the ocean. The extensive limitations due to the aerodynamics of the sails are even more evident, as they were only able to propel the ship in the direction of the wind. The Viking peoples acquired the art of navigation between 500 and 800 AD. The best information on their vessels comes from the remains of the ship of Kvalsund,

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Fig. 2.10 Gokstad Viking ship

Fig. 2.11 a Square rig; b Latin-rig; c spritsail

which dates back to about 600, and especially the Gokstad (Fig. 2.10), sculpted in stone around the eighth century. Both show rigging with a single rectangular sail made of spun linen, reinforced with leather straps. They also show the first arrangements for sailing crosswind, on a course almost at right angles to the direction of the wind. These vessels allowed the Vikings to push as far as Britain and the west coast of Ireland, along the Bay of Biscay, as far as the Mediterranean and into the Adriatic, possibly sailing close to the coast. Later on, they reached Iceland, Greenland and America. With the exception of the changes used on the Viking ships, the element all the vessels referred to have in common is the use of a rectangular sail, called a square rig (Fig. 2.11a). Fixed to the yard, that is a horizontal bar fixed at the mid-point of the front face of the mast, it is perpendicular to the centreline of the hull; in addition, it always takes the wind on the same side, and is pushed in one direction due to its drag action. The position of the sail’s centre of gravity, in line with the centreline of the hull, makes this system exceptionally stable, obviously only when the wind is from the stern.

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Sailing techniques changed radically with the arrival of the fore-and-aft sail (Fig. 2.11b, c). Hoisted to the stern of the mast, and not towards the bow like the square rig, it rotates along the shaft and tends to lie parallel to the ship’s centreline. The wind strikes it on one side and then on the other side, depending on which side it is coming from, pushing the vessel crosswise, by means of lift rather that a drag force. From this point of view, although it is based on purely empirical principles, the fore-and aft sail is one of the first applications of advanced aerodynamic principles. It comes in two different versions: the Latin-rig (Fig. 2.11b) and the spritsail (Fig. 2.11c). The triangular Latin-rig made its appearance even before Christian times, on small vessels sailing between the Aegean islands. Its systematic use began in the Middle Ages, between the seventh and elventh century, giving rise to the gradual disappearance of oars from the vessels, due to the renewed skill in sailing upwind, using sail power. It spread in the Mediterranean in part due to Arab conquests, and to sailors, it soon became one of the best-known symbols of Islam. It is also a sail that is difficult to handle, as it makes the vessel somewhat unstable especially when the wind is from the stern, and its efficiency varies depending on which side the wind is from, which means it demands great seamanship skills. This means that, at least at the outset, its use was limited to small boats used for war, fishing and coastal transport. The first relics of spritsails date back to the second century AD and come from ancient Troy; a third-century sarcophagus depicts a ship fitted with this type of sail in the Port of Ostia [22]. Later, mainly thanks to the Dutch, the spritsail became common in Northern Europe. It is rectangular in shape, raised towards the stern, is kept taught by a bar from the bottom of the mast to the top corner of the sail (Fig. 2.11c) and is good for pressing the wind; similar to the Latin-rig, this property makes it less efficient when the wind is from the stern, and reducing sail size when the wind is strong, is difficult. The spritsail was also limited to small vessels. For these reasons, despite the exceptional advantage of sailing upwind using a fore-and-aft sail, the use of a square rig continued in the Middle Ages being preferred for cargo vessels and large tonnage ships. The great change came in the fifteenth century, when ships from the North, based on Viking ships and fitted with a mast with a square rig, met the ships from the South, with one, two or three masts, with Latin-rigs. This meeting gave rise to three-masted ships, initially called carracks (Fig. 2.12), which combined the advantages of the traditional square rig, with the complex potential of the Latin-rig, ensuring the advantages of both. It had a main mast for the square rig in a central position, an aft mast for the Latin-rig towards the stern castle, and a foremast at the forecastle fitted with a second square rig. Unlike the main square rig, which was used mainly for propulsion, the aft and fore sails were smaller in size and were used to balance the ship and make it easier to handle. Some bibliographical sources state that the Chinese used this Western practice centuries earlier10 [24]. 10 Two books, written by Wan Chen in the third century AD and by Kang Tai, around 260 AD, describe Chinese ships that avoided mutual shielding of sails, by staggering the positions of the

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Fig. 2.12 Carrack

2.6 Wings and Kites From the most ancient times, the idea of being free on the air has been held an irresistible attraction that wings and their metaphysical meaning have been interwoven with man’s dreams and aspirations [18, 25]. According to an ancient Persian legend, in 1500 BC, King Kai Kawus flew on a carriage carried by eagles. Another legend, of Greek origin, says that Alexander the Great (356–323 BC) visited the heavens in a wicker basket pulled by griffins. The most famous legend of this kind, that of Daedalus and Icarus, was told by Ovid (43 BC–17 AD) in his Metamorphoses and the Ars amatoria (Sect. 2.2). Daedalus was an Athenian architect, painter and engineer, with an extraordinary intellect. Accused and found guilty of the death of his nephew Talus, he escaped from prison, taking refuge under King Minos on Crete, along with his son Icarus. Here he built a labyrinth that housed the Minotaur, and he was imprisoned in it himself, along with Icarus, after disobeying the King. In order to gain their freedom, Daedalus made two pairs of wings from eagle feathers, bound together using reeds, linen and

masts, on either side of the ship. A book by Li Ch’üan in 759 AD states that a board was used that was lowered into the water on the leeward side of the ship, to increase its stability. This arrangement appeared in Europe around 1570, built by the Dutch and Portuguese, who traded with China.

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Fig. 2.13 Daedalus and Icarus

wax (Fig. 2.13). Not heeding his father’s warnings, Icarus flew too high in the sky. The sun melted the wax and Icarus fell into the Aegean Sea. The first attempt to fly, somewhere between legend and reality, took place in Magna Graecia [1, 2]. The tale was told by Aulus Gellius (about 130–175) in his Noctes atticae, in which he talked about a mechanical dove built by Archytas of Taranto (about 430–360 BC), a Pythagorist, mathematician, engineer, statistician and man of arms. According to Aulus Gellius, flight was maintained by means of counterweights; forward movement was due to a hidden movement of the air inside the dove. He also stated that Archytas’s dove was able to rise to a great height, harmoniously flapping its wings, “with a great hissing noise and smoke coming out of the tail”. A legend that developed in Roman times indicates Simon Magus (first century AD), the Samaritan wizard spoken about on the apocryphal writing by the Apostles, as one of the precursors of flight. According to that legend, he flew into the sky to convince Nero (37–68 CE) of his divinity. However, he was brought down by St Peter, with an “anti-aircraft shot of well-directed prayers”. He fell to the ground and broke various parts of his body.

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A Nordic tale, from around the fifth century, talks about Wayland, a blacksmith who specialised in making arms, constructing wings to fit to his own body. With these, he snatched up his enemies, took them high in the sky, and let them fall, killing them. A dialogue between Wayland and his brother Egil recounted in Eddas gives a glimpse into interpreting the role of the wind, in terms of aerodynamics [26]. Towards the end of the first millennium, man’s mythological aspiration to fly like the birds began to give way to real experiences [18, 25]. In 852, in Cordoba, an Arab “saint” lost his life during an attempt at free flight. In 1020 an English Benedictine monk and astrologer, Eilmer of Malmesbury (about 981–1069) launched himself from a Spanish tower, with feathered wings, similar to those made by Daedalus; he crashed to the ground after gliding for almost 200 m and suffered only fractures of his legs; he attributed the accident to the lack of a stabilising tail. In 1161, an Arab called Saracen launched himself from a Tower in Constantinople, flapping his wings; in his Saracenica historia, Georgius Elmacinus (1205–1273) recounted that “since his body weight pulled him down with a greater force than his wings could keep him up, he broke his bones and his injuries were such that he did not survive”. Giovanni Regiomontano (1436–1476) built a flying eagle and flew; according to accounts of the time, the flight of the eagle was demonstrated publicly in Nuremberg on 7 June 1470. Similar attempts at flight were made by Senecio of Nuremberg (1496) and by the mathematician Giovan Battista Danti (about 1477–1517) who in 1503 suffered serious injuries during an attempt to fly using wings, from the Tower of Perugia. During the same period, Leonardo da Vinci (1452–1519) (Sect. 2.10), perhaps taking inspiration from the ideas of Roger Bacon (Sect. 2.3), did his famous studies on the human flight. While these experiences were underway in the West, the art of kites was spreading in the East. Precursors to and forerunners of winged craft and aeroplanes (Sects. 4.5 and 7.4) destined to play an essential role in the progress of knowledge about the atmosphere (Sects. 4.5 and 6.2) their origins date back to the earliest times [24, 27], perhaps even in the third millennium BC [2]. The first reference to an Oriental device able to fly freely in the air, dates back to the Chinese author, Mo Tzu (470–391 BC), who talked about a rudimentary attempt to construct an object similar to a kite [27]. In the fourth century BC, Kungshu Phan described his own creation, a timber bird, able to fly for three days without landing [24]. The first kite, about which there is no ambiguity, was described by General Han Hsin in 200 BC; it was built and made to fly in order to estimate the length of a tunnel to be built from his army’s outpost, to the walls of a besieged castle. From then on, kites spread throughout China and in Korea. They were built with a rectangular shape and, at least initially, were used for military purposes. It is said, by way of example, that in 202 AD, under the Han Dynasty, a famous general terrified and put the enemy’s armies to flee, using kites put into flight during the night over their encampments; he attached bamboo to them, which worked like Aeolian harps (Sect. 2.1), emitting ululations. In a similar vein, it is said that in the sixteenth century, during a period of heightened tensions, the Emperor Laing Moo, was unable to keep his army at the palace, awaiting battle. He decided to allow the soldiers to go back to working the land, agreeing with them that kites would be launched as a sign of

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enemy attack, which would serve as an order to return immediately. Having been besieged during the night, the emperor launched kites to call his soldiers. They came up behind the enemy and, by besieging them against the palace walls, were able to defeat them. A Korean legend tells the story of a General, Gim Yu-Sin (596–637), tasked with putting down a revolution. One night his soldiers saw a falling star and interpreted this sign as an indication that they would suffer defeat. In order to raise the troops’ morale, the General built a kite, which he used to raise a ball of fire. The soldiers, believing that the fallen star had risen again in the skies, had their courage restored, and they defeated the rebels. The first description of human flight with kites comes from the Chinese Ch’i dynasty (550–577) [24]. At that time in China, an exercise in piety was popular, known as “the liberation of living creatures”, which meant that fish and birds were freed again after they had been caught. The Buddhists took on this practice, believing that it brought merit to pious men. Kao Yang, the first Emperor (550–559) of the Chi Dynasty, embraced that concept and celebrated his Buddhist ordination at the Tower of the Golden Phoenix, with a ceremony that he himself called “the liberation of living creatures”. The creatures “liberated” were his enemies, lashed to kites made of bamboo mats, and thrown from a 30 m high tower, with the order to fly down to the ground. The story goes that all the prisoners died.11 With the passing of time, and thanks also to the increased Chinese influence in surrounding countries, the use of kites spread to Japan, Burma, Malaysia, Indonesia and India. From Malaysia, kites reached Polynesia and New Zealand. From India, they reached Arabia around 500 AD. In the meantime, the kite took on ritual significance. According to a Balinese Hindu belief, flying kites is the favourite pastime of the gods. In Polynesia, it holds the ring that links man and divinities. In Korea, the name and destiny of children are associated with the flight of kites. In Japan, a kite is made to fly around the homes of unborn babies, so that the wind will drive away the evil spirits of darkness. In Indonesia, they are a privileged means of communicating with the spirits, interpreting the future, and gathering wishes. In Thailand, kites ward off flooding. With the coming of the Sung Dynasty (960–1126 AD), the Chinese began using silk and bamboo kites during religious ceremonies and popular festivals (Fig. 2.14). Later according to Marco Polo (1254–1324) in 1282, kites were used to send tiles and bricks up to workers on the roofs of pagodas or as a means for lifting people12 [24]. Some writings from the same period talk about sentries suspended from kites to look out for the enemy. Others describe the custom of hanging prisoners from kites and throwing them from the castle walls, offering them freedom if they survived. A 11 It is said that in 559, Yuan Huang-T’ou was the first to come back to earth unharmed, after a 2-mile flight. However, he was left to die of hunger. 12 In Manuscript Z, Marco Polo wrote that when a ship had to undertake a voyage, a test was carried out to find out how the trade would go. A grating was taken and attached to its corners, joined at the other end to form a cable. When the wind was strong, an idiot or drunk was sought to tie to the frame. If the frame lifted into the air, it was said that the ship would have a fast, safe voyage. If the frame did not take off, it was said that no merchant would go on board.

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Fig. 2.14 Rectangular Chinese kite [27]

Japanese legend says that Minamoto no Tametomo, a Samurai warrior of the twelfth century, exiled on the Island of Hachijo with his son, saved the boy using a kite. The tradition of kites in Europe dates back to the Roman Empire, when soldiers fixed windsocks to sticks, which filled with air and frightened the enemies. During the Middle Ages, this custom sprang up in numerous countries in Europe and Asia. The first illustration of a European kite dates back to 1346 in De nobilitatibus by Walter de Milemete. It was shaped like a winged dragon, carrying an object similar to a bomb (Fig. 2.15). Konrad Kyeser (1366–1405) provided the first image of a pennant or ensign shaped kite in Bellifortis (1405); it is also to be seen, even more clearly, in a Viennese book from 1430 (Fig. 2.16). The first flat kites, termed a guidon, date back to the fourteenth and fifteenth centuries; initially, they were rectangular with a large tail; later on, from the mid-seventeenth century, they took on a curved, rhomboid shape. It was only from that time that the kite became an object for amusement.

2.7 The First Windmills It is practically impossible to locate when and where windmills first appeared [28]. The first certain reference dates back to the eighteenth century BC, when Hammurabi

2.7 The First Windmills

Fig. 2.15 Illustration of a kite in De nobilitatibus [27]

Fig. 2.16 Pennant or ensign-shaped kite [27]

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Fig. 2.17 a Device powered by a small windmill [28]; b ancient Persian mill

signed a plan in which windmills were used to irrigate the plane in Babylon. In the first century BC, Heron of Alexandria wrote Pneumatics (Sect. 2.3), in which he showed a device driven by a rudimentary windmill, with a horizontal axis (Fig. 2.17a). The first windmills for which there is definite documentation came from the Middle East in the seventh century AD, during the reign of Caliph Omar I, (581–644) [3, 29, 30]. Arab geographers and historians who visited the desert highland plane of Sistan, at the current border between Iran and Afghanistan, referred there was a wind that blew there from June to September that was called the “120-day wind, the wind that kills the cows”. Numerous relics of still intact mills, which some claim pre-date the birth of Christ, show that they were rather rudimentary, with a vertical axis, made of materials available locally and so suitable for the needs of the farmworkers of the period. The wind blew through an aperture on the windward side, followed a route similar to that of a tunnel, and flew out of an aperture on the leeward side (Fig. 2.17b). The effect of the tunnel was to increase the speed of the air that drove the vanes. It only used wind coming from a single direction. The historian al Mas’udi (about 900–965) wrote Praries of gold and precious stone mines (947), in which he told the tale of a Persian slave who appealed to the Caliph over a tax of two silver coins per day, which he deemed excessive; the appeal was rejected, because he was a carpenter who was an expert in building windmills, and so was able to pay the heavy tax. The same work refers to the tradition that has it that the windmills reached Persia via the Egyptians, back in the time of Moses. It also describes the use of windmills to irrigate lush gardens, stating that no people on the earth, made greater use of the wind. In 1283 another Persian expert, al-Qazwini described the use of the Sistan windmills to grind flour, pump water from underground, and redistribute sand mounded up by the wind [31]. Al Dimaschqi, a fifteenth-century historian, wrote [32]: “In Segistan there is a region in which there are a lot of winds and large quantities of sand. Its inhabitants use the winds to turn the windmills, to move the sand from one place to another, so that the winds are subject to them, as they are subject to Solomon. To build the

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Fig. 2.18 Arab windmill (early fourteenth century) [32]

mills, which are driven by the wind, they proceed as follows: they build a tower as high as a minaret, or use another high point on a mountain, hill, or fortress tower. Here they build one building on top of another. The uppermost building houses the windmill that turns and grinds, whereas below there is a wheel that is rotated by the wind” (Fig. 2.18). The text goes on to say that: “Once they had completed building the two buildings, they formed four slits in the lower building, just as one forms slits in walls. However, these are arranged in the opposite manner, because the wider part is towards the outside, and the narrower part to the inside. This forms a channel for the air, so that it enters with some force, like the blacksmith’s bellows. The wider part is at the mouth and the narrower part inside, because this facilitates the wind’s entry, causing it to get into the windmill building, irrespective of the wind direction. When the wind comes in, via the openings formed for it in the windmill building, it encounters a specific ‘loom’, like that used by weavers, which lays the threads on top of one another. (…) The cladding has a large fold, which the air fills and pushes forwards. The air then fills the next, pushes it forward, and then fills the third. This causes the loom to rotate, and as it does so it turns the stone that grinds the wheat”.

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From Persia, windmills spread to Egypt and Arabia where, in the eleventh century, they were used to grind grain and cereals, and for pumping water from underground [33]. The origins of the spread of windmills in the Far East are less certain. It is said that the army of Genghis Khan (Temujin, about 1167–1227) captured the Persian windmill builders and took them to Mongolia to make mills for irrigation. Some believe that windmills in the Far East originated on their own. In 1219, the statistician for the Mongol Empire, Yehlu Chhu-Tshai (1189–1243), documented a Chinese windmill with a vertical axis; similar contraptions are still used by local nomad peoples, for irrigating fields, draining frost and generate electricity. The origin of European windmills is highly controversial. According to the theories with the most backing, they came to Europe from the Orient, first via the merchants, and then due to the Crusades. Others make the opposite claim, that is, that windmills originated in England and arrived in Syria and the Orient via Saxony, as a result of the Crusades [34]. There are numerous legends that have it that the first European windmills date back to much earlier times. An Irish story talks about a King in the third century, Cormac Ulfada, who was in love with Princess Ciarnait. On discovering this treachery, the Queen ordered that the princess be made to operate the wheat mill all day long. To help her, the King appointed a Scots subject to build her a windmill [30]. Whatever the origins of European windmills, their prerogatives differed from those of Oriental windmills. While the Oriental windmill had a vertical axis, the European mills had a horizontal axis and were generally larger, as they tended to be used for whole rural communities, rather than individual farmers. Provisions of the time often included the feudal right to refuse farmers permission to build mills and to oblige them to grind their grains at the Lord’s mill. The prohibition of planting trees around windmills, in order to allow the wind to blow freely [35], was one of the first manifestations of concepts based on micrometeorology (Sect. 6.5). According to most interpretations and the little documented data available, the first reference to a European windmill dates back to 1105 and relates to Arles, a town in South-East France [30]. Subsequently, there is data for windmills in Normandy, from 1180, and in Flanders, from 1190 [34, 36]. The first English windmill for which information is available and was built in 1191 on the plane in Suffolk, on the east coast13 [29, 37]. It is said that Dean Herbert, an old priest at the local church, built it to allow the parishioners to mill their wheat. Abbot Samson, from the nearby monastery that owned the only water mill in the region, ordered his men to destroy it, in order not to have to forego a valuable, heavy tax: the farmers that used it, paid them back by giving them some of their flour. This is an example of a long diatribe around windmills. With the passing of time, farmers more and more often rebelled against Lords, claiming their right to make free use of 13 The major chronicle of English windmills, History of corn milling, was published by Richard Bennett (1844–1900) and John Elton (1898–1904) [37]. It shows that many stories about ancient mills were false, especially that of the concession of a mill to Croyland Abbey in 833. The first reliable reference to a windmill appeared in the Chronicles of Foycelyn de Brakelond and deals with the mill built in 1191 by Dean Herbert at Bury St. Edmunds.

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wind energy; this opposition was to play an essential role in social progress and in the overcoming of medieval obscurantism [34]. The first German windmill, for which there is objective evidence, was built in 1222 on the walls of the city of Cologne, a practice that was to become typical in the late Middle Ages. The first news of an Italian windmill came from Siena in 1237. It is probable that the first Danish windmill dates from 1259. There is a German document from 1274 that speaks about the privilege granted by Count Floris V to the burghers of Haarlem: to pay a tax of 6 shillings to use the windmill compared to 20 shillings to be paid by non-citizens. Another document shows the appearance of windmills in Holland by the end of the thirteenth century; it states that in 1294 Gelderland paid money to repair a mill. In a letter dated 1299, the Duke of Brabante and Limburg, John I, granted Arnoldus the land assigned to him for feudal benefit and permission to build the most useful windmill, along with a hereditary right to free use of the wind. Giovanni da San Gemignano (about 1299–1333) wrote an encyclopaedia for preachers, in which he put topics of a technical nature, for them to use to enrich their sermons; the descriptions of windmills stand out. In 1335, the Italian physicist Guido da Vigevano (1280–1349) designed a fighting machine, powered by a windmill (Fig. 2.19) [31]. Around 1350, Holland was full of water wheels (Fig. 2.20a) and Archimedean screw mills (Fig. 2.20b), to dry out the lakes and swamps in the Rhine delta [5]. The first European windmills of the thirteenth century were called post-mills (Fig. 2.21a). They had a box-shaped base, on which a rotating platform rested, on which the windmill stood. The vanes were of timber, covered in fabric. Each time the wind changed direction, the miller went outside and rotated the mill to suit the direction of the wind, using a long pole that crossed the stair. The windmill was light enough to be rotated by hand; it was strong enough to withstand wind storms and the vibrations caused by the wind acting on the vanes, and the gears for grinding; it was balanced in all positions. Many of these mills lasted for centuries, thanks to the expertise of the medieval builders. At the start of the fourteenth century, builders discovered that, for the mill to adapt to the wind, only the vanes needed to be rotated, not the whole mill. For this reason, the vanes were fixed to a swivelling crown on the roof; this was activated by the miller to align with the direction required. These new generation windmills were more stable and stronger than their predecessors and were referred to as tower mills. In England, they were called “smock mills” and in general had an octagonal section. They were made of timber and painted white (Fig. 2.21b); in some cases, they had a circular section and were built of bricks, covered in pitch. Early models had wooden tracks and slides on the dome. These were later made of iron, and later again, rollers were introduced between the track and the dome. Around 1500 inhabitants of Portugal, Spain, Greece and the Mediterranean Islands began to build small windmills in stone; the vanes were made using wooden shafts radiating out, at the end of which there was a small fabric sail, generally triangular. There are still many of these windmills on the Greek Islands of Mykonos and Rhodes (Fig. 2.22a). In Crete, in the Lassithi plane alone, there are about 10,000 (Fig. 2.22b).

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Fig. 2.19 Fighting machine powered by the wind, by Guido da Vigevano [31]

Fig. 2.20 Mill on the Rhine [35]: a waterwheel; b Archimedean screw

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Fig. 2.21 European windmill [29]: a post-mill; b smock-mill

Fig. 2.22 a Ancient mills, Rhodes (1493); b plane of Lassithi, Crete

They are used to grind wheat and get underground water; it is said that a farmer’s wealth is proportional to the number and size of his mills.

2.8 Climate and Architecture One of the most ancient and profound ways in which the conflict between man and wind manifests itself is man’s desire to protect homes and settlements against the lashing action of cold winds or oppressive conditions, caused by stagnant hot air. The history of mankind is full of varied examples and sometimes curious attempts to improve living conditions by blocking harmful winds or creating pleasant draughts. This topic has its roots in remote eras and owes its first significant progress, especially to the inhabitants of areas subject to extreme weather conditions [38–41].

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Fig. 2.23 Pyramid of Cheops: a picture; b section

The use of wind for ventilation was to be found in Ancient Egypt, at the Pyramid of Cheops (Fig. 2.23a), built between 2550 and 2530 BC. Two straight ducts went out from the North and South walls of the sarcophagus chamber and reached the outside about 75 m above the ground level (Fig. 2.23b). According to the most accredited hypothesis, these created a ventilation system for the tradesmen working inside; the air came in from the upstream (in pressure) duct and exited via the downstream (in suction) duct.14 Around the base of the pyramid, there were some pits that housed the boats the Pharaoh required to sail to heaven; according to the ancient Egyptians, the sun travelled through the sky in a boat, and the Pharaoh did the same. In one of the pits, a boat was found (1954) made of Lebanese cedar wood, disassembled into 1224 parts; when reassembled they formed a hull 43.5 m long and 6 m wide; the hull had no nails, and was kept together by a perfect system of bindings. In the middle of the boat, there was a 9-m long closed cabin; a soaked reed mat was applied to the ceiling. The air entered the closed space via slits, flowed over the mat and cooled the space. The first ties between wind and urban planning manifested themselves in ancient Egypt. Building of the city of Kahun (or El Lahun) (Fig. 2.24a) was begun by King Sosostris II (Sesostris II, nineteenth century BC) between 1897 and 1878 BC, on the occasion of reclamation of the Fayum around Lake Moeris [12], to house those working on the King’s pyramid. The nobles’ quarter, to the North, was separated from the workers’ quarter to the West: the former was exposed to the pleasant breezes from the North, via the Nile Valley, while the second was struck by hot desert winds, coming from the west, using it to protect the homes of the rich [38]. Babylonia, capital of Mesopotamia in the second and first millennium BC, had a rhomboid road grid (Fig. 2.24b). It stood at the crossroads of three main winds: the dry equatorial wind that came from the north-east and lowered the temperature, was attributed to the god Marduk; the cool, reinvigorating north-westerly summer wind, was believed to be a manifestation of Istar, the god of love; the desert wind, 14 According to another interpretation, the diagonal ducts (that cross the pyramid from South to North), are aligned with the stars (which played an important role in Egyptian astronomy and religion), to allow the Pharaoh’s spirit to reach the heavens.

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Fig. 2.24 Layout of: a Kahun [12]; b Babylonia [38]

termed the death wind, came from the south-west and was sent by the god of war. The sides of the rhombus coincided with the directions of the favourable winds. They cut across the hot desert winds, protecting the city from them [38]. Similar bioclimatic concepts were clear in Tell El Amarna (Fig. 2.25a), founded on the Banks of the Nile by King Amenophis IV (Amon-Ofis IV, later Akhen-Aton) in 1376 BC and disappeared after the death of its founder. On closer examination, its layout, which was clearly irregular, showed that all the main roads were aligned with the coolest winds, in order to provide the city with ventilation [38]. In addition, there was a “mulguf” on the roof of many houses, the first natural ventilation system for which there is precise information [40, 41]. It comprised a pair of juxtaposed openings; the wind got into the home via the opening on the windward side and exited via the opening on the leeward side.15 Its use appeared in various paintings found in the tombs of Thebes; the one shown in Fig. 2.25b depicts the home of Neb-Amun, in Gourna and dates back to the 9th dynasty (1305–1196 BC). Baghdad, founded by the Abbasid Caliph El Mansur in 763 BC on the west bank of the Tigris, had weather conditions similar to Babylonia. On the other hand, its layout was circular (Fig. 2.26), clearly for geometric reasons. Soon the city was found to be unbearable climatically; the inhabitants abandoned it and rebuilt their houses on the east bank of the Tigris, arranging them based on principles related to the zone’s climatology. Gradually, Baghdad’s layout became similar to that of Babylonia [38]. One of the first texts that deals with the role of the wind in the life of people and animals, Yajur Veda (Sect. 2.1), dates back to 1000 BC; it is described and commented in the work by Susruta (fourth–fifth century BC), an Indian physician [1]. Feng-shui, in which “feng” means wind or flow of the sky, and “shui” means water or flow of the earth, is a doctrine that flourished in China during the reign of Emperor Huang Ti (259–210 BC). From a cosmological point of view, it sees the universe to be organised in three parts, the sky, man and the earth. From a philosophical aspect, 15 The

opening on the windward side is pressurised, that is, with a force from the outside, inwards. The opening on the leeward side is in suction, with a force from the inside, outwards. The air passes through the building due to the pressure gradient between the two openings.

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Fig. 2.25 a Layout of El Amarna [38]; b Egyptian mulguf [41]

Fig. 2.26 Layout of Baghdad on the west bank of the Tigris [38]

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Fig. 2.27 Feng-shui [42]: a location of a building or city; b flow of ch’i in a building

it states that man and the environment, that is the space between the sky and earth where man lives, are sustained by an invisible but tangible energy,16 called “ch’i”; this “moves turbulently like the wind, but can be trapped and get stagnant, like water”. The art of feng-shui lies in accumulating and distributing the ch’i energy, by a harmonious balance between “yin” (the wet, dark principle, that is, water, implemented in quiet spaces intended for rest), and “yang” (the warm, luminous principle, that is strong wind like breath, specifically in open spaces for vital, vibrant activity). The purpose of this dynamic balance is to harmonise buildings with their surroundings, to increase the success, health, wealth and happiness of the occupants [42]. The most ancient feng-shui texts focussed on placing the building in its environment (Fig. 2.27a). The back of the building was protected by a mountain (the head, creating a parallel with the human body), with lower hills to the side (the arms); in front of the main entrance, there was an open space that sloped down (the trunk), with water at the feet, that is the element bearing the ch’i. The mountain and the hills protected the building against the strong winds that dispersed the energy. According to this scheme, obstacles and alignments that could obstruct the flow of ch’i, or make it too quick and aggressive, were negative. The ch’i must reach the entrance and circulate inside the building, via sinuous paths (Fig. 2.27b). It must then disperse out of the back door and partly through the windows. The orientation of the building, positioning of the outside and inside openings, layout of furniture, water, and gardens were therefore fundamental. The ancient Chinese peoples translated these principles into a series of architectural and urban planning rules [12, 38] aimed

16 In

Greek culture the basic elements are physical substances (Sect. 2.2). In Chinese culture, the five essential elements have an energy meaning and evolve so that water is turned into wood, then fire, earth, metal, and finally back into water. Feng-shui positions these elements, or energies, in buildings.

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at rationalising the flow of air and light and creating barriers in relation to wind and cold. The first documented European manifestation of bioclimatic concepts dates back to the eighth century BC. In Teogonia and Works and days, Hesiod quoted rural precepts in praise of the wind from south, west and north. On the other hand, he denigrated the east wind “that explodes in the liquid power of the open sea and brings serious anguish to living beings” [2]. Hypocrites (about 460–377 BC), who came from Kos and is regarded by many as the founder of scientific medicine, was the author of a treatise, Air, water and places, in which he reported the various reactions of humans to warm and cold winds. He wrote that, “anyone who wishes to really follow medical science, must proceed as follows. First, they must consider what effects each season in the year can produce; because not all seasons are similar but vary greatly in themselves and in their changes. The next point are the warm and cold winds, especially those in winter, but also those that are peculiar to each particular region”. He also stated that, “on arriving in a city with which one is not familiar, the doctor must examine its position in relation to the winds” [2]. He also wrote a book, Epidemics, in which he correlated illnesses with seasonal climate and wind changes. Xenophon (about 430–354 BC), a Greek historian and disciple of Socrates, recommended making the south side of houses higher than the north; this would allow the maximum penetration of sunlight and protection against cold winter winds [43]. Aristotle (384–322 BC) is considered one of the first planners in history [39], due to the concepts expressed in the fourth book of Politics. Applying his own speculations and observations of the wind (Sect. 2.2), he recommended that cities be built on slopes facing pleasant breezes from the east and be protected against the cold winds from the north [12, 43]. The Greeks often put his teachings into practice, highlighting such application in the city of Priene (Fig. 2.28a) [38]. Interest in bioclimatic principles grew further in the Roman Age, thanks most of all to Marcus Vitruvius Pollio (about 70–23 BC), writer, engineer and architect.

Fig. 2.28 a Model of the centre of Priene [38]; b urban layout according to Vitruvius [1]

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De architectura, his work in ten books, written between 25 and 23 BC in honour of Augustus (63 BC–14 AD), is an essential source of knowledge on building techniques, construction materials, types of public and private buildings, urban planning and land surveying. Based on the work of Hermogenes and other Greek architects, Vitruvius developed a humanistic vision of a professional who must combine specialist experience with wide-ranging general culture. “Builders must be capable of writing and drawing well. They must be familiar with geometry, arithmetic and the law, and they must know history, philosophy and astronomy” [13]. Vitruvius suggested dividing a city lot and arranging the road layout so that it would block cold winds, said to be unpleasant, hot winds, said to be unnerving, and wet winds and said to be unhealthy, in dead ends. Referring to the eight main wind directions, he thus proposed forming concentric octagons (Fig. 2.28b), connected by means of eight radiating routes that constituted the city’s main roads. The channelling phenomena were reduced by orienting the sides of the octagon and the main roads, in directions perpendicular to and at an angle to the prevailing winds, respectively [1]. He also proposed rules for locating entrances, terraces, and courtyards of homes, based on the principles of natural ventilation. He also observed that positioning of industries in relation to cities should be dictated by the direction of the prevailing winds [12]. The importance of the last observation is amply confirmed in numerous writings of the time, from which one sees that the urban climate is different from the rural one. Quintus Horatius Flaccus (or Horace), (65–8 BC), a lyric poet and satirist, wrote some odes about pollution in Rome. Seneca (2–65) (Sect. 2.2) wrote17 [44]: “As soon as I left the heavy air of Rome, with the stench of the chimneys that, when they are in use, pour out pestilential smoke and fumes, I was aware of a change in my state of mind.” The Pantheon, built by Agrippa (63–12 BC) and rebuilt by Hadrian (76–138) between 118 and 128 AD, is the only Roman temple still intact. The diameter of the central body (34.3 m) is the same as the building height. The dome, made of a concrete box structure, stands out for its wide circular opening at the top, which is 9 m in diameter (Fig. 2.29a). The air enters via the ample windows under the portico that faces the wind, circulates inside the building and flows out of the opening in the dome18 (Fig. 2.29b, c). It is one of the first ancient buildings that clearly show the study of an efficient natural ventilation system [1]. As a matter of fact, other buildings in the Mediterranean area, especially the trulli in Puglia and dammusi on Pantelleria, made use of the same principles on a smaller 17 The pollution of Rome in Seneca’s time was ahead of the problems that arose in the Middle Ages. In 1273, after London became the prototype for urban pollution, burning coal was banned. A commission was appointed to remedy in 1285. In 1306 King Edward I (1239–1307) forbade the burning of marine coal in furnaces. Queen Elizabeth I (1533–1603) confirmed the ban on burning coal in the city. In 1661 the naturalist John Evelin (1620–1706), wrote Fuminfugium or The inconvenience of air and smoke of London dissipated, together with some remedies humbly proposed, decrying the use of coal in factories. 18 The rain that falls into the Pantheon through the opening in the dome, flows into the drainage openings in the marble floor.

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Fig. 2.29 Pantheon [1]: a interior; b outside pressure; c ventilation system

Fig. 2.30 a Trulli on Alberobello (Puglia); b Dammusi on Pantelleria

scale and at times that are difficult to pinpoint. The trulli (Fig. 2.30a) are buildings that originated in proto-historical times, which are built of unmortared limestone. They are usually circular in plan, but sometimes square (the more ancient), with a conical domed roof. The dammusi (Fig. 2.30b) date back to the Phoenician period and keep a clear Arab influence; they are built of unmortared local lava stone, had a square plan, and are small; with the coming of the Romans the roof, which was formerly flat, took the shape of a dome. In both the trulli and dammusi, the thick walls and the roofs, along with the few, small openings in the façade, ensure thermal inertia: this creates an interior microclimate that preserve heat in winter and cool in summer. With the passing of time, both these structures indicated a need for forming openings in the vaults and perforated chimneys, which facilitated natural ventilation and made the spaces more comfortable.

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Fig. 2.31 a Mesa Verde, Colorado; b Ghardaia, Algeria [45]

The relationship the Island of Pantelleria (from “Bent-el-Riah”, daughter of the wind) has with the wind and deserves some further comments. During the Arab domination, around the eighth century, a very particular custom arose that still applies. In order to protect the vines and olive trees from the wind, the former are kept dwarfed, while the latter are grown, covered in stone, so that the trunk runs along the ground. Lava stone walls were also built, as low as the cultivated crops, used for terracing and especially as windbreaks. This is one of the most ancient uses of a protection technique that was to play an essential role in the agriculture, transport and urban planning sectors (Sects. 8.3–8.6). Despite their use in ancient times, bioclimatic criteria and methods to provide natural ventilation for homes are systematically and frequently referred to from the end of the first millennium, especially in arid regions. The settlement of the Anasazi Indians in Mesa Verde, Colorado (Fig. 2.31a), dates back to about the thirteenth century and is a perfect example of this concept [45]. Built into the rock and facing South, it uses a very efficient natural ventilation system. The air enters via the apertures, circulates on the “kiva” (circular covered space) and flows out via a chimney formed in the ceiling. When there is no wind, circulation is assisted by the central fireplace: the heated air, being lighter, rises through the chimney, drawing in cool area from the outside via the apertures. Ghardaia is a “pentapolis”, that is, a group of five settlements, founded by the Ibadi community in the eleventh century in the M’zab Valley, at 500 m height, in the Algerian part of the Sahara desert (Fig. 2.31b). The stone houses, wedged together or on top of one another, use a “chebeq”, a roughly square hole formed in the ceiling and covered with an iron grating. Windows in the façade are often replaced by slits, through which the air, sucked up by the opening at the top, enters. The “mozabites” regulate the internal ventilation, by adjusting obstruction of the chebeq [45].

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Similar devices are common in Islamic architecture [46]. The most interesting is the “moucharabieh”, an opening made up of a system of finely interwoven wooden slats, which forms a grid with orifices. It shields the sun’s rays, allows a view to the outside, acts as a filter for insects and, above all and facilitates natural ventilation. The air enters the home via the moucharabieh, circulates inside and exits via openings formed in the roof. Natural ventilation by means of openings in the facades and in roofs is improved by the inclusion of devices that protrude from the roof to capture cooler air that is moving faster and is less dusty and humid; they are especially useful in densely built cities that screen one another at street level, preventing enough air from entering through the windows. Known as “wind catchers” [41, 45, 46], these devices spread in Iran, Iraq, Pakistan, Egypt and Arabia from the tenth century. They have single or multiple openings, depending on whether the wind direction is uniform or variable. They work due to the difference in pressure between the catcher’s openings and the other doors and windows on the windward or leeward side. They have a natural selection function: if the inside air is cooler than the outside air, a pressure occurs that prevents the catcher from introducing new air; on the other hand, if the outside air is cooler than that inside, it is expelled by the wind that enters via the catcher and radiates the home. The ambient conditions created by these ventilation systems can be further improved, using methods to humidify the spaces by the evaporation of water. Ancient people who lived in the more arid regions, used this principle by creating routes along which the air passed over the surface of water at a regulated temperature [45, 46]. The water, used frugally, is located on the patio in tanks, fountains, or streams, used to wet the ground or kept in jars at the bottom of the wind catchers or in front of the moucharabieh [46]. The most common use of this humidifying system made use of a “salsabil”, a sloping decorated floor over which water flowed, to increase evaporation [41]. The wind towers that appeared in Iran (Fig. 2.32a) and Arabia from the tenth century are often finely decorated and of significant architectural value. Called “badgir” [41] or “baud geers” [45], they have openings on all four sides (sometimes only on two), so that at least one opening is pressured and one is suctioning [1]. For their entire height, they are fitted with partitions arranged diagonally (Fig. 2.32b). This means that, irrespective of the wind direction, air is conveyed into the home via the pressurised opening, flows through it and, having ventilated the space, flows out via the suctioning opening. The inhabitants regulate this ventilation by opening and closing the links between the various parts of the tower and the building. In place of towers, the Persians sometimes use perforated domes, partly screened by gratings [41]; these suck the hot air from inside, using a mechanism similar to that of the Pantheon. The use of stone chimneys protruding from the roofs spread in Pakistan, especially in Sind and Hyderabad (Fig. 2.33a), between the tenth and the fourteenth century. Similar to periscopes, these had a side opening that faced the prevailing wind. When the wind blows towards the opening, the air enters the house and flows out through the

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Fig. 2.32 a Wind towers, Iran [45]; b indoor ventilation [41]

Fig. 2.33 a Wind catchers in Hyderabad [12]; b indoor ventilation in a building in Cairo [41]

doors and windows. When the wind changes direction, the opening in the chimney creates suction, and the air circulates in the opposite direction. Following the example given by the ancient mulguf (Fig. 2.25b), Egypt made use of large openings emerging from the roofs and facing the prevailing wind; they came in multiple shapes, to the extent of constituting a peculiar element of vernacular architecture [41, 45]. Figure 2.33b shows a famous “qã’a” (an upper floor for guests in the centre of the house) built in Cairo around 1350. It was part of a complex indoor circulation system, partly forced and partly due to convection and played the same role as wind towers.

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Fig. 2.34 a Royal palace of Amber Fort; b Wind palace, Jaipur

In India, there was an ancient practice of studying wind in homes. They were often characterised by three main elements: the courtyard (“tschok”), entrance (“tibari”) and a closed room (“kothri”). The courtyard was surrounded by open rooms, with closed rooms at the corners. The house was built to provide the inhabitants with continuous air circulation [38]. On the roof, there were ventilators that were connected to ducts that went into the house, linking to cool underground rooms. The most important buildings were often the result of precise studies of air circulation. Amber Fort, the capital of the state of Rajasthan, built on high ground overlooking the valley, was home to all the Rajput dynasties that governed the area from the twelfth century until 1728. The current version of the fort, begun in 1591 by the Maharajah Man Singh I, is characterised by four splendid royal palaces (Fig. 2.34a)—Divan-iKhas, Shish Mahal, Jas Mandir and Sukh Mahal—whose walls were endowed with perforated gratings to guarantee the Maharajah a pleasant flow of cool air during the torrid summers and shelter from the cold winter winds. It is by no mere chance that the undisputed symbol of Jaipur, capital of Rajasthan since 1728, is the Hawa Mahal or Wind palace (Fig. 2.34b), built by the Maharajah Pratap Singh in 1799. With the onset of the Renaissance, the Western world was pervaded by fervid activity and innovations, including studies of the wind. As with all sectors of knowledge, diffusion of the new culture drew enormous advantages from the invention of the printing press, in Mainz around 1450, mainly due to the German Johann Gutenberg (1397–1468). Leon Battista Alberti (1404–1472), a Genoa-born architect, was fascinated by the finding of Vitruvius’ books in 1415. Inspired by them, between 1440 and 1452, he

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wrote De re aedificatoria in Florence, a 10-volume work that earned him the name of “Florentine Vitruvius”. Thanks to this work, Alberti promoted an extraordinary growth in interest in architecture and urban planning, in relation to climatic conditions [12]. He suggested careful selection of the site for buildings and settlements, along with a detailed study of the microclimate and materials to preserve the hot or cold, and to protect the space from the sun and the wind. He noted that a city at the foot of a hill and facing the sunset was not healthy, because it would be exposed to the cold night-time breezes. He warned builders about vortexes and currents formed in valleys [43]. To support these concepts, at least two centuries ahead of the extraordinary advance in knowledge about atmosphere of the first half of the seventeenth century (Sect. 3.2), Alberti invented two instruments that are part of the history of meteorology: the hygroscope and the anemometer. In relation to the former, he wrote in De re aedificatoria19 : “I found that a sponge gets impregnated by the humidity in the air, and I then formulated a measurement for weighing the heaviness of the winds, the air, and dryness”. The second was described in Ludis rerum mathematicarum, a work put together shortly before 1450. The instrument comprised a small metal plate, suspended from a bar by means of a hinge, and a weathervane that aligned the plate with the direction of the wind. Due to the pressure of the air on its surface, the plate rotates around a horizontal axis. The speed of the wind is estimated using an arched graduated scale. In the wake of the teachings of Vitruvius and Alberti, Andrea Palladio20 (1508–1580) was also a profound supporter of bioclimatic principles. In his Four books of architecture, he stated that “for each building three things must be considered, without which no building deserves to be praised: these are, its utility or comfort, perpetuity, and beauty. And so one could not call perfect any work that is useful, but for a short period of time, or lasts for a long time, but is not comfortable, or that, having both of these, has no grace about it”. The concept of comfort is inseparable from the effects of climate and nature [43]. The wind, humidity and the sun’s rays are therefore essential parts of an architectural design for buildings, and for urban planning of cities. Among other quotes, in the Third Book, Palladio harked back the importance of a teaching by Vitruvius, in terms of which straight roads parallel to the direction of the strongest winds must be avoided in cities, in order to block channelling of air. In the Second Book, he suggested locating Villas in raised places, “where the air is continuously moved by winds”; he also advised against “building in closed valleys 19 The

description of the hygroscope in De re aedificatoria casts serious doubt on the attribution of this discovery to the German Cardinal Nikolaus Krebs von Cues (1401–1464). In book IV De staticis experimentis of his work Idiota, he describes a device, the weight of which is sensitive to the change in humidity of air. 20 Palladius Rutilius Taurus Aemilianus (fourth century AD), wrote De re rustica, in which he expressed architectural opinions on the villa, showing an in-depth knowledge of Greek architecture. He was inspired mainly by Marcus Cetius Faventinus (third century AD), author of De diversis fabricis architectonicae. Andrea di Pietro della Gondola (Palladio), fascinated by Palladius’s work, brought his name out of oblivion, to the point of obscuring his image.

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Fig. 2.35 Villas of Costozza, Berici Hills, Vicenza [45]

in the mountains”, because “once again, if the winds enter those valleys like narrow channels, they cause too much noise and, if they do not blow there, the air that builds up there will become dense and unhealthy”. Finally, in the First Book, there is a description of the six Villas of Costozza, built by Trenti in the second half of the sixteenth century, on the slopes of the Berici Hills south of Vicenza, in which Palladio’s admiration of the ventilation systems used for them, comes through. These Villas made use of “covoli”, large underground cavities, part natural and part artificial, inside the hill on which the Villas stood. They were linked to the outside via apertures located at various heights on the slopes. The air entered the covoli via the aperture highest up; it passed through them and was cooled21 ; it then reached the basements of the Villas via wind ducts, long underground trenches dug for the purpose22 ; from the basements, the air entered the rooms in the villas via perforated stone or marble roses set into the floor; finally, it flowed out via doors and windows (Fig. 2.35). In the same period, Villa Madama in Rome designed by Raffaello Sanzio (1483–1520), embodied the by then established bioclimatic principles. In the Letter 21 Air circulation through the caves and trenches gives rise to exciting phenomena. The “Wind cave”,

in the Apuan Alps, is made up of a close-knit network of wells and tunnels formed by rain water that penetrates the mountain via cracks. Over millions of years these first became brooks, then streams, and finally underground rivers. The cave has two openings at 627 and 1400 m height. Due to their temperature and pressure differences, in summer the cave has descending currents passing through it, which ascend in winter. These currents are so strong that, during visits, they are blocked by means of a security door. 22 Palladio refers to the “prison of the winds, which is an underground room, formed by the outstanding Mr Francesco Trento, and called Eolia by him, into which many wind ducts opened” (First book, De’ camini).

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by Raffaello to Pope Alexander VII, the artist explained that the location of the rooms and distribution of the spaces were a result of the direction and properties of the local winds: “The Villa is situated half way up Monte Mario that faces straight into the Grecale. And, since on the side that faces Rome, the mountain faces the Scirocco, and the Maestrale in the opposite direction, while the Libeccio and Ponente, and the Grecale, Tramontana and Maestrale (…) to face the Villa into the more healthy winds, I aligned its length with the Scirocco and Meastrale. I took the precaution of not having any windows or any living areas facing the Scirocco, other than those that need the heat.” On the basis of these principles, rational concepts for the urban fabric and builtup territory were formulated, which spread first in Europe and then worldwide, especially in countries of Latin origin [39]. Puebla shows the great care taken in Mexico for orienting the urban fabric; since 1534 the streets are oriented to avoid prevailing winds being channelled through the city. In 1535, Lima, founded in Peru by Francisco Pizarro (about 1475–1541), conformed to a 1523 regulation, in terms of which the direction of the streets must take the sun and wind into account; they are therefore built to be shaded and to have the cool sea breezes passing through them. From 1573, Spanish cities in South and Central America were subject to urban planning laws, based on wind actions: inland cities are built on slopes that ensure their protection; coastal cities are located in such a way that wind does not impede seafarers returning to them from the sea. In the city of Buenos Aires (Fig. 2.36), whose town plan dates back to 1745, the road network was oriented to avoid the prevailing winds being channelled along the main arterial routes [12, 38].

Fig. 2.36 Buenos Aires in colonial times [12]

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Although they do not conform fully to the contents of this paragraph, the great development in the procedures adopted by the mining industry and related metallurgical processes, using principles based on the concept of ventilation, deserves to be highlighted. The first two texts on this topic, Ein Nützlich Bergbüchlein and Probierbüchlein, are anonymous works that date back to the start of the sixteenth century. Vannuccio Biringuccio (1480–1537) wrote De la pirotechnia (1540), the first treatise on this topic. The basic text, De re metallica (1556), is by the German physician Georgius Agricola (1494–1555). In this volume, Agricola illustrated the techniques used to ensure ventilation of underground tunnels [47]. He specifically described three devices: air intakes, fans and bellows. The air intakes were fixed or adjustable. The fixed intakes formed shields that divided the mouth of the ventilation stacks into four parts. Whatever the wind direction, the air entered at least one stack and was conveyed underground. The adjustable intakes used rotating barrels placed on top of stacks: one side of the barrel had a hole in it, and the other side is fitted with a weathervane, which kept the opening facing the wind direction (Fig. 2.37a). The fans took the air underground, by means of cylindrical or rectangular box-shaped drums; in some cases, these were developed to become little windmills (Fig. 2.37b). The bellows were a gigantic version of those commonly used to start a fire. They were used to pump air into the mines. Finally, I wish to talk about an archaeological find made at the end of the twentieth century [29]. Back in 700 AD, the inhabitants of Sri Lanka used wind furnaces to separate metal from rock. Traditionally, furnaces were tall and slender, ventilated using bellows, to raise the fire temperature. In Sri Lanka, the wind did the same job, as furnaces were built on the top of slopes, exposed to the monsoon. According to Gill Juleff, the British archaeologist responsible for the digs, they were used to produce iron and perhaps steel.

Fig. 2.37 a Adjustable air intakes on top of stacks; b fans driven by windmills [47]

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2.9 Structural Damage and Collapse The mechanical actions and effects of wind on structures come in two relatively distinct forms. One relates to destruction caused to settlements, infrastructures and the territory as a whole by storms. The other relates to damage caused to individual structures and especially to the most daring works. In ancient times, destruction in a territory caused by storms was seen as dark signs, divine prewarnings and real punishment dealt out by the heavens. As the centuries passed, man gradually managed to overcome these ancient prejudices and deep-rooted convictions. However, for a long time, the fury of nature was seen as being invincible, and man drew consolation from the illusion that the most damaging phenomena were rare and sporadic. Only in more recent times has the human race begun to gather estimates and information on natural disasters and has come to understand that they are precise realities that follow time intervals and spatial targets, and are governed by specific physical and probabilistic laws. Man has to live with this reality and learn to protect himself against it (Chap. 10). Unfortunately, a lack of data on calamitous events in ancient times prevents accounts being drawn up for that period and delays the formulation of defence strategies against an extraordinarily powerful and aggressive enemy. The situation is different when it comes to damage suffered by individual structures, especially the most daring like bridges and towers. These have always been a symbol of man’s desire to achieve their aspirations and overcome their limits. From the most ancient times, history is full of accounts and information on great successes and calamitous disappointments, in the form of collapses or often ruinous damage. At first, men observed these and recorded them as facts and unavoidable steps in their progress. Subsequently, they strived to understand the causes and correct their errors and came to see damage and collapses [48] as an essential part of the progress of knowledge and pursuit of safety.23 By using this information and revisiting the history of great failures in the past, irrespective of the cause, it is possible to interpret the knowledge of the effects of the wind and its role on the safety of structures, identifying the types of structures, locations and periods in which this phenomenon plays an important role. Ahead in this paragraph, the question of bridges and tall structures is dealt with. The first bridges worthy of note were built by the Greeks, using boats, so that large military contingents could cross even extensive rivers and inlets of the sea. Having been adopted later by the Romans and other ancient peoples as well, these boat bridges are clearly very vulnerable in relation to storms and especially the forces of 23 The concept of structural safety first manifested itself in the Code of Hammurabi (1780 BC). It deals with damage to people, providing for sanctions for damage due to negligence. It particularly states that: “If a building collapses and causes the death of the owner, the builder must be killed. If the collapse of a building causes the death of the owner’s child, the builder’s child must also be killed. If the collapse of a building causes the death of one of the owner’s slaves, the builder is required to provide him with another. If the building suffers damage, this must be repaired at the builder’s expense”.

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Fig. 2.38 a Sixteenth-century depiction of Pons Sublicius [50]; b Ponte Rotto [51]

water and wind. There are many accounts of disasters caused by them coming apart [49]. With a view to creating an efficient, permanent road system, from the seventh century BC, the Romans left an indelible mark on the history of bridges, building them in wood, in a lattice or beam form, or using stone arches. Later, from the first century AD, conglomerate was also used. Their longevity often depended on the laws imposed on the peoples served by bridges, forcing them to see to maintaining them. In addition, most of the bridges still to be seen today have a long history of collapses and complete rebuilds behind them [49]. The first Roman bridge, Pons Sublicius (Fig. 2.38a), was built in timber by Anco Marzio (640–616 BC) across the Tiber; in the sixth century BC, it was chopped down to stop the advance of the Etruscan King Porsenna; having been rebuilt a number of times in wood, in 60 BC the piles were rebuilt in stone [49, 50]. The Bridge of Augustus in Narni, built in 220 BC and reinstated by Agrippa (63–12 BC) in 27 BC, is on the main access road to Rome from the North; for this reason, it has often been destroyed by the Romans themselves, to barricade the city against invaders, or it has crumbled during battles in the area; each time, it has been rebuilt similar to what it was like before. Pons Emilius dates back to 174 BC and was built by Marcus Aemilius Lepido (187–153 BC) with stone pillars and timber decks; it crumbled in 156 BC and was rebuilt with stone arches in 142 BC; it was rebuilt again in 12 BC and crumbled in 1598 when the Tiber flooded; what remains of it (Fig. 2.38b) is called

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Ponte Rotto [49, 50]. Pons Fabricius, built in 62 BC, suffered serious damage during two floods in 23 and 22 BC; it was restored in 21 BC and was once again damaged and extensively restored some centuries later [49, 50]. Trajans Bridge (53–117) on the Danube in Hungary, built by Apollodorus of Damascus (50/60–130) in 104 AD, is made up of a timber lattice structure, supported by 20 stone pillars; according to the account by Cassius Dio (150–230), it was destroyed at the time of Trajan’s death, for fear of enemy invasions; however, the pillars were preserved “to show that nothing is impossible for human ingenuity” [49]. The decline of the Roman Empire also gave rise to the decline in bridges [51]. The Germanic peoples, mainly migratory, abandoned the practice of maintenance, and many Roman bridges fell into ruin. The last important Roman bridge in the west, Ponte Salario over the Aniene, was destroyed by the Ostrogothic King Totila (sixth century) and rebuilt by the Byzantine General Narses (about 478–569) in 565. All the bridges over the Rhine, with the exception of the Trier Bridge, were left to collapse. The bridges that escaped this fate, often owe this privilege to the dedication of individual local noblemen. Bridges came to the fore again in Carolingian times, from the seventh century, when they were once again restored and preserved as a source of wealth, in the form of toll fees. Charlemagne (742–814) relaunched this type of construction by building the Bridge over the Elbe and the timber bridge over the Rhine in Mainz; having been completed in 10 years and deemed indestructible, it was destroyed by fire the year after it was completed. The push to upgrade the road system began again with Louis the Pious (778–840); he built a huge number of bridges and, most of all, reinstated the laws that imposed that they be maintained. Under King Charles the Bald (823–877), son and successor of Louis the Pious, the bridge was once again seen as a tool for blocking the way to invaders; on the one hand, the building of fortified bridges flourished, often reinstating ancient Roman bridges; on the other hand, new bridges were built that could be destroyed quickly and easily. Thanks to the Church as well, which began to grant indulgences for the souls of whoever built bridges, construction of timber and masonry bridges flourished once again in many parts of Europe from the eleventh century. This showed slow but constant progress up to 1500, when a far-reaching evolution occurred, especially in the foundations of masonry bridges. However, the ways in which bridges came apart did not change [49]. London Bridge, built in timber in 963, was destroyed to stop William the Conqueror (1027–1087); rebuilt in 1091, it was destroyed by flooding of the Thames; rebuilt again by William Rufus (about 1056–1100) in 1097, in 1136, it was seriously damaged by fire; it was repaired and it crumbled again and was then rebuilt in Elm wood in 1163, before stone arches were used by Peter Colechurch (?–1205) in 1176. Ponte Vecchio was built in Florence in 972, with a timber structure on stone foundations; in 1177, the arches were rebuilt in stone; it was destroyed by flooding of the Arno in 1333 and rebuilt by Neri di Fioravante in 1345 with strengthened foundations. Avignon Bridge, built at the behest of Benezet of Hermillon (1105–1184) between 1177 and 1185, comprised 21 elliptical arches; it was rebuilt in the fourteenth century and then destroyed by flooding of the Rhine; currently only four arches remain

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Fig. 2.39 a Avignon Bridge; b Rialto Bridge in Venice [51]

(Fig. 2.39a). The timber version of the Rialto Bridge in Venice dates from 1264; due to its degradation caused by weather, it was demolished and rebuilt in 1432 and 1458; it collapsed in 1524 and was rebuilt in wood; it suffered further collapses and consequent repairs in 1528, 1531, 1532, 1533, 1587 and 1588; in 1592 Antonio da Ponte (about 1512–1597) built it again in masonry (Fig. 2.39b). The Holy Trinity Bridge in Florence was destroyed by flooding of the Arno on 1333; it was rebuilt in 1346, collapsed during the flood of 1557 and was rebuilt by Bartolomeo Ammanato (1511–1592), between 1567 and 1569, with strengthened foundations. Pont Neuf, begun in 1378 and completed in 1388, was demolished by ice and rebuilt in 1476; it collapsed during the flood of 1547, was rebuilt in stone between 1575 and 1606, and collapsed again in 1616. The situation differed partly for bridges supported by cables. This type of construction began and developed mainly in Asia, South America and Africa [49, 52]. Bridges with hemp ropes and bamboo, which supported walkways and baskets, appeared in Yunnan, in the Sichuan province of Tibet and reached spans of more than 200 m. The Zha Bridge, which is the first for which there is definite information, dates back to 285 BC. Li Beng, Governor of Sichuan during the Qin Dynasty, built seven bridges around the City of Chengdu in the first century BC. The Quan-Xian Bridge, the first to include multiple spans, dates from the third century BC; it was refurbished a number of times due to wear or degradation of the materials, but is still in existence [52, 53]. The building of bridges supported by iron chains probably dates back to the period between the eighth and fifth centuries BC. Pliny the Elder (23–79) talked about iron chains used to support a bridge over the Euphrates at Zengusa, in the fourth century BC, at the orders of Alexander the Great (356–323 BC). A tablet found in Liuba, in the Shanxi Province, describes the Fanhe Bridge built by General Fangui in 206 BC. Before this discovery, the oldest iron chain bridge for which information is available was built by Jing Dong on the Yunnan in 65 AD. None of this should surprise us: especially in the Mountain regions of the Jichuan and the Yunnan metallurgy reached great quality levels from ancient times. Accounts from the sixth and the seventh centuries AD talk about many bridges supported by iron chains along the pilgrim trail between India and China. Prince Weng-Cheng of the Tang Dynasty introduced the use of this type of bridge in Tibet from the seventh century AD [52, 53].

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Fig. 2.40 a Thang-stong rGyafpo bridge in Bhutan; b San Luis Rey Bridge [54]

Bridges supported by iron chains reached their peak in the fifteenth century, thanks to the Tibetan Monk Thang-stong rGyafpo (1385–1464). Known for his liturgical reforms in Lamaism, even the theological texts talk about his extraordinary skill as a builder (Fig. 2.40a). The Chuka and Docsum Sempa bridges still survive. The Tamchugang Bridge over the Paro River, discovered in 1967, collapsed the next year, after a storm. The Wangdiphodrang Bridge in Bhutan, the most daring and famous, is included in centuries old legends; it is said that it was built many times and was broken down by an evil spirit, blinded by jealousy, as many times. The Monk finally gave up, leaving the chains where they were found more than 500 years later, perfectly preserved due to the lack of rain [52]. At very much the same time as when Thang-stong rGyafpo built fantastic bridges in Tibet, on the other side of the world, the Incas developed similar equally admirable skills. They are documented in Apolgetica historia, written by Friar Bartolomè de Las Casas (1474–1566) between 1527 and 1560 [51]. This period saw the building of the famous road network at the behest of Pachacutec. “An amazing, divine thing, far superior to the Roman work”, it includes two main routes. One is near the coast, the other along the ridge of the Andes, and includes incredible bridges. The most daring of these, the San Luis Rey Bridge at the Apurimac River Gorge (Fig. 2.40b), is the finest example of indigenous engineering in the two Americas. Built around 1350 and 45 m long, it used cables suspended between stone pillars, that supported wooden beams. The inhabitants of the village of Curahuasi took on replacing the

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cables every year, up to 1879 [54]. Accounts indicate as a simple matter of fact that “the strong winds made it oscillate dangerously”. It is therefore evident that in ancient times, bridges made of wood or stone, or supported by iron chains, hemp, or bamboo, suffered damage or collapses of all kinds, due to natural or artificial causes. Besides, there do not seem to be evident traces, excepting for sporadic cases, of serious damage caused by wind. In the same way, it is not easy to find writings in which wind is seen as a critical phenomenon, or even one that caused concern, in terms of the safety of bridges. The situation changed at the end of the eighteenth century, with the appearance of suspension and cable-stayed bridges (Sect. 4.8). Tall structures originated in Egyptian times [55], to glorify dead and deified kings. The first noble tombs, the “mastaba”, date back to 3400 BC; they were parallelepipeds made of crude bricks, with sloping walls, that contained the funeral chapel, statue chamber and burial chamber. The mastaba gave rise to the stepped pyramids, conceived as a hyperbole for stacked mastaba; the Pyramid of Zoser (2737–2717 BC), built in Saqqara under the 3rd dynasty, reached a height of 60 m and was the tallest structure in the world at the time. The stepped pyramids of the 3rd Dynasty, gradually gave way to pyramids with an even surface, under the 4th Dynasty. They were built in stone and bricks, clad in pink granite or limestone; they contained the burial chambers of the King and Queen, and the funeral temple. Access to these was via sloping corridors; some of these acted as air intakes (Sect. 2.8). In El Giza, the greatest Egyptian monumental complex, built close to Memphis, between 2700 and 2500 BC, the Great Sphinx dominates. This 20 m high statue, with the head of a lady, body of a bull, and paws of a lion, gives concrete form to the oriental concept of the guard animal. Adjacent to this, there are the Pyramid of Mycerin (about 2578–2553 BC) 63 m high, the Pyramid of Chefren (about 2603–2578 BC), which stands 143 m high and the Pyramid of Cheops (about 2550–2530 BC), an impressive 230 m sided structure, 146 m high (Fig. 2.23). Apart from sporadic interludes, for about four millennia, it was the tallest structure in the world [56]. The Sumerians attained an evolved urban culture as far back as about 4000 BC [55]. From 2600 BC, they built their cities around a sacred tower known as ziggurat (from the verb “zagaru”, to stand tall). The tower was made up of smaller floors, with a temple at the top, which was the point at which the deities arrived on earth from heaven—the point at which the divine and the earth were joined. Similar construction principles were used later on in Central America [57], at Teotihuacan (second to first century BC) dominated by the Pyramid of the Sun, and especially in the Maya Era (from the second century AD), at the border between Mexico and Guatemala, where there were innumerable temple pyramids. All of these were rigid, heavy structures, with a support base that was so large that it rendered the action of the wind almost irrelevant. It is by no mere chance that these works are still to be seen today, unharmed. The situation changed when several past civilisations decided to go for more slender structures, namely towers [56], one of man’s most ancient and deep-rooted desires: to push upwards, challenging the mysteries of the sky. Lighthouses in the Mediterranean area [56], the stupas in India [58], Chinese and Japanese pagodas [58] and the Islamic minarets [59] are all examples of a new generation of timber and

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masonry buildings that, just like bridges, have a wealth of history of successes and failures, collapses and restorations, and even complete or partial rebuilding. Some of them represent milestones and eternal symbols of man’s constructive skill. They are often made more fascinating by stories of disastrous collapses, which are poorly documented and often shrouded in mystery. The Lighthouse, built on the island of Pharos, near Alexandria in Egypt in 280 BC, was the result of the bringing together of three distinct units stacked on one another, the first with a square plan, the second circular, and the third octagonal. At the top there was the light that could be seen from the sea up to a distance of 50 km. This structure, which was hollow inside, housed the stair and the first rudimentary lift. It fell into ruin in 1303, leaving a lot of uncertainty as to its height to posterity, but was probably between 120 and 140 m. Stupas followed the evolution of Buddhism, going from a modestly sized semispherical mound, to ever higher temple structures. From having been circular, the plan became square, rectangular or cruciform. The basement, characterised by steep steps, added to the creation of vertical slenderness. It reached its apex with the most atypical and amazing Indian building: the Stupa of King Kanishka (2–23) at ShaljiKi-Dheri. Begun in 144 AD and completed in 168, it comprised a stone basement with 90 m long sides and 5 floors, from which a 13 floor wooden building rose, which reproduced the sunshades of the most ancient stupas, on a mega scale. It was 190 or 195 m high, collapsed almost immediately, and now only the foundations remain. For the short time it survived, it was the highest building in the world. The greatest development of the Chinese pagodas occurred from the fifth century AD. The basic concept was similar to the Stupa of Kanishka, with the lower part in stone with a polygonal base, from which a slender timber structure rose, which was decorated and colourful. At most, only the bases of these structures have remained, and current knowledge is based solely on writing and remnants from the time. There is more information on masonry pagodas, which were rarer, but of which some examples have remained. The most famous is the Lin-He Pagoda, in the city of Hang-Zhou, on Mount Yue Lun, near the China Sea coast. Built in 970, it replaced the Pyramid of Cheops as the highest building, taking this limit from 146 to 150 m. It collapsed a few years later and between 1153 and 1163 it was rebuilt up to a height of 60 m, maintaining the configuration of the original base (Fig. 2.41a). There is a curious fact: while information on the reasons for collapses is scanty or missing, there are sporadic texts that praise the capacity of some structures to withstand the forces of nature. The Kaifung Pagoda, built in 1044 on the banks of the Yangtze River, was 54.7 m high, with 12 floors with an octagonal plan shape. The masonry structure, clad in iron coloured majolica tiles, survives today (Fig. 2.41b), having withstood 37 earthquakes, 18 typhoons, and 15 flooding. The situation differs partly for Japanese pagodas, for which there is more documentation. These used timber posts (“shinbashira”) arranged in relation to a central axis, but without any connections to the horizontal portions of the structure and the ground. Their function was to dissipate energy related to wind and seismic actions [60]. Thanks to the absence of connections, these structures are highly flexible with regard to earthquakes. The ample slopes on the roofs also prevent a regular vortex

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Fig. 2.41 a Lin-He Pagoda in Hang-Zhou; b Kaifung Pagoda on the Yangtze River [56]

shedding (Sect. 9.6). The Yakushii Pagoda, in Nara (Fig. 2.42), built in 680 AD, was 34 m high, survived 10 centuries of earthquakes and typhoons, thanks to these principles. Like most of these structures, it was destroyed by fire during the war of 1528. More extensive records are available for a third type of tall building—churches, basilicas, and cathedrals—which spread in the Christian age. Early Christian and Byzantine cultures flourished in the fourth and fifth centuries, resulting in these structures being found in almost all regions of the Roman Empire. Between the seventh and tenth centuries, with the end of Barbaric migrations, the arrival of Charlemagne and his successors on the throne of the Franks, brought with it artistic and cultural renewal—the Carolingian Renaissance—which affected Western Europe. A combination of the early Christian basilica with its long plan, and the Byzantine church with its central plan, gave rise to the cruciform Carolingian church; this also often featured a square tower, not very high, located where the nave crossed the transept. Romanesque architecture, of which Christianity was the essential element, flourished from the ninth to the start of the thirteenth century. Compared to previous periods, it gave rise to many linear and formally pure buildings, characterised by

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Fig. 2.42 Yakushii Pagoda in Nara [56]: a elevation; b section

a marked increase in size in terms of both plan and height. Being during a period in history in which there were still no robust structural concepts, these were often subject to collapse. Cluny Abbey, built in France between 910 and 1130, suffered serious damage immediately after one of its parts was altered. The Cathedral in Mainz (Fig. 2.43a), built between 975 and 1009, burnt before its inauguration; rebuilt in 1036, burnt again on 1081 and 1170, both times during construction. The Cathedral of Speyer, begun in 1030 and completed in 1063, was repaired in 1073 after damage caused by some land subsidence. The Tower of Pisa, begun in 1173 with the aim of reaching a height of 100 m, suffered land subsidence from the outset, causing numerous interruptions and changes to the design [61]; when it was finished in 1350, its height had been reduced to 56 m. Gothic architecture [62] flourished in Europe from the mid-twelfth century to the mid-sixteenth century. The monolithic roofs, typical of previous cathedrals, were replaced by arches and ribs, which supported lightweight panels. They no longer

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Fig. 2.43 a Mainz Cathedral [56]; b Lincoln Cathedral

required continuous support by the walls but were held up by columns and pillars. Many masonry masses were eliminated and, in their place, large windows appeared, which facilitated lighting and reduced loads. Due to the curvature of the arches and ribs, the roofs exerted oblique forces at the support points. These were counteracted by buttresses in the form of rampant arches, or by concentrating the forces on spires or pinnacles, suitably raised and therefore heavy. In this way, by applying the scientific interpretation of Viollet-le-Duc (1814–1879), all the elements that make up the cathedral have a precise structural function. In addition, being partially independent, they allow the building to adapt to any land subsidence. Due to these innovations, Gothic cathedrals took on grandiose size, accentuated by spectacular towers that were ever higher. The damage suffered by these structures has been proportional to their grandeur. The Cathedrals of Arras (1160–1200) and Cambrai (1148–1167) built to the north of Loire, between Burgundy and Normandy, had a short lifetime. The bell tower on the Romanesque Notre-Dame Cathedral in Chartres (eleventh century) was destroyed by fire in 1134; it was rebuilt in the Gothic style and was once again destroyed by fire in 1194. The Romanesque Notre-Dame Cathedral in Rheims suffered the same lot in 1210. This was a prelude to the destruction suffered by the Beauvais Cathedral, which builders intended to make grander than all previous works in terms of size and majesty. The choir section and western part of the transept were probably built between 1125 and 1272. In 1284, the works were interrupted by a series of collapses of the vault in the central nave. Once they began again, the works continued until 1290, when a 153 m tall spire was completed. Having overtaken the Pyramid of Cheops, this made the Beauvais Cathedral the tallest building in the world. However,

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this primacy was also short-lived. The tower collapsed in the same year as it was completed. British Gothic Cathedrals have a somewhat similar history. Canterbury Cathedral stands on the ruins of a previous building destroyed by fire in 1174. In 1323, Ely Cathedral suffered the collapse of the Romanesque cross tower. At the same time, the pillars of Wells Cathedral crumbled under the weight of a tower built on the cross. Lincoln Cathedral (Fig. 2.43b) stands on the remains of a Norman church built between 1075 and 1092. Having been seriously damaged by a fire in 1141 and an earthquake in 1185, it was rebuilt in the Gothic style from 1190. Due to a construction error, the main tower collapsed between 1237 and 1239. Building of a new tower began in 1255 and was completed in 1307, with the erection of a timber spire that replaced the Pyramid of Cheops as the tallest building in the world, standing at a height of 160 m. It held that primacy until 1549 when the spire collapsed during a violent storm. The above deals with collapses due mainly to building errors, the choice of static schemes, and the role of the structure’s own weight, fire, and the degradation of materials. It also highlights the turning point represented by the building of cathedrals fitted with ever more daring spires. By suffering damage and collapses during storms, for the first time, they showed the risks due to wind actions on tall structures. These are highlighted in a mixture of history and novel, by Ken Follet (1949–). In The pillars of the earth [63], Follet recounts the epic of the Knightsbridge Cathedral. This structure, begun in 1136, collapsed in 1142 due to the excessive weight of the vault. Work began again in 1145 but, in 1152, while completing the apse, large cracks appeared in the clerestory and the transepts. The builders understood the correlation between the appearance of cracks and wind storms and so put the damage suffered down to wind actions. During the inspections, as they went up to the highest point of the cathedral, they also understood that the wind speed increased with the height and imposed greater forces on the higher parts of the building. In looking for a way of absorbing these forces, the builders realised that stiffening the naves using buttresses would deprive the cathedral of its lightness and elegance. At the same time, they realised that building arches to resist the wind in the high parts of the side naves, would limit the light penetrating the clerestory. This gave rise to the idea of building large rib elements outside, making them clearly visible; they materialised in form of half arches perpendicular to the walls. These depicted the wings of a flock of birds in formation, about to take flight. Thanks to this intuition, the cathedral was successfully completed and consecrated in 1170 (Fig. 2.44a). Equally emblematic, was the evolution of the shape of cathedral spires. Originally, these were mostly pyramids with a square base; over the centuries the base first became polygonal, then circular; finally, the spire made ever more use of fissures and openings, which increased their transparency. This reduced the wind action and gradually reduced the collapses that characterised the early constructions [64]. One example is shown on Lichfield Cathedral in England (Fig. 2.44b). This Gothic structure stands on the remains of a Norman cathedral, which in turn, replaced an ancient Saxon church. The building, which was begun on 1195 and completed in 1249, has a porous, cone-shaped spire, 77 m high.

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Fig. 2.44 a Knightsbridge Cathedral [63]; b Lichfield Cathedral

2.10 Leonardo da Vinci In the Middle Ages, it was widely believed that some ancient philosophers and scientists, especially Aristotle, had unveiled all the mysteries and solved all the problems in life, and so there was very little left to discover. During the Renaissance, there was a perceivable gradual shift from speculation based on observation, to science based on experience. Leonardo da Vinci (1452–1519) went through this evolution, favouring a new experimental method later known as Galilean, based on direct studying of man, nature, and its phenomena, and on the principle of freedom of research [4, 11, 47]. In this regard, he stated that “real knowledge is the daughter of experience, and experience is the mother of all certainty”. He also maintained that, “many claim the right to criticise me, on the pretext that my claims go contrary to the thoughts of some ancient authors, to whom they give excessive consideration and respect. However, they do not realise that my research arises from pure, simple experience, the only real source of truth”. From the Vinci countryside, while he was still an adolescent, Leonardo arrived in Verrocchio’s workshop (1435–1488) in Florence. Here he underwent an apprenticeship based on daily practice, reading of books and manuscripts, the production of paintings and sculptures, the construction of complex machines, and devices used to give life to festive scenes and to profane and religious theatrical shows. This brought him into contact with various artistic and technical cultures, both past and present, drawing inspiration from them for his future activity [65, 66]. In 1482 he felt he had nothing more to learn from this Florentine setting, and moved to Milan, where he stayed in the Court of Ludovico Maria Sforza (1452–1508) for about twenty years. In the initial stages of this period, his codices filled up with extraordinary machines and contraptions. Subsequently, a Franciscan Monk and friend of Leonardo, Luca Pacioli (about 1445–1517) aroused his interest in mathematics and Euclidean geometry. This was the start of a second creative period, which lasted for about eight years, during which he added greatly to his geographical surveys, investigation of nature, and studies of hydraulics and aerology. The latter part of Leonardo’s life was more varied. In 1502, he was employed by Cesare Borgia (1475–1507), Duke

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of Romagna, as a military architect and engineer. In 1503 he returned to Florence, where he produced Mona Lisa. From 1506, he was once again in Milan called there by the French governor Charles d’Amboise. Between 1514 and 1516, he stayed in Rome, under the protection of Cardinal Giuliano de Medici (1453–1478), where he worked mainly on scientific experiments. In 1517 he moved to France, in the service of King Francis I of Valois-Angoulême (1494–1547). Most of Leonardo’s codices, found to date, deal with the art of mechanics. Starting from a study of “weight, force, percussion, and impetus (…), the offspring of movement”, Leonardo extended his knowledge of five simple machines—the winch, lever, pulley, wedge, and screw—to apply it to more complex mechanisms; using various drive transmission systems, they made it possible to carry out many functions automatically. As part of these studies, Leonardo accepted numerous concepts already known, developing them to the point of going beyond some of his successors like Stevin (1548–1620) and Gilles Personne de Roberval (1602–1675), and ahead of Galileo Galilei (1564–1642) and Isaac Newton (1642–1727) [13]. Within these studies, reference is made to the straight and angular lever theory, in which he anticipated the principle of virtual works, the concept of the moment of a force and the composition of concurrent actions, the equilibrium of bodies on inclined planes, the stability of scales, the polygon of sustentation, centres of gravity, pulleys and cuts, the problem of reaction forces, the theory of the arc and friction, the concepts of force,24 percussion, impetus and weight, the laws of motion, falling bodies, violent movement of projectiles and impact, the strength of materials. In relation to this latter matter, Leonardo understood that a pillar made up of a compact bundle of elements can support much higher loads that the sum of the loads that each can support separately; he also carried out a series of experiments, as a result of which he concluded that the loadbearing capacity of a pillar is proportional to the cube of the diameter and inversely proportional to its length. He also studied the problem of resistance and deflection of a beam made up of a combination of adherent fibres or those simply kept together, showing the difference; he concluded that the loadbearing capacity of a beam is inversely proportional to its length. Even though his results are often contrary to modern knowledge, many see Leonardo da Vinci as the founder of structural mechanics, a genius predecessor of Galileo Galilei [47]. In 1485, Leonardo made instruments that were forerunners of the hygrometer and anemometer. The hygrometer or hygroscope, perhaps based on ideas developed by Alberti (Sect. 2.8), consists of a scale at the ends of which hygroscopic substances (cotton wool, sponge or dried wool) and water repellent substances (wax) are placed. An increase in humidity is indicated by the dish supporting the hygroscopic material

24 Not

all of Leonardo’s definitions are scientifically unquestionable. For example, he wrote: “I say force is a spiritual virtue, an invisible power, that due to an outside accidental violence is caused by movement and located and infused into bodies, which are taken from their natural use and bent, giving them an active life of marvellous power”.

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Fig. 2.45 Anemometer [65]: plate or paint brush type

going down. Leonardo used this instrument to “determine the qualities and magnitudes of the air, and when it was going to rain”. The anemometer was introduced in two alternative forms. The first, very similar to that described by Alberti (Sect. 2.8), is a plate or paint brush type; it is made of a plate that, pushed by the wind, rotates about a pin, along a graduated scale (Fig. 2.45). The second, with conical tubes, is used to check that, for the same wind intensity, the pressure that causes the wheels to turn is proportional to the opening of the cones through which the wind passes. Leonardo spent time, especially from 1508 to 1513, observing flowing water and meditating on the shapes it formed. He studied this in depth by creating timber or glass models of channels, into which he put coloured water or water with little floating objects (Fig. 2.46a); by doing so he used techniques still used today to view the streamlines of flows. Based on these experiences, he wrote On the motion and measurement of water, in which he discussed waves, whirlpools, falling and the destructive force of water, floating bodies, flows in pipes and outflows, mills and other water-powered machines. In this context, Leonardo paid great attention to the distribution of speed in whirlpool structures and the formation of wakes (Fig. 2.46a) [14]. He noted that, when a plate is perpendicular to the flow direction, there is a separation and recirculation area behind it. When the plate is parallel to the flow, the whirlpools form at the leading edge (Fig. 2.46b). Some of Leonardo’s reflections also deal with the law of continuity [5] (Sect. 3.6): looking at the problem of the movement of water in pipes, he maintained that the product of the cross-section of the pipe and the local flow speed remained constant. He also developed new knowledge about for power

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Fig. 2.46 Eddy formation: a separation zones [12]; b behind a plate (Codex Atlanticus) [14]

of steam (Sect. 3.7) making use of an “architonnerre”, or steam cannon, a pot full of water that explodes after a few hours on the fire. Leonardo was the first to study the resistance of bodies in fluids. In Codex Leicester, he introduced the starting points of the future law of the three proportions (Sect. 4.2), maintaining that the resistance is proportional to the speed (a concept that is incorrect) and to the area of the immersed body (a concept that is correct). His writings also showed the first glimpses of the principle of reciprocity, later introduced by Newton [14] (Sect. 4.2): the behaviour of a body immersed in a fluid does not change if the body moves in the still fluid, or if the fluid moves at the same speed as the still body. He also proposed to limit the resistance of bodies, giving them an aerodynamic shape; to do so he drew inspiration from the shape of fishes (Fig. 2.47a) and cannon projectiles (Fig. 2.47b). Finally, Leonardo put time and enthusiasm into studying human flight [66]. From 1485, he worked in a machine, the “ornithopter”, which driven purely by a man’s muscle power, allowed him to fly in the air, flapping the wings like birds (Fig. 2.48a). Perhaps drawing inspiration from the ideas of Roger Bacon (Sect. 2.3), he designed many versions, in which the man takes up various positions. In some he is horizontal, and uses his hands and feet to manoeuvre the mechanism connected to the wings. In others, he uses screens and pulleys. In yet others, the man is in a vertical position, inside a vessel, pushing the pedals with his arms and legs. In designing wings, Leonardo studied the anatomy and flight of birds, interpreting maintenance of flight, forward movement and landing [14]. He identified the bird as an instrument that flies according to mathematical laws that can be reproduced by humankind (Codex on the flight of birds). However, he came up with wings that were too big and articulated (Fig. 2.48b), to be powered by man’s muscular power alone. He therefore moved on to study the flight of birds in relation to whether or not there was wind, for weather conditions, and in terms of aerodynamic aspects. He then abandoned the idea of a device with flapping wings and replaced it with the principle of “flight without the flapping of wings”. He began by observing that large predator birds allow themselves to be carried by the currents and fitted the

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Fig. 2.47 Aerodynamic bodies [65]: a fishes (Codex G); b cannon projectiles (Codex Arundel)

Fig. 2.48 Codex Atlanticus [65]: a prone ornithopter; b articulated wing

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wings on his machines with elementary hinges and articulations that, by means of simple movements, made it possible to look for favourable currents and allow them to convey the person while gliding. He maintained that an area struck by wind is kept up by the compression of the fluid under its surface. Later on, especially from 1507, Leonardo became an ever more avid “aerologist, aerodynamics expert, aero-technician, and observer of the flight of birds”. He was particularly fascinated by the “science of winds” and the complexity of this physical phenomenon. He studied it using experiences carried out in water, laying the basis for subsequent concepts on similarity: “To arrive at the real science behind the flight of birds in the air, one first has to deal with the science of the winds, which we can prove using movement of water, which is the same, and this science will act as a stepping stone to an understanding of the flying bodies in the air and the wind”. In the wake of these concepts, between 1513 and 1518, Leonardo deepened his analysis of atmospheric phenomena, from both an artistic and a scientific point of view. In the artistic field, his descriptions and representations of natural calamities are famous. In the Codex of Windsor, there is a series of drawings depicting floods, whirlpools, and wind vortices that have catastrophic effects on environment and territory, terrifying people and animals and causing them to flee. They provide splendid graphic translations of the famous apocalyptic descriptions, in Leonardo’s style: “One sees dark, cloudy air being battered by the rushing of various winds. One sees ancient plants uprooted and dragged along by the fury of the winds. One sees ruins in the mountains, already stripped by the flowing of their rivers, falling into the same rivers, and filling their valleys”. Embellished by allegorical images, these descriptions provide vivid previews of the technical reports that were to become a practice (Chap. 10). In the field of science, Leonardo linked his study of the wind with the movement of water and the flight of birds. In Manuscript E, he studied the flows in the atmosphere at mountain peaks: “On passing over the clefts in mountains the wind becomes fast and dense, and when it descends on the other side, it becomes thin and slow, like water that comes out of a narrow channel into a wide pond”. He attributed the onset of wind to changes in temperature: “Some of the air condenses into water (or vice versa) and then, the surrounding air rushes into the space left empty”. He analysed rarefaction of the air with altitude: “Since small birds, without feathers, cannot withstand the intense cold of the air at high altitudes in which vultures and eagles and other large birds with lots of feathers, clad with very big plumes, fly; these small birds with weak, laughable wings, can stay up in this low air, which is dense, and would not be able to keep themselves up in the thin air that offers little resistance”. He also used birds, like the colours and floating items he put into water, to visualise the currents of air. He observed that some birds are able to stay in one place in the air, with the wings still and unfurled, near the cliffs at the sea’s edge. He deduced that, when the wind struck the cliffs, it was deflected upwards and gave rise to rising currents (Fig. 2.49). He therefore understood that, like currents in rivers, the winds gave rise to swirls, and that understanding these made it possible to dominate the air. The invention of parachutes, gliders, and the helicopter, based on the Archimedean screw principle [65], are the result of these reflections.

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Fig. 2.49 Ascending currents that keep birds up along cliffs [66]

All Leonardo’s studies had in common the concept that both the supporting of weight and propulsion for flight are due to the same mechanism [26]. Only in the latter stage of his life, ahead of Cayley’s ideas (Sect. 4.5), did Leonardo realise the need to use fixed wings for supporting the weight, and separate mechanisms for propulsion [14].

References 1. Melaragno MG (1982) Wind in architectural and environmental design. Van Nostrand Reinhold, New York 2. Watson L (1984) Heaven’s breath: a natural history of the wind. Hodder and Stoughton, London 3. Whipple ABC (1982) Storm. Time-Life Books, Amsterdam 4. Dampier WC (1929) A history of science and its relations with philosophy and religion. Cambridge University Press, Cambridge 5. Rouse H, Ince S (1954–1956). History of hydraulics. Series of Supplements to La Houille Blanche. Iowa Institute of Hydraulic Research, State University of Iowa 6. Brown S (1961) World of the wind. Bobbs-Merrill, Indianapolis, New York 7. Sorbjan Z (1996) Hands-on meteorology. American Meteorology Society 8. Palmieri S (2000) Il mistero del tempo e del clima: La storia, lo sviluppo, il futuro. CUEN, Naples 9. Hamblyn R (2001) The invention of clouds. Rizzoli, Milan 10. Shaw N (1926) Manual of meteorology. Volume I: meteorology in history. Cambridge University Press, Cambridge 11. Pitoni R (1913) Storia della fisica. Società Tipografia, Turin 12. Aynsley RM, Melbourne W, Vickery BJ (1977) Architectural aerodynamics. Applied Science Publishers, London 13. Benvenuto E (1981) La scienza delle costruzioni e il suo sviluppo storico. Sansoni, Florence 14. Anderson JD Jr (1998) A history of aerodynamics. Cambridge University Press, Cambridge 15. Miller DC (1935) Anedoctodal history of the science of sound. Macmillian, New York 16. Smith DE (1958) History of mathematics. Dover, New York 17. Rao SS (2005) Mechanical vibrations. Pearson, Prentice Hall, Singapore 18. Licheri S (1997) Storia del volo e delle operazioni aeree e spaziali da Icaro ai nostri giorni. Aeronautica Militare, Ufficio Storico, Rome 19. Hardy R, Wright P, Gribbin J, Kington J (1982). The weather book. Harrow House 20. Karapiperis PP (1986, June) The tower of the winds. Weatherwise, 152–154

References 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60.

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Jenks S (1983) Astrometeorology in the middle ages. ISIS 74:185–210 Phillips-Birt D (1971) A history of seamanship. George Allen & Unwin Giorgetti F (2007) History and evolution of sailing yachts. White Star, Vercelli Temple R (2007) The genius of China: 3000 years of science, discovery and invention. Carlton Publishing Group, London Niccoli R (2013) History of flight. White Star, Vercelli von Karman T (1954) Aerodynamics. Cornell University Press, Ithaca Lloyd A, Thomas N (1978) Kytes and kite flying. Hamly, London Cella P (1979) L’energia eolica. Longanesi, Milan Woelfle G (1997) The wind at work. An activity guide to windmills. Chicago Review Press, Chicago Brooks L (1999) Windmills. Metro Books, New York Singer C, Holmyard EJ, Hall AR, Williams TI (eds) (1956) A history of technology. Oxford University Press, Oxford Klemm F (1954) Technik, eine geschichte ihrer probleme. Karl Alber, Freiburg and Munchen Le Courieres D (1980) Energie eollien: Theorie, conception et calcul pratique des installations. Eyrolles, Paris Gipe P (1995) Wind energy comes of age. Wiley, New York Eldridge FR (1980) Wind machines. Van Nostrand Reinhold, New York Ackermann T, Soder L (2000) Wind energy technology and current status: a review. Renew Sust Energ Rev 4:315–374 Bennett R, Elton J (1898–1904) History of corn milling. Simpkin, Marshall and Company, London Egli E (1951) Die neue stadt in landschaft und klima. Verlag fur architektur, Erlenbach, Zurich Aronin JE (1953) Climate and architecture. Reinhold, New York Olgyay V (1963) Design with climate. Princeton University Press, Princeton Fathy H (1986) Natural energy and vernacular architecture. The University of Chicago Press, Chicago Skinner S (2004) Feng Shui style. Periplus, Singapore Markus TA, Morris EN (1980) Buildings, climate and energy. Pitman, London Landsberg HE (1981) The urban climate. Academic Press, New York Gallo C (1998) Architettura bioclimatica. ENEA, Rome Izard JL, Guyot A (1979) Archi Bio. Parentheses, Marseille Wolf A (1935) A history of science, technology and philosophy in the 16th & 17th centuries. George Allen & Unwin, London Levy M, Salvadori M (1994) Why buildings fall down—how structures fail. Norton, New York Hopkins HJ (1970) A span of bridges. David & Charles, Newton Abbot Delli S (1992) I ponti di Roma. Newton Compton, Rome Dani F (1988) Il libro dei ponti. Sarin, Pomezia Peters TF (1987) Transitions in engineering. Birkhauser Verlag, Basel Xiang H (ed) (1993) Bridges in China. Tongji University Press, Shanghai von Hagen VW (1976) Realm of the Incas. Newton Compton, Rome Lloyd S, Muller HW (1986) History of world architecture. Ancient architecture, Electa, Milan Heinle E, Leonhardt F (1988) Towers. Deutsche Verlags-Austalt GmbH, Stuttgart Heyden D, Gendrop P (1989) History of world architecture. Pre-Columbian architecture of Mesoamerica, Electa, Milan Bussagli M (1981) History of world architecture. Oriental architecture, Electa, Milan Hoag JD (1978) History of world architecture. Islamic architecture, Electa, Milan Tamura Y (2003) Design issues for tall buildings from accelerations to damping—Tribute to Hatsuo Ishizaki and Vinod Modi. In: Proceedings of the 11th international conference on wind engineering, Lubbock, pp 81–114 Di Stefano R, Viggiani C (1992) La Torre di Pisa ed i problemi della sua conservazione. Restauro 120:3–63 Grodecki L (1976) History of world architecture. Gothic architecture, Electa, Milan

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63. Follet K (1989) The pillars of the earth. Pan Books, London 64. Baker CJ (2007) Wind engineering—past, present and future. J Wind Eng Ind Aerod 95:843–870 65. Cianchi M (1984) Le macchine di Leonardo. Becocci, Florence 66. Laurenza D (2004) Leonardo: Il volo. Giunti, Florence

Part II

Developments: From the Renaissance to the End of the Nineteenth Century

Chapter 3

The Wind and the New Science

Abstract This chapter starts dealing with the transition from speculation to experience that took place in the two centuries going from the birth of Leonardo da Vinci to the death of Galileo Galilei, showing how the wind culture received stimuli from the evolution pervading the various knowledge sectors, starting with the ones connected to the appearance and diffusion of weather instruments and measurements. Similarly, the revitalised wind culture drew essential concepts and principles from the basic disciplines that arose and developed from the sixteenth century onward, first mathematics and the related tools capable of automatically performing complex and repetitive computations, probability theory, destined to become an essential tool for wind engineering, mechanics, in its broadest meaning, fluid dynamics, that mostly provided direct and innovative contributions to the wind culture, thermodynamics, essential to interpret the Earth atmosphere as a giant thermal machine and as a key issue for the development of the steam machine, which bounded its progress to the measure and knowledge of wind, the gas kinetic theory and an essential reference for the first theories about turbulence. The chapter ends with a synthesis of the main aspects characterising the origins and the first developments of structural mechanics and dynamics, two matters that became increasingly vital to protect human works from wind actions.

An essential part of the transition from speculation, ruled by pure reason, to experience, based on measurements, took place in the two centuries going from the birth of Leonardo da Vinci (1452) to the death of Galileo Galilei (1642) (Sect. 3.1). An in-depth illustration of this topic clearly exceeds the objectives of the book. It is, however, important to notice how the wind culture received significant stimuli, both direct and indirect, from the evolution pervading the various knowledge sectors, starting with the ones connected to the appearance and diffusion of weather instruments and measurements (Sect. 3.2). Fathoming the secrets of the atmosphere on experimental grounds, if anything, became a distinctive element of this period, capable of attracting scholars and ordinary people. This resulted in a huge return to the benefit of science and society, providing firm foundations to pursue the knowledge of wind and of its effects (Chap. 4).

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Similarly, the revitalised wind culture drew essential concepts and principles from the basic disciplines that arose and developed from sixteenth century onward. In such years, mathematics rose to a focal role for the solution and formalisation of problems, of general and specific nature; this originated the need to develop tools capable of automatically performing complex and repetitive computations (Sect. 3.3). The probability theory (Sect. 3.4), destined to become an essential tool of wind science and engineering, made its appearance and grew taking advantage of progress in mathematics and of the fascination for gambling typical of this age. An extensive culture was developed in the field of mechanics, in its broadest meaning (Sect. 3.5); it indissolubly joined with the evolution of mathematics, becoming both its mover and its effect. Fluid dynamics is the discipline that most provided direct and innovative contributions to the wind culture (Sect. 3.6); taking its cue from, and even joining its evolution to the progress of mathematics and mechanics, it established the theoretical and experimental tools to fathom the secrets of airflows and of their many effects. The evolution leading to the foundation of thermodynamics was just as essential (Sect. 3.7); on the one hand, it laid the basis to interpret the Earth atmosphere as a giant thermal machine, with the wind as a fundamental product; on the other hand, it provided essential support for the development of the steam machine, an instrument that indissolubly bound its progress to the measurement and knowledge of wind. A new discipline gaining ground in this period also deserves to be mentioned: the gas kinetic theory (Sect. 3.8): even though apparently removed from wind science, it became an essential reference for the first theories about turbulence, introduced in early twentieth century (Sect. 6.6). Other disciplines, such as chemistry and electrology, provided vital contributions to the knowledge of wind in this period; even if no specific paragraphs deal with them, their most significant elements for the purposes of this book are emphasised all the same. This chapter ends with a synthesis of the main aspects characterising the origin and the first developments of structural mechanics (Sect. 3.9) and of structural dynamics (Sect. 3.10). These disciplines provided a body of knowledge that, with the passage of time, became increasingly vital to protect human works from wind actions and effects. As a whole, this chapter can appear too replete with data and notions not so close to the culture of the wind. However, I hope it can provide a sufficiently broad picture of the period when the knowledge underlying such discipline was born. I also hope the chronology of the evolution of such knowledge can help to understand the reasons that favoured the consolidation of some ideas since the Ancient Ages, and delayed the success of other concepts and tools up to the present day.

3.1 Speculation and Experience Renaissance and humanism inspired evolution of culture from speculation to experience in the late sixteenth and early seventeenth centuries, favouring the growth and maturation of a new scientific vision pervading humanity. Treating the multiplicity

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of the implications characterising this process is virtually impossible and unrelated with the purposes of the book in any case. Two aspects, however, deserve to be discussed because of the repercussions they had on the study of the wind. They relate to the speculative tension taking inspiration from a largely renewed naturalism and to the impetus of the researches aimed at specific sectors rather than universal concepts like those investigated by ancient thinkers. Both such aspects grew on strongly anti-Aristotelian grounds. Man’s propensity towards the comprehension and control of nature unfolded especially in England, thanks to Thomas Moore, Francis Bacon and Thomas Hobbes, and in Italy, on account of Gerolamo Cardano, Bernardino Telesio, Giambattista Della Porta, Giordano Bruno and Tommaso Campanella [1–6]. Thomas Moore (1478–1535), statesman, philosopher and writer, was the author of De optimo statu rei pubblicae deque non Insula Utopia (1516). Here, he criticised the English society and customs through the narration of the life in the imaginary island of Utopia, where individual interests were subordinated to the social ones, everyone had a job, universal education and religious tolerance were common practices and the land was a collective property. In this political system, the inhabitants of the island, who were devoted to the study of the atmosphere, were in possession of such a huge number of climatic data to allow the formulation of reliable weather forecasts. Gerolamo Cardano (1501–1576), mathematician (Sects. 3.3 and 3.4) and philosopher, wrote De subtilitate (1547) and De rerum varietate (1557), which provided evidence of a typically Renaissance naturalistic speculation, inspired by Neo-Platonism and by a sort of “natural magic” that allowed disclosing the principles of the universe. Besides these old-fashioned views, Cardano was the first man of science to reject the theory of the four elements (Sect. 2.2), claiming that earth, air and water were primitive elements, while fire represented a quality of the matter. In his time, he was two centuries ahead of the scientific and speculative debate that would lead to repudiate the phlogiston theory (Sect. 3.7). Cardano was also credited with the first measurement of the wind speed during a storm: by counting the beats of his pulse, he remarked that “wind does 50 paces during a beat”; he then estimated its speed as approximately equal to 30 m/s [1]. Bernardino Telesio (1509–1588), a philosopher with a Renaissance attitude, opposed an inductive method based on the primacy of the senses to the deductive method of Aristotle, questioning his belief to understand the laws of nature through the application of reason only. According to Francis Bacon, Telesio was “the first of the new men”. In De natura rerum iuxta propria principia (1565), he based the knowledge of the universe on the principles of the matter, constituting the prime base of the physical substratum, and opposing forces due to cold and heat, directly proven by the experience of senses. In this way, he established qualitative analogies between the concepts of cold, inertia and immobility, setting the concepts of heat and movement against them. Like Telesio, Giambattista Della Porta (1535–1615), philosopher, scientist, man of letters and a disciple of Gerolamo Cardano, expressed deeply anti-Aristotelian concepts. He acquired renown with Magiae naturalis libri IV (1558), where he maintained only magic could explain and manipulate nature. In 1560, he founded

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“Academia secretorum naturae”, the first society where learned men met to discuss new topics. There, he especially set up a magnificent museum, which was only accessible to those who could announce a new discovery. Unfortunately, a French “friend” informed the Church about a passage from the book of Della Porta where the author wrote on ointments for witches, and the Pope ordered the closure of the Academia. In his old age, Della Porta devoted himself to a scientific treatise in four volumes, De aeris transmutationibus (1610), dealing with meteorological subjects. The first book covered the definition of air and its properties, steam, solar heating, wind classification and origin, air degeneration and diseases. The second described atmospheric phenomena such as rain, snow, hail, dew and frost. The third was dedicated to lightning, thunder, falling stars and comets. The fourth spoke about the sea, its salinity, the motion of waves, lunar influences, rivers and springs; it also discussed the eruptions and earthquakes caused by the subterranean winds flowing in Earth caves. Returning to the concepts of the philosophy of Telesio, Della Porta also thought that air was subject to expansion and compression in relation with the heat and cold caused by the succession of days and nights and by seasons as well. In a style reminiscent of Theophrastus (Sect. 2.4), Della Porta enunciated the properties of every wind and the associated “presagia”, that is, forecasts based on ancient beliefs: ducks flapping their wings foretold wind; if someone dreamed of birds, the next day would be windy; wind inseminated mares. He also formulated an innovative and pioneering concept of wind: it was originated by the space left empty by the heating of humid air that, thrust upwards and compressed, drew other air; wind, therefore, was not derived from exhalation, as maintained by Aristotle (Sect. 2.2), but from evaporation. Giordano Bruno (1548–1600) joined the Dominican Order at the age of 18 and left it in 1576, suspected of heresy. He moved to Paris and then to Oxford: here, he wrote La cena de le ceneri (1584), where he defined Aristotle a poor small-minded intellect, confuted the principles of Aristotelian physics and repudiated the Ptolemaic system for the Copernican one. He also embraced the atomic theory and foreshadowed a system of vortices that anticipated the concept subsequently developed by Descartes. Tommaso Campanella (1568–1639), a Dominican philosopher, took and developed the ideas of Telesio, tracing the natural phenomena back to the action of heat and cold. Referring to Bruno, he defined Aristotle a fool and praised a new culture that “helps us to take Aristotle away from our back and to examine nature through reason and experience, not through the words of men”. In Civitas solis (1602), he described an ideal society, inspired by Plato’s Repubblica, where neither family nor private property existed, the rules and institutions were the expression of the reason of man and the inhabitants followed a natural religion devoted to meteorological studies. Francis Bacon (1561–1626), philosopher, scientist and statesman, founded an experimental and inductive new logic, opposed to the aprioristic, theoretical and deductive Aristotelian and scholastic speculation, inspired by a use of the mind that was “detached and disconnected from the evidence of facts”. Since the works of

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Aristotle were known as the Organon, Bacon published his main work with the Latin title Novum organum (1620). In this work and in his other writings—Essays (1597), Advancement of learning (1605), Le cose pensate e le cose viste (1607), Storia naturale e sperimentale (1622), De augmentis scientiarum (1623) and Instauratio maxima, an unfinished treatise about the whole human knowledge, Bacon rejected the idea that the authority of ancient philosophers was a guarantee of truth and opposed the Renaissance philosophy based on “blind experiments” and on vague and ambiguous premises. Within such thought framework, Bacon showed great interest for atmospheric studies, in some passages of Novum organum (1620) and Historia ventorum (1625), a treatise entirely dedicated to wind analysis. The first one contained the description of an instrument similar to the future thermoscope of Galilei; it also reported an opinion stating that heat is a form of motion rather than a substance. The second one enunciated concepts often far removed from the reality of the physical phenomena; on the other hand, it contained a sentence that is still valid today: “there is not a region of the heaven from whence the wind doth not blow (…) There are some whole countries, where it never rains, or at least very seldom; but there is no country where the wind doth not blow, and that frequently”. Bacon also wrote Nova Atlantis (1627), where he mentioned, from a futuristic and narrative viewpoint, the outstanding technical and scientific achievements occurring on the ideal island of Bensalem (Fig. 3.1). Here, there were air-conditioning devices and towers up to half a mile high, some of them “built on very high mountains”. The scholars of the island used the towers to carry out meteorological observations, monitoring “most meteors, as well as winds, rain, snow and hail”. Bacon also imagined the creation of a scientific research institution at Bensalem, the house of Solomon; this stimulated the foundation, in 1660, of the Royal Society of London, an organisation destined to play a primary role in the divulgation of knowledge [6]. Thomas Hobbes (1588–1679), philosopher and politician, wrote Elementorium philosophiae, a three-part work—De Corpore (1655), De Homine (1658) and De Cive (1642)—respectively, covering natural philosophy, anthropology and politics. Hobbes, a materialist and mechanicist, explained the reality of nature through the concepts of matter, movement, space and time. Since he maintained that any observation of a physical phenomenon is not enough to provide its absolute knowledge, and that observation alone cannot show the infinite circumstances that can take place —“for though a man have always seen the day and night to follow one another hitherto; yet can he not thence conclude they shall do so, or that they have done so eternally. (…) experience concludeth nothing universally. If the signs hit twenty times for one missing, a man may lay a wager of twenty to one of the event; but may not conclude it for a truth”—he is also considered a precursor of the probability theory (Sect. 3.4). It was clear that speculative tension towards a universal view of the nature, when not supported by mathematical instruments and measurements, was doomed to failure. In parallel with this line of thought, a process aimed at harmonising the transition of mechanics from metaphysics to physical science was then originated. Such grounds provided the foundations for premises leading to the inception and develop-

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Fig. 3.1 Bensalem Island, Nova Atlantis

ment of various scientific disciplines, first among them astronomy, to which Nikolaj Kopernik, Tycho Brahe and Johannes Kepler gave essential contributions. In the Discours préliminaire about the Encyclopédie (1751), D’Alembert defined this subject as the “most sublime and certain application of combined geometry and mechanics”; after the study of man, nothing else was more deserving of attention. Nikolaj Kopernik (1473–1543), Polish astronomer and cosmologist, provided a fundamental contribution to this transition process, destroying the old geocentric view of Ptolemy that placed Earth at the centre of the universe. Even though only rudimentary instruments were available to him, in Italy Kopernik developed a new theory, called the heliocentric one, where Earth and other planets revolve around the sun along circular orbits [6]. He provided a conceptual arrangement and a mathematical formulation of this theory in De revolutionibus orbium coelestium, a work published the year after his death. It inflicted a decisive blow to the blind faith in the Aristotelian thought. Years afterwards, the Danish astronomer Tycho Brahe (1546–1601) carried out observations1 destined to play an essential role in the evolution of science near Prague, in the Uranienborg castle on the Hven Island. He especially developed the principle of necessity to support theoretical deductions by means of accurate and systematic observations of the natural phenomena. He, however, used these observations to strongly oppose the heliocentric concept of Kopernik. On this account, 1 Tycho

Brahe made dials that, rotated in any vertical plane, measured the position of celestial bodies; they are considered the ancestors of theodolites.

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he introduced a new theory, partially geocentric and partially heliocentric, known as the geostatic one, with the Moon and the Sun revolving around the Earth, the other planets revolving around the Sun. Johannes Kepler (1571–1630), German astronomer and philosopher, first assistant and then successor of Brahe, reworked the observations of his master in the spirit of Kopernik’s theory. Using Brahe’s instruments, he carried out experiments, through which he formulated his three laws: (1) the orbits of planets are ellipses with the sun occupying one of their foci; (2) the areas described by the radius vector connecting the sun with a planet are proportional to the time spent to cover them; (3) the squares of the revolution periods of planets are proportional to the cube of the major semiaxes of their orbits. The first two laws appeared in Astronomia nova (1609), the third one in Harmonices mundi (1619). The merit for the new scientific thought pervading humanity mostly goes to Galileo Galilei (1564–1642), who put an end to the Middle Age and Renaissance mentality, starting the Modern Age. He destroyed the Aristotelian doctrine, insisting on a scientific conception based on experience and mathematic proof. With Galilei, science renounced to know the absolute truth about things; as a way of compensation, a partial knowledge method, called the Galilean one from then on, arose: it vastly broadened the horizons of the human thought, which had remained stagnant too long. By virtue of this method, scientific activity was separated by any other form of speculation. Indeed, Galilei recognised two types of knowledge: one, according to “Authority”, founded on the Scriptures and aiming at the revelation of God; the other, according to “Reason”, based on the experimental study of nature. Mathematics is the basis of rational knowledge, the absolute certainty into which divine and human thought coincide. He then broke down his method in three separate stages: the “analysis”, through which he translated observations into numerical values, the “hypothesis”, through which he established a preliminary relation among such values, and the “synthesis”, through which he reproduced the physical phenomenon changing its parameters. Galilei wrote: “Devoting and exhausting himself over the works of other without ever raising his eyes to the works of the nature will never turn a man into a scientist”. The life of Galilei was a turmoil of ideas, innovations and discoveries spreading over multiple fields of science, literature and philosophy. Galilei was born in Pisa in 1564; in 1580, he enrolled for medicine studies, but soon he developed new interests for philosophy and mathematics that induced him to abandon the studies he previously engaged in to devote himself to the new disciplines. Thanks to such new interests (Sect. 3.5), in 1583, Galilei discovered the law of pendulum isochronism. From 1589 to 1592, he was professor of physics at Pisa, where he drew some principles of kinematics, published in De motu, first among them the law according to which the falling time of a body is independent of its weight. In 1593, after the Venetian doge Pasquale Cicogna entrusted him with the chair of mathematics at the Studio of Padua, Galilei implemented a rudimentary instrument, later improved in the early seventeenth century, anticipating the thermometer (Sect. 3.2). In 1603, he founded the Accademia dei Lincei in Rome and started studies about the motion of bodies on inclined planes, establishing a relationship between

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this problem and the swings of the pendulum (Sect. 3.5). In 1609, he improved the telescope and used it, for the first time, for scientific purposes. Thanks to it, he achieved great astronomical discoveries and developed fundamental concepts about the randomness of observation errors (Sect. 3.4). In 1610, Galilei was recalled in Tuscany by the Grand Duke Cosimo II dé Medici (1590–1621) and was appointed professor of mathematics at the Studio of Pisa. Here, he wrote Nuncius sidereus and Le rivoluzioni dei mondi celesti, supporting the heliocentric theory of Kopernik on the strength of his astronomical researches. Incited in such direction by Francesco Sizzi (approx. 1585–1618) and Ludovico delle Colonne, he also backed up the concept that such theory could be found in the Bible. He also asserted that the conflict between the scientific thought and the interpretation of the Scriptures is not a symptom of a double truth: it is instead necessary to distinguish the moral and salvific meaning of Scriptures, which often made use of an imaginative language to make themselves understood by people, from the scientific research, which must only be based on “sensible experiences” (the observations of senses) and “certain demonstrations” (mathematical proofs). For such reasons, in 1615, he was reported to the Holy Office for heresy, his works were banned and the ecclesiastic authorities cautioned him against using theology to support the principles of physics [7]. Following this judgement, Galilei remained silent for some years, working on the Saggiatore (1623), inspired by comets. In this treatise and also, partially, in the subsequent Dialogues (1638), he dealt with heat, establishing concepts underlying the future theory of phlogiston (Sect. 3.7). In the same year, the Saggiatore appeared (1623), Urbano VIII (1568–1644), a friend and admirer of Galilei, became Pontiff. Galilei, flattered himself on the arrival of better times and published Dialogo sopra i due massimi sistemi del mondo (1632), a book about comets and tides. On the contrary, he again stood trial “for strong suspect of heresy” and was sentenced to abjuration in his Arcetri villa. Here, he completed Discorsi e dimostrazioni matematiche intorno a due nuove scienze attinenti alla meccanica e i movimenti locali, the founding work of modern mechanics (Sects. 3.5 and 3.9), published at Leyden in the Netherlands in 1638. For this reason, Galilei is considered the symbol of the right of science to pursue the truth, rejecting any interference and limitation by any authority. Discorsi came about in accordance with the classical dialogue genre and were spread over four days [7]: “Three dialogists appear in the work: Salviati, representing Galileo himself, an exponent of the new science; Segredo, the figure of a cultured and profane man, willing to learn without prejudices; and Simplicio, representing the conservative science loyal to the authority of classical texts”. The first and second day (First new science, about the resistance of solid bodies to breakage and What could be the cause of such consistency) made up the basis of the first new science, the strength of the materials and of buildings (Sect. 3.9). The third and fourth day (Other new science, on local movements; that is the constant; the naturally accelerated and The fast, that is projectiles) deal with the other new science, the motion, introducing fundamental principles underlying mechanics (Sect. 3.5), sound theory and structural dynamics (Sect. 3.10).

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With Galilei, humanity turned over a new leaf. The views of Aristotle and of the scholastic fell into decline. The Renaissance faded away, together with its ambitious project to know the universal essence of things. There followed a disorientation from which the clarity of the thought of René Descartes (1596–1650) stood out. Descartes, a French philosopher, scientist and mathematician, is considered the founder of modern philosophy. He likened it to a tree, the roots of which are the metaphysics, the trunk is the physics and the branches are the other sciences, divided into three main disciplines: medicine, mechanics and ethics. Descartes formulated a radical criticism of the Aristotelian thought, based on the principle of authority and on the persuasiveness of tradition, elaborating a new method that allowed separating truth from falsehood. It was based on the belief that knowledge can only be reached by doubting of everything, with the exception of one’s own existence (“cogito ergo sum”). He applied the mathematical method to philosophy, defining the thinking self as the principle on which knowledge is based; God, conversely, is the cause of inborn ideas. On such grounds, he enunciated four rules: “evidence” (the clarity and distinction of thought contents), “analysis” (every problem must be solved in simpler parts), “synthesis” (through which one goes from the simplest forms of knowledge to the most complex ones) and “enumeration” (the review of the analysis and synthesis process). On the basis of such concepts, Descartes composed Le monde and Principles of philosophy, where he explained the formation of the world. In Le monde (1634), he claimed: “Give me extension and motion, and I will build the world”; he also conceived the “theory of vortices” at embryonic level (Fig. 3.2), according to which space is full of matter swirling around the sun. In the Principles of philosophy (1644), Descartes claimed that vacuum cannot exist and that the sole possible form of motion is the vortical or circular one. He also explained that God had bestowed motion to the matter by virtue of countless vortices of every shape, size and speed [6]. The frictions caused by vortices originated small smooth and spherical particles. The fine ones make up the first matter, which gravitates towards the centre of every vortex and there forms luminous suns and fixed stars. The smooth and globular particles, from which the first matter tends to separate, make up the second, or transparent, matter; it moves from the centre of the vortices outwards, following straight lines along which star light is transmitted. The “third matter” makes up the material part of the original particles resisting the damage caused by friction; it originates the opaque bodies, such as Earth, the planets and the comets. In the period elapsing between Le monde (1634) and Principles of philosophy (1644), Descartes drew up three scientific treatises, Dioptrique, Météores and Géometrie, published and digested in its fundamental work, Discours de la méthode (1637). In Dioptrique, he anticipated the undulatory nature of light; Géometrie was the act of foundation of analytical mechanics (Sect. 3.3); Météores covered atmospheric problems and the wind. In Météores, Descartes returned to the concept of the Greek philosophy schools, recognising the existence of four elements on which life is based—air, fire, water and earth—consisting of infinitely divisible particles, different by shape and size, inhomogenously aggregated; air consists of thin particles flowing on each other.

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Fig. 3.2 Descartes’ vortices [6]

Taking inspiration from Della Porta, Descartes maintained that the wind does not derive from exhalation but from evaporation and it consists of air motions caused by forces associated with thermal atmospheric phenomena. He also affirmed the existence of four main winds coming from the cardinal points. Eastern winds blow in the morning and are drier than the western ones. Northern winds, dry, cold and strong, blow by day. Southern winds blow especially at night and are damp. Finally, there are the periodical winds, such as the etesian ones, “which blow after the summer solstice” and the miscellaneous winds such as the “orniti”, “produced by the ruggedness of the Earth surface and by the vastness of the seas” [4].

3.2 Atmospheric Physics and Measurements The presence of Galileo Galilei (1564–1642) and he being favoured by Cosimo II Dè Medici (1590–1621) created the conditions for the Grand Duchy of Tuscany to become, in the seventeenth century, the cradle of remarkable discoveries about natural sciences [1, 2, 6]. They revolved around instruments that quantify atmospheric parameters through measurements, especially thanks to Ferdinando II Dè Medici

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Fig. 3.3 a Galileo’s thermoscope; Torricelli [6]: b mercury barometer; c homonymous pipe; d Ferdinando II’s hygrometer [9]

(1610–1670), who succeeded his father Cosimo II in 1621. Ferdinando II turned out to be a generous patron of fine arts and sciences, as well as a scientist and inventor with talent and personality. In 1609, the year before his return to Pisa (Sect. 3.1), Galilei proved that air expands when heated and contracts if cooled. He took a small glass bottle with a long and thin neck and warmed it holding it in his hands. He then overturned it and dipped the bottleneck in a container full of water (Fig. 3.3a). Air, cooling down, contracted, and water rose along the bottle neck, rising above the container level [8]. This device, the ancestor of all meteorological instruments,2 was called thermoscope in 1617 by Giuseppe Biancani (1566–1624). In 1624, after adding a measurement scale, the Jesuit Father Jean Leurechon (1591–1670) called it thermometer in La récréation mathématique [9]. The invention of the barometer originated from the experiments carried out by Galilei to prove the existence of vacuum and the weight of the atmosphere. During such experiments, described in the Discorsi (1638), he used a syringe to inject compressed air into a glass container with a narrow neck closed by a valve. He weighed the container, emptied it and weighed it again, determining the weight of the air by difference [9]. Reading the Discorsi drove a disciple of Galilei, Rafaello Magiotti (1597–1656) to recommend other tests on this subject. The invitation was accepted by Gasparo Berti (1600–1643); in 1641, he took a lead pipe 12 m long, filled it with water and placed it in upright position, enclosing its two ends in as many water-filled containers. Initially, Berti closed the lower end with a valve, keeping the upper one open. Then, he closed the upper end with a second valve, opening the lower one. Water fell into the lower container, creating a vacuum zone in the pipe section below the upper valve. 2 According

to some bibliographic sources, the first thermometer was invented by the Persian scientist Avicenna (980–1037) in the early eleventh century.

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Evangelista Torricelli (1608–1647) came into contact with Galilei’s ideas attending the lessons of his best disciple, Benedetti Castelli (1577–1644). In 1628, the latter published Della misura delle acque correnti, that instilled into Torricelli a strong interest for the mechanics and the behaviour of fluids. Influenced by these studies, in 1641, Torricelli wrote De motu gravium naturaliter discendentium et proiectorum (1644) where he developed the parabolic equation associated with the motion of the projectiles and of the spurt of a liquid from a hole on the bottom of a tank (Sect. 3.6). It impressed Castelli, who showed it to Galilei. Galilei was so impressed he wanted to know the author. Torricelli then travelled to Arcetri and became the inseparable companion of Galilei in his last three months of life. On the master’s death, in 1642, he was appointed as his successor, that is mathematician and philosopher of the Grand Duke of Tuscany, as well as lector of mathematics at the Studio of Florence. In the meantime, Magiotti described Berti’s experiment to Torricelli, who understood the possibility of improving it by replacing water with a more suitable substance. He then invited a young disciple of his, Vincenzo Viviani (1622–1703), to create vacuum through the use of mercury, called quicksilver at that time. Following such advices, in 1644, Viviani took a glass pipe 1 m long, closed at one end, filled it with mercury and blocked the other end as well. He then turned the pipe upside down, dipped the base into a container filled with mercury and removed the closure. The level of the mercury in the pipe decreased from the height of 1 m up to approximately 76 cm, creating a vacuum zone at the top of the pipe. The first barometer was born. In the same year, Torricelli refined Viviani’s experiment building various devices (Fig. 3.3b, c) [9]. During the experiments, Torricelli understood that the downwards atmospheric pressure exerted on the surface of the mercury in a container is equal to the pressure applied upwards on the mercury in the pipe. By measuring the height of the column of mercury, thus, it was possible to trace atmospheric pressure. Torricelli illustrated the experiments, interpreted their results and explained the implications of his discoveries in two letters he sent to his friend Michelangelo Ricci (1619–1682) in 1644; he wrote: “We live submerged on the bottom of a sea of elementary air that, because of unquestioned experiences, it is known to weigh”. He also justified the behaviour of mercury in view of the “mutations of the air, now heavier and thicker, now lighter and thinner” [8]. He maintained air is heavy near the Earth surface, but becomes lighter moving upwards. Torricelli was also the first one to understand that wind is caused by pressure differences. In his Lezioni accademiche, published in Florence in 1715, he maintained a difference in the rarefaction of air causes an equalisation phenomenon that produces an air current called wind. He illustrated this concept with the example of the cold wind that flows out of the doors of the large Italian churches in the hottest spring days: “The air inside the great buildings in this period is significantly colder and heavier than the air in their surroundings. It then flows out from the doors, like water should do if it was confined inside a building and a breach was suddenly opened on a side” [6]. Thanks to the discovery of the barometer, the scientists arriving in Tuscany from all over Italy and Europe understood how much inaccurate the temperature measurements carried out by Galilei’s thermoscope have been. The latter, having an open end,

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was sensitive to both temperature and pressure changes. Ferdinando II introduced “acquarzente” (ethyl alcohol) instead of water in the thermoscope, sealed the end to eliminate the effect of pressure and fitted a measurement scale (1646), improved by Descartes the following year. In 1665, Christiaan Huygens (1629–1695) proposed to use a scale with two fixed points. Guillaume Amontons (1663–1705) built the first two mercury thermometers3 in 1688 and in 1703 (Histoire de l’Académie des Sciences). In 1714, the German physicist Gabriel Daniel Fahrenheit (1686–1736) confirmed the advantage of using mercury thermometers [9]; six years after, he fitted the thermometer of the first scale bearing his name (1720). Similar scales were introduced by the Swedish astronomer Anders Celsius (1701–1744), who invented the centigrade scale in 1742, and by the British physicist and mathematician William Thomson (Lord Kelvin, 1824–1907), inventor of the first absolute temperature scale in 1848 (Sect. 3.7). The idea of measuring humidity was pursued since the middle of the fifteenth century. The first hygrometers were conceived by Leon Battista Alberti (1404–1472), Nicola Cusano (1401–1464) and Leonardo da Vinci (1452–1519) (Sects. 2.8 and 2.10). In 1557, Gerolamo Cardano (1501–1576) (Sects. 2.4 and 3.1) published De rerum varietate, where he analysed the variation in humidity in relation with the length of dried guts and membranes. A similar technique was used by Santorre Santorio (1561–1636) in 1626. Other hair and rope devices were already in use towards the middle of the sixteenth century. In 1655, Ferdinando II gave a decisive thrust to the development of this type of device implementing the condensation hygrometer,4 precursor and prototype of modern instruments (Fig. 3.3d). Inside a vial, it collected the water drops produced by the condensation of the air flowing around a funnel filled with ice; the amount of collected water being proportional to the humidity of air. On 18 June 1657, Leopoldo I Dè Medici (1640–1705), brother of Ferdinando II, founded the Accademia del Cimento where he gathered, under the “trying and trying again” watchword, erudite men from Italy and from other countries. Here, a new scientific discipline came into existence: atmospheric physics [10], on which the research of academics was focused. With the passing of time, it became a cornerstone for meteorology, micrometeorology and wind engineering. Ferdinando II himself gave a boost to the spreading of instruments in Europe, founding the first international meteorological organisation and building a series of standardised devices he distributed to the observatories in Florence, Pisa, Vallombrosa, Curtigliano, Bologna, Milan, Parma and, later in Paris, Warsaw and Innsbruck. He also designed a consistent procedure to survey pressure, temperature, humidity, wind direction as well as the status of the sky. The results were registered on forms and sent to the Accademia to be collated and processed. The Church did not appre3 Athanasius

Kircher (1602–1680) described a mercury thermoscope in Magnes, sive de arte magnetica (1641). 4 It is said the idea of the condensation hygrometer goes back to a hot and humid day in which the Great Duke Ferdinando II was impressed by the external surface of a glass cup containing a cold beverage; it first misted up, then became covered with water drops, with no liquid coming out from the container.

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ciate this initiative and in 1667, ordered its closure. The most important experiences completed there, however, were collected in a volume, Saggi di naturali esperienze fatte nell’Accademia del Cimento, destined to remain a reference for the physicists of many generations to come. Three stations—Paris, Florence and Vallombrosa—continued operations until the death of Ferdinando II (1670). The Paris station, at the astronomical observatory, survived such date, becoming the reference model still adopted worldwide [8, 9]. The studies started in Tuscany by Galilei and Torricelli continued in France, Germany and England thanks to Pascal, Guericke, Boyle and Hooke. Blaise Pascal (1623–1662) perceived that if Torricelli’s ideas were correct, that is if air really was a heavy ocean extending on the Earth surface, the weight of the air must decrease when moving upwards and atmospheric pressure must also decrease. Pascal attempted in vain to prove this intuition by means of measurements carried out on the roofs of houses using various types of barometers (Fig. 3.4a). In 1647, he published Nouvelles expériences sur le vide, where he described the barometric pressure reduction climbing at the height of 52 m on the Tour St. Jacques-de-laBoucherie in Paris. Finally, he realised the need to carry a barometer at the top of a mountain. Living in Paris and being chronically ill, he asked his brother-in-law, the physicist Florin Perier (1605–1672) who lived on the Auvergne mountains in the southern France, to carry out the test on his behalf. Perier carried out them on 19 September 1648 on the Puy-de-Dome, 1467 m above sea level, confirming Pascal’s intuition: “we discovered that on the peak of the Puy-de-Dome there were 59 centimetres of mercury in the pipe, whereas in the gardens at its base there were 67 centimetres of mercury” [3, 9]. Encouraged by this result, Pascal continued his experiences in the laboratory using a hydraulic press and proved that the pressure acting at a point of a fluid at rest is uniform in all directions. He formulated this fundamental enunciation, known as hydrostatic law or principle of Pascal, in Traitè de l’équilibre des liqueurs (1663). In the first half of the seventeenth century, presumably between 1635 and 1645, a German, Otto von Guericke (1602–1686) built a pneumatic machine to extract air from containers. Weighing the containers before and after the accomplishment of vacuum, he estimated air density as approximately equal to 1.05 kg/m3 , a value not far from the currently recognised average one (ρ = 1.25 kg/m3 ). Thanks to this invention, Guericke carried out many tests about atmospheric pressure. In the first one, in Ratisbon in 1654, he took two hollow hemispheres, perfectly fitting along the equatorial plane, that make up a sphere 45 centimetres in diameter; he proved that is was necessary to apply a high weight to the lower hemisphere to detach it from the upper one (Fig. 3.5a). In that same year, he carried out his most known experiment in the public square of Magdeburg, before the Emperor Ferdinand III of Habsburg (1608–1657) and a huge crowd. He made up a sphere 67 centimetres in diameter by joining two hollow brass hemispheres and drilled a small hole through which he extracted the air. He then harnessed strong horses to each hemisphere, trying to separate them (Fig. 3.5b); the attempt was successful when two groups of eight horses each were used. He commented his results in Experimenta nova (ut vocantur) Magdeburgica de vacuo spatio (1663), where he explained that the uniform pressure

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Fig. 3.4 Experiments with a water barometer by: a Pascal [11]; b Guericke [6]

Fig. 3.5 a Ratisbon experiment; b Magdeburg experiment [6]

exerted by the air on the surface of the sphere, from the outside towards the inside, was very high. He also proved that a hollow and thin sphere, if the internal air was extracted, was destroyed by the weight of the Earth atmosphere. Guericke was also one of the first to recognise the potentiality of the barometer to forecast weather changes. Noticing how the height of the liquid column dropped any time a violent storm was imminent, he performed the first instrumental forecast. He made use of the water barometer of his own invention (Fig. 3.4b), described in Experimenta nova (1672), by means of which he forecasted, two hours before its occurrence, the storm that hit Magdeburg on 9 December 1660. In the same volume,

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Fig. 3.6 First (a), second (b) and third (c) version of the air pumps of Boyle and Hooke [6]

he illustrated evolution of the air thermometer and the first machine producing electrical charges: it consisted of sulphur sphere that, when turned by means of a handle, became electrified if touched with the hand. Robert Boyle (1627–1691), an Irish chemist and one of the founders of the Royal Society, developed the experiences carried out by Torricelli, Pascal and Guericke, availing himself of the help of a young English assistant, Robert Hooke (1635–1703). Together, they perfected Guericke’s pneumatic machine (Fig. 3.6), carrying out tests about vacuum realisation. During them, in 1661, they proved that air is an elastic medium and inferred the first gas law: at the same temperature, the product of the pressure by the volume of a gas, and in particular of air, remains constant. Boyle published this result in 1662, in the appendix to the second edition of New experiments, physico-mechanical, touching the spring of air and its effects, made for the most part in a new pneumatical engine. A few years after, Edme Mariotte (1620–1684), a French priest and physicist, author of famous measurements about the resistance of the bodies immersed in fluids (Sect. 4.2), independently obtained the same law, publishing it in the second (De la nature de l’air) of his four Essais de physique (1676–1679). For this reason, the law is known as the Boyle–Mariotte’s law. In 1665, Boyle published New experiments and observations touching cold, where he criticised the use of air thermometers, too sensitive to pressure, and introduced the word “barometer” to replace the term “Torricelli’s tube”, as the instrument had been called up to that time. He also carried out many experiments with water and siphon barometers (Fig. 3.7a), publishing the results in Continuation of new experiments (1669), which aroused widespread interest, especially because many of these devices were portable. Thanks to these innovations, the measurement of pressure changes became, in many European countries, a social activity, almost a sport. Scientists and amateurs climbed roofs and mountains to measure pressure drops. They made barometers of

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Fig. 3.7 a Boyle’s barometers; b Hooke’s diagram for the daily registration of observations [6]

every shape and size, using any type of liquid from water to cognac [11]. Besides these bizarre aspects, and also thanks to Guerick’s forecast, the belief that barometric measurements were the means to escape astrological predictions and to support the scientific weather forecasting methods came to maturity (Sect. 4.1). In this context, taking inspiration from a project of Francis Bacon [12], Hooke proposed to the Royal Society, of which he in the meantime had become the first administrator of experiments, “a method to achieve a history of the weather” and indications for the daily collection of data (Method for making a history of the weather, 1663). Following such indications, the force of the wind, temperature, barometric pressure and humidity must be measured and expressed with numbers; “the aspect and every visible characteristic of the sky” and its “more remarkable phenomena” must be annotated and described in words (Fig. 3.7b). Hooke also considered necessary to define the main climatic phenomena through specific names rather than through generic descriptions. He also understood that data collected in such a way would have become indispensable for many sectors of life. Humanity was not yet ready to accept so far-sighted and challenging suggestions. Hooke’s intuition, on the other hand, remains an essential step in the history of meteorology and science [13]. In 1665, Hooke invented the wheel barometer (Fig. 3.8a), the first instrument (using mercury) with graduated atmospheric states. In 1667, he designed the first barometer suitable for use aboard ships, where the rolling motion caused by waves made normal instruments useless. In that same year, he built the first pendulum

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Fig. 3.8 Hooke [6]: a wheel barometer; b anemometer

anemometer (Fig. 3.8b), an instrument consisting of a scoop fastened to a horizontal pin that moved along a graduated scale under the effect of the wind pressure; the scoop and the scale revolved around a vertical axis, spontaneously turning in the flow direction [14]. In the meantime, in 1666, Louis XIV (Sun King, 1638–1715) founded the Académie Royale des Sciences in Paris, which was soon chosen by the main European scholars as the discussion forum for new theories. Right from its foundation, it gathered various atmospheric measurements, first among all those of the Paris astronomical observatory. Similar databases were set up in England and in Germany. The former were managed by the English philosopher and politician John Locke (1632–1704), who, from 1666 to 1692 collected measurements of temperature, pressure, wind direction and speed, as well as observations of the state of the sky. The latter were accomplished in Hannover, from 1678 to 1714, by the German philosopher, historian, jurist and mathematician Gottfried Wilhelm von Leibniz (1646–1716), and in Kiel, from 1678 to 1709, by Samuel Reyher (1635–1714). Leibniz used these measures to verify the potentialities of the wheel barometer invented by Hooke as a weather forecasting instrument. With the advent of the eighteenth century, a broad range of new instruments for wind measurement appeared, inspired by different concepts [11, 15]. In 1709, the German philosopher and mathematician Christian Wolff (1679–1753) measured the wind speed through small windmills (Fig. 3.9a) subsequently improved by Johann Georg Leutmann (1667–1736) in 1725, by Richard Woltmann

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Fig. 3.9 Wolf’s (a) and Martin’s (b) windmill anemometers

(1757–1837) in 1790 and by Benjamin Martin (1705–1782) towards the end of the eighteenth century (Fig. 3.9b). Following this principle, Benjamin Biram built two famous aerometers in 1842 and in 1862 (Fig. 3.10). In 1721, Pierre Daniel Huet (1630–1721) presented in Paris a pipe as thin “as a monk habit” [16], which, connected to a mercury-filled pipe and to a wind vane, measured wind speed (Fig. 3.11a). In 1732, Henri de Pitot (1695–1771), French physicist and engineer, member of the Royal Society and of the Académie des Sciences, built the homonymous tube, the “pitometer” (Fig. 3.11b), which he presented in Description d’une machine pour mesurer la vitesse des eaux courantes et le sillage des vaisseaux, which was to bring him great fame [14]. In 1774, James Lind (1736–1812) conceived a vertical U-shaped tube, with an L-shaped end oriented in the direction of the wind by means of a wind vane (Fig. 3.11c); the shift of the liquid in the tube provided a measurement of the wind pressure and, consequently of its speed. Alexander Adie (1775–1859) built a famous version of the Lind tube in 1820. In 1734, Louis Leon Pajot Comte D’Ons-en-Bray (1678–1754) built the first anemograph. It consisted of a wind vane connected to a device that “marks on paper the winds that blew during the twenty-four hours and their different speeds” (Fig. 3.12a); the device was little appreciated in its age, but it marked the start of the construction of many recording instruments [1]. Spring anemometers were introduced by the French mathematician Pierre Bouguer (1698–1758); afterwards, they were improved in 1803 by Von Poschmann,

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Fig. 3.10 Biram’s aerometers: 1842 (a) and 1862 (b) instruments

Fig. 3.11 a Huet’s tube anemometer; b original Pitot tube; c Lind’s anemometer

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Fig. 3.12 a D’Ons-en-Bray’s recording anemometer; b Osler’s anemograph

through the addition of a pointer and, especially, by Abraham Follett Osler (1808–1903), who equipped them with a wind vane and a continuous recording device (Fig. 3.12b) used by the Royal Observatory in Greenwich starting from 1841 [5]. In 1861, the Swiss meteorologist and physicist Heinrich von Wild (1833–1902) built a new pendulum anemometer, which saw widespread use in Switzerland and in the Soviet Union (Sect. 9.4); it consisted of a thin sheet hinged on its upper edge, which orientated itself in the wind direction thanks to a wind vane; speed measurement was defined by the inclination of the sheet. The most innovative instrument, destined to make the greatest impact on the wind culture, was the work of a Dublin astronomer, John Thomas Romney Robinson (1792–1882); he built the first cup anemometer in 1846, describing it in a paper he presented at the Royal Irish Academy in 1850 [17]. Its initial version consisted of four hemispheric cups5 fitted at the vertices of crossed arms revolving in a horizontal plane (Fig. 3.13a). Thanks to the hemi-symmetrical arrangement of the cups, the wind always simultaneously acted on the concave side and on the convex side of a pair of hemispheres. The cups and the arms rotated because the force exerted by the wind on the concave side of a hemisphere was greater than the one applied on the convex side. Soon afterwards, Robinson himself equipped his anemometer with an anemoscope that measured the wind direction (Fig. 3.13b). It was first used in 1856 by the Kew Observatory near Richmond. Faced by an outstanding invention 5 Robinson

itself, afterwards, built three-cup devices (Sect. 6.1).

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Fig. 3.13 Robinson’s anemometers: a initial version; b with an anemoscope

(Sect. 6.1), Robinson also postulated a principle affirming that, regardless of cup size and of arm length, the ratio between the wind speed and the speed of the centre of the cups was approximately constant and equal to 3 [18]. This principle, apparently confirmed by first experiences, was to have negative consequences, generating a huge amount of data, acquired over half a century, smeared by errors.

3.3 Mathematics and Automated Computation The scientific progress from the seventeenth to the nineteenth century drew essential ideas from the simultaneous development of mathematics [2, 6, 12]. It founded its roots in remote times, pregnant with speculation (Sect. 2.3). It changed into a theoretical scientific discipline around the end of the sixteenth century and especially in the seventeenth century, to which the first part of this paragraph is dedicated. In that period, the necessity to have instruments capable of automatically performing complex and repetitive operations was starting to be felt and pursued; it led to the pioneering accomplishments, illustrated in the second part of this paragraph, which came one after the other between the early seventeenth and the late nineteenth century. Johann Müller (1436–1476) (Sect. 2.6), a German astronomer and mathematician known for his translation of Ptolemy’s Almagesto, was the author of De triangulis (1464), a work that is a cornerstone of trigonometry. Gerolamo Cardano (1501–1576) wrote Ars magna (1545), where he reported the resolving formulas of the third and fourth degree equations, developing the studies carried out, respectively, by Niccolò

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Fontana (Tartaglia, 1500–1557) and by his disciple Ludovico Ferrari (1522–1565); he also was the first mathematician to discuss the previously neglected negative and imaginary solutions, as well as a pioneer of the probability theory (Sect. 3.4). Francois Viète (1540–1603), a French mathematician, wrote In artem analyticam isagoge (1591), a work where he indicated unknown quantities with vowels and known terms with consonants; he introduced the use of powers and applied algebra to trigonometry. He also wrote De numerosa potestatum resolutione (1600), a treatise about equations. The use of logarithms was independently introduced by the Scottish John Napier and by the Swiss Joost Bürgi. John Napier (1550–1617) published Mirifici logarithmorum canonis descriptio (1614) and Mirifici logarithmorum canonis constructio (1619) where he, respectively, reported a table for the computation of logarithms and the associated construction criterion; he was also one of the first mathematicians to make use of the decimal point. Joost Bürgi (1552–1632) presented the first table of antilogarithms, that is of the numbers whose logarithm is a natural number; the practical value of this discovery was acknowledged by Henry Briggs (1561–1631) in Arithmetica logarithmica (1624). Albert Girard (1595–1632) proved that an equation has a number of roots equal to its degree (Invention nouvelle en l’algèbre, 1629), validating the existence of negative and imaginary solutions and discussing their importance. He noticed that negative solutions can be represented along an axis with direction opposite to that of the positive solutions. The first ones to deal with infinitesimal calculus were Kepler and Cavalieri. Johannes Kepler (1571–1630) applied it, in a rudimentary form, in Nova stereometria doliorum vinariorum (1615), where he determined the volume of solids of revolution by dividing them into infinite parts and then summing their contributions. Bonaventura Cavalieri (1589–1647), an Italian Jesuit, mathematician and disciple of Galilei, returned to some principles introduced by Democritus and Archimedes (Sect. 2.3); in Geometria indivisibilibus continuorum nova quadam ratione promota (1635), he developed the method of the indivisibles, a criterion dealing with any geometric quantity—the lines, planes and solids—as the set of elementary constituents—points, lines and planes, respectively—designated as indivisible infinites. Giles Persone de Roberval (1602–1675) claimed he had invented the same criterion separately from Cavalieri; according to Roberval, lines were sets of elementary lines, surfaces were aggregations of elementary areas and volumes consisted of elementary portions of the space; he applied this technique to compute the area of many geometric shapes. In 1637, René Descartes (1596–1650) published La géométrie as an appendix to Discours de la méthode. It was a work written with an obscure style, “to leave to the posterity the pleasure of these discoveries”; however, it left an indelible footprint in mathematics. The first two parts represented the foundation deed of modern analytical geometry, which is still known as the Cartesian one: they described curves by means of equations, the methods to obtain straight lines tangent or perpendicular to curves, or areas the latter referred to. The third part was concerned with the theory of equations, introducing the use of the last letters of the alphabet to indicate the unknown quantities and of the first ones to indicate the known terms; it also formulated the rule of signs to

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enumerate the true roots, i.e. the real and positive ones, and the false roots, i.e. the real and negative ones, without covering the imaginary solutions. In the same period, the French mathematician Pierre de Fermat (1601–1665) independently developed the same subject in a work, Ad locos planos et solidos isagoge, much more intelligible and exhaustive than Descartes’ work; this writing, probably completed in 1629, had the sole weakness of appearing after 1636, the year Descartes published La géometrie. On the other hand, it is undeniable that Fermat was the first to use the concepts of tangent and derivative to evaluate the minimum and maximum points of functions; in 1662, moreover, he laid down the basis for extreme principles and variational methods while approaching the problems of the reflection and refraction of light rays. John Wallis (1616–1703) gave a decisive impulse to infinitesimal calculus and to the treatment of geometrical and physical quantities through equations in Arithmetica infinitorum (1655), Mathesis universalis sive arithmeticum opus integrum (1657) and Treatise of algebra (1685); he divided the area under the curve into horizontal strips similar to parallelograms; as their thickness tended towards zero, the sum of their areas tended towards the area subtended by the curve. The English mathematician and theologian Isaac Barrow (1630–1677) developed new contributions to geometry and to infinitesimal calculus especially by virtue of a criterion to determine the tangents to curves; it was published in Lectiones opticae et geometricae (1669) and included the embryonic form of differential calculus. Wallis, processing the results of his own discoveries and of those of Barrow, was the first to realise the reciprocity of the integration and differentiation operations; he also had the merit of exerting a strong influence on the education of his best disciple, Isaac Newton. Following his master’s steps, between 1665 and 1666, Isaac Newton (1642–1727) formulated the basis of the infinitesimal and integral calculus in De quadratura curvarum, appeared as an appendix to Opticks in 1704. He subsequently developed these concepts in Methodus fluxionum (1671), an article published posthumously in 1736. Returning to Wallis’ ideas, Newton demonstrated that differentiation (which he called method of fluxions) and integration (inverse method of fluxions) operations were one the opposite of the other; this concept was only divulged in 1687, the year Newton’s masterpiece, Philosophiae naturalis principia mathematica (Sect. 3.5), was published. Concepts similar to those of Wallis and Newton were autonomously developed by the German mathematician, philosopher and politician Gottfried Wilhelm von Leibniz (1646–1716) between 1674 and 1675 (after Newton’s studies, therefore); he then published such concepts in Nova methodus pro maximis et minimis itemque tangentibus, a paper that appeared on Acta Eruditorum in 1684 (before 1687, therefore). Among other remarkable aspects, Leibniz introduced the concept of derivative as the limit of an incremental ratio; he also perfected the determination of minima and maxima, which Fermat carried out using prime derivatives, by also making use of second derivatives. The priority of these discoveries gave rise to a heated debate, destined to last even after the deaths of Newton and Leibniz. Actually, since Leibniz published his results before Newton, his notation is still adopted.

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Finally, between 1696 and 1697, Jakob Bernoulli (1654–1705), Johann Bernoulli (1667–1748) (Jakob’s brother), the Marquis de L’Hopital (Guillaume-FrançoiseAntoine de Sainte-Mesme, 1661–1704) and Newton himself, made decisive contributions to extrema principles and to the variational methods introduced by Fermat. Jakob Bernoulli was also the first to use the word “integral”. The first calculators,6 archetypes of the modern electronic computers, appeared at the same time [19, 20]. Their appearance was favoured by the bureaucratisation of the modern states, by the increased importance and proliferation of the maritime trade and by military requirements. It is controversial7 [21] whether the first calculator was a product of Leonardo da Vinci’s mind (Fig. 3.14a). John Napier implemented a mechanical system to perform multiplications, known as Napier’s bones (Fig. 3.14b), described in Rabdologiae, seu numerationis per virgulas, libri duo, Edinburgi (1617). In 1623, the German Wilhelm Schickard (1592–1635) built the calculating clock, a machine that developed sums and subtractions, processing numbers with up to 6 digits; it included a sounding mechanism that reported the saturation of its computation capacity. In 1640, Johann Ciermans (1602–1648) wrote Disciplinae mathematicae, in which he described a device equipped with wheels for the performance of multiplications and divisions. In 1644, Blaise Pascal (1623–1662) built Pascaline (Fig. 3.15a), a calculator that performed sums, initially making use of 5 digits; he sold from 10 to 15 machines: the last ones were capable of using 8 digits. In the same period, unaware of Pascaline, Samuel Morland (1625–1695) first invented a machine to perform sums and subtractions, then another machine that performed multiplications and extracted roots; they are illustrated in The description and use of two arithmetick instruments (1673). In 1671, Leibniz designed a machine, which was built in 1694, capable of performing multiplications, divisions and square roots (Fig. 3.15b); its operation, based on the use of only two digits (0 and 1), earned Leibniz the reputation of founder of binary algebra. In 1786, Johann Helfrich von Müller (1746–1830) conceived the difference engine, a machine intended to be used for the tabulation of polynomials; unfortunately, he was unable to raise the funds to build it and his project was forgotten. In 1820, the French Charles Xavier Thomas de Colmar (1785–1870) invented “Arithmomètre”, the first calculator produced on a large scale. The most prominent figure of this historical age was the English mathematician and inventor Charles Babbage (1792–1871). In 1832, he built a difference engine (Fig. 3.16a) similar to Mueller’s one, used by the British Admiralty to process nautical charts; it performed algebraic operations on second-order polynomials, using numbers with up to 6 digits. Babbage 6 The

oldest device to perform repetitive calculations, the abacus or counting-frame, was known since the twentieth century in China. 7 In 1967, a group of American researchers uncovered, in the National Spanish Library in Madrid, some finds of Leonardo including the drawing in Fig. 3.14a, now known as the Madrid Code. Roberto Guatelli remembered that a similar drawing was present in the Atlantic Code. He put the two diagrams side by side and, in 1968, built a replica of what is nowadays called Leonardo da Vinci’s calculator. Many point out that this replica is based on interpretations and intuitions that are absent from Leonardo’s works.

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Fig. 3.14 a Leonardo da Vinci’s calculator; b Napier’s bones [6]

Fig. 3.15 a Pascaline [21]; b Leibniz’s arithmetic machine [6]

also thought over the idea of automatically performing all the arithmetic operations and connecting their results so as to solve, at least as a matter of principle, any algebraic problem. He then went as far as designing, in 1836, the analytical engine, considered by many as the ancestor of the modern digital computers.8 Drawing on and developing the intuitions of Babbage, in 1843, two Swedish printers, George Scheutz (1785–1875) and his son Edward (1821–1881), built a difference engine, equipped with a printer, which performed algebraic operations on third-order polynomials. The Swedish government funded its development, and in 1853 George and Edward Scheutz put into production a machine operating with 15 digits on fourth order polynomials (Fig. 3.16b) [20]. In the meantime, Leibniz’s intuitions about the binary system were reviewed and developed by George Boole (1815–1864), the Irish mathematician who codified the algebra of logic in The laws of thought (1854); he used the 0 and 1 digits to represent false or true propositions; he also algebraically expressed the semantic 8 Using

the description provided by Ada Lovelace Byron (1815–1852), the daughter of the English poet and a disciple of Babbage, the analytical engine was made up of four parts: a memory store, where the temporary data used for the calculation were stored; an arithmetic unit, called mill and driven by a steam engine, in which the operations on the numbers taken from the memory were carried out; a transfer device between the memory and the arithmetic unit, working both ways; a device for the input of data and the output of results. This machine, amazingly modern for its time, performed logic control operation and made use of punched cards on which the calculation program and the numeric data were recorded.

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Fig. 3.16 Babbage’s (a) and Scheutz’s (b) difference engines [20]

behaviour of conjunction (AND), negation (NOT) and opposition (OR). In 1870, William Stanley Jevons (1835–1882) applied this new concept to present the logical engine to the Royal Society, a calculator capable of managing functions of the IF … THEN type. In 1885, in Chicago, Dorr Felt (1862–1830) built the “Comptometer”, the first calculator using keys to enter numbers; in 1889, he invented the desktop printing calculating machine. In 1890, Herman Hollerith (1860–1929) processed the data of the US census at the Massachusetts Institute of Technology (M.I.T.), using punched card tabulators. The year 1892 saw the appearance of the first model of the mythical Brunsviga calculating machine, built in Germany by the Grimme Natalis firm of Braunschweig; it was a fully mechanical machine, in which figures were set through cursors controlled by levers manually handled by the operator, while the execution command (to perform the four operations) was assigned to a crank. Actually, despite the impulse calculators received during the nineteenth century from the intuitions of Babbage, the new needs of a renewed society and the possibility of using industrial mechanical manufacturing, humanity, science and technology were not yet ready to implement the advances that would unfold around the middle of the twentieth century (Sect. 5.3).

3.4 Probability Theory The probability theory arose between the sixteenth and the seventeenth century as an evolution of the calculation of permutations and combinations, spurred by the interest in gambling [22, 23]. In 1526, Gerolamo Cardano (1501–1576) wrote Liber de ludo aleae, the first important contribution to probability theory; the manuscript, found in 1576, after Cardano’s death and published in 1663, analysed the possible combinations deriving from the throw of two or three dice; it also dedicated some chapters to the history of gambling. Cardano also published Practica arithmeticae generalis (1539), where he

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studied the distribution of the stake in gambling, and Opus novum de proportionibus numerorum (1570), a treatise about combinatorial calculus. Within its production as a whole, Cardano introduced embryonic forms of the rule of the product of the probabilities of independent events, developed correct calculations about the number of possible results of experiments with and without repetition and came close to concepts like statistic regularity, the law of large numbers, the definition of probability as a ratio of equiprobable events and the meaning of mathematical expectation. In 1556, in Venice, Niccolò Fontana (Tartaglia, 1499–1557) published Trattato generale di numeri e misure, where he delved into various combinatorial calculus issues. Among these, the most famous is the homonymous triangle, whose nth row, from the top down, lists the binomial factors:   n! n = k k!(n − k)!

(k = 1, . . . , n)

(3.1)

i.e. the coefficients of k order of the expansion of (x + y)n . Galileo Galilei (1546–1642), attracted by gambling, approached this problem in Considerazione sopra il gioco dei dadi (published in 1718), which provided the number of possible outcomes of the launch of three dice and a procedure suitable for the throw of any number of dice. The essential contribution of Galilei to probability theory concerned measurement errors (Dialogo, 1632), an issue that became important after the discovery of the telescope and the first astronomical observations (Sect. 3.1). According to Galilei, “in every combination of observations there is some error, which I believe to be absolutely unavoidable. (…) We know too well that measuring only one height of the pole, with the same instrument, in the same place, by the same observer who repeats the observation thousands of times, a variance of one or, sometimes, of many minutes, will still remain.” He then came up with estimating the errors, reaching the conclusion that small errors are common, whereas larger errors are uncommon. Galilei also suggested discarding any observations providing impossible results. Around the middle of the seventeenth century, the study of the combinatorial calculus and the interest towards gambling produced remarkable advancements, especially thanks to Blaise Pascal (1623–1662), Giles Persone de Roberval (1602–1675), Pierre de Fermat (1601–1665), Christiaan Huygens (1629–1695) and Gottfried Wilhelm von Leibniz (1646–1716). They introduced the modern notation of the discipline, applied the rule of the sum and multiplication of probabilities, used the concepts of statistical dependence and independence and specified the meaning of mathematical expectation. Everything started when a Frenchman, Chevalier de Méré, addressed Pascal and Roberval the following problem: “Two players agree to play a certain number of games. The winner is the one who first wins S games. The play is discontinued ahead of time, when the player who has the advantage has won a < S games and the other one has won b < S games. The problem is how to divide the stakes”. Pascal was impressed by this question and in 1654, wrote Fermat a letter to invite him to analyse

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the problem. This led to an intensive exchange that is considered a turning point, though not exactly the start, of the probability theory. It brought Pascal to publish Application of the arithmetic triangle to the theory of combinations, namely the deed of foundation of combinatorial calculus. Pascal resumed the studies by Tartaglia and proved that, if a coin was tossed n times, the number of different ways the head (or tail) outcome can occur for k times is the binomial factor provided by Eq. (3.1); the probability of occurrence of such event depends on that factor. In 1655, Roberval informed Huygens about the debate between Pascal and Fermat. Huygens, who was in turn impressed by the problem, wrote De ratiociniis in ludo aleae, a treatise published in 1657 and republished several times; it had such a large diffusion to become, in the early eighteenth century, the basic textbook about probability theory. It ended with the formulation of five famous problems (two suggested by Fermat and one by Pascal), the solution of which was not provided, which became a test bench for the scholars of this subject.9 Leibniz (1646–1716) was also attracted by this matter, and in 1666 published Dissertatio de arte combinatoria, where he illustrated the state of the art in combinatorial calculus and developed new theorems concerning permutations and combinations with infinite repetitions. The early eighteenth century was dominated by Ars conjectandi (1713), the posthumous work, divided into four parts, by Jakob Bernoulli (1654–1705) that marked the start of a new era of the probability theory. The first part, A treatise on possible calculations in a game of chance of Christian Huygens with J. Bernoulli’s comments, summarised the main results published by Huygens, enriched by the remarks of Bernoulli, clarified the concept of arithmetic mean, evaluated the additive probability of dependant events and extrapolated the binomial probability function, also known as Bernoulli formula. It provided the Pm,n probability that an event with constant probability of occurrence equal to p takes place m times in n independent experiments:  Pm,n =

 m p m (1 − p)n−m n

(3.2)

The second and the third parts of Bernoulli’s book, The doctrine of permutations and combinations and Application of the theory of combinations to different games of chance and dicing, covered the combinatorial calculus and solved specific problems. Pars quarta, tradens usum et applicationem precedentis doctrinae in civilibus, moralibus et oeconomicis is the core of the book and contains the proof of the first limit theorem of the probability theory, the law of large numbers in simple form. Bernoulli named it main proposition, but today it is known as the golden theorem; its modern enunciation states that “if the probability of occurrence of an event A in a sequence of independent experiments is constant and equal to p, then, for any 9 In 1687, a book attributed to Baruch Spinoza (1632–1677) was found; the second part contained the

solutions of various problems concerning probability theory (Reeckening van kanssen), including the first problem of Huygens. The French mathematician Pierre Rémond de Montmort (1678–1719) was the first to provide the complete solution of the five problems in Essai d’analyse sur les jeux de hazard (1708).

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positive value ε, it is possible to affirm with probability close to 1 what is desired that, for a large enough number n of experiments, the m/n − p difference is smaller than ε in absolute value: P{|(m/n) − p| < ε} > 1 − η

(3.3)

where η is an arbitrarily small number. Thanks to the work of Jakob Bernoulli, in the second half of the eighteenth century, the probability theory drew new vigour from the interest of many science domains, astronomy to begin with. The studies inspired by gambling, on the other hand, were still alive and well. Thomas Simpson (1710–1761) wrote The nature and laws of chances (1740), The doctrine of annuities and reversions (1742), and a paper that appeared in a collection of his works, Miscellaneous tracts on … subjects in mechanics, physical astronomy and speculative mathematics (1757), where he introduced continuous distributions. Reverend Thomas Bayes (1702–1763) laid the foundations of his homonymous formula about the interpretation of probability, providing a measure of how a subjective belief can be changed to take evidence into account. Bayes’ intuitions were revised and updated by Richard Price (1723–1791) in a religious treatise, An essay towards solving a problem in the doctrine of chances by the late Rev. Mr. Bayes, F.R.S., communicated by Mr. Price in a letter to John Canton, A.M., F.R.S., published in 1763.10 In the same year, King Frederick II of Prussia (1712–1786), being short on money for the state coffers, invited Leonhard Euler (1707–1783) to study a national lottery. Euler accepted and gathered the elements of his proposal in Sur la probabilité des séquences dans la Lotterie Génoise, where he studied the probability of occurrence of a number in a sequence of five draws. He continued treating this issue in Reflectiones of a special type of lottery, … and Solutio quarundam quaestionum difficiliorum in calculo probabilium (1785), which were anyway still tied to the solution of specific problems. In 1768, Daniel Bernoulli (1700–1782) (son Johann and grandson of Jakob) published De usu algorithmi infinitesimalis in arte conjectandi specimen, where he introduced the use of the differential calculus in probability theory. He applied the new principles in the medical and moral sectors. In the same period, the naturalists started using probability concepts to verify some assumptions of their sector. One of the first scientists to follow this path, the French Georges-Louis Leclerc Buffon (1707–1788), is known for a treatise in 44 volumes, Histoire naturelle, which broke away from the biblical view of creation and proposed thesis based on observations and comparisons; it had a strong influence on its contemporaries and was a masterpiece of the Enlightenment. Buffon used the concept of probability to justify the hypothesis that the six planets known at his time

10 Some affirm that Bayes’ theorem had been discovered, some years before, by the English scientist

and mathematician Nicholas Saunderson (1682–1739).

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(Earth, Mercury, Venus, Mars, Jupiter and Saturn) had been generated by a collision between the sun and a comet (Epochs of nature, 1740). Buffon’s main contribution to probability theory dates back to 1777 and consists of the solution of the famous Buffon’s needle problem. Originally intended to obtain the value of π, it is regarded by many as the foundation deed of the Monte Carlo method. To illustrate it [24], consider a horizontal plane on which parallel lines are drawn at even intervals equal to a. A needle, with length equal to b < a, is randomly dropped on the plane. The problem consists of finding the probability that the needle intersects a line. For this purpose, let us define X as the distance from the mean point of the needle to the closest line (0 < x ≤ a/2) and Y as the acute angle formed by the needle, or by its extension, with the parallel lines. The needle crosses a line if X ≤ (b/2) sin(Y ) (Fig. 3.17a), an event with probability P = 2b/ (πα). Now, repeatedly drop the needle and let us define P as the ratio between the number m of times it crosses a line and the number n of times it is dropped; the estimate π = 2bn/ (ma) is obtained from P = m/n; the greater the number n of the experiments, the higher is its accuracy (Fig. 3.17b). Jean Le Rond d’Alembert (1717–1783), too provided contributions to probability theory (Reflexions sur le calcul probabilités, 1761), associating his name to great intuitions and sensational blunders. The great intuitions related to the definition of probability for not equipossible events and the limit value below which the probability is negligible. The most famous blunder appeared in Croix ou pile, in the fourth volume of the Encyclopédie ou Dictionnaire raisonne des sciences, des arts et des mestiers (1751–1772) written with Denis Diderot (1713–1784); D’Alembert affirmed that the probability that heads came down when a coin was tossed increased every time the outcome was tails. Taking a cue from Galilei’s astronomical measurements, the probabilistic representation of errors was the subject of systematic studies from the early nineteenth century. Robert Adrain (1775–1843), an obscure Irish mathematician, approached the problem of random errors in a specific field, obtaining the normal distribution as a generalisation of the results obtained (Research concerning the probabilities of the errors which happen in making observations, 1808). Almost simultaneously, Carl Friedrich Gauss (1777–1855), a famous German mathematician and astrologist,

Fig. 3.17 Buffon’s needle problem [24]: a geometry; b convergence of the solution

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treated errors in the study of celestial bodies, obtaining the same law under general conditions (Theoria motus corporum coelestium in sectionibus conicis solem ambientium, 1809). Even though Gauss’ publication came after Adrain’s,11 the impact of his solution was so strong that since then the normal law was called “Gaussian” ever since. Using his notation, the density and distribution functions resulted:   h f () = √ exp −h 2 2 ; π

F() =

1 [1 + θ(h)] 2

(3.4)

 is the error, h12 is a measure of the accuracy of observations and θ is a function of  called error function: 2 θ(t) = √ π

t

  exp −τ2 dτ

(3.5)

0

the values of which are tabled. Gauss used the least squares method to estimate the value of h, claiming its authorship in relation with a previous paper of his dated 1795. Pierre-Simon de Laplace (1749–1827), French astronomer and mathematician, treated probability in two innovative works, Théorie analytique des probabilités (1812) and Essai philosophique sur les probabilités (1814). After having considered not fully known events as probable (“probability is relative in part to ignorance, in part to our knowledge”), Laplace introduced a subjective criterion according to which two events were equally possible if there was no reason to believe “that one of them will occur rather than the other”. In the class of such events, called “equipossible”, he formulated the definition of probability that is nowadays known as classic or aprioristic: “the probability P(A) of the event A is equal to the ratio between the number of possible occurrences favourable to A and the number of all the possible occurrences of the experiment”. Generalising a previous proof of Abraham de Moivre (1667–1754), he also obtained a result today known as the Laplace’s or de Moivre–Laplace’s theorem: for a large enough number of experiments, the binomial probability distribution (Eq. 3.2) tends towards the normal one (Eq. 3.4). The works of Simeon Denis Poisson (1781–1840) in the probabilistic field are collected in Recherches sur la probabilité des jugements en matière criminelle et en matière civile (1837), aimed at determining the probability that the decisions of the courts are right or wrong. Having proved that Bernoulli’s theorem (Eq. 3.3) could not be applied to these problems, Poisson arrived to the law of large numbers in general form: “if n independent trials are performed, resulting in the occurrence or non-occurrence of an event A, and the probability of occurrences of events is not the same in each one of the trials, then, with probability as close to unity as desired, 11 The first expression of the normal distribution dates back to 1753, when Abraham de Moivre (1667–1754), a French scholar of gambling, obtained a particular form of the same as a limit case of the binomial distribution with the increase of the experiments. 12 2 h2 σ2 = 1, being σ the standard deviation of the error.

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one can assert that the frequency m/n of the occurrence of an event A will deviate arbitrarily little from the arithmetic mean p¯ of probabilities of occurrences of events in the individual trials.” In mathematical terms: ¯ < ε} = 1 lim {|(m/n) − p|

n→0

(3.6)

where ε is an arbitrarily positive number. If the probability of A is constant in every experiment, and then p¯ = p, Eq. (3.6) coincides with Eq. (3.3). In the same book, Poisson demonstrated that, for small values of p and large values of n, the binomial distribution (Eq. 3.2) tends towards a limit form, called law of the small numbers: Pm,n =

λm −λ e m!

(3.7)

where λ = np is the average number of A events (with constant probability equal to p) that occur during n experiments. Equation (3.7) was called Poisson distribution for the first time by the Polish statistician Ladislaus Bortkiewicz (1868–1931) in 1898. It is a signal of the growing interest towards this subject in the countries of the Eastern Europe, where Russia became, from the second half of the nineteenth century, the cradle of outstanding developments. Following in the footsteps of the pioneering activity of Sigmund Revkovskii (1807–1893), Victor Yakovlevich Bunyakovskii (1804–1889) and Mikhail Vasil’evich Ostrogradskii (1801–1862), the School of Saint Petersburg was opened (Sect. 5.2) where Pafnutii Lvovich Chebyshev (1821–1894) was the undisputed master. Chebyshev only wrote four works on the probability theory; each one of them is fundamental. In the first, An essay of elementary analysis of probability theory (1846), he laid the basis for obtaining the limit of the errors produced by approximate solutions. In the second, Elementary proof of a general proposition in probability theory (1846), he provided a general demonstration of Poisson’s theorem (Eq. 3.6). In the third, On mean values (1867), he obtained the homonymous inequality: P(|X − μX | ≤ ε) ≥ 1 −

σX2 ε2

(3.8)

where X is a random variable, μX and σX are the mean and the standard deviation of X, ε an arbitrary positive number. In the fourth, On two theorems concerning probabilities (1867), he covered the law of large numbers and the central limit theorem. As regards to the first subject, he obtained a general law that included Eqs. (3.3) and (3.6) as particular; it is known as Chebishev’s theorem and stipulates that “for a value of n large enough, it is possible to affirm with probability arbitrarily close to 1 that the arithmetic mean of the sum of n random variable (X 1 , X 2 , …, X n ) deviates arbitrarily little from the mean of their mathematical expectations (μX1 , μX2 ,… μXn )”:

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 n n 1  1   lim P  Xi − μX  ≤ ε = 1 n→∞ n n i=1 i  i=1

(3.9)

where ε is an arbitrarily positive number. As regards to the central limit theorem, Chebyshev proved that “if the mathematical expectations of n random variables (X 1 , X 2 , …, X n ) are null, and if the mathematical expectations of all their powers are smaller than a finite limit, then the distribution of their sum divided by the square root of two times the sum of their variances tends, for n tending to infinity, to the distribution of a normal random variable with null mean and unitary variance”. He also developed many theorems about the moments of the random variables.

3.5 Mechanics in the Sixteenth and Seventeenth Centuries The evolution of mechanics in the sixteenth and seventeenth century followed tracks parallel to the evolution of mathematics (Sect. 3.3). It is possible to state that many developments of mechanics were made possible by the new instruments of mathematics, and many developments of mathematics were inspired by the need to solve mechanical problems. It was not by chance that the great scholars of these two disciplines often were the same, and that in this period, the frontiers separating them were vague and almost intangible [1, 2, 6, 7, 9, 14, 25]. The mechanics of the sixteenth century was dominated by the contributions of four Italian scientists—Fontana, Cardano, Benedetti and del Monte - and of the Dutch mathematician and engineer Stevin. Niccolò Fontana (Tartaglia, 1506–1557) dealt with dynamic problems, and with the fall of bodies in particular, in De ratione ponderis, Nova scientia (1537) and Questa ed inventioni diversi (1546). Gerolamo Cardano (1501–1576) covered the lever, and simple machines in general, in De subtilitate (1551) and Opus novum (1570). Giovanni Battista Benedetti (1530–1590) perfected the concept of impetus and discussed the fall of bodies in Diversarum Speculationum (1585). Guido Ubaldo del Monte (1545–1607) developed the principle of virtual works in Mechanicorum liber, a text read and assimilated by Galilei, Descartes and Lagrange. In 1586, Simon Stevin (1548–1620) published Beghinselen der Weegconst, where he provided great contributions to the statics of solids and fluids, laying down the embryonic idea of the fundamental law of hydrostatics (the pressure at a point of a fluid at rest is the same in all directions); he also described an experiment carried out with Jan de Groot (1554–1640) [2] in which two lead spheres, one of them weighing ten times the other, were simultaneously dropped from a height approximately equal to 10 m and reached the ground at the same time. Hyppomnemata mathematica (1605–1608), the collection of the main scientific works by Stevin, contains a study of the inclined plane and the resolution of forces through the parallelogram rule; this is why he is considered the initiator of graphic statics. In the same work, there was

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an enunciation and a proof of the principle of virtual works, not very removed from the currently acknowledged one. Between the late sixteenth century and early seventeenth, Galileo Galilei (1564–1642) (Sect. 3.1) imparted an epochal change to mechanics. In 1583, he discovered the law of pendulum isochronism, that is, the independence of its oscillation period from the amplitude of its motion; it is said that the discovery stemmed from a visit to the Cathedral of Pisa and from the observation of the oscillation of a candlestick, of which Galilei measured the period by counting the beats of his pulse. Between 1589 and 1592, he drew fundamental principles of kinematics, collected in De motu, first and foremost the law according to which the fall time of a body is independent of its weight; for this reason, he carried out a famous experiment similar to Stevin’s one: he simultaneously dropped from the top of the Tower of Pisa two bodies having the same shape but different weight, which reached the ground in the same instant [9]. In 1603, he founded the Accademia dei Lincei in Rome and started new studies about the motion of bodies along inclined planes, linking this problem with the oscillations of the pendulum. Afterwards, during the abjuration in his Arcetri villa, Galilei wrote Discorsi e dimostrazioni matematiche intorno a due nuove scienze attinenti alla meccanica e i movimenti locali (1638), which defined the separation between statics and dynamics (Sect. 3.1). There, he introduced the modern concept of force (“what changes the state of rest or of uniform or straight motion of a body”) and the principle of inertia (“everybody perseveres in its state of rest or of uniform motion in a straight line, except in so far as it is compelled to change that state by impressed forces”). The fundamentals of statics introduced by Stevin and Galilei were taken up by Gilles Personne de Roberval (1602–1675), who developed the parallelogram and the funicular polygon rules in Traité des mouvements composés, a work published by the Académie des Sciences in 1693. Pierre Varignon (1654–1722) enunciated the rules still adopted to compose forces and to determine their resultant. He also introduced the cardinal law of statics, affirming that the resultant force and moment of a system of balanced forces are null (Nouvelle mécanique, posthumously published in 1725). René Descartes (1596–1650) approached the collision problem in Discours de la mèthode (1637); he studied the collision of two marbles, recognising the principle of momentum conservation. The same concept was further investigated by John Wallis (1616–1703), who on 26 November 1668 presented to the Royal Society A summary account given by Dr. John Wallis of the general laws of motion, in which he studied the collision between two inelastic bodies moving along the straight line joining their centres of gravity. On 17 December 1668, Sir Christopher Wren (1632–1723), the architect renowned for the project of the St. Paul Cathedral and of many public buildings of his age, illustrated the law of elastic collision to the Royal Society; it was empirically deduced by experimental tests only. Similar tests, carried out by Edme Mariotte (1620–1684), were illustrated in Traité de la percussion ou choc des corps (1677). In 1673, Christian Huygens (1629–1695) acquired considerable renown from Horologium oscillatorium, sive de motu pendulorum ad horologia aptato demonstrationes geometrica, in which he treated, often for the first time, the theory of the

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compound pendulum and of the centre of oscillation, the determination of the gravity acceleration through the use of the pendulum laws, the principles of the centripetal and centrifugal force and the theorem of live forces; he also laid the basis of the geometry of mass, introducing new geometrical–mechanical entities, such as the static moment and the moment of inertia. The study of the pendulum motion was the reference paradigm for the description of any oscillatory phenomenon; for this reason, it represented a decisive step towards the study of all the dynamic problems (Sect. 3.10). The mathematical laws about the collision issue (Tractatus de motu corporum ex percussione, 1703) by Huygens also were remarkably important. Attracted by the astronomical studies of Kopernik, Brahe, Kepler and Galilei (Sect. 3.1), and supported by the advances made by mathematics and mechanics in the first half of the seventeenth century, in 1666, Robert Hooke (1635–1703) announced to the Royal Society he had formulated “a system of the world very different from any yet conceived”. Thanks, in part, to a long collaboration with the astronomer Edmund Halley (1656–1742), he demonstrated he had perceived the universal gravitation law, claiming that all the celestial bodies mutually attract each other. He also reached the conclusion that the attractive force exercised between two bodies is inversely proportional to the square of the distance among them. He divulged this result during a famous lecture, The nature of comets, held in 1682, which was the prelude to Newton’s great discoveries. Isaac Newton (1642–1727) was born the same year Galilei died. He worked for more than 20 years without giving away the exceptional results he had obtained in various fields of knowledge. According to the story, his granddaughter told Voltaire (François-Marie Arouet, 1694–1778) and later divulged by the writer, Newton’s studies originated from a trivial episode, the fall of an apple from a tree during a period he spent in the country when he was little more than twenty years old, and from the belief that the motion of the apple and of the moon derived from the same force. Incited by Halley, Hooke and Wren, Newton let himself be persuaded to report his discoveries to the Royal Society in 1685. Two years later, he published Philosophiae naturalis principia mathematica (1687), his fundamental treatise in three volumes. In the introduction to the first volume, Newton summarised the results previously obtained about collision, remarking that nobody is perfectly elastic; the velocity of the colliding bodies is thus reduced by a coefficient of restitution depending on the material of the bodies. Newton himself performed measurements through which he obtained this quantity for wood, cork, steel and glass. Having exhausted the issue of collision, Newton formulated the three laws of motion. The first, called law of inertia, states that “everybody perseveres in its state of rest or of uniform motion in a straight line, except in so far as it is compelled to change that state by impressed forces”. The second, known as the fundamental principle of dynamics, asserts that the “change of motion is proportional to the moving force impressed, and takes place in the direction of the straight line in which such force is impressed”. The third, known as the principle of action and reaction, affirms that “reaction is always equal and opposite to action; that is to say, the actions of two bodies upon each other are always equal and directly opposite”.

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Actually, the first law of the motion was taken from Galilei and Descartes; the second one was implicit in the works of Galilei; Newton himself acknowledged that many principles of his laws were already contained in the works of Galilei, Wallis, Huygens and Wren. His main contribution, therefore, lies in the accurate and concise definitions of mass, weight,13 momentum, inertia and force, and also in the exemplary and succinct formulation of the three laws. They opened unlimited prospects for a new discipline, dynamics (Sect. 3.10), which became the foundation of the studies concerning fluids (Sect. 3.6), structures (Sects. 3.9), meteorology (Sect. 4.1) and aerodynamics (Sect. 4.2). In the third volume, applying the three laws of motion together with Huygens’ theorems about centrifugal and centripetal force and with the principles of Hooke and Halley on the mutual attraction among bodies, Newton formulated the universal gravitation law, asserting that “there is a gravitational attraction between every two bodies in the universe, and this force is proportional to the quantity of matter of each, and varies reciprocally as the square of its distance”. Starting from this enunciation he deduced, in a bit more than one page, the three laws of Kepler on the motion of planets (Sect. 3.1). The second volume had peculiarities making it different from the other two. Whereas the first and the third volumes flawlessly solved solid mechanics problems debated for a long time, in the second volume Newton covered a largely unexplored subject, fluid mechanics; he did so through a fresh, even if not always flawless, approach [25, 26], creating theories about the elasticity of air, the flow of fluids through orifices, the propagation of waves through water, the oscillation of water inside pipes, the internal friction of fluids, the resistance of bodies in gases and liquids, the propagation of sound in the air. In that same book, two contrasting and widely different views appeared [26]. The first one dealt with the fluid as a continuous medium and led to the viscous or Newtonian model (Sect. 3.6). The second provided a molecular representation of the fluid, considered as “a mass of identical particles, freely arranged at the same distance from each other”; thanks to this model, Newton obtained the law of the three proportions about the resistance of bodies in fluids (Sect. 4.2) and the first mathematical theory of sound (Sect. 3.10); his approach represented reference for subsequent research, carried out by Navier and Poisson, about the constitutive laws of fluids and solids (Sects. 3.6 and 3.9). As a whole, many consider Newton’s treatise as the most important contribution to science; it certainly exerted the strongest influence on the contemporary and future scientific thought.

13 The distinction between mass and weight enunciated by Newton implicitly appeared in the works of Galilei and is explicitly mentioned in a writing of Giovan Battista Baliani (1582–1666), Captain of the Genoese Archers, who distinguished “moles” from “pundus” [2].

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3.6 The Coming of Fluid Dynamics In 1628, Benedetto Castelli (1577–1644) published Della misura delle acque correnti, in which he introduced the law of continuity in the form AV = constant (where A is the cross-section of the flow in a duct and V is the velocity). Actually, when this happened, the same expression had already been proposed by Leonardo da Vinci (Sect. 2.10); its discovery, however, occurred at a much later date. In 1641, inspired by Galilei and Castelli, Evangelista Torricelli (1608–1647) wrote De motu gravium naturaliter discendentium et proiectorum, published in 1644 in Opera geometrica. He observed that the liquid spurt flowing out from a hole on the bottom followed a parabolic trajectory; he also demonstrated that the velocity of the outflow is equal to the velocity acquired by a body freely falling from the height h of the liquid surface (with respect to the hole); it is then equal to the square root of 2gh, where g is the gravity acceleration. Thanks to this demonstration many view Torricelli as the precursor of fluid dynamics. Isaac Newton (1642–1727) gave a new meaning to this discipline in 1687. In the second volume of Philosophiae naturalis principia mathematica (Sect. 3.5), he introduced the concepts underlying the viscous fluids, subsequently called the Newtonian ones. Using a famous example of Theodore von Karman (1881–1963) (Sect. 5.1) [27], “suppose that a book containing many pages is placed on a desk and the upper cover is slowly pushed parallel to the surface of the desk. The pages slide over each other, but the lower cover sticks to the desk. Similarly, fluid particles stick to the surface of a body”; the fluid velocity increases with the distance from the surface according to a gradient that causes a friction of viscous nature between subsequent layers of the fluid; the adherence of the fluid to the surface of the body is due to the molecular structure of the fluid and of the body (Fig. 3.18a). Newton illustrated the same principle thanks to a cylinder rotating in a fluid with angular velocity ωc ; it determines a rotatory motion of the fluid with tangential veloc-

Fig. 3.18 a Fluid flow on a surface at rest; b fluid rotating by the motion of a cylinder

3.6 The Coming of Fluid Dynamics

125

ity inversely proportional to the distance from the axis of the cylinder (Fig. 3.18b). Anticipating such principles by almost three centuries, he affirmed that “the resistance arising from the want of lubricity in the parts of a fluid is proportional to velocity with which the parts of the fluid are separated from each other”, that is, to the velocity gradient dV /dz [26]. Translated in modern language, the shear stress in the fluid is given by: τ=μ

dV dz

(3.10)

where μ is the viscosity coefficient and z the axis perpendicular to the motion direction. The studies of Castelli, Torricelli and Newton represent the prodromes or foundations of the great advancements taking place in the eighteenth century, especially thanks to the evolution of the mechanical and mathematical knowledge. It was not by chance that fluid dynamics received great stimuli by scholars, first of all, Daniel Bernoulli, d’Alembert and Euler, who gave essential contributions to a wide spectrum of scientific disciplines [6, 14, 25, 26]. In parallel with other sectors treated in this chapter, the knowledge of fluid dynamics, however, also evolved by virtue of the growing symbiosis between theory and experience, which indeed became a distinctive element of the researches carried out in the eighteenth and nineteenth century. An organised and systematic treatment of a subject so complex and articulate goes beyond the objectives of a book that intends to highlight, as regards to this historical period, the aspects most connected to the development of the knowledge of wind and its effects. Thus, a summary picture of the evolution of the main physical and mathematical concepts of fluid dynamics is provided hereinafter; the reader may refer to Sect. 4.2 for a presentation of the experimental researches carried out in the field of the resistance of bodies immersed in fluids, especially in the air. Daniel Bernoulli (1700–1782) studied at the University of Basel under his father Johann Bernoulli (1667–1748). In 1724, he published Mathematical exercises; this work brought him so much fame that Peter the Great (1672–1725) invited him to the Academy of Sciences of Saint Petersburg, together with his brother Nikolaus Bernoulli (1695–1726), offering him the chair of mathematics. In 1725, the two Bernoulli brothers moved to Russia, where Nikolaus died eight months later. Daniel would have liked to return to Switzerland, but he was encouraged to remain by his father, who in 1727 sent to him one of his best disciples, Leonhard Euler (1707–1723). From here started a collaboration between Bernoulli and Euler, destined to encompass many scientific fields and to continue after the return of Bernoulli to Basel in 1733. In the period he spent in Saint Petersburg, Daniel Bernoulli wrote Hydrodynamica, sive de viribus et motibus fluidorum commentarii, a work published in Strasbourg in 1738, regarded by many as the foundation deed of fluid dynamics. In this treaty, Bernoulli clarified the concept of continuity or conservation of the mass (“all particles of the liquid in a plane perpendicular to the flow have the same velocity which is inversely proportional to the cross-section”), formulated kinetic theory of gases (Sect. 3.8), defined the first relation between the pressure p and the velocity V of

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fluids in motion. For this, he made use of the Newtonian mechanics and of the vis viva (live force) concept, introduced by Leibniz in 1695 but ascribed to his father Johann by Daniel Bernoulli; accordingly, he reached the result that the state of a fluid with density ρ is governed by the following expression: 1 p + ρ V 2 = constant 2

(3.11)

Equation (3.11) represents the embryonic form of the law that today is known as Bernoulli’s principle. On the other hand, it is interesting to notice how the original writings of Bernoulli neither include any reference to the third addend of the famous invariant trinomial, the term associated to the potential of the gravitational force, nor explicitly report Eq. (3.11) [26]. Bernoulli even got around its application, evaluating the pressure of the fluid through a clever stratagem [14]. It is worth noting that the first to realise the weakness of this reasoning was his father. He perfected it in Nouvelle hydraulique, published in 1743, which Johann Bernoulli predated to 1732 to obtain the authorship of the ideas; this is one of the rare cases of scientific disputes between father and son [9]. Jean le Rond d’Alembert (1717–1783), French mathematician and encyclopaedist14 [28], in 1743, published Traité de dynamique, in which he harmonised the concepts of momentum and energy. He applied this treatment to fluid mechanics in Traité de l’équilibre et des mouvements des fluides pour servir de suite au traité de dynamique (1744) and in Essai d’une nouvelle théorie sur la réesistance des fluides (1752), setting up an elegant formulation that disregarded viscous forces in fluids since they are much smaller than inertial ones. On such bases, he studied the motion of a body immersed in an ideal fluid, which is an inviscid fluid, and determined, applying Bernoulli’s principle, the distribution of the pressure exerted by the fluid on the surface of the body. He obtained an astonishing result: the integral of the pressure gave rise to a null resultant force. Reporting the judgement expressed by Karman [27] two centuries later, this meant “that purely mathematical theory leads to the conclusion that if we move a body through air and neglect friction, the body does not encounter resistance”. D’Alembert returned to this subject in 1768 (Opuscoles mathématiques), enunciating his famous paradox: “I do not see then, and I admit, how one can explain the resistance of fluids by the theory in a satisfactorily manner. It seems to me on the contrary that this theory, dealt with and studied with profound attention, gives, at least in most cases, resistance absolutely zero; a singular paradox which I leave to geometricians to explain”. Regardless of this result, which all the same became a cornerstone of the debate to come about fluid dynam14 Together with Denis Diderot (1713–1784), a French man of letters and philosopher, D’Alembert conceived and directed the redaction of the Encyclopédie ou Dictionnaire raisonne des sciences, des arts et des mestiers (1751–1772), a splendid picture of the knowledge of man in the eighteenth century. L’ Encyclopédie consists of 18 volumes: the first 17 made up its body, and the eighteenth contains tables, supplements and illustrations. D’Alembert dissociated himself from Diderot in 1757, because of their different views about science and scientific method, when the first 7 volumes had already been written.

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ics, d’Alembert provided ideas essential for the development of the discipline. In particular, he introduced the use of the fluid velocity and acceleration components; he also first expressed the principle of continuity in differential form [14]. Leonhard Euler (1707–1783) gave essential contributions to multiple fields of mathematics, where he founded the calculus of variations and developed the theory of complex numbers, of structural mechanics (Sect. 3.9), of vibration mechanics (Sect. 3.10) and of fluid mechanics, in which he provided key elements for the mathematic formulation of the laws of hydrostatics and hydrodynamics. Taking cue from Découverte d’un nouveau principe de mécanique (1750), a paper fundamental for many fields of mechanics (Sect. 3.10), in 1752, Euler wrote Principia motus fluidorum (published in 1761), in which he developed the principle of mass conservation introduced by Daniel Bernoulli. In particular, making use of the new concepts about differential equations and partial derivatives, he expressed the continuity equation for incompressible fluids in the following form: ∂v j =0 ∂x j

(3.12)

where v1 , v2 , v3 are the three components of the velocity with respect to a Cartesian reference system x 1 , x 2 , x 3 . The repetition of the index indicates the summation notation (over j = 1, 2, 3). Between 1753 and 1757, Euler published Principes généraux de l’état d’équilibre des fluides, Principes généraux du mouvement des fluides and Continuation des recherches sur la théorie du mouvement des fluides, where he took up the results by Bernoulli and d’Alembert as well as some ideas in his previous papers to formalise fundamental principles. Among the latter, he introduced the modern concept of hydrostatic pressure, demolishing the axiom according to which pressure is equal to the weight of the column of fluid overhanging a unit surface. He then generalised to compressible fluids his previous continuity Eq. (3.12): ∂ρ ∂(ρv j ) + =0 ∂t ∂x j

(3.13)

Euler also applied the second law of Newton to inviscid incompressible fluids and expressed the dynamic balance among external forces, pressure gradient and gravity; he then obtained the three scalar components (i = 1, 2, 3) of the equations of motion:   ∂vi ∂p ∂vi = ρ fi − + vj (i = 1, 2, 3) (3.14) ρ ∂t ∂x j ∂ xi where f 1 , f 2 , f 3 are the three components of the force (in the case in point, the gravitational one) per unit mass. Pairing Eq. (3.14) with Eq. (3.12), Euler obtained a system of four nonlinear equations thoroughly defining the fluid dynamics problem. Besides, imposing that the motion be stationary and irrotational, he obtained the modern form of the principle historically attributed to Bernoulli [14, 26]:

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V2 p + +  = constant ρ 2

(3.15)

where  is the potential of the gravitational force. Equation (3.15) includes Eq. (3.11) as a particular case. It is remarkable how, despite so many great discoveries, Euler retained the lucidity to affirm that “we still are a long way from a complete knowledge of the motion of fluids, and what I have been able to explain is only a feeble start” [26]. The work of Euler was decisively developed by Lagrange and Laplace. Joseph Louis Lagrange (1736–1813), an Italian mathematician and astronomer of French descent, formulated the calculus of variations in 1755, at the age of 19, giving a solution to the minimum and maximum problems limited to the prime variation of the functional. In 1788, Lagrange published his fundamental work, Mécanique analytique, in which he developed new equations of motion for inviscid fluids. Whereas Eq. (3.14) described the variation of the properties of fluid elements that subsequently occupy fixed positions of the space, Lagrange referred to fluid elements in motion. It is interesting to notice, on the other hand, that this enunciation did not mention any previous work about this subject, making this formulation appear as a downright innovative one. Actually, there was a work by Euler, Researches sur la propagation des ébranlemens dans une milieu élastique (1762), and a letter from Euler to Lagrange (dated 1 January 1760), in which the representation of the motion of fluids nowadays known as Lagrangian was already outlined at embryonic level. Lagrange also introduced the concepts of velocity potential φ and of stream function ψ [14, 29]. In the hypothesis of irrotational motion, there is a scalar function φ of space (and possibly of time), tied to fluid velocity through the relationship: vj =

∂φ ∂x j

( j = 1, 2, 3)

(3.16)

In the hypothesis that the fluid motion takes place in the plane x1 , x2 (∂/∂ x3 = 0) and that the fluid is incompressible, Eq. (3.12) (the continuity one) represents a necessary and sufficient condition for the existence of a scalar function ψ of space (and possibly of time), tied to velocity through the expressions: v1 =

∂ψ ∂ψ ; v2 = − ∂ x2 ∂ x1

(3.17)

This function exists in both the irrotational and rotational motion cases, assuming constant values along the streamlines.

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Pierre-Simon de Laplace (1749–1827) gave an outstanding boost to mathematics,15 probability theory16 (Sect. 3.4), astronomy17 and fluid dynamics, rewriting in an exemplary way the two forms of the equations of motion, since then defined as Eulerian and Lagrangian. In 1789, he presented a paper to the Académie Royale des Sciences in Paris, in which he studied the rings of Saturn, modelling them through infinitely thin layers of fluid balanced under a system of gravitational forces with potential ; in this way, he obtained the equation of the mathematical physics: ∂ 2 =0 ∂x j∂x j

(3.18)

where, for the first time, appeared the operator (∇ 2 = ∂ 2 /∂ x j ∂ x j ), which today is known by his name. The interpretation of the φ and ψ Lagrange’s functions in the light of Eq. (3.18) opened new horizons for fluid dynamics [29]. Replacing Eq. (3.16) into Eq. (3.12), the irrotational motion of an incompressible fluid is governed by the expression: ∇2φ = 0

(3.19)

In other words, the system of four nonlinear equations (in the p, v1 , v2 , v3 unknowns) made up by Eqs. (3.12) and (3.14) was reduced to one linear equation, Eq. (3.19), in the φ unknown. Replacing Eq. (3.17) into Eq. (3.12), the plain motion of an incompressible fluid is governed by the expression: ∂ 2ψ ∂ 2ψ + =0 ∂ x12 ∂ x22

(3.20)

The formulation of the equations commonly referred to as Navier–Stokes’ took place through the contributions of five scientists who left an indelible mark on the fluid dynamics of the nineteenth century: Navier, Cauchy, Poisson, Saint-Venant and Stokes. Louis Marie Henri Navier (1785–1836), a French engineer famous for his studies about the mechanics of solids and structures (Sects. 3.9 and 4.8), provided an essential 15 Around 1770, when he was very young, Laplace developed the homonymous transform; thanks to it, he put the solution of a system of differential equations with suitable initial conditions back to the solution of a system of algebraic equations. 16 In 1776, Laplace wrote Philosophique sur les probabilités, in which he maintained that the laws of time and nature implied a strict determinism; from this, it can be inferred the foreseeability of future states, if an initial state is known. With this concept, Laplace anticipated by a century and a half the foundations of the meteorological forecasts, enunciated by Bjerknes and Richardson at the beginning of the twentieth century (Sect. 6.3). 17 Between 1799 and 1825, Laplace published Mécanique céleste. It contained a study of the vertical balance of the air starting from the observations of Pascal and Perier (Sect. 3.2); since atmospheric pressure decreased with height, air was subject to an upward gradient force; Laplace expressed the balance of this force with the gravity one and obtained the hydrostatic law.

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contribution to fluid dynamics in a 1822 paper, Mémoire sur les lois du mouvement des fluides [30], in which he developed Euler’s equations taking into account internal frictions. He dealt with liquids, like solids, as a set of molecules, which is of punctual masses, subjected to a system of intermolecular forces of an attractive or repulsive type. In this way, he generalised to viscous fluids Eq. (3.14) obtained by Euler for the ideal fluids, attributing to the equation of motion the following form:   ∂vi ∂p ∂ 2 vi ∂vi = ρ fi − +ε ρ + vj ∂t ∂x j ∂ xi ∂x j∂x j

(i = 1, 2, 3)

(3.21)

where ε depends on the viscosity of the fluid, related to the molecular interspace. Augustin Louis de Cauchy (1789–1857) wrote Sur les equations qui expriment les conditions de l’equilibre ou les lois du mouvement interieur d’un corps solide, elastique ou non elastique between 1823 and 1828. The article, published in 1828, contained the brilliant idea [26] of matter being treated as a continuum and its mechanical behaviour being specified through internal pressures, the resultant of which on an element being generally not perpendicular to its surface. Cauchy quantified this concept by a stress tensor that represented a cornerstone of modern mechanics; it satisfied the relationship:   ∂v j ∂vk ∂vi (i, j = 1, 2, 3) (3.22) δi j + μ + Ti j = λ ∂ xk ∂x j ∂ xi where λ and μ are viscosity coefficients; δij is Kronecker’s symbol (δii = 1, δij = 0 for i = j). Applying the hypothesis of an incompressible fluid, the replacement of Eq. (3.12) into Eq. (3.22) shows that the stress tensor only depends on the μ coefficient, defined as dynamic viscosity. Cauchy also applied the principle of momentum to the fluid mass occupying a generic volume at the t instant. In this way, he obtained the equations of motion in their more general form [26]:   ∂ Ti j ∂vi ∂vi + vj = fi + (i = 1, 2, 3) (3.23) ρ ∂t ∂x j ∂x j Simeon Denis Poisson (1781–1840) published Mémoire sur les équations générales de l’équilibre et du mouvement des corps solides élastiques et des fluides (1829) [31], in which he applied Navier’s molecular view and extended the equations of motion from incompressible to compressible fluids [26]. He also modified the Cauchy’s Eq. (3.22), expressing the stress tensor in its modern form:   ∂v j ∂vk ∂vi (i, j = 1, 2, 3) (3.24) δi j + μ + Ti j = − pδi j + λ ∂ xk ∂x j ∂ xi Both the hydrostatic pressure p, present in Euler’s Equation (3.14) and in Navier’s Eq. (3.21), and the viscosity coefficients λ and μ of Eq. (3.22) appear here. Thanks to Eq. (3.24), Poisson clarified a fundamental concept of fluid dynam-

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ics: in the fluid at rest, every point is subjected to the same pressure in any direction; in the fluids in motion, variable stresses from direction to direction appear [14]. Jean Claude Barré de Saint-Venant (1797–1886), the most prominent figure among the French engineers of the École des Ponts et Chaussées (Sect. 3.9), published Note à joindre au mémoire sur la dynamique des fluides (1843) [32], in which he avoided making use of the molecular properties of fluids, undetermined because of their nature, developing the equations of motion in terms of normal and shear stresses of a viscous nature [14]. He also discussed the possibility of not limiting the equations of motion to laminar flows, but to apply them also to turbulent flows. In subsequent papers, he proposed to express the stress tensor in a turbulent flow in relation to the properties of vortex structures. Sir George Gabriel Stokes (1819–1903), an Irishman who held the position of secretary and then president of the Royal Society, published On the theories of the internal friction of fluids in motion (1845) [33], in which he characterised viscous fluids through a constitutive equation that satisfied strong phenomenological considerations translated into four postulates. Imposing that the components of the stress tensor be linear functions of the deformation velocities, Stokes obtained Poisson’s Eq. (3.24) in an “outstandingly natural and incisive” way [26]. When it was replaced in the Cauchy’s Eq. (3.23) and paired to the continuity Eq. (3.13), it originated the Navier–Stokes’ equations. Applying the hypothesis of an incompressible fluid, the replacement of Eq. (3.24) into Eq. (3.23) originates the equation of motion:   ∂vi ∂p ∂ 2 vi ∂vi = ρ fi − + vj +μ ρ ∂t ∂x j ∂ xi ∂x j∂x j

(i = 1, 2, 3)

(3.25)

It is identical to Eq. (3.21) for ε = μ. Paired with Eq. (3.12), it forms a system of four equations with the four unknowns v1 , v2 , v3 and p, which expresses the velocity field of the fluid motion as well as the pressure distribution on the surface of bodies. Stokes also proposed and discussed the homonymous relation between the viscosity constants: 3λ + 2μ = 0

(3.26)

Even though Stokes put it forward with many qualifications and afterwards he even withdrew it, it became an almost universal peculiarity of the scientific literature of the nineteenth and twentieth century [34], depriving the equations of fluid dynamics of a degree of freedom that was there on their foundation. Stokes devoted himself also to the problem of the motion of fluids on solid boundaries [14], reaching the wrong result according to which the only way to reconcile theory and experience is admitting that a fluid in contact with a surface has a non-null velocity [33]. He then assumed the presence of an unknown slipping at the interface between the fluid and the surface, attributing to the velocity growth a parabolic law

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that is function of the distance from the surface. He later returned to this subject [35], declaring he was not sure anymore of what he had previously affirmed. Hermann Ludwig Ferdinand von Helmholtz (1821–1894) gave a clear and rigorous contribution to the concepts devised in the nineteenth century about vorticity and vortex filaments. He also gave an essential contribution to the overcoming of the difficulties implicit in the solution of Euler’s and Navier–Stokes’ equations. By virtue of Helmholtz’s studies, the motion of a fluid is defined as rotational if its elements have a finite angular velocity ω (Fig. 3.19a). The motion of a fluid without elements in rotational or vortex motion is defined as irrotational; in this case, there is a φ velocity potential, defined by Eq. (3.16), thanks to which the motion is called a potential one. Vorticity is defined as twice ω. A vortex filament is a line, either straight (Fig. 3.19b) or curve (Fig. 3.19c), linking elements with rotational motion; an array of straight, side-by-side vortex filaments makes up a vortex street (Fig. 3.19d). Helmholtz proved that, if an incompressible fluid has potential stationary motion, it satisfies Eq. (3.19) in the φ unknown; this equation is solved by imposing suitable boundary conditions; once φ is known, Eq. (3.16) provides the three components of the velocity, v1 , v2 , v3 ; from them, the pressure p is deduced by means of Bernoulli’s principle (Eq. 3.15). If, conversely, the motion is not a potential one, there is at least the possibility of separating it into two portions, an irrotational or potential one and another, rotational and characterised by the presence of vortex filaments and sheets. Helmholtz expanded on the study of the rotational portion in an 1858 work [36] in which he formulated fundamental theorems on vorticity. He returned to this topic in Über discontinuirliche Flüssigkeitswegunggen (1868) [37], in which he investigated the discontinuity surface between fluid portions having different properties.18 The discontinuity surface created the premises to overcome d’Alembert paradox; this problem was chiefly approached by contemplating the motion of an inclined plate

Fig. 3.19 Streamline of a fluid particle, rotation and vorticity (a); straight (b) and curve (c) vortex filaments; vortex street (d) [29] 18 Starting from the Eulerian form of the equations of motion, Helmholtz studied the balance of the separation surface between two masses of air with different temperatures and motions; in this way, he explained the origin of fronts (Sect. 6.3) by applying the concept of fluid dynamics instability.

3.6 The Coming of Fluid Dynamics

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Fig. 3.20 Flow with discontinuity surfaces [27]

in a fluid [14]. According to von Karman [27], “it admits that a discontinuity surface forms at the edge of the plate, so that the latter is followed by a wake composed of dead air, extending past the plate up to infinity” (Fig. 3.20). Under this theory, the plate is subjected to a pressure difference between the face exposed to the fluid and the one immersed in the dead air; it creates a non-null resultant even in the absence of viscosity. This concept was developed independently by Kirchoff and by Rayleigh. In 1869, the German Gustav Robert Kirchoff (1824–1887) published a work, Zur Theorie freier Flüssigkeitsstrahlen [38], in which he applied the discontinuity surface to study the streamlines of a fluid running over an inclined flat foil. In 1876, the English John William Strutt, more known as Lord Rayleigh (1824–1887), wrote On the resistance of fluids [39], where he obtained the force f per unit length acting on an infinitely long, inclined flat plate, immersed in a nonconfined fluid; he also determined the position of its application point. For this, he applied the potential motion theory in the fluid part before the plate and assumed that the pressure of the dead air was equal to that of the undisturbed flow. He obtained the relationships: f = ρV 2 b

3 cos ϕ π sin ϕ ; d= b 4 + π sin ϕ 4 4 + π sin ϕ

(3.27)

where ρ is the density of the fluid, V is the velocity, b is the width of the plate, ϕ is the inclination of the plate with respect to the flow direction, d is the distance between the application point of the force and the centre of the plate (Fig. 3.21a). Rayleigh compared the result obtained with the experimental measurements carried out by Samuel Vince (1749–1821) in 1798 (Sect. 4.2), observing that Eq. (3.27) underestimated f by a factor approximately equal to 2.27. Without providing any additional justifications, he then corrected his expression by means of this factor: f = ρV 2 b

π sin ϕ 4 + π 4 + π sin ϕ π

(3.28)

and made comments about the achieved agreement with satisfaction (Fig. 3.21b).

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Fig. 3.21 a Force exerted by a fluid on an inclined plate; b comparison between Rayleigh’s theoretical results and Vince’s experimental measurements

Examining this discordance in the light of the current knowledge, Rayleigh’s error is obvious: admitting that the pressure of the dead air was equal to that of the undisturbed flow, he left out a contribution to the resultant force, the depression on the rear face of the plate, greater than the one provided by the pressure on the front face. This error demonstrated the reality of a discipline that, despite having made outstanding progress, was still waiting the contribution of Prandtl (Sect. 5.1) to give a correct explanation of an exceptionally complex physical phenomenon. A study carried out by Rayleigh in 1878 to explain the deviant flight of a cut tennis ball [40] is also worth mentioning. He analysed the flow of an ideal fluid around a circular cylinder explaining that, if the cylinder is in relative motion with respect to a uniform flow, or if it uniformly moves in a fluid at rest, the shape of the streamlines is symmetrical (Fig. 3.22a) and the force perpendicular to the direction of the motion is null. If, instead, a circulatory motion is superimposed to the uniform flow (Fig. 3.22b), the velocity increases in point A and decreases in point B. Applying Bernoulli’s principle (Eq. 3.11), in the first case, pressure is equal in A and in B. In the second one, pressure in B is greater than in A; such difference determines a deviant force from B towards A, perpendicular to the relative motion between the body and the fluid. Thanks to this result, Rayleigh explained the Magnus effect, a phenomenon known by artillerymen since the early nineteenth century (Sect. 4.2); it was experimentally demonstrated by the German physicist and chemist Heinrich Gustav Magnus (1802–1870) in 1853 and became the field of great discoveries and heated debates in the twentieth century (Sects. 7.5 and 8.1). Finally, it is necessary to linger on the contribution of Joseph Valentin Boussinesq (1842–1929). In 1872, he presented to the Académie des Sciences Essai sur la théorie des eaux courantes, a treatise published in 1877, in which he provided a complete and systematic synthesis of his previous researches about the motion of fluids [41].

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Fig. 3.22 Magnus effect [27]: a uniform motion; b circulatory motion

He stated that for hydraulics stopping being, in the words of De Saint Venant, “a hopeless enigma”, it was necessary to acknowledge and adopt four principles: (1) the velocities in real fluids quickly and suddenly change from a point to another, causing internal frictions of an order of magnitude totally different from that of homogeneous motion flows; (2) the mean actions exerted on a fluid element do not only depend on the mean local velocity and on its prime derivative, which offers a measure of the relative slipping between adjacent fluid layers, but also and especially on the local intensity of the eddy agitation of particles; (3) it is necessary to investigate the causes of the eddy agitation of the flow, expressing the internal friction coefficient as a function of the same; (4) the equations of motion must not limit themselves to express the dynamic balance of the elementary volumes of fluid in a given moment, but must also take into account the mean values of such relation during short time intervals. Thanks to these considerations, which include the embryonic concepts of separation between laminar and turbulent flows and of the graduation of the motion of fluids to various scales (Sect. 5.1), Boussinesq postulated the principle, known as Boussinesq’s hypothesis, according to which the shear stresses and the transfer of momentum caused by vorticity could be schematised by replacing the viscosity coefficient μ in the Eqs. (3.10) and (3.22) by a new eddy viscosity coefficient μT . He then expressed the stress tensor and the equations of motion in the now classic form (Eqs. 3.24 and 3.25), replacing μ with μT . He observed that, while μ is very small in absence of eddy agitation, μT greatly increases when such agitation is present. A period of approximately twenty years would have to lapse before Reynolds clarified these concepts on both experimental and theoretical bases (Sect. 5.1).

3.7 Thermodynamics and Steam Machines Reviewing the theories about heat formulated over the ages, two lines of thought were recognisable at the end of the seventeenth century, though they were not always clearly distinct [42, 43]. According to the first one, chiefly defended by physicists

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and mathematicians, thermal phenomena were connected to the motion of the atoms making up bodies; no instruments, however, were available to demonstrate and use this theory. The second, supported especially by chemists, relied on the conception of a thin and tangible matter, called caloric. Faced by this alternative, a dualism between motion and matter developed, which would only be slowly solved through experience. Galileo Galilei (1564–1642) espoused the materialistic theory in the Saggiatore (1623) and, partially, in the Discorsi (1638), affirming that the main qualities of the matter are the size, shape, number and velocity of the particles making it up, rather than global parameters previously used, such as heat and cold. He maintained “that those matters that produce and make us feel heat, which we call with the generic name of fire, are a multitude of tiny little bodies, figured up in such a way, moved with great and great speed”. He called these tiny bodies “igniculi”, describing fire as a “peculiar body, which has been created so as to be changed to nothing, which could neither be produced by another body, nor changed in any other one, and the effects of which are heat and light”. The atomic conception of heat brought Robert Boyle (1627–1691) and Robert Hooke (1635–1703) to anticipate concepts subsequently clarified by Lavoisier. Boyle maintained that “heat appears to chiefly consist of that mechanical property of the matter we call motion”. Carrying out laboratory tests, he noted that air is absorbed during the combustion process and metals acquire weight thanks to oxidisation. In the trilogue The sceptical chymist: or chimyco-physical doubts and paradoxes, touching the experiments whereby vulgar sparagists are wont to endeavour to evince their salt, sulphur and mercury to be the true principles of things (1661–1679), Boyle refuted the theory of the four elements (earth, air, fire and water) making up matter (Sect. 2.2), proposing the alternative chemical hypothesis that the base of the substances is to be searched in the principles or in the essence of salt, sulphur and mercury; he also maintained the smallest particles of the matter combine in various ways to form corpuscles the motion and the structure of which originate all the phenomena that can be observed in nature. In Micrographia (1665) Hooke was the first to express the idea that only a part of the air is required to achieve combustion. The materialistic conception of heat found a strenuous defender in Johann Joachim Becher (1635–1682), a German chemist, physiologist, politician and theologian, famous for his researches about the philosopher’s stone and the extraction of gold from sea-sands. In 1669, Becher published Physica subterranea, in which he adopted Boyle’s chemical hypothesis, maintaining that the three fundamental elements (or principles) of the materials are “terra mercurialis” (principle of fluidity, or fluid earth or mercury), “terra lapidia” (principle of solidity, or vitrified earth or salt) and “terra pinguis” (principle of combustion, or flammable earth or sulphur); during the combustion terra pinguis leaves the initial material and is absorbed by air. Many consider Becher’s book as the foundation deed of thermodynamics. Georg Ernst Stahl (1660–1734), a German chemist and physician, developed Becher’s work in Specimen Becherianum (1702). He subsequently published Fundamentals of chemistry (1723), in which he explained combustion and oxidisation

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through the role of flammable earth, an imponderable fluid called “phlogiston” or “caloric”. According to Stahl, a substance emitting heat irradiated tiny phlogiston particles (Galilei’s igniculi); a burning metal produced earthly residues called “lime”; metals consist of a combination of lime and phlogiston. Resuming some concepts by Pierre Gassendi (1592–1655), the Dutch chemist, physician, botanist and philosopher Hermann Boerhaave (1668–1738) attempted to join the atomistic view with the caloric one, maintaining that matter consists of atoms attracting and repulsing each other and by elementary fire particles characterised by ceaseless motion. They are present in all substances (including the cold ones) regardless of state changes and cannot be created. Boerhaave published the most renowned chemistry treatise of his age, Elementa chymia (1732), without ever mentioning phlogiston [44]. The interest towards heat was amplified by the discoveries characterising, in the same period, the construction and use of the first steam machines [6, 45, 46]. Following the example of the Heron’s aeolipile (Sect. 2.3) and of Leonardo da Vinci’s architonnere (Sect. 2.10), the first part of the seventeenth century saw the appearance of various devices to convert steam into energy [45]. Giambattista della Porta (1535–1615) wrote Tre libri dè spiritali (1606), where he described a machine that lifted a water column by steam pressure or condensation. In 1615, Salomon de Caus (1576–1630) spoke about an ornamental fountain driven by the power of steam in Les raisons des forces mouvantes. Giovanni Branca (1571–1640), an Italian architect, perceived that a steam jet can make a wheel fitted with paddles spin; in 1629, he described various turbines based on this principle (Fig. 3.23). Edward Somerset (1568–1628) wrote A century of the names and scantlings of inventions by me already practised (1663), where he illustrated a device to lift water by means of steam. Denis Papin (1647–1712), a French physicist disciple of Huygens, devoted the first years of his career to study how to make use of the energy produced by pressurised steam. Afterwards, he moved to England and collaborated with Boyle and Hooke. In London, between 1679 and 1681, he invented “digestor”, the ancestor of the modern pressure cooker; equipped with a piston inside a cylinder, it brings to mind Guericke’s air pump (Sect. 3.2). Starting in 1687 Papin perfected his device (Fig. 3.24a), proving that steam condensation produced effects comparable with gas depression. He illustrated these results in De novis quibusdam machinis (1690), an essay considered the formal deed of the invention of the steam machine. Papin later perceived the potentiality of steam for transportation systems, in particular as regards to river navigation. In 1704, he sailed up the Fulda River with a boat equipped with wheels driven by a steam device. The sailors of the city of Munden, worried about its illicit use, destroyed the boat. Even so, Papin devoted his last years to explore new uses of steam; he understood, as an example, the importance of his invention to pump the water (Fig. 3.24b) of canals in the tanks of the houses and in fountains. He collected these ideas in The new art of pumping water by using steam (1707). In 1698, the English engineer Thomas Savery (1650–1715) understood the effectiveness of steam to drain seepage water from mines. So, he designed and patented

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Fig. 3.23 Wheels driven by steam power [45]: a chimney of a rolling mill; b stamp-mill

Fig. 3.24 a Papin’s steam machine (1690); b Papin’s high-pressure steam pump (1706) [46]

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Fig. 3.25 a Newcomen’s atmospheric engine [45]; b Watt’s double effect steam machine [46]

The miner’s friend (1702), the first steam machine “to raise water by fire”. Another Englishman, Thomas Newcomen (1663–1729), perfected Savery’s engine in 1705. This machine, called atmospheric engine (Fig. 3.25a) for using steam at atmospheric pressure and at low pressure, became common in many European countries as an effective device to raise water from mines. It was improved around 1755 and exported in the USA, achieving identical success. In the meantime, the applications of the steam machine proliferated. In 1753, Nicolas Joseph Cugnot (1725–1804) performed the first attempts to install boilers on carriages and stagecoaches. In spite of some failures, he continued his researches until he built, in 1770, a powerful vehicle equipped with a front steering wheel and two rear fixed wheels. The use of steam machines in the textile sector started in 1767. After Papin’s experiment, the first working steam boat, even though experimental, was launched by Claude-Francois-Dorothée, marquis of Jouffroy d’Abbans (1751–1832), in 1783. In 1784, James Rumsey (1743–1792) built a steam boat that sailed on the Potomac River in 1786. Between 1785 and 1787, John Fitch (1743–1798) built and patented a similar boat in Pennsylvania. In 1788, Patrick Miller of Dalswinton (1730–1815) and William Symington (1764–1831) built and patented a new steam boat in Scotland. These are prodromes to the great advancements of the nineteenth century (Sect. 4.4). Actually, the evolution of the steam engine was still hindered by the technological and efficiency limits of the first engines. John Smeaton (1724–1792), an English engineer renowned for many achievements in various sectors (Sects. 4.2, 4.6 and 4.7), perfected Newcomen’s machine obtaining interesting results, but not enough to make his products successful on the market. Success crowned the efforts of another Scottish engineer, James Watt (1736–1819), the author of remarkable discoveries leading to the modern steam engine. The first invention by Watt, patented in 1769, was a condenser that reduced the steam loss caused by the alternating heating and cooling of the cylinder. Another innovation consisted in the fact that his engines, unlike the previous ones, performed

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useful work by steam pressure rather than through atmospheric pressure. Watt also invented a method to transform the alternate straight motion of the piston into the continuous rotatory motion of a flywheel, using gearwheels first and then a rod-andcrank system similar to that of future steam locomotives. He also created the double effect principle (Fig. 3.25b), alternatively introducing steam from one and from the other end of the cylinder, to drive the piston both in the outward and in the return run. He equipped the engine with a control valve that kept the flywheel revolution constant. Watt retired from business in 1800 and devoted his last years to the research providing an accurate definition of horsepower; the power unit of measure is called “Watt” to honour him. The next important development of the steam machine was the elimination of the condenser, a principle already guessed by Watt but accomplished by the American Oliver Evans (1755–1819) and by the British engineers Trevithick and Woolf. In 1800, Richard Trevithick (1771–1833) built a high-pressure steam engine with a thermal efficiency remarkably higher than Watt’s low pressure machines. On Christmas Day 1801, he put into operation the first steam vehicle intended for the transport of passengers; it consisted of a coach, called a locomotive from then on, which introduced the boiler exhaust steam into the chimney to increase draft. In 1804, he used his invention to transport loads on rails, moving 25 tons of iron on a railway line 15 km long, from Merthyr Tydfil to Abercynon. In 1808, he built “Catch-me-who-can”, a locomotive capable of travelling at 24 kph on a circular track within an enclosed space. In the same period, Arthur Woolf (1766–1837) built the first double expansion (compound) engines, patented in 1804 and 1805. High-pressure steam was introduced into a cylinder from which, once expanded with ensuing pressure drop, it passed into another cylinder, where it went through a second expansion. Woolf subsequently perfected his devices, building triple and quadruple expansion engines. Actually, in spite of the sensation raised by Trevithick’s invention, the use of the steam machine for rail transport was hindered by various issues, which restricted its diffusion. One of these concerned the adhesion required to prevent the slipping of wheels on rails and the advance of trains: if the locomotive was too heavy, it would break the fragile cast iron rails; if it was too light, it would slip on the rails without gripping. Rack driving wheels and rails were then used to overcome this issue; they proved successful until 1813, when the English mechanic William Hedley (1779–1843) built “Puffing Bill”, a locomotive for the transport of coal at the Wylhalm mines near Newcastle; its weight produced sufficient adhesion by friction to haul a long train without compromising the resistance of rails. Thanks to this result, the first public railway from Stockton to Darlington was built. It was designed by a British mechanical engineer, George Stephenson (1781–1848), previously a builder of locomotives for the transport of minerals at mines and then owner of a workshop that produced locomotives implementing three revolutionary ideas: the direct transmission of the rod-and-crank motion to the driving wheels, the cylindrical boiler and forced draft to activate combustion. The narrow gauge line was inaugurated on 25 September 1825 and was initially used for goods transport only; the pulling power of the locomotive was integrated by the pull of some horses.

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Fig. 3.26 George Stephenson’s Rocket

The first public railway for the transport of goods and passengers using steam locomotives only connected Liverpool to Manchester and was designed by George Stephenson with the assistance of his son Robert (1803–1859). Opened in 1830, it highlighted the performance of “Rocket” (Fig. 3.26), a locomotive capable of pulling a load equal to three times its weight at 20 kph, and a coach full of passengers at 39 kph.19 On the other hand, it also highlighted the persistent refusal of the innovation. Landowners did not want trains crossing their fields. Farmers believed the locomotive was a devil’s work, which frightened animals making cows lose their milk production. The Royal Society appointed a committee to examine the advantages and disadvantages of the railway; it concluded that, if a 50 kph speed was reached, air suction in coaches would have caused the death of passengers by asphyxiation. The spreading of railways was unstoppable; in 1835, they were essential elements in large parts of Great Britain and of continental Europe. Their construction progressed so quickly that, in 1840, there were 10,715 km of operating lines in Great Britain, 6080 km in the German states and 3174 km in France. In North America, the diffusion of railways was dictated by the will to penetrate deeper into continent. Since 1830, the year the first railway for the transport of passengers was inaugurated in Charleston, South Carolina, it proved its superiority with respect to river transport. In 1850, America had 14,500 km of railway lines. In the following decade, their overall extension reached 48,300 km. 19 In 1829, Stephenson won the contract for the Liverpool–Manchester railway, taking part, with his Rocket, to a competition between four participants. Victory was far too easy: an opponent was banned because there was a horse hidden inside his vehicle; the other two locomotives broke down along the route and did not arrive at the finishing line. Rocket carried 13 tons and 36 people, travelling at 36 kph.

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The evolution of the steam machine had a strong impact on the progress of the culture of wind and its effects. The diffusion of railways created the requirements for the construction of suspension (Sect. 4.8) and truss bridges (Sect. 4.9) of increasingly bold design, and therefore subjected to wind actions; it promoted, especially in America, a widespread dissemination of windmills and wind turbines (Sect. 8.1); it became a fundamental instrument at the service of experimental aerodynamics (Sects. 7.1 and 7.2); it entailed new atmospheric pollution issues (Sect. 8.2); it represented a stimulus to the evolution of the researches in the field of thermodynamics: they were originated to support this field, but they also invested many sectors of knowledge, first of all atmospheric motions. Joseph Black (1728–1799), a Scottish physician and chemist, an advocate to the caloric theory, was the first to pose himself the problem of determining if temperature and heat were the same thing. In 1760, he carried out experiments through which he demonstrated that the addition or subtraction of heat did not necessarily modify the temperature. In support of this observation, in 1761, he proved that evaporation and condensation were accompanied by a transmission of heat, since then called latent, which was released or absorbed during state changes at constant temperature. He put the finishing touch to his studies affirming the diversity between temperature (the heat intensity measured by a thermometer) and heat (the amount of energy required to heat or cool a substance). Henry Cavendish (1731–1810), a British physicist and chemist of French descent, carried out the first experiments aimed at defining specific heat; in 1786, he isolated hydrogen, calling it “flammable air” and evaluated its relative density. In 1774, Joseph Priestley (1733–1804), a British chemist and philosopher, isolated oxygen, describing its role in combustion and respiration. The same result was also independently achieved, between 1770 and 1775, by Carl Wilhelm Scheele (1742–1786), a Swedish chemist who understood the role of oxygen, called “fire air” in combustion; his discoveries were reported in Chemical treatise on air and fire (1777), in which he was in doubt on the theory of phlogiston. In 1781, Cavendish and Priestley stated that water “is composed of de-phlogisticated air (oxygen) and of phlogiston (hydrogen)”. By this time, the understanding of combustion and heat had made great advances, even though rooted in the theory of phlogiston. On the other hand, the refusal of this view was ripe and was only waiting for a prominent figure capable of asserting it. The credit for this especially goes to a Frenchman, Antoine Laurent Lavoisier (1743–1794), who is considered the founder of modern chemistry. Lavoisier subverted the tradition progressing from qualitative chemical analyses to quantitative weighting measurements. Thanks to this revolutionary conception he made formidable discoveries between 1772 and 1777. He proved that, even if matter changed its state during chemical reactions, the overall mass remained the same. He studied the composition of water, attributing to its constituents the modern definitions of oxygen and hydrogen. After having unsuccessfully attempted to burn three diamonds in the absence of air, he reached the conclusion that combustion was an oxidisation process that took place through the combination of “the breathable and pure part” of the air, oxygen, with the combustible substance; during this process,

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the burning body increases its weight to the detriment of the breathable part of the air. During this period, Lavoisier kept an intensive collaboration with Pierre-Simon Laplace (1739–1827); it materialised in 1780 with the joint publication of Mémoire sur le chaleur, a milestone for thermal phenomena. Together, they acknowledged the existence of two different views, one concerning the vis viva of atoms, the other concerning the phlogiston. They refrained, however, from choosing one of the two theories: “many phenomena would appear to be favourable to one, but others are more easily explained through the second”. On the contrary, they deemed possible “to make the first hypothesis fall under the second by changing the terms free heat, combined heat and radiated heat with vis viva, loss of vis viva and increase of vis viva”. This was the last assonant voice of a sodality destined to a friendly end in 1784. From then on, Laplace espoused the theory of phlogiston, using it to formulate the equation of state of perfect gases. Lavoisier, conversely, attacked the same theory in Reflexions sur le phlogistique, a work submitted to the Académie Royale des Sciences in 1783 and published in 1786, in which he pointed out all the inconsistencies of the caloric view acknowledging that the combustion took place through the combination of oxygen with flammable materials, a reaction that produced heat and light. He clarified these concepts in his fundamental work, Traité élémentaire de chimie20 (1789), in which he described the experiments carried out to support the new theory; in the same work, he reformed the chemistry dictionary, introducing the terminology that is still in use [44]. Lavoisier also committed himself to political issues, including the reform of the French monetary and fiscal system. He was arrested as “fermier général” (general tax collector) for the intervention of Jean Paul Marat21 (1743–1793), he stood trial before the revolutionary court and was sentenced to death. The Bureau of Arts and Crafts interceded for him, pleading for pardon because of his high scientific merits; the reply of the regime was peremptory: “The republic does not need scientists”. After his death by guillotine, which occurred on 8 May 1794, Lagrange remarked: “An instant has been enough to cause the fall of that head; a hundred years will not be enough to produce another like that”. The Lavoisier’s work was carried on and completed by two British chemists, Rumford and Davy. Benjamin Thompson (Count Rumford, 1753–1814), a scientist of American descent who married Lavoisier’s widow, insisted on the falsity of the theory of phlogiston since 1798, after having observed that the friction produced by the 20 Traité élémentaire de chimie included some ambiguous elements. There is a sentence in which heat is described as “a real and material substance, a very thin fluid that seeps through the molecules of all the bodies and moves them away”. The terms “calorique” and “lumière” were placed at the top of the list of simple or elementary substances. For these reasons, not everyone recognises Lavoisier as the main denigrator of the theory of phlogiston [43]. 21 The Swiss physician Jean Paul Marat is the author of Recherches physiques de la feu (1780), in which he criticized and refused Lavoisier’s theory of combustion. Lavoisier made the mistake of ridiculing him in public. Subsequently, when he became a Jacobin leader of the French Revolution, Marat launched the fatal attack to Lavoisier from his newspaper, L’ami du peuple.

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boring of cannons developed a practically inexhaustible amount of heat. Sir Humphry Davy (1778–1829) confirmed this concept in 1799, carrying out an experiment during which he melted two ice cubes by means of the friction produced by rubbing. In the same period in which the rejection towards the theory of phlogiston grew, the British chemist and physicist John Dalton (1766–1844) corroborated the idea that the study of heat transcended the specific issue of combustion and involved many other sectors of science and life, first of all the atmospheric field. Around 1787, he started meteorological observations during which he noticed that thermally insulated air increased its temperature when compressed and decreased it if expanded; he also demonstrated that rainfall did not depend on the variation of atmospheric pressure, but on the reduction of temperature. Above all, he thought over the knowledge that brought him to formulate atomic theory (1803). Published in 1808, in A new system of chemical philosophy, it affirmed that matter was composed by atoms with different weight, combined according to simple numerical ratios. The progress of mechanics and mathematics favoured a renewed interest towards the theoretical systematisation of thermal effects. It was not by chance that the first applications of these studies to atmospheric physics were developed by two mathematicians, Fourier and Poisson. At embryonic level, they laid the concept that was to prevail in the twentieth century depicting the atmosphere as a giant thermal machine and wind as an essential product of it. Jean Baptiste Joseph Fourier (1768–1830), disciple of Lagrange and Laplace at the École Normale Supérieure, carried out tests about heat propagation in Grenoble; in parallel, he formulated the homonymous series and transform between 1807 and 1822, applying it to model temperature changes in solids. The results were published in Théorie analytique de la chaleur (1822), which also included the heat propagation laws. When circumscribed to the monodimensional case, they assume the form: H = −ρcK

∂T ∂z

∂T κ ∂2T ∂2T = =K 2 2 ∂t ρc ∂z ∂z

(3.29) (3.30)

where H is the heat flow, that is the amount of heat crossing the unit surface in the unit time t, T is the absolute temperature, z is the direction along which propagation takes place, κ is the thermal conductivity coefficient, ρ and c are the density and the specific heat, K = κ/ ρc is the thermal diffusivity coefficient; κ, ρ, c and K are constant quantities depending on the material. Two years after the publication of his treatise, in 1824, Fourier stated that the atmosphere acted like the glasses of a greenhouse allowing the luminous rays of the sun to pass through but retaining the heat radiations of the ground (Sect. 8.2). Siméon Denis Poisson (1781–1840), disciple of Laplace and successor of Fourier at the École Polytechnique, provided essential contributions to probability (Sect. 3.4) and heat theories. The results on heat appeared in Sur la chaleur de gaz et des vapeurs (1823) and in Théorie mathématique de la chaleur (1835). Poisson examined the

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adiabatic change of a parcel of ideal gas—that is, a thermodynamic change that took place with no heat exchange with external environment—and obtained the three laws that today are known as Poisson’s equations of the reversible adiabatic: T V γ−1 = constant;

pV γ = constant; T p (1−γ)/γ = constant

(3.31)

with T, V and p being, respectively, the absolute temperature, the volume and the pressure, γ = cp /cv is the adiabatic index, i.e. the ratio between the specific heat at constant pressure and at constant volume (on the average, in dry air, γ = 1.4). From the third Eq. (3.31), it follows that a parcel of air (treated as an ideal gas) that initially is at the temperature T and at the pressure p, moving adiabatically until it assumes the pressure p0 , acquires the following temperature:  T0 = T

p0 p

 γ−1 γ (3.32)

The value of T 0 corresponding to p0 = 1.000 millibar is defined as the potential temperature θ. It has an important meaning in many thermodynamic problems and in atmospheric stability (Sect. 6.6). Modern thermodynamics originated in mechanics, when the latter started to pose itself the problem of interpreting thermal phenomena in their broadest meaning [47–49]. Nicolas Leonard Sadi Carnot (1796–1832), a French physicist and military engineer who studied at the École Polytechnique, laid the bases of the new science in Reflexions sur la puissance motrice du feu et sur les machines propres e developper cette puissance (1824), in which he defined heat as the “cause of all the main motions that can be observed on Earth, from winds to clouds and rain and, recently, motive power of the machines destined to replace men in the more unpleasant and heavier jobs”. In the same chapter, he noted that the theory of fire machines was still at an embryonic stage “and the attempts carried out to improve it are still, in a large part, performed at random”. He also noticed that “the machines that do not draw their motion from heat, the ones having as motive power the strength of men or animals, a waterfall, an airflow, etc., can be studied in every detail through the mechanical theory. All the cases are contemplated, all the possible motions are subject to firmly established principles, applicable to any circumstances. This is the peculiar nature of a complete theory. Clearly, such a theory is not yet available for fire machines. It will become so only when the laws of physics will be sufficiently extensive and generalised to allow us envisaging all the effects of heat acting in a particular way on anybody.” This is the view of a genius [43]. Carnot founded his theory on two principles: (1) to produce mechanical power, it is necessary to have a hot body and a cold one; (2) heat must flow from the hot body to the cold one with a mechanical counterpart. A machine converting all the available energy into mechanical power, i.e. with no thermal losses, is called ideal and, subsequently, a Carnot machine. He also formulated one of the first enunciations

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of the second principle of thermodynamics. His work received little consideration, in part because he espouses initially the theory of phlogiston and in part because it was judged too conversational and not enough scientific. Thankfully, Carnot’s worth was understood by Benoit Paul Emile Clapeyron (1799–1864), a French physicist educated, like Carnot, at the École Polytechnique who in 1834 published Sur la puissance motrice de la chaleur, in which he transformed Carnot’s ideas from a conversational form into a mathematical formulation. In this paper, Clapeyron provided essential contributions to the second principle of thermodynamics. He inferred a differential equation, nowadays known with his name, to determine the heat of vaporisation of liquids. He combined Boyle’s (Sect. 3.2) and Gay-Lussac’s (Sect. 4.5) laws, obtaining the equation of state of perfect gases: pV = RT

(3.33)

where V is the volume, T is the absolute temperature, R is a constant peculiar to the gas. The contributions of Carnot and Clapeyron corroborated the idea that the work performed and the heat produced were tied by an identity relationship. This idea was developed by Julius Robert von Mayer (1814–1878) a German physician and physicist, whose experiments were originated by a journey during which he noticed that the changes of the atmospheric temperature altered the blood colour as well as metabolism. Expanding on such observations, Mayer proved that, when air is compressed, the performed work is converted into heat. In 1842, he calculated the numerical value of the mechanical equivalent of heat (a calorie is equal to 4186 J). The English physicist James Prescott Joule (1818–1889), also known for his researches on electricity, achieved the same discovery between 1840 and 1850. He, having obtained the relation between thermal and mechanical energy, is considered the discoverer of the first principle of thermodynamics.22 The unit of measure for work and energy is named after him (a Watt is equal to one Joule per second). Hermann Ludwig Ferdinand von Helmholtz (1821–1894) formalised the first principle of thermodynamics, or of energy conservation: “since energy can be neither created nor destroyed, the sum of the quantity of heat delivered to a system and of the work performed on it corresponds to an increase of the internal energy of the system itself”. This definition was reported in Uber die erhaltung der kraft (1847), where Helmholtz introduced potential energy, initially called tension force. In this work, he also enunciated the mathematical foundations of the universal law of energy conversation, demonstrating that even when energy appears to be lost it is actually converted into heat. The English physicist and mathematician William Thompson (1824–1907), more commonly known as Lord Kelvin, in 1848, investigated the concept of temperature and introduced the absolute thermodynamic scale named after him. In 1851, 22 Using the relation provided by the German physicist Max Planck (1858–1947), the first principle of

thermodynamics is simply the principle of energy conservation applied to the phenomena involving the production or absorption of heat.

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analysing Carnot’s and Clapeyron’s concepts, Kelvin formulated a new enunciation of the second principle of thermodynamics: “It is impossible to build a cyclic machine having as sole effect the production of work, subtracting heat to a sole source”. The following year, collaborating with Joule, he understood that the cooling of an expanding gas is due to the work performed against external pressure, at the expense of internal energy; this phenomenon is known as Joule–Thomson effect. In 1850, the German physicist and mathematician Rudolf Julius Clausius (1822–1888) inspected the meaning of energy conservation and, taking inspiration from Carnot, introduced a new function called entropy. Making use of it, Clausius wrote On a modified form of the second fundamental theorem in the mechanical theory of heat (1854) and On the application of theorem of the equivalence of transformations to the internal work of a mass of matter (1862), subsequently collected with other papers in La théorie mécanique de la chaleur (1868). Resuming the work of Joule, he also provided a new enunciation of the first principle of thermodynamics, i.e. “mechanical work can be converted into heat, and, inversely, heat into work, in such a way that one is always proportional to the other”, completing such principle by means of the expression23 [43]: dQ = dU +

RT dv J v

(3.34)

It affirms that the elementary heat delivered to a gas (dQ) can be traced to two contributions: the first (dU) is equal to the sum of the sensible heat and of the internal work, the second (Pdv/J) is associated to the produced external work, being J the equivalent of Joule. Clausius also provided the first simple and effective enunciation of the second principle of thermodynamics: “It is impossible to accomplish a spontaneous heat transfer from a colder body to a hotter one”. In the same period, William John Macquorn Rankine (1820–1872), a British engineer and physicist also known for his contributions to civil engineering (Sect. 4.8), published Outlines of the science of energetics (1848–1855), in which he laid unitary bases for mechanics and thermodynamics. He wrote that “the energy, or capability of performing changes, is the characteristic common to the different states of the matter to which all the diverse branches of physics refer. All the laws of nature can then be reported to those concerning energy in its various forms and the possibilities of mutual transformation. (…) All kinds of work and energy are homogeneous; every kind of energy must be able to perform any kind of work. The amounts of energy can be measured by means of the amount of work they allow performing”. Afterwards, he published Manual of the steam engine and other prime movers (1859), developing the theory of the homonymous cycle. He introduced a new absolute temperature scale named after him. He defined as adiabatic a process taking place with no heat exchange with the outside. Applying Rankine’s concepts to dry adiabatic processes, between 1866 and 1868, the Austrian meteorologist Julius von Hann (1839–1921) inferred, independently 23 The system formed by the law of continuity, the Navier–Stokes’ equations and the first principle of thermodynamics provides a complete description of the state of fluids and of the air in particular.

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from Helmholtz (1865), the first physically correct theory about the foehn wind24 and an estimate of the temperature increase in descending air currents (1 °C for every 100 m drop). He also stood out for some important meteorology and climatology treatises (Die erde als ganzes, ihre atmosphare und hydrosphare, 1872; Handbuch der klimatologie, 1883; Atlas der meteorologie, 1887, Lehrbuch der meteorologie, 1901). Operating in the same direction, in 1881, Henri Louis Chatellier (1850–1936) formulated a principle fulfilled by many atmospheric motions: “imposing any change to a system, it reorganises itself to oppose the change”. Dry air, as an example, expands when it rises (because pressure decreases as height increases) and adiabatically cools down. The same air, moving down, adiabatically warms up. In both cases, the temperature changes accompanying the vertical motions of the air corresponds to 1 °C every 100 m; this quantity is nowadays known as “dry adiabatic lapse rate” [9]. These are signals of a new reality destined to indissolubly bind thermodynamics and meteorology.

3.8 The Kinetic Theory of Gases The kinetic theory of gases explains their thermodynamic behaviour relating the macroscopic properties of the matter (temperature, pressure and volume) with the microscopic properties of the particles (position, velocity, momentum and kinetic energy) [1, 2, 25, 43]. In the framework of the scientific disciplines originated between the seventeenth and the nineteenth century, it played a leading role in various sectors of fluid dynamics (Sect. 3.6) and thermodynamics (Sect. 3.7); it also represented a basic reference for the theories about turbulence introduced in the first half of the twentieth century (Sect. 6.6). The first rudiments of the kinetic theory of gases appeared in a letter written by Robert Hooke (1635–1703) to Robert Boyle (1627–1691) in July 1662. Hooke affirmed that the particles of bodies, in continuous motion, change their direction because of the collision with bodies at rest or with other moving particles. According to Hooke, “the particles can also be shaped as a hairspring, like that of a clock; but when they rotate they potentially become spheres, since they defend a spherical space from being entwined with the space travelled by another of these same globules”. The pressure exerted by the globules can constrain the particles in a smaller space, without reducing their circular motion [1]. 24 The

foehn wind (Sect. 6.4) occurs when a moving mass of air meets a mountain and is forced to climb along its ridges. If the mountain is high enough, the ascending air condensates, causing rains in the valleys and snow on the peaks; after becoming dry and cold, then, it passes over the crest and descends the opposite ridge, adiabatically heating itself. This type of wind is frequent along the Alpine arc, especially on the Swiss and Austrian sides, and in many other countries, where it assumes local denominations. The most well-known ones are the chinook, which blows on the east side of the Rocky Mountains, the samul, on the Iranian mountains of Kurdistan, and the bohorok, which in Sumatra is linked to the monsoon.

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Isaac Newton (1642–1727) approached this issue in Principia Mathematica (1687), recognising that an increase in air temperature enhances the vibration of its component atoms and causes thermal expansion [43]. Jakob Hermann (1678–1733) carried out the first measurement of the heat produced by the motion of the molecules making up the matter, reporting the results in Phoronomia (1716); from them, he inferred the relationship: p = K ρ¯v2

(3.35)

where the pressure p is a manifestation of heat, v¯ is the mean velocity of the molecules, ρ is the density of the matter, K is a constant depending on the examined body. The first actual formulation of the kinetic theory of gases is due to Leonhard Euler (1707–1783). In a work that took its cue from Descartes’s theory of vortices (Tentamen explicationis phaenomenorum aeris, 1729), he schematised air as a mass of spherical molecules spinning in strict contact with each other [25]: “Above a spherical core of ether, there is a core of the true substance of air, that is in turn covered by a shell of water. Air pressure is a manifestation of the centrifugal force that accompanies the rotation; the proportion between water and the true substance of air is an index of humidity. The apparent density of the air is the mean density of the compound molecules”. Euler assumed that, for a given temperature, the linear velocity v of the motion of air and water molecules is the same. From this, he derived an equation of state according to which the pressure p of the dry air is provided by: p≈

1 2 ρv 3

(3.36)

Euler’s theory was still far removed from the reality for lack of statistical bases. On the other hand, it contained conceptually correct ingredients. Equation (3.36), in particular, expresses the macroscopic parameter p as a function of the microscopic quantity v. The first statistical embryo of the kinetic theory of gasses was introduced by Daniel Bernoulli (1700–1782) in a passage of Hydrodynamica (1738) written in 1733. Figure 3.27 shows a piston, below which lies a cylinder containing “very tiny corpuscles brought here and there with a very swift motion” and “practically infinite in number”. The weight P of the piston represents the atmospheric pressure; it is balanced by the collision of the corpuscles on its bottom surface. If the piston is lowered, the number and the violence of the collisions with the corpuscles increases; the same occurs heating the gas contained in the cylinder. After the pioneering contributions of Hermann, Euler and Bernoulli, the kinetic theory of gases remained almost forgotten until the early nineteenth century, when John Herapath (1790–1869) wrote On the physical properties of gases (1816) and A mathematical investigation into the causes, laws, and principal phaenomena of heat, gases, gravitation, etc. (1821), in which he used Bernoulli’s model to explain the changes of state, diffusion phenomena and sound propagation. This work, also because of some incorrect concepts about temperature, triggered a scientific dispute

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Fig. 3.27 Illustration of Daniel Bernoulli’s kinetic theory of gases [49]

during which Sir Humphry Davy (1778–1829), the president of the Royal Society, opposed the new theory. Inspired by Euler and Herapath, in 1851, James Prescott Joule (1818–1889) published Some remarks on heat and on constitution of elastic fluids, in which he calculated the speed of the molecules. Like Euler, Joule reached the conclusion that the temperature was proportional to the square of the molecular velocity; unlike him, he believed the motion of the molecules to be translational and, as a consequence, that the temperature was proportional to the vis viva. August Karl Krönig (1822–1879) took over the concepts introduced by Bernoulli in Grundzüge einer theorie der gase (1856), in which he maintained that “using the laws of the probability theory, we can replace total chaos with complete regularity”. He then formulated a mechanical model founded on four hypotheses: (1) a chemically balanced gas is schematised by a system of point masses, or rigid bodies, called molecules; they move randomly and the number of molecules moving in one direction is, on the average, the same of those that move in the opposite direction; (2) the volume of the molecules is negligible with respect to the volume of vacuum; (3) intermolecular forces are negligible, with the exception of those occurring on collision; the molecules, therefore, move at constant velocity until they collide with other molecules or with the walls of the container; (4) molecular collisions are perfectly elastic, since a confined and isolated gas shows no tendency to lose pressure.

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Starting from these hypotheses, Krönig developed a theory by which he attained this relationship: p = ρ v¯ 2

(3.37)

It differed from the correct expression, p = ρ v¯ 2 /3, only due to a trivial material error [25]. Despite this, Krönig’s work received great renown and respect in its times; it is still considered by many as the starting point of the modern kinetic theory of gases. It is worth noting that in 1845, then before the contributions of Joule and Krönig, John James Waterston (1811–1883) sent a paper to the Royal Society, On the physics of media that are composed of free and perfectly elastic molecules in a state of motion, that, using a model similar to Bernoulli’s, developed a brilliant formulation of the kinetic theory of gases. This work, rejected and forgotten for almost half a century, was rediscovered by Rayleigh in 1891 and published in 1893, restoring its dignity as a milestone [25]. Another work by Waterston is also worth mentioning, Note on the physical constitution of gaseous fluids and a theory on heat, which appeared in the final part of Thoughts on the mental functions (1843), published by an obscure Edinburgh publishing house and passed unnoticed like the previous one. It contained the first definition of the “mean free path”, namely the mean distance travelled by molecules between two subsequent collisions. Uninformed about this exceptional intuition, Clausius “introduced” this concept in 1857. Between 1859 and 1866, James Clerk Maxwell (1831–1879) carried out studies, the results of which are collected in Illustrations of the dynamical theory of gases (1860), Theory of heat (1871) and On the results of Bernoulli’s theory of gases as applied to their internal friction, their diffusion, and their conductivity for heat; they raised the kinetic theory of gases to a level of abstraction and rigour close to the modern systematisation of this discipline. Starting from the same hypotheses formulated by Waterston, Maxwell obtained the distribution of the velocity of the molecules contained in a given quantity of gas in equilibrium. This formulation, known as Maxwell’s law, assumes the form:     kT 4N m 3 2 v exp − n(v)dv = √ p 2kT 2mv2

(3.38)

where n(v)dv is the number of molecules with velocity ranging from v to v + dv, N is the overall number of molecules, p is the pressure, T is the absolute temperature, m is the mass of each molecule and k is a non-dimensional parameter subsequently called Boltzmann’s constant. By applying Eq. (3.38), it is possible to obtain the mean value of various quantities, molecular velocity and kinetic energy in particular, and to interpret many physical phenomena of fluid dynamics and meteorology. By way of example, the mean kinetic energy of the molecules contained in a gas is given by the relationship:

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Ec =

3 kT 2

(3.39)

It provides a microscopic interpretation of the temperature, highlighting its dependence from the mean quadratic value of the molecular velocity. The pressure of a gas contained inside a vessel, likewise, is an effect of the collision of the molecules against walls; it then depends on their momentum. The same concepts allow formulating an elegant interpretation of viscosity. For this purpose, let us examine a fluid flowing in parallel layers (i.e. with laminar motion, Sect. 5.1) such as, for example, the bidimensional flow in Fig. 3.18a. Applying the kinetic theory of gases, the molecules making up the fluid move with a continuous, rapid and irregular motion. The molecules crossing the generic surface α (α = a,…g) from the top downwards possess a momentum (in the z-direction) higher than the one of the molecules they come across with; thus, they tend to accelerate the underlying fluid layer. The molecules crossing the surface α from the bottom upwards, on the other hand, possess a momentum lower than that of the molecules they meet; thus, they tend to slow down the above fluid layer. This determines the inception of dragging and slowing shear stresses τ, respectively, equal and opposite; consistently with Eq. (3.10), they are proportional to the velocity gradient ∂ V /∂z by means of the dynamic viscosity coefficient μ. It, therefore, increases with temperature since, if the velocity gradient is equal, shear stresses are as higher as the molecular agitation velocity is higher. Starting from Maxwell treatment, in 1872, Ludwig Boltzmann (1844–1906) extended the kinetic theory of gases to any physical system consisting of a high number of components; making use of the progress in probability theory, Boltzmann went as far as to found a new discipline, stochastic mechanics, to which the American mathematician and physicist Josiah Willard Gibbs (1839–1903) also provided key contributions. Among its countless fields of application, in 1905, Albert Einstein (1879–1955) applied the principles of this discipline to formulate the Brownian motion theory.

3.9 Structural Mechanics Quoting a passage of Edoardo Benvenuto’s book [7], “historically, the structural mechanics is divided into two great periods: the first, in which, in the absence of accurate stress and deformation concepts, the ‘firmitas’ of the structure was left to the mutual arrangement of its parts, so as to avoid the onset of kinematic motions, and the shape of an arch or of a vault, or of the suitably shaped quoins of a masonry, represented the variable on which it was necessary to operate to obtain self-balanced systems of active and reactive forces; in the second period, conversely, after a structural shape is assigned, the strength properties of the material are investigated so that no breakage takes place and the size of the members are determined to keep internal forces within allowable limits.” Discorsi e dimostrazioni matematiche intorno a due

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Fig. 3.28 a Galilei’s problem [7]; stress distribution in the fixed end section of a cantilever beam [6]: b Galilei (1638); c Hooke (1678) and Leibniz (1684); d Mariotte (1686) and Jakob Bernoulli (1694); e Parent (1713)

nuove scienze attinenti alla meccanica e i movimenti locali, the work of Galileo Galilei published in 1638 (Sect. 3.1), marked the watershed between these two periods. The first day (Scienza nuova prima, intorno alla resistenza de i corpi solidi all’essere spezzati) marked the passage between the two conceptions and is considered by many the foundation deed of structural mechanics.25 In the second day (Quale potesse essere la causa di tal coerenza), the strength of materials and structures was discussed, in particular, the Galilei’s problem, that is, the breaking strength of a cantilever beam with a load at its free end (Fig. 3.28a) [7, 50]. Galilei observed that the load produces a bending of the beam that increases from the free end, where it is null, towards the fixed end, where it is greatest; in this section, the lower edge of the beam behaves as a fulcrum and the tension stress is uniformly distributed (Fig. 3.28b). Galilei also noticed that the presence of a distributed load produces a bending moment that increases with the square of the distance from the free end; to preserve the uniform stress, then, it is necessary to increase the height of the beam in the direction of the constraint. It is the first time the shape of a structural element is discussed on rational bases instead of being passed down by experience. Discorsi (1638) was translated and published in English in 1665. Most copies of this book were lost during a fire in 1666. Thankfully, this happened after the Royal

25 Around 1500, Leonardo da Vinci provided pioneering contributions to material science and struc-

tural mechanics. In 1620, Isaac Beeckman (1588–1637) observed that the fibres at the convex and concave edge of a bent beam are respectively tensioned and compressed. Galilei and his successors demonstrated how such an observation was not necessarily foregone in that age.

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Fig. 3.29 a Hooke’s springs [7]; b Hooke’s flexural beam [7]

Society assigned the study of the book to a committee that included Hooke among its members. Taking his cue from this lucky circumstance, in 1678, Robert Hooke (1635–1703) published in London Lectures de potentia restitutiva, or of spring explaining the power of springing bodies,26 in which he postulated the law of nature (Fig. 3.29a): “In any elastic body it is true that the force or power required to bring it back to its natural position is always proportional to the distance or space from which it is removed, both in case of rarefaction, that is of separation of its parts from each other, and in case of condensation, that is of squeezing of parts drawn close”. Hooke applied this principle to a flexural beam (Fig. 3.29b) observing, unlike Galilei, that “a piece of dry wood bends in such a way to rarefy the fibres of the convex side and to condensate the fibres of the concave side”; he also noticed the existence of a neutral plane with neither rarefaction nor condensation (Fig. 3.28c). In Hooke’s diagrams, the conservation of the plane section, a concept commonly attributed to Navier (1826), is implicit. Edme Mariotte (1620–1684) obtained a simplified formula to size pipes with regard to breakage in Traité du mouvement des eaux et des autres corps fluides, a posthumous work published in 1686. Here, he approached the problem of the cantilever beam, reaching conclusions different from those of Galilei and Hooke. Making use of experimental tests, he maintained that stress linearly varies along the height of the beam, from a null value in the fulcrum at the lower edge of the fixed 26 Hooke illustrated his discoveries through three anagrams. The first one, “Ut pendet continuum flexile sic stabit continuum rigidum inversum”, suggests that a stable arch must have the (inverted) shape of a catenary. The second, “Ut tensio sic vis”, establishes that the power of a spring is proportional to its tension. The third, “Ut pondus sic tensio”, indicates the proportionality between tension and extension.

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155

end section, up to its maximum value at the upper edge (Fig. 3.28d). Analysing the beam supported at both ends, Mariotte also demonstrated that the same beam, when fixed at both ends, sustained a double load, concentrated on its centreline. Gottfried Wilhelm von Leibniz (1646–1716), learning about these results before they appeared, published on Acta Eruditorum Demonstrationes novae de resistentia solidorum (1684), in which he praised the work of Mariotte but criticised the wrong hypothesis according to which the neutral fibre is at the intrados of the fixed end section. Leibniz also clarified the concept of stress, used integral calculus to associate the bending moment with the distribution of stresses and expressed the relationship between the bending moment, the curvature and the moment of inertia. The opinions on this subject, however, remained very discordant. In 1691, Jakob Bernoulli (1654–1705) compared the issue of the elastic rod (or flexural beam) with that of the rope, observing that the first was more complex than the second. He published the solution of this problem in Curvatura laminae elasticae, which appeared on Acta Erutirorum in 1694. Here, Bernoulli espoused the ideas of Mariotte and maintained that the neutral fibre was at the intrados of the fixed end section (Fig. 3.28d). Afterwards, he wrote Véritable hypothèse de la résistance des solides, avec la démonstration de la courbure des corps qui font ressort (1705), in which he formulated the first relationship between stress and deformation; it was intended as a property of the material. The work of the French Antoine Parent (1666–1716) was collected in Researches de mathématique et de physique (1713). In his most important paper, De la véritable mécanique des résistances relatives des solides, et réfléxions sur le système de M. Bernoulli de Bale, Parent resumed Hooke’s scheme of the flexural beam (Fig. 3.29b), confirmed the absence of normal stresses on the neutral plane, divided the beam into two parts in correspondence with such plane and observed the deformation in Fig. 3.30a. He also felt that the beam lost its capacity to behave like a whole, since the separation deprived it of the essential contribution of stresses different from the ones orthogonal to the cross-section: the shear stresses. He understood that, in order to restore the integrity of the beam, it was necessary to restore the effect of such stresses by means of nails or other elements (Fig. 3.30b). He perceived the possibility of moving the compressed zone away from the tensioned zone by means of effective connections between the two parts. He provided an innovative interpretation of the behaviour of truss beam, which in the past were used on purely empirical bases.

Fig. 3.30 Parent’s shear stresses [50]: a beam disconnected along the neutral plane; b tension and compressed parts reconnected

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3 The Wind and the New Science

Parent understood that to determine the normal stresses and to obtain the position of the neutral axis, it was necessary to also take into consideration the equilibrium of the longitudinal forces besides that of the moments. He also discussed the possibility that normal stresses were nonlinear functions of the beam height (Fig. 3.28e). It was necessary to wait until the end of the eighteenth century before Coulomb clarified such concepts. With the advent of the eighteenth century, structural mechanics left its embryonic stage and showed a significant evolution. The theories formulated in the seventeenth century, as well as new studies concerning structural dynamics (Sect. 3.10), equilibrium stability and the microscopic interpretation of the macroscopic laws of elasticity, came to maturity. Experimental tests on materials and structures evolved, becoming the link between theory and application; with them, the awareness that theory can be an essential support for design gained ground. Daniel Bernoulli (1700–1782) evaluated the elastic equilibrium as a minimum problem, imposing an extreme value of the potential energy compatible with suitable restraints to displacements. Euler followed this suggestion in 1744; in Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes and in the associated annex, Additamentum I de curvis elasticis, he provided essential contributions to the variational calculus of elastic lines. In the same work, he clarified the meaning of critical load; the treatment, developed by removing the hypothesis of small displacements, was repeatedly perfected between 1757 and 1778. In the same period, Euler published Genuina principia doctrinae de statu aequilibri et motu corporum tam perfecte flexibilium quam elasticorum (1771), in which he formulated the indefinite equations about beam equilibrium. In 1773, Charles Augustin Coulomb (1736–1806) presented a paper to the French Academy, Essai sur une application des règles de maximis et minimis à quelques problèmes de statique relatifs à l’architecture, published in 1776. Making use of the results of experiences, he expounded discoveries concerning the laws of friction, shear stresses, solid breakage and beam bending. He separated the concept of friction from that of cohesion. He differentiated static from dynamic friction as well as sliding from rolling friction. He developed a breakage criterion founded on a new conception of shear stresses, applying it to the pressure of the earth, to retaining walls and to the working of arches. Finally, resuming some intuitions of Parent, he gave a complete form to the beam bending theory. The English Thomas Young (1773–1829) took part in the debate about the Thomas Telford’s (1757–1834) project of the new London Bridge. Since he desired to build the bridge with a single span consisting of a cast iron truss structure, Telford entrusted Young with the performance of tests on the material. During the tests, Young introduced the concept of elastic modulus, a quantity that today is known with his name, presenting it in 1807 (Of the equilibrium and strength of elastic substances). Young also first treated the problem in which a column subject to combined bending and compression stress would not be perfectly straight, highlighting the role of imperfections and tolerance. He also provided a criterion to evaluate the maximum eccentricity a column can withstand retaining its section wholly compressed; he proved that, for a rectangular section, eccentricity must stay in the median third.

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In parallel with the macroscopic view of elasticity, a microscopic interpretation destined to achieve great success in the nineteenth century also developed. In the Queries added to the second edition of Optics or a treatise of the reflections, refractions and colours light (1717), Newton maintained that elasticity was a consequence of the attraction among the atoms making up bodies. This idea was shared by Pieter van Musschenbroek (1692–1761) in Physicae experimentales et geometricae dissertationes (1729), in a spirit close to the old Aristotelian physics (“vis interna attrahens”). The first attempts to free the interpretation of elasticity from the prejudices of natural philosophy were carried out by Jacopo Belgrado, in De corporibus elasticis disquisitio physico-mathematica (1748), and by Jacopo Riccati, in Verae et germanae virium elasticarum leges ex phaenomenis demonstratae (1761); they approached the problem in mechanical terms, maintaining that the “vis elastica” originated from the succession of infinite infinitesimal collisions. New developments of this subject are credited to Ruggero Giuseppe Boscovich (1711–1783) (1763), Simeon Denis Poisson (1781–1840) (1812), Pierre-Simeon Laplace (1739–1827) (1819) and, especially, to Louis Navier (1785–1836) (1821). The progress of the scientific knowledge about materials and structures received a decisive impulse from the diffusion of the experimental activity, mainly related to beams (mostly wooden ones), and from the divulgation of their results by means of tables. Among other contributions [12], in 1729 van Musschenbroek published Dissertatione physicae experimentales et geometricae, in which he discussed the diversity of behaviour of solids subject to tension, bending and compression, describing some equipment for load tests (Fig. 3.31a); he also provided important results about the limit compression load for thin poles in relation with their length. In 1742, Henry Louis Du Hamel (1700–1781) developed a remarkable idea to strengthen wood (in Réflexions et expériences sur la force des bois): observing the difference in strength between tensioned and compressed fibres, he proposed to insert a strengthening material in the weak parts; he so anticipated the mixed structures, namely the truss beams composed by elements of different metals (Sect. 4.9) and reinforced concrete (Sect. 4.7). In 1798, Pierre-Simon Girard (1765–1836) published Traité analytique de la résistance des solides et des solides d’égale résistance, where he described tests on wooden beams carried out using sophisticated equipment (Fig. 3.31b); he interpreted his own work by quoting a sentence by d’Alembert (from Elémens de philosophie) summarising the evolution of experience in the eighteenth century: “Experience will not only be useful to confirm theory, but distinguishing itself by theory without suppressing it, it will lead to new truths, that theory alone would not have been able to achieve”. The results of these tests received increasing attention thanks to some popular works about the role of the engineer and his activity. The six volumes by Bernard Forest de Belidor (1693–1761), La science des ingénieurs, published in 1729 and reprinted up to 1830, stand out among others (Principles of mechanics applied to the research of the dimensions to give to the cladding of fortifications, so that they are balanced with the thrust of the grounds they must support; Mechanics of the vaults, the thrust of vaults, the method to determine the size of their piers; About construction

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Fig. 3.31 Experimental investigations of van Musschenbroek [7] (a) and Girard (b)

materials, their properties and ways to lay them; Construction of military and civil buildings; Decoration of buildings, explanation of the peculiar terms of Architecture Orders; Method to perform estimates for the construction of fortifications and civil factories). They had an essential impact on the formation of the new figure of the engineer, which took on connotations differing from those of the architect, especially in France. While the Académie d’Architecture, active since 1671, was prone to take inspiration from the humanistic and artistic aspects, the years 1747 and 1748 saw the foundation, respectively, of the École des Ponts et Chaussées and of the l’École des Ingénieurs de Mézières, both of them based on the scientific and technical knowledge. The turning point happened in 1794, with the inauguration of the École Centrale des Travaux Publics. The following year, it became the École Polytechnique, summoning as teachers scientists like Joseph Louis Lagrange (1736–1813), Gaspard Monge (1746–1818), Gaspard De Prony (1755–1839), Jean Baptiste Joseph Fourier (1768–1830) and Simeon Denis Poisson (1781–1840), who were entrusted with the task of laying the foundations of technical learning on solid mathematical, mechanical, physical and chemical knowledge bases. So, a strict relationship between physical–mathematical sciences and technical–engineering applications came into being. To cap it all, in 1806 Napoleon Bonaparte (1769–1821) established the École des Beaux-Arts as the antagonist of the École Polytechnique; this aggravated the split between architecture and engineering, intensifying the crisis of identity of the former towards the scientific progress of the other. Thanks to these innovations, in the early nineteenth century, the École Polytechnique was the fulcrum of the French scientific culture. Prominent scientists were drawn around this school: Louis Navier (1785–1836) was among them. In 1821, he presented to the French Academy Mémoire sur les lois de l’equilibre et du mouvement des solides élastiques, a work published in 1827 that provided an analytic deduction of the relation between the molecular actions and the phenomenological description of the behaviour of solids; it marked the start of the modern theory of elasticity.

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In the meantime, Navier collected his lessons at the École des Ponts et Chaussées in Résumé des lecons (…) sur l’application de la mécanique, a book published in 1826; it was judged by many as the first complete work of structural mechanics; it influenced the engineering of the nineteenth and twentieth century, favouring the separation from Galilei’s breakage calculus, towards the study of the service state of elastic structures. Navier was also the author of Rapport et mémoire sur les ponts suspendus, a treatise he wrote on his return from several study trips to England he made between 1821 and 1823; this work, much celebrated even as a consequence of the prominence of his author, gained great influence, even though often not positive, on the cable-supported bridges of the nineteenth (Sect. 4.8) and of the early twentieth century (Sect. 9.1). At the same time, between 1821 and 1828, Augustin Louis de Cauchy (1789–1857), another French engineer educated at the École des Ponts et Chaussées who joined the teaching staff of the École Polytechnique, wrote Cours d’analyse de l’École Polytechnique (1821), Le calcul infinitésimal (1823) and Lecons sur les applications du calcul infinitésimal à la géometrie (1826–1828), in which he clarified the infinitesimal calculus. In 1828, Cauchy extended Navier’s approach in Sur l’équilibre et le mouvement d’un système de points matériels sollecités par des forces d’attraction ou de répulsion mutuelle and De la pression ou tension dans un système des points matériels, in which he developed the concept of stress still in use today, the big theorem (“the knowledge of the stresses on three distinct elementary surfaces is sufficient to determine the stress on any other elementary surface”), the concept of main stress, the indefinite equations of equilibrium, the metric of deformation and a general definition of the elastic constitutive law. From this moment, structural mechanics made unrelenting advancements [12]. The necessity to follow them in detail, however, fades away, at least for the purposes of this book. By that time, the concepts affecting the building of structures in which the first conflicting relationships with wind actions have already come to light (Sects. 4.8 and 4.9).

3.10 Music, Sound and Vibration Discussing three apparently distinct subjects like music, sound and vibrations in the same paragraph may appear as a bizarre decision. In the culture of the seventeenth, eighteenth and nineteenth centuries, however, they were so connected as to make any different approach very complicated. The interest in music and sound developed since the antiquity, first in the legends about the Aeolian harp (Sect. 2.1), then through the contribution of Pythagoras, Aristotle, Aristoxenus, Lucretius, Vitruvius (Sects. 2.2 and 2.3) and many others. The study of the mechanisms and of the physical properties of sound [1, 2, 6, 25, 51–53] took on a scientific character from the seventeenth century, thanks to Galileo Galilei (1564–1642), in Discorsi e dimostrazioni matematiche intorno a due nuove scienze attinenti alla meccanica (1638). Taking his cue from the law of

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pendulum oscillation, he studied the relationship between the vibration of strings and the emission of sound. In opposition to Aristotle, who attributed the diversity between sharp and low sounds to their different velocity of propagation in the air, Galilei proved that the pitch of the sound depends on the frequency at which the string vibrated and is a function of three parameters: its length, weight and tension. He also proved the sound vibrations were transmitted in the air with a wavelike motion and that sounds propagated faster in liquids and solids than in the air. Galilei was also the first to highlight the phenomenon of resonance, discussing the occurrence of “sympathetic” vibrations27 : “The string, once touched starts and continues its vibrations. These vibrations make the surrounding air vibrate and tremble; the tremble and the ripples extend for a wide space and impact against all the strings of the instrument itself and of other nearby ones as well. The string, which is taut in unison with the touch-needle, being arranged to make its vibrations to the same time, starts moving a little at the first pulse and when the second, the third, the twentieth and many more reach it, all of them in their adjusted and periodical times, it finally receives the same tremble of the touch-needle, and it is clearly visible how it expands it vibrations just at the space of its motive”. Galilei compared this phenomenon to that of a pendulum that transmits its motion to a pendulum at rest. He also enunciated the embryonic laws of harmony and dissonance, subsequently explained through the concepts of in-phase and out-of-phase waves. In the same period, the French mathematician Marin Marsenne (1588–1648) measured the return time of the echo, obtaining an estimate of the speed of sound in the air with an error smaller than 10%. He published the first scientific treatise about this subject, Harmonicorum liber (1636), illustrating various experiments to determine the relation between the sound pitch and the length, the thickness and the tension of a string made of different materials. He demonstrated that, all other parameters being equal, the following proportions applied: na = nb



pa ; pb

na = nb



qb ; qa

na b = ; nb a

na db = ; nb da

na = nb



ρb ρa

(3.40)

where n is the vibration frequency, p is the weight that sets the string in extension, q,  and d are the weight, the length and the diameter of the string, ρ is the specific weight of the material; the a and b indices refer to two distinct strings. Marsenne discovered that a vibrating string produced, beside the fundamental note, overtones with frequency nk = kn1 , being k a natural number greater than 1 and n1 the fundamental frequency of the string. He noted that, when the fundamental tone faded out, overtones became clearly audible, since they lasted longer. Marsenne informed Descartes about his discovery; the latter, in his reply, associated the overtones to independent vibrations of limited parts of the string. 27 Before Galilei vibrations were interpreted, at popular level, as the effect of a kind of sympathy of strings as regards to the vibrating one. They attracted the interest of Leonardo da Vinci who wrote: “The blow struck in the bell will make a similar bell reply and move a lot; the played string of a lute will make another similar string of similar voice in another lute reply and move, and this you will see by placing a straw over a string similar to the played string”.

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Fig. 3.32 Experience of Noble and Pigot [6]

Two Englishmen William Noble and Thomas Pigot (1657–1686) devoted themselves to the same issue. In 1673, unaware of Descartes’ interpretation, they carried out a famous experiment (Fig. 3.32) [6]: “Let AC and ag (a) be two nearby strings, made so that the fundamental note produced by the vibration of AC is the first octave of that of ag; AC, therefore, is in unison with each half of ag. If AC is played, the two halves of ag, that is ab and bg, both vibrate, while the mean point b remains motionless. Likewise, if the AD string, the fundamental note of which is the twelfth above that of ad (b), is played, ad vibrates in three equal parts, ab, bc and cd, while the points b and c remain motionless. And so on (c, d)”. The test of Noble and Pigot was reported by John Wallis (1616–1703) in the Philosophical Transactions of April 1677. According to Wallis, by then it was known that making a string of an instrument vibrate, it caused the vibration in unison of all the nearby strings. The novelty in the experiment of Noble and Pigot was that the same string could produce multiple notes. Similar experiments were carried out by Robert Hooke (1635–1703) and Joseph Sauveur (1653–1716) in the late seventeenth century. During these experiments, Sauveur coined the term acoustics to describe the science of sound [51]. He introduced the concepts of node and anti-node to indicate the points of rest and of maximum amplitude of a vibrating string. He confirmed that the same string can vibrate and play in several different ways: taking into consideration Fig. 3.33 [6], it can vibrate without nodes on the fundamental note (AA), with two nodes a and a1 producing an overtone (BB) or through a combination of elementary forms of vibration (CC). Indeed, if no particular measures were used to prevent vibrations of the AA or BB type, CC is the usual form in which the string vibrates. Such results, published in 1701 in the Mémoires de l’Academie des Sciences of Paris, were the embryo of modal analysis. Saveur was also the first to study the phenomenon of the beating occurring when two organ pipes with slightly different tones were played simultaneously. In 1715, the British mathematician Brook Taylor (1685–1731) published a treaty, Methodus incrementorum directa et inversa, in which he developed the homonymous series he used to analyse vibrating strings. In the same treatise, he linked Marsenne’s

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Fig. 3.33 Overtones and harmonic combinations [6]

proportions (Eq. 3.40), obtaining the analytic expression of the fundamental frequency of a string: 1 n1 = 2



gp q

(3.41)

where g is the gravity acceleration. The study was carried out attributing a sinusoidal law to the vibration shape and did not mention the frequencies of higher modes. Similar studies were carried out by Colin Maclaurin (1698–1746) and published in A treatise of fluxions (1742). Beside these discoveries, a concept as groundless as rooted persisted. In the spirit of similar disputes about the transmission of heat (Sect. 3.7) and light [6], scholars like William Derham (1657–1735) (1705), Jean-Jacques D’Ortous De Mairan (1678–1771) (1737) and Johann Heinrich Lambert (1728–1777) (1768) insisted on the existence of one or more species of thin particles, mixed with air, physically carrying the sound. On the other hand, many scientists, including Johann and Daniel Bernoulli, Euler and Lagrange, used the new tools of the differential calculus (Sect. 3.3), and in particular partial derivatives, to delve into the study of sound and music on theoretical bases. They set their attention on the pitch and tone of the sounds produced by various instruments and on the sound transmission mechanism in different media. In this spirit, a connection between acoustics and mechanics came into existence: it laid the foundations of the modern dynamics of structures [25, 52, 53]. In 1727, Johann Bernoulli (1667–1748) experimentally studied the vibration of a taut string without mass, along which N equal and evenly spaced weights were applied. Using a quasi-static device, he determined the fundamental frequency of the string for N = 1–7.28 Like Taylor, he did not mention the frequencies of the higher modes. Daniel Bernoulli (1700–1782) was the first to approach this problem. Initially, he studied the bifilar pendulum, i.e. a string with no mass to which two weights were 28 The

same model had previously been studied by Huygens only for the case N = 1.

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applied; using a quasi-static device, he demonstrated the existence of two main modes and evaluated their characteristic shapes and frequencies. Afterwards, he generalised this experience by means of a string with N applied weights, highlighting as many distinct vibration modes, each one of them with its own shape and frequency. He also understood that a heavy string had infinite vibration modes. In the same period, Leonhard Euler (1707–1783) wrote Mechanica, sive motus scientia analytice exposita; it was published in 1736 and established the foundations of dynamics as a rational science. Starting from the definitions of force (“a cause that produces or alters the motion of bodies”) and inertia (“the faculty inherent in all bodies to remain at rest or in uniform straight motion”), Euler maintained that the use of the principle of causality led to equalise the cause to the effect. From this, the fundamental relation of dynamics was derived: fdt = d(mv)

(3.42)

where f is the force vector, t is the time, m is the mass and v is the velocity vector. Equation (3.42) is a system of differential equations necessary and sufficient to describe the motion. Using this result, in 1734, Euler and Daniel Bernoulli studied, for the first time, the differential equation of the small transversal oscillation of an elastic prismatic beam, obtaining the vibration modes through a series expansion. Between 1734 and 1739, Bernoulli proved that the vibrations of strings and beams may involve single vibration modes or their combinations; this aspect was called “principle of co-existence of the small oscillations” by Bernoulli. In 1739, Euler published the first scientific essay about the theory of music, Tentamen novae theriae musicae, in which he used Taylor’s Eq. (3.42) to evaluate the pitch of the sounds. In the same year, Euler developed the experimental and theoretical analysis of a simple oscillator subjected to a harmonic load, highlighting the phenomenon of resonance in analytic form. He also determined the general integral of the linear differential equations with constant coefficients, simplifying the study of the transversal vibrations of prismatic beams. Starting from this result, in 1743, Euler and Bernoulli set the boundary conditions of the beams with fixed, hinged and free ends; they evaluated six possible forms of oscillation and determined the whole sequence of the characteristic frequencies and modes for four of them. Euler’s memoranda were more exhaustive and elegant; Bernoulli, who experimentally verified most of his results, was better in knowing the physical phenomena [25]. It was the prelude to the publication of De moto corporum flexibilium (1744) and Découverte d’un nouveau principe de mécanique (1750), in which Euler expressed, for the first time, Newton’s second law in the now classic form: f x = max ;

f y = ma y ;

f z = maz

(3.43)

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where f x , f y , f z and ax , ay , az are the Cartesian components of the force and of the acceleration. In these works, Euler studied a taut string, schematised by means of N equal concentrated masses connected by springs. He obtained the general solution of the equation of motion as the combination of N particular solutions, each one of them corresponding to a main mode with a given frequency and a characteristic oscillation shape. He calculated the value of the multiplicative factors of the terms of the combination, by applying an initial shift at the end mass. Daniel Bernoulli obtained a similar result in 1753 on more physical grounds. Joseph Louis Lagrange (1736–1813) developed the analytic solution of the vibrating string in a paper published by the Academy of Turin in 1759. He assumed that the string was composed by a finite number of evenly spaced identical masses and demonstrated the existence of a number of eigenfrequencies equal to the number of the masses. He also demonstrated that, as the number of the masses tended towards infinity, the frequencies of the discrete system tend to those of the continuous string. In the same year, Euler approached for the first time the study of a bidimensional continuum instead of a monodimensional one, obtaining the equation of motion of a membrane assimilated to a fibre network; he used it to determine the vibration modes and the natural frequencies related to circular and rectangular geometries, through which he studied the sound of drums. In 1762, Daniel Bernoulli formulated the theory of organ pipes, establishing analogies with the sounds of strings. In 1784, Charles Augustin Coulomb (1736–1806) studied, on theoretical and experimental bases, the torsional oscillations of a metal cylinder sustained by a wire; he assumed that the resistance to torsion was proportional to the angle of rotation and derived the first equation of the torsional motion. In 1786, Giordano Riccati29 (1709–1790) studied the vibration of the beams free at both ends and those of the membranes taut on their contour. It was the prelude to the publication of Mécanique Analitique (1788), in which Lagrange introduced a variational principle applicable to any mechanical system. He approached the study of the systems consisting of point concentrated masses, the motion of which was described by generalised co-ordinates later called Lagrangian, and arrived at the homonymous equation of analytic dynamics: dL d dL − =Q dt dq˙ dq

(3.44)

where L is the Lagrangian function, i.e. the difference between the kinetic and the potential energy, Q is the external force, q is the free or Lagrangian co-ordinate. In parallel, the interest in the rational comprehension of sound became widespread. Jean-Philippe Rameau (1683–1764), a French composer and musical theorist, demonstrated that a string can only emit the fundamental sound when excited at half its length, then on it fundamental vibration mode (Principes d’harmonie, 1750). The Italian violinist Giuseppe Tartini (1692–1770) observed that, simultaneously 29 The

father of Giordano Riccati, Jacopo Riccati (1676–1754), attempted to establish the first dynamic theory of elasticity for a long time.

3.10 Music, Sound and Vibration

165

producing two sounds, a third sound was also heard, with frequency equal to the difference between the frequencies of the two initial sounds (Trattato di musica secondo la vera scienza dell’armonia, 1754); he subsequently carried out studies about beatings called “combination sounds” (Dè principi dell’armonia musicale, 1767). Similar researches were carried out by the German organist Georg Andreas Sorge (1703–1778). Ernesto Chaldini (1756–1827), a scholar in acoustics and dynamics, discovered that the longitudinal vibrations of strings (1787) and rods (1796) were governed by the same laws valid for pipes; he subsequently devoted himself to the vibration of plates and to the sound of drums. In 1809, the Academy of France invited Chaldini to give a demonstration of his experiments [52]. He spread a thin layer of sand on a vibrating plate, highlighting complex vibration modes. Napoleon Bonaparte, who was present at the experiment, was so impressed to make a 3000 francs award available to the Academy for the first one capable of analytically interpreting this phenomenon. In October 1811, at the expiration of the notice, only one participant showed up, the French mathematician Marie-Sophie Germain (1776–1831). Lagrange, one of the judges, found an error in the differential equation of motion. The Academy did not assign the award and reopened the contest up to October 1813. Germain presented herself again with the correct solution, but she was not granted the award because of the lack of physical explanations of her assumptions. The competition was again reopened up to 1815, when Germain, at her third attempt, won the competition despite the reserves of some judges. Later, it was proved that the equation of motion was correct, but the boundary conditions were wrong. It was necessary to wait until 1850 for Gustav Robert Kirchoff (1824–1887) to provide a flawless solution.

References 1. Pitoni R (1913) Storia della fisica. Società Tipografico-Editrice Nazionale, Turin 2. Dampier WC (1929) A history of science and its relations with philosophy and religion. Cambridge University Press, London 3. Brown S (1961) World of the wind. Bobbs-Merrill, Indianapolis, New York 4. Palmieri S (2000) Il mistero del tempo e del clima: La storia, lo sviluppo, il futuro. CUEN, Naples 5. Shaw N (1926) Manual of meteorology. Volume I: Meteorology in history. Cambridge University Press 6. Wolf A (1935) A history of science, technology and philosophy in the 16th & 17th centuries. George Allen & Unwin, London 7. Benvenuto E (1981) La scienza delle costruzioni e il suo sviluppo storico. Sansoni, Florence 8. Whipple ABC (1982) Storm. Time-Life Books, Amsterdam 9. Sorbjan Z (1996) Hands-on meteorology. American Meteorology Society 10. Vittori O (1992) L’atmosfera del pianeta terra: Struttura e fenomeni. Zanichelli, Bologna 11. Aynsley RM, Melbourne W, Vickery BJ (1977) Architectural aerodynamics. Applied Science Publishers, London 12. Hardy R, Wright P, Gribbin J, Kington J (1982) The weather book. Harrow House 13. Hambly R (2001) The invention of clouds. Picador, New York 14. Rouse H, Ince S (1954–1956) History of hydraulics. Series of Supplements to La Houille Blanche. Iowa Institute of Hydraulic Research, State University of Iowa

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15. Bender CB (1882) The design of structures to resist wind-pressure. Proc Inst Civil Eng, LXIX, pp 80–119 16. Baynes CJ (1974) The statistic of strong winds for engineering applications. Ph. D. Thesis, The University of Western Ontario, London, Ontario, Canada 17. Robinson JTR (1850) Description of an improved anemometer for registering the direction of the wind and the space which it traverses in given intervals of time. Trans R Irish Acad 22:155–178 18. Handbook of meteorological instruments. Part I: Instruments for surface observation. Meteorological Office, Her Majesty’s Stationery Office, London (1956) 19. Goldstine HH (1972) The computer from Pascal to von Neumann. Princeton University Press 20. Colombo U, Lanzavecchia G (ed) (2002) La nuova scienza. Vol. 3: La società dell’informazione. Libri Scheiwiller, Milan 21. Zientara M (1981) The history of computing: a biographical portrait of the visionaries who shaped the destiny of the computer industry. CW Communications, Redditch Worcs, UK 22. Todhunter I (1865) A history of the mathematical theory of probability. Cambridge University Press 23. Maistrov LE (1974) Probability theory. A historical sketch. Academic Press, New York 24. Kottegoda NT, Rosso R (1997) Statistics, probability, and reliability for civil and environmental engineers. McGraw-Hill, New York 25. Truesdell C (1968) Essays in the history of mechanics. Springer, Berlin 26. Truesdell C (1953) Notes on the history of the general equations of hydrodynamics. Am Math Mon LX:445–458 27. von Karman T (1954) Aerodynamics. Cornell University Press, Ithaca 28. Proust J (1985) Recueil de planches sur les sciences, les arts libéraux et les arts mécaniques. Hachette, Paris 29. Anderson JD (1998) A history of aerodynamics. Cambridge University Press 30. Navier CLMH (1827) Mémoire sur les lois du mouvement des fluides. Mémoires l’Acad Sci 6:389–416 31. Poisson SD (1831) Mémoire sur les équations générales de l’équilibre et du mouvement des corps solides élastiques et des fluides. J l’École Polytech 13:139–186 32. De Saint-Venant B (1843) Note à joindre au mémoire sur la dynamique des fluides. C R Séances Acad Sci 17:1240–1244 33. Stokes GG (1845) On the theories of the internal friction of fluids in motion. Trans Camb Philos Soc 8:287–305 34. Buresti G (2015) A note on Stokes hypothesis. Acta Mech 226:3555–3559 35. Stokes GG (1851) On the effect of the internal friction of fluids on the motion of pendulums. Trans Camb Philos Soc 9: 8–106 36. Helmholtz H (1858) Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. J Angew Math 55:25–55 37. Helmholtz H (1868) Über discontinuirliche Flüssigkeitsbewegungen. Monatsberichte der Königlichen Akademie der Wissenschaften zu Berlin, pp 215–228 38. Kirchhoff G (1869) Zur Theorie freier Flüssigkeitsstrahlen. J die reine Angew Math 70:289–298 39. Rayleigh Lord (1876) On the resistance of fluids. Philos Mag Ser 5: 430–441 40. Rayleigh Lord (1878) On the irregular flight of a tennis-ball. Messenger Math 7:14–16 41. Boussinesq J (1877) Théorie de l’écoulement tourbillant. Mém présentés par divers savants à l’Acad des Sci 23:46–50 42. Parolini G, Del Monaco A, Fontana DM (1983) Fondamenti di fisica tecnica. UTET, Turin 43. Calì M, Gregorio P (1996) Termodinamica. Progetto Leonardo, Bologna 44. Leicester HM (1956) The historical background of chemistry. Wiley, New York 45. Singer C, Holmyard EJ, Hall AR, Williams TI (eds) (1956) A history of technology. Oxford University Press, NewYork 46. Klemm F (1954) Technik, eine geschichte ihrer probleme. Karl Alber, Freiburg - Munchen 47. Truesdell C (1980) The tragicomical history of thermodynamics 1822–1854. Springer, New York

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Cardwell DSL (1971) From Watt to Clausius. Heinemann, London Truesdell C (1984) Rational thermodynamics. Springer, New York Hopkins HJ (1970) A span of bridges. David & Charles, Newton Abbot, UK Lindsay RB (1966) The story of acoustics. J Acoust Soc Am 39:629–644 Rao SS (2005) Mechanical vibrations. Pearson, Prentice Hall, Singapore Cannon JT, Dostrovsky S (1981) The evolution of dynamics: vibration theory from 1687 to 1742. Springer, New York

Chapter 4

The New Culture of the Wind and Its Effects

Abstract The advent of the new science addressed in Chap. 3 provided the bases for the foundation of a renewed culture of the wind and its effects. This chapter deals with this topic by illustrating the first rational approaches to meteorology and weather forecasting, a varied set of pioneering measurements of the resistance of bodies in the air, the adoption of scales to quantify the intensity of wind and its effects. In parallel, it points out how the new culture about the wind increasingly interacted with the life of humans and their works, strengthening the dualism between the wind as a source of life and progress and the wind as an instrument of death and devastation. On the one hand, it then presents the wind exploitation as a tool for the propulsion of vessels with increasingly efficient sails, the links between wind and flight in scientific research, and the improved efficiency of windmills. On the other hand, it focuses on the appearance of a new generation of fascinating structures, on the sensitiveness of cable-supported and truss bridges to wind loading, on the indifference of the designers towards the emerging concepts about vibrations.

The advent of the new science, which pervaded humanity and every sector of knowledge since the sixteenth century (Chap. 3, Sect. 3.1), provided essential instruments and ideas for the foundation of a new culture of wind and its effects. The diffusion of the atmospheric instruments and measurements (Sect. 3.2) as well as the advances in mathematics (Sect. 3.3), mechanics (Sect. 3.5), fluid dynamics (Sect. 3.6) and thermodynamics (Sect. 3.7) provided new and firm foundations to rationally approach the study of meteorology and weather forecasting (Sect. 4.1). The resistance of bodies in fluids, in this case in air (Sect. 4.2), became the subject of a vast, multidisciplinary interest. A broad agreement developed about the necessity to adopt scales to quantify the intensity of wind and its effects (Sect. 4.3). In parallel, the new culture of the wind increasingly interacted with the life of humans and with their works, strengthening the ancient dualism between the wind as a source of life and progress and the wind as an instrument of death and devastation (Sect. 2.1). Humanity made use of the renewed knowledge of wind to better exploit this phenomenon as a means of propulsion for vessels with increasingly efficient sails (Sect. 4.4). The links between wind and flight grew in the context aimed towards © Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_4

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scientific research (Sect. 4.5). Technological evolution improved the efficiency of windmills and favoured their diffusion (Sect. 4.6). The new tools of structural mechanics (Sect. 3.9) and the evolution of material technology taking place during the Industrial Revolution favoured the appearance of a new generation of original and fascinating structures (Sect. 4.7). Some of them, especially metal bridges supported by cables (Sect. 4.8) or with truss structure (Sect. 4.9), showed a peculiar sensitiveness to wind actions, highlighting the dangers of this phenomenon. The indifference of designers towards the new concepts about vibrations (Sect. 3.10) was typical of this age. As a whole, this chapter provides a picture of knowledge not entirely associated with the wind and its effects. On the other hand, the culture about this phenomenon, seen either as a friend or a foe, was by then deeply ingrained in humankind and increasingly attracted scientific interest under many perspectives. The conditions that would lead, in the first half of the twentieth century, to the foundation of scientific disciplines aimed at dealing with specific issues related to wind (Chaps. 5–10) had arisen.

4.1 The First Meteorology Studies Leaving medieval obscurantism behind, from the fifteenth century and especially from the sixteenth, scepticism towards astrology grew stronger (Sect. 2.4). At the same time, in the evolutionary spirit pervading humankind, the interest for the scientific interpretation of meteorological phenomena and for weather forecasting on rational bases also grew as well. This was a consequence of the evolution of atmospheric instrumentation (Sect. 3.2) and of two conditions specific of this age: the invocation of the role of the wind in history and the fabulous adventures of the first explorers. Mankind first realised that storms were capable of subverting the course of history and that the knowledge and forecasting of weather might be strategically important from the political and military viewpoint. The search for episodes supporting this theory became a fashion and provided countless examples (1215–1294) [1–4]. In 480 BC, Themistocles (approximately 530–462 BC), commanding a Greek fleet of 360 small ships, waited for a gale to attack Xerxes, commanding a Persian fleet of 1400 large ships; he won because of the difficulty of controlling the Persian heavy ships under strong winds. In 1281, the huge fleet of the Mongol emperor Kublai Khan (1215–1294) was wiped out by a typhoon while it was getting ready to invade Japan. In 1588, England retained its dominance of seas, as well as its independence, with the aid of a storm that destroyed the Spanish Invincible Armada. In this age, moreover, the ships of the first explorers (Sect. 4.4) sailed across the oceans and humanity sympathised with these epic deeds, realising that a better knowledge of winds and weather phenomena would have allowed safer travel as well as new discoveries. Christopher Columbus (1451–1506), Vasco da Gama (1469–1524), Ferdinand Magellan (1480–1521), William Dampier (1652–1715) and James Cook

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(1728–1779), to quote only the most famous ones, acquired a mass of information about weather and climate essential for the progress of knowledge in the eighteenth century and brought to the attention of the world the central role of the wind [5]. Many maintain that Christopher Columbus was the precursor of weather and wind forecasts [4]. According to Michele da Cuneo, his companion in adventure, mister Armirante (the admiral) “when sailing, was able to indicate, by only looking at a cloud or at a star by night, the incoming weather and if bad weather was to be expected”. During his voyages between Europe and America, Columbus acquired such accurate knowledge of the trade winds of the northern hemisphere to be able to plan his routes so as to always sail before the wind; he travelled at southern latitudes when sailing westwards and at northern latitudes when sailing eastwards. He also became expert in the dynamics of tropical storms. It is said that in the summer of 1502, while he was in Santo Domingo, having sensed the arrival of a hurricane, he alerted the Governor of Hispaniola, who was about to sail for Spain with a fleet laden with goods. The governor sailed despite Columbus’ warning and lost 20 ships and 500 crewmen [6, 7]. Fascinated by the new reality, the Royal Society dedicated the first volume of its transactions, Directions for sea-men (1666), to this subject, drawing up a detailed description of how seafarers had to collect meteorological data, especially information about winds [8]. In 1671, Ralph Bohun (1639–1716) published Discourse concerning the origins and properties of wind in Oxford; many consider it as the first scientific attempt to explain wind in its manifestations. Bohun illustrated the ground for his work in the preface: “Considering the unsuccessful attempts of severall Authors who have adventur’d upon this difficult part of meteorology, I was sufficiently discourag’d from exposing to publick view those collections, which I had sometime made concerning the causes and properties of winds. But afterward, by reason of my residence in a place principally concern’d in naval affairs (where I had frequent opportunities of conversing with the most experienc’d of our sea captains) I began to compare the observations of their voyages, with the writings of the most celebrated of the ancient, and modern philosophers which I judg’d the only expedient to arrive at a more perfect history of winds”. He therefore wrote about the works of various philosophers and scientists who dealt with this subject, presenting his work as a “fuller account both of the regular, and tempestuous winds, the land and sea breezes, and other particulars which most writers had past by in silence”. He also apologised for any possible errors, maintaining that, “no exact demonstration to be expected in physiological sciences, I might challenge the freedom of my own thoughts, reserving for others the same liberty, (…), and to interpret nature as they please”. Bohun, besides some rather questionable statements, formulated some fascinating theories. He discussed the formation of stormy clouds and their capability to produce tornadoes as well as “a sudden puff of wind, driven from between two clouds, with a violence displosion of the air, that descends almost perpendicularly to the Earth1 ”. He also discussed the 1 The

reference to a column of air coming down from a storm cloud anticipated by three centuries, the studies on downbursts (Sects. 7.3 and 10.2).

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causes of hurricanes and described the locations where they most often occur; he noticed the presence of violent circumferential air currents around a calmer centre. In the meantime, the advancements in mathematics (Sect. 3.3), mechanics (Sect. 3.5) and fluid dynamics (Sect. 3.6) laid the basis for the foundation of the study of such phenomena [7–11]. It was not by accident that Edmund Halley (1656–1742), an English astronomer and friend to Newton, with whom he shared his scientific thinking, was the one to impose a shift to meteorology. Halley is renowned for having discovered and studied the comet bearing his name, in 1682, and for persuading Newton to divulge the results he achieved in 1685 (Sect. 3.5). His contributions to the knowledge of atmospheric motions were inspired by the observation he performed during the voyages he made to catalogue the stars of the southern hemisphere and by the information gathered by the Royal Society through the explorers of that age. Making use of such information, in 1686, Halley published An historical account of the trade winds and monsoons,… [12], where he pointed out, for the first time, that the wind is due to “the action of the sun’s beams upon the air and water, as he passes every day over the oceans”. He also understood the existence of huge movements of cold air heading from the poles to the equator. He explained that the equator, being closer to the energy source represented by the sun, receives a greater amount of sunrays than the other parts of the Earth. As a consequence, this causes the formation of a hot air belt around the equator; such hot air belt tends to move upwards, while the cold air coming from the poles tends to occupy its former place. Taking advantage of his knowledge of the tropical–equatorial belt, Halley properly described doldrums, typical of the latitudes between 10° South and 10° North, the flows crossing the equator and trade winds, that is the winds blowing with almost constant direction and speed (approximately 5 m/s) in the belt of each hemisphere between 10° and 30° of latitude. Establishing a link between trade winds and the local warming of the earth surface, Halley took up an intuition of Francis Bacon, who attributed the equatorial breezes to the expansion of air caused by solar heat (Historia naturalis et experimentalis de ventis, 1638). He understood the circulation nature of the wind and the presence of upper currents heading in the direction opposite to those at ground level (“the north-east trade wind below will be attended with a south-westerly above and the south-easterly with a north-west wind above”).2 Halley also provided the first interpretation of monsoons. He understood that every air current is an element of a more general circulation system and that the monsoon, far from being an independent phenomenon, is simply a local variation of the trade winds. During the summer months, the continental areas warm up faster than ocean waters and wind blows from the cold ocean to the warm land; in the winter months, it blows in the opposite direction. In other words, the monsoon is a breeze on a planetary scale. 2 Hooke also discussed the cause of trade winds and the circulatory character of the wind (Posthumous

works, 1705): “the natural tendency of air to move from regions of higher pressure to regions of lower pressure would cause winds to blow at ground level towards the equator, from which they returned poleward at a higher level, thus maintaining a constant circulation of air”.

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Fig. 4.1 Halley’s wind chart (1688) [12]

In 1688, besides the world magnetism map, Halley drew up the first wind chart (Fig. 4.1). He reported monsoons and trade winds on the Indian Ocean, introducing the use of arrows3 : “I believed it necessary to adjoin a scheme, showing at one view all the various tracts and courses of these winds. (…) I could think of no better way to design the course of the winds (…) than by drawing of stroaks”. He was however unable to explain why cold polar air, instead of reaching the equator along a meridian, came from north-east in the northern hemisphere and from south-east in the southern one [2, 3]. He interpreted such phenomena as a consequence of the apparent day motion of the sun. Finally, in 1697, Halley devoted himself to a popular activity at that time: obtaining the height of mountains from the difference in the atmospheric pressure between their base and their top. In that period, he installed the barometer designed by Hooke for marine use (1667, Sect. 3.2) aboard paramour, the first vessel equipped to sail for scientific purposes only. He personally took command of this vessel and sailed for a long voyage of study in the South Atlantic between 1698 and 1700 [5]. The outstanding figure of Halley cannot eclipse the contribution of many other scholars, who confirm the widespread interest towards meteorology. In 1687, John Tulley (1639–1701), the American father of weather forecasts, published a collection of prognostic rules concerning storms, wind, rain and even eclipses [13]. In 1689, Francois Lamy (1636–1711) divulged the first observations about tornadoes,4 publishing a paper about the physics of air vortices in Paris. A posthumous treatise by Geminiano Montanari (1633–1687), Le forze d’Eolo. Dialogo fisico-matematico sopra gli effetti del vortice, o fia turbine, detto negli Stati Veneti la Bisciabuova [14], describing the phenomenological aspects of the vortex5 that devastated Venice on 29 July 1686, appeared in 1694. The Dialogo, clearly influenced by Galilei’s 3 Halley’s wind chart highlights a bizarre detail. The arrows representing the wind are limited to the

ocean. 4 Between 1586 and 1590, the passengers of some British ships sighted, off the North Carolina coast,

vortices called great spouts. In 1643, the governor of Massachusetts, John Winthrop (1588–1649), described a sudden gust, perhaps a thunderstorm front, moving from Lynn to Hampton, along a 58 km path. 5 In 1749, Ruggero Giuseppe Boscovich (1711–1787) described the shape of a cloud from which a tornado was originated.

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Fig. 4.2 Whirlwinds by Geminiano Montanari [14]

works, contained a reference to the Astrologia convinta di falso (1685) in which the author, appealing to Francesco Gonzaga (1466–1519), declared his will to neglect the opinions of Aristotle and Peripatetics and to look for the nature of winds by means of a clearer doctrine, i.e. that of Descartes and his followers. Montanari indicated the whirlwind as the “Bisciabuova” (from “biscia”, snake, and “buova”, from the Longobard term “bauga”, ring, circle or chain), providing magnificent pictures (Fig. 4.2). William Dampier (1652–1715), an English buccaneer and explorer famous for his voyages in the Caribbean Sea, through the Isthmus of Panama, along the shores of South America and Africa, in the Atlantic and Pacific Ocean, up to the Philippines, China, Australia and Sumatra, in 1697 wrote A new voyage round the world, in which he provided a picture of the winds of the planet, especially trade winds and tropical storms; he drew a wind chart (Fig. 4.3) in which he reported the Indian monsoon and highlighted the alternate seasonal character of wind in the Arabian Sea and in the Bay of Bengal6 ; he was the first to understand the similar nature of the China Sea typhoons and of the hurricanes in the Atlantic Ocean. In 1698, captain Langford published a paper about the hurricanes of the West Indies in the Philosophical Transactions of 6 Further

descriptions of wind in the Indian Ocean came from Joseph Huddart (1741–1816) (The oriental navigator, 1785), James Capper (1743–1825) (Observations on the winds and monsoons, 1801) and James Horsburgh (1762–1836) (Directions for sailing to and from the East Indies, China, etc., 1817).

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Fig. 4.3 Dampier’s wind chart (1697) [8]

the Royal Society of London, Sailors Hornbook, in which he described five storms occurred between 1657 and 1667; he maintained that his observations made possible to foresee the hurricane that destroyed Nevis on 19 August 1667 [15]. In 1723, James Jurin (1684–1750), an English physician and secretary of the Royal Society of London, took up Hooke’s suggestions (Sect. 3.2) and studied the diffusion of epidemics, linking the evolution of weather with the various types of diseases. This is why he invited scholars, through the Philosophical Transactions, to collect atmospheric measurements according to common standards, in compliance with detailed instructions about instrumentation, to record the results on a register and to send a copy of the latter to the Royal Society every year. Unlike previous attempts, this invitation was favourably accepted and the Royal Society collected many data from all over the world. A network, similar to the Medici one (Sect. 3.2), came then into existence; it ceased to operate in 1735. In 1735, anticipating Coriolis’7 solution by a century, George Hadley (1685–1768), an English man of law and natural science enthusiast, published Concerning the cause of the general trade winds [16], in which he observed that, applying Halley concepts, trade winds should head perpendicularly to the coast; both Halley’s chart itself and seafarers, conversely, reported an oblique incidence. Hadley judged Halley’s model incomplete, intuitively explaining the inclination of wind in view of the earth rotation. He observed that, as the earth (parallels) diameter increases from 7 In

1835, Gaspard Gustave de Coriolis (1792–1843) enunciated a famous theorem for the systems possessing a rotatory motion. It affirmed that the absolute acceleration is the sum of the relative acceleration, of the dragging acceleration and of the complementary acceleration; the latter corresponded to an apparent force, perpendicular to the direction of the motion, which is nowadays known as Coriolis’ force. By means of this theorem, he demonstrated that a body moving on a rotating surface, e.g. a mass of air on the earth’s surface, exhibits a trajectory curved with respect to the surface. Coriolis also introduced the 1/2 term, until then missing, in the expression of the kinetic energy; he also was the first to call “work” the product of a force by a displacement [3].

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Fig. 4.4 Hadley’s cellular circulation

the poles to the equator, the rotation speed of the parallels increases likewise. Because of this difference in speed, a mass of air moving from the poles to the equator along a meridian reaches the equator at a position standing back from the starting one. Since earth rotates eastwards, wind comes from north-east in the northern hemisphere and from south-east in the southern one. Hadley, referring to Halley’s intuitions and taking advantage of the data collected by Jurin at the Royal Society, understood that the motion of air took place in accordance with circulation processes that, from that time on, were named after him. He identified the existence of two great cells—one in the southern hemisphere and the other in the northern one—within which the equatorial hot air, after raising upwards, moves towards the poles; when it reaches them, it cools down, falls towards the ground and returns to the equator (Fig. 4.4) [2, 3]. Such intuitions remained practically unknown until John Dalton (1766–1844) (Sect. 3.5) divulged and partially rediscovered them in Meteorological observations and essays (1793). Halley’s and Hadley’s theories treated storms as stationary phenomena, evolving over time but not in space. Benjamin Franklin (1706–1790), American statesman, physicist and writer, overcame such concept in 1743, proving that perturbations are moving phenomena and that the wind direction does not coincide with the trajectory along which a perturbation moves [2]. The comprehension of this phenomenon stemmed from a bizarre occurrence [6, 15, 17]. Franklin could not observe a lunar eclipse, expected to occur in Philadelphia at about 9 pm on 21 October 1743, because of a storm, locally known as a northeaster rolled through Philadelphia, which darkened the sky over the city; the storm was named after the wind coming from northeast. Later, when Boston newspapers arrived, Franklin was surprised to see that in that city the eclipse had been observed, because the storm arrived there later than in Philadelphia. Thanks to this intuition, he realised that performing realistic weather forecasts required measurements on a synoptic scale, i.e. spread across areas several hundred kilometres wide. Jean le Rond D’Alembert (1717–1783) also contended with the interpretation of mechanisms producing the wind in Reflection sur le cause generale des vents, a paper dedicated to the Emperor of Prussia, Frederick II (1712–1786). Here, he formulated the first mathematical theory of atmospheric motions, proving that they are caused by the attractive forces of the sun and of the moon. In 1746, a jury of the Academy

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of Sciences of Berlin, presided by Euler, awarded him a prize for the elegance of the treatment. Regrettably, his results did not relate to the physical reality [3]. Towards the mid-eighteenth century, the synthesis of performed studies and acquired experiences strengthened the opinion that only the realisation of extensive measurement networks would allow further advancements of the meteorological knowledge and of the weather forecast capability. Between 1776 and 1778, Jurin’s ideas were resumed by the Société Royale de Médecine under the aegis of Louis XVI. Montmorency Louis Cotte (1740–1815), a French meteorologist and clergyman, author of Traité de météorologie (1774), made operational a network of stations guaranteeing regular and detailed reports about medical and meteorological issues. Jean Charles de Borda (1733–1799), a French mathematician, physicist and engineer, used Cotte’s data to examine the data simultaneously taken by various French stations for 15 consecutive days of 1777; he demonstrated that the changes in the atmospheric pressure propagated over space and time in relation to the wind speed and direction. In 1784, also thanks to the success of such results, the network counted 70 stations, including, besides the French ones, some other located in the Netherlands, Germany, Austria, Persia and USA. Antoine Laurent Lavoisier (1743–1794), impressed by De Borda’s results, proposed to institute a worldwide network. At the end of a long and hectic campaign promoted since 1779 to make the scientific and public opinion aware of this issue, in 1790 he wrote on the Literary Magazine: “The forecasting of the changes that will occur in the state of the weather is an art possessing its principles and rules, which required great experience as well as the attention of a very capable physicist; (…) an art based on the regular daily observation of the changes (…) of the barometer, of the wind speed and direction at various altitude, and also of the hygrometric status of the air. With all these elements, it is almost always possible, and very likely, to forecast how the weather will be like one or two days in advance; we believe, therefore, that it would not be impossible to publish a ‘forecast gazette’ every morning; it would be very useful for the society itself” [9]. In the meantime, the awareness the proper operation of a network required a specific institution materialised. In 1780, the Elector Palatine of the Rhine, the prince Karl Theodor von Pfalz (1724–1799), founded the Societas Meteorologica Palatina, an organisation associated with the Academy of Science and Letters of Mannheim. The network, taking inspiration from the Medici model, consisted of 57 stations at reliable cultural institutions. The observations, published in the Ephemerides Societatis Meteorologicae Palatinae (1782–1795), were used for the first synoptic meteorology and climatology studies. The Palatine networks also ceased operating prematurely. In 1799, the naturalist Jean Baptiste Pierre Antonie de Monet, Knight of Lamarck (1744–1829), for some time a collaborator of Lavoisier and Laplace, published Annuaires météorologiques, a treatise criticised for its astrological component (Sect. 2.4) that, however, represented the first example of a meteorological yearbook. It contained complex descriptions of the effects of the moon and of the planets on climate, related to weather forecasts in the space of a year. Lamarck emphasised their unre-

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liability, explaining it through the shortage of available data. He then launched the umpteenth appeal for the collection and filing of measurements [18]. It should also be noticed that in 1802 Lamarck published About the shape of clouds, where clouds were classified according to five categories (increased to six in 1804). In the same year, Luke Howard (1772–1864) delivered a lecture about this subject at the Askesian Society [18]; it was the prelude to the publication of a book, On the modifications of clouds [19], where he formulated the fundamental pattern of all the subsequent classifications of clouds. Howard himself also published the first book about urban climatology (1818); the second edition (1820) and especially the third one [20] highlighted the alteration of meteorological parameters in urban centres, opening the door to new studies that were to become increasingly important with the passing of years. Emilien Renou (1815–1902) got this message in 1855, reporting many data about the climate of Paris [21]. With the advent of the nineteenth century, the analysis and comprehension of weather phenomena made outstanding progress, especially in Germany, USA and England. In Germany, Alexander von Humboldt (1769–1859) carried out extensive studies about weather conditions, proposing two alternative views of earth climatology. On the one hand, he identified the ideal solar climate, which would occur in the absence of atmospheric motions; on the other hand, he placed the actual climate, linked to planetary winds. He then evaluated the temperature distribution on our planet, recognising its correlation with the alternation of seasons and with the distribution of lands and seas; he surmised that the variation of temperature over time and space plays an essential role in atmospheric circulation. In 1817, he represented temperature through isotherms [22]. In 1820, making use of the data collected by the Palatine Society, Heinrich Wilhelm Brandes (1777–1834), a German astronomer, mathematician and engineer, published Beiträge zur witterungskunde, where he described the European weather in all the days of the year 1783.8 Afterwards, he published Dissertatio physica de repentinis variationibus in pressione atmosphaerae observatis (1826), reporting synoptic charts in which lines join points with identical pressure deviation from a reference value; he also reported arrows the direction and length of which, respectively, provide the wind orientation and speed. Figure 4.5 shows a synoptic chart of Western Europe as reworked by Hugo Hildebrandsson (1838–1925) and Léon Teisserence de Bort (1855–1913), in Les bases de la météorologie dynamique (1898–1900), on the basis of Brandes’ original drawings, which have been lost [11]. In 1828, Heinrich Wilhelm Dove (1803–1879), a German physicist and meteorologist, published Ueber barometrische minima, where he stated that tropical cyclones possess not only translation, but rotation as well9 ; they rotate counterclockwise in the northern hemisphere and clockwise in the southern one. In 1837, Dove [23] corre8 Since the telegraph had not yet been invented, Brandes constructed his first synoptic charts thanks

to information he received by mail. concept that storms are vortex phenomena was introduced by the geographer Bernhardus Varenius (1622–1650) in Geographia naturalis (1650).

9 The

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Fig. 4.5 Synoptic chart of Western Europe [11]

lated clouds and rain to pressure changes, formulating one of the first theories about atmospheric systems [3]; starting from the ideas of Halley, Humboldt and Kämtz, he also developed the concept that monsoons are an essential part of the general circulation; besides, he broadened the knowledge of doldrums and flows crossing the equator [8]. In 1840, he published Law of storms, in which he maintained that perturbations are originated by the conflictual encounter of cold and dry polar currents from north-east and of warm and humid equatorial currents from south-west. Starting from Dove’s studies, in 1848 John Brocklesby (1811–1889) first classified winds [24] (Sect. 6.4), dividing them into constant, periodical and variable ones. Constant, or trade, winds are present on each hemisphere, in a belt 30° wide around the equator, and are part of the planetary circulation. Periodical winds blow in alternate directions: they include monsoons, and the Atlantic Coast breezes in the USA. Variable, or irregular, winds do not have a fixed direction. In the meantime, following Humboldt, Ludwig Kämtz (1801–1867), a German meteorology professor, drew a chart of earth temperature [24, 25]. Having more avail-

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able data, it highlighted the warming of continents, an essential piece of information to explain monsoons and, more in general, the planetary circulation. In the USA, the concepts of Halley, Hadley and Franklin were resumed by William Redfield (1798–1857), an engineer fascinated by meteorology, who in 1831 published a revolutionary theory about the American cyclones originated at the tropics [26]. It took its cue from the hurricane that struck Long Island, near New York, in 1821 (Sect. 10.1), highlighting some bizarre elements: trees were bent by wind in different directions, in relation to the place they were located; some areas were struck by wind, in successive times, with identical intensity but opposite direction. Redfield deduced that storms striking the American coast actually were great masses of air rotating counterclockwise. He explained that the wind accompanying them did not move on horizontal planes, but with a spiral-shaped converging motion, ascending inside the vortex and descending in the peripheral zone. At the centre of the vortex, there is a calm area, subsequently called the eye. These storms originate in the two belts between the tropics and the equator: their diameter sometimes exceeds 1600 km, and they move at approximately 50 km/h and affect areas up to 5000 km in size. Studying the prevailing trajectories of hurricanes, Redfield was also one of the first to note that some of them reached Europe. This theory was confirmed by the observations carried out in the island of Barbados and in the Gulf of Mexico by William Reid (1791–1858), an English colonel and Governor of Bermuda. In 1838, he published a treaty [27] about tropical storms, including wind charts, vortex trajectories, suggestions for sailing routes and descriptions of the most famous storms. Reid was the first to note that in the two hemispheres, besides the direction of rotation, the trajectories travelled were also opposed. He insisted on the necessity of knowing tropical storms as a whole and of collecting data worldwide. For this purpose, he established important contacts with the East India Company that, at the suggestion of Reid, issued criteria for the acquisition of observations to its officers. He finally collected the results of his studies in a book published in 1849 [28]. The English Captain Henry Piddington (1797–1858), coordinator of such observations, divulged the results in the shape of charts in a series of 40 papers appearing in the Journal of the Asiatic Society of Bengal from 1839 to 1855. In 1842, he published a book [29] in which he coined the term “cyclone”, comparing wind vortices with the coils of a snake, and used the terms breeze, gale, storm and hurricane to graduate wind intensity (Sect. 4.3). He interpreted storm surge (Sect. 10.1), stating that it is caused by the joint action of wind and of the raising of the sea surface, due to the decrease in atmospheric pressure caused by the tropical cyclone. While Redfield, Reid and Piddington focused on the description of storms, James Pollard Espy (1785–1860), an American professor of meteorology, attempted to explain their causes. He founded his theories on the role of the water vapour in the thermodynamics of atmosphere and on the “new” adiabatic process and convection concepts (Sect. 3.7); thanks to them, he provided an interpretation of the meteorological phenomena and, especially, of the foehn winds. From 1831 to 1838, Espy entered into debate with Redfield, admitting that storms start when moist air, heated by the earth’s surface, rises in a column as it were “climbing up a chimney”: “When

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Fig. 4.6 a Espy’s model; b Redfield’s model [2]

the air near the surface of the earth becomes more heated or more highly charged with aqueous vapor (…) its equilibrium is unstable, and up moving columns or streams will be formed. As these columns rise, their upper parts will come under less pressure, and the air will therefore expand; as it expands, it will grow colder about one level and a quarter for every hundred yards of ascent (…). The ascending columns will carry up with them the aqueous vapor which they contain, and, if they rise high enough, the cold produced by expansion from diminished pressure will condense some of its vapor into cloud (…). As soon as the cloud begins to form”, the latent heat released by condensation results in a violent expansion of air and storms. Besides this great intuition, Espy had the unhappy idea that wind blew radially, because of the centripetal force [3], towards the ascending column. A synthesis of his theories was included in a 1840 illustrated note to the French Academy of Sciences, Brief outline of the theory of storms, and in a 1841 book, The philosophy of storms [30]. Redfield and Espy spent long years quarrelling violently. They did not understand that, had they combined the best parts of their theories (Fig. 4.6), they would have explained cyclonic systems [2] almost a century before the Bergen School (Sect. 6.3). Between 1836 and 1846, Elias Loomis (1811–1889), an American professor of mathematics, published a series of papers including synoptic charts that reported the weather situation every 6 h, including isobars, winds, clear or cloudy sky areas as well as rain and snow zones. Loomis discussed a cyclonic mechanism that partially

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Fig. 4.7 First transversal cross-sectional view of a front (Loomis, 1841)

confirmed Espy’s enunciation: the storm starts with a convective current of thermal origin, strengthened by the latent condensation heat; the pressure decrease is accompanied by the expansion of the air and by the formation of surface winds blowing towards the centre, which restore the atmospheric balance [11]. He also provided a pioneering description of front: “when (…) a hot and cold current, moving in opposite directions, meet, the colder, having greater specific gravity, will displace the warmer, which is thus suddenly lifted from the surface of the earth, is cooled and a part of its vapor precipitated” (Fig. 4.7). Loomis’ thought was collected in A treatise on meteorology, published in 1868. Loomis was also the first to evaluate wind speed through the damage caused. He observed some blunt planks a tornado embedded in the ground to a depth of almost half a metre. He simulated the phenomenon by shooting the same planks with a gun and estimated that the energy needed to embed them would require a speed approximately equal to 1000 km/h. Either the experience or calculations performed were wrong, but the technique used anticipated the current practices (Sect. 10.2). In 1842, the American Captain Matthew Fontaine Maury (1806–1873) was appointed as Chief of the U.S. Navy Department of Charts and Instruments, with the purpose of collecting the available data in the shape of wind charts for sailing purposes. Maury, thanks to the availability of a huge mass of data, first produced a chart of the atmospheric circulation. Afterwards, starting in 1847, he drew wind charts that were freely provided to seafarers in exchange for data. Every chart referred to a sea zone (Fig. 4.8); the scheme was divided into squares corresponding to the months of the year and to wind directions; every mark indicated a wind observation performed by a ship. Since 1850, Maury completed his charts with the sailing routes [31]. During the First International Meteorology Congress, held in Bruxelles in 1853, the decision to officially adopt Maury’s charts was taken following a joint initiative by the USA and Great Britain. Thanks to this decision, in 1855 Maury published a book10 [32] that sold so well to require five re-editions in the first year only. In 1853, another German meteorologist, James Coffin (1806–1873), published Winds of the Northern Hemisphere, where he collected wind charts produced by processing measurements coming from 579 stations in the northern hemisphere. Thanks to them, he perceived the existence of three planetary belts arranged along 10 Maury envisaged two cells for every hemisphere. It was an advancement with respect to Hadley’s

model, but still behind the tri-cellular Ferrel’s model.

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Fig. 4.8 Maury’s wind chart representing a 55° sea area off the coast of Southern Asia [8]

parallels, which were the location of different pressure fields and as many circulation cells [3]. Christoph Henricus Buys Ballot (1817–1890), a Dutch physicist, meteorologist and geologist, pinpointed the concept that wind blows along isobars and that the low pressure area, in the northern hemisphere, is at the left of the wind. In 1857, he formulated an empirical rule, later called Buys Ballot’s law: “in the Northern Hemisphere a person who stands facing away from the wind has high pressure on the right and low pressure on the left; in the Southern Hemisphere, the reverse would be true” [1, 3]. In 1861, G. Jinman published Winds and their courses [33], where he proposed the first model of an extra-tropical cyclone. Even though it was neglected for years, it contained principles that are correct even in current knowledge. According to Jinman, in the northern hemisphere “a storm has two sides formed by two distinct currents of air flowing in opposite directions and crossing each other on either side of the centre

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Fig. 4.9 Jinman’s model of the extra-tropical cyclone [33]

(Fig. 4.9). The western frontal line was recognised as the sharper of the two, and here the winds fly from south-west to north-east”. Many believe that Jinman’s Intuitions represent the seed of the polar front theory developed by the Bergen School in the early twentieth century (Sect. 6.3). The second half of the nineteenth century was overshadowed by the figure of the French–American meteorologist William Ferrel (1817–1891). In 1856, he published Essay on the winds and currents of the ocean [34], where he perfected Hadley’s concepts in view of the data of Maury and Coffin, laying the foundations of Ferrel’s law: “everybody moving on the Earth surface is subjected to a shift to the right in the northern hemisphere and a shift to the left in the southern hemisphere”. He also developed the tri-cellular model still applied to represent the circulation phenomena on a planetary scale. Ferrel started his paper by observing that “the earth is surrounded on all sides by an exceedingly rare and elastic body, called the atmosphere. If the specific gravity of the atmosphere and of the ocean were everywhere the same, all the forces of gravity and of pressure which act upon any part of them, would be in exact equilibrium, and they would forever remain at rest. But as some parts of the earth are much warmer than others, and air and water expand and become rare as their temperature is increased, their specific gravities are not the same in all parts of the earth, and hence the equilibrium is destroyed, and a system of winds and currents is produced. It is proposed (…) to inquire into the effects which are produced, both in the atmosphere and in the ocean, by this disturbance of equilibrium, and by means of a new force which has never been taken into account in any theory of winds and currents (…).” Ferrel, approaching atmospheric motions, observed that “from about the parallel of 28° on each side of the equator the winds on the ocean, where they are not influenced by any local causes, blow steadily towards the equator, having also a western motion,11 producing what are called the north-east and south-east trades. At the meeting of these currents near the equator there is a calm called the equatorial 11 Ferrel

called western and eastern the wind, respectively, heading west and east. Today, western and eastern winds are those blowing from west and east.

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Fig. 4.10 Ferrel’s tri-cellular circulation: a 1856 [34]; b 1859–1860 [35]

calm-belt, or the doldrums, where the air rises up and flows in the upper regions towards the poles, until it arrives near the 28°, where it is met by an upper current flowing from the poles. The meeting of these upper currents produces an accumulation of atmosphere from under which the air flows out in both directions on account of the increased pressure; a strong and steady current, as we have seen, towards the equator, and another not so strong and somewhat variable over the middle latitudes, towards the poles, having at the same time an eastern motion, and producing what are called the passage-winds. As this current flows at the surface towards the poles, it gradually rises up and returns in the upper regions towards the equator, meeting the upper current from the equator near the tropics as has been stated. (…) But there are numerous observations (…), which show that the currents flowing over the middle latitude towards the poles, do not extend to the poles, but that the atmosphere above a certain latitude, has a tendency to flow from the poles, producing another meeting of the air at the surface near the polar circles similar to the one at the equator, except that the currents are comparatively feeble and consequently the belt of meeting not so well defined, and that here also air rises up and flows each way in the upper regions towards the equator and the poles. If then there were no continents, or other local causes of disturbance, the motions of the atmosphere would be as represented in the following diagram (Fig. 4.10a), in which the direction of the wind is represented by the arrows, and the external part of which represents the motion of the air in the plane of the meridian”. This system prevails on the oceans; on the continents, it is altered by mountain ranges. Ferrel strengthened his tri-cellular model remarking that “the atmosphere everywhere presses upon the surface of the earth (…). This pressure, however, is not the same in all parts of the earth, but varies in different latitudes (…).” He then quoted Espy’s studies, according to which “there are three belts where the barometer stands below the mean, with almost constant rain and snow—one near the equator, one near the arctic circle, and one near the Antarctic circle—and also that there are, certainly

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two belts in the outer borders of the trade-winds, where the barometer stands above the mean, and almost certainly two regions more—one around the north pole and the other around the south pole—where the barometer stands above the mean”. On the basis of these concepts, he explained his theory producing atmospheric motions maintaining that “there are four principal forces which must be taken into account in a correct theory of the winds. The first arises from a greater specific gravity of the atmosphere in some places than others. A second force arises from the tendency which the atmosphere has, when, from any cause, it has risen above the general level, to flow to places of a lower level. When, from any cause, a particle of air has been put in motion toward the north or south, the combination of this motion with the rotatory motion of the earth produces a third force, which causes a deflection of the motion to the east when the motion is to the north, and a deflection to the west when it is toward the south. The fourth and last force arises from the combination of a relative east or west motion of the atmosphere with the rotatory motion of the earth. In consequence of the atmosphere’s revolving on a common axis with that of the earth, each particle is impressed with a centrifugal force”. Ferrel remarked that Hadley’s theory took into account the first three forces but ignored the fourth one. It then provided an explanation of the trade winds, but it could not interpret many other atmospheric motions. The latter are conversely explained by the four forces described above. This also explains why Ferrel’s law cannot be considered as a simple consequence of Coriolis’ principles. Ferrel’s paper also contained a magnificent description of hurricanes and storms. “Hurricanes are generally supposed to be produced by the meeting of adverse currents, which produce gyratory motions of the atmosphere at the place of meeting. That they may receive their origin and first impulse in this way, we think is very probable; but that violent hurricanes, extending over a circular area nearly one thousand miles in diameter, and continuing for ten days, and proceeding with increasing violence from the torrid zone to high northern latitudes, depends upon any primitive impulse alone, we think is very improbable. For if even any part of the atmosphere should receive such an impulse as to produce a most violent hurricane, friction would soon destroy all motion and bring the atmosphere to rest. (…) Hurricanes then, and all ordinary storms, must begin and gradually increase in violence by the action of some constantly acting force, and when this force subsides, friction brings the atmosphere to a state of rest. This force may be furnished by the condensation of vapor ascending in the upward current in the middle of the hurricane, in accordance with Professor Espy’s theory of storms and rains”. Ferrel also expressed himself about the long-standing diatribe on the circular or radial motion of storms: “It has been established by Redfield, Reid, Piddington, and others, that all hurricanes and ordinary storms have a gyratory motion around a centre (…). There are some however, amongst whom is Professor Espy, who deny the gyratory character of storm entirely, and contend that there is only a rushing of the air from all sides below towards a centre, without any gyration. We think this gyratory character of storms has been too well established to admit of any doubt. No one, however, has ever given any satisfactory reason why these gyrations in the one hemisphere are always sinistrorsal and in the other destrorsal. (…) We shall now

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Fig. 4.11 Deviatory action caused by the earth’s rotation

undertake to show that there cannot be a rushing of air from all sides towards a centre (…), and that the tendency to a distinct kind of gyration in each hemisphere, is (…) a necessary consequence, for the action, upon the atmosphere, of the four forces which we have taken into consideration in the first part of this essay”. Continuing his studies, between 1859 and 1860, Ferrel published The motions of fluids and solids relative to the earth’s surface [35]. He started observing that in his previous “essay [34] it was inconvenient to use any mathematical formulae, and consequently the results merely of only a partial and imperfect investigation of the subject were given; but it is thought that an account of the importance of the subject, it deserves a more thorough investigation. It is proposed, therefore, (…) to go into a complete analytical investigation of the general motions of fluids surrounding the earth, and of projectiles at its surface, arising from disturbing forces and the earth’s attraction, combined with the modifying forces arising from its rotation on its axis.” Accordingly, in the first part Ferrel examined the general equations of motion related to the Earth surface, applicable to both fluids and solids; the following parts first deal with the motions of the fluids surrounding the earth and then apply their results to explain the motions of the atmosphere, of storms, of hurricanes and of ocean currents, justifying the atmospheric circulation tri-cellular pattern12 (Fig. 4.10b). Ferrel also provided a mathematical proof of Buys Ballot’s law. Following the interpretation reported in [3] based on modern knowledge, a mass of air horizontally pushed by the force produced by the pressure gradient (F G ) tends to move from the high-pressure (H) area to the low-pressure (L) one (Fig. 4.11a). During this motion, with velocity V, the mass is subjected to a deviatory force (Coriolis’ one) (F c ) that changes its heading (Fig. 4.11b) until the balance between the gradient force and the deviatory one is reached; when this occurs, air flows with velocity V g in parallel with the isobars (Fig. 4.11c).13

12 To honour their discoveries, today the circulatory motions at the subtropical and intermediate latitudes are known as Hadley’s and Ferrel’s cells. 13 In 1916, Sir William Napier Shaw (1854–1945) called “geostrophic” the wind velocity parallel to straight isobars, at the top of the atmospheric boundary layer.

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In his last years, Ferrel wrote Meteorological researches [36] and A popular treatise on the winds [37], where he resumed, perfected and expanded the analyses of the atmospheric motions he himself enunciated, discussing them in relation to his observations carried out in different parts of the world [9, 38]. The first work is scientific in nature, and the second is a popular one. Ferrel shifted from a planetary view to the study of the wind phenomena occurring in relatively small areas and within relatively short periods of time; he took into consideration and discussed monsoons, land and sea breezes, cyclones and anticyclones, foehn and katabatic winds, tornadoes and thunderstorms. He observed wind phenomena in contact with the ground, noticing that wind speed increases with height and that the presence of valleys and hills upsets the flow; for this reason, he has a place among the precursors of micrometeorology. Ferrel also discussed the accuracy of the measures carried out by means of cup anemometers, noticing that they are reliable for speeds up to 5–10 mph, but imply increasing errors at higher speeds; he was among the first to understand the importance of this issue as regards wind actions on buildings. Ferrel discussed the actions of tornadoes on buildings, pointing out that such phenomena cause speeds up to 500 km/h and pressures exceeding 11,500 N/m2 ; he deduced that [38] “if the centre of such a tornado passed suddenly over a building with closed windows and doors, the sudden expansion of the air in the building due to this 3 ins. differences of barotropic pressure might reach 211 lbs. per sq. ft. of surface, plenty enough to blow cellular doors from their fastenings, blow out windows and ordinary doors, burst out walls, blow up roofs, and wreck buildings”. He also provided a pioneering explanation of the thunderstorm cells, depicting the inception of an updraft, its cooling and condensation, the precipitations (even strong ones) and, finally, the appearance of a downdraft (Fig. 4.12); he also discussed the cyclone areas more favourable for the formation of thunderstorms. In the period Ferrel achieved great discoveries, the meteorological culture made many other advancements.

Fig. 4.12 Ferrel’s thunderstorm picture [37]: a single cell; b multiple cells

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Francis Galton (1822–1911), one of the founders of the London Meteorological Society, coined the term “anticyclone” in 1863, defining the properties of this phenomenon. It is characterised by the occurrence of feeble winds, rotating in direction opposite to that of the cyclone, by the subsiding movement of air from high to low altitudes and by relatively clear weather. Theodor Reye (1838–1919) and Henry Peslin applied the first law of thermodynamics to interpret, in 1864 [39] and in 1868 [40], respectively, Espy’s theory about the release of the latent heat in convective currents. In 1874, Camille Flammarion (1842–1925) unveiled the secrets of the upper structure of the hurricane [41]. Cato Maximilian Guldberg (1836–1902) and Henrik Mohn (1835–1916) perfected Ferrel’s equations between 1876 and 1880 [42]. In 1888, the English meteorologist Ralph Abercromby (1842–1897) published Weather, where he represented the low-pressure centre around which the cyclone evolves with the letter “L” and the high-pressure centre around which the anticyclone develops with the letter “H”. He defined five secondary phenomena: the “promontory” or “wedge” (a strip of high pressure with roundish or acute angle isobars protruding from an anticyclone), the “trough” (a low-pressure corridor with acute angle or triangle-shaped isobars protruding from a cyclone), the “secondary cyclone” (a secondary low-pressure centre), the “saddle” (a low-pressure area between two anticyclones and two depressions) and the “slope” (a zone of decreasing pressure bound by practically straight and parallel isobars). This convention is still in use. The turning point in weather forecasting took place in the middle of the nineteenth century, thanks to the improvement of the telegraph. Carl Kreil (1798–1862), meteorologist, astronomer and director of the Observatory of Prague, first understood its importance for meteorology and in 1842 proposed its use to gather the atmospheric observations carried out by measurement networks in real time. The same idea gained ground in the USA and in England, which felt the importance of using the telegraph, within a broad meteorological network, to alert seafarers about incoming storms. With such premises, the first telegraphic companies were set up and the acquired information was quickly spread. In 1849, the physicist Joseph Henry (1797–1878) proposed to telegraph operators to replace the traditional “O.K.” transmitted at the morning opening of their offices, with a weather report consisting of a single word: “clear, rain, …”. That same year, the English astronomer James Glaisher (1809–1903), one of the pioneers of balloon flight (Sect. 4.5), set up a network of nearly thirty stations with the collaboration of the electric telegraph company and of the Daily News London newspaper; thanks to the latter, he published information on the wind speed and direction and on the weather conditions every day. Such information was reported on the first synoptic charts exposed at the 1851 London International Exhibition. In the same period, six modern meteorological institutions appeared in Europe: The Prussian Meteorological Institute (1847), the Central Physics Observatory of Saint Petersburg (1849), the Austrian Central Institute for Meteorology and Magnetism (1851), the French Meteorological Society (1852), the Dutch Meteorological Institute (1854) and the Meteorological Department of the British Board of Trade (1854). The first international meteorology conference, held in Brussels in 1853,

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brought together the delegates of the maritime powers interested to detect and study the atmospheric phenomena; it marked the beginning of the international meteorological co-operation. Urbain Jean Joseph Leverrier (1811–1877), the discoverer of Neptune and director of the Paris astronomical observatory, gave a fundamental contribution to this process. Pointing out the effects of the storm that destroyed the French fleet at Balaclava on 14 November 1854, he persuaded Louis Napoleon (Napoleon III, 1808–1873) to set up a vast meteorological network. The network, authorised in 1855 and operational from 1857, consisted of 19 stations linked by telegraph, including Paris, Saint Petersburg, Bruxelles, Geneva, Madrid, Turin, Rome, Vienna and Lisbon. In 1863, Leverrier founded a meteorological service in Paris that diffused weather forecasts and synoptic charts [5]. Holland set up a similar network in 1859. On 21 May 1861, Buys Ballot established the first weather forecast and storm alert service, starting the tradition of issuing warnings and to transmit them to port authorities. He attempted to improve the accuracy of his information from 6 December 1866, introducing a new instrument in the Dutch network: the aeroclinoscope, used to identify the centre of depressions and the pressure gradient of cyclonic systems. In 1854, the English government entrusted the direction of the Meteorological Department of the Board of Trade, from which the Meteorological Office would originate, to Robert Fitzroy (1805–1865), a captain and future Admiral in the Royal Navy. In this position, he made available to ship captains meteorological information acquired through effective instruments. In particular, he directed the design and issuance of a new barometer, called Fitzroy, installed in every port and that could be consulted by captains before sailing away. In 1859, Great Britain was shocked by the death of 450 people in the shipwreck of the steamship Royal Charter in a gale off the Welsh coast. Fitzroy then set up a network of 15 ground stations transmitting daily weather reports at fixed hours by means of telegraph. Thanks to this network, he instituted an alert system that became operational in 1860 [2, 3] and in April 1861 issued the first weather forecasts from London. It was the prelude to the publication, in 1863, of his famous book, The weather book [43], in which he collected his seafaring experiences and observed that the essential element for weather forecasting is not pressure, but its gradient. For this reasons, he maintained “that observations of the wind and barometer should be made and recorded more frequently” and that “prolonged comparisons, and judicious inferences drawn from them, afford the means of foretelling wind and weather during the next following period” [44]. He also perceived that cyclones were originated by the encounter of air masses with different temperatures and that they were organised into families (Sect. 6.3). This is why he is considered as one of the pioneers of synoptic meteorology. Unfortunately, in spite of so many intuitions and of such foresight, the quality of the forecasts provided by his offices remained so poor that the Royal Society arrived to mock him. Fitzroy, deeply embittered, took his own life on 30 April 1865. In 1861, Francis Galton invited the English meteorologists to transmit him the weather maps through the telegraph to extrapolate a synthesis; the result was reported in Meteorographica or methods of mapping the weather, where over 600 maps were

4.1 The First Meteorology Studies

191

reported; this work was perfected by Galton himself in 1863 and by Alexander Buchan (1828–1907) in 1868 [11]. The USA set up a network of 500 stations that telegraphed reports to the Washington headquarters at the Smithsonian Institution every day. It did not publish actual forecasts, but divulged daily weather charts to be interpreted by users. In 1863, Francis Capen tried to persuade Abraham Lincoln (1809–1865) of their importance for war tactics. The words spoken by the President on 28 April 1863, however, showed his mistrust against them: “It seems to me that Mr. Capen knows nothing about the weather in advance. He told me three days ago that it would not rain again till the 30th of April or 1st of May. It is raining now and has been for ten hours. I cannot spare any more time to Mr. Capen” [2]. The Observatory of Toronto, starting in 1871, met with better success and became the core of the Canadian Weather Service. Its goal, by then a traditional one, was to alert people and seafarers on storms. It introduced the innovation of collecting and processing climatological information in the Monthly Weather Review magazine. It also produced, for every station, the first wind roses [45]. The American interest towards weather forecasts drew a strong impulse from Abbe and Finley. Cleveland Abbe (1838–1916) interpreted the weather charts, explaining their meaning to readers. He had the merit of quantifying the evolution of wind on the basis of probability. The official bodies remained sceptical up to 1868, when 530 people died at sea during two storms. From that time on, the Congress understood the usefulness of the new theories and in 1870 it authorised the army to set up a forecast and warning network under the auspices of the Army Signals Corps, initially tasked with forecasting storms on the Great Lakes and on the East Coast.14 The number of operational stations increased from 24 in 1870 to 284 in 1878. Each one of them telegraphed its report to the Washington headquarters at 8 a.m. and 8 p.m., providing data about atmospheric pressure, wind speed and direction, relative humidity, cloud cover and the observed sun, fog, rain or snow conditions. Abbe understood the role, and pursued the installation, of high-quality instruments, calibrated in accordance with uniform international standards (Treatise on meteorological apparatus and methods, 1887). At the Washington office, a team of meteorologists reported the measured data on charts and issued bulletins for the next 24 h. They represented very information, which nonetheless became a part of daily life. They were initially called “probabilities” by Abbe; in 1876, they were designated as “indications”; finally, in 1889, they were officially named “forecasts”15 [5]. John Park Finley (1854–1943) was the first meteorologist who attempted forecasting tornadoes. His figure and his methods were controversial [46]; it is however undeniable he opened new courses (Sects. 6.4 and 10.2) and many of his intuitions 14 In

November 1870, Increase Lapham (1811–1875) issued the first meteorological alert for the arrival of a storm on the Great Lakes [15]. 15 Abbe coined the term “prediction” in his 1889 book (Preliminary studies for storm and weather predictions). In a 1902 book (Physical basis of long-range forecasting), he instead used the term “forecast”.

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are still up-to-date. In 1882, he collected data on the tornadoes in the USA [47] and started his collaboration to the Monthly Weather Review and the Weekly Weather Chronicle. On 10 March 1884, he produced the first 8-h forecast, complete with charts. For a long time, he produced two daily forecasts, and then he shifted to one per day. He divided the land into sectors considered, in relation to local conditions, as favourable or unfavourable to the occurrence of tornadoes. He simultaneously verified the correctness of his forecasts and updated the land classification criteria. He notified the American Meteorological Journal of the results of his research, demonstrating that in 28% of the cases tornadoes struck the favourable areas and only in 1% of the cases they struck the other sectors. Finley also campaigned for the institution of a forecast centre in Kansas City; his efforts were fruitless, but his ideas turned out to be prophetic. Over 60 years later, in 1954, the U.S. Weather Bureau set up a tornado defence centre in that city (Sect. 10.2). Shortly afterwards, England rediscovered the practice of alert on stronger scientific bases [11]. Between 1879 and 1885, Robert Henry Scott (1833–1916) [48], William Clement Ley16 (1840–1896) [49] and Ralph Abercromby [50] laid the foundations of the currently acknowledged principles aimed at preserving human life in the areas subject to catastrophic wind phenomena (Chap. 10). Unfortunately, the possibility of sighting the storms and to issue alerts was still hindered by the difficulty of quickly communicating with the ships at sea. The reports from the sea came by mail or when the ships arrived at ports. The situation changed when Guglielmo Marconi (1874–1937) invented the radio (Sect. 6.2). As a matter of fact, not even the advent of scientific meteorology subdued the interest for the forecasts based on astrology (Sect. 2.4) [51]. In 1686, the Englishman John Goad (1616–1691) wrote Astrometeorologica, a work inspired to Ptolemy and Francis Bacon, in which he enunciated four criteria: (1) earth’s atmosphere is affected by planets; (2) atmospheric phenomena depend on the relative position of planets; (3) there are mathematical laws correlating weather and the relative position of planets; (4) the study of the influence of planets on atmospheric phenomena is essential for farmers and seafarers. Such criteria produced a renewed interest for this subject, and from the eighteenth century the diffusion of the astrological almanacs grew exponentially. The scientific crimination of astrometeorology and the low cost of almanacs both contributed to make this subject increasingly popular. The symbol of this reality is the most renowned American of this age, Benjamin Franklin [17]. On the one hand, he made remarkable discoveries in meteorology and electricity (Sect. 4.5); on the other hand, he divulged his ideas by publishing, every year from 1733 to 1756, the Poor Richard’s almanac (Fig. 4.13a), in which he ridiculed astrological forecasts; as a matter of fact, he sold 10,000 copies of his product each year.

16 In

1872, Ley published a paper, Laws of the winds prevailing in Western Europe, in which he provided an advancement in the description of fronts. According to Ley, they entail a sudden change in the direction of the wind, accompanied by a fierce storm and an instantaneous temperature drop.

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Fig. 4.13 a First page of the first edition of Franklin’s almanac [17]; b vignette about Zadkiel published by Punch on 17 October 1863 [51]

The most famous almanac was founded in 1699 by Francis Moore (1657–1715), a British astrologist and physicist; it was first entitled Old Moore’s almanac, later changed into Moore’s vox stellarum, and sold 107,000 copies in 1768 and almost 400,000 copies at the start of the nineteenth century; besides simple ephemerides, it contained astrological forecasts of the weather conditions, of natural disasters and of the most favourable periods for agriculture and for political and military operations. Its most important competitors were the Raphael’s almanac, appeared in 1826, and the Zadkiel’s almanac, founded in 1831 by the astrologist Richard James Morrison (Zadkiel Tao-Sze, 1794–1874) (Fig. 4.13b). Other successful similar works include the Seaman’s almanack, published by Robert Henry Scott of the Meteorological Office starting in 1869, and the De la Rue’s indelible diary, published from 1870 onwards by James Glaisher (1809–1903) of the Royal Observatory of London (Sect. 4.5) and by Edward Thelwall of the Trinity College of Cambridge. The proliferation of the almanacs found an important support in the renewed scientific interest for astrology as a science capable of explaining atmospheric phenomena. In 1815, William Herschel (1738–1822), the astrologist who discovered

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Uranus, studied the influence of moon on the weather. His studies were divulged by John Claudius Loudon (1783–1843) in the Encyclopedia of gardening, comprising the theory and practice of horticulture (1835). Patrick Murphy (1782–1847) published many works on the ties between meteorology and astronomy, in particular Anatomy of the seasons (1834) and Meteorology considered in its connexion with astronomy, … (1836). In Barometrographica (1847), Luke Howard noted that the barometer fluctuations showed a periodicity linked to the gravitational effects of the moon and analysed the correlation between the weather and the relative position of the earth, of the moon and of the sun. In 1862, the Journal of astronomic meteorology and record of the science and phenomena of the weather studied atmospheric phenomena on the basis of practical astronomical principles. James Alfred Pearce Jr. (1840–1920), the publisher of the Zadkiel’s almanac since 1874, was also the author of The weather guide-book (1864) and Textbook of astrology (1879).

4.2 The Resistance of Bodies in Fluids The study of the resistance of bodies in fluids [52–54] has its roots in the research of Leonardo da Vinci (1452–1519) (Sect. 2.10). He maintained that such resistance was proportional to the surface of the body (a correct concept) and to the velocity of the fluid (a wrong concept). He also introduced the embryonic idea of the reciprocity concept formulated by Newton at a later time. Galileo Galilei (1564–1642) (Sect. 3.5) first assessed the resistance of bodies in the air measuring their free-fall time during some experiments carried out on the Tower of Pisa and then through the measurement of the oscillation of bodies installed on pendulums [52]. He reached the conclusion that resistance was proportional to the density of the fluid (a correct concept) and to the speed of the bodies (a wrong concept, like Leonardo da Vinci’s). Between 1668 and 1669, a committee of the Académie Royale des Sciences of Paris, composed by Christian Huygens (1629–1695), Edme Mariotte (1620–1684), Jean Picard (1620–1682) and Gian Domenico Cassini (1625–1712), carried out experiments on bodies in water currents. Analysing the results, Huygens first understood that the resistance of bodies in fluids was not proportional to the velocity, but to its square. He however delayed the divulgation of this discovery up to 1690. Edme Mariotte, prior of a monastery near Dijon and father of the French experimental methods [53], carried out experiences during which he measured the impact of various free-falling bodies on some surfaces. He left some water fall (Fig. 4.14a) on the end of a beam (N) by a vertical pipe (M) and measured the resulting force through a weight (Q) that counterbalanced the beam at the opposite end. He repeated these experiences leaving the water fall from various heights, creating impacts with different velocities; in such a way, he independently proved that the resistance of the bodies in fluids was proportional to the square of the velocity [54]. This result was published in Traité de la percussion ou choc des corps (1673).

4.2 The Resistance of Bodies in Fluids

195

Fig. 4.14 Mariotte’s experiences [52]: a water fall measurements; b balance measurements of the wind force on an inclined plate

Mariotte subsequently introduced a measurement technique destined to become a cornerstone of the current experiences in wind tunnels and in towing tanks. After some failed attempts to evaluate the force of the wind on trees, he built a balance to measure the force induced by air on inclined plates (Fig. 4.14b) and mill sails; he also measured the force of the water on hydraulic wheels, discussing the role of the inclination of the surface. During these tests, he confirmed that the force exerted by fluids on the bodies they impact with was proportional to the square of the relative velocity. He also showed that the resistance of an inclined plate was proportional to the square of the speed and to sin2 ϕ, where ϕ is the angle between the plate plane and the flow direction.17 He collected these results in Traité du mouvement des eaux et des autres corps fluides, a posthumous work published in Paris in 1686. The treatise was divided into five parts: the first one dealt with the properties of the fluids and the causes of wind; the second described the results of his aerodynamic and hydrodynamic experiences; the third, the fourth and the fifth dealt with specific hydraulic issues [52]. Isaac Newton (1642–1727) approached the problem of the resistance of bodies in fluids in the second book of Philosophiae naturalis principia mathematica (1687) (Sect. 3.5), where he came to the conclusion that it chiefly depended on the viscosity of the fluid and on the mass to move. He then expressed the resistance as the sum of 17 According

to De Saint Venant, the sine-squared law was introduced by Ignace Gastoni Pardies (1636–1673), a Jesuit that in 1671 experimentally proved that the wind pressure on the sails of the ships was proportional to sin2 ϕ, where ϕ is the angle between the sail plane and the flow direction [55].

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4 The New Culture of the Wind and Its Effects

two terms: one proportional to the velocity and the other to its square; he then added a third constant term representing the fluid cohesion. He subsequently described some experiences in which he made a sphere sway in the air and in the water by means of a pendulum, estimating the resistance R in relation to the reduction of the oscillations. He expressed this quantity through this law (proposition XL): R = A1 V + A2 V 3/2 + A3 V 2

(4.1)

where A1 , A2 and A3 are empirical constants and V is the maximum velocity of the sphere during the oscillation. He obtained many values of A1 , A2 and A3 , changing the diameter of the sphere and the length of the pendulum. He concluded that the first two terms of the trinomial are generally negligible, while A3 is proportional to the square of the diameter and to the density of the fluid. The famous law of the three proportions (Proposition XXIII) will stem from this. It states that the resistance of a body immersed in a fluid (R) is proportional to the density of the fluid (ρ), to the area of the projection of the maximum surface of the body perpendicularly to the flow direction (A) and to the square of the velocity (V )18 : R=

1 2 ρV AK 2

(4.2)

where K is a non-dimensional factor called drag coefficient. This formula assumed great importance because, being referred to a fluid in a broad sense, it could be applied to both water and air. Newton also formulated the principle of reciprocity, which still represents the foundation of the measurements in wind tunnels and towing tanks: the forces exchanged between a solid body and a fluid are the same, either if it is the body to move in the fluid, initially at rest, with uniform velocity, or if it is the fluid to move, with the same velocity, towards the fixed body [53]. This remark gave impulse to the aerodynamic and hydrodynamic experimental research. The law of the three proportions represents a turning point in the knowledge of the resistance of bodies in fluids as well as the starting point for studies destined to play a major role in many scientific sectors. They gained ground in the eighteenth century and followed two complementary lines: the first one generalised Eq. (4.2); the second led to build various devices aimed at measuring resistance. Considering the evolution of Eq. (4.2) first, it became widely used in a form slightly different from the original one. Indicating the pressure exerted by a fluid on a body with P = R/A, it is provided by the expression (Fig. 4.15a): P = αV 2 K 18 Thanks

(4.3)

to ballistic experiments, Newton already knew that the concept that associated the force with the square of the velocity failed when the velocity came close to that of the sound. Newton himself provided significant contributions to the knowledge of the velocity of the sound in the air [52].

4.2 The Resistance of Bodies in Fluids

197

Fig. 4.15 Perpendicular (a) and inclined (b) plates with regard to the wind

where α = ρ/2. At the temperature of 0 °C and at the pressure of 760 mm Hg, α = 0.066 with V in m/s and P in kgf/m2 (indicating kilograms-force by kgf); α = 0.0027 with V in mph and P in lb/ft2 . Other researchers of that age used the law of the three proportions, and especially Newton’s demonstration in the Proposition XXXIV, to deduce the resistance of an inclined flat plate in the air”. In this way, they proved that the pressure on the plate is defined by the sine-squared law (Fig. 4.15b): Pϕ = P sin2 ϕ

(4.4)

where P is the pressure on a plate perpendicular to the flow direction and ϕ the inclination of the plate. The sine-squared law soon became the cause of fiery disputes [55]. In 1725, Willem Jacob’s Gravesande (1688–1742) wrote a natural philosophy work in which he challenged its correctness; he also maintained that the following relationship: Pϕ = P sin ϕ

(4.5)

provided better estimates than Eq. (4.4) for small values of ϕ. Colin Maclaurin (1698–1746) defended Eq. (4.4), using it in 1742 to evaluate the inclination of mill sails that provided the maximum wind thrust. With the passing of time, the sine-squared law was wrongly attributed to Newton and for this reason was blindly accepted [52]. It represented a serious obstacle to the progress of aerodynamics and aviation: its application corrupted the design of the first airplane wings, creating a sense of mistrust towards flight.19

19 Drag (D) and lift (L) are the forces per unit length on the wing of an airplane parallel and orthogonal to the relative speed of the flow:

D = Pϕ b sin ϕ = Pb sin3 ϕ;

L = Pϕ b cos ϕ = Pb sin2 ϕ cos ϕ;

L/D = 1/tgϕ

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The implementation of equipment aimed at measuring the resistance of bodies in fluids favoured the advancement of experimental aerodynamics and hydrodynamics. They offered support for the theoretical models of fluid dynamics (Sect. 3.6), dealt with a broad range of issues associated with the resistance of bodies with elementary shapes (especially plates, prisms, cylinders and spheres) and provided answers to various problems of great interest at that time. Prominent researches focused on the most effective shapes for projectiles, mill sails, hydraulic wheels and ship hulls. In an age still far away from Reynolds’ principles (Sect. 5.1), the role and the consequences of the law of the three proportions stood out. It sanctioned the indifference of assessing the resistance and to quantify it by K (Eq. 4.2) carrying out measurements both in water and in air. Even avoiding digressing in the hydraulic sector [53], it is thus essential to discuss some hydrodynamic experiences destined to also affect the aerodynamic field. Benjamin Robins (1707–1751), a British military engineer, engaged in tests about the resistance of air to projectiles on behalf of the British Army. Starting from the studies carried out by Jacques Cassini Jr. (1677–1756) in 1707, he built the ballistic pendulum around 1743. The pendulum, hanging from a horizontal axis, consisted of a massive iron plate fastened to a wooden block intended to receive the impact. The block, after being hit by the projectile, moved and described an arc of a circle. By measuring the length of the arc, and knowing the masses of the projectile and of the pendulum, the velocity of penetration in the air and, therefore, the resistance were obtained by a simple calculation based on the momentum theorem and on pendulum motion law. Robins also developed a second device, the whirling arm, destined to play an essential role in aerodynamics and aviation. Initially, he used it to optimise the shape of projectiles; later, thanks to the principle of reciprocity, he obtained the force of the wind on bodies, measuring their resistance to the penetration in air. The device consisted of a rod, 120 cm long, revolving around a vertical axis by means of a string, a pulley and a counterweight (Fig. 4.16). At first, Robins measured the joint resistance of the arm and the body through a weight that impressed a given velocity to the arm. He subsequently measured the resistance of the arm alone, varying the weight until it reproduced the previous speed. Finally, he obtained the resistance of the body as the difference between the two measures [52]. The experiences carried out by Robins are illustrated in two papers, New principles of gunnery containing the determination of the force of gunpowder and investigation of the difference in the resisting power of the air to swift and slow motions (1742) and Resistance of the air and experiments relating to air resistance (1746), presented to the Royal Society. The results confirmed that the resistance is proportional to the square of the velocity. They also proved, for the first time, that two bodies with the same frontal surface, but with different shapes, can have different values of resistance. By virtue of such results, the Royal Society awarded Robins with the 1746 Copley Medal. From these expressions, it is possible to infer that L is small for small values of ϕ; to fly, then, it is necessary to increase the wing area, arriving to an impossible size, or the angle ϕ. In this latter case, however, D grows faster than L. The ratio L/D expressing wing efficiency, therefore, decreases [54].

4.2 The Resistance of Bodies in Fluids

199

Fig. 4.16 Robins’ whirling arm [54]

During his experiences, Robins noted that the projectiles rotating around their axis were subjected to a transversal force that deviated them from a straight trajectory. Such phenomenon, now known as Magnus effect, would be explained almost a century and a half later (Sect. 3.6). John Smeaton (1724–1792), an English engineer, designer and builder of windmills (Sect. 4.6), ports, drainage works and the Eddystone Lighthouse erected on the cliffs of Plymouth between 1756 and 1759 (Sect. 4.7), is also known as a builder of steam engines (Sect. 3.7) and the author of brilliant writings in the field of mechanics. In 1759, the Royal Society awarded him with the Copley Medal, for a paper [56] in which he reported the results of his first researches on models. He began by affirming that “it is very necessary to distinguish the circumstances in which a model differs from a machine in large; otherwise, a model is more apt to lead us from the truth rather than towards it. Hence, the common observation is that a thing may do very well in a model that will not answer in large. And, indeed, though the utmost circumspection be used in this way, the best structure of machines cannot be fully ascertained, but by making trials with them, when made of their proper size”. In other words, he affirmed that only the comparison with full-scale measurements could confirm the validity of the tests carried out on a different scale [52]. Smeaton’s paper is organised into three parts. The first two parts describe hydrodynamic tests on models of paddle wheel. The third illustrates aerodynamic tests on windmill sails (Sect. 4.6). Smeaton observed that, “in trying experiments on windmill-sails, the wind itself is too uncertain to answer the purpose: we must therefore have recourse to an artificial wind. This may be done two ways; either by causing the air to move against the machine, or the machine to move against the air. To cause the air to move against the machine, in a sufficient volume, with steadiness and the requisite velocity, is not easily put in practice: To carry the machine forward in a right line against the air, would require a larger room that I could conveniently meet

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Fig. 4.17 Whirling arm: a Smeaton’s [56]; b Borda’s [52]

with. What I found most practicable, therefore, was to carry out the axis, whereon the fails were to be fixed, progressively round in the circumference of a large circle”. Smeaton then examined again the whirling arms independently built by “Mr. Rouse, an ingenious gentleman of Harborough in Leicestershire” and by Mr. Ellicott, “on behalf of the renowned Mr. B. Robins”. He built a synthesis of these devices: the arm supporting the sails rotated by hand; the sails rotated by means of a weight; and co-axial with their rotation axis (Fig. 4.17a). He carried out 19 campaigns of tests to determine the optimum shape of the mill sails in relation to the wind speed. In [56], Smeaton also reported a table, “communicated to me by my friend Mr. Rouse”, which is considered as the first wind intensity scale (Sect. 4.3). It quantifies

4.2 The Resistance of Bodies in Fluids

201

the pressure on mill sails through a drag coefficient K = 1.82, which replaced into Eq. (4.3) provides the relationship: P = 0.00492 V 2

(4.6)

where V is expressed in mph and P in lb/ft2 . This expression was very successful among civil, naval and aeronautical engineers and among the architects of the nineteenth century [57]. It became so commonly used that, at the start of the twentieth century, the memory of the presence of the drag coefficient K would be lost. It was then “perfected” through the addition a second drag coefficient C, assuming the form: P = 0.00492 V 2 C

(4.7)

C, usually set as greater than one, will then play the role of a hidden safety factor. Jean Charles de Borda (1733–1799) carried out measurements of the resistance of bodies in air by a whirling arm called “Aerodrome”, very similar to the one used by Robins [53]; he described this device and his tests in a paper, Expériences sur la résistance des fluides, presented to the Académie des Sciences in 1763. In 1767, he published a second work with the same title, where he described similar measurements of the resistance in water of bodies of various shapes (spheres, plates, prisms, cylinders, cones and wedges) (Fig. 4.17b), confirming that the resistance is proportional to the square of the velocity and depends on the shape of the body. He obtained similar values for the resistance of a sphere and one half of this with the convexity exposed to the flow; from this, he wrongly deduced that the resistance of bodies only depended on the shape of the surface exposed to the flow [52]. On the other hand, he was the first to perceive the role of interference: placing a pair of spheres on the whirling arm, he noticed that the overall resistance did not match the sum of the resistances of the two spheres; this phenomenon was called “Borda effect” for a long time. Regardless of the historical value of these experiences, Rouse, Robins, Smeaton and Borda failed to grasp a fact. When a whirling arm was used, the air (or water) tended to rotate with the body. This made impossible to exactly know the relative velocity of the body in the fluid [52, 53, 58]. Unlike the whirling arm method, where the bodies subject to resistance measurements travelled along circular trajectories, the towing tank technique provided measurements of the resistance in water of bodies towed with a straight motion. This technique, first applied in 1746 by Pierre Bouguer (1698–1758), received remarkable stimuli at the end of the eighteenth century, thanks to the researches carried out by the French engineers [52]. In 1771, Charles Bossut (1730–1814) published Traité théorique et expérimental d’hydrodynamique, where he discussed the difficulties of large-scale experiments and the falsity of the experiments based on models in exceedingly little scale. He then recommended the use of average scale models, which allowed recognising the effect searched for without impairing the required accuracy.

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In 1775, Bossut, Jean Le Rond d’Alembert (1717–1783) and the Marquis Antoine de Condorcet (1743–1794) were entrusted by the French government with the measurement of the resistance of various boats in relation to the development of the inland navigation on canals. To this end, they built a towing tank 30 m long, 15 m wide and 2 m deep, in which they measured the resistance of models towed by cables. They concluded that the resistance was as higher as the canal cross-section was smaller. This result anticipated a fundamental issue in wind tunnel tests (Sect. 7.2): blockage. Following these researches, D’Alembert published Nouvelle expériences sur la résistance des fluides (1777), where he analysed the square sine law. He concluded that it was reliable for inclination values between 50° and 90°, while it led to wrong results for lesser angles. Pierre Louis Georges Du Buat (1734–1809) was the author of Principes d’hydraulique, a work in three volumes published in 1779, 1786 and 1816. The last part describes over 100 experiences carried out, both in water and in air, to measure the resistance of bodies with different shapes. Thanks to them, Du Buat confirmed that the results obtained with different fluids are interchangeable, scaling the respective densities. He also disproved the principle, tacitly accepted since Newton’s times, that the resistance of a body in a fluid only depends on the pressure on the forward part of the body. Making use of piezometers arranged on the whole surface and connected to a pressure gauge, he proved that the rear part of the body contributes to its resistance through the “non-pressure”, or suction, that occurs in that area. By so doing, he belied the conclusion to which Borda arrived, namely that the shape of the rear part played a marginal role. He also proved that the drag coefficient is linked to the ratio between the diameter of the surface impacted by the fluid and the length of the body along the motion direction. Perhaps because of a measurement error, he came to a wrong conclusion, currently known as the “Du Buat’s paradox”: “the force exerted upon a stationary body by moving water is greater than that required to move the same body at the same relative speed through still water” [52]. Du Buat also reworked the results of Bossut, d’Alembert and Condorcet, noting that the fluid particles whose motion is affected by the body are enclosed in a cylindrical surface with its axis parallel to the motion direction and with cross-section equal to 6.46 times the cross-section of the body; in other words, the fluid is undisturbed at a distance from the body equal to ¾ of its diameter.20 Finally, an article by Charles Augustin Coulomb (1736–1806), Expériences destinées à détereminer la cohérence des fluides et les lois de leur résistance dans les mouvements très lents (1800), deserves to be mentioned: it described tests on bodies with elementary shapes in water and suspended by means of a brass wire subjected to torsion. The resistance offered by the fluid was obtained from the dampening of the torsional motion. 20 In

1829, Jean Victor Poncelet (1788–1867) published Introduction à la mécanique industrielle, where he interpreted Du Buat’s law maintaining that resistance tests can be performed in a pipe with a cross-section sufficient to contain all the fluid particles whose motion is affected by the body, and with surfaces not creating friction; the resistance of the body can be obtained from the momentum variation of the fluid between the current cross-section and the one shrunk by the presence of the body. This hypothesis was used by De Saint Venant in Sur la resistance des fluides (1847).

4.2 The Resistance of Bodies in Fluids

203

The above-mentioned studies originated a vast literature about experimental research in fluid dynamics,21 in particular on the measurement of the resistance of bodies in fluids. William Herbert Bixby (1849–1928) [37], Joseph Cottier [55] and Alexander Gustav Eiffel [59] provided an extensive review of these studies. In 1782, Samuel Vince (1749–1821) carried out many experiences with the whirling arm, published in 1798 on the Philosophical Transactions of London, which highlighted a still common belief: the face exposed to the flow is subjected to the hydrodynamic and to the hydrostatic pressure; the downwind face is subjected to the hydrostatic pressure only. Similar experiences with the whirling arm were carried out in 1783 by Richard Lovell Edgeworth (1744–1817), between 1786 and 1788 by Charles Hutton (1737–1823), and in 1826 by Thibault. Between 1785 and 1790, Reinhard Woltmann (1757–1837) completed previous experiences with the whirling arm, measuring the resistance of fixed bodies in water currents. From 1835 to 1836, three Captains, Guillaume Piobert (1757–1837), Arthur Morin (1795–1880) and Isidoire Didion (1798–1878) hanged bodies to silk ropes reeled on a pulley; a brush connected with the pulley traced the law of the motion from which air resistance is obtained; the results were published in 1842 [60]. Table 4.1, obtained through Eq. (4.3) [37, 59], summarises the main results of the experiences carried out from 1690 to 1836 on thin plates, square- or circle-shaped, perpendicular to the direction of the relative velocity between the fluid and the body. The drag coefficient K shows a very high spread. The growing of tests and results was not sufficient to establish a solid culture in aerodynamics and hydrodynamics; on the contrary, it highlighted increasingly doubts and uncertainties. Colonel N.V. Duchemin captured this reality in 1842, publishing a splendid state of the art of such knowledge in the mid-nineteenth century [61]. The opening words of his paper are enlightening: “What is the resistance withstood by a body when it moves in a fluid at rest or when it is swept by a moving fluid? This question is, among those still to be solved by the physical and mathematical sciences, one of the most important because of its many applications. It has been a subject of research for mathematicians and physicists for approximately two centuries. (…) Such works have hitherto provided more contributions to mathematical advancements than to the solution of this question; this occurs because theories seldom match the observed facts and the latter, because of their isolation and, above all, the scarce matching highlighted above, are far from being able to inspire full and complete trust. We are then forced, to orientate ourselves in applications, to use unsafe approximations that often deviate from the truth”.

21 In

1797, Giovanni Battista Venturi (1746–1822) published Recherches expérimentales sur le principe de communication latérale dans les fluides, where he described the measurements carried out by means of an equipment by Giovanni Poleni (1683–1761). He studied fluids subjected to sudden cross-sectional changes, proving that the shrinking and diffusion due to the introduction and exit of a flow in a cylindrical pipe produced vortices. Replacing the cylinder with two truncated cone sections, the first converging and the second diverging, Venturi eliminated vortices and retained the desired velocity and pressure variations. These are essential principles for the evolution of wind tunnels, which will take place at the end of the nineteenth century (Sect. 7.2).

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Table 4.1 Drag coefficients of thin plates perpendicular to the flow Author (year)

Fluid

Method

Plate

K

Mariotte (1690)

Water

Fixed plate in current

Square

1.26

Bouguer (1746)

Water

Towed body

Square

1.24

Rouse and Smeaton (1759)

Air

Whirling arm

Rectangular

1.82

De Borda (1763)

Air

Whirling arm

Square

1.38

Coulomb (1780–1790)

Air

Whirling arm

–

1.10

Vince (1782)

Air

Whirling arm

Circular

1.34

Rouse and Smeaton (1782)

Air

Whirling arm

–

1.44

Edgeworth (1783)

Air

Whirling arm

–

1.64

Hutton (1786)

Air

Whirling arm

Square

1.24–1.42a

Woltmann (1785–1790)

Water

Fixed plate in current

–

1.34

Thibault (1828)

Air

Whirling arm

–

1.66–1.90b

Piobert, Morin, Didion (1835–1836)

Air

Free fall

Various shapes

1.36–1.67

aK bK

= 1.24 for A = 0.011 m2 ; K = 1.42 for A = 0.021 m2 = 1.66 for A = 0.5 ft2 ; K = 1.90 for A = 1 ft2

Duchemin illustrated the measurements, he personally carried out in 1829, about the penetration of projectiles in air and, more generally, on the resistance of bodies in fluids. He aimed at interpreting the disagreement among different experiences and formulating simple forecasting formulas. Actually, he confirmed the doubts about the dependence of the drag coefficient on the involved parameters. Returning to the results by Du Buat, Duchemin wondered if it is true that the resistance of a fixed body in a fluid flow is equal to that of a body moving, at the same velocity, in a fluid at rest. He strengthened his doubts taking into examination measurements by Smeaton, Thibault and himself. He noted, by way of example, that the pressure on the rear face of the bodies varies in relation to the type of test carried out. He observed that “if the density of the liquid is the same both at rest and in motion, this is not true for air that, because of compressibility, is as denser as smaller is its volume”. In this way, he cast the shadow of doubt on a concept acquired since the time of Newton; air compressibility only becomes significant when air moves at speeds close to, or exceeding, the speed of sound. Similar, but more well-founded, doubts regarded the comparison between straight and circular motion tests, especially in relation to the swept area and the velocity. Straight motion tests proved that the resistance of thin plates is proportional to the exposed area. De Borda’s circular motion tests [62, 63] highlighted that the ratio between the resistance and the exposed area tends to increase with the size of the body. According to Du Buat, the resistance of a body in circular motion is greater than the resistance in straight motion of the same body, and the larger the size of

4.2 The Resistance of Bodies in Fluids

205

the body and lesser the radius of the described circumference, the greater it is. Other Duchemin’s data highlight the dependence of the drag coefficient on the relative velocity of the fluid; this fact is essential, since most tests carried out up to the midnineteenth century referred to rather low velocities. The conclusion was discouraging: “there were many causes of variation of the drag coefficient for which neither the size nor the reason is known”. On the other hand, besides these pessimistic observations, Duchemin had the merit of perfecting the knowledge about pressure on inclined plates. His experiments led him to criticise the sine-squared law (Eq. 4.4) and to propose the following new expression:   2 sin ϕ (4.8) Pϕ = P 1 + sin2 ϕ which from that time on was used by engineers and architects worldwide for many years. Actually, in Duchemin’s age, there were no sufficient elements to achieve satisfying results. A series of concepts—the transition from the laminar regime to the turbulent one, the dependence of the resistance on the Reynolds number, the formation of the boundary layer, the separation and the vortex wake (Sect. 5.1)—and instruments—efficient engines and wind tunnels (Sect. 7.2)—required to achieve a radical change were still to establish themselves.

4.3 Wind Intensity Scales Section 4.1 discusses the knowledge that took shape between the sixteenth and nineteenth centuries as regards the origins and characteristics of wind phenomena, especially on the background of circulation at the planetary scale. With regard to the same period, Sect. 4.2 introduces the concepts and experimental techniques originating the procedures to evaluate wind actions on bodies in air. With the exception of isolated cases, both of them leave the quantitative definition of wind intensity aside. The velocity V to take into account to evaluate wind actions was the subject of a heated debate between the late eighteenth and the early nineteenth centuries [62]. Charles Hutton (1737–1823) proposed V = 124 mph. Giuseppe Toaldo (1719–1798) described a storm that crossed Italy from Venice to Naples in 1783; it reached V = 96 mph. According to Reinhard Woltmann (1757–1837), the wind, in tropical climates, could reach V = 102 mph. Charles Augustin Coulomb (1736–1806) carried out measurements by means of feathers left free to fly in storms; he reached the conclusion that V = 120–136 mph is a conservative maximum value (Théorie des machines simples, Paris, 1821). In this debate, there was no hint that V could depend on the height above the ground; there was no reference to the fact that V could be the mean value of the velocity or the gust peak; no consideration was given neither

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4 The New Culture of the Wind and Its Effects

to the randomness of wind phenomena, nor to the use of the probability theory to determine V. The will to classify or graduate wind intensity emerged in 1663, when Robert Hooke (1635–1703) proposed to the Royal Society of London “a method to produce a history of the weather”. He was the first to perceive the necessity of qualifying the main atmospheric phenomena by means of names instead of descriptions. Daniel Defoe (1660–1731) was an English writer and journalist, author of The storm [64]. This book provides a vivid description of the great storm, which struck England between November 26 and December 3 in 1703, reaching its peak in the night of November 26. It caused the death of 123 people on the land and of 8000 seafarers, including 1500 Royal Navy sailors. It left huge numbers of uprooted trees and collapsed buildings in its wake. Standing out among the latter, the tile roof of Westminster Abbey and the structure of Ely Cathedral suffered damage, the Eddystone Lighthouse was destroyed (and subsequently rebuilt by Smeaton, Sect. 4.7) and more than 400 mills and countless churches were unroofed [6]. Observing the situation in London, where 21 people died and more than 200 were seriously injured, Defoe wrote: “The streets lay so covered with tiles and slates, from the top of the houses, especially in the out-parts, that the quantity is incredible, and the houses were so universally stript, that all the tiles in fifty miles round would be able to repair but a small part of it”. Defoe perceived the need to use more accurate terms to classify atmospheric events. He then introduced a table with 12 levels, related to the following definitions: “stark calm, calm weather, little wind, fine breeze, small gale, fresh gale, topsail gale, blows fresh, hard gale of wind, fret of wind, storm, tempest”. He judged this approach essential to interpret historical assertions: “Without conventional terms to speak of the present, how is it possible to get a meaning from the descriptions of the past?” Robinson Crusoe, his famous novel published in 1719, definitely met with much greater interest. The shift occurred thanks to John Smeaton (1742–1792) who, in his 1758 paper [56], reported the first wind intensity scale, “compiled by Mr. Rouse”. It consists of a table (Fig. 4.18) in which several velocity levels (V ) are associated with as many pressure levels on mill sails (P) (Eq. 4.6). Besides that, the names commonly adopted in that age to indicate the wind strength were assigned to the different velocity and pressure levels. The innovative circumstance standing out was the concept that wind pressure on mill sails could be interpreted as an objective instrument for a conventional graduation of the state of the wind and its action. As it often happens, new ideas took a long time before being recognised, especially in sectors different from the one where they originated. In witness of this, in 1769 William Falconer (1732–1769) published the first edition of the universal marine dictionary [65]. Under “wind” he wrote: “if the wind blows gently, it is called a breeze; if it blows harder, it is called a gale, or a stiff gale; and if it blows with violence, it is called a storm or hard gale”. This sentence became a rudimentary wind scale with three levels (“breeze”, “gale” and “storm”). Ignoring the scale of Rouse and Smeaton, it was used to classify and define the intensity of wind phenomena aboard vessels for almost half a century.

4.3 Wind Intensity Scales

207

Fig. 4.18 Rouse’s intensity scale for wind velocity and pressure [56]

The Rouse and Smeaton scale attracted Alexander Dalrymple (1737–1808), a Scottish geographer, cartographer and explorer, the first hydrographer of the Royal Navy and a collector of pictures and drawings of marine subjects. He judged this scale a precious lesson to improve maritime meteorology and recommended its use, in a revised form, in the marine field. He convinced himself “that it would be very useful to have a series of prints of sea pieces to explain the levels and gradations of wind from a Calm to a Storm, which gradations are so well expressed in pictures in my own collection” [18]. In 1790, therefore, Dalrymple prepared a scheme of “the said gradations of wind taken from the sea journals compared with Mr. Smeaton’s scale from the work of windmills” [18]. Unfortunately, he was removed from his position and left his work unfinished. Dalrymple’s work was recovered by William Burney of Gosport (1762–1832), who in 1815 compiled an updated and enlarged version of Falconer’s universal marine dictionary. Under “breeze”, he wrote: “Mr. Dalrymple, late hydrographer to the Right Honourable the Lord Commissioners of the Admiralty and East India Company, scientifically arranged the wind in the following order: (1) faint air; (2) light air; (3) light breeze; (4) gentle breeze; (5) fresh breeze; (6) gentle gale; (7) moderate gale; (8) brisk gale; (9) fresh gale; (10) strong gale; (11) hard gale; (12) storm”. Unfortunately,

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4 The New Culture of the Wind and Its Effects

the original idea of linking every term to objective facts was lost. The same limit was implicit in the wind scale formulated in 1820 by William Scoresby Jr. (1789–1857) [66], adopting 13 levels: (1) calm, (2) almost calm air, (3) light breeze, (4) gentle breeze, (5) brisk breeze, (6) fresh breeze, (7) strong breeze, (8) brisk gale, (9) fresh gale, (10) strong gale, (11) very strong gale, (12) hard gale and (13) storm. Dalrymple’s ideas, known and prized by that time, were only waiting to be finalised. This was accomplished by Sir Francis Beaufort (1774–1857), Irish Hydrographer and Commander in the Royal Navy [18]. He acquired a huge sailing experience, covering himself with glory for the courage and gallantry displayed during the Napoleonic Wars; because of the wounds he suffered during such wars, he was assigned to command HMS Woolwich, which in the meantime had been demoted to a storeship. In 1805, while he awaited to leave Portsmouth in a convoy tasked to chart the hydrography of the Rio de la Plata, he bitterly wrote [2]: “To a storeship! Good Heavens! It is for the command of a storeship that I have spilled my blood, sacrificed the prime of my life, tragged out a tedious economy in foreign climates, wasted my best hours in professional studies (…) For a storeship, for the honour of carrying new anchors abroad and old anchors home! For a ship more lumbered than a Dover packet, more weakly manned than a Yankee carrier!”. Beaufort had the great virtue of overturning his initial despair, taking advantage of the idle days to devote himself to study the marine climate. For years, sailing the seas, he registered the cloud cover, temperature, visibility, precipitations and the wind (Fig. 4.19a). He then decided to use his expertise to define and quantify wind phenomena; on 13 January 1806, he wrote on the captain’s log: “Hereafter I shall estimate the force of the wind according to the following scale, as nothing can convey a more uncertain idea of wind and weather than the old expressions of moderate and cloudy, etc. etc.”. Below this entry, he reported his first scale, divided into 14 levels from “calm” (0) to “storm” (13), complete with a series of abbreviations to describe any weather. In this form, Beaufort’s scale retained qualitative properties only. It happened that Beaufort, who made friends with Dalrymple, was informed by the latter about the Rouse and Smeaton scale as regards windmills. Encouraged by Dalrymple, Beaufort applied the same principle to the rigging of a square-rigged ship (Sect. 4.4). He then established a relationship among the three peculiar elements of the scale—the level of intensity, the name of the phenomenon and the description of its elements on the vessel—and rewrote the scale passing from 14 to 12 levels22 (Fig. 4.19b). Even though he was sure of the validity of his idea, his scale was hardly recognised and applied. In 1829, Beaufort was appointed Hydrographer for the Royal Navy, the former Dalrymple’s position: this assignment gave him enough influence to promote the use of his scale. He recommended it to Robert Fitzroy (1805–1865), the captain of the brig Beagle: “The state of the wind and weather will, of course, be inserted; but some intelligible scale should be assumed, to indicate the force of the former, instead of the ambiguous term ‘fresh’, ‘moderate’, and c., in using which no two people agree; 22 Beaufort defined as “hurricane” the twelfth and maximum level of his scale, attributing to this term the meaning of “exceptionally violent storm”.

4.3 Wind Intensity Scales

Fig. 4.19 Beaufort’s log (a) and second scale [2] (b)

209

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4 The New Culture of the Wind and Its Effects

some concise method should also be employed for expressing the state of the weather. The suggestions contained in the annexed printed paper are recommended for the above purpose” [18]. Fitzroy saw the usefulness of the scale and the delicacy of the missions he was tasked with. He then asked Beaufort to find a fellow traveller sharing his enthusiasm for science and capable to carry out naturalistic research as well. Beaufort selected a young, freshly graduated Englishman, Charles Darwin (1809–1882). Fitzroy took him along in a legendary expedition (1831–1836). At the end of the voyage, which Darwin spent helping Fitzroy in the application of the wind scale, Darwin published his first famous book, Notebooks on the transmutation of species (1836), in which he founded the theory of evolutionism; the preface was dedicated to Beaufort.23 In the meantime, Beaufort became an admiral and imposed his scale on all the vessels of the Royal Navy (1838), making a huge mass of weather information compatible and uniform [67]. Many English seafarers acquired so much trust in Beaufort to pay him a supreme praise [2]: “Trust in God and the Admiral charts”. Others noted, conversely, that the use of the Beaufort scale turned the logbooks into legal deeds about the behaviour of captains at sea and in battle; some went as far as to think that the true purpose of the scale was providing judges with evidence about errors and disobediences. Even so, the Beaufort scale was officially acknowledged by the First International Meteorological Conference in Bruxelles (1853). Its use in international telegrams was launched shortly afterwards, incorporating it in the world climatologic vocabulary. In the meantime, steam propulsion replaced sails (Sect. 4.4): since 1906, the scale ceased making reference to sails and quantified wind velocity through wave motion. Later on, it was extended to wind effects on the land24 and still represents an essential tool for sailors, meteorologists, engineers and architects [2].

4.4 Sail Propulsion and Sailing Events changing the history of the humankind took place between 1487 and 1522. In August 1487, the Portoguese Bartolomeu Diaz (1450–1500) left Lisbon: King João II (the Perfect Prince, 1455–1495) instructed him to continue the exploration of the west African coast started in 1481. In February 1488, Diaz rounded the southern 23 Similar praises were included in the book published by Fitzroy in 1863 [43]: “Praise Beaufort, who

has used and introduced this synthetic approximate estimation method through a scale expressed in numbers rather than in vague words, …”. 24 In 1923, Sir George Clarke Simpson (1878–1965), director of the English Meteorological Office, extended the Beaufort scale to the land; in 1926, Sir William Napier Shaw (1854–1945) reported this scale in his Manual of meteorology [11]. In 1946, the Beaufort scale was broadened up to the 17th level; the levels from 13 to 17 were used to identify hurricanes, typhoons and tornadoes. In 1951, the World Meteorological Organization added further changes to the scale. Today, specific scales are used for tropical cyclones (e.g. the Saffir–Simpson scale) and tornadoes (e.g. the Fujita and Torro scales).

4.4 Sail Propulsion and Sailing

211

end of the African continent, calling it Cabo Tormentoso. When he returned to Lisbon, in December that same year, King João II renamed it Cape of Good Hope, interpreting the feelings of European merchants, who considered this passage essential for the prosperity of the Old Continent. On 3 August 1492, the Genoese Christopher Columbus (1451–1506), sponsored by Ferdinand II (the Catholic, 1452–1516) and Isabel of Spain (1451–1504), took out to sea from Palos to reach Asia sailing westwards. Taking advantage of the constant trade winds at medium latitudes, on 12 October 1492 he landed at Guanahani, one of the Bahama islands he renamed San Salvador. He subsequently landed in Cuba and named it Juana, and then in Hispaniola, which nowadays is divided between the Dominican Republic and Haiti. Columbus returned to Spain in March 1493, persuaded that the islands he had explored were located in the seas of Asia. He undertook three other expeditions, sailing from Spain in September 1493 and in May 1498 and 1502, during which he reached the islands of Dominica, Guadalupe, Antigua, Trinidad and Santo Domingo; he also landed in Panama and Venezuela, sailing along the coast of South America up to the estuary of the Orinoco River. Another presumably Genoese explorer, John Cabot (approx. 1450–1499), guessed that the lands reached by Columbus might not be in Asia. Cabot, sponsored by King Henry VIII of England (1457–1509) to carry out an exploration voyage following a more northern route, sailed from Bristol on 20 May 1497. The voyage ended the following month with the arrival to a land that was believed to be part of northeastern Asia. As a matter of fact, it was the island of Newfoundland, the coast of Maine or New Scotland. After his return to England, Cabot received support from the king for a new expedition to reach Japan; he sailed again from Bristol in May 1498 and then he disappeared. His mission, however, remains important because it laid the foundations for the future English colonisation of North America; moreover, it provided geographers with scientific information about the vastness of the American continent, encouraging the search for a north-west passage towards the east. Little over one month after the departure of the first Cabot expedition, another Portuguese explorer, Vasco da Gama (1469–1524), reached India circumnavigating Africa. Sponsored by King Manuel I of Portugal (1469–1521), he sailed from Lisbon on 8 July 1497 and rounded the Cape of Good Hope 13 weeks later. He sailed up the east coast of Africa up to Mombasa, crossed the ocean taking advantage of the monsoon and, on 20 May 1498, arrived at Calicut, on the Indian coast of Malabar. He returned to the home country in September 1499, proving that the Indian Ocean was not the closed sea imagined by ancient Greeks. Lisbon became the main European centre for spice trade, laying the basis of the Portuguese Empire in East Africa, India and Indonesia. A third Portuguese explorer, Ferdinand Magellan (1480–1521), realised that Southern America was not connected to the mysterious “great southern continent”, and declared to be willing to reach the East sailing westwards, over the southern end of America. This proposal was accepted by the Spanish crown and by German bankers, who sponsored the expedition. Magellan put out to sea from Sanlúcar de Barrameda on 20 September 1519, sailed along the coast of Africa up to the present Sierra Leone, then crossed the Atlantic and reached Southern America. From there,

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sailing along the Brazilian coast, he arrived in Southern Patagonia. The expedition set sail again on 24 August 1520 and, on October 21, crossed the strait it was later renamed after him. On November 28, the three remaining ships reached the open sea, which was called Pacific because of its apparent smoothness. They sailed up the west coast of South America, crossed the ocean and reached the Philippines where, on 27 April 1521, Magellan was killed by the natives. The command of the remaining ship went to Juan Sebastián de Elcano (1476–1526) who, after rounding the Cape of Good Hope, completed the circumnavigation of the planet arriving in Seville on 8 September 1522. From that day, Europe was aware that the earth is a sphere and all the oceans are connected. These amazing events, shrouded by the fascination for the unknown and adventure, gave the Western civilisation the possibility to redesign earth’s geography, to trace routes and to establish relations to new populations. The ocean voyages also represented essential tools to improve the knowledge of the weather and of the earth’s climate, generating a wealth of meteorological information (Sect. 4.1) that went beyond scientific culture. All this was made possible by the renewed maritime capability of using the wind by means of increasingly efficient sails and vessels (Sect. 2.5) [44]. From this perspective, wind, starting as a source of life, became a driving force for progress. It is interesting how many important undertakings were associated with smallsized vessels. The first expedition of Columbus made use of Santa Maria, a carrack approximately 28 m long and of two caravels, Pinta and Niña, approximately 15 m long. Cabot’s Matthew was a three-masted merchant ship, very fast but only 22 m long. Magellan’s Trinidad, the first vessel to circumnavigate earth, was 22 m long and with a width not exceeding 6 m. As to the prototype of this type of ship (Fig. 4.20), it was generally equipped with three masts—the main mast, the foremast and the mizzenmast—and five sails—the main course, the fore course, the mizzen latin sail (the only non-square sail), the topsail and the spritsail. Such rigging gave the ship excellent balance and manoeuvrability characteristics in various wind conditions. This was indeed the beginning of a period during which the vessel size tended to increase; the area of the sail plan, characterised by increasingly complex rigging, also increased. Initially, the main course, which descended from the single sail of the ancient single-masted vessels, was the one with the greatest area; the other sails only fulfilled an auxiliary function. Later, the size of the fore course and of the main topsail increased to achieve a more uniform distribution of the sails. The increase in the size of vessels and the unwillingness to make use of sails with an exceedingly large area required the addition of other sails that, in turn, required new masts, lines and tackles. The fore topsail made its appearance to balance the main topsail; a second mizzenmast, called Bonaventure and rigged with another latin sail, was also added. The three-masted ship with five sails (Fig. 4.21a) became a four-masted vessel with seven sails (Fig. 4.21b). Frequently, an outrigger extending over the stern was added for the Bonaventure sail. Often, a topgallant sail was added above the mizzen sail and a latin topsail was put above the Bonaventure sail. The top spritsail, hoisted on

4.4 Sail Propulsion and Sailing

213

Fig. 4.20 Typical fifteenth century caravel

Fig. 4.21 a Three-masted ship with five sails, sailing with a crosswind [44]; b Mayflower [44], the ship used by Pilgrim Father to cross the Atlantic in the seventeenth century

a mast at the end of the bowsprit, also appeared. As early as the second half of the sixteenth century, the largest ships were rigged with a set of sails as much complex as inefficient. It gave rise to a tangle of cables so intricate it made manoeuvering increasingly difficult and averages increasingly common. In the same period, especially on small vessels, remarkable development of foreand-aft sails took place, thanks to the peoples living on the shores of the Atlantic and of the northern seas and to the Dutch, who adopted them in their turbulent and shallow coastal waters; they also used them to cross mud banks and river estuaries, where the sea bottom and the shore represented a threat.

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Fig. 4.22 Origin of the gaff-sails from the latin sail

In this situation, the first to appear was the most important and versatile of the fore-and-aft sails (Fig. 2.11), the triangular one bent on the bow stay; it improved the characteristics of the boat rigged with a single spritsail near the bow, making boats more manoeuvrable. The advent of the gaff-sail made an additional advance; it was derived from the latin sail to mitigate its weakness. The gaff, the lug and the Portuguese mainsail25 (Fig. 4.22) were obtained by removing the part of cloth before the mast. The key aspect of this advancement was that the new fore-and-aft sails, introduced on smaller vessels to make them more manoeuvrable, also became common on large merchant and military ships, providing them with increased speed, manoeuvrability and capability to sail close to the wind. This occurred between the late seventeenth century and the early eighteenth century, when the ships-of-the-line became lighter, removing useless decorations. The forecastle disappeared, the stern became lower, and its shape changed from square to rounded; the hull was sheated with copper to protect it from corrosive agents, the masts were strengthened, and the sail area increased. Staysails and jibs replaced the spritsail and the top spritsail; a gaff-sail fitted with gaff, and boom replaced the latin sail on the mizzenmast. This evolution represented a strongly innovative element: instead of a single foreand-aft sail, the mizzen latin sail, ships were now fitted with many fore-and-aft sails among the square-rig sails. The jib, pushed forward thanks to the bowsprit and 25 Before such evolutions, perhaps from some millennia, the peoples of the Far East used a formidable mainsail, called Chinese, with characteristics—easy sail reduction, battens, the curvature of the trailing edge—subsequently introduced in the modern Western mainsails.

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supported by other triangular sails, formed a system of bow sails. The staysails, between the masts, increased the capability of the ship to sail close to the wind. The gaff-sail gave better performance than the latin sail. This is how the typical eighteenth century ship came into being. It was fitted with four small triangular sails between the bowsprit and the foremast; they were called, from stem to stern, flying jib, jib, fore staysail and storm staysail. The foremast, mainmast and mizzenmast were rigged with five four-sided sails of various sizes: the lower ones were called foresail, mainsail and, if present, mizzen sail. Above them, there were three sails called foretopsail, main topsail and mizzen topsail. Above the latter, from stem to stern, there were the fore topgallant sail and the fore royal sail; the main topgallant sail and the main royal sail; and the mizzen topgallant sail and the mizzen royal sail. Triangular sails called main staysail, main topmast staysail and main topgallant staysail were fastened on stays between the mainmast and the foremast. Sometimes, staysails were added between the main mast and the mizzenmast; in this case, they were called, from the bottom, mizzen staysail, mizzen topmast staysail and mizzen topgallant staysail. A small gaff-sail fitted with gaff and boom was bent astern, fitted on the mizzenmast. The current knowledge about the sail system of this period is strengthened by the publication of the first works about shipbuilding that gained ground, especially in France, since the late seventeenth century. They indicated great interest for the hydrodynamic properties of hulls but little attention for the aerodynamic efficiency of sails. Among the most famous books, the following are worth mentioning: Théorie de la manoeuvre des vaisseaux (1689), by Bernard Renau d’Elicagaray (1652–1719); Architecture Navale (1695), by F. Dassié; Théorie de la construction des vaisseaux (1697), by Father Paul Hoste (1652–1700); and the three works by Pierre Bouguer (1698–1758), Traité du navire de sa construction et de ses mouvemens (1746), De la manoeuvre des vaisseaux ou traité de mécanique et de dynamique (1757), and Nouveau traité de navigation contenant le théorie et la pratique du pilotage (1760), which gave an essential contribution to the development of model tests in towing tanks (Sect. 4.2). Denis Diderot (1713–1784) and Jean Le Rond D’Alembert (1717–1783) dedicated a section of the Encyclopedie (1751–1772) to the Architecture Navale-Marine, including wonderful tables of the sailing ships (Fig. 4.23a) [68]. In 1768, Frederik Hendrik af Chapman (1721–1808) published in Sweden, Architectura navalis mercatoria, where he illustrated the projects of almost 200 vessels; he also developed a new experimental technique, towing the models in the towing tank by means of pulleys and counterweights: there was no optimum hull, but rather trim conditions most suited for any different speeds. HMS Endeavour, the ship aboard which the British explorer James Cook (1728–1779) made the first of his three voyages (1768–1779), proved the evolution of sail techniques in the three centuries following the cycle of undertakings performed between 1487 and 1522. It was similar to Santa Maria in size and was also fitted with three masts; unlike Santa Maria, which had four sails, HMS Endeavour had eight of them. She adopted a main course, a topsail and a topgallant sail on the fore and main masts, and a square topsail on the mizzenmast; on her bowsprit, like Santa Maria, it used a spritsail. The only fore-and-aft sail of the Santa Maria was

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Fig. 4.23 Tables from the Encyclopedie [68]: a sailing warship; b Dutch yacht

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the latin mizzenmast sail, while HMS Endeavour had five: the mizzenmast gaff-sail, a jib and the fore staysail, as well as two staysails between the mainmast and the fore mast, a main topgallant staysail and a main topmast staysail. Thanks to these sails, it was exceptionally manoeuvrable. While both merchant ships and warships displayed the advances described above, a new type of boat made its appearance: the “yacht” [69, 70], which was to become the repository of the sail tradition and a symbol of technological progress. This word appeared in Histoire de la marine française (1551), to indicate a pleasure boat; it was derived from Nordic words like “yagd” (in Danish and German), “yagt” (in Swedishes and Dutch) and “yat” (in Lappish), meaning “to hunt”, “fast” e “swift”, respectively. The Danish has been using the term yacht since the seventeenth century, referring it to nimble and small vessels, probably for coast defence. The English defined the yacht as a boat for the pleasure of its user. Indeed, such use had ancient roots: in Istoria dell’origine, e progressi della nautica antica (1785), Stanislao Bechi related about pleasure crafts used by Seleucus IV Philopator (218–175 BC), Cleopatra (69–30 BC) and Caligula (12–41). “Yachting” originated between the late fourteenth and the early fifteenth centuries, when Zealand, the current Holland, became the leading world power in maritime trade. The latter was managed by rich families of shipowners, who showed their status by competing with each other using ships—the “jachten”—so magnificent and ornamented to be called “speeljachten”, i.e. pleasure yachts. They became fashionable so quickly that, in 1622, Amsterdam was the location of the first harbour reserved to pleasure crafts.26 It gave shelter to small boats, 6–10 m long, which introduced important innovation: in an age when all the ships still used square or latin sails, they rigged a gaff-sail, which remained very efficient even when the boat sailed close to the wind. The passion for yachts gained ground among the British nobles thanks to King Charles II Stuart (1630–1685). In 1660, during a visit in the Netherlands, the notables of the Dutch East India Company presented him with Mary, a superb yacht that is considered the ancestor of all future pleasure craft27 ; Mary was 26 m long and was rigged with a gaff mainsail and a jib. The first yacht race took place in London on 1 October 1661, from Greenwich to Gravesend and back. Two descendants of Mary, Catherine and Anne, challenged each other: at their helm, respectively, there were King Charles II,28 who won the competition, and his brother, James II Stuart, Duke of York (1633–1701). Actually, the regatta, like most of the subsequent ones, was more a parade than a proper race. 26 In 1622, the port of Amsterdam was filled with yachts as soon as it was completed. Amsterdam then proceeded with the construction of a second port reserved to pleasure craft. It was completed in 1625, but soon it was also filled to capacity, requiring the construction of a third port, opened in 1642. 27 There were yachts in England before 1660. The most famous were Rat of Wight, launched at Cowes in 1588, and Disdain, launched at Chatham in 1604. 28 Charles II was doubtlessly the father of yachting. After having brought Mary in England and won the first race, he ordered the construction of 26 yachts, including the famous Fubbs; most of them were built by Peter Pett (1630–1699), the shipwright considered as the first “yacht designer”.

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The first yacht club, the Water Club of Cork Harbour, was founded at Cork in Ireland in 1720; its charter still represents a benchmark today for nearly all yacht clubs worldwide. William Falconer (1732–1769) included the term yacht in the Dictionnaire universel de la marine (1769). Diderot and D’Alembert published the first technical table depicting a yacht (Fig. 4.23b) in the section of the Encyclopedie (1751–1772) dedicated to Architecture Navale-Marine. The first British yacht club was founded in 1770 at Starcross on Devon. Cumberland Fleet, the first yacht club on the Thames, founded in 1775, soon became the Royal Thames Yacht Club, one of the most famous clubs in the world. In 1815, the Royal Yacht Squadron was founded in Cowes, on the Island of Wight: the most gorgeous yachts of British nobles gathered here; Cowes became the capital of yachting and, starting in 1826, hosted the Cowes Week, the most important sailing event of that age, organised under the patronage of the Royal Yacht Squadron and of the Royal Thames Yacht Club. For a long time, it retained social and luxurious peculiarities that prevailed on the sporting competition. The first offshore race took place in 1771 in the English Channel, between the Third Duke of Richmond (Charles Lennox, 1734–1806) and Sir Alexander Smith. The first sailing competition in ocean waters took place in Tasmania, in 1838, organised by the Royal Hobart Regatta Association; it started a series of races destined to play a key role in the technological development of sailboats. Even though New York was the evolution of New Amsterdam, a European settlement founded by Dutch in 1625, yachts were not used in America for a long time. Its economic conditions did not favour the export and building of pleasure craft. Francy, depicted in a 1717 engraving while crossing the bay of New York, is the first known American yacht (Fig. 4.24a). Nearly a century later, in 1794, Union sailed from Newport with a crew of twenty-three young men aboard. They circumnavigated the globe, in four years, for the pleasure of knowing new worlds and different cultures: it was the start of the cruising yacht. The epic of the American yachts started in 1816, when a rich family of Dutch shipowners built Cleopatra’s Barge (Fig. 4.24b), a luxurious but classic yacht, which in 1817 crossed the Atlantic up to the Italian shores. The Boston Boat Club, the first yacht club of the USA, was founded in 1830. The New York Yacht Club, a club destined to play a prominent role in sail navigation, was established in 1844. In the meantime, the first American races took place: they originated the definition of boat classes and of racing rules. The first bets were also made at this time. The greatest impulse to the advance of American yachting came from the Stevens family,29 known worldwide for their great engineering works. Robert Livingston Stevens (1787–1856), engineer, inventor and patron of arts, especially known in the railway sector, favoured the experimentation of revolutionary shapes and techniques. He designed Onkahye (1840) and Maria (1847), which 29 In

1874, Colonel John Stevens III (1749–1838), the father of Robert Livingston, John Cox and Edwin Augustus Stevens, purchased the land where now stands the Stevens Institute of Technology. Later on, he was a pioneer of steamboats. In 1825, he designed the first American locomotive (Sect. 3.7).

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Fig. 4.24 a Francy; b Cleopatra’s Barge [70]

highlighted his ideas: to forget the past by making use of new theories, advanced technologies and innovative materials. Maria, in particular, was the opposite of Cleopatra’s Barge: an essential boat, conceived to guarantee the highest possible speed. John Cox Stevens (1785–1857), the first commodore of the New York Yacht Club, understood that American yachting was ready to compete with the English masters; in 1850, he entrusted George Steers (1820–1856) to design a boat for challenging them. The schooner America, first proved its worth by victoriously facing Maria and then crossed the Atlantic to confront the English in a Royal Yacht Squadron race; the prize consisted of the Hundred Guinea Cup. The race took place in 1851, was 53 miles long and consisted of the circumnavigation of the Isle of Wight. America, skippered by Dick Brown, defeated the English opponents and became a legend. Unlike other yachts, conditioned by luxury, its lines were essential. It was conceived and built with the sole purpose of winning, and introduced important technical innovations: her sails were made of machine-woven cotton, and then they were less porous and more efficient than the English sails, which were made of hand-woven hemp. John Cox Stevens brought the Hundred Guinea Cup to the New York Yacht Club, promising to give the English their revenge in American waters; this was the start of the America’s Cup, still the world’s most famous sail race. Edwin Augustus Stevens (1795–1868) offered a lavish inheritance to science and engineering, leaving testamentary provisions and funds to establish a college named after his family. The Stevens Institute of Technology was opened in 1870 at Hoboken, New Jersey; it established the first curricular path in mechanical engineering, becoming synonymous with technological excellence and advancement. Its laboratories were to host hydrodynamic tests that will keep the America’s Cup in the USA for nearly a century (Sect. 7.5). In the meantime, scientific knowledge in the hydrodynamic field was taking shape. In 1850, Philip Marrett (1820–1857) wrote Yachts and yacht building (1865, 1872),

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where he set out a theory to design hulls without resorting to tests on models; Archibald Cary Smith (1837–1911) put it into practice in 1870 designing Vindex, the first hull conceived on theoretical principles. In 1865, William John Macquorn Rankine (1820–1872) carried out experiences on the resistance met by water into pipes, using the results to formulate a new theory about hull resistance. In 1872, William Froude (1810–1879) built a towing tank 90 m long, 11 m wide and 3 m deep in Torquay; thanks to it, he gave an outstanding contribution to the model tests of ships, achieving similarity conditions for the effects of both viscous and gravitational actions [71, 72]. In 1873, Vanderdecken, assumed name of William Cooper, published Yachts and yachting, a work in which he compared the performance of various hull types. The formidable epic of sail navigation for mercantile and military purposes finally came to an end. In spite of its exceptional beauty and charm, its limits were clear: its effectiveness depended on wind speed and direction, the cruise speeds it allowed were low, and the more the ship was larger, the more its use became complex. The advent of steam propulsion (Sect. 3.7), though less poetic, represented too strong a temptation even for a conservative sector like the marine industry. It was first used as an aid for sailing ships (Fig. 4.25a). In April 1838, Sirius and Great Western30 completed the first two Atlantic crossings using steam, and the future of sailing ships was decided. Merchant ships turned to steam around the mid-nineteenth century. In the second half of the nineteenth century, the navies also surrendered to this appeal; they kept the myth of the sail alive through their training ships (Fig. 4.25b).

Fig. 4.25 a SS Savannah: mixed sail and steam propulsion; b Amerigo Vespucci

30 The

giant Great Eastern, designed by Isambard Kingdom Brunel (1806–1859) (Sects. 4.8 and 4.9) was also known for the laying of the first telegraph cable from Europe (Ireland) to America (Newfoundland), in 1865. The cable, 3700 km long, was first reeled inside three tanks in the ship hold and then was laid on the sea bottom. The event was celebrated as the eighth wonder of the world.

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4.5 Flight Experiences and Scientific Research The diffusion of kites (Sect. 2.6) and the studies of Leonardo da Vinci (Sect. 2.10) represent the prelude of the advancements made by flight between the eighteenth and the nineteenth centuries. It is probably premature to affirm that flight, in this age, rose to the level of science. Assuredly, it placed itself at the service of science and contributed to its progress concerning atmospheric and aerodynamic knowledge. The measurements described in Sects. 3.2 and 4.1 shared a common element: they were taken near the ground or on the sea; as a consequence, they provided information about the portion of atmosphere closer to the earth’s surface. This trend changed since the mid-seventeenth century when, using kites, the first upper air measurements were taken [5, 73]. In 1749, Astronomer from Edinburgh, Alexander Wilson (1714–1786), flew a train of six kites, all of them equipped with a thermometer, up to 600 m height; thanks to this experiment, performed in Scotland, Wilson determined the change in the atmospheric temperature in relation to the height above ground. In 1752, Benjamin Franklin (1706–1790) launched, during a thunderstorm, a kite fitted with a metal rod and with a metal key tied at the end of the silk thread that held the kite (Fig. 4.26); in this way, he proved the presence of electricity in the air,31 determined the relationship between the lightning and the generated energy, and laid the grounds of modern theories about thunderstorms (Sects. 6.3 and 10.2). He did not realise, however, how lucky he had been: the silk thread holding the kite remained dry; the following year, a Russian professor died struck by a lightning while repeating Franklin’s experiment with a wet silk thread [17, 74]. In 1822, Reverend George Fisher (1794–1873) and Sir William Edward Parry (1790–1855), during their arctic voyages, used kites equipped with thermometers [75]. In 1825, James Espy (Sect. 4.1) discovered the researches performed by Wilson and carried out new kite launches to substantiate his meteorological theories; in 1835, he joined the Franklin Kite Club: it mustered up a group of scholars who performed atmospheric measurements by means

31 The Dutch physicist Pieter van Musschenbroek (1692–1761) invented the electric capacitor around 1745 at the Leyden University. It was known as a “Leyden jar” and consisted of a glass container with its interior and exterior coated with two sheets of tinfoil. In 1746, using a Leyden jar, Franklin built the first electric machine. Continuing this research, in 1750 he wrote to Peter Collinson (1694–1768), a member of the Royal Society of London, proposing him to place a pointed metal rod at the top of a tall tower, to capture the electricity of clouds and to prove that lightning is electrical discharge. This letter was published by the Royal Society in 1751 (Experiments and observations on electricity). In the same year, this idea was put in practice by the French physicist Thomas Francois D’Alibard (1703–1799), who hoisted an iron rod approximately 12 m long on the roof of a building. The experiment was successful and was reported to the Académie Royale des Sciences of Paris. In the meantime, Franklin carried out his experiment with the kite (1752), proving that atmospheric electricity is of the same nature of the electrostatic charges previously obtained. He formulated a theory according to which electricity is a fluid that is present in the matter. He also proposed the idea, now known as the charge conservation law, that an electrical charge was never destroyed or created, but rather transferred from a material to another. Franklin also installed the first lightning rod in Philadelphia and published its description in the Poor Richard’s Almanack of 1753 (Sect. 4.1). Some sources judge Franklin’s discoveries comparable with Newton’s ones [17].

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Fig. 4.26 Benjamin Franklin, kite experiment [17]

of kites. In 1847, the Kew British observatory flew kites to measure the changes in temperature and wind direction in relationship to height [76]. The study of upper air received great impulse from hot air balloons [3, 77, 78]. Their conception dated back to the second century BC, when the Chinese made miniature balloons by filling eggshells with hot air [79]. A book of that time, The ten thousand infallible arts of the prince of Huai-Nan, describes this pastime: “eggs can be made to fly in the air by the aid of burning tinder”. A remark added to the text explains “to take an egg, remove the contents from the shell and then ignite a little mugwort tinder inside the hole so as to cause a strong air current. The egg will of itself rise in the air and fly away”. In the thirteenth century, Roger Bacon (1214–1292), taking inspiration from Archimedes, convinced himself that air could support bodies exactly like water does; he proposed to fill a thin metal globe with two substances, “ethereal air” and “liquid fire”, of which he did not give any detail besides their names. In 1670, the Jesuit Francesco Lana Terzi (1631–1687) published Prodromo, ovvero saggio di alcune inventioni nuove premesso all’arte maestra. Here, he described a flying ship supported by four copper spheres inside which vacuum was made [77, 80]: the ship would ascend when ballast was removed and would descend when air was introduced through valves. He did not manage to build his invention for lack of funding; had he built it, the spheres would have been crushed by atmospheric pressure (Sect. 3.2).

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Father Bartolomeu Lourenco de Gusmao (1685–1724), Brazilian Jesuit and Mathematician known as the “Voador”, invented the “Passarola”, a tiny balloon filled with hot air “to go by air as we go by land or by sea, but much faster” [81]. He reportedly carried out his first experiment in a boulevard of the royal palace of Lisbon on 8 August 1709, in the presence of the Portuguese King and Queen. In spite of this and other attempts,32 the first lighter-than-air flying device is attributed to two brothers, Joseph-Michel (1740–1810) and Jacques-Etienne (1745–1799) Montgolfier, the owners of a paper mill near Lyon. In 1782, attracted by the smoke rising during a fire, they first made bags, then containers and balloons, made of paper and silk and provided with a hole on their bottom; when filled with heated air, the famous “Montgolfier gas” (as a matter of fact, it was air, the density of which decreased when it was subjected to high temperatures), they rose in the air. On 4 June 1783, before a large crowd, the Montgolfier brothers flew a balloon with 10 m diameter. On 19 September 1783, the same was flown near Versailles—in the presence of King Louis XVI (1754–1793) and of the members of the Académie Royale des Sciences—carrying aboard a sheep, a goose, a cock and a barometer; it landed smoothly after a journey 3 km long. The first human flight took place on 21 November 1783 at Annonay, near Paris, before 400,000 people; a balloon made of paper produced by the Montgolfier brothers, filled with air heated by means of a brazier fitted on a circular platform, took off carrying aboard Jean Francois Pilatre de Rozier (1754–1785) and Francois d’Arlandes (1742–1809). It was called “Montgolfier balloon” to honour its inventors. In the same year, the French physicist and chemist Jacques-Alexandre-César Charles (1746–1823) built “Globe”, a rubberised silk balloon that was subsequently called “Charlière”; it was filled with hydrogen instead of hot air and was fitted with a gas control valve to stop its ascent at the desired height. On 1 December 1783, Charles and Nicolas Robert (1758–1820) lifted off from the gardens of Les Tuileries in Paris, bringing a thermometer and a barometer with them; they completed a 43 km journey in two hours. After touching land, Robert left the balloon; Charles lifted off again and ascended at over 1000 m above the ground, where he measured a temperature equal to −5 °C, a 13 °C drop from the temperature at ground level. Thanks to these experiences, in 1787 Charles formulated the homonymous law; its original enunciation maintained that, in any transformation at constant pressure, for every temperature increase equal to 1 °C, the volume of the gas increases by a fraction equal to 1/273th of the volume it would occupy at 0 °C. In its modern meaning, it states that, in the transformations at constant pressure, the volume of a gas is proportional to its absolute temperature. We also owe Charles the law stating 32 Henry Cavendish (1731–1810) noted that the specific weight of hydrogen, called “flammable air”, was lower than that of the air; he did not associate his discovery with the perspectives of balloon flight. Such perspective was understood by Joseph Black (1728–1799), professor of chemistry at the Glasgow University, who saw the possibility of lifting light containers filled with hydrogen. Neither him nor Tiberio Cavallo (1749–1809) managed to acquire such containers [80]. The same can be said of Jacques Galien, author of L’art de naviguer dans les airs (1755, 1775), who proposed to build a globe, larger than Avignon and as high as a mountain, made of “good cloth waxed on both faces, full of air lighter than usual”.

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that, in the transformations at constant volume, gas pressure is proportional to the temperature. 1785 was a dramatic year in the history of aerostatic balloons. Two Frenchmen, Pilatre de Rozier (the first man to fly in a balloon) and Jean-Pierre Blanchard (1753–1804), organised, each one of them on his own, the first attempt to cross the English Channel. Blanchard beat Rozier, and on 7 January 1785 he made the historical crossing with John Jeffries (1744–1819), an American scholar who paid a large sum to carry out barometric, thermometric and hygrometric measurements; the results, reported to the Royal Society, proved that the mean temperature decrease gradient was approximately 5 °C/km.33 Rozier, flustered by the success of its rival, anticipated the time of his flight that he performed, with Pierre Angel de Romain, on 15 June 1785. They used two balloons, filled with hydrogen and hot air, failing to realise the danger of bringing them into contact. The balloon lifted off from Boulogne but, when it reached 100 m height, burst and fell to the ground, causing the death of both passengers; the disaster caused sensation, highlighting the risk of these epic attempts. Actually, this did not stop the enthusiasm for balloon flights: they proliferated in every part of Europe and USA. The knowledge about gases drew huge advantages from these undertakings, and it was not by accident that it was associated with the pioneers of balloon flight. In 1802, Louis-Joseph Gay-Lussac (1778–1850) generalised the two laws of Charles on constant pressure and volume transformations and linked them with the Boyle— Mariotte’s law (Sect. 3.2) about constant temperature transformations, laying the foundations of the perfect gas law. Two years later, Gay-Lussac and Jean-Baptiste Biot (1774–1862) made the first balloon ascents for purely scientific purposes; on 27 August 1804, they rose up to 4000-m height (Fig. 4.27a); on September 16, GayLussac, alone, ascended up to 7000 m. During these ascents, they performed pioneering observations about the properties of the atmosphere. They collected air samples that, when analysed in laboratory, did not show significant changes with height in their composition. They discovered, conversely, that the presence of water vapour decreased as height increased. They confirmed that temperature also decreased as height increased. In 1808, encouraged by his results, Gay-Lussac enunciated the homonymous law about gaseous volumes or combinations; it establishes that when two gases combine there is a rational ratio between their overall volume and the volume of the compound that has formed (as long as the compound is also gaseous). It was the prelude to the perfect gas law, enunciated in 1811 by the Italian natural philosopher and chemist Amedeo Avogadro (1776–1856); it translates in the relationship: pV = n RT

33 Actually,

(4.9)

in the troposphere, up to nearly 11 km height, there is an almost constant negative temperature gradient equal to 6.5 °C for every km of height.

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Fig. 4.27 a Gay-Lussac and Biot at 4000 m height; b Zenith balloon

where n = NV/A is the number of moles of the gas, N the number of the molecules per unit volume V, A = 6.0221353 × 1023 the Avogadro number, and R = 8.314 JK−1 the gas universal constant. In 1852, the superintendent of the Kew Observatory, John Welsh (1824–1859) made a balloon flight departing from Vauxhall Gardens [75]. He realised that previous temperature measurements were affected by errors due to solar radiation and eliminated this issue by introducing thermometers inside metal tubes equipped with internal forced air circulation. Thanks to this expedient, he made measures through which he first demonstrated the existence of atmospheric belts, located between 4- and 7-km height, where the temperature decrease stops. Similar studies were developed between 1862 and 1866 by two Englishmen, the balloonist Henry Coxwell (1819–1900) and the astronomer James Glaisher (1809–1903), who repeatedly ascended up to 11-km height to measure the pressure, the humidity and the acoustic and electromagnetic properties of the upper air. Glaisher, a founding member of the Meteorological Society (1850) and of the Royal Aeronautical Society (1866), reported the results of his experiences in various treatises; the most renowned Travels in the air was published in 1867. New tragedies afflicted increasingly daring and risky undertakings. In 1875, the Zenith balloon (Fig. 4.27b), with Théodor Sivel (1834–1875), Gaston Tissandier (1843–1899) and Joseph Crocé-Spinelli (1845–1875) aboard, reached the 8600m height with terrible consequences: anoxia took the lives of Sivel and CrocéSpinelli. In 1897, August Andrée (1854–1897), Nils Strindberg (1872–1897) and

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Knut Fraenkel (1860–1897) carried out the first exploration of the North Pole with a balloon; their remains were to be found in 1955. The development of aerostatic balloons and of the lighter-than-air flight did not reduce the interest towards the machines, idealised by Leonardo da Vinci’s ornithopter (Sect. 2.10), that could allow humankind flying like birds [77, 80]. The period between the seventeenth and the nineteenth centuries, on the contrary, was full of devices driven by human muscle power. In 1628, Paolo Guidotti from Perugia lost his life during a flight attempt. In 1630, Hezarfen Ahmet Celebi (1609–1640), a mythical Turkish aviator, performed a gliding flight with rudimentary wings; he jumped from the Galata Tower of Istanbul and reached the opposite shore of the Bosphorus, covering 6 km in 5 min; the information was reported by Evliya Celebi (1611–1682) in 1635 (Voyages of Evliya Celebi) and by John Wilkins (1614–1672) in 1638 (The Discovery of a World in the Moone). In 1648, Tito Livio Burattini (1617–1681) tested a flying machine with many wings in Warsaw with little success. In 1680, the Italian mathematician Giovanni Alfonso Borrelli (1608–1679) published De motu animalium, in which he demonstrated that human muscles were not sufficient to fly like birds. In 1742, the Marquis of Bacqueville (Jean-François Boyvin de Bonnetot, 1688–1786) broke his legs flying over Paris with a kind of glider. In the early nineteenth century, Louis Navier (1785–1836) showed that man had, proportionally, a muscular power equal to 1/92nd of that of birds. In a context of attempts taking inspiration from empiricism, the prominent scientific figure of Sir George Cayley (1773–1857) stands out: he was an Englishman considered by many the true father of aviation and of heavier-than-air flight [73, 78]. He first affirmed the necessity of overcoming the concept of flight lift obtained by flapping wings and perceived that this aim could be achieved moving an inclined surface, on condition that enough mechanical power to compensate the resistance of air was available. In 1799, Cayley engraved on a silver disc the image of an airplane equipped with a fixed wing providing lift, two vertical tails to provide a stabilising effect and two blades to propel it (Fig. 4.28). On the other face of the coin, he drew a diagram in which he decomposed the resultant force on the wing into two components, a drag and a lift one, in contrast to the square sine law (Sect. 4.2). In 1804, Cayley, driven by the desire to corroborate his intuitions through experience, started a series of tests with a whirling arm (Sect. 4.2) during which he carried out accurate measurements of plates with a small pitch in relation to the flow direction, obtaining results close to the correct ones [54]. He first measured the drag and the lift of a wing model, writing in his diary (Aeronautical and miscellaneous notebook, 1799–1826): “It was found by experiment that the shape of the hinder part of the spiddle is of as much importance as that of the front in diminishing resistance. (…) I fear, however, that the whole of this subject is of so dark a nature as to be more usefully investigated by experiment than by reasoning (…) and in absence of any conclusive evidence from either, the only way that presents itself is to copy nature; accordingly I shall instance the spiddles of the trout and woodcock”. He then measured the perimeter of various cross-sections of trout and obtained a highly efficient wing profile (Fig. 4.29) [53]. These ideas went unnoticed; the extraordinary worth of Cayley was only to be understood from 1940, almost a century past his death.

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Fig. 4.28 Cayley’s coin [54]

Fig. 4.29 Cross-section of a trout [53]: a Cayley’s drawing; b comparison (circles) with a low resistance wing profile (N.A.C.A. 63A016)

Cayley was also the inventor and builder of machines anticipating aeronautical discoveries. Perceiving that the use of balloons was limited by the impossibility to control their heading, in 1804 he designed a balloon equipped with an engine connected to a propeller, which favoured its forward movement in the desired direction; he then anticipated the origin and development of dirigibles, which would come into being in the second half of the nineteenth century. In 1809, he discussed the premises for controlling airplane flight, recommending the use of internal combustion engines to propel them [82]. He also designed many gliders (Fig. 4.30a), which represented the evolution of the old kites (Sect. 2.6). Cayley’s studies and projects were illustrated in a series of works, On aerial navigation [82], published between 1809 and 1810; they are considered a cornerstone of aerodynamics and aviation. In 1843, Cayley designed the “convertiplane” (Fig. 4.30b), a kind of helicopter equipped with four sets of rotating blades to provide lift and with two propellers for

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Fig. 4.30 a Cayley’s glider [83]; b Cayley’s convertiplane [84]

horizontal movement. In 1852, he published Governable parachute [83], where he proposed to launch his aircraft from balloons or dirigibles. In 1853, he built “New Flyer”, or sailplane, which carried out the first flight with a man aboard in Yorkshire [73, 84]. Following Cayley’s steps, in 1842 William Samuel Henson (1812–1888) designed and patented “Aerial Steam Carriage”, the first airplane (with a huge 46 m wingspan) pushed by propellers driven by a steam engine (rated at 30 HP). In 1848, his associate, John Stringfellow (1799–1883), modified Henson’s project and built a model launched by an elastic cable: the machine did not manage to fly, but had enough lift to glide for approximately 40 m. In 1871, Alphonse Penaud (1850–1880) modified some of Cayley’s drawings to build the model of an airplane that, launched by hand, made a 40-m flight over the Tuileries Gardens in Paris; lift was achieved by a propeller driven by elastic bands first twisted and then released; according to some sources, it was the first aircraft fitted with a horizontal surface near its tail to guarantee stability [53]. Another French, Victor Tatin (1843–1913), tested an airplane model propelled by a compressed air engine. In 1877, the Italian Enrico Forlanini (1848–1930) successfully tested the model of a helicopter lifted by two propellers driven by a steam engine. These were premonitory signs of the advances of aeronautics that would take place in the early twentieth century (Sect. 7.4); they will have huge impact on many sectors of wind science and engineering.

4.6 The Diffusion of Windmills

229

Fig. 4.31 Cornelisz’s windmill [85]

4.6 The Diffusion of Windmills From the late sixteenth century, windmills became an essential element of the life and society, first in Europe and then in America [85]. In 1582, the first mill appeared in the Netherlands: it was used to squeeze olives. In 1586, the first paper mill was built to meet the huge request following the invention of the printing press. In 1589, Cornelis Dircksz Muys built the first mill conceived to drain marshes; it was fitted with a tilted shaft linked to an Archimedean screw. Around 1590, Stevin (1548–1620) patented a mill for experimental purposes; his works, published over 300 years later, reported the first links between the wind pressure on sails and the amount of water drained from marshes [86]. In 1592, Cornelis Cornelisz (1562–1638) built the first sawmill patented in 1593 (Fig. 4.31). The turning point in the use of the Dutch windmills took place between 1608 and 1612 when Beemster Polder, an area 3 m below the sea level, was drained by means of 26 mills, with an overall power rating equal to less than 50 HP. Afterwards, Jan Adriaanszoon Leeghwater (1575–1650), a hydraulic engineer, drained Schermer Polder in four years; he used 14 windmills into a basin from which water was transferred through 36 additional mills, into a loop-shaped canal that flowed into the North Sea [87]; during the operation, Leeghwater measured the work of the mills in relation to the amount of water pumped from marsh lakes. From that time up to the mid-nineteenth century, the Dutchmen used windmills to reclaim their land below the sea level (“God created the world, but Dutchmen created the Netherlands”). The image of the Netherlands became then indissolubly linked to that of its mills. Englishmen also used windmills to drain marshes [74]. The first windmills fulfilling this function appeared in 1588 in Lincolnshire. The local inhabitants, mostly hunters and fishermen, opposed this intervention by destroying the mills. For similar reasons, in the early seventeenth century, woodcutters and carpenters destroyed the

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first sawmill built in Deptford, near London. These were the first signs of a social diatribe destined to erupt in many European countries; it saw, standing on opposite fronts, the builders, the entrepreneurs and the millers on one side and, on the other side, those who considered the windmills as a factor conflicting with the performance of their work. With this dispute on the background, windmills became political, artistic and literary subjects. Miguel de Cervantes Saavedra (1547–1616) used them in Don Quixote (1605–1615) to dissert of the dilemma if machines were mere instruments in the hands of man or possessed an existence of their own. According to the Mancha knight, the windmills in the “ancient and famous Montel country” were enemies to challenge to duel; Sancho Panza, his prosaic squire, considered them simple tools. The main novelty of this period was the growing interest of science and technology towards windmills [86, 88]; it led to the first drawings showing constructive details. The first printed picture of a windmill appeared in Theatrum Instrumentorum by Jacques Besson (1540–1573), published in 1578. It consisted of a horizontal rotor with four arched sails, placed under a dome-shaped cover; it was used to pump water from underground. The most famous drawings were published by Agostino Ramelli (approximately 1531–1600) in Paris (Le diverse et artificiose machine, 1588); they showed a post-mill (Fig. 4.32a) and a tower mill (Fig. 4.32b) used to grind wheat (Sect. 2.7). In the second half of the seventeenth century, there was a growing interest towards the use of windmills to extract seepage water from mines, a heartfelt issue at that time

Fig. 4.32 Drawings by Ramelli [86]: a post-mill; b tower mill

4.6 The Diffusion of Windmills

231

Fig. 4.33 a Bevel gear designed by Leibniz for a windmill [88]; b windmill, Encyclopédie [68]

[88]. In 1679, following the suggestion of the court adviser and of the Clausthal mines, the Duke Johann Frederick proposed Gottfried Wilhelm von Leibniz (1646–1716) to design a wind machine to lift water out of shafts. Leibniz declared he was ready to build a prototype at his own cost and to follow its experimental operation for a year. The machine was built in 1681, but it did not work as intended. It performed properly when the wind intensity was average; if wind was feeble, it ceased to work; every time, wind was strong a sail, or the mechanism rod or some other part of the cage gear wheel broke down. Leibniz did not feel discouraged and designed a new machine fitted with a bevel gear for variable speed transformation (Fig. 4.33a). He described it in Wasserhebung mittels der kraft des windes, an essay published some years later: “The wind machines to extract the water in mines from deep shafts have these issues: with a strong wind the bars turn too fast and something easily breaks down, and in case of feeble wind their strength is insufficient; since only long bars are used, with the rod applied once closer to and once farther from the centre or from oscillating drum, so that the run is once decreased and once increased, the piston in the pump cylinders moves too slowly and water is again lost. To avoid this trouble, I invented this system that, in my opinion, is the most perfect proposal ever done” [88]. The first diagrams for the construction of windmills appeared in the second edition of a book by Mathurin Jousse (1575–1645), L’art de charpenterie (1702). Later on, Bernard Forest de Belidor (1693–1761) wrote La science des ingénieurs (1729) and Architecture hydraulique (1737–1753), in which he collected a huge amount

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of information about engineering knowledge in his age. In the second treatise, he replaced the classical rectangular shape of mill sails with a vaguely streamlined cross-sectional shape. The Encyclopédie (1751–1772) by Diderot and D’Alembert provided a picture of the technology and use of mills in the eighteenth century. The chapter on agriculture included tables, taking inspiration from the work of Jousse and from books published in Amsterdam (Pieter Linpergh, Architectura mechanica of moole-boek, 1727; Leendert van Natrus, Jacob Polly and Cornelis van Vuuren, Groot volkomen moolenboek, 1734, 1736; Johannis van Zyl, Theatrum machinarum universale of groot algemeen moolen-boek, 1761), which described the work of mills and provided a guide for building them; unlike Jousse, who relied on verbal descriptions, the Encyclopédie reported drawings, often complete with dimensions, of the constructive details (Fig. 4.33b). It can then be inferred that the typical Dutch windmill of the eighteenth century, with sails nearly 30 m long and with its horizontal shaft 15 m above the ground, had a power rating nearly equal to 10 CV; it was a remarkably perfected machine, but retained a wooden structure that dissipated most power in its transmission gear; it was also subjected to frequent failures, and so it was unsuitable for continuous operation. The chapter about architecture and construction showed the use of windmills to cut stones into slabs, to pulverise clay, to crush concrete and mastic. Treatise on mills and millwork (1861), a book written by William Fairbairn (1789–1874) in 1861, provided a picture of the proficiency of the millwrights in the eighteenth century: “The millwright of former days was to a great extent the sole representative of mechanical art, and was looked upon as the authority in all the applications of wind and water under whatever conditions they were to be used, as a motive power for the purposes of manufacture. He was the engineer of the district in which he lived, a kind of jack-of-all-trades, who could with equal facility work at the lathe, the anvil, or the carpenter’s bench. In country districts, far removed from towns, he had to exercise all these professions, and he thus gained the character of an ingenious, roving, rollicking blade, able to turn his hand to anything, and, like other wandering tribes in days of old, went about the country from mill to mill, with the old song of ‘kettles to mend’ reapplied to the more important fractures of machinery. Thus the millwright of the last century was an itinerant engineer and mechanic of high reputation. He could handle the axe, the hammer, and the plane with equal skill and precision; be could turn, bore, or forge with the ease and despatch of one brought up to these trade, and he could set out and cut in the furrows of a millstone with an accuracy equal or superior to that of the miller himself. (…) Generally, he was a fair arithmetician, knew something of geometry, levelling, and mensuration, and in some cases possessed a very competent knowledge of practical mathematics. He could calculate the velocities, strength, and power of machines: could draw in plan and section, and could construct buildings conduits, or watercourses, in all the forms and under all the conditions required in his professional practice; he could build bridges, cut canals, and perform a variety of work now done by civil engineers. Such was the character and condition of the men who designed and carried out most of the mechanical work of this country, up to the middle and end of the last century. Living

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233

Fig. 4.34 Post-mill [89] (a) and tower mill [86] (b) equipped with a fantail

in a more primitive state of society than ourselves, there probably never existed a more useful and independent class of men than the country millwrights. The whole mechanical knowledge of the country was centred amongst them” [88]. Thanks to these books, it is possible to reconstruct the evolution of the windmill construction techniques, starting from a picture of the early post-mills and tower mills up to the innovations that gained ground from the mid-eighteenth century [86]. In 1745, the Englishman Edmund Lee patented “fantail”, a kind of circular fan fitted on the mill rear and consisting of small directional vanes [74, 89]. In the case of post-mills (Fig. 4.34a), it was connected with a track, laid on the ground, which turned around the building. In the case of tower mills (Fig. 4.34b), the track was laid around the roof. This device automatically oriented the sails in the wind direction, and the miller could stay inside the mill when the wind changed its direction, avoiding the need to manually rotate the sails. In 1758, Euler published Recherches plus exactes sur l’effet des moulins a vent, where he studied the efficiency of mills in relation to the length and pitch of their sails. He noted that the knowledge about the resistance of bodies (Sect. 4.2) was too limited to accurately determine the aerodynamic wind actions on the sails [52]. In 1759, Smeaton published the results of his famous tests with a whirling arm (Sect. 4.2), which had been performed to evaluate the most efficient shape for mill sails [56]. Up to that time, sails were made using flat and slanted wooden frames, cov-

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ered with cloth; Smeaton proved that the higher power and efficiency were obtained by rotating the sails along their axis of nearly 20° (like the propellers of modern airplanes) [74]. This result had clear and immediate effects on the evolution of sails taking place in the second half of the eighteenth century [68]. In 1772, the Scottish Andrew Meikle (1719–1811) removed the cloth covering from mill sails, putting an end to the manual work of bending the sails in relation to the wind speed. He replaced the cloth with thin wooden sheets, similar to those of sun-blinds, adjusted through springs controlled by the miller from inside the mill [74, 90]. They adjusted sail opening in relationship to the wind speed to control the revolution speed of the sails. In 1789, Stephen Hooper from Margate, Kent, invented and patented the “rollerreefing sail”. Instead of the shutters of spring sails, he used small “roller blinds”. Thanks to them, it was possible to simultaneously close and open the sails without interrupting the operation of the mill. Between 1776 and 1806, Hooper obtained four patents for as many windmills. The most known had hexagonal plan and a vertical shaft. The vertical sails were fitted on a rotor, and their pitch was fixed. Outside the rotor, there were shutters hinged on the outer side; they could be adjusted to direct the wind on the sails or closed to stop the rotor. The available drawings (Fig. 4.35a) do not explain how the issue of screening the downwind sails from the wake generated by the upwind ones had been solved [85]. The English William Cubitt (1785–1861) applied the systems by Meikle and Hooper, obtaining the “patent sail”. It used weights and counterweights outside the mill, which automatically controlled the opening of the sails [77, 82]. It was patented in 1807 and adopted in England but not in the Netherlands. In 1860, Catchpole, a millwright from Sandbury, Suffolk, invented “air brake”, a pair of shutters parallel to the sail axis, arranged along its edge (Fig. 4.35b). Their closure increased the surface of the sail; their opening drained the wind flow. In that same period, the first annular sail, with a 15-m diameter and equipped with patent sail shutters, appeared near Haverhill, Suffolk (Fig. 4.35c); four similar mills were built in East Anglia between 1860 and 1861 [89]. They were the precursors of the wind pumps that were to invade America towards the end of the nineteenth century (Sect. 8.1). The appearance and diffusion of windmills in America are a debated issue. It is said that, in his third voyage to West Indies, Christopher Columbus (1451–1506) brought along a millwright; the American crops, however, were different from the European ones, and the mills were adapted to grind sugar cane [90]. The presence of mills on the American continent is certain from the mid-seventeenth century [74, 90], when the first Dutch settlements were established (Sect. 4.4). As early as 1660, New Amsterdam was characterised by a long strip of windmills from Battery up to Park Row. Against this background, Brooklyn, the Hudson River valley and other areas near New York filled out with mills assigned to the most varying functions (Fig. 4.36a). The East River boatmen used them as meteorological and signalling devices: they refused ferrying passengers when the mill sails were struck; this indicated the arrival of a storm. In a short time, the mills became so important that, in 1784, the official

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235

Fig. 4.35 a Hooper’s vertical axis windmill [85]; b mill sail equipped with air brake [86]; c tower mill with annular blades [86]

Fig. 4.36 a Windmill along the Hudson River [74]; b seal of the city of New York (1784)

seal of the city of New York (Fig. 4.36b) displayed four mill sails and two flour barrels. Many sources maintained the mills were the precursors of the American skyscrapers. With the arrival of European settlers, especially from the eighteenth century onwards, windmills spread throughout North America. The French built them in

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Canada, the English along the shores of their colonies. The Atlantic coast was quickly filled with a belt of mills easily visible to those who arrived from the sea.

4.7 The Structures of the Industrial Revolution Robert Hooke published the first study about the internal structure of iron and steel in Micrographia (1665) [91]. The first experiments about the production of iron in a blast furnace using mineral coal were carried out in 1709 by Abraham Darby I (1678–1717) in England near Coalbrookdale, in a rented old furnace. In 1747, the first printed report about the new technique to produce iron using coke appeared. In 1755, John Smeaton used the new material to manufacture cast iron tools. In 1767, Abraham Darby III (1750–1791) cast the first rails. From that time on, the use of iron spread throughout Europe, being mostly used to build bridges, building pillars and frames, covers and towers [92]. The first iron bridge was built by Abraham Darby III and John Wilkinson (1728–1808) between 1775 and 1779 on the Severn River; it is known as the Coalbrookdale Bridge (Fig. 4.37a), from the name of the Darby’s foundry location. It consisted of a semicircular arch 30 m long and 14 m high. It introduced the innovation of prefabrication and on-site connection, transposing the tradition of wooden arches to cast iron. The second iron bridge, Sunderland Bridge (Fig. 4.37b), began with an idea by Thomas Paine (1737–1809), American writer and politician of English origin, submitted to Benjamin Franklin in 1788; the latter understood that America was not ready to realise a project like that and suggested him to travel to England. Here, some say that Rowland Burdon (1756–1838) appropriated of Paine’s drawings and built, between 1793 and 1798, an impressive bridge with a lowered arch covering a 72-m span. Conditions were not met, conversely, to build the Condon Bridge on the Thames in London, a cast iron bridge with a 183-m span, designed by Thomas Telford (1757–1834) in 1801 adopting Paine’s system. The use of cast iron became common, however, for bridges supported by cables; after a fleeting appearance in

Fig. 4.37 a Coalbrookdale Bridge on the Severn River; b Sunderland Bridge [92]

4.7 The Structures of the Industrial Revolution

237

Fig. 4.38 a London library; b Bibliotéque Nationale in Paris [92]

America towards the end of the eighteenth century, they were built in England from the start of the nineteenth century and, later on, in various parts of Europe (Sect. 4.8). The use of cast iron columns revolutionised buildings, allowing an exceptional use of internal spaces as well as innovative aesthetical solutions. They were first used in 1794 in the London Library (Fig. 4.38a). John Nash (1752–1835) used cast iron columns in the royal palace of Brighton, built between 1818 and 1821. Afterwards, they gained ground, especially thanks to Henri Labrouste (1801–1875), who from 1843 to 1850 built the Bibliothèque Sainte-Geneviève in Paris, the first public building into which cast iron and steel were used from the foundations to the roof. Labrouste repeated this experience with the Bibliotèque Nationale in Paris (1858–1868) (Fig. 4.38b), in which he achieved the peak of the combination between cast iron in the core of the building and brickwork along its perimeter. The use of cast iron columns represented the first step towards a more extensive use of iron in building members. The first multi-storey building where iron played a dominant role was the Philip and Lee cotton spinning mill, built in 1801 at Salford, near Manchester, by Matthew Boulton (1728–1809) and James Watt (1736–1819). The building layout was a 42 by 13 m rectangle, and it was seven storeys high, an exceptional height in that age. It retained the perimeter brickworks with load-bearing functions but made use, for the first time, of an internal metal frame. To achieve this, cast iron columns were paired with the first I-beams. The floors rested on brick vaults levelled by means of concrete mix. The accuracy of the drawings and details reflected the experience of machine designers. The principles by Boulton and Watt achieved full development in the English refinery designed by William Fairbairn (1789–1874) in 1845. The eight-storey building retained the pattern consisting of the perimeter load-bearing brickwork with an internal metal frame in cast iron and malleable iron. The floors, instead of brick vaults, used iron arches covered by concrete mix up to the floor level. The passage to a structural concept in which the weight of the building was integrally borne by a metal skeleton took place between 1871 and 1872, when Jules Saulnier (1817–1881) built the Menier Chocolate Factory (Fig. 4.39a) at Noisiel sur Marne, near Paris. The structure rested on four piers in the bed of the Marne, which

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Fig. 4.39 a Menier chocolate factory; b loft storey of a spinning mill [92]

is the source of the motive power driving the machinery. Four hollow square metal beams with a continuous pattern (the two ends were cantilevered) rested on piers; the facade frames were reinforced by metal braces that were typical, until then, of wooden works only. Roofing represented the most common use of iron in the first half of the nineteenth century. The first metal roof, built in 1786 by Victor Louis (1731–1800) for the Théatre Francais in Paris, highlighted important intuitions of a static nature, in particular the ties countering thrusts and the slanted rafters that helped the arch to absorb the concentrated forces transmitted by the stays to which the ceiling was hung. The use of iron for roofing works in England gained ground for industrial buildings, in particular for spinning mills (Fig. 4.39b). The change from the traditional wooden roof trusses to the new metal ones brought into existence lighter and less bulky roofing, which allowed housing the mechanical spinners in the loft storey. Continental Europe was instead attracted by using iron in the roofing of theatres, warehouses and markets, which until then was made of wood. The first application dates back to 1811: the wooden dome of the Corn Exchange in Paris, burned in 1802, was replaced by an iron and copper structure. This was the first time an architect, François-Joseph Belanger (1744–1818), and an engineer, François Brunet, co-operated fulfilling different functions. Afterwards, the matching of iron and glass started gaining ground. The first examples were the Galerie d’Orleans in the Palais Royal in Paris (1829–1831), by Pierre François Léonard Fontaine (1762–1853), and the Botanical Garden Greenhouse (1833), again in Paris, by Charles Rouhault de Fleury (1801–1875). Other examples were the Madeleine Market in Paris (1824) and the Hungerford Fish Market in London (1835), which included the first roofing elements in bending regime and even as cantilever. The competition for the construction of the Grandes Halles in Paris (1853) is also worth mentioning: the victory of the design by Victor Baltard (1805–1874) deprived two exceptional works, the ones designed by Hector Horeau (1801–1872) and Eugene Flachat (1802–1872), of the possibility of being built. Later, Alexander Gustav Eiffel (1832–1923) and the architect Louis Auguste Boileau (1812–1896)

4.7 The Structures of the Industrial Revolution

239

Fig. 4.40 a Crystal palace, London; b Palais de l’Industrie, Paris, 1855 [92]

built the Magasin au Bon Marché in Paris (1876); the roofing was characterised by a skilful alternation of glass skylights and iron walkways suspended from the ceilings. In Europe, the consecration of iron took place in the second half of the nineteenth century for two chief reasons. The first depended on the evolution of the quality of material and production equipment: on the one hand, machines for the production of rolled steel and reinforcement bars made their appearance; on the other hand, especially thanks to the development of the Bessemer process to purify cast iron, it was possible to obtain high-quality steels. The second reason was associated with the outbreak of the international exhibitions and the requirement to cover large areas in a quick and reversible way: iron appeared to be custom-made for such use, and the history of the exhibitions became entwined with the history of iron, engineering and architecture. The first International Exhibition was held in London in 1851, inside the Crystal Palace (Fig. 4.40a). The builder, Joseph Paxton (1801–1865), drafted a modular design calibrated on the size of the largest glass pane available at that time (1.2 m); he carried out the construction by means of a system of small prefabricated units: the wooden curved frames housing the glass, the iron truss beams on which panes rested and the cast iron pillars supporting the beams. The connections between the metal parts were secured by means of bolts. The building was completed in six months. This was the prelude to the exceptional development of metal construction, marked by the four subsequent international exhibitions, which were held in Paris in 1855, in 1867, in 1878 and in 1889. The centre of attraction of the 1855 Paris Universal Exhibition was the Palais de l’Industrie (Fig. 4.40b), a rectangular building with a high central nave with a 48-m span, flanked by a double order of arcades. Iron truss beams, in part forged by hand, were used here for the first time. The huge glass panes provided a nearly blinding effect. The free space was not broken by connecting ties. The building, however, did not convey the feeling of lightness typical of metal buildings by that time. The 1867 Paris Exhibition was held inside arcades that, as a whole, formed a building with a polycentric plan. The roofing was accomplished through Polonceau roof trusses or latticeworks, with the exception of the main gallery, known as the

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Fig. 4.41 a Main entrance, Paris, 1878; b Galerie des Machines, Paris, 1889 [92]

Galerie des Machines. Its skeleton consisted of pillars, supporting iron lattice tied arches (with a 35 m span). The chief builder, Jean Baptiste Krantz (1817–1899), availed himself of the collaboration of an outstanding young assistant: Gustav Eiffel; many maintain that some magnificent works of this exhibition already bore his unmistakable mark. The 1878 Paris Exhibition was not very spectacular but with great technical meaning. The main entrance gave an emphatic and debatable image (Fig. 4.41a). But a glass wall stood out on its sides: it was, once again, a design of the young Eiffel destined to become a benchmark model for architecture. Behind the main entrance, there were parallel arcades flanked by the Galerie des Machines, designed by the engineer De Diou. He studied the stresses in the materials, arriving at the most suitable shape, a compound beam capable of withstanding stresses without tie rods. The 1889 Paris Exhibition marked the apex and the end of the Parisian exhibitions. The arcades and the roofing of the three previous ones reached their peak in the Galerie des Machine (Fig. 4.41b), designed by the engineer Paul Cottacin (1865–1928) and by the architect Charles Luois Ferdinand Dutert (1845–1906). It was 115 m wide and 420 m long, and its cubic volume was unprecedented. The glass windows and the lightness of the metal structure gave an elusive feeling of the border between the internal and the external spaces. So, it looked like a trick of fate that, after almost 100 years from iron appearance, after that metal construction especially ventured along the horizontal plane taking on the issues of bridges and roofing, while the Palais des Machines achieved the maximum plan development, just in Paris, within the same exhibition, beside this palace, there was, unprecedented, the most dazzling and overwhelming example of a vertical structure: the Eiffel Tower (Fig. 4.42a). It conquered the record of the highest structure in the world, bringing it to the height of 301.75 m. It was a dramatic event: from 2520 BC, when the Pharaohs built the Great Pyramid (146 m) (Sects. 2.8 and 2.9), to 1884, when the stone stele of the George Washington Monument (169 m)

4.7 The Structures of the Industrial Revolution

241

Fig. 4.42 a Tour Eiffel, Paris, 1889; b Fhakya-Khan’s prediction

was completed, mankind improved by 23 m, with a growth gradient equal to 1 m every 191 years. With his iron tower, Eiffel made a 133 m upward jump. Gustave Eiffel studied at the Burgundy, at the Ecole Polytechnique and at the Ecole Centrale. After having contributed to many works for the first Parisian exhibitions, his activity as an engineer gained ground all over the world. He built harbours in Chile, churches in Peru and in the Philippines, locks for Russia and for the Panama Canal. He designed the metal frame for the Statue of Liberty, which in 1885 was the highest structure in America (93.47 m). He built bridges in Egypt, Italy, Russia, Hungary, Greece, Vietnam, Cambodia, Southern America, Portugal, Spain and France, becoming the master of high elegantly manufactured metal towers and suspended arches, most of them of the two hinge types. The most famous of these were the bridges on the Douro in Portugal (1876–1877) and the Garabit Viaduct on the Thuyer River (Sect. 4.9); here, Eiffel used graphic, analytical and experimental methods to optimise the shape of parabolic arches and to solve apparently unresolvable erection issues. On 1 May 1886, when the contest of ideas for the 1889 Exhibition was announced, it invited the competitors “to study the possibility of erecting a tower with square cross-section, 125 m sides at its base and 300 m high on the Champ de Mars”; the deadline was set for the 18 of that same month. In the 17 days allowed to participants to conceive the tower, 107 projects were submitted. Eiffel won the competition despite the reserves formulated by the judging committee about fires and elevators. The convention was signed on 8 January 1887. The excavations started at the same

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time. In February, the last attempt to stop the works took place: “We, the writers, painters, sculptors and architects, come, in the name of the French decency and of this threat to the French history, to express our deepest indignation as regards to the erection of this unnecessary and horrible Eiffel Tower in the core of our capital city”. It was also defined as a “laughable mercantile conception of a machine manufacturer”, “laughable tower looming over the city as the black chimney of a factory”, “repulsive column of screwed sheet plate”. Even so, the foundation was completed in 4 months. The erection of the metal parts lasted 22 months, requiring the work of 50 engineers who prepared 1700 executive drawings, for an overall total of 18,038 elements. The individual pieces were lifted by means of cranes located on the ground; after the completion of the first platform on 10 April 1888, the cranes were disassembled and then reassembled on the platform. The tower was completed on 31 March 1889, one month before the opening of the Exhibition. The chorus of protest, in the meantime, turned into exaltation; Le Figaro celebrated the event writing: “Glory to (…) industrialist who erected this stairway to heaven”. On the other hand, there was no shortage of fears towards an unprecedented work: Fhakya-Khan, a famous Indian fakir, predicted the collapse of the tower during a wind storm (Fig. 4.42b). Eiffel had the merit of remaining insensitive to these opposed feelings and to understand that the tower represented an exceptional occasion to perform new scientific experiences (Sects. 6.1, 6.5 and 7.1). Unlike Europe, America mainly developed the use of iron and steel for the construction of multi-storey buildings that, a bit at a time, became skyscrapers. James Bogardus (1800–1874) started this process in 1848 in Manhattan, erecting a fivestorey building, the first of its kind, in which the load-bearing function of the still self-bearing perimeter walls was transferred to iron pillars supporting the floors. Afterwards, Bogardus built buildings and warehouses, including the Harper & Brothers publishing company (1854), where the dominant aspect was represented by the matching of glass and iron on the facade. His two most famous works, conversely, were never built: a Surreal Factory (1856) (Fig. 4.43a), an everlasting manifesto of the use of steel, and a huge metal structure conceived for the first New York World’s Fair (1853). The works of Bogardus had a formidable impact on the city of New York and on America as a whole. People first thought that his buildings would have collapsed under their own weight or burned, and would have been struck by lightning or smashed down by winds; then, they acquired trust in them. The builders, conversely, immediately understood the enormous advantages in terms of construction speed and work economy; they remained uncertain on the construction of higher buildings because of the difficulty of moving among storeys using the stairs. This limit disappeared in 1853, when Elisha Graves Otis (1811–1861) built the first elevator equipped with a safety system. In a short time, it became part of the American civil building construction, opening the way for the development of the skyscrapers of the late nineteenth and early twentieth centuries (Sect. 9.2). The Eiffel Tower itself owed most of its success to the invention of the elevator. A new generation of structures had come into being: thanks to iron, they were lighter, more flexible and less dampened of the previous ones; as a consequence, they

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Fig. 4.43 a Surreal Factory, Bogardus’ projects [92]; b Eddystone Lighthouse, England

were more exposed to wind actions. Some, especially cable-supported (Sect. 4.8), girder and truss (Sect. 4.9) bridges, immediately showed this trend. Others, including roofing, skyscrapers and the new structures of the technological age (chimneys, antennas, towers, tanks, etc.), were to show a conflictual relationship with the wind since the beginning of the twentieth century (Sect. 9.2). Despite the exceptional spread of iron, it is not possible to ignore that in the same period, though more discreetly and less conspicuously, concrete, a material of which the ancient Romans were masters, made its comeback (Sect. 2.9). In 1774, John Smeaton achieved a triumph with the reconstruction of the Eddystone Lighthouse in England (Fig. 4.43b), in which he bound masonry using a mix of quicklime, clay, sand and pressed iron slag: hydraulic lime. Probably, this was the first time it was used since the time of the Romans. Smeaton came to this result through experiments started in 1750 and described in A narrative of the building and a description of the construction of the Eddystone Lighthouse with stone (1793). This construction, quite sensational for its innovative contents, promoted new experiments and achievements [92, 93]. In 1796, James Parker produced the first quick-setting concrete. In 1800, Lesage made a high-strength hydraulic material. In 1818, Louis-Joseph Vicat (1786–1861) obtained the formula of the artificial composition of hydraulic lime. In 1824, Joseph Aspdin (1788–1855) produced the Portland cement. In 1829, Fox developed a system to build floors that used concrete as filling material between iron beams; it was patented in 1844, and the next year it was used in the William Fairbarn’s multi-storey refinery. The reinforced concrete appeared in 1849, when Joseph Monier (1823–1906), a gardener at the Orangerie in Versailles, made some flower containers by dipping an iron grid in the concrete. He continued developing this idea until 1877, when he patented it; the subsequent year, he attributed to iron reinforcements the role of tension-resistant elements in beams. In

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those same years, Thaddeus Hyatt (1816–1901), an American lawyer who had moved to England, published Account of some experiments with Portland cement concrete combined with iron as a building material (1877), a paper through which he spread the knowledge of reinforced concrete. It became commonly used from 1890, when it was employed by Ernest Leslie Ransome (1844–1917) in USA and by Francois Hennebique (1842–1921) in France.

4.8 Cable-Supported Bridges in the Nineteenth Century The construction of cable-supported bridges dates back to ancient times (Sect. 2.9). The scientific interest for this structural typology originated in Europe in the early seventeenth century. Between 1614 and 1615, Isaac Beeckman (1588–1637) studied a suspension bridge in which the weightless cable was subjected to distributed vertical loads; he arrived to the correct conclusion that the cable deformed itself according to a parabola [94]. Faustus Verantius (1551–1617) is the author of Machinae novae, a work published in Florence in 1615 and in Venice in 1617, where he described ingenious inventions, including three innovative suspension bridge typologies (Fig. 4.44): “pons unius funis”, “pons canabeus” and “pons ferreus” [95]. In a fragment of the Discorsi (1638), Galilei expressed his opinion that the catenary, that is the position assumed by a heavy cable fastened at its ends, was a parabola. Christian Huygens (1629–1695) approached this same issue in 1646, demonstrating that the cable of a suspension bridge was parabolic; the same cannot be said of the catenary. In 1673, the French Jesuit Ignace Gastoni Pardies (1636–1673) published La statique ou les forces mouvantes, in which he demonstrated that the catenary cannot be parabolic. The discussion flared up between 1690 and 1691, when a memorable issue of Acta Eruditorum collected three different solutions by Gottfried Wilhelm von Leibniz (1646–1716), Jakob Bernoulli (1654–1705) and Christiaan Huygens. According to Clifford Truesdell (1919–2000), “for 1690, the three solutions, in order of delivery, show the mathematics of the future, of the present and of the past”. Between 1697 and 1698, Jakob Bernoulli clarified this issue, formulating the general equations of the catenary and of the flexible cable subjected to any distribution of tangent and normal forces [94]. The first European bridge supported by iron chains dates back to 1734 and was built by the Saxon army at Glorywitz, on the Oder River [91]. The first European metal bridge supported by cables appeared in 1741 in England, on the Tees River near Winch; it consisted of a footbridge with its deck laid on forged iron chains (Fig. 4.45a); it collapsed in 1802 because of the corrosion of the iron, causing the death of one or two individuals [91]. The first suspension bridge with a stiffened deck appeared between 1796 and 1801 in the USA thanks to James Finley (1762–1818), a judge, politician and engineer [91, 95] who built Jacob’s Creek Bridge (Fig. 4.45b). It consisted of a thin deck L = 21 m long and B = 3 m wide; it made use of a pair of strong side parapets, consisting

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Fig. 4.44 Faustus Verantius [95]: a Pons unius funis; b Pons canabeus; c Pons ferreus

of truss beams linked with the deck. The bridge, patented in 1808, had an appreciable overall stiffness and the capacity of spreading vertical loads [96]. Finley repeated himself by building two similar bridges at Brownsville in Pennsylvania, one at Cumberland in Maryland and one on the Potomac near Washington. All of them were less than 50 m long, and their characteristics were similar to the Jacob’s Creek Bridge. Encouraged by these successes, Finley attempted a more daring solution in Massachusetts, where he built the Essex-Merrimac Bridge, a bridge with four spans, each one of them 75 m long, which showed excessive deformations; he intervened by creating an intermediate support in the centre of each span, but the operation failed and the bridge were demolished. Finley tried again the multiple span suspension bridge solution in 1809 near Schuylkill Falls, but it collapsed in 1811 during the passage of a herd; it rebuilt it, but the bridge collapsed again in 1816, this time for the excessive loads of snow and ice. It was a bad start that slowed, presumably without justification, the laying of American suspension bridges. They were successful, conversely, in England [91, 95, 97, 98], especially thanks to Samuel Brown (1776–1852), an engineer and captain of the Royal Navy. He provided an essential contribution to the divulgation of the iron chains, transferring their use from the marine environment to the cables of suspension bridges. In 1813, Brown designed and built the first European bridge with a stiffened deck on the Tweed River in Scotland; the main span (L = 91 m) was supported by 12

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Fig. 4.45 a Footbridge on the Tees River [92]; b Jacob’s Creek Bridge [95]

chains of links 5 cm in diameter. In 1817, John Redpath and Brown built King’s Meadows Bridge on the Tweed River (Fig. 4.46), a cable-stayed footbridge with a single span (L = 33.6 m and B = 1.2 m). In the August of the same year, John e William Smith completed the construction of the Dryburgh Abbey Bridge on the Tweed River (Fig. 4.47), a chain-stayed bridge (L = 79.3 m and B = 1.2 m) with a coexisting partial suspension system. The Union Bridge on the Tweed River near Norham Ford (Fig. 4.48a), designed by Brown and opened on 26 July 1820, was the first bridge intended for the passage of heavy carriages; the main span (L = 137 m and B = 9 m) was supported by 12 chains, 6 on each side, arranged in pairs on 3 levels. Brighton Chain Pier, in Scotland, was a bridge designed by Brown and opened in 1823; it consisted of four spans, each of them L = 65.7 m long, suspended by chains. On 30 January 1826, after 7 years of works, Menai Strait Bridge, in Wales, designed by Thomas Telford (1757–1834), was opened; with a central span L = 177 m long and two 79-m-long side spans, and B = 8.5 m wide, it was the new

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Fig. 4.46 King’s Meadows Bridge [95]

Fig. 4.47 First Dryburgh Abbey Bridge [95]

bridge with the longest span in the world. Montrose Bridge on the Esk River in Scotland, a suspension bridge designed by Brown and supported by two chains on each side (L = 126 m and B = 7.9 m), was opened in December 1829 [99]. In the same year, the competition for the construction of Avon Bridge, at Clifton near Bristol was announced; the examination of the submitted projects provides an overview of the knowledge of that period; the victory went to the project of Isambard Kingdom Brunel34 (1806–1859); the construction, started in 1831 and often interrupted for economic and administrative reasons, was finished in 1864 (Fig. 4.48b) [100]. The common elements shared by all these bridges were the magnificence and heaviness of their masonry towers and the thin decks, practically devoid of longitudinal stiffening girders. Most of them did not even have the strength and stiffness reserve Finley placed in the parapets. They were, especially in the suspension version, sufficiently rigid as regards side actions, but too deformable against vertical and torsional motions [97]. The French government, struck by this evolution, sent Louis Navier (1785–1836) to England to examine the new constructive reality, in 1821 and in 1823. When he returned from his second journey, Navier wrote Rapport et mémoire sur les ponts suspendus [101], divided into three parts. 34 Brunel

submitted four projects to the judging committee, chaired by Thomas Telford; Telford rejected them all, proposing a project of his own. Following the protests of the public opinion, the committee was forced to repeat the competition, naming one of Brunel’s projects as the winner. The bridge, which is still in use, is 215 m long and 9.5 m wide. Its deck is 75 m above the river.

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Fig. 4.48 a Union Bridge [91]; b Avon Bridge

In the first part, Navier illustrated the evolution of the various types of cablesupported bridges, classifying them as cable-stayed, suspension and mixed (cablestayed/suspension). The beginning of the second part expressed a critical judgement about cablestayed bridges35 [102], which contributed to stop their evolution for many years. Navier then developed a new theory for the design of suspension bridges, nowadays called “Navier’s” or “unstiffened bridge” theory [103]. Returning to the catenary equation obtained by Jakob Bernoulli at the end of the seventeenth century, and developing a demonstration carried out by Nicholas Fuss (1755–1826) in 1794 to show that a cable subjected to a distributed load assumed a parabolic shape, Navier formulated a method to evaluate the effects of a load concentrated on the centreline like, by way of example, a road or railway load. Considering the deck as devoid of stiffness and the hangers as non-extensible, the deformation of the deck was equal to that of the cable. Assuming, moreover, that the distributed load was much greater than the concentrated one, Navier proved that the deck deformation was proportional to

35 Navier’s judgement on cable-stayed bridges was negative for three reasons: scientifically, because

of the disasters occurred in England, socially, because it did not bring any economic advances, and symbolically, because it was conceived by an architect, Bernard Poyet (1742–1824), not by an engineer.

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the concentrated load and to the initial sag f of the cable,36 and inversely proportional to the distributed load and to the span length L. He then suggested to limit the vertical motion using reduced f/L ratios. This caused an increase of the tension in the cable, which was rectified by increasing its cross-section [102, 104]. Navier also dwelt on the wind perpendicular to the bridge axis, considering only its horizontal actions; however, he did not take it into account in his theory, confining himself to alert his readers about the dangerousness of its effects [103]. In the third part, Navier applied his principles to design Pont des Invalides, a suspension bridge with a single span L = 150 m long, built in 1823 on the Seine in Paris. He realised a f/L = 1/17 ratio, much smaller than the typical values of the English bridges of that age (f/L = 1/7–1/12). Because of a pier failure [52], the bridge collapsed after three years (1826); there was no time, then, to evaluate the consequences of his design choices as regards the cables and the deck. From England, suspension bridges, in part thanks to Navier’s works, gained ground in many European countries. This diffusion was accompanied by important technical innovations [91, 95, 97]. In 1825, the five Seguin brothers—Marc (1786–1875), Camille (1793–1852), Jules (1796–1868), Paul (1797–1875) and Charles (1798–1856)—built the TainTournon railway bridge on the Rhone River near Lyon, using, for the first time, cables assembled by means of iron wires instead of chains. In 1830, Louis-Joseph Vicat (1786–1861), a French engineer educated at the École Polytechnique and at the École des Ponts et Chaussées, published a report in the Annales des Ponts et Chaussées in which he presented “air spinning”, a revolutionary technique to assemble on site the wires making up the cable; it allowed reducing the work for the realisation of a cable by 18%, manufacturing a few large cables as a replacement for many smaller ones and using easily available equipment. Vicat also developed fundamental studies on the connection of cables to anchor blocks and on the corrosion at the contact between cables and concrete. He never had the satisfaction of applying his discovery in a project of his own; he however opened a new era in the construction of suspension bridges. Joseph Chaley (1795–1861) came to know Vicat’s studies during the construction of the Grand Pont Suspendu on the Sarine at Freiburg in Switzerland (Fig. 4.49) and changed the execution of the cables and their anchorages accordingly. The project envisaged 4 cables, each one consisting of 1056 wires 3 mm in diameter: the cables were instead prefabricated with strands, each one of them consisting of 20 wires; they were subsequently hoisted and connected to the structure. Grand Pont Suspendu, completed in 1834 with a central span L = 273 m long, was the new longest bridge in the world [95]. Between 1836 and 1839, applying similar principles to another bridge, less innovative (L = 102 m and B = 7.2 m), but exceptionally important from an historical perspective, Joseph Chaley and Théodore Julien Bordillon built the Pont de la Basse-Chaine on the Maine River in Angers. In 1840, moreover, the Pont de la 36 The sag f of the cable is the difference in height between its highest point (the saddle at the tower top) and its lower point (the centreline of the span).

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Fig. 4.49 Grand Pont Suspendu [95]

Roche-Bernard on the Vilaine River in Brittany (L = 195 m) was opened; it was designed by Leblanc, the chief engineer of the Ponts et Chaussées. A new generation of bridges of rare beauty and eternal appeal was born: it entrusted its image to decks so thin they appeared intangible. Since it exhalted, more than any other constructive typology, wind action, it provided the first, often dramatic, messages about the dangers to which flexible, slender and light structures are exposed. The engineers of this period were not ready to understand such teachings [91, 96]. Dryburgh Abbey Bridge, opened in August 1817, showed, since the first days, oscillations of the deck and accelerations of the chains at the passage of pedestrians. On 15 January 1818, it collapsed because of wind actions. Navier [101] described the event observing that “vibrations became so strong that the longer inclined chains were broken, the deck was swept away and the structure was completely destroyed. Many eyewitnesses of the event agreed on reporting that the vertical movement of the bridge deck was almost equal to its horizontal movement and that it appeared to be so fierce that if an individual had been on the bridge he would have been hurled in the river”. He attributed the collapse “to the lack of stability of the inclined chains”, confirming his attention, like that of most engineers of that age, was fully dedicated to cables, with no consideration for the deck. The reconstruction of the bridge, assigned to Samuel Brown, was carried out in three months, increasing the width of the deck and adding, in the style of Finley, stiffening parapets. Some sources stated that Union Bridge collapsed in early 1821 during a storm, six months after it had been opened; according to other bibliographic sources, conversely, it was one of the few bridges to survive. The cable-stayed bridge on the Saale River near Nienburg in Germany (L = 78 m), built in 1824, collapsed under the weight of

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Fig. 4.50 Brighton Chain Pier collapse, 1836

crowd in 1825. The third span of the Brighton Chain Pier collapsed because of the wind on 15 October 1833; it was rebuilt in early 1836, but on November 30 of the same year it collapsed again because of wind actions (Fig. 4.50). The Nassau Bridge in Germany (L = 75 m), designed by Lossen and Wolf, collapsed in 1834. On 19 March 1830, three months after its inauguration, 700 people crowded Montrose Bridge to watch a regatta; as they moved from a side to the other to follow the passage of boats, a chain broke and the bridge fell down causing the death of many people. It was rebuilt, but it collapsed again on 11 October 1838 during a storm; the chronicles reported that “an undulating motion was observed during the storm” and “this motion was greatest at about midway between the towers and the centre of the roadway” [96]. Menai Strait Bridge showed unique conditions [105]. Its chains vibrated asynchronously before the inauguration, on 30 January 1826. They were connected to dissipate energy, but they vibrated again seven days after the opening, causing damage to the deck, which was strengthened. In 1833, the bridge was subjected to bending and twisting vibrations requiring new strengthening. It started vibrating again in January 1836: some suspension cables broke, the bridge lost most of its torsional stiffness, and peak-to-peak displacements of 5.3 m occurred; the rotation of the deck reached 30°; thankfully, the wind died down and the bridge survived. It was repaired, but the same phenomenon repeated itself in the night between 6 and 7 January 1839; this time, the wind continued and the deck was destroyed. The repeating crises of Menai Strait Bridge had the positive effect of highlighting some little considered aspects. A wind perpendicular to its axis produced vertical “undulations” and torsional rotations, with no appreciable along wind motions. The engineers involved in the 1836 reconstruction seconded the necessity of increasing

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the stiffness of the deck to protect it from the “vertical wind pressures”. The new crisis of the bridge, in 1839, originated a debate from which it emerged that the wind caused small periodic forces that resonated with the bridge and caused great oscillations. James Meadows Rendel (1799–1856) proposed to mitigate them strengthening the deck by rigid truss beams. He applied this concept to the reconstruction of Montrose Bridge in 1838, installing a wooden truss beam 3 m high [103]. The most tragic event regarded the Pont de la Basse-Chaine. In 1850, on a day of strong wind, it showed strong oscillations; a platoon of 478 soldiers arrived and decided to cross it despite the almost prohibitive weather; a cable anchorage failed, and the bridge fell down causing the death of 226 soldiers. Probably, this was the greatest disaster in the history of bridges. A committee appointed to study the event, highlighting the corrosion of anchorages, suggested inspecting works built with the same technique, that is, in practice, all. The anchorage of the Grand Pont Suspendu, built by Chayley, the designer of the Pont de la Basse-Chaine, caused great alarm: it showed such advanced corrosion to bring the bridge close to collapsing; it was then reinforced by means of new paired cables [106]. The crises concerning European cable-supported bridges were not finished. Pont de la Roche-Bernard in France was partially destroyed in 1852, during a storm. In 1872, during another storm, the Constantine suspension bridge on the Seine collapsed. Avon Bridge still stands, as a monument to Brunel’s genius. While an alarmed Europe witnessed this terrible series of collapses and set about a long pause for reflection, cable-supported bridges received great impulse in America by Roebling and Ellet, two engineers with different mindsets [91, 96, 107]. John Augustus Roebling (1806–1869), a German, studied engineering at the Royal Polytechnic Institute in Berlin, where he investigated suspension bridges with Johann Friedrich Wilhelm Dietlein (1782–1837); at the same time, he studied philosophy with Georg Wilhelm Friedrich Hegel (1770–1831), who considered him his best student. Roebling graduated in 1826, and in 1831 he moved to Philadelphia, where, from 1837, he worked at the Pennsylvania Canal Company; it manufactured cableways which at that time were subjected to many collapses due to cable breakdowns. Roebling had the idea of replacing traditional cables by strands of helical wire; he obtained a patent (Methods of manufacture of wire rope, 1842) and started manufacturing them. Charles Ellet Jr. (1811–1862), an American officer, travelled to Paris from 1830 to 1831 to study engineering at the École Polytechnique, directed by Navier, and specialised in suspension bridges. He visited the construction sites where some great works, especially Grand Pont Suspendu, were being built. After his return to USA in 1840, he signed an agreement to build a suspension bridge in Fairmount to replace the Colossus of Lewis Wernwag (1769–1843), a famous wooden bridge burnt in 1838 [108]. Roebling, having heard of this project, remembered his German studies on suspension bridges and offered Ellet his collaboration. Ellet avoided being helped by Roebling, and between 1841 and 1842 built the first American bridge supported by cables made of metal wires. Like all the French bridges of this period, the deck (L =

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109 m) lacked any longitudinal stiffening and the bridge showed ample vibrations. It remained in service until 1874, when it was replaced by a double-deck bridge. In the meantime, in 1841 Roebling published construction principles and criteria aimed at opposing wind effects on suspension bridges. His works pointed out the opinion that to successfully build bridges, like any other engineering works, it was necessary to perceive crisis modes and to avoid their occurrence [109]. Roebling was fascinated by Brunel’s bridges and by the technique proposed by John Scott Russell (1808–1882) in 1839, and used by Brunel himself, to adopt reversed chains linking the bottom edge of the deck to the base of the towers [109]. In 1844, Roebling signed an agreement to build an aqueduct on Allegheny River in Pittsburgh. This was his first opportunity to build a suspension structure and to put his ideas into practice. He seized it by building, in 1845, an aqueduct with seven spans, each one of them 49.4 m long, supported by cables produced by himself. From this moment, Roebling’s activities became frantic. From 1845 to 1850, he built four new aqueducts (including a famous one on the Delaware River near Lackawaxen in 1848) as well as his first suspension bridge, Monongahela Bridge in Pittsburgh, where he installed, besides his cables and the reversed chains, a longitudinal stiffening girder and his famous intuition, stays radiating from the top of the piers towards the deck, as an addition to the suspension cables and hangers [107]. The bridge, begun in 1845 and completed in 1846, consisted of eight spans; each one of them was 57.3 m long. The towers were made of cast iron. The cables, like those of Roebling aqueducts, were assembled using the air spinning technique. The turning point in the careers of Roebling and Ellet and in the history of bridges occurred in 1847. The competitions for the projects of the Wheeling Bridge on the Ohio River and of the Niagara Bridge were announced. Ellet won both of them; absurdly, this meant success for Roebling [90, 109]. Roebling proposed to build the Wheeling Bridge by three spans, 90, 180 and 90 m long. Ellet won the competition with the project of a bridge consisting of a single 1010-ft-long span (L = 308 m and B = 6 m) supported by 12 cables. The Wheeling Bridge, completed in 1849 (Fig. 4.51a), was an amazing, incredibly light bridge. It offered an image of rare slenderness and boldness. Not only it was the longest bridge in the world, but it also was the first with a span exceeding the 1000 ft limit.

Fig. 4.51 a Ellet’s Wheeling Bridge, 1849 [107]; b Roebling’s Niagara Bridge, 1855 [104]

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Ellet applied Navier’s theory, building taut cables with f/L = 1/14. He not only rejected the idea of the rigid truss deck, but in 1851 wrote a report in which he defined this technique “a charlatan proposal”. In that same report and in other subsequent works, he proved he knew the issue of the vertical oscillations caused by the wind, but he judged them as not dangerous [103]. Wheeling Bridge showed undulatory motions even under the action of breezes. On 17 May 1854, the wind was strong and the bridge behaved “like a ship in a storm. At one time it rises to nearly the height of the towers, (…) twists along the entire span”, then it collapsed [96] causing sensation. Roebling was first contacted to supply the cables; then, he was entrusted with the reconstruction of the bridge, which he completed in 1867, installing inclined stiffening stays. The history of the Niagara Bridge is a classic of structural and wind engineering [91]. The list of the competition envisaged four winners: Ellet, Serrell, Roebling and Keefer, in sequence. It was established that each of them would build his project at different locations and in subsequent years. In November 1847, Ellet was entrusted with the construction of a road and railway bridge, to be completed within 1 May 1849. Despite the little available time, he devoted more time to promoting its image than to the structural design. He organised a kite competition among the local kids, offering a prize to the first to reach the opposite bank. Starting from the string of the winner, he then made an increasingly larger cable; when it reached the desired size, Ellet crossed the river in a basket hanging from the cable by means of a pulley. Finally, he built a bridge very similar to the Wheeling Bridge. It did not fall, but it was subjected to frequent damage caused by wind and soon it had to be demolished. The second bridge on the Niagara, the Lewiston-Queenstone Bridge, built by Edward Wellman Serrell (1826–1906), consisted of a single span (L = 318 m and B = 6 m). When it was finished in 1851, he took the record for the longest bridge in the world away from the still standing Wheeling Bridge. Roebling swamped Serrell with letters through which he indicated the dangerousness of the structure and proposed to stiffen it with inclined cables. Serrell accepted Roebling’s suggestion after the bridge had repeatedly vibrated. In January 1864, the inclined cables were disconnected for maintenance. Once the operation was ended, they remained disconnected because of an oversight. The bridge collapsed on 1 February 1864. The third bridge over the Niagara, the one built by Roebling in 1855, was a masterpiece. It consisted of a single span (L = 280 m) with two decks on different levels: the upper one (B = 7.3 m) used by the railway and the lower one (B = 4.6 m) by the road traffic especially by horse carriages. The side links between the two deck levels originated a strong truss caisson D = 5 m high (Fig. 4.51b). Roebling also increased the stiffness of the bridge by means of cable stays radiating from the top of the towers towards the deck and of cable stays starting from the lower edge of the caisson and anchored to the ground. In this way, he realised its more known principle of opposing wind actions using several measures together: “Professional and public opinion having been adverse to Suspended Railway Bridges”, Roebling wrote, “the question now turns up, what means have been used in the Niagara Bridge, to make it answer for Railway traffic? The means employed are Weight, Girders, Trusses, and

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Stays. With these any level of stiffness can be insured, to resist either the action of trains, or the violence of storms, or even hurricanes; and in any locality, no matter whether there is a chance of applying stays from below or not. And I will here observe, that no Suspension Bridge is safe without some of these appliances. The catalogue of disastrous failures is now large enough to warn against light fabrics, suspended to be blown down, as it were, in defiance of the elements. A number of such fairy creations are still hovering about the country, only waiting for a rough blow to be demolished” [103]. In 1950, Steinman (Sect. 9.1) defined this excerpt “a classic in engineering literature”. Roebling’s design philosophy rejected the principle of weighing down the bridge as an end in itself. On the contrary, Roebling remarked that a pure increase in weight not matched by an increase in stiffness might become the instrument of destruction. In this way, he implicitly stated the importance of dynamics as regards wind actions. On the other hand, being unable to translate these concepts in mathematical form, he protected himself building bridges so rigid to guarantee behaviours compliant with the engineer’s experience, hence of the static type [103]. Once the works were completed, Roebling was so proud of the bridge to say that “no vibrations whatever” and to inform his family that “no one is afraid to cross”. Mark Twain (1835–1910), instead, wrote that “you drive over to suspension bridge and divide your misery between the chances of smashing down two hundred feet into the river below, and the chances of having a railway-train overhead smash down onto you” [107]. The fourth bridge over the Niagara, assigned to the Canadian engineer Samuel Keefer (1811–1890), was built before the Falls. It was named Clifton Bridge and was opened in January 1869 after two years of work; thanks to its span L = 386 m long (B = 3 m), it became the new longest bridge in the world. He started vibrating just after the inauguration, and in 1872, the original wooden deck was replaced by a stiffened metal plate. After a while, again because of wind actions the wooden towers also vibrated; they were rebuilt in steel in 1884. All these interventions were not sufficient, and the bridge was completely rebuilt in 1888. It collapsed because of wind actions between 2 and 3 a.m. on the morning of 10 January 1889. J. M. Hodge, the Niagara Falls physician who was the last to cross it around midnight, reported that “the bridge rocked like a boat in a heavy sea and at times it seemed to tip up almost on its very edge” [96]. Taking inspiration by Roebling’s railway bridge over the Niagara (1855), in 1857 Peter Barlow (1776–1882) carried out experiences on suspension bridge models, through which he demonstrated the feasibility and inexpensiveness of this solution. In 1858, William John Macquorn Rankine (1820–1872) published Applied mechanics, which represented the Bible of bridges for over half a century. Using Barlow’s experiences, Rankine developed the first theory for the calculation of suspension bridges that took into account the interaction between the cable and the deck [110]. He noted the former belief that a suspension bridge with a truss deck would require a beam so rigid to make the suspension with cables unnecessary; Barlow’s experiments proved that a light truss girder was sufficient to provide a suitable stiffness [103].

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Fig. 4.52 Cincinnati-Covington Bridge [104]

Rankine’s theory retained Navier’s hypothesis according to which the permanent distributed load was integrally absorbed by the cable; the stiffened deck transformed the accidental concentrated load into an uniform load, thanks to which the cable retains its parabolic shape; dealing with hangers as inextensible, the cable and the deck share the same deformation. Rankine was aware of approximations, but he justified them by virtue of simple results. It is also important to notice that Rankine’s theory allowed considering the stiffening due to the truss deck but excluded the possibility of representing Roebling’s cable stays [103]. On the other hand, the engineers of this period, starting with Charles Balthasar Bender [111], gave no credit to these cable stays, attributing Roebling’s success solely to the stiffness of his decks. Thus, they did not feel the necessity of adopting a model that also took into account the cable stays. In the meantime, Roebling, at the height of success, in 1856 designed the Cincinnati-Covington Bridge (Fig. 4.52) over the Ohio River, leaving the executive responsibility to his son Washington Augustus Roebling (1837–1926) in 1865. The bridge, opened on 1 January 1867, consisted of a central span L = 322 m long and of two side spans, each of them 86 m long. It held the record for the longest bridge in the world until the construction of the Clifton Bridge (1869). It was the prelude to Roebling’s masterpiece, the Brooklyn Bridge on the East River in New York (Fig. 4.53a), which many consider as the greatest achievement of the nineteenth century engineering [107]. The bridge consisted of two levels, the upper one for road use and the lower one for the railway, connected by vertical and diagonal elements making up a rigid and strong truss caisson. Being unable to use stays below the deck, Roebling gave an essential role to the cable stays running from the top of the towers to the bridge floor (Fig. 4.53b). They stabilised the cables and the hangers but above all, using Roebling’s own words, they ensured the stiffness of the deck: “But my system of

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Fig. 4.53 Brooklyn Bridge: a New York, 1883 [104]; b cable stays

construction differs radically from that formerly predicted, and I have planned the East River Bridge with a special view to fully meet the destructive forces of a severe gale. It is the same reason that, in my calculation of the requisite supporting strength, so large a proportion has been assigned to the stays in place of cables”. These stays were called “storm-cables” by Roebling. The design of the Brooklyn Bridge was approved on 21 June 1869. Roebling died on July 22 of the same year, and the responsibility for works passed to his son, by then a known and respected engineer. Without disrupting his father’s design, Washington Augustus Roebling carried out some changes conceived in view of the future development of the road and railway traffic. When the works were completed in 1883, the Brooklyn Bridge, thanks to its L = 486-m-long span, beat any previous record. It remains impressed in the heart and in the eyes of the engineer as the utmost example of culture and skill. It directs the America of the twentieth century towards a generation of bridges safe with regard to vibrations but, often, too heavy. Absurdly, a new series of collapses was about to occur; they were caused by the enemy that is the wind twin: equilibrium instability [91, 112] (Sect. 4.9).

4.9 The Girder and Truss Bridges of the Nineteenth Century While Europe and America lived through different epics of the history of suspension bridges (Sect. 4.8), the diffusion of railways and the evolution of materials encouraged the development of new theories and analysis procedures that originated two new construction typologies: metal girder and truss bridges.

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Fig. 4.54 a Conway River Bridge; b Britannia Bridge on the Menai Strait [91]

George Stephenson (1781–1848) (Sect. 3.9) was the first to understand that the use of the railway could not disregard bridges. He then devoted himself, with his son Robert, to design railway bridges. Robert Stephenson (1803–1859), reaping the inheritance of his father and being involved in the construction of the London–Chester–Holyhead railway, undertook the construction of three railway bridges. The first one, over the Dee River near Chester, consisted of three cast iron truss spans, each one 30 m long. It collapsed on 24 May 1847, six months after the opening, while a train was passing on it and caused the death of five people [113, 114]. The other two bridges, over the Conway River and over the Menai Strait, introduced the use of tubular girders with the railway travelling inside them. The Conway River Bridge (Fig. 4.54a), built between 1845 and 1849, consisted of a single span. The Britannia Bridge on the Menai Strait (Fig. 4.54b), made of wrought iron between 1846 and 1850, represented Stephenson masterpiece, as well as a reference point for structural engineering; the bridge consisted of four continuous spans: two end spans 70 m long and two central spans 140 m long. Initially, Stephenson studied a suspension bridge, taking inspiration from Telford’s works; the design of the deck was unsuitable for the passage of trains, and then Stephenson opted for tubular spans supported by suspension cables. Subsequent analyses and experiments carried out during construction proved that the tubular cross-section was so strong to make the aid of cables unnecessary [97]. The two large holes visible at the top of each tower (Fig. 4.54b), intended for the passage of cables, give witness to this bizarre design path. The analyses and the experimental tests performed during the construction availed themselves of two outstanding consultants. Benoit Paul Emile Clapeyron (1799–1864) for the first time applied to a large structure his three moments equations, later published on the Comptes Rendus of 1857 [115]. Sir William Fairbairn (1789–1874), designer of metal ships and buildings (Sect. 4.7), in 1846 carried out breaking tests on models of tubular girders; Fairbairn, observing that collapses occurred because of the local instability of compression plates, proposed the use of

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Fig. 4.55 Palladio’s statically determined truss beams [94]

Fig. 4.56 Squire Whipple’s redundant truss beams [91]

stiffeners to prevent buckling. The latter became a distinctive element of the Britannia Bridge and, from then on, of all large area metal plates. In the meantime, especially thanks to Swiss emigrants, American bridge builders acquired growing interest and proficiency in the use of truss beams. Starting from the patterns introduced by Andrea Palladio (1508–1580) in I quattro libri dell’architettura (1571) (Fig. 4.55), Theodore Burr (1771–1822) (1815), Ithiel Town (1784–1844) (1835), Stephen Long (1784–1864) (1840), William Howe (1803–1852) (1841, 1842), Thomas Willis Pratt (1812–1875) with his father Caleb (1844), James Warren (1846, 1848) and Squire Whipple (1804–1888) (1847, 1848) [91, 94, 116] brought forth a literature that highlighted a fundamental dualism. Palladio’s statically determined truss beams favoured the use of simple design calculations. The addition of stiffening elements taking inspiration from experience (Fig. 4.56) made the structure redundant and potentially safer. It also determined, on the other hand, more complex design conditions under which it was unclear how to distinguish the tension parts from the compression ones without appropriate calculation procedures. Squire Whipple, the most prominent designer and scholar of this period, stood out because of the publication of A work on bridge building [117], in which he emphasised the importance of evaluating the effects of mobile loads and their most unfavourable position; he suggested analytical and graphical methods to determine the internal forces and the stresses in statically determined structures, distinguishing the elements subjected to tension from those subjected to compression; he recommended to use cast iron for compression elements and the cheaper wrought iron for the tension ones; he also quoted the exceptional properties of steel, but he considered it too expensive for engineering applications. Whipple’s book was the prelude to various treatises about truss beams. Herman Haupt (1817–1905) published a book about the construction of bridges (General the-

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ory of bridge construction, 1851) that, like Whipple’s, will be very popular among engineers. George Finden Warr published Dynamics, construction of machinery, equilibrium of structures and the strength of materials (1851), in which he illustrated the evolution of truss bridges and their calculation procedures. Johann Wilhelm Schwedler (1823–1892) (Theorie der Brückenbalkensysteme, 1851), Karl Culmann (1821–1881) (Die Graphische Statik, 1866) and August Ritter (Elementare Theorie und Berechnung eisernen Dach und Brücken Construktionen, 1870) formulated the first calculation methods for statically determined truss structures, as regards beams with canonical cross-sections. Starting from the pioneering studies of August Ferdinand Mobius (1790–1868) (Lehrbuch der Statik, 1837), William Rankine (1820–1872) (Applied mechanics, 1858), James Clerk Maxwell (1831–1879) (On reciprocal figures and diagrams of forces, 1864) and Luigi Cremona (1830–1903) (Le figure reciproche della statica grafica, 1872) dealt with latticeworks of hinged rods loaded with forces applied in the nodes. The analysis of the statically determined or indeterminate beams, developed by Luigi Federico Menabrea (1809–1896) (Nouveau principe sur la distribution des tensions dans les systèmes élastiques, 1858), Alfred Clebsch (1849–1925) (Theorie der Elasticitat fester Korper, 1862) and James Clerk Maxwell (1864), achieved formal perfection with Carlo Alberto Castigliano (1837–1884) (Intorno ai sistemi elastici, 1873), Heinrich Franz Bernard Muller Breslau (1851–1925) (Die graphische Statik der Baukonstruktionen, 1887) and Otto Mohr (1835–1918) (Abhandlungen aus dem Gebiete der technischen Mechanik, 1915) through the principle of virtual works [94]. Thanks to the increasingly advanced knowledge, a new generation of railway bridges with metal truss structure appeared since the mid-nineteenth century [95, 118]. Isambard Kingdom Brunel (1806–1859) built the Windsor (1849), Chepstow (1852) and Saltash (1855) bridges. Joseph Cubitt (1811–1872) built the Newark Dyke Bridge over the Trent River near Newark (1851–1853). Charles Liddell (1813–1894) and L.D.B. Gordon built the Crumlin Viaduct (1853–1857). Between 1867 and 1874, the captain James Buchanan Eads (1820–1887) built the Great Bridge in St. Louis [97], a fabulous bridge with three truss arch spans (L = 153, 158, 153 m) (Fig. 4.57a). Some of his thoughts on safety are remarkable. Dealing with the issue of considering tornadoes as design actions or not, Eads noted that such phenomena entailed high velocities and pressures; however, the probability that one of them struck a given bridge was so small that its analysis could be overlooked. Gustave Eiffel (1832–1923) was a master of truss bridges with double-hinged parabolic arches, such as the Ponte Maria Pia over the Douro River in Portugal (1875–1877, L = 160 m) and the Garabit Railway Viaduct (Fig. 4.57b) in the French Massif Central, over the Truyére River (1879–1880, L = 165 m). This latter highlighted the importance Eiffel gave to wind actions. The girder, with an overall length of 564.65 m, rested on the arch key, on two small intermediate piers and on a series of truncated pyramid pylons. To withstand the vertical loads, Eiffel conceived a “croissant” arch, with increasing thickness from the hinges to the key point; he wrote that “this shape is especially suited to withstand dissymmetrical stresses, since it allows achieving a remarkable thickness in the most stressed parts of the arch”. To absorb the wind loading, estimated as equal to the sum of the weight of the girder and its

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Fig. 4.57 a Great Bridge, St Louis; b Garabit Viaduct, France [15]

overloads, Eiffel increased the width of the arch from 6.28 m at the key points to 20 m at its base. Not all the designers of metal truss bridges were so careful about wind effects. Sir Thomas Bouch (1822–1880) [91, 119], English manager and engineer of the Edinburgh and Northern Railway, attempted to cross the estuaries of the Tay and the Forth by railway bridges to no avail. He then resorted to a service of ferry boats equipped with rails, which started in 1851, obtaining an astounding success: in about 10 years, it arrived to carry 75,000 wagons per year. Bouch then exploited the position achieved to resume his old project: the construction of bridges over the Tay and the Forth. At that time, he had become known and powerful, and he obtained both assignments. He designed the two bridges around 1870. The design of the railway bridge over the Tay [91, 114] envisaged an iron truss beam that reached a maximum height of 27 m above sea level; it consisted of 85 truss spans of variable length, between 8 and 75 m. The unusually slender piers were made of cast iron, with wrought iron bases. It extended on an overall length exceeding 3 km and was, in its whole, the longest bridge of the world. The design of the railway bridge over the Forth envisaged two truss spans, each one of them L = 488 m long, supported by suspension cables and additional stay cables. Bouch produced four projects (Fig. 4.58): three used the classic ratio f/L = 10, and the fourth adopted f/L = 4 to limit the tension stresses in the chains [119]. Each project envisaged the construction of the longest span in the world. For various reasons, the construction started with the Tay Bridge, followed by the Forth Bridge. The Tay Bridge was located at a site known for strong winds. On 2 February 1877, during the construction, a wind storm caused the collapse of two spans and the death of a worker [120]. In spite of this, the bridge was opened on 31 May 1878 (Fig. 4.59a). At 7 p.m. on 28 December 1879, 18 months after the opening, the wind gusts reached a 145 kph speed. At 7.20 p.m., during the passage of a train, 13 spans and 12 metal piers collapsed (Fig. 4.59b) [114, 120]. All the 75 passengers of the train died, together with an occasional bystander struck by a heart attack.

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Fig. 4.58 Forth Bridge: Thomas Bouch’s design alternatives [91]

Fig. 4.59 Tay Bridge: before [114] (a) and after (b) the collapse

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The Tay Bridge collapse originated a vast juridical, technical and scientific debate about wind actions and effects on structures and, in particular, on bridges. Starting from the causes of the disaster and the responsibilities of the designer, it allowed summarising the knowledge, the design practices and the safety of the bridges of that age [38, 118–120]. First, it is worth noting that assessing wind actions on truss bridges without the aid of a wind tunnel (Sect. 7.2) was very difficult, if at all possible. The design tradition of the first half of the nineteenth century seldom considered the assessment of the wind in calculation reports and regulations. The tradition of using horizontal stiffening members dimensioned according to empiricist criteria was often held valid. In the rare cases in which an explicit calculation was performed, wind actions were schematised as an uniform pressure on the members of the upwind face plus a fraction of those of the downwind face, estimated on intuitive bases. Since this ignored the effects due to the vortex wake (Sect. 5.1) of the deck, generally it was not on the safe side. As regards wind pressure, the source most accredited by designers was still Rouse’s table as reported by Smeaton [56]. Many engineers, as well as competent authorities, came to the conclusion it was too conservative. Edwin Clark (1814–1894) strengthened this concept in The Britannia and Conway tubular bridges (1850), a work destined to cause bad consequences; after examining Rouse’s and Smeaton’s suggestion to apply a pressure equal to 50 lb/ft2 on structures “exposed to hurricanes”, Clark proposed to replace such value with 20 lb/ft2 . Rankine (1858) was one of the few recommending higher values (55 lb/ft2 ), but his advice was ignored by nearly everyone. Bouch, who had to design the Tay Bridge in this context of great uncertainties, applied to the Royal Astronomical Society, asking for information about the wind at the site. Anticipating the concepts of coherence and aerodynamic admittance, still far away from being understood, the society answered that some small surfaces of the bridge might be subjected to pressures up to 40 lb/ft2 ; as regards the bridge as a whole, it was sufficient a pressure equal to 10 lb/ft2 . Bouch accepted this suggestion and submitted it to the control committee of the railway organisation, which considered this choice as a suitable one. The committee tasked with the analysis of the reasons of the Tay Bridge collapse concluded its works formulating rules for the calculation of wind actions on bridges. As regards girder bridges with fully enclosed shape, the recommended pressure value was P = 56 lb/ft2 on the whole height of the bridge, including the emerging part of the train. As regards girder bridges with open shape and truss bridges, the same pressure had to be applied to the exposed area of the deck, of the train and of the upwind face of the girder; the sheltered parts of the girder should instead be subjected to a pressure P = 28, 42 or 56 lb/ft2 , in relation to the shelter ratio. In witness of existing uncertainties, the required safety factors were equal to 4 for tension and compression stresses and to 2 for the overturning. It is also worth mentioning that the disaster of the Tay Bridge was not an exceptional event. After the collapse of Stephenson’s bridge over the Dee River near Chester (1847), in 1870 two spans of a bridge collapsed in Decatur, Alabama; in

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1876, a bridge over the Ashtabula Creek in Ohio fell down; in 1877, two spans of a bridge near Omaha, Nebraska, were destroyed; on 27 November 1882, the Inverythan Bridge in Aberdeen also fell down; in 1887, the collapse of the Chatsworth Bridge in Illinois caused the death of 84 people; on 1 May 1891, Norwood Junction in London fell down [116, 120, 121]. The chronicles reported that, in the USA, 20 metal truss bridges collapsed every year [116]. Despite the many extenuating circumstances highlighted above, the English court recalled that, regardless of the suggestions received by Bouch, the designer remained responsible of his work [91, 119]. The judgement was very hard: “this bridge was badly designed, badly constructed and badly maintained and (…) its downfall was due to inherent defects in the structure which must, sooner or later, have brought it down. Sir Tomas Bouch is (…) mainly to blame and (…) responsible”. Following this judgement, Bouch was barred from his profession. On 13 January 1881, while the central pier of the second bridge designed by Bouch emerged from the Forth River, the English railway board stopped any further work (Fig. 4.58). Above all, fears were raised by the adoption of the same value of the design wind pressure value, P = 10 lb/ft2 = 480 N/m2 , which was used for the Tay Bridge. Once again, nobody noticed that a committee approved this choice [118]. In the meantime, some engineers were invited to submit new projects for the Forth Bridge, with the condition that is “should gain the confidence of the public, and enjoy a reputation of being not only the biggest and the strongest, but also the stiffest bridge of the world” [118]. On 30 September 1881, John Fowler (1817–1898) [122] and Benjamin Baker (1840–1907) obtained the assignment with the project of a majestic cantilevered bridge with a Gerber deck (Fig. 4.60a). They used the Fowler’s experience in bridge design (1864–1871), and the studies published by Baker in papers appeared on the Engineering magazine in 1867 [123]; in these papers, Baker showed a great capability of explaining statics on physical bases, maintaining that the adopted structural typology, nearly unknown in England, was the most suitable for long-span bridges.

Fig. 4.60 Forth Bridge: a Benjamin Baker’s human beam [124]; b picture [125]

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Fig. 4.61 a Baker’s tests near the Forth Bridge [127]; b wind pressure field on a surface

The Forth Bridge [91, 118, 119, 124–126], started in 1883 and completed in 1889,37 was a wonderful work. It consisted of two continuous spans, each one L = 521 m long, and took the length record away from the Brooklyn Bridge without making use of suspension cables. Each span consisted of two cantilevered ends, each one 207 m long, and of a double-hinged girder, 107 m long (Fig. 4.60b). The hinges eliminated the thermal stresses and made the girder statically determined. The bridge introduced the innovative use of steel and tubular sections in the main compression elements. During the construction, Baker, aware of the importance of the moment and of the attention of everyone, noticed that “there exists a lamentable lack of data respecting the actual pressures of wind on large structures”, and that neither him nor Mr. Fowler provided contributions towards the solution of this problem. He then decided to analyse the relationship linking the wind pressure and the size of the structure building three screens: one of them had an area equal to 300 ft2 ; the area of the two other screens was equal to 1.5 ft2 ; one of the two smaller screens was free to rotate in the wind direction (Fig. 4.61a). After two years of observations, Baker came to the 37 The construction of the Forth Bridge caused the death of 47 workers, approximately 1% of the work force (4500). The chronicle of that time barely reported this, considering it a routine occurrence for this type of works [116].

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Fig. 4.62 a Main pillar of the Forth Bridge [84]; b bridge over the Quebec River [112]

conclusion that the wind pressure on the larger screen was approximately equal to 2/3 of that on the smaller screens. He then carried out a second series of tests on a surface equal to 6000 ft2 , discovering that the pressure was almost halved with respect to the one acting on the smaller screens [57, 127]. Baker explained the results he obtained observing that “the uniform velocity and pressure in a wind (…) can never obtain near the surface of the earth or in the neighbourhood of any bridge or other structure capable of causing eddies. Unsteady motion must be the rule (…) and the threads of the current moving at the highest velocity will strike an obstruction successively rather than simultaneously, so that the mean pressure per square foot on a large area must be less than that on a small surface” [127]. In this way, he explicitly introduced the concept of the wind velocity and pressure coherence, one of the cornerstones of wind engineering. In other words, he proved that, because of the irregularity of the wind or, more precisely, of its partial correlation, when the velocity and pressure are highest at a point, in other relatively close points they can even assume much smaller values. So, the P ratio between the resulting force R and the swept area (Fig. 4.61b) is as much higher as the area is smaller (Pa = Ra /a > PA = RA /A for a < A). Actually, Baker failed to find the courage of using the principles he himself enunciated and built the Forth Bridge, a huge structure, applying the pressure imposed by the Board of Trade without taking into account the reducing effects due to the noncontemporaneity of maximum local pressures. By so doing, he also started in Europe, like Roebling in America, a generation of rigid and heavy bridges (Fig. 4.62a), fatefully exposed to the danger of equilibrium instability (Fig. 4.62b).38 On the other 38 Forth Bridge lost its record as the longest span in the world in 1917, when the railway bridge over

the Quebec River near Saint Lawrence in Canada was completed; it was similar to the Forth Bridge with a 459 m central span [92, 113, 115, 121]. The design and work supervision were assigned to Theodore Cooper (1839–1919) that availed himself of Norman R. Mc Lure as his assistant. On 27

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hand, his experiments had the merit of stimulating model tests and full-scale experiments that proliferated, in any part of the world, since the end of the nineteenth century (Sects. 7.1–7.3).

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

Watson L (1984) Heaven’s breath: a natural history of the wind. Hodder and Stoughton, UK Whipple ABC (1982) Storm. Time-Life Books, Amsterdam Sorbjan Z (1996) Hands-on meteorology. American Meteorology Society, Boston, MA Hughes P (1987) Hurricanes haunt our history. Weatherwise 40:134–140 Hardy R, Wright P, Gribbin J, Kington J (1982) The weather book. Harrow House, Swanage Brown S (1961) World of the wind. Bobbs-Merrill, Indianapolis, New York Anthes RA (1982) Tropical cyclones: Their evolution, structure and effects. American Meteorology Society, Boston, MA Fein JS, Stephens PL (eds) (1987) Monsoons. Wiley, New York Palmieri S (2000) Il mistero del tempo e del clima: La storia, lo sviluppo, il futuro. CUEN, Naples Wolf A (1935) A history of science, technology and philosophy in the 16th & 17th centuries. George Allen & Unwin, London Shaw N (1926) Manual of meteorology. Volume I: Meteorology in history. Cambridge University Press, Cambridge Halley E (1686) An historical account of the trade winds and the monsoons, observable in the seas between and near the tropicks, with an attempt to assign the phisical cause of the said winds. Phil Trans Roy Soc London, 16:153–168 Canfield NL (1987) Forecasting tricentennial. Bull Am Meteor Soc 68:779–780 Montanari G (1694) Le forze d’Eolo. Dialogo fisico-matematico sopra gli effetti del vortice, o fia turbine, detto negli Stati Veneti la Bisciabuova. Ad instanza d’Andrea Poletti, Parma Tannehill IR (1938) Hurricanes: their nature and history; particularly those of the West Indies and the southern coasts of the United States. Princeton University Press, Princeton, NJ Hadley G (1735) Concerning the cause of the general trade winds. Phil Trans Roy Soc London 39:58–62 Essig M (2006) Inventing America. The life of Benjamin Franklin. Rutledge Hill Press, Nashville, Tennessee Hamblyn R (2001) The invention of clouds. Pan Macmillan, London Howard L (1804) On the modifications of clouds. Taylor, London Howard L (1833) Climate of London deduced from meteorological observations. Harvey & Darton, London Renou E (1855) Instructions météorologiques. Annuaire Soc Meteorol de France 3:73–160 von Humboldt A (1817) Récherches sur les causes des inflexions de lignes isotherms. Mémoirs de Physique de la Soc d’Arcueil, Paris, p 3

August 1907, Mc Lure notified Cooper that some bracings had been subject to abnormal movements. The day after, by telegram, Cooper ordered to stop the works and to wait for him. The company, which was late with its deadlines and burdened by penalties, ignored this order. On August 29, the bracings failed because of instability and the bridge fell under Cooper’s eyes, while he was arriving at the construction site: 85 workers lost their lives. After the error was corrected, the construction restarted and continued up to the lifting of the central section of the span. On 11 September 1916, during this operation, the metal cables supporting the span failed, killing 11 workers. This proved that “heavy” was not a synonym of “safe” and only the return to suspension bridges would allow overcoming longer distances (Sect. 9.1).

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23. Dove HW (1837) Meteorologische Untersuchungen. Sander’sche Buchhandl, Berlin 24. Kämtz L (1840) Vorlesungen über Meteorologie (trans: Walker CV (1845)). A complete course of meteorologie, Baillière, London 25. Kämtz L (1847) Über die windverhältnisse an den nordküsten des alten festlandes. Bull. de l’Acad. St. Petersburg, Class. Sci. Phys.-Math. 5:294–314 26. Redfield WC (1831) Remarks on the prevailing storms or the Atlantic coast or the North American States. Am J Sci 20:17–51 27. Reid W (1838) The law of storms. Weale, London 28. Reid W (1849) The progress of the development of the law of storms and of the variable wind. Weale, London 29. Piddington H (1842) The sailor’s hornbook for the law of storms. Wiley, New York 30. Espy JP (1841) The philosophy of storms. Little and Brown, Boston 31. Maury MF (1854) Explanations and sailing directions to accompany the wind and current charts. Biddle, Philadelphia 32. Maury MF (1855) Physical geography of the sea and its meteorology. Harper, New York 33. Jinman G (1861) Winds and their courses: or a practical exposition of the laws which govern the movements of hurricanes and gales with an examination of the circular theory of storms, as propounded by Redfield, Sir William Reid, Piddington, and others. George Philip and Son, London 34. Ferrel W (1856) An essay on the winds and currents of the ocean. Nashville J Med Surg 11:375–389 35. Ferrel W (1859, 1860) The motions of fluids and solids relative to the earth’s surface. In: Mathematical monthly, 1, 140–148, 210–216, 300–307, 366–376; 2, 89–97, 339–346, 374–382, 397–406 36. Ferrel W (1887–1882) Meteorological researches. Governing Printing Office, Washington 37. Ferrel W (1889) A popular treatise on the winds. Wiley, New York 38. Bixby WH (1895) Wind pressures in engineering construction. Eng News 33:174–184 39. Reye T (1864) Über vertikale Luftströme in der Atmosphäre. Zeits. für Mathematik und Physik, 9:250–276 40. Peslin H (1868) Sur les mouvements généraux de l’atmosphère. Bull. Hebd L’Ass Sci France, 3 41. Flammarion C (1874) The atmosphere. Harper, New York 42. Guldberg C, Mohn H (1876) Études sur les mouvements de l’atmosphère. Brøgger, Christiania, Oslo 43. Fitzroy R (1863) The weather book: a manual of practical meteorology. Longman, London 44. Phillips-Birt D (1971) A history of seamanship. George Allen & Unwin, Crows Nest 45. Baynes CJ (1974) The statistic of strong winds for engineering applications. Ph.D. Thesis, The University of Western Ontario, London, Ontario, Canada 46. Galway JG (1985) J.P. Finley: the first severe storms forecaster. Bull Amer Meteor Soc 66:1389–1395 47. Finley JP (1882) Character of six hundred tornadoes. In: Professional Papers of the Signal Service, No. VII, Washington Office of the Chief Signal Officer 48. Scott RH (1879) Weather charts and storm-warnings. Kegan Paul, London 49. Ley C (1880) Aids to the study and forecast of weather. Metetorological Office Publication No. 40, London 50. Abercromby R (1885) Principles of forecasting by means of weather-charts. Metetorological Office Publication No. 60, London 51. Anderson K (1999) The weather prophets: science and reputation in Victorian meteorology. Hist Sci 37:179–216 52. Rouse H, Ince S (1954–1956) History of hydraulics. In: Series of Supplements to La Houille Blanche. Iowa Institute of Hydraulic Research, State University of Iowa 53. von Karman T (1954) Aerodynamics. Cornell University Press, Ithaca 54. Anderson JD (1998) A history of aerodynamics. Cambridge University Press, Cambridge

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55. Cottier JGC (1907) A summary of the history of the resistance of elastic fluids. Mon Weather Rev, Aug, 353–356 56. Smeaton J (1759) An experimental enquiry concerning the natural powers of water and wind to turn mills, and other machines, depending on a circular motion. Phil Trans R Soc London, 51:100–174 57. Davenport AG (1977) Wind engineering—ancient and modern—the relationship of wind engineering research to design. In: Proceedings of the 6th Canadian congress of applied mechanics, Vancouver, pp 487–502 58. Aynsley RM, Melbourne W, Vickery BJ (1977) Architectural aerodynamics. Applied Science Publishers, London 59. Eiffel G (1910) La resistance de l’air. Examen des formules at des expériences. Dunod et Pinat, Paris 60. Piobert G, Morin AJ, Didion I (1842) Mémoires sur les lois de la résistance de l’air. Mémorial de l’Artillerie 5:553–632 61. Duchemin NV (1842) Recherches experimentales sur les lois de la resistance des fluides. Memorial de l’Artillerie 5:65–379 62. Bender CB (1882) The design of structures to resist wind-pressure. In: Proceedings of the institution of civil engineers, LXIX, pp 80–119 63. Fines (1881) On the measurement of wind-pressure—incompleteness of Borda’s formula. In: Comptes rendus de l’Association Francaise pour l’evancement des sciences, p 457 64. Defoe D (1704) The storm: or a collection of the most remarkable casualties and disasters which happen’d in the late tempest, both by sea and land. Sambridge, London 65. Falconer W (1769) An universal dictionary of the marine: or, a copious explanation of the technical terms and phrases employed in the construction, equipment, furniture, machinery, movements, and military operations of a ship. T. Cadell, London 66. Jr Scoresby W (1820) An account of the Arctic regions, with a history and description of the Northern Whale-Fishery. Constable, Edinburgh 67. Forrester FH (1986) How strong is the wind? The origin of the Beaufort Scale. Weatherwise 39:147–151 68. Proust J (1985) Recueil de planches sur les sciences, les arts libéraux et les arts mécaniques. Hachette, Parigi 69. Sciarrelli C (1970) Lo yacht: origine ed evoluzione del veliero da diporto. Mursia, Milan 70. Giorgetti F (2003) Storia ed evoluzione degli yacht da regata. White Star, Vercelli 71. Froude W (1872) Experiments on the surface-friction experienced by a plane moving through water. In: Proceedings, 42nd meeting of the British association for the advancement of science, pp 118–124 72. Froude W (1875) The theory of “streamlines” in relation to the resistance of ships. Nature, 13, 50–52, 89–93, 130–133, 169–172 73. Lloyd A, Thomas N (1978) Ktes and kite flying. Hamlyn, London 74. Woelfle G (1997) The wind at work. An activity guide to windmills. Chicago Review Press, Chicago 75. Handbook of meteorological instruments (1961) Part II: instruments for upper air observations, meteorological office, London, Her Majesty’s Stationery Office 76. Ronalds F (1847) Experiments made at the Kew observatory on a new kite apparatus for meteorological observations. Phil Mag London 31:191–192 77. Niccoli R (2002) La storia del volo. White Star, Vercelli 78. Shevell RS (1983) Fundamental of flight. Prentice Hall, Englewood Cliffs, NJ 79. Temple R (2007) The genius of China: 3,000 years of science, discovery and invention. Carlton Publishing Group, London 80. Licheri S (1997) Storia del volo e delle operazioni aeree e spaziali da Icaro ai nostri giorni. Aeronautica Militare, Ufficio Storico, Rome 81. Saramago J (1982) Memorial do convento. Caminho, SARL, Lisbona 82. Cayley G (1809, 1810) On aerial navigation. Nicholson’s J Nat Philos Chem Arts, 24, 164–174; 25, 81–87, 161–173

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Cayley G (1852) Governable parachutes. Mech Mag LVII:241–244 Reese P (2014) The men who gave us wings. Pen and Sword Aviation, UK Hills RL (1994) Power from wind. Cambridge University Press, Cambridge Singer C, Holmyard EJ, Hall AR, Williams TI (eds) (1956) A history of technology. Oxford University Press, Oxford Eldridge FR (1980) Wind machines. Van Nostrand Reinhold, New York Klemm F (1954) Technik, eine geschichte ihrer probleme. Karl Alber, Freiburg - Munchen Wailes R (1954) The English windmill. Routledge and Kegan Paul Ltd., London Brooks L (1999) Windmills. Metro Books, New York Hopkins HJ (1970) A span of bridges. David & Charles, Newton Abbot, UK Gedion S (1981) Space, time and architecture. Harvard University Press, Cambridge, MA Mezzina M (ed) (2001) Costruire con il cemento armato. UTET, Turin Benvenuto E (1981) La scienza delle costruzioni e il suo sviluppo storico. Sansoni, Florence Peters TF (1987) Transitions in engineering. Birkhauser Verlag, Basel Finch JK (1941) Wind failures of suspension bridges or evolution and decay of the stiffening truss. Eng News Rec, 13 Mar, pp 74–79 Billington DP (1983) The tower and the bridge. Princeton University Press, New Jersey Scott R (2001) In the wake of Tacoma: suspension bridges and the quest for aerodynamic stability. American Society of Civil Engineers, New York Rendel JM (1841) Memoir of the Montrose suspension bridge. In: Minutes of the Proceedings of the institution civil engineers, London, vol 1, pp 122–127 Mitchell-Baker D, Cullimore MSG (1988) Operation and maintenance of the Clifton Suspension Bridge. Proc Inst Civ Eng 84:291–308 Navier L (1823) Rapport et Mémoire sur les ponts suspendus. Imprimerie Royale, Paris Billington DP, Nazmy A (1990) History and aesthetics of cable-stayed bridges. J Struct Eng ASCE 117:3103–3134 Buonopane SG, Billington DP (1993) Theory and history of suspension bridge design from 1823 to 1940. J Struct Eng ASCE 119:954–977 Troitsky MS (1977) Cable-stayed bridges. Crosby Lockwood Staples, London Provis WA (1842) Observations on the effects produced by wind on the suspension bridge over the Menai Strait, more especially as relates to the injuries sustained by the roadways during the storm of January, 1839; together with brief notices of various suggestions for repairing the structure. Trans Inst Civ Eng III:357–370 Gremand MA (1881, June) The strengthening of the Fribourg Suspension Bridge. Bulletin de la Société Vaudoise des Ingénieurs et des Architectes, p 11 Shapiro MJ (1990) A picture history of the Brooklyn Bridge. Dover Publications, New York Nelson LH (1990) The Colossus of 1812: an American engineering superlative. American Society of Civil Engineers, New York Petroski H (1993) Failure as source of engineering judgement: case of John Roebling. J Perf Constr Facil ASCE 7:46–58 Rankine WJM (1869) A manual of applied mechanics. Charles Griffin, London Bender CB (1872) Historical sketch of the successive improvements in suspension bridges to the present time. Trans ASCE 1:27–43 Middleton WD (2001) The bridge at Quebec. Indiana University Press, Bloomington, IN Lewis PR, Gagg C (2004) Aesthetics versus function: the fall of the Dee Bridge, 1847. Interdisc Sci Rev 29:177–191 Sibly PG, Walker AC (1977) Structural accidents and their causes. Proc Inst Civ Eng 62:191–208 Clapeyron PBE (1857) Calcul d’une poutre élastique reposant librement sur des appuis inégalement espacés. Comptus Rendus 45:1076–1077 Heins CP, Firmage DA (1979) Design of modern steel highway bridges. Wiley, New York Whipple S (1847) A work on bridge building; consisting of two essays, the one elementary and general, the other living original plans, and practical details for iron and wooden bridges. Utica, New York

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Part III

Fundamentals: From the Late Nineteenth Century to the Mid-Twentieth Century

Chapter 5

Scientific Progress and Its Impact on Wind

Abstract This chapter deals with fluid dynamics, probability theory and automatic computation. Just in the first half of the twentieth century they displayed major improvements, both in general terms and as regards the basic tools for the knowledge of wind that would come to maturity in the second half of the twentieth century. After almost two centuries of trials, fluid dynamics overcame the doubts about D’Alembert’s paradox and the resistance of bodies, formulating the founding principles of the boundary layer, of the vortex wake, and of the transition from laminar to turbulent flows. The probability theory, reorganised on axiomatic grounds, produced a broad range of developments including extreme value theory, principal component analysis, random processes and Monte Carlo methods. The appearance of the electronic computer gave rise to advances firstly addressed to meteorological forecasts, then aimed to solve the increasingly complex problems posed by the renewed culture of the wind.

The period from the sixteenth to the late nineteenth century (Chaps. 3 and 4) marked the foundation of basic scientific disciplines. Of course, their progress was not exhaustively attained in that period. In most cases, however, their advancement level was sufficient to guarantee the timing and conceptual interpretation of the essential elements for the development and consolidation, especially in the twentieth century, of many subjects behind the current culture of wind and its effects. Within this framework, three disciplines represent as many exceptions: fluid dynamics (Sects. 3.6 and 5.1), probability theory (Sects. 3.4 and 5.2) and automatic computation (Sects. 3.3 and 5.3). In the first half of the twentieth century, they displayed major improvements, both in general terms and as regards the basic tools for the knowledge about the wind that would come to maturity in the second half of the twentieth century. After almost two centuries of trials, fluid dynamics overcame the doubts about D’Alembert’s paradox (Sect. 3.6) and the resistance of bodies (Sect. 4.2), formulating the founding principles of the boundary layer, of the flow separation and of the vortex wake and of the transition from laminar to turbulent flows (Sect. 5.1). They laid the foundation for decisive developments in many sectors, including meteorology (Sect. 6.3), micrometeorology (Sect. 6.5), bluff-body aerodynamics

© Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_5

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(Chap. 7) as well as wind actions and effects on the environment, territory (Chap. 8) and structures (Chap. 9). The probability theory (Sect. 3.4), reorganised on axiomatic grounds, went through a refoundation period (Sect. 5.2) that laid the bases of the modern discipline and produced an almost unlimited range of developments and new trends—extreme value theory, principal component analysis, random processes and Monte Carlo method—making up the foundations and tools of the scientific and technological knowledge that is nowadays the base of the turbulence theory (Sect. 6.6), wind climatology (Sect. 6.8), wind actions and effects on the environment, territory (Chap. 8) and structures (Chap. 9) and wind vulnerability and risk analyses (Chap. 10). The appearance of the electronic computer during the Second World War (Sect. 5.3) marked a turning point in terms of automatic computation, characterised by amateurish attempts for a long time (Sect. 3.3). Its first developments were related to meteorology and forecast issues (Sect. 6.3), then it became the main instrument to solve the increasingly complex problems of fluid and structural mechanics posed by the renewed culture of wind. This chapter provides a brief summary of the three above-mentioned subjects. It will be the last one to be relatively general in nature. At the end of this overview, the treatment from Chap. 6 on will only specifically deal with subjects associated with the wind and its effects.

5.1 Fluid Mechanics Nineteenth-century fluid dynamics was heavily influenced by D’Alembert’s paradox and the inability to come through it. It, therefore, developed along two almost independent directions. On the one hand, the mathematical treatment of the equations of motion achieved a high level of thoroughness and completeness (Sect. 3.6), but it led to results contrary to experimental measurements (Sect. 4.2). On the other hand, engineers, being sensitive to technological advancements and to the applicative importance of the problems related to fluid motion, developed empirical methods based on experimental data; the results obtained intensified the feeling that the high thoroughness of the equations was scarcely important if the same were unable to reproduce the physics of the phenomena involved. This was especially conspicuous as regards to Navier–Stokes equations: when they were applied to viscous fluids, they were practically unresolvable; when viscosity was disregarded they became easily integrable, but led to utterly wrong results. This appeared unexplainable, especially for the two most important fluids, air and water, which are characterised by low viscosity. The question was, how it was possible that neglecting viscous forces, minor in comparison with other forces, could lead to such large errors. The situation changed between the end of the Nineteenth century and the start of the First World War, a period which saw a succession of remarkable discoveries that opened the door to modern fluid mechanics and laid the foundations of decisive developments in the

5.1 Fluid Mechanics

277

Fig. 5.1 Strouhal [2]: a whirling arm; b experimental results

fields of meteorology, micrometeorology, aerodynamics, aeronautics and of the wind actions and effects on environment and structures. ˇ ek Strouhal, 1850–1922) [1] carried out experIn 1878, Vincenc Strouhal (Cen˘ iments [2] using a whirling arm (Fig. 5.1a). He placed a cylindrical element (M) between two supports (A) connected to a column (K). M was made to whirl around K by means of a wheel (S), manually driven at a constant speed. Strouhal used a Koenig’s sonometer to estimate the intonation of the produced sound, i.e. the wind tone or the frequency N, and proved that it depended on two sole parameters, the diameter D of the element and the velocity V with which it moved through air, being almost proportional to V and almost inversely proportional to D (Fig. 5.1b). He also noted that the wind tone was generated both by rigid bars (continuous lines) and by stretched metal wires (dotted lines); in the second case, however, sound intensity greatly increased when the frequency N of the tone coincided with the natural frequency n0 of the wire, realising a resonance phenomenon. Attributing an analytical form to the diagrams in Fig. 5.1b: N=

SV D

(5.1)

where S is a non-dimensional number approximately equal to 0.195 for rigid bars, 0.185 for metal wires. From Eq. (5.1), it follows that the critical velocity for which resonance takes place is given by: Vcr =

n0 D S

(5.2)

In 1879, Horace Lamb (1849–1934) published Mathematical theory of the motion of fluids, which was bound to become the classic treatise on fluid dynamics. An extended and revised version was republished in 1895 with a new title, Hydrodynamics [3], subsequently updated several times up to 1935. Every edition included the innovative elements of discipline subject to constant evolution; as a whole, the series of these publications provides a picture of the advancement of the state of the art.

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5 Scientific Progress and Its Impact on Wind

Fig. 5.2 Reynolds’ sketches: transition from laminar to turbulent flow [4]

In 1883, Osborne Reynolds (1842–1912) completed fundamental experiments about the flows in pipes [4]. He connected a long glass pipe with a tank and observed the characteristics of the flow by means of a dye he introduced at the pipe inlet (Fig. 5.2). When the flow speed was low, the dye formed a thin line, parallel to the pipe axis. By increasing the flow speed, Reynolds discovered the existence of a threshold value beyond which the thread suddenly began to strongly wave while the dye diffused within the whole pipe. In other words, the flow changed from a laminar to a turbulent one. Actually, this transition was first observed by the German engineer Gotthilf Heinrich Ludwig Hagen (1797–1884) [5, 6] in 1854. Reynolds, however, was the first to prove that this phenomenon was governed by the non-dimensional parameter: R=

VD ν

(5.3)

where V is the mean speed of the flow; D is a characteristic length, in this case the pipe diameter; ν = μ/ρ is the kinematic viscosity of the fluid, being μ the dynamic viscosity and ρ the mass per unit volume. The parameter R expresses the ratio between the inertial forces, proportional to ρV 2 /D, and the viscous forces, proportional to μV/D2 , acting on the moving fluid. When this ratio is small, the viscous forces prevail and the motion is laminar. When this ratio is large, the inertial forces prevail and the motion becomes turbulent. The ratio value at which the transition takes place is defined as the critical one.1 In 1908, Arnold Sommerfeld (1868–1951) designated the parameter R as the “Reynolds number” [6]. 1 Reynolds’

experiments proved that the transition from laminar to turbulent regime took place in a circular pipe for a R value nearly equal to 2300. In view of the current knowledge, the flow is laminar for R ≤ 2000 and is turbulent for R ≥ 4000. The 2000 ≤ R ≤ 4000 range is defined as the transition domain.

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279

Reynolds also formulated, in 1894, the fundamental rule for decomposing the parameters s of a fluid into a mean part s, slowly varying over time and then with a tendentially infinite period, and into a zero mean fluctuating part s  , quickly varying over time and then with a finite period [7]: s = s + s

(5.4)

Equation (5.4), when applied to the velocity and pressure components (s = vi , p; i = 1, 2, 3) of incompressible fluids, allows breaking down the system of the continuity Eq. (3.12) and Navier–Stokes’ Eq. (3.25) into two equation systems: ∂v j =0 ∂x j

  ∂vi vj ∂vi ∂p ∂ 2 vi ∂vi = ρ fi − + vj +μ −ρ ρ ∂t ∂x j ∂ xi ∂x j∂x j ∂x j

(5.5a) (i = 1, 2, 3)

(5.5b)

and: ∂vj ∂x j

=0

   ∂vi vj ∂v ∂v ∂ 2 vi ∂vi ∂ p ∂vi + vj i = − +μ +ρ ρ + v j i + vj ∂t ∂x j ∂x j ∂x j ∂ xi ∂x j∂x j ∂x j

(5.6a) (i = 1, 2, 3) (5.6b)

where the repetition of the index j indicates the summation notation, vi vj is the covariance of vi and vj (i, j = 1, 2, 3). The first system (Eq. 5.5a, b), called “primary” or “mean-mean” by Reynolds, provides the mean parts of the velocity and pressure. The second system (Eq. 5.6a, b), called “secondary” or “relative-mean”, provides their fluctuating parts. Equation (5.5b), nowadays known as Reynolds’ equation, coincides with the original Navier–Stokes Eqs. (3.25) with two variations: (1) the terms vi (i = 1, 2, 3) and p are replaced by their means; (2) a new term (−ρ∂vi vj /∂ x j ) depending on the covariance of the turbulent fluctuations appears besides the term (μ ∂ 2 vi /∂ x j ∂ x j ) associated with the viscous nature of the fluid. Reviewing the stress tensor (Eq. 3.24) in the light of this result, its mean part can be expressed in the following form:   ∂v j ∂vi − ρvi vj (i, j = 1, 2, 3) T i j = − pδi j + μ + (5.7) ∂x j ∂ xi

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5 Scientific Progress and Its Impact on Wind

where the term proportional to μ defines the viscous stresses of a laminar nature. By analogy, the term associated with the covariance of the fluctuations defines the stresses of a turbulent nature, from now on called apparent or Reynolds stresses2 : τt = −ρvi vj

(5.8)

The ratio between the sizes of the Reynolds stresses and of the viscous stresses gives rise to the non-dimensional quantity R (Eq. 5.3); it, as reaffirmed by Reynolds [7], determines the tendency to assume a laminar or turbulent behaviour for the flow. Reynolds stresses constitute a symmetrical tensor. Its presence in Eq. (5.5b), therefore, creates six new unknown quantities in the primary system: the three variances and the three covariances of the three components of the velocity. Thus, they give rise to concepts that are fundamental but not sufficient to develop the formulation. Their introduction, however, represented a turning point (Sect. 6.6): it highlighted the probabilistic character of turbulence and opened a wide-ranging debate, still in progress, about the most effective way to make the Reynolds tensor explicit. The historical turning point in fluid mechanics is due to Ludwig Prandtl (1875–1953), who is now recognised as the founder of modern fluid dynamics3 [5, 8]. In 1904, at the Third International Mathematics Congress held at Heidelberg, he presented an eight-page paper,4 Über Flüssigkeitsbewegung bei sehr kleiner Reibung (“About the motion of fluids with little friction”) [9], in which he unified theory and experience. In this paper, one of the most important scientific contributions of all times, Prandtl displayed his outstanding ability to understand physical phenomena and to translate them into rigorous but intuitive mathematical formulas. Availing himself of simple experiments carried out in a small tank he built in Göttingen with his very own hands (Fig. 5.3), he demonstrated that, in a not very viscous fluid like air or water, viscosity only affected the flow in a thin layer in contact with solid surfaces, called “grenzschicht” or “boundary layer”,5 where vorticity is concentrated. Outside 2 Reviewing

Boussinesq’s contribution (Sect. 3.6) in the light of Reynolds’ results, it amounts to expressing Eq. (5.7) in the form:   ∂v j ∂vi T i j = − pδi j + μT + (i, j = 1, 2, 3) ∂x j ∂ xi where μT is the eddy viscosity coefficient. Reynolds’ demonstration, therefore, expressed in a mathematical form the concept introduced by Boussinesq in physical and phenomenological terms: the μT parameter is strongly dependent on the turbulent agitation of the flow. 3 In his 1894 book, Progress in flying machines, Octave Chanute (Sect. 7.4) wrote: “Science has been awaiting the great physicist, who, like Galilei or Newton, should bring order out of chaos in aerodynamics, and reduce its many anomalies to the rule of harmonious law”. Chanute died in 1910, without making the acquaintance with Prandtl. 4 In 1928, when he was questioned by Goldstein about the succinctness of his famous paper, Prandtl replied that he had no more than 10 min available for the presentation and then he did not believe necessary to write more than what he would have told. 5 In his work presented in 1904 and published in 1905 [9], Prandtl used the “boundary layer” (“Grenzschicht”) term only once; he often resorted, instead, to the “transition layer” (“Übergangsschicht”) term. The “boundary layer” term was extensively used by Blasius in his 1907 doctorate thesis.

5.1 Fluid Mechanics

281

Fig. 5.3 Channel and wheel built by Prandtl to study the boundary layer [9]

Fig. 5.4 Boundary layer and irrotational flow [41]

this layer, the fluid can be considered as irrotational and, therefore, it can be treated as an inviscid one, applying the principles formulated by Helmholtz (Sect. 3.6); the motion within the boundary layer, in turn, is controlled by the motion of the free flow (Fig. 5.4). At a time when the primary system of the Reynolds Equation (5.5a, b) was not yet sufficiently known, Prandtl treated the flow as a stationary, incompressible and bidimensional one, applying the Navier–Stokes Eqs. (3.12) and (3.25) to the boundary layer that developed near a thin flat plate (Fig. 5.4). These equations, nowadays known as Prandtl’s boundary layer equations, assumed the form: ∂v ∂u + =0 ∂x ∂y   ∂u ∂u ∂p ∂ 2u ρ u +v =− +μ 2 ∂x ∂y ∂x ∂y

(5.9a) (5.9b)

In 1925 Prandtl judged such term unsatisfactory but resigned himself to its use considering its diffusion.

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5 Scientific Progress and Its Impact on Wind

Fig. 5.5 Boundary layer separation on a flat plate [9]

where x = x 1 is the direction of the flow and y = x 2 is the direction orthogonal to the plate; u = v1 and v = v2 are the velocity components along the x and y axes. Prandtl took advantage of the thinness of the boundary layer to introduce the hypothesis that, inside it, the pressure p did not change along y but assumed a known value, a function of x, associated with the potential flow. In this way, Eq. (5.9a, b) is a system of two equations with two unknown quantities, u and v, which can be solved by associating to it the boundary conditions u = v = 0 for y = 0 (absence of relative motion between the fluid and the wall) and u = U(x) for y tending to infinity, being U the known velocity of the potential flow. Prandtl applied his equations to numerically obtaining the first expression of the resistance of a thin flat plate parallel to the direction of the flow (on a face). It is provided by:  D = 1.1b U 3 μρl

(5.10)

where b and l are the width and the length of the plate, respectively. In the same paper, Prandtl demonstrated that when a boundary layer is subjected to a negative pressure gradient in the direction of the solid surface, i.e. when the external flow accelerates, its thickness decreases and the vorticity inside it is carried towards the surface; in other words, the boundary layer is squashed. The opposite phenomenon takes place when a boundary layer is subjected to a positive pressure gradient along the surface, which is called “adverse pressure gradient”. In this case, its thickness quickly increases and the vorticity is carried outwards until it creates the separation of the boundary layer (Fig. 5.5). This phenomenon takes place at a point, called separation point, where the condition ∂u/∂y = 0 exists for y = 0. Downstream this point, a retrograde flow occurs near the surface and the potential flow field is drawn away from the wall. Prandtl substantiated this phenomenon by means of many pictures (Fig. 5.6). Thanks to these enunciations, Prandtl convincingly surpassed, after over one and a half century of fruitless attempts, D’Alembert’s paradox. His work was striking for the maturity of the ideas exposed therein. Actually, other works had already dealt with the boundary layer and its connection with the shear resistance of surfaces. Such explanations, however, were weak and often wrong; besides, both the equations and any reference to separation were missing [10]. Thanks to Prandtl, the Kaiser Wilhelm Institut fur Stromungsforschung, the world pilot centre in fluid mechanics, was founded at Göttingen in 1904. It stood out because

5.1 Fluid Mechanics

283

Fig. 5.6 Boundary layer separation from a rounded body [9]

of three main aspects [5]: the formulation of analysis methods inspired neither by mathematical abstractions nor by empirical criteria, but rather by practical applications of physical reasoning; the development of experimental techniques destined to become reference models; the education of excellent analysts, researchers and teachers. Among the many contributions standing out, there were the first closed circuit wind tunnel (Sect. 7.2) and its instrumentation (Pitot tubes, pressure sensors, dynamometric balances), the studies about turbulence and the resistance of bodies as well as the aerodynamic theory of wing profiles in subsonic and supersonic flows (Sect. 7.4). Above all, a school of exceptional importance blossomed out; it included, among many others, Paul Richard Heinrich Blasius (1883–1970), Theodore von Karman (1881–1963), Albert Betz (1885–1968), Carl Wieselsberger (1887–1941), Jakob Ackeret (1898–1981), Walter Tollmien (1900–1968), Hermann Shlichting (1907–1982), Otto Flachsbart (1898–1957) and Johann Nikuradse (1894–1979). In the wake of the famous Prandtl’s work, several publications destined to become milestones of fluid dynamics came out one after the other between 1905 and the start of the First World War. In 1907, Blasius presented his doctorate dissertation, Boundary layers in the fluids with small friction [11], under the supervision of Prandtl, where he solved Eq. (5.9a, b) in the boundary layer near a thin flat plate parallel to the flow direction (Fig. 5.4). Accordingly, Blasius conventionally defined the thickness δ of the boundary layer as the height y in correspondence of which u = 0.99U; he then obtained: 5 δ =√ x Rx

(5.11)

where Rx = U x/ν is a Reynolds number related to the distance x from the leading edge of the plate. He also obtained the shear stress τ0 of the flow on the surface and the resistance of the plate (on a face): 0.332 τ0 (x) = √ ρU 2 Rx  D = 0.664b U 3 μρl

(5.12) (5.13)

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5 Scientific Progress and Its Impact on Wind

Finally, he determined the drag coefficient cD defined by the relationship: cD =

D 1 ρU 2 bl 2

1.328 = √ Rl

(5.14)

Equation (5.13) represents an evolution of the original Prandtl’s Equation (5.10); it will be further improved by Töpfer [12] in 1912 through the application of a numerical approach. It is essential to notice that Eqs. (5.11)–(5.13) are solutions of Eq. (5.9a, b), where the Reynolds stresses associated with the turbulent fluctuations do not appear; they refer, therefore, to a laminar boundary layer. The extension of Prandtl’s equations to the turbulent boundary layer is, as a matter of principle, immediate. Applying Eqs. (5.4) and (5.5a, b), Eq. (5.9a, b) assumes the form: ∂v ∂u + =0 ∂x ∂y   ∂p ∂ 2u ∂u ∂v ∂u  v +v =− +μ 2 −ρ ρ u ∂x ∂y ∂x ∂y ∂y

(5.15a) (5.15b)

where, beside the initial unknown quantities u and v, now u and v, a new unknown term appears: the covariance u  v of the u  and v fluctuations. Actually, its presence is a formidable complication. It can be expressed by solving the system in the fluctuations (Eq. 5.6a, b) or by parametrising such quantity on experimental grounds. The difficulty of this operation will represent a serious obstacle to the solution of the equations of motion in turbulent boundary layers, originating a debate that will develop after the First World War. Before dealing with this issue, it is however essential to dwell on other important events taking place from 1911 to 1915. In 1911, Prandtl supervised Hiemenz’s doctorate dissertation about flow separation and pressure distribution around a circular cylinder [13], which brought about fundamental consequences. Hiemenz pointed out to Prandtl the flow oscillated behind the cylinder (Fig. 5.3); Prandtl replied that, obviously, the cylinder was not circular. Hiemenz verified that the cylinder was circular; he went back to Prandtl and told him the flow continued to oscillate. Prandtl replied that the channel was obviously not symmetric [6]. Even though he had nothing to do with this research, Karman, the most distinguished among Prandtl’s students, was intrigued by Hiemenz’s experiments and went to the channel every morning to verify if the flow had stabilised. Since this never occurred, he convinced himself that the phenomenon must have a physical explanation. He then started studying the problem and, between 1911 and 1912, he explained the concepts behind the vortex wake destined to be named after him [14]. Karman noticed that a double array of alternating vortices formed behind a cylinder of infinite length, immersed in a fluid flow. The vortices at the top array rotate clockwise, those at the bottom array rotate counterclockwise (Fig. 5.7). Karman himself acknowledged that, even though the vortex array was named after him, it

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Fig. 5.7 Double array of alternating vortices behind a circular cylinder [6]

Fig. 5.8 Double array of vortices [6]: symmetrical (unstable) (a) and asymmetrical (b) arrangement

had been already known before he was born [6]. By way of example, an ancient painting in a church in Bologna depicted St. Christopher carrying the infant Jesus on his shoulders while he crossed a stream; the painter drew alternating vortices behind the feet.6 Similar vortices behind obstacles in fluid flows had been observed by an English scientist, Henry Reginald Arnulpht Mallock (1851–1933) [15] and, in 1908, by the French Henry Bénard7 (1874–1939) [16], who was jealous because they were named after Karman and not after him [6]. Karman’s contribution to the double array of vortices especially regarded the fluid dynamics concepts behind the physical phenomenon. He was the first to prove that the symmetrical arrangement (Fig. 5.8a) is unstable and that only the asymmetrical arrangement of the vortices (Fig. 5.8b) could be stable, as long as the ratio h/l = 0.28056 between the distance h between the two arrays and the distance l between two consecutive vortices of the same array [14, 17] is accomplished. He also demonstrated that there is a theoretical link between the width of the vortex wake and the resistance of bodies. The wider the vortex wake is, the higher the resistance becomes. 6 Communication 7 In

of Prof. Masaru Matsumoto, University of Kyoto, Japan. his 1908 paper [16] Bénard was the first to call the S quantity in Eq. (5.1) Strouhal number.

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The problem of the transition from the laminar regime to the turbulent one and the role, this phenomenon played as regards to the width of the vortex wake, and then to the resistance of bodies, was made clear in particular circumstances. In 1912, Prandtl in Göttingen and Eiffel in Paris independently measured the resistance of a sphere, each one of them using his own wind tunnel (Sect. 7.2). Prandtl obtained a value of the drag coefficient almost double of the Eiffel’s one. They exchanged the results of their respective experiments and an engineer of Prandtl’s team said: “Oh, M. Eiffel forgot a factor of two. He calculated the coefficient referred to ρV 2 and not to ρV 2 /2” [6]. When this statement came to Eiffel’s knowledge, he first felt insulted, then he carried out new measurements, varying the velocity V of the flow and the diameter D of the sphere. During these tests, he demonstrated that, above a given threshold of V, for a given value of D, the resistance of the sphere actually showed a sudden decrease [8, 18] (Fig. 5.9). He was however unable to understand the reason why this happened. Prandtl explained this phenomenon in 1914 [19], demonstrating that the boundary layer can be either laminar or turbulent. He also demonstrated that the separation of the flow, and then the resistance of bodies, is governed by the transition of the boundary layer from the laminar regime to the turbulent one. In Karman’s words [6]: “Turbulence is not confined to the flow in tubes but also occurs, for example, in the flow just adjacent to the surface of a body moving in a fluid, the so-called boundary layer. The flow in this layer may be laminar at low Reynolds numbers and may become turbulent when the Reynolds number exceeds a certain critical value. This change has a favourable consequence because the violent intermingling of particles enables the turbulent layer to stick to the surface better than does the laminar layer, which contains less kinetic energy and leaves the surface earlier. At low Reynolds numbers, especially in the range where the drag coefficient of a sphere or cylinder is almost constant and has the larger value, the boundary layer is laminar and the early separation of the flow creates a broad wake filled by vortices. Then, at a certain higher Reynolds number, the flow in the boundary layer becomes turbulent, the separation is delayed, and the size of the wake is reduced. This explains the relatively sudden reduction of the drag coefficient at a certain Reynolds number”. Prandtl substantiated his interpretation by means of a famous experiment [19]. “A fine wire ring was put around a sphere a short distance in front of the separation point of the laminar layer. The wire disturbed the flow in the boundary layer, so that the transition to turbulence, and hence the sudden drop of drag, concurred at a smaller Reynolds number. Paradoxically, therefore, although the wire ring was an additional obstacle, the total drag was reduced by the presence of the wire because laminar separation was prevented” [6]. Wieselsberger [20] highlighted this phenomenon by introducing fumes in the wind tunnel (Fig. 5.10). From that time on, expressing the drag coefficient of bodies as a function of the Reynolds number became a standard practice [6]. In the same period (1911), Dimitri Pavlovitch Riabouchinsky (1882–1962) (Sect. 7.2) gave essential contributions to dimensional analysis. It was the prelude to the formulation of the π theorem, a cornerstone of similarity criteria, developed by the American physicist Edgar Buckingham (1867–1940) between 1914 and 1915

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Fig. 5.9 Eiffel’s measurements of the resistance of spheres [8, 18]

[21, 22]. It stated that, given a problem described by equations containing n physical variables that can be expressed as functions of k independent fundamental quantities, the same problem can be fully described by p = n − k non-dimensional variables constructed by using the original variables; two problems governed by the same non-dimensional parameters are defined as similar. In 1915, Rayleigh synthesised his discoveries with Strouhal’s and Karman’s ones. Starting from the observation that a violin string vibrated alongwind and crosswind, he proved [23] that alternating vortices explained the myth of the Aeolian harp (Sect. 2.1). He also interpreted the variation of the parameter S in Eq. (5.1)

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5 Scientific Progress and Its Impact on Wind

Fig. 5.10 Flow behind a sphere [32]: a laminar boundary layer; b boundary layer made turbulent by means of a thin iron wire ring wound around the sphere

(Fig. 5.1), called Strouhal’s number, from S = 0.195, for large D values, to S = 0.185, for small D values, as a function of the Reynolds number. The advent of the First World War stopped advancements in fluid dynamics. When the war ended, these resumed with renewed impetus. In 1921, Karman [24] and Pohlhausen [25] applied the momentum principle, in its integral form, to the mass of the fluid occupying a given volume at a generic instant. Thanks to this criterion, boundary layer equations are not satisfied for every streamline, but within a volume, called the control volume. This technique, which opened the doors to many approximate solutions, would meet with huge success and would be widely accepted by the international scientific community. The great discoveries made in Göttingen between 1904 and 1921, however, continued to arouse little interest elsewhere: this was presumably due to the use of the German language and to the hermetic nature of Prandtl’s papers [10, 26]. The situation changed around the mid-1920s.8 In 1922, Prandtl and Richard Edler von Mises (1883–1953) founded the International Association for Applied Mathematics and Mechanics (GAMM) of which Prandtl was the first president, from 1922 to 1933. The first systematic measurements about the development of the boundary layer were carried out from 1924. In 1925, Prandtl formulated the mixing length theory and Prandtl himself, in 1927, delivered a memorable lecture, the fifth Wilbur Wright Memorial Lecture, at the Royal Aeronautical Society of London [27]. From this moment on, the recognition for the outstanding contribution of the Göttingen School grew according to an exponential curve, as witnessed by the succession of the works on fluid dynamics [6, 28–33]. Summing up the evolution of the discipline methodically represents an exceedingly complex task and goes beyond the purposes of this book anyway. Keeping in mind these purposes, it is however possible to single out some subjects destined to play essential roles in the wind science: the boundary 8 In

the fifth edition of Lamb’s book, Hydrodynamics [3], published in 1924, there was a brief paragraph about the boundary layer, with the following words dedicated to Prandtl: “The calculations are necessarily elaborate, but the results (…) are interesting”. In the sixth edition, published in 1932, a whole chapter was dedicated to the boundary layer, including the equations of motion.

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Fig. 5.11 Transition of the boundary layer along a plate from laminar to turbulent [36]

layer and its transition from the laminar regime to the turbulent one, the motion of fluids in the pipes and the dual problem of the motion of fluids on a flat plate, the solution of the equations of motion in the boundary layer and the universal laws of velocity, the wake separation and vortex shedding, the wall jet. The first measurements of the boundary layer close to a thin flat plate parallel with the flow direction were performed between 1924 and 1928. They aimed at verifying Blasius’ solution and at examining the transition of the boundary layer from the laminar regime to the turbulent one. The experiments carried out during the dissertation of Van der Hegge-Zijnen [34] under the supervision of Mauritius Burgers (1895–1981) [35] did not solely rely on the classic visualisation by means of fumes, but also made use of a hot-wire anemometer (Sects. 6.1 and 7.2). Hansen’s measurements [36] (Fig. 5.11) proved that the transition took place for Rx ∼ = 3.2 × 105 ; during such transition the boundary layer showed a remarkable increase of its thickness. In 1929, Tollmien [37] theoretically proved that this transition took place for Rx = 9.13 × 104 . In 1935, Tollmien himself [38] demonstrated that the presence of a point of inflection in the velocity profile u(y) (Fig. 5.5) was not only a necessary condition for the flow to be unstable [39], but such condition was also sufficient. The experimental study of the transition made progress between 1934 and 1939, when Hugh Latimer Dryden (1898–1965) [40, 41] carried out measurements so accurate they became a benchmark for any future theoretical and experimental research. In 1940, under the leadership of Dryden, Galen Brandt Schubauer (1904-?) and Skramstad [42] carried out new measurements, during which they obtained flows with very low turbulence levels; the tests demonstrated that the transition could also take place

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5 Scientific Progress and Its Impact on Wind

for Rx = 2.8 × 106 , highlighting it was influenced by turbulence. Similarly, accurate experiments were carried out by Nikuradse [43] in 1942; he demonstrated that the boundary layer was also greatly influenced by the shape of the plate leading edge and by the possible presence of a small pressure gradient in the external flow (parallel to the plate). A vast literature highlighting the role of the surface roughness [44–46] also developed at the same time. Increasing this quantity, the Reynolds number for which the transition occurred from the laminar regime to the turbulent one decreased; in other words, roughness advanced the transition by causing additional perturbations besides those generating the turbulence. If the local roughness was large, as it was the case of the wire wound around Prandtl’s sphere, the transition took place at that point [19, 20]. The motion of fluids inside pipes plays a key role for the purposes of this book considering its dualism as regards the boundary layer on flat plates. In 1921, Prandtl [47] resumed the analyses about the shear resistance of smooth circular pipes crossed by turbulent flows carried out by Blasius [48] in 1911, expressing the profile of the mean flow velocity through the relationship:  yv 1/7 u ∗ = 8.74 v∗ ν

(5.16)

√ where y is the distance from the pipe wall, v∗ = τ0 /ρ is the shear velocity and τ0 is the wall shear stress. Indicating the mean flow velocity along the pipe axis as U (U = u for y = r, r being the radius), Eq. (5.16) can be rewritten in the form: u U

=

 y 1/7 r

(5.17)

which represents the first application of the power law in fluid mechanics; the 1/7 exponent derives from the range of the Reynolds numbers within which Blasius’ pipe resistance law stands true. In 1923, Hopf [49] published a state of the art about the shear resistance of rough pipes, demonstrating the existence of two different forms of roughness: for dense and homogeneous roughness elements, the resistance depends on the k/r ratio, where k is the reference height of the roughness; for sparse and prominent roughness elements, the resistance depends on the same ratio and on the Reynolds number. In 1927, Prandtl [50] analysed the formation of a turbulent boundary layer on the surface of a thin and smooth flat plate parallel with the flow direction. The solution, unlike Blasius’ rigorous one about the formation of a laminar boundary layer [11], made use of many simplifying hypotheses. Besides the one already adopted by Blasius, who assumed a null longitudinal pressure gradient and, therefore, a constant velocity U of the potential flow, Prandtl supposed that the boundary layer was turbulent from the leading edge of the plate. Above all, he instituted a parallelism between the pipe and the plate, through which he attributed to the mean velocity u of the flow the power law:

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 y 1/7 u = U δ

(5.18)

which represents the analogous of Eq. (5.17), having replaced the radius r of the pipe with the thickness δ of the boundary layer (Fig. 5.4) and, as a consequence, U with U. On the basis of this assumption, which from then on became the subject of a wide-ranging debate [33], Prandtl expressed the thickness δ of the boundary layer, the shear stress τ0 and the drag coefficient cD of the plate (on a face) as: δ 0.37 =√ 5 x Rx 0.0288 τ0 (x) = √ 5 ρU 2 Rx D 0.074 cD = 1 2 = √ 5 Rl ρU bl 2

(5.19) (5.20) (5.21)

which correspond to Eqs. (5.11), (5.12) and (5.14) in the hypothesis of a laminar boundary layer. There is a vast literature aimed at correcting Eq. (5.21) to take into account that the boundary layer actually is laminar at first and then becomes turbulent [33]. The knowledge of flows inside pipes received impulse from Nikuradse’s experiments. In 1932, he carried out tests about the wall shear stresses and the mean velocity profiles in smooth pipes [51]. The mean velocity profile for R = U r/ν = 4 × 103 to 3.2 × 106 is represented with close approximation by the power law:  y 1/n u = U δ

(5.22)

where n is as much higher as the Reynolds number is higher (n ∼ = 6 for R = 4 × 103 , 5 6 ∼ ∼ n = 7 for R = 10 , n = 10 for R = 3.2×10 ). The following year (1933), Nikuradse [52] carried out new measurements on rough pipes thanks to which he proved that, for the same value of the Reynolds number, the velocity gradient near the wall is as lower as the roughness is higher (n ∼ = 4 ÷ 5). In 1934, Prandtl and Schlichting [53, 54] generalised the results obtained by Nikuradse for rough pipes [52], analysing the formation of a turbulent boundary layer near the surface of a rough and thin flat plate, parallel to the flow direction; the results were provided in graphic format and were approximated by the relationship:   y 0.2  x δ 0 3 5 2 × 10 < (5.23) = 0.341 < 5 × 10 x x z0 where y0 is the roughness length of the wall, examined in more detail hereinafter. The resolution of the equations of motion in turbulent regime saw a turning point between 1925 and 1926, when Prandtl [55, 56] formulated the mixing-length theory. He treated the simplified case of the flow inside pipes or channels, indicating the

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Fig. 5.12 Mixing length and momentum transport [36]

direction of the flow parallel to the solid wall as x and the perpendicular direction as y (Fig. 5.12). He then imposed that the mean velocity satisfied the u = u(y), v = w = 0 conditions, and expressed the Reynolds stresses (Eq. 5.8) as:    du  du (5.24) τt = ρl 2   dy dy where du/dy is the mean velocity gradient along y and l is the mixing length. Using the explanations provided by Prandtl in [55, 56] and in his subsequent works, this quantity “can be considered as the diameter of the fluid masses moving as a whole”, or “as the distance crossed by a fluid mass before it mixes with the adjacent masses” losing its identity, or as “something similar to the mean free path in the kinetic gas theory” (Sect. 3.8). With respect to the last definition, it must be noticed that the kinetic gas theory refers to the microscopic movement of molecules; the mixing length theory, conversely, regards the macroscopic movement of agglomerates of fluid particles. It is also worth noting that in Eq. (5.24), the Reynolds stresses related to turbulent fluctuations are concordant with the laminar shear stresses of a viscous nature (Eq. 3.10) and, therefore, are additive with respect to the latter. To prove this observation using an interpretation referable to Prandtl (Fig. 5.12), consider a fluid particle at the height y1 −l, provided with a mean velocity u(y1 −l). It moves to the new height y1 , where, by virtue of a v > 0 fluctuation, the u(y1 ) mean velocity exists. Since, on the average, the particle retains its momentum with no changes, by increasing u, always on the average, u  < 0. Then, u  v < 0. A similar interpretation clarifies the physical meaning of Eq. (5.24). Assuming u 1 = u(y1 ) − u(y1 − l) ≈ l(du/dy)1 , because of the momentum conservation, then |u  | = u 1 ≈ l(du/dy)1 . Generalising such position to the turbulence component v’, and therefore assuming |v | ≈ l(du/dy)1 , Eq. (5.24) derives.

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It is also worth noticing that, applying Eq. (5.24), the turbulent viscosity coefficient introduced by Boussinesq (Sect. 3.6) assumes the form:    du  (5.25) μT = ρl 2   dy from which it is possible to infer that, while according to Boussinesq μT is, like μ, a property of the fluid, according to Prandtl such parameter is a “local function” of the fluid [33]. On the other hand, Eq. (5.25), by also treating l as a property of the fluid, and then attributing it a constant value, would lead to the inconsistency μT = 0, where u is a relative minimum or maximum value (e.g. in the pipe centre). In 1930, Karman [57] provided the first expression of the mixing length l as a function of spatial co-ordinates, and then of the local properties of the flow. To achieve this result, he assumed that the turbulent fluctuations were similar at all the points of the field, i.e. they only differed through spatial and time scale factors, proposing this law:    du/dy    (5.26) l = κ 2 d u/dy 2  where κ ≈ 0.36–0.38 is a universal constant, subsequently called Karman constant. Replacing Eq. (5.26) into Eq. (5.24), the Reynolds stresses result to be: τt = ρκ2

|du/dy|3 (du/dy) (d2 u/dy 2 )2

(5.27)

from which τt depends on the shape of the mean velocity profile but does not depend on its intensity. In 1931, Betz [58] provided a magnificent interpretation of Eqs. (5.26) and (5.27). The expression of the mixing length as a function of the spatial co-ordinates of the flow field opened the doors to deducing the mean velocity profile once the properties of the turbulence are known. Such laws are called universal velocity distributions. Karman [57] started these studies by applying Eq. (5.27) to a duct with a constant pressure gradient in the flow direction x and obtained the law:  



r−y r−y 1 U −u = − ln 1 − + (5.28) v∗ κ r r where r is the pipe radius or the semi-height of the channel, u = U for y = r. Equation (5.28), nowadays known as the “velocity-defect-law”,9 has remarkable 9 Before

Karman, other authors obtained expressions of the “velocity-defect law” on empirical and experimental bases. Among them, it is worth noting to cite Henry Philibert Gaspard Darcy (1803–1858) (Recherches expérimentales relatives au mouvement de l’eau dans les tuyaux, 1857) and his assistant, Henry Emile Bazin (1829–1917) (Recherches hydrauliques, 1865).

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properties. Firstly, neither the roughness k nor the Reynolds number R explicitly appears. It also fails both at the duct centre, where the τt = 0 inconsistency for y = r remains, and close to the wall, where u tends to infinity for y tending to 0. Applying the results of Nikuradse’s experiments [51, 52], between 1932 and 1933 Prandtl [59, 60] assumed that near the wall, with the exception of a thin layer adhering to it, which he called laminar sub-layer, the mixing length was given by the relationship: l = κy

(5.29)

where κ ≈ 0.4 [51, 60]. Replacing Eq. (5.29) into Eq. (5.24), the Reynolds stresses result to be:  τt = ρκ2 y 2

du dy

2 (5.30)

Prandtl also supposed that the Reynolds stresses near the wall remained constant, i.e. τt = τ0 . He replaced such position in Eq. (5.30) and, integrating, expressed the mean velocity profile through the logarithmic law:   y u 1 v0 = ln (5.31) + v∗ κ y0 v∗ where v0 = u(y0 ), being y0 a suitable reference value of y. Imposing v0 = 0, y0 was named roughness length and Eq. (5.31) became:   y u 1 (5.32) = ln v∗ κ y0 which is nowadays known as the “law-of-the-wall”. Imposing y0 = r, instead, u = U and a new expression of the velocity-defect-law takes place:   r U −u 1 = ln (5.33) v∗ κ y Figure 5.13 compares Eq. (5.33) with Eq. (5.28). Equation (5.31) is the basis for the thorough and homogeneous development of the universal velocity distributions. Applying dimensional analysis, and, in particular, the π theorem:   v∗ y0 k v0 (5.34) =ϕ , v∗ ν y0

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Fig. 5.13 Universal velocity distribution in a duct [33]: (1) Prandtl’s Equation (5.33); (2) Karman’s Eq. (5.28)

Equation (5.34) highlights three possibilities: (1) when v0 /v∗ only depends on the Reynolds number v∗ y0 /ν, a smooth wall turbulent regime exists; (2) when v0 /v∗ only depends on the relative roughness k/y0 , a rough wall turbulent regime exists; (3) when v0 /v∗ depends on both the v∗ y0 /ν and k/y0 parameters, an intermediate turbulent regime exists. The smooth wall turbulent regime takes place if the wall rough spots are so low to remain within the laminar sub-layer, the thickness δ of which is given by the relationship δv∗ /ν = N∗ . In this case, within the turbulent core, Eq. (5.31) assumes the form10 : u 1  v∗ y  + bl = ln v∗ κ ν

(5.35)

while the mean velocity profile in the laminar sub-layer is linear: u v∗ y = v∗ ν

(5.36)

Applying the results by Nikuradse with smooth pipes [51], N∗ = 11.6, bl = 5.5. The rough wall turbulent regime takes place when the increase of the Reynolds number reduces the thickness δ of the laminar boundary sub-layer and the rough 10 The

fact that the exponent of the power law defined by Eq. (5.22) decreases as the Reynolds number increases leads to suppose the existence of an asymptotic profile to which u tends when viscous stresses become evanescent with respect to turbulent ones. Such profile is provided by Eq. (5.35) [33].

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Fig. 5.14 B = br coefficient (Eq. 5.37), as a function of kv∗ /ν [52]

spots stick out from the latter. In this case, δ tends to become proportional to k while, in the turbulent core, Eq. (5.31) assumes the form: u 1 y + br = ln v∗ κ k

(5.37)

where, applying Nikuradse’s results for rough pipes [52], br depends on the Reynolds number kv∗ /ν (Fig. 5.14); in the full roughness regime, br = 8.5. It is interesting to notice that Karman’s treatment [57] focused on the turbulent core of the flow, while Prandtl’s assessments [59, 60] concentrated on the flow portion closer to the wall. Izakson [61], in 1937, and Millikan [62], in 1939, independently proved, applying dimensional analysis without introducing any hypothesis on the mixing length, that the logarithmic profile is the direct consequence of the existence of an overlapping zone shared by the two domains. It is also worth noticing that the theory formulated by Prandtl and developed by other authors to assess the velocity of the flow in the boundary layer required the previous knowledge of the pressure at its top, which was unknown. Sydney Goldstein (1903–1989) [63] was the first to deal with this issue in 1930, laying the foundations to formulate the step-by-step solutions subsequently developed by Prandtl [64], Görtler [65] and Hartree [66] between 1938 and 1939. At the first step, the boundary layer is assumed to have infinitesimal thickness; the fluid is considered as inviscid, and Eq. (3.19) is solved by imposing ∂φ/∂n = 0, where φ is the velocity potential and n is the direction orthogonal to the wall; in this way, the distribution of the shear stress τ0 and of the pressure p are obtained, which reproduces D’Alembert’s paradox. At the second step, the boundary layer adjacent to the wall is considered, and Eq. (3.19) is solved again in the potential field, imposing that the fluid velocity

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297

Fig. 5.15 Strouhal number (solid line) and drag coefficient (dotted line) for fixed cylinders with circular cross-section [67]

at the boundary of such domain is the same one found at the top δ of the boundary layer; from there, a new distribution of the pressure p in the boundary layer is obtained. Afterwards, the shear stresses and the thickness of the boundary layer are assessed, repeating the analysis until a satisfying tolerance is achieved. The study of the vortex shedding from circular cross-section cylinders was developed in parallel. Between 1924 and 1925, Ernest Frederck Relf (1888–1970) and Simmons [67] and Dryden and Heald [68] studied the dependence of the Strouhal number on the Reynolds number for fixed cylinders (Fig. 5.15). In the sub-critical regime S = 0.19; in the critical regime S increased twofold; in the super-critical regime, the wake becomes aperiodic. In 1926, Arthur Fage (1890–1977) and Johansen [69] developed a research about the structure of the vortex wake. Ruedy [70], in 1935, and Landweber [71], in 1942, carried out measurements of the lift of cylinders due to vortex shedding. Landweber himself [71] and Spivak [72] performed pioneering experiments on sideby-side cylinders. In the meanwhile, in 1937, Gutsche [73], resuming the observations by Rayleigh, explained the sound of marine propellers in relation to resonant vortex shedding. In 1952, Gongwer [74] explained the sound of some struts of submarine crafts. In 1956, Karman identified the vortex wake as the cause of the vibrations of submarine periscopes and transmission lines. He also maintained that the collapse of the Tacoma Bridge (Sect. 9.1) was triggered by the resonant vortex shedding [6] (Sect. 9.7). In the same period (1954–1955), in the wake of the pioneering works by Kovasznay [75] and George David Birkhoff (1884–1944) [76, 77], Anatol Roshko (1923–2017) [78, 79] carried out studies on the flow regimes around bluff-bodies

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Fig. 5.16 Satellite image of the Jan Mayen Island

within a fluid in relative motion. Roshko, measuring the velocity and the spectral content, classified such regimes in accordance with the shape of the body, the Reynolds number and the surface roughness. It was the prelude to the publication of increasingly specialised papers [80, 81] and of the first state of the arts [82, 83] about this subject. In parallel, thanks to the evolution of atmospheric monitoring (Sect. 6.2), the Karman wake was observed on larger scales [84]. The Norwegian weather station in the Jan Mayen Arctic Island was the first to notice periodical changes in the atmospheric pressure that Heinz Helmut Lettau (1909–2005) [85], in 1939, attributed to horizontal vortices (Fig. 5.16). In 1949, Wehner [86] hypothesised that Mount Beerenberg, which towers over the island (2400 m), produced a Karman wake under suitable wind conditions. At the start of the 1960s, with the advent of satellites (Sect. 6.2), many similar phenomena were discovered; the most famous ones regard the Madeira and Guadalupe islands. The issue of a jet flow that, impinging on a flat wall perpendicular to its axis, radially spreads out at a right angle was first approached in 1956 by Glauert [87]. He recognised that this subject had never received attention and held as examples the vertical take-off of an aircraft or the water jet from a tap falling into a basin. He did not understand he was laying down a milestone in the study of the thunderstorm downbursts (Sect. 6.4), one of the major themes of modern wind engineering. Glauert developed the theory of the radial wall jet, both laminar and turbulent. He assumed the radial flow was restrained by the surface roughness and formulated the equations of the boundary layer to find a solution in which the velocity profile remained unchanged in the flow direction, as it happens for the atmospheric boundary layer (Sect. 6.7). For the laminar flow, he solved the problem in closed form. As regards to the turbulent flow, he approached the problem introducing the eddy viscosity through the Prandtl’s model [88]; he discovered that in this case the solution

5.1 Fluid Mechanics

299

coincided with the laminar one, but it was not consistent with Bakke’s experimental results [89]. He then went on to schematise the eddy viscosity through the Blasius’ model [48]; unlike the Prandtl’s one, the latter gave better results near the wall. Finally, he adopted a mixed procedure consisting in using Blasius’ eddy viscosity near the wall and Prandtl’s one away from it. In this way, he showed that the velocity profile near the wall depended on the radial distance from the jet centre and, slightly, on the Reynolds number. The changes provided by this model were so small they could not be detected by Bakke’s experiments [89].

5.2 Probability and Random Processes Under the enlightened direction of Pafnuty Lvovich Chebyshev (1821–1894), the School of Saint Petersburg (Sect. 3.4) produced eminent students: among them, Andrey Andreyevic Markov (1856–1922) e Aleksandr Mikhailovich Lyapunov (1857–1918) [90] stood out as the most remarkable. Markov, decorated with a gold medal by the University of Saint Petersburg in 1878 for the results obtained about differential equations, from 1880 started providing essential contributions to the number and probability theories. He demonstrated the limit theorem expressing the distribution of the sum of independent and dependent random variables. He generalised the demonstration of some of Chebyshev’s theorems, even though he remained bound to the use of the moments:

 mk = E X k =

∞ x k f X (x)dx

(5.38)

−∞

E[•] being the statistical mean operator and f X (x) the density function of the X random variable; in his treatments, Markov required that moments exist and are 2 2 finite for any order (Sur les racines de l’équation ex ∂ m e−x /∂ x m = 0, 1898). He also published The calculus of probabilities (1913), where he introduced sequences of random variables that are now called Markov chains or processes11 ; their application was used in the study of Brownian motions, diffusion theory and quantum mechanics. In 1892, Lyapunov published his fundamental work on the stability of motion in Russian; it was translated into French in 1907 [91], but received little attention until the 1940s, when it became a cornerstone of mechanics and dynamic systems. His first famous work on probability theory, Sur une proposition de la théorie des probabilités, published in 1900, removed Markov’s constraints on the use of moments. Starting from some pioneering intuitions of Laplace and Lagrange, Liapunov introduced the

Markov chain is defined as simple if the probability of the result of the (n + 1)-th experiment only depends on the result of the n-th experiment; if, conversely, it depends on the results of the previous k experiments, it is called a composite Markov chain of the k-th order.

11 A

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5 Scientific Progress and Its Impact on Wind

novel concept of a characteristic function defined as the mean value of the eiθX random variable:

φX (θ) = E e

iθX



∞ eiθx f X (x)dx

=

(5.39)

−∞

where the integral converges for all the θ values and for any f X (x) density function. Its use entails exceptional advantages: unlike moments, it exists for any random variable and is biunivocally linked to the density function through a pair of Fourier transforms and inverse transforms; the characteristic function of the sum of independent random variables is the product of the characteristic functions of each random variable; this allowed Lyapunov to demonstrate the central limit theorem in a more general way than Chebyshev and Markov. Lyapunov himself generalised this theorem in three 1901 essays, Nouvelle forme du théorème sur la limite de probabilité, Sur un théorème du calcul des probabilités and Une proposition générale du calcul des probabilités; it gave the cue for many works, published by Jarl Waldemar Lindeberg (1876–1932) [92], Sergei Natanovic Bernstein (1880–1968) [93] and William Feller (1906–1970) [94] between 1922 and 1935, which led to the modern enunciation of this theorem. Unfortunately, besides the just mentioned contributions to mathematics and physics, groundless applications of probability theory appeared in other sectors. The Russian Pavel Alekseevich Nekrasov (1853–1924), by way of example, published Probability theory (1896), in which he used the probability for political purposes, adducing pseudo-scientific explanations; it provoked the outrage of Markov, Lyapunov and other famous scientists. In 1914, the renowned mathematician Emile Borel (1871–1956) published Le hasard, in which he described the use of probability theory and mathematics in the biological, social and moral fields; many passages were unjustified and misleading [90]. This may be explained by the continuing lack of a clear and univocal definition of probability. The first decades of the twentieth century, thus, saw the emergence of a drive aimed at a new foundation of the discipline based on assumptions not open to questions or interpretations; this leads to the research for axiomatic grounds. Jules Henri Poincaré (1854–1912) anticipated this trend in Calcul des probabilités (1912), which became a reference text. On the other hand, it was increasingly clear that Laplace’s classic definition of probability (Sect. 3.4) was inadequate: referring to equipossible events is a tautology of equiprobable events; this excludes the application of the theory to other events and highlights the circular nature of this definition. The first attempt to provide an axiomatic basis to the probability theory was carried out by Bernstein. In 1917, he published An essay on the axiomatic foundations of probability theory, which represents the foundation deed of this new trend. It was developed by Bernstein himself in some works collected in a book, Probability theory, published in 1927. It grounded a theory based on three axioms [93]. The first axiom, of comparability of probabilities, postulates that “if a is a particular case of A in the strict sense, then P(a) < P(A); conversely, if for events a1 and A the inequality P(a1 ) < P(A) holds, then P(a1 ) < P(a), where a is a certain particular case of A in the

5.2 Probability and Random Processes

301

strict sense”. The second axiom, of incompatible (disjoint) events, postulates that “if it is known that A and A1 are incompatible, and, moreover, that B and B1 are also incompatible, while P(A) = P(B) and P(A1 ) = P(B1 ), then the probability of C, which consists in the occurrence of A or A1 , is equal to the probability of C 1 , consisting in the occurrence of B or B1 ”. The third axiom, of combination of events, postulates that “if a1 is a particular case of A1 , then P(a) = P(a1 ), if P(A) = P(A1 ) under given conditions, provided the probability acquired by a after A occurs is equal to the probability acquired by a1 after A1 occurred”. The strongest objections to the classic definition of probability came from Richard Edler von Mises (1883–1953), a German scientist who set his attention to whether probability was a mathematical discipline or a branch of science using appropriate methods. He leaned to the second interpretation and founded a new theory, the so-called frequentist one, based on the collective concept. According to Mises, a collective was a sequence of infinite measurements of similar observations, each one of which produces a result belonging to a given space; the probability exists if the collective exists. Starting from such assumptions, in 1930 Mises published Veroyatnost’i statistika, translated into English in 1939 [95], in which he formulated two axioms. Let m be the number of cases among the first n observations of a physical phenomenon, for which the outcome determined by the observations belongs to the subset S. The first axiom postulates that for n tending to infinity, the limit of the ratio m/n is equal to P(S); this limit exists for every proper subset S of R. The second axiom states that the limit of P(S) does not change for every sequence of measurements provided the outcome is not known in advance. In other terms, Mises acknowledged a strict correlation between frequency and probability; indeed, he defined probability as the limit of the frequency. Andrey Nikolaevich Kolmogorov (1903–1987), the founder of the Moscow probability school with Aleksandr Yakovlevich Khinchin (1894–1959), and a major figure in the atmospheric turbulence field (Sect. 6.6), challenged Mises’ hypotheses. He remarked that it would be necessary to perform an infinite number of experiments to affirm the existence of the limit. He also criticised Mises’ concept according to which probability was not a property of an event but a consequence of an experiment. He was likewise critical towards Bernstein: he contested that the numerical value of the probability was a derivation rather than a primitive entity. Accordingly, in 1933 Kolmogorov published Grundbegriffe der wahrscheinlichkeitsrechnung, a book translated into English in 1950 [96], in which he founded the modern axiomatic probability theory. It was based on five axioms [90]: (1) “if two random events A and B belong to the collection F, then events A or B (A∪ B or A+ B), A and B (A ∩ B), not A and not B (A ∩ B) are also contained in F; (2) F contains the set E and all its singletons; (3) to each set A in F is assigned a non-negative real number P(A). This number is called the probability of the event A; (4) P(E) equals 1; (5) if A and B have no elements in common, then P(A + B) = P(A) + P(B). Finally, in case of an infinite field F, an additional axiom was supplemented: (6) for a decreasing sequence of events A1 ⊃ A2 ⊃ A3 ⊃ . . . of F, the intersection of which is empty, the following statement holds: for n tending to infinite, then P(An ) = 0”.

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5 Scientific Progress and Its Impact on Wind

In this framework, probability theory entered a phase of progressive consolidation, attested by the publication of works aimed at setting the discipline in an increasingly general way [97, 98]. In parallel, various study fields destined to play key roles in modern wind science started their development: extreme value theory, principal component analysis, random processes and Monte Carlo method. The first researches about extreme values, with the exception of a reference to a 1709 writing by Nicolaus Bernoulli (1695–1726), dates back to the second half of the nineteenth century. They took their cue from the need to discard the unreliable values in the collections of the data obtained over repeated measurements; they found a fertile field of application with astronomers, which used them in the measurement of stars,12 and then almost exclusively applied to Gaussian distributions. In particular, in 1925, Leonard Henry Caleb Tippett (1902–1985) [99] calculated the distribution of the maximum value of a parent Gaussian population as a function of its size. Unfortunately, at that time it was not yet known that the Gaussian distribution, even though rich of simple and expressive properties, involved extreme value distributions that were among the most complex to assess; this caused huge difficulties that hindered the development of extreme value theory. Edward Lewis Dodd (1875–1943) [100] was the first to study the extreme values of a non-Gaussian population in 1923. In 1927, Maurice René Fréchet (1878–1973) [101], starting from a non-Gaussian population, introduced the novel concept of asymptotic distribution of the maximum value; his work was published on a “remote” journal and went almost unnoticed. The turning point took place in 1928, when Sir Ronald Aylmer Fisher (1890–1962) and Tippett [102] published a fundamental work on extreme values; besides Fréchet’s asymptote, they found two additional asymptotic distributions associated with different distributions of the parent population; they also demonstrated the reasons of the slowness with which the Gaussian distribution converged towards the asymptote, justifying the sterility of previous researches. Thanks to Fisher and Tippet, the type I, II and III asymptotic distributions assumed a form close to the current one. Let X be a random variable associated with a parent population; let Y be the maximum value of a sample of n elements of X. For n tending to infinity, the distribution function of Y tends tho the three possible asymptotic forms: FY (y) = exp{−exp[−α(y − u)]} (−∞ < y < ∞)    μ k FY (y) = exp − (y > 0) y    y k FY (y) = exp − (y < 0) η

(5.40) (5.41) (5.42)

where α > 0, μ > 0, η < 0, k > 0. 12 The paper by Benjamin Peirce (1809–1880), Criterion for the rejection of doubtful observations (1852), and the posthumous treatise by William Chauvenet (1820–1870), A manual of spherical and practical astronomy (1878), are especially significant.

5.2 Probability and Random Processes

303

In 1936, Mises [103] classified the parent distributions according to the asymptotic distribution deriving from them; he also formulated the conditions of validity of the three asymptotes. In 1943, Gnedenko [104] completed Mises’ demonstration, indicating the necessary and sufficient conditions for convergence. He proved that the distribution of Y tends to the first asymptotic form (Eq. 5.40, which Gnedenko called Nr. 3) when the parent population is unlimited (− ∞ < X < ∞) and the tail of its distribution, in the direction of the maximum value, is of the exponential type. The distribution of Y tends to the second asymptotic form (Eq. 5.41, called Nr. 1) when X is limited to positive values (0 < X < ∞) and the tail of its distribution, in the direction of the maximum value, follows a power law. The distribution of Y tends to the third asymptotic form (Eq. 5.42, called Nr. 2) when X is limited to negative values (− ∞ < X < 0) and the tail of its distribution, near zero, follows a power law. In 1948, Samuel Stanley Wilks (1906–1964) [105] published the fundamental work about order statistics, an inference method that would become widely used in the field of extreme values. The study of extreme value distributions achieved its full maturity in the 1950s. In 1953, the National Bureau of Standards [106] published the first calculation tables for maximum values. In 1954, Emil Julius Gumbel (1891–1966) [107], Johnson [108] and Ruy Aguiar da Silva Leme (1925–1997) [109] used extreme values in various engineering issues, especially structural safety. In 1955, Jenkinson [110] developed the generalised extreme value distribution, a function containing the three asymptotic distributions as particular cases:  1/k  (5.43) FY (y) = exp − 1 − αk(y − γ) For k tending to 0, Eq. (5.43) tends to the type I distribution (Eq. 5.40); for k < 0, it tends to the type II distribution (Eq. 5.41), provided y > (γ + 1/αk); for k > 0, it tends to the type III distribution (Eq. 5.42), provided y < (γ + 1/αk). Equation (5.43), published in a paper in the Norwegian language, remained practically unknown almost until the end of the twentieth century. In 1958, Gumbel published his famous book [111], one of the most known texts in all scientific sectors. It provided a clear and exhaustive description of the maximum value distributions. It generalised the Mises’ expressions of the asymptotic type II (Eq. 5.41) and III (Eq. 5.42) distributions, rewriting them in the modern form:    μ−ε k FY (y) = exp − (y > ε) (5.44) y−ε     w−y γ (y < w) (5.45) FY (y) = exp − w−η for any ε, being w > η, γ > 0.

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5 Scientific Progress and Its Impact on Wind

Gumbel, applying the symmetry law, also obtained, for every asymptotic form of the maximum value Y, the corresponding distribution of the minimum value Z. They are: FZ (z) = 1 − exp{−exp[α(z − u)]} (−∞ < z < +∞)    μ−ε k FZ (z) = 1 − exp − (z < ε) z−ε     z−ε γ (z > ε) FZ (z) = 1 − exp − η−ε

(5.46) (5.47) (5.48)

where μ < ε, η > ε. Gumbel also obtained the transformation laws among different distributions. He showed the use of order statistics and probability papers to estimate model parameters. He noticed that the type I, II and III asymptotic distributions were the most important but not the sole ones; other asymptotes may also exist for specific parent distributions. He developed countless examples applied to every branch of engineering. The origin and development of the Weibull distribution deserve an independent mention. It is provided by the expression:   γ  x (x ≥ 0) FX (x) = 1 − exp − η

(5.49)

being η, γ > 0; Eq. (5.49) coincides with Eq. (5.48) for X = Z and ε = 0. It was already implicit in the formulations of Fréchet [101], of Fisher and Tippett [102] and of Gnedenko [104]; it indeed belonged to the class of extreme distributions, in particular of the minimum distribution of the type III. Its practical application, however, dates back to 1933, when Paul Rosin (1890–1967) and Erich Rammler (1901–1986) obtained it in relation to the grinding and pulverisation of solid materials [112]. In 1939, Ernst Hjalmar Waloddi Weibull (1887–1979) independently published two papers on the breakage of solids where he obtained the distribution function in Eq. (5.49) [113] and its statistical moments [114]. A turning point took place in 1951, when Weibull himself wrote a paper in which he pointed out the extent of its application field [115]. In 1958, Gumbel [111] used for the first Eq. (5.49) to represent the mean wind speed distribution at ground level (Sect. 6.8). Principal component analysis (PCA) is one of the most well-known and widespread probabilistic methods. Born around the end of the nineteenth century, it links its development, in the first part of the twentieth century, to two other techniques joined with it under the conceptual and mathematical aspect [116]: singular value decomposition (SVD) and factor analysis (FA). In simplified and reductive terms, SVD consists in expressing a n × p rectangular matrix V as: V = AB∗

(5.50)

5.2 Probability and Random Processes

305

where * denotes the conjugate transpose matrix, A is the n × n unit matrix of the left singular vectors, i.e. the eigenvectors of VV* , B is the p × p unit matrix of the right singular vectors, i.e. the eigenvectors of V* V,  is the p × n pseudo-diagonal matrix of the singular values, namely the square roots of the eigenvalues of both VV* and V* V. Due to these properties, SVD is a fundamental method to solve undetermined and impossible linear systems of equations, providing the minimum mean square error. Through PCA, an n-variate random vector v is expanded into the series of normal vectors: v=

n 

φk x k

(5.51)

k=1

where φk is the k-th eigenvector of the covariance matrix Cv of v, x k (k = 1,… n) are uncorrelated random coefficients; they are referred to as the principal components of v, and enjoy the property that their variances are the eigenvalues of Cv . Ordering the principal co-ordinates in the sense of decreasing variances, it is often possible to obtain an accurate representation of v by truncating the series in Eq. (5.51) after the first few terms. The link between PCA and SVD is apparent when considering V as a matrix whose p columns collect the observations of the random vector v and Cv = VV∗ / p; in this case, unless p, A and  are the matrices of the eigenvectors and of the eigenvalues of Cv , respectively. FA is a method by which an n-variate random vector v can be expanded as: v=

n 

ψk yk + e

(5.52)

k=1

where n ≤ n, ψk is a vector referred to as the k-th factor loading, yk (k = 1, . . . n) are the weighting coefficients referred to as common factors, e is a vector of residual errors referred to as specific loads. Likewise PCA, also FA achieves the dimensional reduction of a random vector; however, while PCA pursues this aim through operations on intrinsic properties of the random vector, its covariance matrix, FA implies the formulation of suitable models for factor loadings, common factors and specific loads. Between 1873 and 1874, Eugenio Beltrami (1836–1900) [117] and Marie Camille Ennemond Jordan (1838–1922) [118] independently carried out the SVD of a square matrix. In 1889, James Joseph Sylvester (1814–1897) [119] applied SVD to a square matrix, carrying out an algebra exercise in which PCA implicitly appeared. Between 1907 and 1915, Erhard Schmidt (1876–1959) [120], Hermann Weyl (1885–1955) [121] and Leon Autonne (1859–1917) [122] developed the first theorems about SVD. In 1934, Carl Henry Eckart (1902–1973) [123] used SVD to diagonalise the quadratic forms of the kinetic and potential energy of molecular systems, decoupling the natural shapes of the motion. A few years later, in the field of psychometrics, Eckart and Young [124, 125] proposed the modern form of the SVD of a rectangular matrix.

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5 Scientific Progress and Its Impact on Wind

It is generally acknowledged that PCA was introduced by Karl Pearson (1857–1936) [126] in 1901 in the biological field; he obtained the lines and planes that better approximate a set of points in an n-dimensional space, providing a geometrical interpretation of such technique. It is likewise generally accepted that FA was introduced by Charles Spearman (1863–1945) [127] in 1904, in the psychological and psychometrical field. In the same field, Harold Hotelling (1895–1973) [128] published, in 1933, the fundamental work on PCA, deriving it as a particular case of FA. Starting from a set of correlated variables, he found a reduced set of uncorrelated variables that effectively reproduced the starting set; with such goal, he identified Spearman’s common factors with principal co-ordinates, selecting these quantities to maximise their contribution to the overall variance of the original variables. In 1936, Hotelling [129] and Girschick [130] developed PCA independently from FA; they also highlighted the focal role of SVD as the basic technique to determine the principal co-ordinates. Two circumstances are worth highlighting. The first one regards the lack of balance between the development and divulgation of PCA, FA and SVD and their limited application to technical and complex cases, which became a standard practice from the 1950s, especially in meteorology (Sect. 6.3) [116], thanks to the advent of electronic computers (Sect. 5.3). The second circumstance regards the fact that, in all the above-mentioned studies, the realisations were independent occurrences of random vectors; extending the horizon to the measurement of physical phenomena carried out at a series of points in space at different times they were actually correlated. Their treatment, then, will only be made possible by the development of the theory of processes and by the evolution of principal component analysis into Proper Orthogonal Decomposition (discussed later in this paragraph). The study of the random processes started between the late nineteenth century and the early twentieth century, thanks to two works by Sir Arthur Schuster (1851–1934) [131, 132] concerning the periodicity of meteorological phenomena. He expressed the X(t) random process as: X (t) = X (t) + X  (t)

(5.53)

where X (t) is the slowly varying mean value of X(t) and X  (t) is the residual nil mean fluctuation of X(t) around X (t). Schuster expressed X (t) as a linear combination of q harmonic functions: X (t) =

q 

A j cos(ω j t + ϕ j )

(5.54)

j=1

where ωj and ϕj , respectively, are the circular frequency and phase of the j-th harmonic; the ωj values are assessed through a method, subsequently called of “hidden periodicity”, based on the analysis of a function called “periodogram”. As regards to X  (t), Schuster considered it a Gaussian white noise.

5.2 Probability and Random Processes

307

In 1921, Sir Geoffrey Ingram Taylor (1886–1975) [133] laid the foundations of the statistical theory of turbulence (Sect. 6.6). To this end, he introduced various principles of the theory of processes, first among all the definition of the autocorrelation function of the stationary processes: R(τ) = E[X (t)X (t + τ)]

(5.55)

where τ is the time lag. Taylor also formulated many theorems about the properties of this function: it is even, it identifies itself with the mean quadratic value for τ = 0, it tends to the square of the mean value for τ tending to plus or minus infinity. In 1927, George Udny Yule (1871–1951) [134] gave a new contribution to the theory of processes. He discretized time t and expressed the value of X at t as a linear combination of its previous m values: X t = a1 X t−1 + . . . + am X t−m + ηt

(5.56)

being ηt a sequence of identically distributed non-correlated normal random variables (i.e. a white noise). In the future, a process expressed through Eq. (5.56) will be defined as an autoregressive one of m order and indicated by means of the AR(m) acronym. In 1937, Evgeny Evgenievich Slutsky (1880–1948) [135] gave a new contribution to random processes, expressing X t as the linear combination of a sequence of identically distributed, uncorrelated normal random variables: X t = b0 ηt + b1 ηt−1 + . . . + bn ηt−n

(5.57)

In the future, a process expressed through Eq. (5.57) will be defined as a moving average one with order n and indicated by means of the MA(n) acronym. In 1938, Herman Ole Andreas Wold (1908–1992) [136] proved that autoregressive and moving average methods represent particular cases of a general framework dealing with stationary type random processes in their broadest meaning. Thanks to this vision, the statistical study of time series became an integral part of probability theory. It was the prelude to the joint use of the AR and MA methods that, especially since the 1970s, will originate the ARMA methods and their derivatives, destined to play a central role in the forecasting, control and simulation of random series [137]. In the same period, Norbert Wiener (1894–1964) and Khinchin made fundamental contributions to the harmonic analysis of stationary functions and processes. At that time, it was known that, under extremely general conditions, a periodic function can be expressed in a Fourier series as a linear combination of infinite sinusoidal and cosinusoidal functions. Using the complex notation, such series assumes the form: x(t) =

∞  k=−∞

Ak eiωk t

(5.58)

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5 Scientific Progress and Its Impact on Wind

in which ωk = 2πk/T (k = 0, ±1, ±2, . . .), being T the period of x(t). Under likewise general conditions, a non-periodic but absolutely integrable function can be expressed through the Fourier integral: ∞ x(t) =

p(ω)eiωt dω

(5.59)

−∞

where p(ω) is the Fourier transform of x(t). The Ak coefficients and the p(ω) function provide, in the two cases, an exhaustive representation of the harmonic content of x(t). In 1930, Wiener [138] noted that the sample functions of stationary processes can be expressed neither by Eq. (5.58) nor by Eq. (5.59): they are not periodic in general and doubtless, they are absolutely not integrable. In other words, Fourier analysis lost its meaning in the most important case of the theory of processes. On such ground, Wiener developed the “generalised harmonic analysis”, through which it is possible to express any function as: ∞ x(t) =

eiωt dP(ω)

(5.60)

−∞

where P(ω) is the Fourier-Stieltjes transform,13 or generalised Fourier transform, of x(t). It includes, as particular cases, the Fourier series (for periodical functions, dP(ω) = Ak for ω = ωk , otherwise 0), and the Fourier integral (for non-periodical, but absolutely integrable functions, dP(ω) = p(ω) dω). It also provides an harmonic synthesis of all the functions that cannot be traced back to these two cases. In 1934, applying Wiener’s generalised harmonic analysis to stationary processes, Khinchin [139] provided a fundamental enunciation, nowadays known as the WienerKhinchin’s theorem. Thanks to it, the autocorrelation function is expressed by the following relationship: ∞ R(τ) =

eiωτ dF(ω)

(5.61)

−∞

where F(ω) is a real function, defined as power spectral distribution, which possesses the properties of the distribution functions.14 In the most typical case in which F(ω) is 13 Thomas Joannes Stieltjes (1856–1894) was a Dutch mathematician known for his studies about integrals. 14 Using Lebesgue’s decomposition theorem, any distribution function may be written as F(x) = a1 F1 (x) + a2 F2 (x) + a3 F3 (x), being ai ≥ 0 (i = 1, 2, 3), a1 + a2 + a3 = 1; F 1 is an absolutely continuous function (anywhere continuous and differentiable for almost any x), F 2 is a step function with a finite or infinitely enumerable number of steps, F 3 is a singular function (continuous, with a null derivative almost everywhere). In case of probability distributions, F 1 and F 2 respectively

5.2 Probability and Random Processes

309

absolutely integrable, then dF(ω) = S(ω)dω, being S(ω) the power spectral density; it is linked with the autocorrelation function through a pair of Fourier and inverse Fourier transforms: ∞ R(τ) =

S(ω)eiωτ dω

(5.62a)

−∞

1 S(ω) = 2π

∞

R(τ)e−iωτ dτ

(5.62b)

−∞

which represent the classic (simplified) form of the Wiener-Khinchin theorem. In 1938, Taylor [140] obtained the same expressions, independently from Khinchin, within the statistical theory of turbulence (Sect. 6.6). A new contribution to stationary processes was provided by Wiener [141] in 1949. Among many other developments, the 1940s saw the discovery of two formulations destined to play a key role in wind engineering: the Karhunen and Loeve series and the threshold crossing theory. Proper orthogonal decomposition (POD) generalised PCA from random vectors with independent realisations to random processes with a given correlation structure. It appeared between 1943 and 1947 thanks to four apparently independent contributions provided by Damodar Dharmananda Kosambi (1907–1966) [142], Michel Loève (1907–1979) [143], Karhunen [144], Marek Kac (1914–1984) and Arnold John Frederick Siegert (1911–1995) [145]. Loève designated this technique Karhunen-Loève series expansion in a book he published in 1955 [146], which contributed to spread its knowledge.   In its original form, let X(t) be a nil mean random process and  t, t  its covariance function; let also  λk and ψk (t) (k = 1, 2,…) be the eigenvalues and the eigenfunctions of  t, t  , provided by the solution of the Fredholm integral equation15 of the second type:  (t, t  )ψk (t  )dt  = λk ψk (t) (5.63) D

where D is the time domain of the X(t) process. It can be expressed by means of the following series:

correspond to continuous and discrete random variables. In the case of power spectral distributions, F 1 and F 2 respectively refer to continuous and discrete harmonic contents. In both cases, F 3 corresponds to pathological conditions that are unlikely to be present in real problems. 15 Erik Ivar Fredholm (1866–1927) was a Swedish mathematician known for his contributions to integral equations. Equation (5.63) was discussed in a paper, Sur une classe d’equations fonctionnelles, which appeared on Acta Mathematica in 1903.

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5 Scientific Progress and Its Impact on Wind

X (t) =

∞ 

λk ξk ψk (t)

(5.64)

k=1

where ψk (t) are deterministic shapes, called process modes; ξk are uncorrelated random variables (with nil mean and unit variance). In the late 1960s, John Leask Lumley (1930–2015) [147] will generalise such treatment to multi-variate and/or multi-dimensional processes [148], entrusting POD with a focal role in turbulence and aerodynamics first, then in most engineering sectors [116]. The threshold crossing theory originated between 1944 and 1945 from Stephen Oswald Rice (1907–1986) [149, 150]. He considered a nil mean stationary process X(t) and evaluated the mean number of up-crossings of the ζ threshold per unit time. He proved that such value is given by: ∞ x˙ f XX˙ (ζ, x)d ˙ x˙

ν(ζ) =

(5.65)

0

where f XX˙ (x, x) ˙ is the joint density function of X (t) and of its X˙ (t) prime derivative. If the process is a Gaussian one, Eq. (5.65) is integrable in closed form and results:   ζ2 ν(ζ) = ν0 exp − 2 2σX

(5.66)

where v0 is the expected frequency of the process: ν0 =

1 σX˙ 2π σX

(5.67)

being σX and σX˙ , respectively, the standard deviations of X (t) and X˙ (t). In the same papers [149, 150], working on a 1877 contribution by Rayleigh [151], Rice expressed the x(t) sample function of the X(t) stationary process through the relationship: x(t) =

N  √  2 S(ωk )ω cos(ωk t + ϕk )

(5.68)

k=1

where ω is the circular frequency, discretized in a series of values ωk (k = 1, 2, … N) with step ω, ωk = ωk + δωk ; δωk and ϕk , respectively, are uniformly distributed harmonic intervals and random phases. It is the embryo of the Monte Carlo methods formulated since the 1970s to simulate random processes (Sect. 11.1). The threshold crossing theory was developed in the early 1950s, especially by Siegert [152, 153]. Cartwright and Longuet-Higgins [154] used it in 1956 to obtain the first distribution of the Xˆ maximum value of a X(t) stationary process. They demonstrated that such distribution only depends on two quantities: the σX standard

5.2 Probability and Random Processes

311

deviation of the process and a ε parameter indicating the amplitude of its spectral content:  ε=

m 0 m 4 − m 22 m0m4

(5.69)

where: ∞ mk =

n k E(n)dn (k = 0, 2, 4)

(5.70)

0

E(n) being the power spectrum (called energy spectrum by Cartwright and LonguetHiggins) of the process, as a function of the frequency n = ω/2π, m 0 = σX2 . When ε tends to zero, i.e. the power spectrum is a narrow band one, the distribution function of Xˆ assumes the form proposed by Rayleigh [155] in 1880: 

xˆ 2 FXˆ (x) ˆ = 1 − exp − 2 2σX

 (xˆ ≥ 0)

(5.71)

When, conversely, ε tends to 1, it tends to the Gaussian distribution. It was the prelude to a new genre of studies that gained ground in the 1960s and especially in the 1970s. With the advent of the 1950s, process theory entered its mature age, as witnessed by many books of a general nature [156–160] and by the first states of the art papers [161]. This progress was characterised by the plurality and diversity of the disciplines that, recognising the strategic role of process theory, gave their contribution to it from various viewpoints. The most prominent include electric engineering and the theory of servo-mechanisms [156], automatic control [158], telecommunication theory [160], fatigue analysis under random load cycles [162, 163] and random dynamics, a topic first used in the aeronautic sector (Sect. 7.4), then in the structural one (Sect. 9.6). Another worth mentioning genre saw the light in the late 1950s: the harmonic analysis of digital signals [164, 165]. Waiting for the developments that would mature from 1965 with the introduction of the Fast Fourier Transform (FFT) [166], it had immediate consequences in the analysis and interpretation of atmospheric turbulence (Sect. 6.6). Monte Carlo methods, i.e. the procedures based on the artificial generation of long sequences of random numbers, were first used by Georges-Louis Leclerc Buffon (1707–1788) in 1777 (Sect. 3.4). In 1927, Tippett [167] published a table with 41,600 random numbers obtained from demographic data. In 1939, Maurice George Kendall

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(1907–1983) and Babington-Smith [168] used a mechanical machine to produce a table with 100,000 random numbers.16 The term “Monte Carlo” dates back to 1944 and is associated with the roulette considered as a tool to generate random numbers. It was introduced by John von Neumann (1903–1957) (Sects. 5.3 and 6.3) and Stanislaw Marcin Ulam (1909–1984), members of the Manhattan Project Team at the Los Alamos Scientific Laboratory in New Mexico, as a coded word associated with the studies about the diffusion of neutrons for the development of the atomic bomb (Sect. 5.3). In 1946, Neumann suggested the “Middle-Square Method”, one of the first methods for the computational generation of random numbers; it was based on the calculation of the square root of a random number and on the extraction of its centre digits to obtain the subsequent number, but it met with little success. In 1948, Derrick Henry Lehmer (1905–1991) proposed the “Linear Congruential Generators”, the basic method from which most modern procedures were derived. In 1951, Neumann published the first state of the art on the artificial generation of random numbers [169], highlighting the paradox of using a computer, a deterministic machine, to generate sequences of random numbers: “Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin. (…) There is no such thing as a random number. There are only methods to produce random numbers.” It was the prelude to an increasingly vast and varied literature that gained ground since the 1960s. The joint use of process theory and Monte Carlo methods, which became commonplace in the 1970s, represents the foundations of new methods for simulating random fields, destined to play a key role in the treatment of atmospheric turbulence, aerodynamic wind actions and structural response.

5.3 The Advent of the Electronic Computer Taking up the narration of the evolution of computers, interrupted in Sect. 3.3 at the end of the nineteenth century, it is inevitable to mention, even though briefly, an outstanding figure whose life straddled the nineteenth and twentieth centuries, Nikola Tesla (1856–1943). A physicist, inventor and engineer, Serbian by birth and then naturalised as an American citizen, he is known for his revolutionary contributions in electromagnetism, wireless transmission, theoretical and nuclear physics, robotics and information technology. In the latter sector, he introduced the “gate” or “switch” concept, patented in 1903; it would play a key role in the future evolution of calculation tools. His admirers define Tesla as “the man who invented the twentieth century”. His denigrators portray him as a sort of “mad scientist”. This was the last time, at least for a while, it was possible to write about automatic computation without pairing its evolution and use with warfare reasons. From this 16 In the 1950s, RAND Corporation produced a table with 1,000,000 random numbers. After the correction of an error, the table was published in 1955.

5.3 The Advent of the Electronic Computer

313

moment, they represent the focal element of a development destined to lead to the electronic computer in the course of the Second World War [170–174]. The figures providing contributions to this epic, now mentioned as the founding fathers of computer sciences, in their time had often to deal with dramatic choices and decisions. Vannevar Bush (1890–1974) was an American engineer whose renown is connected to the atomic bomb, to the idea of “memex”, the concept anticipating the current international Web, and to the implementation of analogue computers. Bush first sought the analytical solutions of the differential equations governing the electric power distribution networks. The difficulty of such problem convinced him that it would have been more profitable to devote his efforts to the implementation of equipment capable of simulating the problem subjected to examination and of providing approximate solutions. For such purposes, he built seven analogue computers, the most famous of which was the mechanical differential analyser installed at the MIT in 1925. This machine, based on the ideas expressed by Charles Babbage (1792–1871) a century before (Sect. 3.3), solved differential equations with up to 18 independent variables. It would then be produced in many models, used during the Second World War to calculate the ballistic trajectories of projectiles. Konrad Zuse (1910–1995), an aeronautic engineer considered by many as the inventor of modern computers, started his career as an aircraft designer (Sect. 7.4), taking advantage of the development of the German Air Force associated with the advent of Nazism. He soon became interested in computer sciences, so as to be able to quickly and effortlessly carry out the computations required by his projects. With this goal in mind, in 1936 he designed a fast and versatile machine, Z1 (Fig. 5.17a), completed in 1938. Its structure was similar to that of modern computers: it was programmable and was equipped with memory units and an autonomous computation unit; instructions were introduced by means of a punched celluloid tape similar to a movie film, which was also used to write the computer replies. Moreover, it made use of an original system of mechanical memories consisting of levers and notches driven by an electric motor, which made it resemble a large phone exchange. During the Second World War Zuse also used relays, initially for the computation units of a new machine, Z2 (1938–1939), and then for all the components of his last project, Z3. The latter, completed in 1941 (Fig. 5.17b) was the first computer managed through a program. Memory capacity was equal to 64 words, each one of them consisting of 22 bits; the program was recorded on a punched tape; the machine was equipped with 2600 relays; a multiplication required 3–5 s. Claude Elwood Shannon (1916–2001) was an American engineer and mathematician considered the father of communication theory. In his master thesis, Symbolic analysis of relay and switching circuits (1938), he proved that the flow of an electric signal through a network of “on” or “off” switches followed the same rules applicable to the “true” and “false” symbolic values of the Boolean algebra; he thus demonstrated it was possible to design circuits for processing any operation; he also laid the theoretical foundations of the digital information coding and transmission system. During his doctorate thesis, An algebra for theoretical genetics (1940), Shannon collaborated with Vannevar Bush at the implementation of a differential analyser. In 1948, he published A mathematical theory of communication where he dealt with the

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5 Scientific Progress and Its Impact on Wind

Fig. 5.17 a Z1 (1938); b Z3 (1941)

issue of reconstructing the information transmitted by a sender; during this research he coined the term “bit” to indicate the elementary unit of information. The following year he demonstrated the sampling theorem,17 through which he studied the representation of a continuous (analogue) signal by means of a discrete set of samples taken at regular intervals (digitalisation). Alan Mathison Turing (1912–1954) was a British mathematician and logician, considered one of the fathers of computer sciences. In 1936, he published On computable number, with an application to the Entscheidungsproblem, where he described an ideal mechanism and a calculation model now known as the Turing machine. During the Second World War, he placed his mathematical capabilities at the service of the English Communication Department to decipher the coded German communications, encrypted by means of the Enigma system designed by Arthur Scherbius (1878–1929). In particular, he resumed the studies carried out by the Polish Cipher Office that in 1938 led to the construction of Bomb (Fig. 5.18a), a calculating machine first used by the Polish counter-espionage and by the English one to decipher the German secret messages. In 1942 Turing, making use of such experiences, built Colossus (Fig. 5.18b), a precursor of computers able to quickly and efficiently decipher Nazi codes. In 1950, he wrote Computing machinery and intelligence, where he proposed a criterion to assess the capability of a machine to show intelligence; it is now known as the Turing test and represents a cornerstone for the future studies on artificial intelligence. In 1937, George Robert Stibitz (1904–1995), a Bell Telephone researcher, used rejected relays, electric bulbs and tin boxes to build, in the kitchen of his home, an electromechanical adding machine he called Model K (“kitchen”). The following 17 Starting from the researches carried out by Harry Nyquist (1889–1976) about the transmission of information (Certain topics in telegraph transmission theory, 1928), in 1949 Shannon formulated the modern version of the sampling theorem (Communication in the presence of noise). It, now known as the Nyquist-Shannon’s theorem, defines the sampling frequency of a signal to avoid distortion. Given a f (t) signal with finite band amplitude (with an harmonic content limited by the ns frequency), and being known the minimum signal sampling frequency (n = 1/ t, being t the sampling time), it must be at least equal to twice the maximum frequency of the signal (n ≥ 2ns ).

5.3 The Advent of the Electronic Computer

315

Fig. 5.18 a Reconstruction of Bomb (1938); b Colossus (1942)

Fig. 5.19 Harvard Mark I (1943) [174]

year, Bell Telephone gave him the job of building a relay calculator able of performing arithmetic calculations on complex numbers. Stibitz’s machine (Complex Number Calculator, subsequently called Model I Relay Calculator), completed in 1940, consisted of 3000 relays, connected through 800 km of electric connections. The calculation program was read from a punched paper tape, data introduction took place through a keyboard or punched cards and the machine was controlled by means of teleprinters connected to phone lines. In the same years, at the Harvard University, the mathematician Howard Hathaway Aiken (1900–1973) designed a calculator that solved any mathematical problem, especially differential equations. Supported by Thomas John Watson (1874–1956), general manager of IBM, in 1943 he built Automatic Sequence-Controlled Calculator Mark I (ASCC, later known as Harvard Mark I) (Fig. 5.19), an electromechanical programmable calculator based on the use of batteries of relays, 20 m long and weighing 5 ton. Almost simultaneously, between 1939 and 1943, John Vincent Atanasoff (1903–1995) and Clifford Berry (1918–1963) created, at the Iowa University, the first binary electronic computer, Atanasoff Berry Computer (ABC), for the solution

316

5 Scientific Progress and Its Impact on Wind

of systems of linear equations. It consisted of modules capable of performing additions or subtractions on binary numbers, using electron tubes instead of relays. The memory consisted of capacitors fitted on two revolving cylinders, which memorised “0” when discharged or “1” when charged. It carried out one addition per second. The input and output used cards, with burned rather than punched holes, manufactured by IBM. It was the prelude to the implementation of the first complete electronic system adaptable to any mathematical problem. In 1938, John William Mauchly (1907–1980), a physicist devoted to statistical studies in meteorology at the Carnegie Institute in Washington, designed a faster computer. Like Atanasoff, Mauchly opted for electronic switching, building a “harmonic analyser” he presented at the annual conference of the American Association for the Advancement of Science in 1940. In that same year, Mauchly became a teacher at the Moore School in Philadelphia. Here, he met an engineer, John Adam Presper Eckert (1919–1995), and jointly wrote The use of vacuum tube device in calculating, which aroused the interest of the Army General Staff and of the Ballistic Research Laboratory. In 1942, this laboratory gave Mauchly and Eckert the task of building an “electronic differential analyser” intended to increase the speed of calculation for projectile trajectories, which was completed between 1944 and 1945. ENIAC (Electronic Numeric Integrator And Calculator) was born.18 It was a 30-ton monster that occupied an area of 200 m2 and made use of 17,648 electronic tubes, which dissipated a power of 150,000 W (Fig. 5.20a). It carried out 5000 additions and 333 multiplications per second and read data through punched cards; the program was fed into the computer by a connection panel. Even before ENIAC was operational, in 1944 Mauchly and Eckert proposed to build another computer, (EDVAC) Electronic Discrete Variable Automatic Computer, the design of which envisaged several improvements compared to the architecture of ENIAC. Like ENIAC, EDVAC was developed at the Moore School of Electrical Engineering of the University of Pennsylvania, on behalf of the U.S. Army Ballistics Research Laboratory. It involved a formidable consultant, John von Neumann (1903–1957). Neumann, a Hungarian mathematician naturalised as an American citizen, is one of the most prominent scientific personalities of the twentieth century19 ; his contri18 ENIAC was presented to the press on 14 February 1946, creating sensation: the neon lamps indicating the status of the computation units were covered with ping-pong balls cut in half and turned on and off creating suggestive lighting effects. The term “electronic brain” came into existence with ENIAC. It was definitively turned off at 11:45 on 2 October 1955. 19 John von Neumann, Leo Szilard (1898–1964), Edward Teller (1908–2003) and Eugene Wigner (1902–1995), formed the so-called Hungarian clan, the core of the group that developed the atomic bomb Manhattan Project in Los Alamos. Besides being Hungarian, they also shared the same Jewish origins and the need to seek refuge from Nazi persecution in the U.S. It is said that Enrico Fermi (1901–1954), one of the prominent figures of the Manhattan Project, was sceptical about the existence of extra-terrestrial beings; one day Szilard told him: “they are already here, and you call them Hungarians”. Neumann came from a different planet. When he was 10, he fluently spoke four languages. During the gymnasium he was flanked by a university tutor who followed him with mathematics. At the age of 22 he graduated in chemical engineering in Zurich and in mathematics in Budapest, associating with Karman, Einstein and David Hilbert (1862–1943). In Los Alamos,

5.3 The Advent of the Electronic Computer

317

Fig. 5.20 a ENIAC (1945); b EDVAC (1949) [174]

butions ranged over set theory, functional analysis, topology, statistical mechanics, quantum physics, economy, biological evolution, cybernetics, information technology, games theory, artificial intelligence, fluid dynamics, meteorology, ballistic missiles and atomic bomb. In 1944, while studying turbulence and its nonlinear differential equations, he made the acquaintance of Aiken and Stibitz and of their Harvard Mark I machine. At the same time, he made the acquaintance of Mauchy and Eckert and became aware of their attempt to build a machine capable of performing 300 operations per second. Neumann, intrigued by this prospect and encouraged by Carl Gustaf Arvid Rossby (1898–1957), appreciated, among the other potential uses of the computer, the possibility of being able to solve complex applied mathematics problems and, above all, the problem of weather forecasts (Sect. 6.3). Even though he was interested in Harvard Mark I and ENIAC, Neumann perceived that these behemoths were quite limited, almost completely lacking memory and flexibility; they were, in other words, “dumb” machines. He then joined the design team of EDVAC and wrote a revolutionary document, First draft of a report on the EDVAC (1945), which represents the foundation of the so-called von Neumann’s architecture. It established that an electronic computer was programmable only if the program was neither rigidly allocated in the hardware, nor sequentially read from punched tapes; instead, it has to reside in a quick-access memory, called software, together with the data to process and the constants. the challenges among Richard Feynman (1918–1988), Fermi and Neumann on the most complex mathematical problems were famous: the first used a mechanical calculator, the second wrote on paper scraps, the third solved them in his mind.

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Thanks to Neumann’s intuitions, the design of EDVAC entered a new dimension. It was a binary computer capable of performing additions, subtractions, multiplications and divisions; it had instructions to control the program flow; its memory consisted of 1000 44-bit words (then upgraded to 1024 words). Physically, it consisted of: (1) a magnetic tape for data reading/writing; (2) a control unit with an oscilloscope; (3) a management unit that received the instructions from the control unit and from the memory and directed them to other units; (4) a unit that performed the logic arithmetic operations on two operands and transmitted the result to the memory after its correctness was verified by a duplicated unit; (5) a timer; (6) a dual memory unit consisting of two sets of 64 elements of mercury acoustic lines, with a capacity equal to eight words per line; (7) three temporary tanks each holding a single word. EDVAC was completed in 1949 and consisted of over 6000 electronic tubes and 12,000 diodes; it consumed 56 kW of electric power, occupied an area equal to 45.5 m2 and weighed 7850 kg (Fig. 5.20b); it performed an addition in 864 μs and a multiplication in 2900 μs. The modern age of electronic computer had begun. From then on, the evolution of computers took on a frenetic pace, characterised by a progression factor (size, capabilities and computing speed) with a magnitude of ten every five years. Limiting this description to few important moments, in 1948 Wallace Eckert (1902–1971) completed (SSEC) Selective Sequence Electronic Calculator, the first IBM computer: it was a hybrid machine with a vacuum tube logic unit and a relay memory; part of the program was in the memory and the rest was configurable from the control panel. In the same year, Maxwell Newman (1897–1984) and Freddie Calland Williams (1911–1977), at the University of Manchester, UK, built Manchester Mark I, which many consider as the first true computer; the programs, in a fully digital form, were entered by means of a keyboard. In 1951, Ferranti, Manchester, built the commercial version of Mark I and sold eight machines. In the same year, Eckert e Mauchly built UNIVAC (Universal Automatic Computer), the first US commercial computer: it had an ultra-sound memory of 1000 12-digit words and was able to carry out 8333 sums or 555 multiplications per second. This evolution, however, would not have been place if the practice of programming in machine language had persisted. It was made possible by the appearance of languages, close to the customary mathematical one and understandable by the machine, which dictated the operations to be performed through a transcoding program, called compiler, with no need to access the computer operating modes. The first programming language, Plankalkül, was developed by Zuse between 1942 and 1946 to give instructions to Z1; its first applications regarded chess game. In 1949, Short Code appeared in the USA: it was the first language used on a computer by directly intervening on its electronic circuits. In 1951, Grace Murray Hopper (1906–1992) started developing A-O, the first compiler used from 1957 with the MATH-MATIC name. Starting in 1954, John Warner Backus (1924–2007) developed a new language, (FORTRAN) Formula Translating System, and the associated IBM compiler; in 1957, it was capable of automatically generating machine codes starting from formulas written in mathematical notation, with performances comparable with manually performed coding. FORTRAN, favoured by IBM policy, which refrained

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from patenting it, became the scientific language par excellence, representing the foundation of all the subsequent languages that came into existence between 1957 and 1958, in particular COBOL, ALGOL, LISP and APL. Thanks to these languages, programming, which until then had been associated with circuits and then with hardware, became a software issue. Information technology was born, together with a new generation of numerical methods and calculation programs focused on every sector, first among them meteorology, fluid dynamics and structural behaviour.

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56. Prandtl L (1926) Uber die ausgebildete turbulenz. Verhandlungen des zweiten internationalen kongresses fur technische mechanik, Zurich, pp 62–74 57. von Kármán T (1930) Mechanische Ähnlichkeit und Turbulenz. Nachr Ges Wiss Göttingen Math Phys Klasse. 58–76. (English translation in NACA TM 611, 1931) 58. Betz A (1931) Die von Kármánsche Ähnlichkeitsüberlegung für turbulente Vorgänge in physikalischer Auffassung. Z Angew Math Mech 11:397 59. Prandtl L (1932) Zur turbulenten Stromung in Rohren und laengs Platten. Ergebn Aerodyn Versuchsant Göttingen 4:18–29 60. Prandtl L (1933) Neuere Ergebnisse der Turbulenzforschung. Z Ver Deutsch Ing 77:105–114 61. Izakson AA (1937) On the formula for velocity distributions near walls. Tech Phys USSR 4:155–162 62. Millikan CB (1939) A critical discussion of turbulent flows in channels and circular pipes. Proc 5th Int Congr Appl Mech, Cambridge, Mass. 1938, 386–392 63. Goldstein S (1930) Concerning some solutions of the boundary layer equations in hydrodynamics. In: Proceedings of the Cambridge philosophical society, vol 26. pp 1–30 64. Prandtl L (1938) Zur Berechnung der Grenzschichten. Z Angew Math Mech 18:77–82 65. Görtler H (1939) Weiterentwicklung eines Grenzschichtprofiles bei gegebenen Druckverlauf. Z Angew Math Mech 19:129–141 66. Hartree DR (1939) A solution of the laminar boundary-layer equation for retarded flow. ARC R&M 2426 67. Relf EF, Simmons LFG (1924) The frequency of the eddies generated by the motion of circular cylinders through a fluid. ARC R&M, 917 68. Dryden HL, Heald RH (1925) Investigation of turbulence in wind tunnels by a study of the flow about cylinders. NACA Technical Report 231 69. Fage A, Johansen FC (1927) The structure of vortex streets. ARC R&M 1143 70. Ruedy R (1935) Vibrations of power lines in a steady wind. Can J Res A 13:99–110 71. Landweber L (1942) Flow about a pair of adjacent parallel cylinders normal to a stream. Report 485, In: David W. Taylor model basin, Washington, DC 72. Spivak HM (1946) Vortex frequency and flow pattern in the wake of two parallel cylinders at varied spacing normal to an air stream. J Aeronaut Sci 6:289–301 73. Gutsche F (1937) Das, singen’ von schiffsschrauben. Z Ver Dtsch Ing 81:882–883 74. Gongwer CA (1952) A study of vanes singing in water. J Appl Mech 19:432–438 75. Kovasnay LSG (1949) Hot wire investigations or the wake behind cylinders at low Reynolds numbers. P R Soc London, Ser A 198:174 76. Birkhoff GD (1952) A new theory of vortex streets. P Natl Acad Sci 38:409–410 77. Birkhoff GD (1953) Formation or vortex streets. J Appl Phys 24:98–103 78. Roshko A (1954) On the development of turbulent wakes from vortex streets. NACA Rep. 1191 79. Roshko A (1955) On the wake and drag of bluff bodies. J Aeronaut Sci 22:124–132 80. Tritton DJ (1959) Experiments on the flow past a circular cylinder at low Reynolds numbers. J Fluid Mech 6:547–567 81. Humphreys JS (1960) On a circular cylinder in a steady wind at transition Reynolds numbers. J Fluid Mech 9:603–612 82. Wille R (1960) Karman vortex streets. Adv Appl Mech 6:273–287 83. Marris AW (1964) A review on vortex streets, periodic wakes, and induced vibration phenomena. J Basic Eng Trans ASME 86:185–193 84. Berger E, Wille R (1972) Periodic flow phenomena. Ann Rev Fluid Mech 4:313–340 85. Lettau H (1939) Atmosphaerische turbulenz. Akademische Verlagsgesellschaft, Leipzig 86. Wehner H (1949) Untersuchung mikrobarographischer wellen auf Jan Mayen. Dissertation University of Leipzig, Akademie-Verlag, Berlin 87. Glauert MB (1956) The wall jet. J Fluid Mech 1:625–643 88. Prandtl L (1942) Bemerkungen zur Theorie der freien Turbulenz. Z Angew Math Mech 22:241–243 89. Bakke P (1957) An experimental investigation of a wall jet. J Fluid Mech 2:467–472 90. Maistrov. A historical sketch LE (1974) Probability theory. Academic Press, New York

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91. Lyapunov MA (1907) Problème général de la stabilité du mouvement. Ann Fac Sci Toulouse. 9:203–274. (translation of a 1893 Russian paper on Comm Soc Math Kharkow) 92. Lindeberg JW (1922) Eine neue Herleitung des Exponentialgesetzes in der Wahrschienlichkeitsrechnung. Math Zeit 15:211–225 93. Bernstein SN (1927) Sur l’extension du théorème limite du calcul des probabilités aux sommes de quantités dépendantes. Math Ann 97:1–59 94. Feller W (1935) Über den Zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung. Math Zeit 40:521–559 95. von Mises R (1939) Probability, statistics and truth. MacMillan, New York 96. Kolmogorov AN (1950) Foundations of the theory of probability. Chelsea, New York 97. Cramér H (1937) Random variables and probability distributions. Cambridge University Press, London 98. Parzen E (1960) Modern probability and its applications. John Wiley, New York 99. Tippett LHC (1925) On the extreme individuals and the range of samples taken from a normal population. Biometrika 17:364–387 100. Dodd EL (1923) The greatest and the least variate under general laws of error. Trans Am Math Soc 25:525–539 101. Fréchet M (1927) Sur la loi de probabilitè de l’écart maximum. Ann de la Soc Polonaise de Math Cracow 6:93–125 102. Fisher RA, Tippett LHC (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc Cambridge Phil Soc 24:180–190 103. von Mises R (1936) La distribution de la plus grande de n valeurs. Revue Math de l’Union Interbalkanique, Athens 1:141–160 104. Gnedenko BV (1943) Sur la distribution limite du terme maximum d’une serie aléatorie. Ann Math 44:423–453 105. Wilks SS (1948) Order statistics. Bull Am Math Soc 54:6–50 106. National Bureau of Standards (1953) Probability tables for the analysis of extreme value data. Appl Math Ser. 22 107. Gumbel EJ (1954) Statistical theory of extreme values and some practical applications. Nat Bureau of Stand, Appl Math Ser 33 108. Johnson LG (1954) An axiomatic derivation of a general S-N equation. Industrial Math 4:1 109. Silva Leme RAD (1954) Os extremos de amostras ocasionais e suas applicações à engenharia. Thesis, University of São Paulo 110. Jenkinson AF (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart J Roy Meteorol Soc 81:158–171 111. Gumbel EJ (1958) Statistics of extremes. Columbia University Press, New York 112. Rosin P, Rammler E (1933) The laws governing the fineness of powdered coal. J Inst Fuel 7:29–36 113. Weibull W (1939) A statistical theory of the strength of materials. Ingeniörsvetenskapsakademiens Handlingar N. 151, Stockolm 114. Weibull W (1939) The phenomenon of rupture in solids. Ingeniörsvetenskapsakademiens Handlingar 153, Stockolm 115. Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech ASME 18:293–297 116. Solari G, Carassale L, Tubino F (2007) Proper orthogonal decomposition in wind engineering. Part 1: a state-of-the-art and some prospects. Wind Struct 10:153–176 117. Beltrami E (1873) Sulle funzioni bilineari. G di Mathematiche di Battaglini 11:98–106 118. Jordan MC (1874) Mémorie sur les Formes Bilinéaires. J Math Pures Appl 19:35–54 119. Sylvester JJ (1889) On the reduction of a bilinear quantic of the nth order to the form of a sum of n products by a double orthogonal substitution. Messenger Math 19:42–46 120. Schmidt E (1907) Zur Theorie de linearen und nichtlinearen Integralgleichungen. I Teil. Entwecklung willkurlichen Funktionen nach System vorgeschreibener. Math Ann 63:433–476 121. Weyl H (1912) Das Asymptotische Verteilungs gesetz der Eigenwert linearer partieller Differentialgleichungen (mit einer Anwendung auf der Theorie der Hohlraumstrahlung). Math Ann 71:441–479

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122. Autonne L (1915) Sur les matrices hypohermitiennes et sur les matrices unitaires. Ann Univ Lyon 38:1–77 123. Eckart C (1934) The kinetic energy of polyatomic molecules. Phys Rev 46:383–387 124. Eckart C, Young G (1936) The approximation of one matrix by another of lower rank. Psychometrika 1:211–218 125. Eckart C, Young G (1939) A principal axis transformation for non-hermitian matrices. Bull Am Math Soc 45:118–121 126. Pearson K (1901) On lines and planes of closest fit to systems of points in space. Phil Mag 2:559–572 127. Spearman C (1904) General intelligence, objectively determined and measured. Am J Psych 15:201–293 128. Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 24:498–520 129. Hotelling H (1936) Simplified calculation of principal components. Psychometrika 1:27–35 130. Girshick MA (1936) Principal components. J Amer Statist Assoc 31:519–528 131. Schuster A (1898) On the investigation of hidden periodicities with application to a supposed 26-day period of meteorological phenomena. Terr Mag Atmos Elect 3:13–41 132. Schuster A (1906) On the periodicities of sunspots. Phil Trans Ser A. 206:69–100 133. Taylor GI (1921) Diffusion by continuous movements. Proc London Math Soc 20:196–212 134. Yule GU (1927) On a method of investigating periodicities in disturbed, series with special reference to Wolfer’s sunspot numbers. Phil Trans, Ser A 226:267–298 135. Slutsky E (1937) The summation of random causes as the source of cyclic processes. Econometrika 5:105–146 136. Wold HO (1938) A study in the analysis of stationary time series. Almquist and Wicksell, Uppsala 137. Box GEP, Jenkins GM (1976) Time series analysis forecasting and control. Holden-Day, Oakland, California 138. Wiener N (1930) Generalized harmonic analysis. Acta Math 55:117–258 139. Khinchin AJ (1934) Korreltionstheorie der stationaren stochastischen prozesse. Math Ann 109:604–615 140. Taylor GI (1938) The spectrum of turbulence. Proc Roy Soc London, A 164:476–490 141. Wiener N (1949) Extrapolation, interpolation and smoothing of stationary time series. MIT Press, Cambridge, Massachussets 142. Kosambi DD (1943) Statistics in function space. J Indian Math Soc 7:76–88 143. Loeve M (1945) Fonctions aléatoire de second ordre. Compte Red Acad Sci, Paris 220 144. Karhunen K (1946) Zur spektraltheorie stochastischer prozess. Ann Acad Sci Fennicae 1:34 145. Kac M, Siegert AJF (1947) An eplicit representation of a stationary Gaussian process. Ann Math Stat 18:438–442 146. Loeve M (1955) Probability theory. Van Nostrand, New York 147. Lumley JL (1970) Stochastic tools in turbulence. Academic Press, New York 148. Carassale L, Solari G, Tubino F (2007) Proper orthogonal decomposition in wind engineering. Part 2: theoretical aspects and some applications. Wind Struct 10:177–208 149. Rice SO (1944) Mathematical analysis of random noise. Bell Syst Tech J 23:282–332 150. Rice SO (1945) Mathematical analysis of random noise. Bell Syst Tech J 24:46–156 151. Rayleigh Lord (1877) Theory of sound. MacMillan, London 152. Siegert AJF (1951) On the first passage time probability problem. Phys Rev 81:617–623 153. Darling DA, Siegert AJF (1953) The first passage problem for a continuous Markov process. Ann Math Stat 24:624–639 154. Cartwright DE, Longuet-Higgins MS (1956) The statistical distribution of the maxima of a random function. Proc Roy Soc London, Ser A 237:212–232 155. Rayleigh Lord (1880) On the resultant of a large number of vibrations of the same pitch and of arbitrary phase. Philos Mag 10:73–78 156. James HM, Nichols NB, Phillips RS (1947) Theory of servomechanisms. McGraw-Hill, New York

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157. Davenport WB, Root WL (1956) An introduction to the theory of random signals and noise. McGraw-Hill, New York 158. Lanning JH, Battin RH (1956) Random processes in automatic control. McGraw Hill, New York 159. Hannan EJ (1960) Time series analysis. Methuen, London 160. Middleton D (1960) An introduction to statistical communication theory. McGraw-Hill, New York 161. Parzen E (1961) An approach to time series analysis. Ann Math Stat 32:951–989 162. Miles JW (1954) On structural fatigue under random loading. J Aero Sci 21:753–762 163. Mark WD (1961) The inherent variation in fatigue damage resulting from random vibration. Ph.D. Thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology 164. Blackman RB, Tukey JW (1959) The measurement of power spectra from the point of view of communications engineering. Dover Publications, New York 165. Parzen E (1961) Mathematical considerations in estimation of spectra. Technometrics 3:167–190 166. Cooley JW, Tukey JW (1965) An algorithm for the machine calculation or complex Fourier series. Maths Comput 19:297–301 167. Tippett LHC (1927) Random sampling numbers. Cambridge University Press 168. Kendall MG, Babington-Smith B (1939) Second paper on random sampling numbers. Suppl J R Stat Soc 6:51–61 169. von Neumann J (1951) Various techniques used in connection with random digits. Appl Math Ser 12:36–38 U.S. National Bureau of Standards 170. Rosen S (1969) Electronic computers: a historical survey. Comput Surv 1:7–36 171. Goldstine HH (1980) The computer: from Pascal to von Neumann. Princeton University Press, New Jersey 172. Zientara M (1981) The history of computing: a biographical portrait of the visionaries who shaped the destiny of the computer industry. CW Communications, Redditch Worcs, UK 173. Augarten S (1984) Bit by bit: an illustrated history of computers. Ticknor and Fields, New York 174. Colombo U, Lanzavecchia G (ed) (2002) La nuova scienza, In: La società dell’informazione, vol 3. Libri Scheiwiller, Milan

Chapter 6

Wind Meteorology, Micrometeorology and Climatology

Abstract This chapter addresses wind knowledge between the late nineteenth century and the first half of the twentieth century. First, it examines the evolution of ground-level and upper air measurements, emphasising the revolution related to the appearance of remote monitoring. It then discusses the understanding and forecasting of circulation phenomena on a planetary scale, highlighting the dualism between the deterministic and probabilistic view, and the genesis of wind classification, underlining the existence of various phenomena with different space and timescales. Later on, it addresses the growing importance given to the physical processes that occur in the thin atmospheric belt in contact with the Earth surface, which originated micrometeorology and the two turbulence representations that arose in this period: the phenomenological and the statistical theory. In turn, they produced the first models of the wind speed close to the ground that took place through a mixture interfacing theory, experience and empiricism. Finally, this chapter addresses wind climatology and the first distributions of the wind speed.

Wind is one of the most studied and examined subjects in history. Since antiquity, it played an essential role in mythology (Sect. 2.1), in philosophical speculation and in the observation of nature (Sect. 2.2), in the first experiences on physical phenomena (Sect. 2.3) and in the astrological interpretation of meteorology (Sect. 2.4). A transition from speculation to experience occurred with the advent of Renaissance (Sect. 3.1): it was made possible by the first instruments for the measurement of atmospheric parameters (Sect. 3.2) that, together with the developments in fluid dynamics (Sect. 3.6) and thermodynamics (Sect. 3.7), led to the foundation of meteorology through a long and complex process taking place between the seventeenth and the nineteenth centuries (Sect. 4.1). The situation changed between the late nineteenth century and the first half of the twentieth century, when the knowledge of the wind evolved towards the modern view, making use of the advancements in fluid mechanics (Sect. 5.1), probability and process theory (Sect. 5.2) and automatic computation (Sect. 5.3). A comprehensive analysis of such process is an arduous task. Above all, it is difficult to organise a pattern of the various trends and of the interrelations among them.

© Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_6

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This chapter, even though the author is well aware that the proposed pattern is only one of the many possible alternatives, deals with the wind by first examining the evolution of its measurement. With such aim, Sects. 6.1 and 6.2, respectively, cover ground level and upper air measurements, emphasizing the revolution associated with the appearance of remote monitoring. Meteorology, thanks to the availability of a large amount of increasingly accurate measurements, made formidable advancements due to the understanding and forecasting of circulation phenomena. Section 6.3 deals with such issues on a planetary scale, highlighting the dualism between the deterministic and the probabilistic view. Section 6.4 discusses the genesis of wind classification, underlining the existence of various phenomena, characterised by different space and timescales. Simultaneously, scholars became aware of the fact that, even though understanding the wind requires a broad view of the atmosphere, the physical processes affecting mankind are limited to a thin atmospheric belt in contact with the Earth surface. The need to deepen the knowledge about the latter originated a new discipline, micrometeorology, whose founding moments are outlined in Sect. 6.5. The study of the atmosphere near the Earth surface highlights the role of turbulence and of the mechanical and thermal convection. Section 6.6 illustrates the two main turbulence models arising in this period: the first, called the phenomenological one, came from fluid mechanics (Sect. 5.1); the second, defined as the statistical one (Sect. 5.2), was derived from atmospheric sciences; both of them are based on the analogy between the molecules making up gases and the eddies making up turbulence. The role of wind tunnel tests is also highlighted in this paragraph. The first models of the wind speed close to the ground (Sect. 6.7) originated from the foundation of micrometeorology, from the theoretical and experimental studies about turbulence, from the generalisation of the boundary layer theory to the atmospheric field and from on-site measurements. They made up, therefore, a mixture interfacing theory, experience and empiricism. Section 6.8 illustrates the first models representing wind climatology through the distributions of the parent population and of the extreme speed values. They make use of the advancements in the probability theory, availing themselves of the first databases. By and large, a relatively complete and mature picture of the wind comes to light, even though it is still characterised by a sectorial and partially unconnected view of the various subjects. The still missing element is a consistent approach linking meteorology and micrometeorology, identifying, for every wind phenomenon, a model clearly describing the mean velocity, the turbulence parameters and the link between these quantities. In the second half of the twentieth century, this view would consolidate as regards extra-tropical cyclones. It is still a subject for debate for tropical cyclones and, above all, for meso-scale wind phenomena, tornadoes and thunderstorms first and foremost.

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6.1 Ground-Level Measurements Towards the end of the nineteenth century and, mostly, in the 20th one, the interest in atmospheric phenomena created the conditions for an hectic development of anemometric instruments. It is documented by two texts written 70 years apart from each other. The first, by Cleveland Abbe (1838–1916) (Sect. 4.1), was written in 1887 on behalf of the U.S. Army (Treatise on meteorological apparatus and methods). The second was the Handbook of meteorological instruments published by Her Majesty’s Stationery Office of London in 1956 [1]. Based on these and subsequent contributions [2, 3], wind measurement instruments were divided into two groups, according to whether they detect the direction (wind vanes) or the speed (anemometers). In turn, speed measurement instruments were classified into three groups: rotating anemometers, divided into cup and propeller or windmill types, pressure anemometers, divided into tube and plate types, and hot-wire anemometers, exploiting the thermal conductivity of the air. Wind vanes (Fig. 6.1) originated from the first instrument that appeared on the Tower of the Winds in Athens (Sect. 2.4). These are bodies asymmetrically mounted on a vertical shaft, around which they can freely rotate. They assume a position in which the resultant force passes through the axis of rotation and has a point of application on the downwind side. In a steady wind, they guarantee an accuracy usually equal to 1 deg; their response to direction changes is a complex and still debated subject. Cup anemometers were first built by John Thomas Romney Robinson (1792–1882) (Sect. 3.2) using four hemispheric cups; later, their inventor experimented with the three-cup version and this configuration became definitive thanks to the studies carried out in Canada by John Patterson (1872–1956) [4] in 1926. In their fully developed version, they consist of three half-conical cups fitted at the ends of three arms spaced by equal angles, which rotate around a vertical axis (Fig. 6.2). The rotation of the cups is measured by means of mechanical counters, or through electrical contacts or generators [1]. Under constant wind conditions, the rotation speed of the cups v depends on the wind speed V. Such dependency can be expressed through the relationship: v = v0 + a1 V + a2 V 2 + . . .

(6.1)

where v0 is the threshold, associated with friction, below which the instrument does not work (in the first half of the twentieth century the most sensitive instruments were able to operate above v0 = 0.4 m/s); a1 , a2 , … are coefficients initially obtained by installing the anemometer aboard locomotives and identifying their speed with the wind speed; such values were later obtained through wind tunnel tests (Sect. 7.2). Patterson proved that the linear approximation of Eq. (6.1) (a2 = a3 = … = 0) is generally reasonable. The coefficient a1 = 3 suggested by Robinson (Sect. 3.3), however, is unacceptable; it ranges from 2.5 to 3.5, depending on the geometry of the cups and on the length of the arms.

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Fig. 6.1 Wind vanes [1]

Fig. 6.2 Three-cup anemometer [1]

The situation changes under variable wind conditions. The experience acquired in the early twentieth century proved that the cups accelerate quicker for a speed increase than they decelerate for its decrease. It follows that, when the wind is variable, the anemometer overestimates its speed [5, 6]. It is also worth noting the time required by cup anemometers to respond to the changes in V; such reaction times are so high to make this instrument unsuitable to record quick speed changes [1].

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Fig. 6.3 a Aerometer [1]; b Sanuki’s airplane type anemometer [8]; c pressure tube [1]

Propeller or windmill anemometers drew attention since 1900, when Eiffel installed a six-blade device on the tower bearing his name (Sects. 4.7 and 6.5). They became common after the Second World War, with the development of the aerometer and of the airplane type anemometer. The aerometer (Fig. 6.3a) consists of a horizontal rotating shaft, fitted with light fins mounted on radial arms and of a revolution counter device; the rotating shaft is aligned with the wind speed through a vane [7]. The airplane type anemometer [8] drew impulse from the studies carried out between 1945 and 1950 by Friez Carpenter in the USA and by Sanuki [9] in Japan (Fig. 6.3b), who made it suitable for operation under extreme wind conditions. Also the response of propeller or windmill instruments, like that of cup anemometers, is too slow to measure quick speed changes. Pressure tube anemometers (Fig. 6.3c) derive from Pitot’s and Lind’s instruments (Sect. 3.2). Their operation is based on Bernoulli’s law: 1 ps + ρV 2 = pt 2

(6.2)

where ps is the static pressure, pt is a constant quantity defined as the overall load, and V is the wind speed obtained from the difference between pt and ps . Air enters through an upwind horizontal intake and is blocked inside the tube creating pt ; ps occurs in the vertical part of the tube, which communicates with the external air through right-angle holes. The difference in pressure is measured by a pressure gauge. Pressure tube anemometers were subjected to remarkable developments in Great Britain, thanks to the English meteorologist William Henry Dines (1855–1927). Between 1888 and 1889, he added to the Pitot tube, a wind vane, a tank and a floating pen, through which he continuously recorded wind speed and direction (Fig. 6.4) [10, 11]. The main advantage of this instrument is that the tube can be mounted at the top of a pole, without particular maintenance requirements, while the recorder can be placed at another location. On the other hand, Dines’ anemometer, especially in earlier versions, did not provide accurate measurements for small values of the wind speed since the wind vane cannot quickly turn itself in the wind direction. Studies

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Fig. 6.4 Components of the Dines’ anemometer [10]

Fig. 6.5 Anemometers [8]: a Dines’; b RAE; c Meteorological Office Mk II

about the accuracy of this instrument and its evolutions, carried out by Giblett [12] in 1932 at the National Physical Laboratory (NPL) in Teddington, demonstrated its capability to measure mean speeds over periods up to 5 s. Subsequent developments led to three different instruments, known as Dines’ (Fig. 6.5a), RAE (Fig. 6.5b) and Meteorological Office Mk II (Fig. 6.5c) anemometers [8]. Since the conversion of pressure into velocity in pressure tube anemometers implies assigning a mean value to air density, they are not well suited for marine environments, because of saltiness, or in mountains, where atmosphere is rarefied; on the other hand, they are excellent for wind tunnel use. Plate anemometers are descended from the pendulum and thin sheet instruments by Leon Battista Alberti (Sect. 2.8), Leonardo da Vinci (Sect. 2.10) and Robert Hooke (Sect. 3.2). They consist of a rectangular, sometimes circular, plate supported by a spring and turned perpendicularly to the wind direction by means of a wind vane; wind speed is measured through plate movement or spring compression. The

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first instruments were not able to capture small speed values, were not accurate in strong winds and were exceedingly slow to respond to speed changes. Since the early twentieth century, the plate became lighter and the spring stiffer, so as to make their response quasi-static; the instrument, therefore, became more sensitive to quick speed changes and more suited to record turbulence. In 1931, Sherlock and Stout [13] evaluated its properties. Subsequent evolutions of the plate anemometer, developed in France, in USA and especially in England thanks to the Electrical Research Association (ERA), led to the strain gauge anemometer [14]. Hot-wire anemometers solved the issue of accurately measuring quick speed changes. They consist of an electric wire (usually made of platinum, some centimetres long and with diameter between 0.002 and 0.1 mm) whose resistance is kept constant, at high temperature, by providing the electrical power required to replace the heat lost because of the cooling action of wind. It was conceived in 1909 by Dimitri Pavlovitch Riabouchinsky (1882–1962) [15] at the Aerodynamics Institute of Koutchino (Sect. 7.2). Its diffusion was due to Louis Vessot King (1886–1956), who in 1914 formulated the heat loss theory for a cylindrical wire orthogonally immersed in a fluid flow with speed V and temperature T 0 [16]. If the wire is heated by an electric current with intensity I such that the wire temperature and resistance are T and R, then:  √  R I 2 = K + c V (T − T0 ) (6.3) where K is a constant depending on the heat losses due to irradiation and convection and c is a constant depending on the properties of air and on the wire diameter. Keeping I and R constant and T very large (at least 500 °C), Eq. (6.3) assumes the form: √ I 2 = I02 + B V

(6.4)

where I 0 is the value of I for V = 0; B is a constant to be empirically determined. Thanks to such formulation and its evolutions, the new instrument was developed by Johannes Martinus Burges (1895–1981) in Netherlands, and by Hugh Latimer Dryden (1898–1965) and Galen Brandtl Schubauer (1904–1992) in USA. In 1929, Dryden and Arnold Kuethe (1905–2000) [17] evaluated the response time of this instrument to speed changes, proving that its response is as quicker as the wire is thinner. Thus, the hot-wire anemometer is excellent for sheltered environments [18]. A bit at a time, it became the most used instrument in wind tunnels, whereas it is not suited for outdoor monitoring.

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6.2 Upper Air and Remote Measurements The interest for high atmospheric layers grew in parallel with the development of the meteorological measurements near the Earth surface. It received a formidable impulse in the nineteenth century, thanks to the evolution of kites and balloons (Sect. 4.5). Physicists, chemists and meteorologists took instruments at increasingly higher heights, obtaining an increasingly exhaustive picture of the atmosphere. The common element of such experiences is the repetition, adopting suitable devices when required, of the operations carried out on the Earth surface or on the sea (Sect. 3.2). From the late nineteenth century, upper air atmosphere monitoring took on different characteristics: balloons and kites showed marked advancements; the technological progress between the late nineteenth century and the early twentieth century brought to light new instruments that, paired with balloons and kites, determined measurement potentialities hitherto unthinkable. The distinctive element of this evolution was the loss of interest towards scientific missions by balloons. It unfolded from 1875, because of too many deaths due to unsafe equipment, of exceedingly high costs and of the scarce accuracy of results, especially as regards temperature. This situation gave rise to two trends. On the one hand, the role of kites and their potentialities were reassessed on renewed grounds [19, 20]: they became cheaper and easy to use, and favoured a better exposure for instruments. On the other hand, the peculiarities of ballons changed: they were equipped with plastics envelopes, filled with hydrogen, helium, ammonia or methane, fitted with airtight and pressurised gondolas, no more used to carry people, becoming pilot or sounding balloons. The first was used to plot wind speed and direction. The second, equipped with meteorographs, expanded as it ascended through increasingly rarefied air; when its diameter increased from 3 to 6 times the balloon, it bursted and instruments with collected data returned to the ground by means of a parachute. Thanks to these advancements, balloons and kites became widespread at the meteorological observatories worldwide, representing a distinctive and valuable element for them [21, 22]. The first upper air wind measurements were carried out by Paul Schreiber, between 1873 and 1874, and by Urbain Jean Joseph Leverrier (1811–1877), in 1874, analysing the drift of pilot balloons. Schreiber repeated himself in 1885, detecting the position of his balloons through a pair of theodolites 5 km away from each other; he used upper air measurements to improve weather forecasts [23]. Around 1883, the English meteorologist Douglas Archibald used a pair of kites [24] to assess the wind speed profile [25] (Sect. 6.5): the smaller upper kite supported, through a wire, the lower greater one; Biram aerometers were fitted on the tail of the latter (Sect. 3.2); the height of kites was estimated through a theodolite. In 1885, Archibald replaced the silk wire with a sturdier and cheaper light metal wire; it allowed to reach greater heights with no risk of losing instruments [1].

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Between 1887 and 1892, the German meteorologist Richard Assmann (1845–1918) and Rudolf Hans Bartsch von Sigsfeld (1861–1902) built a new instrument to measure humidity and temperature: the psychometer. Making use of a screen that sheltered it from solar radiation, it performed the first accurate upper air temperature measurements (Sect. 4.5). Shortly after, two Frenchmen, Gustav Hermite and Georges Besancon (1866–1934), launched the first sounding balloons with autonomous recording devices: in 1892, they reached a height of 7.6 km; in 1893, they arrived up to 16 km. In that same year, Lawrence Hargrave (1850–1915), a British engineer emigrated to Australia (Sect. 7.4), invented the box kite. The advantages of parallel sails had already been known for some time; Hargrave, however, connected them by orthogonal stabilising surfaces, starting a generation of kites characterised by great stability and suited to carry out accurate atmospheric measurements [26]. The use of box kites for meteorological purposes became systematic in 1894, when the Blue Hill Observatory was founded near Boston in the USA. It performed regular launches of kites and stag beetles equipped with a meteorograph conceived by Charles Frederick Marvin (1858–1943); this device, called “baro-thermo-hygroanemometer”, simultaneously recorded atmospheric pressure, temperature, humidity and wind speed. In 1896, a French meteorologist, Léon Teisserenc de Bort (1855–1913), founded the Trappes Observatory near Paris. Aiming at ensuring the French participation to an international campaign of studies, he installed two theodolites 1318 m away from each other, using them to measure the height and speed of the clouds. In the same period, he explored the atmosphere by meteorographs, installing them aboard stag beetles (1897) and sounding balloons filled with helium (1898). Similar experiences were carried out in Germany by William Assmann (1862–1920) [27, 28]. In 1901, he used balloons with expanding rubber envelopes to carry his psychometer onboard and to develop, like de Bort, accurate measurements in the upper air layers. De Bort and Assmann came to the same conclusions. Air temperature decreases with height by approximately 6 °C per km up to approximately 11 km; the thermal gradient and the top of this layer change with seasons and latitude. Above 11 km temperature becomes approximately constant, with values between −52 and –54 °C. With no very high-altitude soundings available, the height up to which this atmospheric belt extends was estimated to be equal to 21 km first and then to 40 km. At the end of his experiments, de Bort called the atmospheric layer in contact with Earth surface where temperature decreases “troposphere”; he defined as “stratosphere” the atmospheric layer at constant temperature. Assmann and Sir William Napier Shaw (1854–1915) called the surface between these layers “tropopause”. William Henry Dines (1855–1927) started studying the upper air layers between 1901 and 1902. He collaborated with Shaw, using balloons and Hargrave’s box kites. Between 1905 and 1907, Dines [29] built two ultra-light meteorograph balloons, which were in widespread use up to the end of the 1930s. Dines’ meteorograph kites were just as famous [30]: they were made up of a light wooden frame incorporating instruments connected to a pen that marked data on a circular target rotated by a

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Fig. 6.6 Koutchino Aerodynamics Institute [32]: a sounding balloon; b theodolite

clock; wind speed was detected by an anemometer that measured wind pressure on one or more light spheres, consisting of ping-pong balls mounted on spiral springs. The evolution of theodolites took place in the same period. The first theodolite specifically conceived to detect the position of balloons and kites was designed by Alfred Auguste de Quervain (1879–1927) in 1905 [31]. Scientific and technological contributions originated a protocol for upper air meteorological measurements that entered in widespread use worldwide. In 1903, Scotsmen used kites during an expedition in Antarctica. From 1905, the Koutchino Aerodynamics Institute (Sect. 7.2) carried out sounding balloon launches (Fig. 6.6a) detected by theodolites (Fig. 6.6b) [32]. Other tests were carried out in Moscow by Rykatcheff, in England by Charles John Philip Cave (1871–1950), in Germany by Hugo Hergessell (1859–1938). India and Egypt built their first stations in 1905 and 1907, respectively. Despite such evolution, these techniques still retained remarkable shortcomings. With clouds or fog, detecting pilot balloons was impossible. The use of sounding balloons and kites also implied the issue of bringing back to the ground the instruments and the measurements in good conditions. The advent of the First World War and the advances in aeronautics (Sect. 7.4) originated an atmospheric monitoring technique that would be subjected to great development, especially for tropical cyclones (Sect. 10.1). In 1912, near Frankfurt, Ferdinand von Hiddessen (1887–1971) carried out the first meteorological survey aboard an airplane [21]. Douglas [33] recommended such practice even in peacetime. The turning point in upper air measurements came in the early twentieth century, when Guglielmo Marconi (1874–1937) invented the radio. Around 1896, after many experiments carried out in the family country house in Pontecchio, he built a device equipped with two antennas, a transmitting and a receiving one, by which he transferred intelligible signals, i.e. radio waves, over a distance nearly equal to 2400 m.

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His discovery received little credit in Italy, so in 1896 he patented the wireless telegraph system in Great Britain and founded the Marconi’s Wireless Telegraph and Signal Company in London. In 1899, he transmitted radio signals in France through the English Channel. In 1901, using a train of kites, he accomplished the first transatlantic communication between Poldhu in Cornwall and St. John’s in the Canadian island of Newfoundland. Shortly after, the radio was adopted by British, Italian and US ships, becoming a key onboard instrument. Thanks to this invention, the ground meteorological information network, hitherto managed through telegraph, received a new flow of information coming from seas and oceans, first from the areas where tropical cyclones developed [34]. The first weather communication received by radio from a ship on high seas dates back to 3 December 1905 and was transmitted by S.S. New York. A public transatlantic wireless telegraphy service was set up in 1907: it allowed weather forecasts (Sect. 6.3) and storms warning (Sect. 10.1). The first communication about the sighting of a hurricane, near the Yucatan coast, dates back to 26 August 1909 and was transmitted by S. S. Cartago. That same year Marconi was awarded the Nobel Prize for physics. The invention and the development of the radio influenced upper air monitoring, originating substantial advancements. They can be referred, in order of appearance, to telemetry, radio-sounding, radio-tracking and radio-theodolites [21]. The first attempt to transmit data through telemetry from a kite dates back to 1917 and was carried out by Friedrich Herath (1889–1974) and Max Robitzsch (1887–1952) using the kite cable. The tests aimed at transmitting data without using the cable started later. The first ones, carried out in Germany in 1921 and in the USA in 1923, were not successful. The radio-sound (Fig. 6.7a) is a compact set of meteorological instruments (for temperature, pressure, humidity, wind speed and direction) and of a radio transmitter (powered by small batteries and capable of transmitting measurements to a ground station), taken in the upper air by a balloon. It was also equipped with a small parachute to recover instruments. Its first application was carried out by Pierre Idrac (1885–1935) and Robert Bureau (1892–1965) [35] near Trappes; in 1927, they sent a balloon with a radio-sound in the stratosphere, receiving clear signals. In the same year, the Russian meteorologist Pavel Alexandrovich Molchanov (1893–1941) built a radio-sound to improve weather forecasts [36]; it was first launched on 30 January 1930 from the Moscow Geophysical Institute. Paul Duckert (1900–1966) came up with new evolutions (1931–1933) of this technology [37, 38]. Radio-tracking of pilot balloons allowed determining the upper air wind; it was first used in 1928 by Blair and Lewis [39] at the U.S. Army Signal Corps; in 1935, it was perfected by Corriez and Perlat [40] at the Office National Météorologique in Paris. It used measurements simultaneously taken by two stations. Starting in 1938, the NPL developed ultrashort wave systems to measure wind speed in the upper air. A full picture of this evolution was provided by Smith-Rose and Hopkins [41] in 1946. The optical theodolite detected the height of balloons by means of a single station; the first measurements were carried out in 1937 in USA [42]. The invention of

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Fig. 6.7 a Radio-sound; b radio-theodolite [21]

the radio-theodolite (Fig. 6.7b), developed by the U.S. Signal Corps Engineering Laboratory during the Second World War, represented a source of new remarkable advancements in the meteorological field. In parallel with the evolution of the radio for atmospheric monitoring, the radar (radio detection and ranging), an electronic system that makes use of the propagation of radio waves to locate objects invisible to the naked eye and to determine their distance, speed, shape and size, made its appearance. It uses a high-frequency transmitter emitting electromagnetic pulses with wavelength ranging from a few centimetres to approximately 1 m. The waves propagate until hitting an object partially reflecting them. The reflected waves travel backwards along their previous path and reach the station, where a receiver is located. By measuring the time T elapsed between the emission of the pulse and the echo return, the distance d = cT /2 to the target is evaluated, being c the light speed. The radar, thus, is an evolution of the radio, based on the laws governing the reflection of electromagnetic radiation. The German engineer Christian Hülsmeyer (1881–1957) understood the importance of using radio echoes to avoid collisions in maritime navigation and built a radio locator patented in 1904. In 1924, the British physicist Edward Victor Appleton (1892–1965) discovered that ionosphere, i.e. the ionised layer of high atmosphere, reflected the longest radio waves1 ; Appleton, making use of this property, used radio echoes to evaluate the height of ionosphere. In 1925, the Americans Gregory Breit (1899–1981) and Merle Anthony Tuve (1901–1982) independently repeated this

1 Appleton’s discovery was exceptional. Since electromagnetic waves travel in a straight line through

Earth’s atmosphere, the long-range transmission of radio waves is prevented by the curvature of the Earth surface. This was the reason why Marconi used kites for his first transatlantic transmission. This limit was overcome thanks to the ionosphere property to reflect long waves. Short waves, that are not reflected, can only be transmitted at short ranges.

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experiment, coming to the conclusion that ionosphere approximately extended at heights between 60 and 500 km. The first complete radar set was built in 1935 by the British physicist Robert Alexander Watson-Watt (1892–1973), who developed a system to locate enemy aircraft by the Radio Department of the NPL. In the same period, the U.S. Naval Research Laboratory built a similar device. In 1939, two British scientists, Henry Boot (1917–1983) and John Randall (1905–1984), invented the “resonant cavity magnetron”, which generated powerful high-frequency radio waves. It would fill an essential part in the evolution of the radar and, later, of the lidar (light detection and ranging), a device using microwaves produced by a laser that would play a key role from the second half of the twentieth century. The use of the radar to locate enemy planes and ships became widespread during the Second World War. It was soon understood, however, that it had the capability of highlighting meteorological phenomena. This became evident on 20 February 1941 on the southern coast of England, when a radar sighted a hail-producing thunderstorm 7 miles away [43]. In 1943, the Meteorological Office in London installed the first meteorological—later called primary—radar to detect upper air winds. In that same year, Germany built “Fledermaus”, the first secondary meteorological radar. Unlike the primary one, which detected a passive echo coming from the target by means of a single station, the secondary radar used an active response; it then required, instead of one reflection, an automatic retransmission, through which it guaranteed higher range. A new and revolutionary monitoring system, called “remote”, had come into existence. In past experiences, the instrument was located at the measurement point. Radio favoured data transmission without changing this principle. Radar radically altered such criteria, performing measurements far away from the place where it was located. Thanks to this principle, since 1945 the radar favoured great advancements in the sighting, knowledge and classification of tropical cyclones (Fig. 6.8a) [34, 44], tornadoes (Fig. 6.8b) [45] and thunderstorms [46, 47]. Actually, radar gave rise to huge advancements in target detection, but was not as effective to detect its motion. Such limit was overcome by the Doppler radar, named after the Austrian physicist and mathematician Christian Johann Doppler (1803–1853), who first observed the phenomenon on which its operation was based. It became known as the “Doppler effect” and consisted in a change in the frequency of a wave emitted by a source in relative motion with respect to the observer. Using this principle, the Doppler radar made radio signals bounce, up to long distance, on the raindrops moved by wind in storms: the frequency increases as the storm moves closer or decreases when the storm moves away. The simultaneous use of multiple Doppler radars increases accuracy [48]. The first studies about the use of the Doppler radar for meteorological purpose were carried out by Barratt and Browne [49] in 1953, and by Brantley and Barczys [50] in 1957. The turning point took place in June 1958, when Smith and Holmes [51] of the U.S. Weather Bureau used a Doppler radar to detect and study a tornado near El Dorado in Kansas (Fig. 6.9). In 1961, Roger Lhermitte and David Atlas (1924–2015) [52] used a Doppler radar to determine the wind speed profile: during

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Fig. 6.8 a Radar picture of the Carla hurricane (1961), the first one shown in TV; b formation of a tornado hook recorded in March 1953 by the radar of the Illinois State Water Survey [45]

Fig. 6.9 Smith’s and Holmes’ Doppler Radar [54]

storms, it detected water drops; under clear sky conditions, it detected the insects or other elements carried by the wind. Studies on the development of the Doppler radar to detect thunderstorms and tornadoes are reported in [53, 54]. In the meantime, the age of space exploration had begun. The first project of a rocket equipped to measure atmospheric parameters, including wind speed, was developed in USA in 1945. It was not built because, since 1946, V2, the first German military rocket, was available for meteorological purposes. The first observations in

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Fig. 6.10 a TIROS 1; b first picture of the atmosphere from TIROS 1 (1 April 1960)

the ozonosphere were carried out by means of this rocket in 1947. From then on, a competition to reach increasingly higher heights started; the interest of such missions for the wind, conversely, tended to decline. On 4 October 1957, the Soviet Union launched the first orbiting artificial satellite, Sputnik I. The second, Sputnik 2, was launched on 3 November 1957. On 31 January 1958, while Sputnik 2 was still in orbit, USA launched their first satellite, Explorer 1. In October 1958, NASA (National Aeronautics and Space Administration) was founded, the US space agency that put into orbit satellites for civilian and military purposes. Among these, Vanguard 2, launched on 17 February 1959, is worth mentioning. It was designed to measure the distribution of the cloud cover on the day part of its orbit and to determine the density of the upper air in relation to latitude, longitude, season and solar activity. The satellite consisted of a magnesium sphere 50.8 cm in diameter; it contained two optical telescopes, two photocells and a radio transmission system. Power was generated by mercury batteries. It was the prelude to the placement into orbit of the first meteorological satellite, TIROS 1 (Television and Infrared Observation Satellite, Fig. 6.10a), launched on 1 April 1960 by Cape Canaveral in Florida. It contained two TV cameras and two magnetic tape recorders where pictures were stored; power was provided by batteries powered by 920 solar cells. It remained operational for 78 days: in this period, it recorded 22,952 images of the Earth atmosphere (Fig. 6.10b). The climax of its activity occurred on 10 April 1960, when TIROS 1 detected, 1300 km east of Brisbane, a cyclone everyone else had missed: it was the start of the space sighting of storms and of the placement in orbit of satellites suited to fathom the secrets of the atmosphere for the safety of the planet.

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6.3 Meteorology and Weather Forecasts Despite the efforts made since ancient times to understand atmospheric phenomena (Sects. 2.4, 3.1 and 4.1), in the late nineteenth century science was distrustful of meteorology and of the possibility to perform effective weather forecasts. The situation changed in the first half of the twentieth century thanks to the evolution of fluid dynamics (Sect. 5.1) and to the advancements in atmospheric measurements both at ground level (Sect. 6.1) and especially in the upper air (Sect. 6.2). From the mid-twentieth century, such progress has been linked with the evolution of computers (Sect. 5.3). The foundation of modern meteorology originated in Norway, due to Vilhelm Frimann Koren Bjerknes (1862–1951). He inherited an unshakable faith in the ability of science to explain the physical world through mathematics from his father Carl Anton Bjerknes (1825–1903), a mathematics professor and a scholar of fluid dynamics. Bjerknes nourished his passion such love during his studies in France with Jules Henri Poincaré (1845–1912) and in Germany with Heinrich Hertz (1857–1894), with whom he collaborated to researches in electrodynamics and electromagnetism. Bjerknes returned in Norway as a physics professor at the Stockholm University and resumed Helmholtz’s [55] and Kelvin’s [56] theorems on vorticity (Sect. 3.6). He noticed that both of them treated the fluid as incompressible. The analysis of atmospheric and oceanic motions made this hypothesis unacceptable and required taking into account the role of thermal phenomena (Sect. 3.7). He then reformulated the problem, assuming the fluid as compressible and pairing fluid dynamics and thermodynamics equations. So, in 1898, Bjerknes published On a fundamental theorem of hydrodynamics and its applications particularly to the mechanics of the atmosphere and the world’s oceans [57], where he drew up the general theorem of large-scale circulation [58]. On the momentum of this result, he decided, at the age of 40, to dedicate the rest of his life to meteorology and weather forecasting. In particular, he aimed at determining future atmospheric states, being the current one known, through the sole use of the laws of fluid dynamics and thermodynamics. In 1904, Bjerknes published Weather forecasting as a problem in mechanics and physics [59], a paper in which he conceived the first mathematical method for weather forecasting [60]. It consists of the solution of a system of differential equations at the partial derivatives, including Navier–Stokes equation (dealing with the fluid as compressible), the continuity (or mass conservation) equation, the perfect gas equation and the first law of thermodynamics in Helmholtz’s form (Sect. 3.7). The unknown quantities of this problem were the three components of the wind speed, the temperature, the pressure and the density of air as functions of space and time. Bjerknes ran into two difficulties almost insurmountable in his time: the lack of suitable computation instruments and the assignment of initial conditions. He approached the first one through a graphic solution that turned out to be difficult, burdensome and inaccurate. He was almost powerless before the second: to know future atmospheric states, it needed to have complete measurements of the current state; despite the advancements in instrumentations and monitoring networks, the

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time was still unripe. With such premises, Bjerknes’ dream was doomed to fail. Despite this, he planted the seed of concepts destined for brilliant prospects. His perseverance led to the achievement of great strides forward in understanding meteorological phenomena and weather forecasting on qualitative bases [48]. Bjerknes lived in the USA from 1905 to 1907: when he returned in Europe, he collected his conceptions in Dynamic meteorology and hydrography [61], a work published in 1910 with the cooperation of his three assistants: a Swedish, Johan Wilhelm Sandström (1877–1956), and two Norwegians, Olaf Martin Devik (1886–1987) and Theodor Hesselberg (1885–1966). In 1912, he was invited to lead the Geophysics Institute of Leipzig. In this period, imperial expansion and war perspectives aroused great interest for meteorology in Germany. Bjerknes benefited from such interest, obtaining huge funds for research. The idea that atmosphere was a giant plant where the thermal energy provided by the sun was transformed into the wind kinetic energy originated in Leipzig. Unfortunately, with the outbreak of the First World War, Bjerknes was no more required to provide generic studies, but accurate weather forecasts for military strategy plans. In 1917, thankfully, Norway invited him to return to his homeland. Bjerknes accepted and, flanked by his son Jacob Aall Bonnevie Bjerknes (1897–1975) and by Halvor Solberg (1895–1974), founded the Bergen Geophysics Institute, the cradle of modern meteorology. Here, he published On the dynamics of the circular vortex with applications to the atmosphere and to atmospheric vortex and wave motion (1921), where he summarised his main ideas. In the meantime, Norway, because of the war, found increasing difficulties to import cereals. It then understood the need to improve its agricultural production and entrusted Vilhelm Bjerknes with the task of organising a national weather forecast service. Bjerknes delegated the responsibility of the forecasts for west and east Norway on his son Jacob and on Solberg, respectively; he developed the network of weather stations, collected measurements at the Bergen School and processed them to spread information on the evolution of weather. In the meantime, Jacob Bjerknes used his father’s data to develop the embryo of the cyclone model, considered one of the main discoveries of meteorology in the twentieth century. It took shape between 1919 and 1922 [48]. In 1919, Jacob Bjerknes [62] realised that the pressure field only partially explained cyclonic phenomena. They had to be interpreted by studying the air masses travelling across the atmosphere. According to Bjerknes, the genesis of cyclones layed in the discontinuity surface separating the hot air masses of equatorial origin from the cold air masses coming from the poles. A three-dimensional view came then into being: storms were not characterised by Redfield’s simple circular configuration, but rather by a complex sickle-shaped pattern closer to Jinman’s interpretation (Sect. 4.1). In 1920, Solberg identified the link between two subsequent cyclonic storms and formulated a theory, according to which cyclones are linked to one another and not isolated events [63]. Using a metaphor by Wilhelm Bjerknes, they “follow each other like pearls on a string” [48]. Thanks to this concept, the Bergen School proved the existence of a wavy surface—the polar front—which separated the cold air masses of the polar cell from the hot air masses of the tropical cell (Sect. 4.1). The “front”

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term derived from military terminology and was used to describe the conflict that took place because of the violent thermal gradient between cold and hot air masses along the discontinuity surface. Cyclonic storms represented the fiercest battles of an atmospheric war affecting the whole Earth. In 1921, Bjerknes and Solberg [64] noted that “the laws of physics show that clouds form when cooling of atmospheric air condensates the moisture content. Further physical investigations show that the condensated water drops fall out as rain as soon as they grow large enough to attain a falling velocity greater than the ascending velocity usually occurring in the clouds”. Accordingly, the issue of the rain was to find the conditions under which large air masses are cooled sufficiently to provoke condensation. The adiabatic cooling by expansion is the most effective process that causes such conditions. In turn, this is due to ascending motion, which rapidly brings the air from layers of high pressure to layers of lower pressure. This “reduces the problem of the rain formation to the following principal one: What are the conditions for the development of strong ascending motions?” Bjerknes and Solberg understood that they laid in cyclones and, in particular, in two mechanisms: warm front air pushing upwards a retreating wedge of cold air, and cold front air advancing wedge and displacing warm air upwards. In that same year (1921), Vilhelm Bjerknes took up the conceptions exposed in [61], integrated them with the studies developed in [62, 64] and published a paper [65] in which he joined Ferrel’s circulation mechanism (Sect. 4.1) with the Bergen’s view of the polar front. In such spirit, he discussed the existence, on each hemisphere, of four circulative cells: the first two were the classical Hadley and Ferrel cells, the third and the fourth came into being, on theoretical bases, from splitting the polar cell into two cells, respectively, developing in the eastern and western polar zones (Fig. 6.11a). He acknowledged that there was no reason to attribute sufficient stability to this circulation system. He then formulated a reasoning that led him to a new one (Fig. 6.11b): the two polar circulations came back to be joined into the classic one; however, “the cyclones and anticyclones are introduced in their proper places as essential links in the mechanism of circulation”. This was the prelude to the famous 1922 paper in which Jacob Bjerknes and Solberg [66] merged their theories into a model, known as the cyclogenetic—or polar front—theory, which is still used to construe the genesis and evolution of extra-tropical cyclones.

Fig. 6.11 Bjerknes [65]: a four-cell circulation system; b its evolution

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They maintained that “the cyclone (Fig. 6.12) consists of two essentially different air masses, the one of cold and the other of warm origin. They are separated by a fairly distinct boundary surface which runs through the centre of the cyclone. This boundary surface is imagined to continue, more or less distinctly, through the greater part of the troposphere, being everywhere inclined towards the cold side at a small angle with the horizon. In the case of eastward-moving depressions on the northern hemisphere, the warm air is conveyed by a south-westerly or westerly current on the southern side of the depression. At the front of this current, the warm air ascends the wedge of colder air and gives rise to the formation of precipitation (warm front rain). The warm current is simultaneously attacked in its flank by cold air masses from the rear of the depression. Thereby, part of the warm air is lifted and precipitation is formed (cold front rain)”. The above-described cyclone actually corresponds to an intermediate stage of its life cycle. In the subsequent stages, because of the Earth rotation, it becomes a cold air homogeneous vortex that expends the kinetic energy it receives. Generally, new cyclones develop along the thermal boundary surfaces that cross an existing “mother cyclone”. Figure 6.13a shows the most typical situation in which, at the end of the cold front surface, cold air turns westward and flows parallel to the boundary; in this way, the situation shown in Fig. 6.12 takes place and the new cyclone starts developing as a slight wave of the cold forward surface of the mother cyclone. In turn, “the newly formed cyclones may again create conditions for the development of further new ones, so that a long series of cyclones may be formed like waves on one single boundary surface (Fig. 6.13b). The boundary surface, connecting such a series of cyclones in the temperate zone, will separate the cold air of polar origin from the warm air supplied to the cyclones from the subtropic highs. The boundary surface thus marks the temporary southern limit of the polar air masses, a property which has suggested the name “polar front surface”, and correspondingly for its line of intersection with the ground: the “polar front”. The polar front is generally a wavy line, in continual motion through all latitudes of the temperate zone, bordering large tongues of polar and tropical air. The tongues of tropical air form the warm sectors of the young travelling cyclones, and the intermediate tongues of polar air constitute the moving wedges of high pressure between successive cyclones”. “In a series of cyclones formed on one and the same polar front, each cyclone usually follows a track lying south of that of the preceding cyclone. After a certain number of such cyclones, the polar front reaches the region of the subtropic Highs, from whence a steady transport of air takes place through the trade-winds towards the equator. (…) When the polar air from the rear of one cyclone enters into the trade winds, the next cyclone will usually appear on a more northern track, and follow a new polar front, which is not directly connected with the previous one. The resulting periodicity of the position of cyclone tracks enables us quite formally to divide the cyclones into groups, which we call ‘cyclone families’. Each family begins with the first cyclone travelling along a track north of that of the preceding cyclone, and ends with the cyclone travelling so far south that it brings the polar air down into the trade wind system. All cyclones of one family are thus formed on one and the same polar

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Fig. 6.12 Bjerknes’ and Solberg’s model [66]: vertical cross-sectional view of the initial stage (top); plan view (centre) and vertical cross-section (bottom) of the mature stage

Fig. 6.13 a Development of a new cyclone on the thermal boundary surface that crosses the mother cyclone; b development of a series of new cyclones on a single boundary surface [66]

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front.” Anticyclones form between the right flank of a polar current and the tropical current to the west of it, between two successive cyclone families. This model was perfected by Tor Harold Percival Bergeron (1891–1976), one of the most brilliant students of the Bergen School. He started from the consideration that in each hemisphere, there are two air masses, a hot one and a cold one, separated by as many wavy lines making up the polar front. Inside every main air mass, there are other masses, smaller but important for atmospheric evolution. Bergeron proposed a classification of the latter [67]. Depending on the region where they develop, they are to be called polar (P), arctic (A) or tropical (T) ones; they are to be classified as continental (c) or marine (m) ones; they are to be characterised by the (w) or (k) suffix, according to whether they are hotter or colder than the surface below them. Despite so many developments, the weather forecasts based on Vilhelm Bjerknes’ ideas remained a dream. The Bergen School, taking into account the globality of models, understood that the only way to carry out effective forecasts was to set up a circumpolar weather service with the involvement of all the countries located at medium latitudes. Twenty years elapsed before such principle was subscribed. While these advancements came into being, Lewis Fry Richardson (1881–1953), an Englishman with a leading role in weather forecasting [48, 60, 68, 69], studied physics and mathematics at the Cambridge University, applying the finite differences method to heat transmission. Fascinated by the Bergen School, he studied weather forecasts from 1911 to 1919. Such activity took shape in 1922 with the publication of a treatise, Weather prediction by numerical process [70], in which he applied the finite differences method to bring Vilhelm Bjerknes system of differential equations back to a system of algebraic equations. In the same book, he developed the equations to forecast rain, the warming and cooling of the planet due to solar and Earth radiation, and the transfer of heat and humidity between the Earth and the atmosphere. Richardson manually applied his method to carry out a 6-h forecast of a past event.2 His initial data referred to 7:00 GMT on 20 May 1910. This choice depended on the availability of a series of excellent measurements: some of them were tabulated by Vilhelm Bjerknes, and others referred to observations carried out by balloons. The grid plan where the system was solved, representing Central Europe (Fig. 6.14a), had step of approximately 200 km. In the vertical direction, four levels, at 2, 4, 7 and 12 km above sea level, were used. Overall, the model included 125 volumes. In the cells indicated with “P”, altimetric data on pressure and humidity as well as the value of temperature in the atmosphere were available to Richardson. In the cells indicated with “M”, wind speed and direction, besides air density, were available. The integration over time was performed in two 3-hour steps. The forecasts, limited to the two central cells, provided abysmal results: the numeric evolution of the surface pressure was one hundred times greater than the observed one. Richardson explained the error as due to the quality of the initial data and to the lack of upper air measurements.

2 In 1916, when his treatise was nearly completed, Richardson sensed the need to make an example.

He worked on it from 1916 to 1919. Being a conscientious objector, he refrained from carrying out military service, and in this period, he divided his time between forecasts and the aid to soldiers.

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Fig. 6.14 a Area of the Central Europe on which Richardson performed the first numerical weather forecast; b Richardson’s forecast factory [69]

Richardson’s error does not invalidate the greatness of his view: the willingness to publish a work the results of which are clearly wrong. He was so certain the path he had taken was right he envisaged the “forecast factory” (Fig. 6.14b), an army of 64,000 human computists, each one of them provided with desk computing machines, so fast to anticipate the evolution of weather.3 3 Reporting

Richardson’s words [70]: “After so much hard reasoning, may one play with a fantasy? Imagine a large hall like a theatre, except that the circles and galleries go right round through the space usually occupied by the stage. The walls of this chamber are painted to form a map of the globe. The ceiling represents the north Polar Regions, England is in the gallery, the tropics in the upper circle, Australia on the dress circle and the Antarctic in the pit. A myriad computers are at work upon the weather of the part of the map where each sits, but each computer attends only to one equation or part of an equation. The work of each region is coordinated by an official of higher rank. Numerous little ‘night signs’ display the instantaneous values so that neighbouring computers can read them. Each number is thus displayed in three adjacent zones so as to maintain communication to the North and South on the map. From the floor of the pit a tall pillar rises to half the height of the hall. It carries a large pulpit on its top. In this sits the man in charge of the whole theatre; he is surrounded by several assistants and messengers. One of his duties is to maintain a uniform speed of progress in all parts of the globe. In this respect he is like the conductor of an orchestra in which the instruments are slide-rules and calculating machines. But instead of waving a baton he turns a beam of rosy light upon any region that is running ahead of the rest, and a beam of blue light upon those who are behindhand. Four senior clerks in the central pulpit are collecting the future weather as fast as it is being computed, and despatching it by pneumatic carrier to a quiet room. There it will be coded and telephoned to the radio transmitting station. Messengers carry piles of used computing forms down to a storehouse in the cellar. In a neighbouring building there is a research department, where they invent improvements. But these is much experimenting on a small scale before any change is made in the complex routine of the computing theatre. In a basement an enthusiast is observing eddies in the liquid lining of a huge spinning bowl, but so far the arithmetic proves the better way. In another building are all the usual financial, correspondence and administrative offices. Outside are playing fields, houses, mountains and lakes, for it was thought that those who compute the weather should breathe of it freely”. Here, “computer” and “calculator” are used with the meaning of “people performing calculations”.

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At that time, few people understood the importance of Richardson’s work, and none of them was inclined to engage in months of manual work to investigate the reasons behind the failure of his forecast. Besides that, the evolution of atmospheric monitoring (Sect. 6.2) and the advancement of aeronautics (Sect. 7.4) provided elements to improve forecasts in practical and qualitative terms. In the meantime, there was a significant growth in the interest for upper air atmospheric phenomena and for their correlation with what takes place near Earth surface. William Henry Dines (1855–1927), a pioneer of the exploration of upper air (Sect. 6.2), processed his measurements between 1912 and 1925, providing results [71] later used by Jacob Bjerknes and Erik Herbert Palmén (1898–1985), a Finnish meteorologist raised at the Bergen School, to study cyclones [72–74]. It is worth mentioning the curiosity, and the subsequent studies, about the strong upper air streams. They were noticed in the nineteenth century during experiences with kites and balloons; they were interpreted, however, as occasional events. The first scientific survey of such phenomena was carried out by the Japanese meteorologist Wasaburo Ooishi (1874–1950) during the launch of balloons near the Mount Fuji in the early 1920s. Between 1923 and 1925, Ooishi proved the existence of strong streams over Japan in all seasons. Unfortunately, he published his results in Esperanto and they remained almost unknown. On 7 December 1934, during experimental flights, the American flyer Wiley Hardeman Post (1898–1935) met a strong tailwind at 6000 m height. The following year, the European countries of the World Meteorological Organisation started studying the upper air layers of the atmosphere to forecast cyclones; this confirmed the existence of streams, without interpreting their causes and properties. A peculiar aspect of this period was the migration of the best students of Vilhelm Bjerknes to the USA. The most famous of them, Carl Gustaf Arvid Rossby (1898–1957), had studied the polar front with Jacob Bjerknes at the Geophysics Institute of Leipzig; he also spent a period at the Lindenberg Observatory, carrying out upper air measurements by means of kites and balloons. In 1925, Rossby obtained a grant “to study the application of the polar front theory to American weather”. He then moved to the USA, first at the Weather Bureau in Washington, then as meteorology professor at the Chicago University. He had to spend almost ten years before the Bergen School conceptions were accepted by American meteorologists. In this period, however, Rossby did not restrict himself to divulge the Norwegian discoveries: he also made new, formidable progress, as witnessed by two papers published in 1939 and 1940 [75, 76]. Rossby first studied the wavy form of the polar front and the curved trajectories of the western streams (“westerlies”) that developed in the upper air, at the interface between the cold polar air masses and the tropical hot ones. He discovered that they formed wavy troughs, usually from 4 to 6 in number, extending into the warmer southern air and tending to move eastward. The curved limits of the troughs, subsequently called planetary or Rossby waves, matched the surface fronts along which cyclone families lined up. The meanders of the polar front evolved over time (Fig. 6.15a, b); when they became pronounced (Fig. 6.15c), they tended to detach masses of cold or hot air (Fig. 6.15d) originating cyclones and anticyclones. There

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Fig. 6.15 Evolution of polar front meanders

was a strong relationship, therefore, between upper air winds and the storms below them at the middle latitudes. Rossby interpreted the causes of the westerly upper air streams, for which he coined the term “jet stream”, in relation to Coriolis force. The hot air of tropical origin, moving northwards (in the northern hemisphere), rotated counterclockwise; the cold air of polar origin, moving southwards, rotated clockwise; a wavy demarcation line was then originated between hot and cold air, which was characterised by a violent thermal and pressure gradient. The jet stream originated near this boundary followed its meanders due to the deviatory action of the Coriolis force. To prove his theories, which were also backed by strong mathematical formulations, Rossby carried out a famous experiment. He filled a baking tin with water, heating its edges and cooling its centre; he then made the water rotate and highlighted the meanders of the waves that developed between the cold and hot parts of the liquid. Rossby also proved that the equations of the atmospheric motions formulated by Vilhelm Bjerknes and used by Richardson could be drastically simplified, without impairing their correctness, in relation to the scale of the problem. In this way, he laid the foundations of dynamic meteorology and of the advancements that atmospheric sciences and weather forecasts would make shortly [68, 77–81]. With the advent of the Second World War, the wind role was once again linked to military issues. In 1943, during a Royal Air Force raid on the Gironde, in France, airplanes met tailwinds that pushed them towards their target; on the return leg, the same winds, now coming from the front with speeds up to 380 km/h, caused the

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Fig. 6.16 Jet streams in the tri-cellular system: a cross-section; b three-dimensional view

stall of aircrafts and forced crew members to bail out over enemy-occupied ground, where they were captured. In 1944, American bombers met the winds discovered by Ooishi between Kyoto and Tokyo; such winds, blowing at 260 km/h, did not allow accurate bombing. Rossby in person organised the training of American flyers in jet streams. Once the war was over, between 1946 and 1947, other researchers from the Chicago University continued Rossby’s studies on jet streams. Palmén, who in the meantime emigrated to the USA to work with Rossby, proved the existence of two jet streams in each hemisphere [82]; these develop near the tropopause, at the interface among the three cells shown in Fig. 6.16. This originates a complex system, where the tri-cellular motions that mostly develop along meridians are flanked by circulatory phenomena tendentially directed along parallels. The first jet stream, designated as the “circumpolar” one, is quite narrow; it occurs between 5 and 7 km heights, even though sometimes it reaches 12 km; it wanders between 30°N and 70°N latitudes, in the separation area between the polar and the Ferrel cell. The second jet stream, called the “sub-tropical” one, is located between 9 and 13 km heights, even though sometimes it reaches 16 km; it develops between 20°N and 50°N latitudes, in the separation area between the Ferrel and Hadley cells. They are generally stable; sometimes, however, they break or split and then reform. Wind speed is in the range of 160–240 km/h, but can also exceed 400 km/h. Figure 6.17 shows two of the first upper air wind charts, drawn in 1953 [68]. In this period, airlines started using the knowledge about jet streams to reduce flight times and fuel consumption. The first airline following this path was Pan Am, which since 18 November 1952 flied from Tokyo to Honolulu at 7600 m height; thanks to this decision, flight time dropped from 18 to 11.5 h. In the meantime, the dream of Vilhelm Bjerknes and Richardson to forecast the future states of the atmosphere by numerically solving a mathematical problem was crowned in the USA, following Rossby’s steps. The main authors of this breakthrough were the Hungarian John von Neumann (1903–1957) and the American Jule Gregory Charney (1917–1981) (Sect. 5.3). After the war, Neumann wanted to show the potentialities of computers to mankind by solving a problem extremely complex and fascinating for public opinion. He convinced himself that the issue most closely meeting such requirements was weather

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Fig. 6.17 Absolute topography of the 500 (a) and 200 (b) mb surface (in the dark grey area, wind speed exceeds 100 knots; in the light ones, wind speed is between 50 and 100 knots) [68]

forecasting. He then proposed Rossby to model atmospheric circulation through equations of motion so simplified and schematic a computer could solve them. Rossby espoused the idea and proposed to establish a small team of meteorologists to support Neumann. They both agreed that the focal point of the project was the development of such theoretical simplifications to make it possible to numerically solve the primitive equations without impairing the quality of the solution. The proposal transmitted to the U.S. Navy envisaged that the team established itself at the Institute for Advanced Study in Princeton, New Jersey, coordinated by Harry Wexler (1911–1962) and supported by three Scandinavian consultants: Rossby, Harald Ulrik Sverdrup (1888–1957) and Jacob Bjerknes, who in the meantime had moved to the USA. On 1 July 1946, the U.S. Navy accepted this proposal and a “Conference on meteorology” was organised on 29 and 30 August 1946 with the aim of setting up the work team; it was the first world conference on numerical weather forecasting. The meeting led to involve Hans Panofsky (1917–1988), Gilbert Hunt (1916–2008) and Philip Thompson (1922–1994). The chief result was the encounter between Neumann and Charney, who was dazzled by the project conception. Charney was taken up with his doctorate thesis in the atmospheric field. Inspired by Bjerknes’ descriptive view and by Rossby’s deductive reasoning, it discussed the instability of westerly streams at middle latitudes and formulated a new interpretation of the formation of cyclones, known as the “baroclinic instability theory”. Charney developed his models on analytical grounds, carrying out calculations by hand, and perceived the need to simplify the primitive equations. He then resumed a criterion enunciated in 1928 by Richard Courant (1888–1972), Kurt Friedrichs (1901–1982) and Hans Lewy (1904–1988) [83] and understood that the failure of Richardson’s forecasts did not only depend on the lack of computation power, but was implicit in his model. It reproduced the complete equations of fluid dynamics and thermodynamics,

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including gravitational and sound waves. They were endowed with small amplitude and were uninfluential for meteorological phenomena, but could be amplified by the calculation method to such an extent as to cover the physical phenomena of interest. Charney then formulated two approximations, called hydrostatic and geostrophic, through which he improved and simplified Richardson’s model. To better explain such approximations, consider the quasi-steady hydrostatic balance between the weight force and the vertical pressure gradient; it is expressed by the relationship: dp = −gρ dz

(6.5)

where z is the upward vertical axis, p is the pressure, g is the gravity acceleration, and ρ is the air density. If pressure p and air density ρ are measured independently, small inaccuracies create small differences between great forces that numerically originate violent vertical accelerations. Likewise, consider the quasi-steady geostrophic balance between the horizontal pressure gradient and the Coriolis force; it is expressed by the relationship: dp = −ρ f Vg dy

(6.6)

where y is an horizontal axis orthogonal to isobars, which are assumed to be straight, heading from the high-pressure area to the low-pressure one, f is the Coriolis parameter, and V g is the geostrophic velocity parallel to the isobars. If pressure p and velocity V g are measured independently, small inaccuracies create small differences between great forces that numerically originate violent horizontal accelerations. In 1947, thanks to these intuitions, Charney [84] formulated a hierarchy of filters that almost completely eliminated both issues. At the same time, he joined Neumann’s and Rossby’s work team. In that year, the United Nations (UN) founded the World Meteorological Organization (WMO) to coordinate and standardise the meteorological information on a worldwide level. It was the prelude to formidable discoveries. Between 1948 and 1949, Charney pinpointed one of the major issues of meteorology, i.e. the plurality of space and timescales related to atmospheric phenomena, developing the “quasi-geostrophic” or “barotropic equivalent” model [85, 86], a mainstay of the forthcoming forecasts.4 In the meantime, he persuaded Neumann that, in order to correctly simplify the numerical problem and to interpret its results, the team would have to include additional first-rate meteorologists. In this spirit, between 1948 and 1951, the initial team expanded with the arrival of personalities like Arnst Eliassen (1915–2000) and Ragnar Fjörtoft (1913–1998) from Scandinavia, the Swedish analyst Bert Rickard 4 Charney’s

model represented the slow and low-frequency motions, removing gravity waves and fast, high-frequency acoustic waves. It can then be interpreted as a low-pass filter. Many consider this model one of the most prominent twentieth century contributions to atmospheric and oceanographic sciences.

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Fig. 6.18 Plan grid used for the first forecast carried out by ENIAC

Johannes Bolin (1925–2007) and Joseph Smagorinsky (1924–2005), John Freeman, George Platzman (1920–2008) and Norman Phillips (1923-) from the USA. In the meantime, a decision was taken: forecast results were to be considered as appropriate if they were comparable with the synoptic estimates of an expert forecaster. It was the start of a teamwork leading to increasingly effective results [87, 88]. Paradoxically, it was favoured by the endless delays in the activation of EDVAC (Sect. 5.3), the computer Neumann intended to use to carry out forecasts. The postponements forced the team to transfer their work on ENIAC to Aberdeen, Maryland. The first numerical forecast was developed on April 1950 [89]. Charney, Fjörtoft, Freeman, Platzman, Smagorinsky and Neumann contributed to it. The preparation of the analysis started on 5 March 1950 and required 33 days and 33 nights of almost uninterrupted work. The initial data were provided by the U.S. Weather Bureau and were related to 03:00 UTC hours of 5 January 1949. Figure 6.18 shows the layout map grid of the 1916 points on which the system of the nonlinear differential equations was solved by the central finite differences technique. The forecast, carried out 24 h in advance at 5500 m height, required approximately 24 h of machine time. The results were considered satisfying by the forecasters and by Richardson, who was informed about the experiment. The age of numerical weather forecasting had come into being. In August 1952, Neumann proposed the use of computers to the U.S. Weather Bureau. From 1953 onward Scandinavian and American meteorologists continuously exchanged their workplaces, developing numerical forecasts. In February 1954, the U.S. Weather Bureau, Air Force and Navy set up the Joint Numerical Weather Prediction Unit.

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At the same time, the first training courses about the use of computers to carry out forecasts were started in the USA, Norway and England. In 1955, Neumann and Charney created the General Circulation Research Section from the U.S. Bureau, with Smagorinsky as director. This section became the General Circulation Research Laboratory in 1959 and the Geophysical Fluid Dynamics Laboratory in 1963. In the meantime, the collaboration among Smagorinsky, Neumann, Charney, Phillips and Thompson became intense [90, 91]. Between 1955 and 1956, they developed numerical forecasts on two levels; in 1959, the integration of the primitive equations was carried out on nine levels. While these advancements took place, new stances came into existence: they extended forecasts from the deterministic sector, where they were developed, towards a view inspired by probability, process theory (Sect. 5.2) and chaotic systems. The two scholars that mostly contributed to lay these foundations were Smagorinsky and Edward Lorenz (1917–2008), a meteorology professor at the M.I.T. Smagorinsky was a student of Lorenz. The probabilistic view of weather forecasts developed in the early 1950s. There was a growing awareness that the use of different discretisation models, different sets of initial data and/or simplified models of the primitive equations (Charney’s studies originated various filters) led to dispersed results that, as such, could be interpreted through probabilistic methods. Also the consideration came into light that the future states of the atmosphere depended on such a huge number of variables, according to laws so complex, to constitute random processes governed by parameterised equations of fluid dynamics and thermodynamics. Also, Smagorinsky conceived the idea of developing forecasts over long time spans to simulate the evolution of the Earth climate: in this way, the concept of deterministic forecast lost its meaning and the statistical interpretation grew stronger. The new view of forecasts compelled analysts to face the difficulty of managing exceedingly large data sets. They included series of many meteorological parameters acquired through measurements or forecasts with discrete time steps over increasingly longer time spans and on increasingly broader grids of points distributed over space. This originated the requirement to contain the burden of analyses by compacting the data representation. At first, the analyses appeared impossible due to the lack of suitable calculation tools. Subsequently, new perspectives opened up, leading to the first statistical forecasts [92, 93] linked to principal component analysis (PCA) and to proper orthogonal decomposition (POD) (Sect. 5.2). It is odd to notice that the meteorology and climatology sectors developed these methods autonomously and recognised the common matrix of their approaches afterwards. This occurred at the end of the Second World War, at the M.I.T. and in the Soviet Union (Sect. 5.2), simultaneously with Charney’s and Neumann’s studies in Princeton. In 1948, Wadsworth et al. [94] approached the short-term statistical forecast of the atmospheric pressure at the sea level on the northern hemisphere. They expressed the meteorological parameters as the sum of a mean term and a series of empirical orthogonal functions (EOFs), weighed by coefficients determined through the least squares method under the condition of minimising the number of terms of the series describing the field with given accuracy. With such condition, the EOF identified

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itself with the PCA and the POD. Wadsworth, Bryan and Gordon evaluated the eigenvalues and the eigenvectors of a 91 × 91 covariance matrix. They involved a lot of people to perform manual calculations that went on for weeks and came to the conclusion that seven EOFs were sufficient to reconstruct 89% of the whole variance of the field. In this way, they proved the effectiveness of this procedure as well as the impossibility of manually managing it. The situation changed from 1951, when the M.I.T. installed Whirlwind, a powerful electronic computer. In 1956, resuming the study carried out in 1948 [94] in the light of the quasi-geostrophic method developed by Charney, Lorenz [95] carried out a new forecast of the pressure field anomaly at 500 mb height, referred to the month of January of the years from 1947 and 1952. He arranged a 64-point grid straddling across the USA and Canada and, by numerically applying the EOF method, proved that the first nine principal coordinates were sufficient to reproduce 88% of the variance of a 1-day forecast. Lorenz’s article is considered a milestone. It was the prelude to the experiment that Lorenz carried out in 1961, taking inspiration from the concepts by Poincaré in Science et methode (1908). According to Poincaré, small uncertainties about the initial state of the atmosphere were propagated and amplified through the solution of the primitive equations, to the extent of rendering the forecast unreliable. Lorenz twice simulated the evolution of the same atmospheric state, using the same mathematical model [27]. The first time he carried out the simulation on the whole period of the forecast. The second time he broke the forecast into two stages, initialising the second one with the final stage of the first. The results were different. Lorenz looked for the error, and then he understood and proved that the initial state of the second stage had been assigned by numbers with 3 decimal digits, while the analyses in the first stage had been carried out with 6 decimal digits. In other words, a truncation error in the initial conditions caused huge errors in the solution. Analysing this result, Lorenz remarked that the error propagated and amplified from a certain instant onward. He then proved, by applying chaos theory to meteorology for the first time [96], that reliable forecasts over long periods required tendentially infinite accuracy in the assignment of the initial conditions. Illustrating such impossibility with the famous example about the consequences of a butterfly flapping its wings,5 Lorenz proved that forecasts could be effective over periods of a few days. 5 The

butterfly effect is a poetic expression introduced in literary grounds by Jacques Salomon Hadamard (1865–1963) in 1890 and divulged by Pierre Maurice Marie Duhem (1861–1916) in 1906. The idea of the possible consequences of the flap of a butterfly’s wings appeared in a story published by Ray Bradbury (1920–2012) in 1952, A sound of thunder, in which a butterfly living in the time of dinosaurs had an essential role in the development of the English language and in a political election. Commenting his 1961 numerical forecasts, Lorenz [96] noted that “one meteorologist remarked that if the theory were correct, one flap of a seagull’s wings could change the course of weather forever”. In his subsequent writings and lectures, he replaced the seagull with the more poetical butterfly. The title of a conference he held in 1972 at the 139th Convention of the American Association for the Advancement of Science, Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas, was selected by the conference organisers since he forgot to provide it.

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6.4 Wind Classification Meteorology, in parallel with the developments in the understanding of atmospheric motions on a planetary scale and in particular of mid-latitude cyclones, started approaching small-scale atmospheric events in an increasingly systematic manner [97]. In 1922, Sir Harold Jeffreys (1891–1989) [98] imparted a new direction to this sector publishing the first wind classification.6 Jeffreys dealt with the problem in a theoretical form, at first by expressing the equations of motion in the full form of the dynamic balance introduced by Lamb [99]: 

   du ∂ 2u ∂p ∂ 1 − 2ωv cos θ = − +ρ U + ω2 2 + kρ(R + z) 2 dt ∂θ ∂θ 2 ∂z (6.7a)     dv ∂ 2v ∂p ∂ 1 ρ + 2ωu cos θ + 2ωw sin θ = − +ρ U + ω2 2 + kρ 2 dt ∂φ ∂φ 2 ∂z (6.7b)     ∂p ∂ 1 2 2 dw − 2ωv sin θ = − +ρ U+ ω  (6.7c) ρ dt ∂z ∂z 2 ρ(R + z)

where u, v, w are the three components of the wind speed at time t in a point P with coordinates θ, φ, z: θ is the angle between the perpendicular to the Earth surface through P and the polar axis, φ is the longitude, z is the height of P above the Earth surface; ρ is the air density, R is the Earth radius,  is the distance from the point P to the polar axis, ω is the Earth angular revolution speed, p is the atmospheric pressure, U is the potential of the external forces, and k is the eddy viscosity coefficient. The following relationship also holds true: d ∂ u ∂ v ∂ ∂ = + + + dt ∂t R + z ∂θ  ∂φ ∂z

(6.8)

In Eq. (6.7a–c), the left-hand-side terms are the product of a mass by an acceleration given by the sum of two terms: the speed change of a non-revolving system and the effect of Earth rotation. The right-hand-side terms are the sum of three forces: the pressure gradient, the external force and the surface friction force. Jeffreys introduced many simplifications. He hypothesised that the sole external force is the gravitational one and that z is small with respect to R. He assumed that the vertical component of the wind speed is small with respect to the horizontal one, that Rdθ= dx and dφ = dy (x and y being the southward and eastward coordinates of P, respectively), and that wind phenomena are restricted to a portion of atmosphere so small to make 6 Sir

William Napier Shaw’s suggested Jeffreys to formulate a quantitative theory on katabatic winds. Jeffreys understood it was first necessary to clarify how they differed from other winds, but no framing of various wind types existed. He then devoted himself to wind classification.

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possible to disregard the cosθ and sinθ variations inside such area. Equation (6.7a–c), therefore, becomes: 1 ∂p ∂ 2u du − 2ωv cos θ = − +k 2 dt ρ ∂x ∂z 1 ∂p ∂ 2v dv + 2ωu cos θ = − +k 2 dt ρ ∂y ∂z 1 ∂p 0=− −g ρ ∂z

(6.9a) (6.9b) (6.9c)

where g is the gravity acceleration. Jeffrey observed that the force caused by the pressure gradient plays an essential role and it is necessarily balanced by another force of the same magnitude. Starting from here Jeffreys’ wind, classification identified three wind phenomena called Eulerian, geostrophic and antitriptic, where the gradient force is respectively balanced by the inertial, Coriolis and friction force. In the case of the winds called Eulerian, in honour of whom first wrote the equations of motion, the Coriolis and friction forces are small with respect to the inertial one; Eq. (6.9a–c), therefore, becomes: 1 ∂p du =− dt ρ ∂x dv 1 ∂p =− dt ρ ∂y 1 ∂p 0=− −g ρ ∂z

(6.10a) (6.10b) (6.10c)

In the case of the winds called geostrophic by Sir Napier Shaw, the friction and inertial forces are small respect to the Coriolis one; Eq. (6.9a–c), therefore, becomes: 1 ∂p ρ ∂x 1 ∂p 2ωu cos θ = − ρ ∂y 1 ∂p 0=− −g ρ ∂z

−2ωv cos θ = −

(6.11a) (6.11c) (6.11c)

In the case of the winds defined antitriptic by Jeffreys, the inertial and Coriolis forces are small with respect to the friction force. In this case, Eq. (6.9a–c) becomes: 0=−

∂ 2u 1 ∂p +k 2 ρ ∂x ∂z

(6.12a)

0=−

∂ 2v 1 ∂p +k 2 ρ ∂y ∂z

(6.12b)

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Table 6.1 Wind classification according to Jeffreys [98] Scale

Winds

Planetary

General circulation

Eulerian

Continental

Monsoons

British Isles

Mid-latitude cyclones

Small

Tropical cyclones

#

Tornadoes

#

Geostrophic Antitriptic

Thermal

# # #

Sea/land breezes

#

Valley/mountain winds

#

Foehn/katabatic winds

#

0=−

1 ∂p −g ρ ∂z

(6.12c)

On the basis of this first classification level, Jeffreys introduced a second one, in which he divided winds into four families related to their extension and with the zone where they develop; they include: (a) planetary scale phenomena causing the general circulation; (b) continental scale phenomena, including monsoons, with significant differences respect the general circulation; (c) phenomena on a scale comparable with the British Isles, in particular mid-latitude cyclones; (d) small-scale phenomena, with size—at least in one direction—within some tens of kilometres; they include tropical cyclones, tornadoes, sea and land breezes, valley and mountain winds as well as foehn and katabatic winds. Finally, Jeffreys intersected his two classifications, obtaining the scheme in Table 6.1; beside the Eulerian, geostrophic and antitriptic winds, it included a fourth wind, caused by a thermal gradient. Tropical cyclones are atmospheric events towards which mankind feel awe, in part because of their destructive effects, in part because of the difficulty of understanding their secrets (Sect. 4.1). Thanks to the advancements in atmospheric monitoring, meteorology and communication systems, by the early 1940s a huge amount of data on such events had been collected. Accordingly, the areas and the periods of the year in which they develop, their most common trajectories and their consequences were rather well known (Sect. 10.1). There were, in other words, plenty of elements to formulate their statistical and phenomenological picture [34]. Remarkable difficulties still remained, conversely, as regards to the understanding of their mechanisms and the forecasting of their evolution. From such reality, a vast interest sparked off, aimed at two subjects: modelling and forecasting [100]. After the pioneering stage in which Grady Norton (1894–1954) [48], director of the hurricane forecast centre at the U.S. Weather Bureau from 1935 to 1954, became a legend for his ability to sense the trajectories of storms based on his experience, the modelling and forecasting of the tropical cyclone entered the scientific stage between

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the 1940s and the 1950s [101]. In 1940, Gordon Dunn (1905–?) [102] developed a procedure to identify its position and to follow its evolution in the subsequent 24 h. In 1947, Depperman [103] formulated the first model of the tropical cyclone, schematising it as a modified Rankine vortex.7 The most innovative contribution came from Herbert Riehl (1915–1997), a German meteorology professor at the Chicago University, who in 1944 was sent by Rossby at the new tropical meteorology centre of the Puerto Rico University to study hurricanes. Before then, resuming concepts introduced by Dove and developed by Abbe (Sect. 4.1), many researchers [104, 105] attempted extending Bjerkness’ and Solberg’s theory to tropical cyclones. Analysing Dunn’s data, Riehl conversely proved the existence of pressure waves moving, at a fairly regular rate, from Africa towards the American East Coast, sometimes reaching the Pacific Ocean. A hundred of such waves—hereinafter referred to as “easterly waves”—developed every year, in the summer and in the autumn; approximately 7 or 8 of them became hurricanes.8 With such premises, Riehl made huge advances in the interpretation of the physical phenomena governing tropical storms. In 1948, he described their dynamics and the conditions required for their development [106]. In 1954, he published a book [107] in which he attributed the causes of tropical cyclones to atmospheric instabilities taking place near the equator, approximately between −10° and +10° latitude. In 1960 [108], he clarified their energetic source, namely the latent heat released by the condensation of water vapour over the oceans, and the transformations that kept them active. The first models to forecast the evolution of hurricanes appeared at the same time. One of them was developed in 1956 [109]: it used the zonal (along parallels) and the southern (along meridians) components of the geostrophic velocity to start a regression based on historical case studies of similar phenomena. It was the prelude to the formulation of methods where the dynamic model of the cyclone was paired with a statistical–climatological procedure to appreciate its evolution [110, 111]. Soon after satellites started transmitting images of the formation and evolution of tropical storms (Sect. 6.2); even so, the modelling of tropical cyclones is still one of the most unsettled and, in part, controversial meteorology issues [100]. The study of the wind phenomena associated with thunderstorm cells took advantage of the evolution and diffusion of radar (Sect. 6.2). It dealt with frontal winds, already considered within polar front theory (Sect. 6.3), downdrafts and updrafts as well as tornadoes, the most destructive natural event (Sect. 10.2). The scientific interest for thunderstorm winds appeared in the mid-nineteenth century, thanks to the works on the role of electrical and thermal phenomena. In 1839, Jean Charles Athanase Peltier (1785–1845), a French physicist and meteorologist, maintained that all the strongest local storms were caused by air electricity. His 7 According

to Depperman, a mature tropical cyclone consists of four zones: (1) an external region with wind speed increasing towards the interior and limited convection; (2) a belt, in the internal portion of which the wind reaches hurricane intensity, with gale lines and intense convection; (3) a ring that is the seat of strong precipitations, gales and maximum speed; (4) the eye, inside of which a quick drop of the speed takes place in the direction of the centre. 8 In America, a tropical cyclone is defined as a hurricane when the wind speed reaches 100 km/h.

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assertions inspired theories and interpretations that originated a heated debate in the late nineteenth century [112]. On 5 June 1880, John Tice, “The Weather Prophet of St. Louis”, published an article on the Cincinnati Inquirer where he wrote that electricity was the cause of all meteorological phenomena, including wind, cloud, rain, hail and snow. In the same period, James Craig Watson (1838–1880), director of the Washburn Observatory, Madison, wrote that attributing the origin of tornadoes to electricity was “inconceivable and opposed to any science law”. This issue came before many American courts for insurance disputes and John Park Finley (1854–1943) was entrusted to explain the origin of storms. For such purpose, in 1882 he examined the electrical properties of 600 tornadoes [113] and wrote Scientific Resumé of Tornado Characteristics (1887), where he noted the occurrence of lightnings before and after each of them. He also remarked that there were no objective reasons to assert that electricity was the cause of the tornado; he expressed the opinion, however, that only electricity could bring forth a phenomenon “so sudden, dreadful, irresistible and terribly destructive”. Shortly after, Möller [114], in 1884, and William Morris Davis (1850–1934) [115], in 1894, published the first thunderstorm and downdraft models. In 1911, Alfred Lothar Wegener (1880–1930) [116] contributed to develop the knowledge of atmospheric thermodynamics. In 1921, the Estonian meteorologist Johannes Peter Letzmann (1885–1971) (Sect. 10.2) interpreted the tornado as an instability phenomenon characterised by a downward circulation towards its centre and by an upward circulation at its periphery [117, 118]. The following year Charles Franklin Brooks (1924–1983) [119] treated the thunderstorm as a thermodynamic engine. In 1937, the English meteorologist Sir George Clarke Simpson9 (1878–1965) and Scrase [120] carried out measurements through which they clarified the distribution of electrical charges in thunderstorms (Fig. 6.19). They proved that the upper part of the thundercloud is positively charged, whereas the central part is mostly negative; a small centre of positive electrical charges is sometimes present in the lowest part of the cloud, where rain is formed. In 1938, Suckstorff [121] provided the first interpretation of the causes that create an updraft of hot air in the thunderstorm. The turning point in the knowledge of thunderstorm cells took place between the late 1940s and the early 1950s, mostly thanks to Horace Robert Byers (1906–1998), an American meteorologist who was a pioneer of meteorological aviation, synoptic weather forecast, convective storms, cloud physics and weather modification. He was a master in scientific research organisation and management, who surrounded himself with important figures and provided them with the best work environment. Byers, a former student of Rossby and the author of meteorology books [79, 122], gained his renown by heading the Thunderstorm Project, carried out between 1946 9 In

1910, Simpson was the meteorologist of Robert Falcon Scott’s (1868–1912) “Terra Nova” Antarctic expedition. In his role of director of the U.K. Meteorological Office, he generalised the use of the Beaufort scale from the sea to the mainland (Sect. 4.3). He also proposed an amendment of the Beaufort scale, known as the Simpson scale, to define wind strength. The Saffir–Simpson scale, which defines the intensity of hurricanes (the scale ranges from 1 to 5, and the 5° corresponds to hurricanes with wind speed exceeding 249 km/h), was developed in 1971 and applied from 1973.

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Fig. 6.19 Distribution of electrical charges in the thundercloud [45]

and 1947 by the U.S. Weather Bureau, Army Air Force, Navy and the National Advisory Committee for Aeronautics10 (later the NASA). The project identified as a priority the knowledge of nine elements: (1) updrafts and downdrafts; (2) inward and outward horizontal motions; (3) horizontal and vertical temperature gradient; (4) electric fields; (5) rain distribution and intensity; (6) temperature changes at ground level; (7) pressure changes at ground level; (8) fluctuations in the surface wind speed; (9) turbulence and wind gusts. To acquire such information, two sites were selected in Florida and in Ohio, both of them characterised by flat terrain. Airplanes detected vertical motions as well as horizontal and vertical temperature gradient. Horizontal motions were monitored by balloons tracked by radar. Rain, temperature, pressure and wind speed at ground level were measured through a network of 55 stations spaced by 1 mile in Florida and 2 miles in Ohio; every station was equipped with pluviometers, hygrothermographs, baro10 During the Second World War, researches were carried out on flight in adverse weather. Despite this, towards the end of the war a phenomenon that caused several accidents in aviation was still mostly unknown: the thunderstorm. Many research projects were then arranged, the importance of which was highlighted by the American Airlines with a letter they sent to the Civil Aeronautics Board in 1943. That was the origin of many initiatives leading, in early 1945, to a large project on thunderstorms that commanded for peaceful purposes many aircrafts and equipment used for military purposes.

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Fig. 6.20 Thunderstorm cells arrangements [125]: a randomly; b in squall lines

graphs, cup anemometers and wind vanes. Turbulence and gusts were measured by anemometers and accelerometers equipped with photographic systems. Radars unified the collected data and localised the airplanes (Sect. 6.2). The detection of the electrical fields represented a serious issue [123, 124]. Measurements proved that a thunderstorm is a violent form of convection11 [125, 126]. It appears like a wild cloud, accompanied by lightnings and thunders, gusty winds, heavy rain and, every now and then, hail. It consists of cells arranged either randomly (Fig. 6.20a) or in squall lines12 [127] (Fig. 6.20b). In every cell, a process lasting around 30 min and evolving over three stages (Fig. 6.21) takes place: (a) the cumulus stage in which, because of unstable phenomena of a convective nature, an updraft of hot air takes place, originating a large cumulus; (b) the mature stage, in which the cumulus becomes a cumulonimbus, intense precipitations occur and, beside the updraft of hot air, a downdraft of cold air appears: the latter diffuses at ground level, causing sudden wind changes, a temperature drop and an increase in pressure; (c) the dissipative stage, in which the updraft exhausts itself, the thunderstorm loses strength and vanishes. The final report of the project, published by Byers and Roscoe Braham [128] in 1949, is a milestone of meteorology.

11 Atmospheric convection is like the one that occurs in a fluid layer made unstable by the addition or subtraction of energy in a limited area. It was reproduced in a laboratory for the first time by Henri Bénard (1874–1939) in 1901 [125]. He prepared a fluid layer, 1 mm thick, on a metal plate heated to uniform temperature. The upper layer was free and in contact with air at lower temperature. This led to the formation of many vortex cells, which created updrafts in the centre of the cells and downdrafts at the interface between adjacent cells. Taking his cue from this study, in 1916 Lord Rayleigh reproduced theoretically Benard’s experiments [126]. He imposed a small disturbance at the base of a resting layer of liquid, heated from below, disintegrating it into vortex cells. He thus proved that the convective instability of a fluid layer between two horizontal planes was governed by its vertical thermal gradient. 12 The squall line is a line of thunderstorm cells or strong winds due to instability. They are shortlived, are accompanied by thunder, lightning and precipitations, occur along the front of a cyclone. In 1950, Tepper [127] explained that first a sudden increase of the surface pressure occurs. Then, a quick wind shift occurs followed by a temperature break and gusty winds, the start of rainfall and the pressure maximum. All happens in a few minutes.

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Fig. 6.21 Thunderstorm cell cycle [128]: cumulus (a), mature (b), and dissipative (c) stage

In the meantime, Irving Langmuir (1881–1957), Vincent Schaefer (1906–1993) and Bernard Vonnegut (1914–1997) opened the age of weather modification through cloud seeding (Sect. 10.1). Byers was struck by the potentialities of the new discoveries. He then put his mind to this subject and in 1951 was appointed as head of the Artificial Cloud Penetration Project to which he transferred the best assistants who flanked him in the Thunderstorm Project. Thanks to this project, the Chicago University consolidated its primacy in meteorology, giving new contributions to the physics of clouds [129]. In 1953, Byers summoned a Japanese professor of meteorology, Tetsuya Theodore Fujita (1920–1998), who would assume a leading role in the discipline, providing key contributions to the downburst and tornado understanding and to the assessment of damage due to such phenomena (Sect. 10.2). The results of the Thunderstorm Project provided inspiration for many researches. New models that improved Byers’ and Braham’s one were developed; the most famous, by Wichmann [130] in 1951, generalised the diagram shown in Fig. 6.21 to the case of asymmetrical thunderstorms. Also, new theories were originated, including the one proposed in 1950 by Richard Segar Scorer (1919–2011) and Franz Henry Ludlam (1920–1977) [80, 131], who interpreted laboratory experiments; known as “bubble theory”, it did not schematise the convective cloud through a single updraft, but as a series of bubbles that came one after the other, each one in the wake of the previous one. Up to the end of the 1950s, however, there were no objective elements to clarify what theory was closer to reality [45]. An unexpected problem arose in this period. The studies carried out up to the late 1940s agreed that the thunderstorm downdraft was weakened, and so incapable of producing violent outflows parallel to the Earth surface, when it reached the ground [132]. Willbrord Müldner (1906–1981) [133] observed, instead, that the thunderstorm striking Nuremberg on 22 July 1948 caused the fall of many trees in a radial pattern of a 3–5 km area. From then on, a number of witnesses attested that the

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downdraft that impacts over the ground is expelled from the centre outward with surface gusts up to 100 km/h.13 In 1955, Ross Gunn (1897–1966) [134] carried out the first measurement of the electricity in a tornado. It was the prelude to the 1960 paper by Vonnegut [135], where the first electric theory of such phenomena was introduced. It was based on the concept that a thundercloud produced 10–20 lightnings per second, equivalent to 10 KW of power. Vonnegut noted that many tornadoes, as well as waterspouts, did not show any electrical phenomena and stated that electrical energy could transform into mechanical energy through two processes: in the first one, proposed by Lucretius, lightnings heat the air and produce a vortex of thermal nature; in the second, ionised air is accelerated by an electrical field. Neither explanation is convincing. Shoreline breezes are phenomena known since antiquity. By day, the coldest air moves from the sea to the land, originating sea breezes; by night, the phenomenon reverses and warm air moves from the land to the sea, originating land breezes. The first mathematical treatment of breezes was developed by Jeffreys in 1922 [98]. He interpreted this phenomenon through the balance of the surface friction force and of the pressure gradient caused by the different warming of the land and of the sea. Kobayasi and Sasaki [136] as well as Arakawa and Utsugi [137] applied Rayleigh’s convective theory [126] in order to integrate Jeffreys’ model with the presence and transfer of vertical heat. Haurwitz [138] and Schmidt [139] generalised this formulation through a linear theory that included Coriolis force. William Harvey Pierson, Jr. (1911–2008) [140] extended these models by taking into account the turbulence generated by the surface friction as well as the thermal contrast between the land and the sea; his studies were corroborated by the observations by Brunt [77] and Willett [141]. Friedrich Defant [142] treated the breezes as circulative cells, in accordance with Rayleigh’s convection theory [126]; his solution interpreted the periodical character of the local circulation and its size as a function of the difference in temperature between the sea and the land. It was the prelude to Defant’s 1951 fundamental article [143], where he provided a qualitative description of sea and land breezes that is considered a benchmark. Because of their different specific heat, water heats and cools more slowly than the ground, which tends to transfer heat to the air more quickly. By day, therefore, the ground heats up and heats the air above it, which tends to raise by virtue of the turbulent mixing due to atmospheric instability. The expansion of the air over the ground causes a fall in pressure with respect to pressure over water; the thickening of the upper air over the ground, on the other hand, causes a rise in pressure with respect to the pressure over water at the same height. This causes a circulatory motion where hot upper air migrates from the shore to the sea; the cool surface air migrates from the sea towards the land and is named sea breeze (Fig. 6.22). By night, the situation is reversed. The ground cools down more quickly than water, and the circulation changes its direction. The migration of surface air from the land towards the water is called land breeze.

13 In

1976, Fujita will define the “downburst” as a downdraft dangerous for airport operations.

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Fig. 6.22 Sea breeze [143]

Defant observed that the occurrence and the properties of the breezes depend on geographic position, season and time. Sea breezes go as far as 15–50 km inland in temperate regions and up to 145 km in the tropics; land breezes go as far as 10 km over water. The height of the atmospheric layer affected by breezes varies from 150 m for small lakes, to 200–500 m for great lakes and seashores, and up to 1300–2000 m in tropical coastal areas. The intensity of breezes covers the whole range of the Beaufort Scale: it ranges from 0 to 3 near small lakes, increases to values from 4 to 5 along seashores and can reach storm levels in tropical zones. Soon afterwards, Pearce [144], Estoque [145] and Fisher [146], taking advantage of the advent of computers, carried out the first numerical integrations of the nonlinear hydrodynamic equations, simulating breezes by means of two-dimensional models. The study of the local winds with a thermal origin developing in valleys and along their slopes dates back to the late nineteenth century, thanks to the pioneering research of the Austrian Julius Ferdinand von Hann (1839–1921) [147, 148]. Such studies continued in the early twentieth century [149, 150] up to the publication of a series of papers in which Wagner [151, 152], between 1929 and 1938, illustrated the phenomenological aspects of the coexistence and interaction of two phenomena: valley and slope winds. The first ones originate a three-dimensional circulation in the valleys. The second ones include the winds blowing up and down the slopes of valleys and mountains; they are respectively called anabatic and katabatic winds. In 1942, Prandtl formulated a stationary model of katabatic winds [153], which Defant generalised to the non-stationary case in 1949 [154]. Two years later, Defant [143] provided a setting for anabatic and katabatic winds in the context of valley circulation (Fig. 6.23). Thanks to these studies, in the early 1950s it became clear that, by day, the slopes exposed to sun absorb more heat than the valley line; the hot airflows up along the mountainsides towards the peaks, while the cooler air of the valley lines rises to replace it. This generates an airflow moving from the bottom upwards, known as valley breeze, which falls into the category of anabatic winds. By night, the situation is reversed: the previously warmer areas shed their heat and the cool and heavier airflows down towards the valley lines. This generates an airflow moving from the top downwards, known as mountain breeze, which falls into the category of katabatic winds. Both phenomena involve moderate speeds. Katabatic winds, in some peculiar geographic conditions, can reach very high intensity, even higher than those of hurricane winds. In this case, they are also called fall winds.

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Fig. 6.23 General pattern of valley and slope winds [143]

The strongest katabatic winds, or those most recurring in specific geographical contexts, are divided into two types: those warmer than the surrounding air and the cooler ones.14 The warm variant of the katabatic wind occurs when a moving air mass meets a mountain range and moves up its slopes. When the range is high enough, water vapour in air condenses, causing rain in the valley and snow on the peaks: the air becomes dry and cold, crosses the range and quickly moves downhill on the opposite slope, where it is subjected to adiabatic heating; such flow, known as Foehn,15 is common on the Swiss and Austrian side of the Alps. Hann formulated the first model of the slope wind [147] in 1866. Subsequent literature about Foehn is extensive [155]. The cold variant of the katabatic wind occurs when a mass of very cold air, after having crossed a mountain range or a plateau, meets a sudden fall of the ground level, with warmer and stagnant air lying above it. The cold air moves down because of the gravitational effect and, converting its potential energy into kinetic energy, acquires speed, often up to devastating levels. This phenomenon is evident along the Dalmatian coast, especially in Rijeka and Trieste where it is known as bora [156, 157], and in the Gulf of Lion, where the situation is made worse by the channelling into Rhone valley; the deriving wind is called mistral [158].16 The strongest wind speeds occur in Greenland and in Antarctica, where the katabatic wind has been the subject of theoretical and experimental researches [159] since the time of the first expeditions (Sect. 8.4).

14 The term “katabatic” (from the Greek “katabatikos”, “running downhill”) is currently used only for the winds cooler than the surrounding air. 15 In Italian, the Foehn is called “favonio”, the Latin “favonius” the Roman used to call the west wind. This wind is called zonda in Argentina, chinook in the Rocky Mountains, devil’s wind in San Francisco, Santa Ana wind in Southern California, sharav or hamsin in Israel, hamsin in Arabia, Nor’wester in Christchurch, New Zealand, Halny in the Carpathians, Samul on the Iranian mountains in Kurdistan, Bohorok in Sumatra. 16 The cold version of the katabatic wind occurs in many other areas worldwide, like Japan, where it is known as Oroshi, and in Novorossiysk, where the bora reaches the northern coast of the Black Sea coming from Caucasus.

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There is still an issue to discuss, studied in the first half of the twentieth century under the speculative aspect and for its importance for flight: the forced ascent of the air along the slopes of a mountain range and the formation of stationary waves behind it. The state of the art published by Corby in 1954 provides a general picture of this topic [160]. He classified these studies into three families: observations and experience, theoretical analyses and experiments on models. The first observations were carried out by Masano Abe in 1929 [161]. He documented the motion of clouds over the Mount Fuji through a series of photographs that highlighted undulations behind the mountain. Since the first days of glider flight, pilots made use of updrafts of thermal origin on the windward front of mountain ranges. Starting in 1930, they began to report flight experiences in atmospheric waves. In 1939, McLean took advantage of stationary waves to perform the first ascent on the leeward front of a mountain range [162]; he proved that stationary waves can reach 3350 m height. The pilots of powered aircraft first documented these waves between 1951 [163] and 1952 [164]. In the same period, Förchtgott [165], a glider flight instructor, examined various mountain places in Bohemia, using light airplanes and instrumented gliders; he also studied the motion of clouds, the trajectories of fumes and the flight of birds. Thanks to such experiences, he formulated a subjective but plausible theory. He noticed that stationary waves only appeared if the atmosphere was stable or neutral, if the wind was perpendicular to the range crest, and if its direction changed very little with the height. He also noticed how the topography of the upwind front was of little importance, whereas downwind waves were especially remarkable where steep slopes were present. The theoretical analyses about the perturbations caused by mountain ranges derived from a study performed by Kelvin in 1886 [166]; he treated the flow as incompressible, homogeneous and inviscid. In 1906, Lamb [99] extended this formulation to neutrally stratified currents. Both of them showed the formation of gravitational stationary waves behind the obstacle, as long as the flow speed was less than a critical value depending on its depth. Actually, atmosphere is more complex: on hot days, it is stable; it is also compressible, so it is not possible to identify a layer with finite thickness; finally, disregarding both Earth rotation and Coriolis force is unacceptable. Between 1946 and 1948, Queney [167] assumed the flow as laminar and isentropic, disregarded surface friction and took Coriolis force into account. The problem, schematised as bidimensional, was approached through a perturbation technique. The motion was assimilated to an adiabatic disturbance superimposed on the background flow. Bringing together the Navier–Stokes and continuity equations as well as the one expressing the isentropic nature of the flow, a strongly nonlinear system was obtained. Assuming that both the disturbance and the obstacle were small with respect to the background flow, the system was then linearised and led to a second-order partial differential equation from which the perturbation was obtained. The shape of the range was initially assumed to be a sinusoid, then a bell. Queney obtained various solutions, associated with the size of the obstacle. If the obstacle depth is in the order of 1 km (Fig. 6.24a) atmospheric stability and Earth

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Fig. 6.24 Queney’s flow categories [167]: obstacle depth in the order of 1 (a) and 100 (b) km

rotation play a secondary role; the perturbation steadily decreases with increasing distance. If the obstacle depth is in the order of 10 km, Earth rotation remains negligible, but stability becomes important; no lee waves occur. If the obstacle depth is in the order of 100 km (Fig. 6.24b), both stability and Earth rotation are important; a train of stationary waves is originated downwind the obstacle. Between 1949 and 1955, Scorer [168, 169] criticised Queney’s results, judging them inconsistent with the observation of the cloud motion and with the experiences of glider pilots. He then formulated a new model in which he retained the hypotheses of laminar, frictionless, stationary and isentropic flow; on the other hand, he took into account the vertical variation in stability and in wind shear, limited his analyses to 50 km deep obstacles and disregarded Coriolis force. He proved that the flow perturbation is very sensitive to the various situations. All these solutions were based on the hypothesis of small perturbations and on the linearisation of the equations of motion. Long overcame this limitation between 1953 and 1954, formulating the first nonlinear model [170, 171]. He introduced, however, some approximations; in particular, he considered the flow as uniformly stratified, frictionless, and with a speed profile independent from height. The first experiments on models were carried out in Tokyo by Masano Abe in 1929 [161]. He attempted to create conditions similar to those of the atmospheric boundary layer in a wind tunnel. He studied the formation of clouds and the wind speed on the slopes of Mount Fuji in a duct 0.8 m wide, 0.35 m high and 0.9 m long, the model being in the 1:50,000 scale. Abe implemented the speed profile by means of auxiliary fans and flow interruptions; he created the thermal stratification by placing dry ice on the floor; he reproduced Earth rotation through fans on the side wall of the tunnel. He realised, moreover, the first topographical model in history. He continued these experiments up to 1942 [172]. Between 1929 and 1939, Field and Warden carried out experimental tests about the wind field of the Rock of Gibraltar at the NPL [173]. They were performed

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Fig. 6.25 Rock of Gibraltar model [173]

because of many air accidents attributed to wakes generated by topography. The tests, carried out with a 1:5000 scale model (Fig. 6.25) without taking into account atmospheric stability, confirmed that the primary cause of accidents was represented by the downwind waves at the Rock in particular wind conditions. Subsequent field measurements, carried out by sounding balloons and theodolites, provided similar results. In 1936, Marie-Joseph Kampé de Fériet (1893–1982) [174] carried out tests in the wind tunnel of the Fluid Mechanics Institute in Lille, France, to examine the vortex structures due to Mount Cervino (1936); neither Earth rotation nor thermal stratification was reproduced. Similar studies were carried out in 1947 at the NPL [175] to simulate topographically complex terrains, and in 1951 by Rouse [176] on large models of mountains inside hangars; the flow was generated by fans, with no stability control. These experiments were criticised by Batchelor and Scorer in the early 1950s, who expressed serious reserves about measurements carried out paying scant attention to similarity. Given the wide range of different events, the tendency developed to classify wind phenomena in relation to their time and spatial scale following Jeffreys. In 1951, Fujita [177] used for the first the “micro” prefix for very small-scale atmospheric phenomena in contradistinction to the “synoptic” term applied to cyclones. In 1956, Fujita himself, Herman Newstein and Morris Tepper (1916–) [178] published the first manual on meso-scale analysis, using such expression to identify wind phenomena with scale ranging from 10 to 100 km. In 1959, the American Meteorological Society published the first meteorology glossary [179]. Tepper [180] defined meso-scale meteorology as the link between macroscale atmospheric motions and local weather, introducing the first quantitative classification of macroscale (with surface extension larger than 483 km), meso-scale (from 16 to 160 km) and micro-scale (smaller than 8 km) wind phenomena. He criticised some of Charney’s concepts, maintaining that motions smaller than the macroscale were not “meteorologically insignificant” and could not be treated as “meteorological

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noise”. They were instead vitally important for weather forecasts and for the energy characterising atmospheric circulation. These concepts, at first hardly accepted, then gradually recognised especially thanks to Smagorinsky17 [181], are today universally acknowledged and applied.

6.5 Micrometeorology Quoting the definition provided by Sir Oliver Graham Sutton (1903–1977) in the very title of his famous book [182], micrometeorology is “a study of physical processes in the lowest layers of the earth’s atmosphere”. Sutton observed that “in the historical development of meteorology, interest has centered chiefly on the broader aspects of climate and weather, processes which involve large regions of the earth’s surface and great depths of the atmosphere. In recent years, however, more and more attention has been paid (…) to the detailed study of phenomena which occur in the layers of the air nearest the ground. (…) Although such features are of minor importance when viewed on the climatological atlas of the farecaster’s synoptic chart, they may profoundly affect human welfare and economy and for this reason, if for no other, are worthy of serious study”. Sutton also stated that “the development of micrometeorology as an exact science demands not only the examination and interpretation of highly accurate observations made in the layers of air adjacent to the surface but also a study of the physical processes which give rise to microclimates. This implies a detailed knowledge of the motion of air near a solid or liquid boundary of variable shape and changing temperature. The outstanding feature of such motion is that the flow is normally turbulent, so that considerable mixing takes place. It is to this fact that the lower atmosphere owes many of its characteristic properties on which much of life depends”. In view of this conception and of the period in which it was devised, it would appear that micrometeorology, intended as the study of the physical phenomena occurring in the air layer shrouding the Earth, is a development of the Prandtl’s boundary layer theory (Sect. 5.1), revised through a change of scale in the light of the motions of the air masses taking place in the atmospheric belt that is not affected by ground effects. Assuredly, it is not so. Micrometeorology came into existence between the late nineteenth century and the early twentieth century on independent grounds. It often anticipated, under different prospects, concepts subsequently or simultaneously introduced by Prandtl and by the Göttingen School in the field of fluid dynamics. 17 In 1963, Smagorinsky published a revolutionary paper [181]. He included wind speed, atmospheric pressure, Earth and Sun radiation, cloud cover and precipitations among the variables of the primitive equations, taking into account the turbulence that develops on scales smaller than the grid size of the numerical model. This conception, developed by Douglas Lilly (1936–1998) between 1966 and 1967, originated the Smagorinsky–Lilly model. It represents a cornerstone of the large eddy simulation (LES) and of the future developments of computational fluid dynamics (CFD) (Chap. 11).

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Fig. 6.26 Stevenson’s mean wind speed profile [183]

Sutton, considered by many as the founder of micrometeorology, was the first to make the effort of synthesizing the different views of fluid dynamics and meteorology into a homogeneous scientific set. Many attributed the first micrometeorological study [183] to Sir Thomas Stevenson (1818–1887). He evaluated the wind change in relation to the height above ground carrying out, from 1878 to 1880, simultaneous measurements by means of anemometers along a pole 15 m high in a plot of farmland. They proved that the speed increased with height: it followed an almost parabolic law up to approximately 5 m, where the ground caused strong disruption to the wind; from 5 to 15 m the growth was almost linear. Stevenson, taking into account the irregularity of the flow in contact with the ground, represented this law by a single parabola, with its vertex approximately 22 m below the ground (Fig. 6.26). It is considered as the first wind speed profile proposed in the literature. From September 1883 to June 1884, Archibald [184, 185] carried out new measurements by means of a pair of kites, Biram anemometers and a theodolite. Even though only the results of a few experiences were available because of several accidents, Archibald noticed that wind speed increased up to nearly 150 m eight. He also remembered some estimates performed by Vettin in 1883 sighting the movement of clouds and, above all, the formula of the speed profile V he proposed [25]:

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 z 1/n V (z) = V (h) h

(6.13)

where z is the height above ground, h is a reference height, and n = 4 is a parameter that assigns the shape of the profile. Archibald noted his measurements confirmed the qualitative reliability of Eq. (6.13), but also highlighted how n assumed values from 2 to 7. At the same time, he maintained that the available data were too scarce to set a forecast law. He then confirmed Vettin’s choice, n = 4, as a reasonable value. Equation (6.13) proposed by Vettin and Archibald in the meteorological field was the first expression of the power law; it anticipated by almost 40 years Eq. (5.17) obtained in 1921 by Prandtl [186] in the fluid dynamics field (Sect. 5.1). A few years after these measurements, a remarkable figure appeared on the meteorological scene: Alexander Gustav Eiffel (1832–1923). When the tower named after him was completed in 1889 (Sect. 4.7), Eiffel understood it represented the occasion and the tool to carry out scientific experiences. He then carried out, between 1889 and 1894, a campaign of experimental tests [187], the results of which are still of great interest for physicians, physicists, meteorologists and engineers [188–190]. After such experiences, Eiffel, fascinated by these studies and disappointed because of some attacks about the construction of the Panama Channel, decided to leave the engineering profession and to devote the rest of his life to scientific research in atmospheric and aerodynamic sciences (Sects. 7.1 and 7.2). The results he obtained were no less important than those he achieved in structural design. Eiffel understood that the tower was a meteorological observatory capable of describing, like never before, the changes in atmospheric parameters in relation to the height. He built a shelter for a meteorological equipment at the tower top (Fig. 6.27a), where he put a barometer, a thermometer, a hygrometer, an anemometer and a wind vane. He recorded the pressure at 312.90 m height and the temperature and humidity at 301.80 m, integrating the temperature measurements with the data detected by two stations at 123 and 197 m. The anemometer fitted at 305 m height consisted of a revolving vertical pin supporting a horizontal bar: on one side, there were 6 fins tilted by 45 deg, on the opposite side two V-shaped plates turning the anemometer in the wind direction (Fig. 6.27b); recordings were collected on a roll that executed a complete revolution in one day (Fig. 6.27c). Wind direction was measured by two wheels fitted on a horizontal bar that rotated on a vertical pin. The data were compared with the measurements at ground level of the Bureau Meteorologique, 480 m away from the tower, in an area fairly free from obstructions. Eiffel was possibly the first engineer to understand the importance of wind actions on structures. He devoted his main efforts to their measurement, writing that “during my engineering career, wind has always been a concern for me, because of the exceptional size of my structures. It represented an enemy I always had to fight against. My studies to determine its strength have gradually led me to study other meteorology aspects and to build a complete weather measurement station” [190]. From the latter, he obtained results whose interpretation was decisive for the subsequent developments of wind engineering.

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Fig. 6.27 Eiffel Tower [187]: a meteorological equipment shelter; b anemometer and wind vane; c roll for wind recording

Fig. 6.28 Recordings of wind speed and direction, on 12 November 1894 [187]

Eiffel, comparing the wind speed at the tower top and at the ground level, noticed a ratio from 2 to 6, depending on weather conditions. He also noticed remarkable differences in the wind direction. Figure 6.28 shows the recordings carried out on 12 November 1894, during one of the fiercest storms that struck Paris in that period. At 7:00 A.M., the storm centre was at the end of the English Channel, where the barometer fell by 19 mm during the night; it reached Denmark on 13 November at 7:00 A.M. after having crossed the whole Western Europe and the Northern and Central France in particular. At the top of the tower, wind speed twice reached 42 m/s, at 6.13 and 6.18 P.M., whereas it was equal to 13.7 m/s at the height of 20.9 m, on the terrace of the Bureau Meteorologique. Eiffel also understood the limits of his measurements by examining the recordings of Samuel Pierpont Langley (1834–1906) [187], an astronomer, meteorologist and aviation pioneer (Sect. 7.4), secretary of the Smithsonian Institution in Washington and director of the Allegheny Observatory in Pittsburgh. The latter were carried out

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using light Robinson anemometers, placed on a tower at 47 m height. Langley noticed “the diagrams show the remarkable property that the more wind absolute speed is higher, the more wind fluctuations are marked. In case of strong winds, air moves tumultuously and speed can increase up to a time (…), and then drop to calm, then increase again, (…) This observation confirms my assumptions about the inadequacy of the recording to express the actual swiftness of such variations. Since the speed is calculated before the measured interval between two electrical contacts, an instant stop (…) is represented by the recording as a simple slowdown of the wind and significant events like those I just mentioned necessarily go unnoticed, even to the most sensitive equipment. It is easy to understand, however, that the more contacts are frequent, the more the recording will approach the reality; with this purpose in mind, I took care to establish a contact at every half-revolution of the windmill, which will then generally provide multiple recordings per second”. “To provide a more accurate picture I would take the first five and half minutes of the diagram shown in Fig. 6.29. The diagram marked as ‘ABC’ is obtained by means of an ordinary anemometer of the meteorological office for the passage of two miles of wind. The wind speed, (…) 10.28 m/s at the beginning of the considered period, drops to 8.95 m/s, for the first mile. This is the ordinary anemometric recording (…) that is called ‘wind’, i.e. the conventional wind of the aerodynamics treatises, in which it is considered a practically continuous flow. It is entirely different, however, if we examine the track recorded at the same time, from second to second, by and exceptionally light anemometer. The initial speed of 10.28 m/s, at 12 h, 10 min and 18 s, increases to 14.70 m/s in 10 s and then, in the subsequent 10 s, goes back to its primitive value; it then increases again, in 30 s, up to 16.10 m/s, with similar oscillations that even include, at a given moment, an absolute calm.” Eiffel did not have doubts about the importance of these observations and hoped that similar experiences could be repeated using anemometers more sensitive to speed changes. This was the only way [187] “that will make it possible to represent a phenomenon, so little known and of so great interest, of which we cannot accurately measure neither speed nor pressure. The mean speeds provided by usual instruments are only, at least from the viewpoint of engineering and structure stability, of marginal interest. Wind pulses, conversely, with their actual intensity at each instant are of vital importance, which remains to be determined”. These Eiffel’s words confirm the Reynolds’ principles (Sect. 5.1), according to which the instantaneous speed is the sum of a mean part, which slowly changes over time, and of a fluctuating part, which quickly changes over time; they also highlight the importance of the harmonic content of the fluctuations to evaluate the wind-excited structural response (Sect. 9.6). In the same spirit, Eiffel examined the recording of the wind at the top of the tower during the storm that struck Paris on 6 September 1899 (Fig. 6.30) [187]. The progress of the curve showed the strength of the wind gust that begun at 8:52 P.M. as well as the increase in speed, from 4 to 42 m/s; it remained stable for 3–4 min, then returned to small values after 9:30 P.M., rotating by approximately 180 deg between 7 P.M. and 1 A.M. Through this figure, Eiffel documented one of the first non-stationary wind phenomena in the literature; they are currently studied worldwide.

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Fig. 6.29 Wind speed recording by Langley [187]

Eiffel, using his tower, also performed the first measurements of the vertical component of the wind speed by means of a device consisting of four flat tabs canted at 45 deg, joined to a vertical rotating shaft through four cross-arms. The rotation direction changed with the direction of the vertical speed. The device was enclosed in a vertical cylinder with open ends, which reduced the perturbations due to the horizontal speed. The test proved that updrafts prevailed on downdrafts; both of them were much smaller than the horizontal components [187]. Eiffel, not contented with these results and, conversely, increasingly intrigued to penetrate the secrets of the wind, devoted himself to set up a network of 25 weather stations [191]. He looked after the simultaneousness of acquisitions, the homogeneity of instrumentation, the protection from extreme phenomena and the recording of daily

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Fig. 6.30 Wind speed and direction at the top of the Eiffel Tower on 6 September 1899 [187]

maximum and minimum values. From 1903 to 1912, he published a collection of synoptic charts that represents the basis of modern French meteorology. In the same period (1893–1896), Fridtjof Wedel-Jarlsberg Nansen (1861–1930), a Norwegian explorer, scientist and statesman, Nobel Prize winner for peace in 1922, reached 86°14 latitudine north, during a polar expedition aboard the Fram, a ship built to withstand the pressure of ice. During this mission, famous for its consequences on wind energy (Sect. 8.1), Nansen noticed that the ice movement caused by the wind did not follow the air direction, but diverged to the right by nearly 20–40 deg [192]. He explained this phenomenon as a consequence of the Earth rotation. He also observed that water layers immediately below the surface, which was dragged by the grazing wind action of wind, were diverted with respect to the upper ones. Upon his return home, Nansen discussed this issue with a Swedish oceanographer, Vagn Walfrid Ekman (1874–1954), a student of Vilhelm Bjerknes. Ekman, pushed by Nansen and inspired by Hadley, Coriolis and Ferrel on the effects of the Earth rotation (Sect. 4.1), formulated a new mathematical theory about the ocean currents caused by the wind; it appeared in two papers, published in Swedish in 1902 [193] and in English in 1905 [194]. The second paper improved and expanded the first one. Ekman first dealt with the currents caused by the wind and by the Earth rotation. He assumed that the ocean surface was flat, the wind speed and direction were uniform on the whole boundary, the ocean was infinitely deep and the water was incompressible and in stationary motion. He applied the Navier–Stokes system formed by Eqs. (3.12) and (3.25), adopting a Cartesian reference with its origin on the water surface: x = x 1 and y = x 2 lay on such surface; z = x 3 being vertical and pointing downward. He treated the monodimensional problem, imposing ∂/∂x = ∂/∂y = 0. He assumed that the forces per unit mass were only due to the Earth rotation, and then f x = 2vω sinϕ and f y = 2uω sinϕ with u = v1 , v = v2 ; ω is the Earth rotation angular speed and ϕ the latitude. The equations of motion are resulted as follows:

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Fig. 6.31 Ekman spiral [194]

d2 u + 2a 2 v = 0 dz 2

(6.14a)

d2 v − 2a 2 u = 0 dz 2

(6.14b)

√ where a = ρω sin ϕ/μ , ρ is the density, and μ is the viscosity of the water. From there, he obtained:  π − az (6.15a) u = V0 e−az cos 4  π v = V0 e−az sin − az (6.15b) 4 where V 0 is the speed of the current for z = 0, then on the water surface:   T0 dv T0 V0 = ; T0 = −μ √ =√ dz z=0 2μρω sin ϕ μa 2

(6.16)

T 0 being the shear stress exerted by wind at the air/water interface, directed along y. Figure 6.31 shows the speed profile, highlighting that the direction of the current at the surface is turned by 45 deg to the right (in the northern hemisphere) with respect to the wind direction. The longer arrow refers to the speed of the water surface; the shorter arrows indicate the speed at the depths z = kπ/10a (k = 1, 2, …). By representing each arrow at its depth, it is possible to infer a spiral profile now known as Ekman spiral. After finishing this demonstration, Ekman solved the case of the ocean with finite depth. He then treated the situation in which, besides the friction and Coriolis forces, a pressure gradient due to an uniform slope of the water surface was present. Finally, he examined the role of μ, which had previously been considered as a constant. For such purpose, he remembered Boussinesq’s treatment (Sect. 3.6) and recommended replacing the parameter μ, typical of laminar flows, with the eddy viscosity coefficient μT . He noticed the inadequacy of considering this quantity as a constant and

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proposed to assume μT as proportional to the speed gradient along z, interpreted as a measurement of the vorticity:  μT = C

du dz

2

 +

dv dz

2 (6.17)

C being a constant. Ekman, on the basis of Eq. (6.17), solved the equations of motion again, noting that the new assumption quantitatively—but not qualitatively—changed the previous spiral pattern. He also observed that this theory could be applied both to ocean currents and to atmospheric motions. Nansen’s observations leading to the Ekman spiral emerged because of the concomitance of two conditions: the presence of icebergs and the arctic latitude. The same phenomenon was difficult to note elsewhere; therefore, it was not very important. Even so, it turned out to be so essential as regards atmospheric motions and the wind representation that now few remember that the true origin of the spiral was linked to the study of currents. Ekman’s publications [193, 194] date from 1902 and 1905, before and just after 1904, the year Prandtl introduced the boundary layer (Sect. 5.1): a turning point in the culture of fluids, with unimaginable consequences for the culture of wind, took place in this period. The comparison between Ekman’s oceanographic view and Prandtl’s fluid dynamic one stresses the correspondence between these two aspects, that from then on were destined to intertwine and to be summed up, highlighting a key difference. Prandtl, dealing with bodies in fluid currents, treated boundary layers with almost evanescent thickness. Ekman, studying oceans, identified boundary layers of great thickness: they refer to the portion of water where the vorticity is concentrated and where the spiral profile due to the Coriolis’ force occurs. In the following years, the study of the wind in contact with the ground benefited of initially sporadic and scarcely linked contributions. Among the most prominent ones, there was the first study of the wind in cities [195], published in 1909 by the German meteorologist Victor Kremser (1858–1909). In the first ten years of measurements, he estimated an average speed of 5.1 m/s; in the subsequent ten years, it dropped to 3.9 m/s. Kremser attributed this change to the increase in the height of buildings. He thus stressed, at embryonal level, the role of ground roughness and of its evolution on the wind profile. In 1913, Rawson [196] observed turbulent motions whose intensity decreased with height; he thus highlighted the dualism between the mean wind speed profile, restrained by the ground, and the turbulence, enhanced by the surface friction. In 1914, Gordon Miller Bourne Dobson (1889–1976) [197] studied the mean speed profile on a plot of farmland, making use of pilot balloons (Fig. 6.32a). The tests confirmed the adequacy of Eq. (6.13) with n = 7. They also proved that the mean wind speed did not change above 450–600 m height. The analysis of these works sheds light on the interest towards the two most peculiar aspects of the wind, the mean speed profile and atmospheric turbulence, which were still treated as unconnected subjects. Sir Geoffrey Ingram Taylor (1886–1975),

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Fig. 6.32 Wind speed and direction profiles: a measured by Dobson [197] through pilot balloons; b theoretically obtained by Taylor [198], reproducing the conditions of Dobson’s measurements

mathematician, meteorologist and fluid dynamics scholar, one of the most eminent scientists of the twentieth century, was the first who overcame this pattern and proceeded with the joint examination of the mean flow and of the fluctuations. In 1915, he published the first of a series of papers (Sect. 6.6) that laid the foundations of the modern theory of turbulence [198]; it was based on a model that represents a kind of generalisation of the kinetic gas theory. According to the theory developed by Maxwell and Boltzmann in the late nineteenth century (Sect. 3.8), a gas is not a continuous medium but a set of molecules that can be schematised through elastic spheres, with mass and size, which move randomly at very high speed and repeatedly collide into each other. Taylor attributed to turbulent flows a granular structure with concentrated masses, the supreme example of which is the Karman wake; the molecules of the kinetic gas theory were then replaced by eddies in which, like in molecular impacts, the large-scale mixing concept prevails [182]. In this way, instead of deriving the turbulence properties from the mean flow, the mean flow was treated as a consequence of turbulence. The words with which Taylor started his 1915 paper [198] placed such concepts in his time and context: “Our knowledge of wind eddies in the atmosphere has so far been confined to the observations of meteorologists and aviators. The treatment of eddy motion in either incompressible or compressible fluids by means of mathematics has always been regarded as a problem of great difficulty, but this appears to be because attention has chiefly been directed to the behaviour of eddies considered as individuals rather than to the average effect of a collection of eddies. The difference between these two aspects (…) resembles the difference between the consideration of the action of molecule on molecule in the dynamical theory of gases, and the consideration of the average effect, on the properties of a gas, of the motion of its molecules.”

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“It has been known for a long time that the retarding effect of the surface of the earth on the velocity of the wind must be due, in some way, to eddy motion; but apparently no one has investigated (…) whether any known type of eddy motion is capable of producing the distribution of wind velocity which has been observed by meteorologists, and no calculations have been made to find out how much eddy motion is necessary in order to account for this distribution. The present paper deals with the effect of a system of eddies on the velocity of the wind and on the temperature and humidity of the atmosphere.” Taylor approached the subject treating the vertical propagation of heat due to eddy motions. Using a modern notation, he expressed the heat flow through a surface with unit area, orthogonal to the direction z, through the relationship: H = ρc p w θ

(6.18)

where ρ is the density of the air, cp is the specific heat of the air at constant pressure, w θ is the covariance of w and θ , being w and θ , respectively, the vertical component of the turbulence and the fluctuation of the potential temperature (Eq. 3.32). Developing Eq. (6.18), Taylor obtained:  H = −ρc p

 1 ∂θ wd 2 ∂z

(6.19)

where w is an indicative value of the upward vertical speed of the air; d is the mean height through which an eddy moves before it mixes with the adjacent ones; θ is the mean potential temperature. Starting from Eq. (6.19), Taylor obtained the heat propagation law in the atmosphere: ∂θ = ∂t



 2 1 ∂ θ wd 2 ∂z 2

(6.20)

observing its strong similarity with the heat propagation law in a solid medium. Comparing Eqs. (6.20) and (3.30), he then had the idea of quantifying the heat transfer in the atmosphere through a parameter, called eddy conductivity coefficient κT , defined as: κT 1 = wd ρc p 2

(6.21)

Replacing Eq. (6.21) into Eqs. (6.18)–(6.20), it follows: w  θ = −

∂θ κT ∂θ = −K T ρc p ∂z ∂z

(6.22)

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6 Wind Meteorology, Micrometeorology and Climatology

H = −κT

∂θ ∂θ = −ρ c p K T ∂z ∂z

κT ∂ 2 θ ∂ 2θ ∂θ = = KT 2 2 ∂t ρc p ∂z ∂z

(6.23) (6.24)

where K T , by analogy with Fourier’s parameter K, is called eddy diffusivity coefficient. Equations (6.23) and (6.24) are the extension to turbulent flows of the Eqs. (3.29) and (3.30) obtained by Fourier in 1822 to describe heat propagation in solid media. Taylor obtained the data required to apply and substantiate his theories thanks to experiments carried out by means of kites launched by the Scotia exploration ship, used for ice research in the North Atlantic, and by other British, German and Danish ships. After completing this first part of his study, Taylor went on to analyse atmosphere in its whole, noting that eddies in turbulence vertically transferred not only heat but also humidity and momentum. He then approached the problem associated with the momentum transfer through a treatment similar to the above-described one, concluding that this phenomenon is governed by the eddy viscosity coefficient18 μT (Sect. 3.6). It is provided by the relationship: μT 1 = wd ρ 2

(6.25)

that allowed him determining the Reynolds stresses as τt = −ρu  w = μT ∂u/∂z (Eq. 5.8). The equality of Eqs. (6.21) and (6.25) also links κT with μT , i.e. κT = c p μT . Taylor credited eddy viscosity as the cause of the variation of the mean wind speed with height near Earth surface. He affirmed that near the ground, eddy viscosity prevents mean speed from reaching the intensity, and due to atmospheric pressure and Coriolis force, it achieves away from the ground. He defined the gradient speed and direction as the values at the height where the wind is not affected by eddy viscosity. He noted that the gradient height varied from 200 to 1000 m and the wind direction at the ground diverged by approximately 20 deg from the gradient direction. He then applied, like Ekman, the Navier–Stokes system formed by Eqs. (3.12) and (3.25), introducing a Cartesian reference system with its origin on the Earth surface: x = x 1 and y = x 2 ; z = x 3 is vertical and points upward. Assuming that the external forces per unit mass are due to Earth rotation and to an uniform pressure gradient G along y, f x = 2vω sinϕ and f y = G − 2vω sinϕ (u = v1 , v = v2 ). The equations of the horizontal motion result:

18 During

tests with pilot balloons on the Salisbury Plain, Taylor proved that the eddy viscosity coefficient is 100.000 times greater than the kinematic viscosity molecular coefficient: turbulent friction, then, surpassed molecular friction up to make it evanescent. He would carry out new tests on the Eiffel Tower [68].

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μ d2 u − 2ωv sin ϕ = 0 ρ dz 2

(6.26a)

μ d2 v G + 2ωu sin ϕ = 2 ρ dz ρ

(6.26b)

u = A2 e−a z cos(az) − A4 e−a z sin(az) + VG

(6.27a)

v = A2 e−a z sin(az) + A4 e−a z cos(az)

(6.27b)

and they admit the solution:

a being the parameter already introduced by Ekman in Eqs. (6.14a, b) and (6.15a, b), V G is the gradient speed,19 directed along x and orthogonal to the pressure gradient G, which occurs for z tending to infinity: VG =

G G = 2 μa 2 2ρω sin ϕ

(6.28)

Taylor assigned the values of the A2 and A4 constants through boundary conditions, admitting the presence of sliding between the air and the Earth surface. He thus obtained a mean wind speed at the ground level V S provided by the expression: VS = cos α − sin α VG

(6.29)

where α is the rotation angle (analytically obtained) between the wind direction at the ground level and at the gradient height. Taylor compared his solution (Fig. 6.32b) with the result previously obtained by the Norwegians Cato Maximilian Guldberg (1836–1902) and Henrik Mohn (1835–1916) (Études sur les mouvements de l’atmosphère, 1876), similar to Eq. (6.29) but without the term −sin α, and with the experimental data obtained by Dobson [197] through sounding balloons (Fig. 6.32a). The latter comparison shows excellent concordance. The ancient expression by Guldberg and Mohn, conversely, was unreliable. Taylor also applied his equations to identify some general trends he hoped would receive future confirmation. He observed that the angle of rotation of the wind at ground level decreased with speed, the ratio between the wind speed at the ground level and at the gradient height decreased with speed, the gradient direction occurred at higher heights than the gradient speed and both these quantities, once reached, are then exceeded and finally stabilised at a higher height. Taylor was also the first to propose the concept of mean eddy size, indicating the length d in Eqs. (6.21) 19 In

1916, Sir Napier Shaw first called “geostrophic” the wind speed due to the balance between the Coriolis’ force and the pressure gradient, ignoring the centrifugal force due to the curvature of isobars. In other words, the geostrophic speed is the gradient speed assuming that isobars are straight lines.

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6 Wind Meteorology, Micrometeorology and Climatology

and (6.25) as an underestimation of such quantity; this view is the embryo of the subsequent definition of the integral scales of the turbulence (Sect. 6.6). A peculiar aspect is worth noting. Nearly ten years after the papers by Prandtl on the boundary layer and by Ekman on the spiral, Taylor’s paper [198] did not mention them but reintroduced, in a different framework,20 many of their peculiar aspects. The thin boundary layer near the body wall, indicated by Prandtl as the site of eddy motions, implicitly reappeared in Taylor’s paper, with the same definition and extended to an atmospheric belt several hundred metres high above Earth surface. Taylor never explicitly mentioned the spiral shape of the profile; however, he pointed out its existence in analytical (Eq. 6.29) and physical (the rotation angle between the wind at the ground level and at the gradient height) terms. In 1916, Taylor published a new paper [199] in which he discussed the analogy between the shear force exerted by a rough plate on a fluid and the friction force of the Earth surface, populated by trees and buildings, in relation to the wind. He expressed both forces (per unit surface) as: FS = kρVS2

(6.30)

where k is a non-dimensional quantity called skin friction coefficient, ρ is the fluid density, and V S is the flow speed near the surface. Taylor, making use of the eddy viscosity concept [198] and of the related equations, proved that the Earth surface involved k = 0.002 − 0.003, just less than the value k = 0.004 of rough pipes.21 He also noted that such parameter is not so sensitive to the speed and to the Reynolds number. He did not provide, however, any link between k and the roughness of the terrain. Trying to draw some preliminary conclusions, at the time of the First World War the foundations of micrometeorology were laid; they originated from varied sectors and often followed parallel and independent paths. Once the war was over, the various subjects concerning the wind merged into three fields not easy to set out: the theory of turbulence (Sect. 6.6), the representation of the wind in the atmospheric boundary layer (Sect. 6.7) and its probabilistic modelling (Sect. 6.8).

6.6 The Theory of Turbulence The advancements of fluid mechanics in the early twentieth century (Sect. 5.1) and the birth of micrometeorology (Sect. 6.5) provided incentives and ideas for the study 20 Taylor did not mention Prandtl and Ekman probably due to closeness of their papers and to the different fields in which they were published: Prandtl’s theory appeared in German language, in an applied mathematics and fluid mechanics environment; Ekman’s one was set in oceanography. 21 Comparing Taylor’s Eq. (6.30) obtained in atmospheric sciences with Eqs. (5.14) and (5.21) introduced by Blasius and Prandtl in fluid dynamics, the k coefficient is equal to half the C D drag coefficient.

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383

of turbulence. The greatest boost to this development, like in other fields (Sects. 5.2, 5.3, and 6.3), came from the arms race that broke out in the years straddling the First World War. In this context, the study of the propagation of explosive processes and of the turbulent diffusion of toxic gases in the atmosphere became essential. Such activities received a particular stimulus in 1916, when the British government created the Royal Engineers Experimental Station, a chemical warfare research centre [68] in Porton, on the Salisbury Plain. Thanks to it and to Taylor’s pioneering research on eddy diffusion, the study of turbulence gained huge advantages, which impinged on the evolution of the newborn micrometeorology. The first advances in this field are mainly due to Richardson, Taylor himself and Schmidt, between 1920 and 1925, and to Prandtl and Karman, between 1925 and 1933. In 1920, Lewis Fry Richardson (1881–1953), resuming some concepts introduced by Reynolds in 1894 and by Taylor [198] in 1915, published a paper [200] in which he laid the bases of energy cascade and atmospheric stability. As regards the energy cascade, Richardson maintained that the eddies forming the turbulence were thermodynamic engines in a gravitational atmospheric field involving the conservation of energy: the larger eddies extract their energy from the mean flow, are unstable and split into increasingly smaller eddies; thus, the kinetic energy flows from large to small scales; the smaller eddies, of molecular size, dissipate the energy inherited from the larger eddies in viscous form. He also quoted a 1918 paper by Wilhelm Schmidt; it was rich in data, but contained an error in the development of the equation of thermodynamics. Richardson returned to this subject in his famous 1922 treatise on weather forecasts [70] (Sect. 6.3), coining a verse in rhyme considered as one of the most famous passages of the wind literature: “Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity”. As regards atmospheric stability,22 Richardson quoted some unpublished researches carried out by Taylor in 1914. He made the simplifying hypothesis that air was dry and defined the production or suppression of turbulence as a function of the ratio between the “buoyant production”, namely the potential energy linked to thermal, or natural, convection through the gravitational or buoyancy force, and the “shear production”, namely the kinetic energy linked to the forced, or mechanical, convection through the friction force at the interface between the atmosphere and the Earth surface23 ; later on, this ratio will be called Richardson number. More precisely, adopting a modern language and formalism, even though in compliance 22 Consider

a unit air mass in vertical hydrostatic balance (Eq. 6.5). The position of the mass is defined as fundamental. Any other position obtained by applying a vertical translation is defined as varied. If the mass remains in equilibrium in the varied position, the equilibrium is neutral. Otherwise, it is stable or unstable, according to whether the mass tends to return to the fundamental position or to leave it. 23 The vertical motion of air masses is called convective. Thermal or natural convection refers to motions occurring when an air mass is lighter or heavier than the surrounding air; this is usually due to atmospheric warming or cooling phenomena. Mechanical or forced convection identifies motions induced by obstacles on the Earth surface; on flat ground, it identifies with the vertical turbulence components caused by the frictions exerted by the Earth surface.

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with Richardson’s concepts [200], the following two non-dimensional parameters are defined as gradient Richardson number Ri and flux Richardson number Rf:  Ri =

  g/θ ∂θ/∂z (∂u/∂z)2

 ; Rf =

 g/θ w θ

u  w (∂u/∂z)

(6.31)

where g is the gravity acceleration, θ = θ+θ is the potential temperature24 (indicating with θ and θ the mean value and the fluctuating component of θ, respectively), u  w and w θ are, respectively, the covariance of u and w and of w and θ . Ri and Rf are linked by the relationship: Rf =

κT Ri c p μT

(6.32)

where κT and μT are the eddy conductivity and viscosity coefficients, respectively (Sect. 6.5). It is interesting to notice that replacing Eqs. (6.21) and (6.25) into Eq. (6.32), the Ri = Rf relation originates. Under unstable conditions, the natural convection enhances the production of tur-  bulence. This causes a negative gradient of the potential temperature25 ∂θ/∂z < 0 and a positive—directed upward—heat flux (w θ > 0), originating negative values of the Richardson number (Ri < 0, Rf < 0). Under stable conditions, natural convection tends to suppress the production of  turbulence. This causes a positive gradient of the potential temperature ∂θ/∂z > 0 and a negative—directed downward—heat flux (w θ < 0), originating positive values of the Richardson number (Ri > 0, Rf > 0). There is a limit, defined as the critical value of the Richardson number Ric ,26 in correspondence of which turbulence is fully suppressed. Under neutral atmospheric conditions, natural convection disappears and the production of turbulence is only due to mechanical convection. This   nullifiesthe gradient of the potential temperature ∂θ/∂z = 0 and of the heat flux w θ = 0 , setting the dry air conditions, the potential temperature θ is linked to the absolute temperature T through Eq. (3.32). All the considerations made here and in Sect. 3.7 can be extended to the wet case by replacing θ with its virtual value θv ≈ θ (1 + 0.61q), q being the specific humidity of air. 25 Differentiating both members of Eq. (3.32) with respect to z and applying Eq. (6.5): 24 Under

T ∂θ ∂T g = + θ ∂z ∂z cp From here, it is possible to infer that the three situations where ∂θ/∂z is smaller, greater or equal to zero match the three cases where  >  a (unstable equilibrium),  <  a (stable equilibrium) and  =  a (neutral equilibrium), where Γ = −∂ T /∂z and  a = g/cp are defined as lapse rate and adiabatic lapse rate, respectively. The ∂ T /∂z = −g/c p condition corresponds to an adiabatic state. Temperature inversion is defined as an atmospheric stability condition so strong to originate a positive gradient of the absolute temperature; it can be especially detrimental to the dispersion of pollutants (Sect. 8.2). 26 In the light of current knowledge, Ri ≈ 0.20–0.25. There are cases in which Ri ≈ 1. c c

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385

Richardson number to zero (Ri = Rf = 0). Richardson proved that this situation takes place when the wind speed is so high to determine a mixing of the atmosphere that, because of its swiftness, is adiabatic.27 Using the primitive equations, the wind speed becomes independent of the thermal state of the atmosphere. This observation turned out to be essential for the evaluation of the wind actions and effects on structures (Chap. 9). Since their safety under wind loading is generally associated with extreme speed values, this authorises to use wind models based on the neutral atmospheric condition hypothesis. Such assumption will become so widespread to be uncritically used even outside its field of validity. This occurs, by way of example, in wind-structure interaction phenomena associated with small speed values, as it often happens for the resonant vortex shedding (Sect. 9.7), or in fatigue assessment for repeated (and then frequent) wind actions. In 1921, Taylor [201] resumed some considerations in his previous 1915 work [198], noting that “turbulent motion is capable of diffusing heat and other diffusible properties through the interior of a fluid in much the same way that molecular agitation gives rise to molecular diffusion. In the case of molecular diffusion the relationship between the rate of diffusion and the molecular constants is known; a large part of the Kinetic Theory of Gases is devoted to this question. On the other hand, nothing appears to be known regarding the relationship between the constants which might be used to determine any particular type of turbulent motion and its ‘diffusing power’”. To simply approach this problem, Taylor schematised the turbulence as a homogeneous stationary random process, i.e. a process with statistical properties invariant over time (stationarity hypothesis) and space (homogeneity hypothesis); he considered the fluid as incompressible and assumed its mean velocity directed along the x-axis; he then searched for the link between the Lagrangian and Eulerian treatments, in particular the law linking the variance of the displacement of a particle, x(t) = x(x(0), t), to the variance of its speed u(t). With such aims, he wrote a paper that is a milestone of process theory (Sect. 5.2), the foundation deed of the statistical theory of turbulence and the theoretical basis of the studies on the turbulent diffusion of pollutants (Sect. 8.2). Taylor provided some theorems about random processes among which the definition of the autocorrelation function (assuming the mean value as nil) and its properties stand out. He used his own theorems to determine the statistical parameters of a turbulent flow that diffuses fluid properties such as temperature, smoke content, dyes or other elements identifiable with fluid particles. For this reason, he set himself in a Lagrangian context and proved the following fundamental theorem: 1d 2 X = u X = u2 2 dt

t

R˜ uL (ξ)dξ

(6.33)

0

27 Atmosphere is considered neutral when the mean wind speed at 10 m height is greater than 10 m/s.

Often, almost neutral conditions hold for lower speeds.

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6 Wind Meteorology, Micrometeorology and Climatology

where X(t)= x(t) – x(0) is the distance travelled by a particle over time t; R˜ uL (ξ) = u(0)u(ξ)/u 2 is the Lagrangian correlation coefficient of u, assessed in two successive instants (0, ξ) for the same particle. Equation (6.33) brought the eddy diffusion problem back to the study of the autocorrelation function of the speed, opened new prospects to the statistical analysis of turbulence and laid the foundations of the link, subsequently established by Taylor himself, between the Lagrangian and the Eulerian views. Starting from Eq. (6.33), Taylor obtained two laws that subsequently represented the bases of the first studies on the turbulent diffusion of atmospheric pollutants (Sect. 8.2). He first treated the limit case in which t is so small that R˜ uL (ξ) ≈ 1, and Eq. (6.33) takes the form: 

X 2 = t u2 (6.34) from which it is possible to infer that the standard deviation of X is proportional to t. He then treated the limit case in which t is so large that R˜ uL (ξ) ≈ 0, and Eq. (6.33) becomes: 

2 X = 2TL tu 2 (6.35) from which it is possible to infer that the standard deviation of X is proportional to the square root of t; T L is the Lagrangian timescale: ∞ TL =

R˜ uL (ξ)dξ

(6.36)

0

Taylor noted that the concepts and expressions introduced above are properly met by the law:   ξ (6.37) RuL (ξ) = exp − TL and recalled a study by Richardson including a description of experiences on the diffusion of smoke from a source. Similar remarks were reported by Dobson on the emission from a factory chimney. Both of them observed that the surface containing the fumes is conical in shape near the source; farther away, it is a paraboloid. This is in accordance with the dependence of the standard deviation of X first on t, for short distances (Eq. 6.34), and then on the square root of t, for long distances (Eq. 6.35). In 1925, Richardson [202] carried out field experiments by means of which he confirmed and physically interpreted his 1920 theory [200]. He discussed atmospheric conditions and the value of the Richardson number that determine the suppression of turbulence. In the same year, Wilhelm Schmidt (1883–1936) published Die massenaustausch in freier luft (Mass exchanges in the atmosphere, 1925), where

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387

he provided a picture of the eddy viscosity, conductivity and diffusivity coefficients previously discussed by Taylor [201]. They were called exchange coefficients (“austauschkoeffizienten”) and are, in turbulent flows, the molecular counterpart of the kinetic gas theory. In the same period (1925–1926), Prandtl [203] formulated the mixing length theory (Sect. 5.1). Like Taylor’s theory, this model took its cue from the kinetic gas theory (Sect. 3.8), got inspired by statistical concepts and interpreted the motion of the fluid through the Lagrangian view; on the other hand, it entailed assessments based on empirical or semi-empirical physical concepts. Prandtl’s model, as distinct from Taylor’s statistical theory, was thus known as the empirical or phenomenological theory of turbulence. In the kinetic gas theory, the molecular mean free path is the space travelled by a molecule, on the average, between two successive impacts. In turbulent flows, a similar quantity does not exist, because fluid particles are subjected to complex and “ambiguous” [188] mixing phenomena. Prandtl overcame this limit by conceiving a length, called the mixing length, which could be interpreted as the mean path along which an eddy retains its identity. Unlike the molecular free path, it varies in the flow field and has no clear physical meaning. His proposal to experimentally evaluate such length, never completed by an effective test procedure, is the main limit of the new model that, on the other hand, led to results with exceptional theoretical and applicative importance. In 1930 Karman [204] resumed Prandtl’s treatment, providing a more general viewpoint. He acknowledged that the mixing length had no specific physical meaning and could not be measured; it could, however, be assessed through plausible hypotheses or obtained by measuring physical quantities such as the shear stresses or the speed profile. He then assumed that the images of the turbulent flow close to any two points were similar and only differed through space and timescale factors [188]. This led to the first expressions of the mixing length (Eq. 5.26) and of the velocity-defect-law (Eq. 5.28). Between 1932 and 1933 Prandtl [205, 206] took into consideration Karman’s advancements and developed a definition of the mixing length (Eq. 5.29) from which the law of the wall (Eq. 5.32) and a new form of the velocity-defect law (Eq. 5.33) derived. These models, together with the experimental development about flows inside ducts, originated studies aimed at determining the so-called universal speed distributions. This led to a vast literature about the power law and the logarithmic profile (Sect. 5.1) that, merged and integrated with similar models deduced in the atmospheric field (Sects. 6.5 and 6.7), had remarkable consequences on the representation of wind and its effects on structures. Taylor captured the analogies between his researches and the models of the Göttingen School in a 1932 paper [207], in which he noted that Prandtl’s mixing length theory was based on the hypothesis that every particle of a fluid in turbulent motion retained the momentum typical of its initial layer until it lost its identity by mixing with particles of another layer. He also noticed that his 1915 formulation [208] was based on the same grounds but with a difference, i.e. that the particles in a turbulent motion did not retain their momentum but rather their vorticity. He then

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developed the two theories in parallel, stressing their difference and the conditions under which they coincided. Additional comparisons were developed by Sydney Goldstein (1903–1989) [209] and by Taylor himself [210] in 1937. Neither Taylor’s statistical theory, which was at an embryonal stage, nor Prandtl’s empirical theory, which soon became well known and widely applied [182], clearly explained the multiplicity of physical phenomena characterising the turbulence. If anything, they highlighted the complexity due to the three-dimensional nature of the turbulence field, to the nonlinear properties of the equations of motion and to the random variation, over time and space, of the speed. The words uttered by Sir Horace Lamb (1849–1934) in 1932 [27] were symptomatic. During a lecture at the British Association for the Advancement of Science, he affirmed that, should he someday go to heaven, he would have liked to receive from God some explanations about two subjects: quantistic electrodynamics and fluid turbulence. Unfortunately, he was only optimistic as regards the first issue. As a matter of fact, a thorough evolution was taking place. The wind tunnel, developed to measure the aerodynamic resistance of bodies (Sect. 7.2), had become a multidisciplinary device that gave answers to many problems. In the case under examination, it allowed to produce turbulent flows and eddy structures easier to measure—and thus more scientifically effective—than those in the actual wind. The first experiences were carried out jointly at the National Bureau of Standards and at the National Advisory Committee for Aeronautics (NACA) in the USA (Sect. 7.4), at the NPL in Teddington, England, and at the Göttingen laboratories in Germany. In 1931, Dryden and Kuethe [211, 212] carried out experimental tests to evaluate the effects of turbulence on the aerodynamic loading of spheres and airplanes. The measurements were conducted at three wind tunnels of the National Bureau of Standards, using hot-wire anemometers connected to an amplifier and to a compensating device. Various shapes and positions of the honeycomb panels were studied to find the arrangement most suited to minimise turbulence. Even though they were aimed at other objectives, these tests provided information about turbulence that turned out to be essential. In 1934, Townend [213] used a duct with a 7.6 cm side square cross-section to repeat, at the NPL, experiences similar to those he carried out with Arthur Fage (1890–1977) in a water channel [214]. The duct used a high contraction ratio, a drilled zinc diaphragm and a honeycomb minimising turbulence. The measurement of the three turbulence components (Fig. 6.33) was carried out by examining movies that captured the change in the refractive index of the air heated by means of a spark generated by two thin electrodes within the flow. The statistical analysis of the results pointed out that turbulence had Gaussian distribution (Fig. 6.34a), the correlation coefficients of different components at the same point were small (Fig. 6.34b), and their standard deviations were equal at the duct centre. In the same year (1934), still at the NPL, Simmons and Salter [215] used a wind tunnel with a 30 cm side square cross-section to carry out historical measurements. The turbulence was created by a grid consisting of horizontal and vertical bars 1.27 cm thick, forming a mesh with holes measuring 2.54 × 2.54 cm. They recorded the speed using hot-wire anemometers and an oscilloscope designed by Taylor. They observed

6.6 The Theory of Turbulence

389

Fig. 6.33 Discrete time measurements of the longitudinal and vertical turbulence components [213]

Fig. 6.34 a Histograms of the ratio between the longitudinal turbulence and the mean speed; b correlation between different turbulence components at the same point [213]

that speed fluctuations were small with respect to the mean speed of the flow and evaluated their distribution. Near the grid, the density function was sensitive to the position of the measurement28 and often showed dissymmetrical shapes. Moving approximately 25 cm away from the grid, the flow was so diffused and mixed to originate symmetrical density functions with Gaussian shape; they revealed that turbulence intensity dropped downstream the grid. Still in 1934, in Göttingen, Prandtl and Reichardt [216] carried out tests to evaluate the effects of thermal stratification. They used a rectangular test chamber, 1 m wide and 0.25 m high, in which they implemented the vertical temperature profile required 28 The

distribution changed if the measurement point was downstream a bar or a gap of the grid.

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6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.35 Turbulence correlation coefficients [216]

to create the desired thermal stratification. To make this possible, the ceiling was heated by steam and the floor was cooled by water. It is the first wind tunnel of the type in the future would be called a meteorological one (Sect. 7.3). The tests were carried out changing the flow speed and, as a consequence, the Reynolds number. Turbulence was artificially created by grids. Measurements were carried by hot-wire anemometers to appreciate quick speed fluctuations. The correlations among the three turbulence components were obtained (Fig. 6.35); both the Reynolds stresses and the shear velocity were then deduced from them. The turning point occurred between 1935 and 1936, when Taylor resumed his 1921 paper [201] and, using the theoretical and experimental developments of the last 15 years, he established the bases of the modern statistical theory of turbulence [217]. He first pointed out that turbulence consists of eddies characterised by a broad range of sizes. This concept led Prandtl and Taylor to introduce, each one independently of the other, a mixing length similar to the mean free path of the kinetic gas theory. Such length derived from the idea that eddies were similar to concentrated air masses behaving like gas molecules, retaining their identity (momentum or vorticity) until they mixed with the surrounding flow. Before such clearly crude concepts, Taylor introduced two new turbulence scales, l1 and l 2 , which are functions of the correlation of the speed of the same particle at two different instants and of two different particles at the same instant, respectively; the first provides a Lagrangian view, the second an Eulerian view. Aiming at this goal, Taylor resumed Eq. (6.33) and developed the two limit cases previously treated (Eqs. 6.34 and 6.35) in an innovative way. He observed that “if the diffusion is taking place in a stream of air moving with velocity U and if the spread is observed at a small distance x downstream from the source (the elapsed time is) t = x/U ”. Replacing this assumption in Eq. (6.34), valid for small t values, it becomes:



X2 u2 = x U

(6.38)

The remark leading to Eq. (6.38) has a huge historical and conceptual value. It is the first expression of the so-called Taylor hypothesis, i.e. of the link between the

6.6 The Theory of Turbulence

391

space and time structure of turbulence. Revised in a modern perspective, it affirms that, in a Lagrangian system referred to the mean flow, turbulence does not change as time varies; i.e., it is frozen and advected by the mean speed of the flow. Taylor then examined the dual case concerning large t values and rewrote Eq. (6.33) as:  ∞ 1 d 2 2 2 X = l1 u = u R˜ uL (ξ)dξ 2 dt

(6.39)

0

whose result is:  l1 =

∞ u2

R˜ uL (ξ)dξ

(6.40)

0

Equation (6.40) defines a characteristic length, whose form is similar to the mean free path in molecular diffusion. It then represents a Lagrangian measure of the mixing length, with the novelty of not being dependent on the age-old and unsolved physical problem of mixing. Taylor then studied the speed correlation coefficient at two different points in the same instant R˜ uE (x) = u(0)u(x)/u 2 . It is large if the distance z between the two points is small in comparison with the size of the eddies; in the opposite case, it is small. It is then a decreasing function of the ratio between x and the size of the eddies. Thanks to this principle—the embryo of the future coherence concepts—Taylor defined a new length: ∞ l2 =

R˜ uE (x)d x

(6.41)

0

which represents an Eulerian measure of the mean size of the eddies, the concept that originated the modern definition of the integral scales of turbulence (Sect. 6.7). After finishing the first part of this work, Taylor noted that the theory he developed assuming the stationarity and homogeneity simplificative hypotheses could be made simpler and more expressive through the introduction of isotropy as a third hypothesis; that is to say that the statistical properties of turbulence are invariant with reference to any rotation of the axes. For this purpose, he mentioned the measures made between 1932 and 1934 by Fage and Townend [213, 214] at the NPL, which proved that the standard deviations of the three turbulence components at the duct centre were almost equal. Taylor recalled some measurements he carried out in 1927, which confirmed the isotropy hypothesis even in the atmosphere, as long as the distance from ground was sufficient. He then applied this third hypothesis to develop new theorems on the dispersion and energy dissipation of turbulence in

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6 Wind Meteorology, Micrometeorology and Climatology

viscous form, opening a path that would lead to a large body of literature founded on three key hypotheses: stationarity, homogeneity and isotropy. Finally, Taylor devoted a large portion of his paper to interpret and validate the expounded theory, in the light of wind tunnel tests generating turbulence by means of grates, grids and honeycomb panels. He examined the results of Simmons and Salter [215], Prandtl and Reichard [216], Dryden and Kuethe [211, 212] and Schubauer [218]. Thanks to them, he specified the validity field of Eq. (6.38) and established an empirical link between l 1 and l2 . He observed that artificially generated turbulence retained the mark of the pitch M of the grid producing it. This originated the l1 ≈ 0.1 M and l 2 ≈ 0.2 M values; as a consequence, l2 ≈ 2l1 . Unlike other studies, which received vast approval after a long time, Taylor’s statistical theory of turbulence was immediately accepted by the international scientific community that developed, starting in the late 1930s, a flood of papers and books that fully configured the discipline in the early 1950s. Karman himself, one of the pioneers and founders of the empirical theory, espoused Taylor’s statistical approach, providing many contributions to its development. In parallel, a set of studies started in the micrometeorological field to verify the validity of the homogeneity, isotropy and Taylor hypotheses in the atmospheric boundary layer; where the latter were not reliable, empirical formulas were deduced to correct their results (Sect. 6.7). Between 1937 and 1938, Dryden and his research team at the National Bureau of Standards and at the NACA [219, 220] were the first to take advantage of Taylor’s innovations [217] and to carry out pioneering wind tunnel tests through which they measured the intensities, autocorrelation functions and scales of turbulence. The turbulence was generated by means of five grids with variable pitch M. The u turbulence component in the mean flow direction x was measured through hot-wire anemometers at two points—1 and 2—first transversally (in the y direction) [219] and then longitudinally (in the x direction) [220] arranged with reference to z; the measurements were carried out by varying the x = |x 2 − x 1 | and the y = |y2 − y1 | distances between the two points, as well as the d distance of the points downstream the grid. They showed that, far enough from the grid and the tunnel walls, turbulence was isotropic; the correlation coefficients and the turbulence scales were then given by the relationships: u 1 (x1 )u 2 (x2 ) ˜ u 1 (y1 )u 2 (y2 ) ˜ R(x) = ; R(y) = 2 u u2 ∞ ∞ ˜ ˜ Lx = R(x)dx; Ly = R(y)dy 0

(6.42)

(6.43)

0

Figure 6.36 shows the correlation coefficients of u in the y direction for three different grids. Measurements, carried out for d = 40 M, were corrected to take into account the presence of the wire. The processing of these measurements proved that the correlation coefficients are well approximated by the empirical formulas:

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393

Fig. 6.36 Autocorrelation coefficients in the transversal direction [219]



y x ˜ ˜ ; R(y) = exp − R(x) = exp − Lx Ly

(6.44)

the longitudinal correlation coefficient being greater than the transversal one. This was the prelude to the publication, in 1938, of two papers in which Simmons and Salter [221] and Taylor [222] analysed the turbulence harmonic content for the first time. Simmons and Salter [221] carried out measurements at the NPL, in a wind tunnel with a 1.2 m side square cross-section. Turbulence, like in their previous experiments [215], was generated by a grid and measured by hot-wire anemometers. Unlike in the past, however, Simmons and Salter developed a process through which, being the time variation of u known, they obtained its power spectral density. Taylor started his paper [222] by observing that “when a prism is set up in the path of a beam of white light, it analyses the time variation of electronic intensity at a point into its harmonic components and separates them into a spectrum. Since the velocity of light for all wavelengths is the same, the time variation analysis is exactly equivalent to a harmonic analysis of the space variation of electric intensity along the beam”. Resuming the study by Simmons and Salter [221], he discussed the link between the normalised power spectrum F of the turbulence at a fixed point and the normalised correlation function between pairs of simultaneous fluctuations at two points at a distance x in the direction of U: R˜ uE (x) = u(0)u(x)/u 2 . Taylor observed that u 2 F(n) is the power content of the turbulence for the frequencies ranging from n to n + dn; thus, invoking a theorem by Rayleigh, u 2 is the sum of the power contents of all the harmonics: ∞ F(n)dn = 1 0

(6.45)

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6 Wind Meteorology, Micrometeorology and Climatology

Taylor also noted that low-frequency eddies were large in size, whereas highfrequency eddies had increasingly smaller sizes. Two consequences stem from this: (1) the harmonic content of turbulence and the spectral function F(n) decrease with the frequency n; (2) the correlation of large eddies decays with the distance x between two points at a slower rate than that of small eddies. This established a link between the turbulence harmonic content and the Richardson’s energy cascade; in addition, this laid the foundations of the future developments about coherence (Sect. 6.7). With such premises, Taylor resumed a concept expressed, in embryonal form, in [217]: “if the velocity of the air stream which carries the eddies is very much greater than the turbulent velocity u, one may assume that the sequence of changes in u at the fixed point is simply due to the passage of an unchanging pattern of turbulent motion over the point”. This assumption, known as Taylor hypothesis or frozen turbulence theory, establishes that the correlation is perfect if fluctuations are measured at the first point at the time t and at the second point at the time t + x/U. The following rule is then valid: R˜ xE (x) = R˜ uL (ξ)

(6.46)

provided that ξ = x/U. Equation (6.46) defines the link between the Lagrangian R˜ uL (ξ) and Eulerian R˜ uE (x) correlations. Thanks to Eq. (6.46) Taylor, applying the Wiener–Khinchin theorem (Sect. 5.2), proved that the power spectrum and the Eulerian correlation function are a Fourier pair: R˜ xE (x) =

F(n) =

4 U



+∞ F(n) cos −∞ +∞

 2π nx dn U

  2π nx R˜ xE (x) cos dx U

(6.47)

(6.48)

0

The accuracy of Eqs. (6.47) and (6.48) was demonstrated through a comparison with the results obtained by Simmons and Salter [221] (Fig. 6.37). Taylor, assuming n = 0 in Eq. (6.48), obtained: F(0) =

4 U

∞

R˜ xE (x)dx

(6.49)

0

which, replaced into Eq. (6.41), provided a new expression of the mean size of the turbulence eddies: l2 =

U F(0) 4

(6.50)

6.6 The Theory of Turbulence

395

Fig. 6.37 Theoretical and experimental [221]: a power spectra; b autocorrelation functions

Finally, Taylor was the first to notice that the decreasing accuracy with which F(n) is known as the frequency increases precludes the possibility of reliably calculating the integral: ∞ I =

n 2 F(n)dn

(6.51)

0

He thus anticipated, by almost half a century, the debate on the estimation of the peak wind speed [223]. A few months after Taylor’s paper [222], Dryden [220] applied the new formulation to his own expressions of the turbulence longitudinal correlation coefficient (Eq. 6.49) and obtained the first analytical expression of the power spectrum F(n) of the longitudinal turbulence component: 4 U F(n) = 4π 2 n 2 L 2x Lx 1 + U2

(6.52)

where U is the mean speed of the flow and L x is the longitudinal turbulence scale. Karman [224, 225] perceived the importance of expressing the spatial correlation function of the turbulence, which Taylor limited to the longitudinal component and to the separation in the flow direction, by means of a tensorial form that took into account the three components of the fluctuations at any two points in space. This made inserting the isotropy hypothesis in the formulation immediate. For such purpose, Karman considered a Cartesian reference system x 1 , x 2 , x 3 with origin in O and versors i1 , i2 , i3 ; u 1 (P ,t), u 2 (P ,t), u 3 (P ,t) and u 1 (P ,t), u 2 (P ,t), u 3 (P ,t) are the three turbulence components u1 , u2 , u3 (in directions x 1 , x 2 , x 3 ), at the points P

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6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.38 Turbulence: a space structure; longitudinal (b) and transversal (c) correlation

(x 1 , x 2 , x 3 ) and P (x 1 , x 2 , x 3 ), respectively, at time t; r = (x 1 − x 1 )i1 + (x 2 − x 2 )i2 + (x 3 − x 3 )i3 is the distance between P and P ; r = r (Fig. 6.38a). Karman, applying these definitions and the homogeneous flow hypothesis, attributed to the spatial correlation tensor of the turbulence the form: u i u j R˜ i j (r) =  (i, j = 1, 2, 3) u i2 u 2j

(6.53)

2 2   2 Using the isotropy hypothesis, u 2 1 = u 2 = u 3 = u and u i u j = 0 (∀i  = j), Eq. (6.53) takes the simplified form:

R˜ i j (r) =

u i u j u 2

(i, j = 1, 2, 3)

(6.54)

where R˜ i j (0) = δi j is the Kronecker’s operator. Moreover, invoking the properties of tensors: ri r j R˜ i j (r) = [ f (r ) − g(r )] 2 + g(r )δi j (i, j = 1, 2, 3) r

(6.55)

where f (r) and g(r) are two functions that identify the value of R˜ ii (r) when P and P are, respectively, aligned along x i , i.e. r = ri = (x i − x i )ii (Fig. 6.38b), or along x j , i.e. r = rj = (x j – x j )ij , being i = j (Fig. 6.38c). Then, f (0) = g(0) = 1. Karman, assuming that the fluid is incompressible and applying the continuity Eq. (3.12), proved the following theorem: f (r ) − g(r ) = −

r d f (r ) 2 dr

(6.56)

according to which R˜ i j (r) (Eq. 6.55) is univocally defined by the scalar function f (r) only. Taylor [222] experimentally verified this model through the measurements

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397

Fig. 6.39 Spectral domains of turbulence

carried out by Simmons and Salter [221]; this confirmed that the turbulence produced in wind tunnels reasonably meets the isotropy hypothesis. In 1941, another advancement took place thanks to Andrey Nikolaevich Kolmogorov (1903–1987), one of the most renowned mathematicians of the twentieth century. Having provided formidable contributions to axiomatic probability theory (Sect. 5.2), functional analysis, random processes and Markov chains, he burst into the field of turbulence with two revolutionary papers [226, 227]. He observed that the isotropy hypothesis was appropriate for flows generated by grids in wind tunnels, but was unsuited to the real case of the atmosphere. He then developed a new theory, through which he introduced the “local isotropy” concept. It was valid for large Reynolds numbers, in a small domain of the four-dimensional space (x 1 , x 2 , x 3 , t), away from the ground and from other types of irregularities. Kolmogorov resumed the principles of energy cascade, assuming that turbulent motions could be represented through a broad range of subsidiary motions, characterised by different length scales, and that energy was continuously transferred from large scales to small ones. He then divided the spectral content of turbulence into three domains, characterised by different geometrical scales (Fig. 6.39). The low-frequency dominant spectral content is associated with large-size eddies that extract their energy from the flow through mechanical and thermal convection. The representative geometrical scale for such eddies was indicated with L and was comparable with l2 (Eq. 6.41). The high-frequency spectral content is associated with small-size eddies that dissipate energy as heat through the work of viscous forces. Kolmogorov assumed that, for large Reynolds numbers, the representative statistical quantities for these eddies are universally and uniquely defined by the kinematic viscosity coefficient ν and by the rate of energy dissipation per unit mass ε. He then proved, applying similarity theory, that their geometrical scale is provided by the relationship:

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6 Wind Meteorology, Micrometeorology and Climatology

 η=

ν3 ε

1/4 (6.57)

This length is currently called Kolmogorov’s scale or micro-scale. Kolmogorov observed that, for large Reynolds numbers, the micro-scale η and the scale of the large eddies L are separated by various orders of magnitude. Between them, therefore, there is a broad range of scales r, related to eddies that are small in comparison with L and large in comparison with η, then η r L . In this domain, called inertial, no energy production or dissipation takes place. Kolmogorov assumed that the representative statistical quantities for scale r eddies are universally and uniquely defined by r and ε. He proved that, assuming that turbulence is homogeneous and applying similarity theory, the function f (r) (Eqs. 6.55 and 6.56) is provided by the relationship: f (r ) = 1 − βε2/3r 2/3

(6.58)

where β is an universal constant. The counterpart of f (r) in the domain of the wave numbers κ is the spectral energy function E(κ). It is linked to f (r) through the following pair of relationships: u2 E(κ) = π f (r ) =

2 u2

 sin(κr ) − cos(κr ) dr κr

(6.59a)

  sin(κr ) 1 − cos(κr ) dκ E(κ) κr (κr )2

(6.59b)



∞ f (r )(κr ) 0

∞ 0

2

from which the following formula was obtained: E(κ) = α ε2/3 κ−5/3

(6.60)

α being an universal constant. Noting that the wave number κ is proportional to the frequency n, Eq. (6.60) highlights the most famous result of Kolmogorov’s theory: in the inertial domain, the spectral content of the turbulence is proportional to n−5/3 . This result contradicted Eq. (6.52), obtained by Dryden [220] in 1938, according to which the spectral content of turbulence, in the high-frequency domain, is proportional to n−2 rather than to n−5/3 . On the other hand, it is worth remarking that, in the meantime, Eq. (6.52) obtained much support. Accordingly, in the 1950s a diatribe erupted between the supporters of the spectral laws proportional to n−2 and the supporters of the ones consistent with Kolmogorov’s theory and then proportional to n−5/3 (Sect. 6.7). This diatribe was strengthened by the fact that whereas Dryden founded his deductions on experimental grounds, Kolmogorov formulated his theory with no instruments and measurements suited to substantiate it. Considering that the disquisition was a very fine one and regarded frequencies whose measurement

6.6 The Theory of Turbulence

399

required sophisticated instruments, it was necessary to wait for a long time before the technological evolution could confirm the validity of Kolmogorov’ hypotheses and results. The new formulation of turbulence theory, together with the advancements of process theory and wind tunnels tests, originated a research zeal that ran through the 1940s. In 1943, Dryden [228] verified Taylor’s and Karman’s theories through wind tunnel tests. In 1947, George Keith Batchelor (1920–2000) [229] made Kolmogorov’s formulation more systematic. Alexander Mikhailovich Obukhov (1918–1989) [230], Lars Onsager (1903–1976) [231], Werner Karl Heisenberg (1901–1976) [232] and Carl Friedrich Freiherr von Weizsäcker (1912–2007) [233] independently formulated similar models. Others used wind tunnels and hot-wire anemometers to check the homogeneity and isotropy hypotheses [234, 235] and to investigate the energy cascade and the decay of turbulence. In 1948, Karman [236] made a new essential step by observing that all the analyses carried out until then were aimed at mathematical and physical aspects; on the other hand, no effort had been made to discover the laws expressing the correlation functions or the actual spectral functions. Aiming at such goal, he carried out wind tunnel tests, generating a stationary, homogeneous, isotropic and neutral turbulent flow. He verified Kolmogorov’s theory in the inertial sub-range and searched for a spectral energy function fulfilling the conditions of Eq. (6.60) for high wave numbers; he also reproduced the measurements for small values of κ and n. He obtained the relationship: (Lκ)4 E(κ) = αε2/3 L 5/3  17/6 1 + (Lκ)2

(6.61)

where L is a length representing the geometrical scale of the turbulence. Equation (6.61) soon became the basis and the reference of all subsequent spectral models. The same year Karman obtained Eq. (6.61), Heisenberg [232] plunged into Kolmogorov’s micro-scale, demonstrating the existence in this domain of the law: E(κ) =

 γε 2 κ−7 2ν2

(6.62)

where γ is an universal constant. The comparison between Eqs. (6.60) and (6.62) highlights the change in the spectral slope for large values of κ: in the inertial subrange E(κ) ∝ κ−5/3 ; in the domain of the viscous dissipation E(κ) ∝ κ−7 . The set of Eqs. (6.60)–(6.62) covers the whole range of the wave numbers and frequencies, highlighting different trends in the three domains of the energy cascade (Fig. 6.39). In 1949, Batchelor [237] made another fundamental step for the statistical theory of turbulence. He resumed Karman’s turbulence space correlation tensor Rij (r) [224, 225] and defined its counterpart in the domain of the wave numbers. It was called space spectral tensor and was defined by the relationships:

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6 Wind Meteorology, Micrometeorology and Climatology

1 E i j (κ) = (2π )3

∞ ∞ ∞

−∞ −∞ −∞ ∞ ∞ ∞

Ri j (r) =

Ri j (r)e−iκ r dr1 dr2 dr3 T

T

E i j (κ)eiκ r dκ1 dκ2 dκ3

(6.63a)

(6.63b)

−∞ −∞ −∞

where κ = i1 κ1 + i2 κ2 + i3 κ3 is the vector of the wave numbers and Rij (r) is the inverse Fourier transform of E ij (κ). On the basis of this formulation, Batchelor proved that, in the hypothesis of isotropy, just as f (r) was sufficient to reconstruct the complete correlation tensor Rij (r), E(κ) is sufficient to reconstruct the complete spectral tensor E ij (κ) through the relationship: E i j (κ) =

κi κ j  E(κ)  δ − i j 4π κ2 κ2

(6.64)

where κ = κ. Batchelor also applied the Taylor hypothesis to link the correlation and spectral space tensors with the correlation time tensors and the corresponding spectra. He did not deal with analytical solutions related to specific functions, but laid the ground for the development of the turbulence models currently in use. As an example, the application of these theories to Eq. (6.61) leads to the expressions:

ωSii(ω) σ2

0.319ωL/u ωS11(ω) = 5/6 2 σ 1 + 1.791(ωL/u)2   0.053ωL/u 3 + 14.329(ωL/u)2 = (i = 2, 3)  11/6 1 + 1.791(ωL/u)2

(6.65a) (6.65b)

where S ii (ω) is the power spectrum of the i-th turbulence component, being i = 1 the direction of the mean wind speed u; ω = 2πn is the circular frequency. Equation (6.65a, b), known as Karman’s spectrum, defines a model that still is one of the most used to assess wind actions and effects on structures [238]. Strengthened by these advancements, the statistical theory of turbulence reached the height of maturity in the 1950s. Between 1953 and 1959, Batchelor [239], Albert Alan Townsend (1917–2010) [240] and Hinze [241] published three classical books about turbulence. In 1956, Batchelor founded the Journal of Fluid Mechanics and remained its editor for 40 years.

6.7 Wind in the Atmospheric Boundary Layer In the wake of the progress made by atmospheric monitoring (Sects. 6.1 and 6.2), of the birth of micrometeorology (Sect. 6.5) and of the evolution of turbulence theory (Sect. 6.6), the first half of the twentieth century was characterised by the proliferation

6.7 Wind in the Atmospheric Boundary Layer

401

of theoretical and experimental studies on the profile of the mean wind speed and on the statistical parameters of the turbulence in the boundary layer in contact with the Earth surface. Even though it was known that the two problems were closely linked, some propension to treat them—at least partially—as independent subjects still persisted. This helps, if nothing else, to introduce a first level of schematisation in a topic replete with contributions so articulated to make it almost inextricable [182, 242]. Some inconsistency in the notation is functional to preserve the original symbols. The studies about the profile of the mean wind speed derived from the first researches carried out by Stevenson [183] and Archibald [184] at the end of the nineteenth century (Sect. 6.5). They led to express such profile through a power law (Eq. 6.13) confirmed by Wing in 1915 by means of anemometric measurements performed in Ballybunion at two Irish radio towers, 91 and 150 m high; thanks to them, Wing assigned the 1/n = 1/7 value to the exponent of the power law [243]. The convergence of the opinions approving the power law was broken by Hellmann [244] in 1917 and by Chapman [245] in 1919. They noticed, carrying out measurements of the mean speed, that the logarithmic law provided a better representation of the data. Chapman observed that, especially in strong winds, the power law also provided reasonable approximations; in this way, he gave rise to a dualism that is still the subject of wide-ranging discussions. In the early 1930s, the analyses about the profile of the mean speed received a boost, especially by Karman, Prandtl, Rossby and Montgomery. They published a series of papers in the fluid dynamics and atmospheric fields, which established the foundation of this discipline; the timing and conceptual link of these papers are worth mentioning. In 1930, Karman [204] provided the first expression of the mixing length (Eq. 5.26), laying the foundations of the developments that led, in the fluid dynamics field (Sect. 5.1), to the velocity-defect law. It is valid far from the boundaries, i.e. in the flow core. In 1932, Rossby [246] resumed the analyses by Ekman [193, 194] and Taylor [198], applying exchange coefficients (Sect. 6.5), and reformulated them making use of Prantdl’s mixing length in the form introduced by Karman [204]. Rossby developed his theory in the complex field, obtaining:   √  h − z 1+i 2 Ws iψs U + iV =1− 1− e Ug Ug h   Ws 1 = cos ϕs − √ sin ϕs Ug 2

(6.66) (6.67)

where U and V are the horizontal components of the mean speed, parallel and

orthogonal to the isobars; U g is the wind speed at the gradient height h; Ws = Us2 + Vs2 is the wind speed at the ground level; ψs ≈ ϕs ; ϕs is the rotation angle between the wind speed at the ground level and at the gradient height. Equation (6.66) is now

402

6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.40 Rossby spiral [246]

known as Rossby spiral (Fig. 6.40). Notice the difference between Taylor’s Eq. (6.29) and Rossby’s Eq. (6.67). In 1932, Prandtl published two papers almost simultaneously with Rossby [246]. In the first one [205], he introduced an expression of the mixing length (Eq. 5.29) that, unlike Karman’s one, was valid near the wall (with the exception of the laminar sub-layer); thanks to it, he laid the foundations of the logarithmic law of the wall in fluid dynamics (Sect. 5.1). In the second paper [247], he showed the applicability of his own theories to the boundary layer the develops in contact with the Earth surface, establishing a link between fluid dynamics and atmospheric sciences. Prandtl assumed that the atmosphere is characterised by an adiabatic temperature distribution; i.e., it is neutrally stratified. He modified his own Eq. (5.29) attributing to the mixing length near the ground the new expression: l = κ(z + z 0 )

(6.68)

where κ is Karman constant and z0 = sε is the roughness length, being ε the average height of the roughness elements on the ground and s ≈ 1/30. Thanks to Eq. (6.68), the mean speed profile results:   1 z + z0 (6.69) u(z) = u ∗ ln κ z0 where z is the height above the ground and u* is the shear velocity. The shear stress is constant in the atmospheric layer adhering to the ground, τ = τ0 , and the surface drag coefficient is given by: cD =

2κ2 τ0   = 1 0 ρu 2 (z 1 ) ln2 z1 z+z 2 0

where z1 is an appropriate reference height.

(6.70)

6.7 Wind in the Atmospheric Boundary Layer

403

Prandtl noticed that the power law, by then in widespread use in the meteorological sector, and the logarithmic profile, fundamental in fluid dynamics, did not contradict one another: on the contrary, they were in perfect accord near the ground; he reinforced this remark by observing that the logarithmic profile is the limit of a power law with a very small positive exponent. He interpreted the variation of the exponent, noticed by many authors, as the consequence of measurements carried out on terrains with different roughness and under atmospheric conditions with different thermal regimes. On this basis, in 1935 Rossby [248], in collaboration with Raymond Braislin Montgomery (1910–1988), took up his 1932 paper [246], highlighting the inconsistencies it contained. Rossby and Montgomery noted that the previous solution by Rossby led to a mixing length l and to an equivalent eddy viscosity coefficient μT both increasing towards the ground; such increment should be physically limited by the Earth surface. They also noted that the concept of speed at ground level, introduced by Taylor [198] and used by Rossby [246], was generic or unclear; the inconsistency between Eqs. (6.29) and (6.67) was symptomatic. Rossby and Montgomery concluded that the previous solution provided by Rossby became faulty at the ground. They rectified it by dividing the atmospheric belt perturbated by Earth surface into two layers with different behaviours; this model is still a basis of this discipline. The first layer, in contact with Earth surface, between the ground and the height H, is thin and is governed by Prandtl’s laws [247]. It was subsequently called “inner boundary layer”. The mixing length is defined by Eq. (6.68), the mean wind speed is given by Eq. (6.69), the flow direction is constant, and the shear stress τ = τ0 is invariant with the height and is given by Eq. (6.70). The second layer, from the height H to the gradient height H + h, is governed by Rossby’s laws [246]. It was then called “outer boundary layer”. The mixing length linearly decreases with height as:   k h − z l= (6.71) √ 2 where z’ is the height, measured from the top H of the layer adhering to the ground; k ≈ 0.065. The mean speed and the wind direction assume the spiral trend defined by Eq. (6.66), having replaced z with z’ and W s with W H , being WH = u(H ) (Eq. 6.69). Moreover: h = 3k

9k 2 Ug u∗ = sin(ϕs ) f 2 f

(6.72)

f = 2sin(φ) being the Coriolis coefficient,  the angular rotation speed of the Earth and φ the latitude. Rossby and Montgomery, by imposing that the mixing length, the mean speed and the wind direction are continuous at the interface between the two layers, obtained:

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6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.41 Rotation angle ϕs between the wind at the ground level and at the gradient height as a function of z0 and U g , for φ = 43°27 [248]

kh κ(H + z 0 ) = √ 2 √   Ug 2κ 2 2κ 1 1 cot(ϕs ) − √ exp = f z0 9k 2 sin(ϕs ) 3k 2

(6.73) (6.74)

Assuming that z0 is small, Eq. (6.73) originates the simplified formula H = 0.12 h. The first member of Eq. (6.74) expresses a non-dimensional quantity subsequently called Rossby number.29 Figure 6.41 exemplifies Eqs. (6.72)–(6.74), showing that the rotation angle between the wind at the ground level and at the gradient height is as greater as the terrain is rougher and the mean wind speed is intense. Rossby and Montgomery also understood an essential aspect: with the mean speed at a given height (e.g. through a measurement), the roughness coefficient (assigned through experience) and the latitude of the site being known, it is possible to obtain the whole profile of the mean speed. They also carried out measurements from which they inferred that the roughness of the sea surface depended on the mean speed; they proved that the roughness coefficient of urban sites assumed values with magnitude z0 = 1 m; they understood that the wind profile changed in relation to the atmospheric stability and expressed such dependency as a function of Richardson’s number (Sect. 6.6). An extensive literature, characterised by various innovative and diversified contributions, developed in parallel with the studies by Karman, Prandtl, Rossby and Montgomery. Rossby number is defined as Ro = V /(L f ), V and L being a speed and a length, f the Coriolis parameter. Ro is the ratio of the centrifugal acceleration to the Coriolis’ one. When Ro is small, the Coriolis force dominates (e.g. in cyclones); when Ro is large, the Coriolis force is negligible (e.g. in tornadoes). 29 The

6.7 Wind in the Atmospheric Boundary Layer

405

In 1930, Scrase [249] proposed a power law with exponent 1/n = 0.13. In 1931, Mildner [250] carried out measurements on the Leipzig airfield using pilot balloons tracked by pairs of theodolites; he simultaneously measured the thermal state of the atmosphere, studying the correlation between the speed and the temperature. In 1932, Ali [251] carried out similar tests in Agra, near Calcutta, interpreting the daily evolution of the mean wind speed profile in relation to thermal conditions. Analogous studies were carried out by Sutton [252] and by Durst [253], in 1932 and 1933, respectively. In 1935, William Watters Pagon (1885–1973) [243] compared various profiles in the literature on theoretical and experimental grounds (Fig. 6.42), suggesting a power law with exponent 1/n = 0.157. He discussed the effect of orographic features, observing that the presence of hills and mountains could be equated to half-prisms or cylinders and studied by means of the principles of aerodynamics; he noticed that the mean wind speed at the top of a triangular hill exceeds the value at its base by 50%. Pagon also mentioned experiences carried out by Heinrich von Ficker (1881–1957) by pilot balloons; he measured a speed equal to 3.3 m/s at the ground level; at the top of a mountain 1000 m high, the speed was 26 m/s; climbing above the peak, it decreased to 13 m/s, highlighting the flow acceleration at the top of the ridge. In 1936, Harald Ulrik Sverdrup (1888–1957) [254] compared the logarithmic profile and the power law. He expressed himself for the first one, as long as this is used in adiabatic conditions and near the ground; he also proposed a method to obtain the roughness length. He simultaneously noted that the power law, even though not theoretically justified, provided excellent approximations and had the advantage of being simpler to apply: it was a concept close to what is currently acknowledged. In 1937, Paeschke [255] collected many experimental data about the mean wind speed profiles, evaluating the accuracy with which they are represented by the power law (Eq. 6.13) and by the logarithmic law (Eqs. 5.32 and 6.69). Paeschke reported the power law in a diagram where the abscissa was the logarithm of the speed, while the ordinate was the logarithm of the height (Fig. 6.43a); by observing that in this scale the profiles are practically linear, he validated the correctness of the power law and obtained the 1/n exponent as a function of the terrain roughness. As regards the logarithmic law, Paeschke observed that the presence of massed roughness elements caused a grazing flow at their top; this was equivalent to ideally raise the ground level to a height zd , subsequently called zero-plane displacement and to modify the mean speed in accordance with the relationship:   1 z − zd (6.75) u(z) = u ∗ ln κ z0 Paeschke reported the profiles of the mean wind speed in a diagram in which the abscissa was the logarithm of the height reduced by zd , while the ordinate was the mean speed divided by the shear velocity (Fig. 6.43b); observing that the profiles were practically linear, he validated the correctness of Eq. (6.75) and obtained both z0 and zd . On the basis of the results obtained, Paeschke formulated one of the first classifications of the n, z0 and zd parameters for smooth grounds (Table 6.2). He also

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6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.42 Comparison among various mean wind speed profiles [243]

Fig. 6.43 Mean wind speed [255]: a power law; b logarithmic profile

6.7 Wind in the Atmospheric Boundary Layer Table 6.2 n, z0 and zd parameters according to Paeschke [255]

407

Terrain type

n

z0 (cm)

zd (cm)

Snow-covered plains

5.00

0.5

3

Göttingen airport

4.30

1.7

10

Fallow fields

4.00

2.1

10

Meadows with low grass

3.85

3.2

20

Meadows with high grass

3.60

4.0

30

Grain fields

3.50

4.5

130

Beet fields

3.00

6.7

45

measured the wind speed in urban areas, but this was invalidated by the proximity of buildings. In 1939, Jacobs [256] carried out the first wind tunnel tests to study how the mean speed profile was modified downstream a change in terrain roughness. In the same year, Heinz Helmut Lettau (1909–2005) [257] defined the atmospheric belt between the Earth surface and the gradient height, i.e. the height where the wind is not influenced by the effect of the ground, as the atmospheric boundary layer (ABL) or the planetary boundary layer (PBL). With the advent of the 1940s and 1950s, the efforts aimed at interpreting and representing the structure of the wind increased and the literature became crowded with papers expressing concepts close to the current ones. Above all, many experimental tests were carried out to clarify the reliability of models proposed and to identify their parameters. Between 1942 and 1943, Charles Warren Thornthwaite (1899–1963) [258, 259] carried out accurate measurements of the mean wind speed from the ground to the 10 m height, observing that, in a neutral regime, the profile was linear in a logarithmic scale; it instead tended to assume different concavities in relationship with the thermal regime and, then, with the stability (Fig. 6.44). In 1946, Obukhov [260] introduced a new scale parameter typical of the exchange processes in the atmospheric belt in contact with the ground, where the shear stress τ and the heat flux q are invariant with height. He observed that such processes are governed by three parameters: g/θ, u ∗ and H/(ρcp ). He then applied Buckingham’s π theorem (Sect. 5.1) and obtained the length: L=−

u 3∗ κ gθ ρcHp

=

u ∗ u  w κ gθ w θ

(6.76)

Obukhov called this quantity “height of the sub-layer of dynamic turbulence” or just “length scale”; over a few years, it would become the key parameter of atmospheric stability called “Obukhov length”. In 1947, Percival Albert Sheppard (1907–1977) [261] noted that there were many measurements, both in pipes and in wind tunnels, of the drag exerted by rough walls on turbulent flows; there were no measurements, instead, of the drag exerted by the

408

6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.44 Mean wind speed profile in relationship with the thermal regime [259]

Earth surface on the wind. For such purpose, he built an experimental device on the Salisbury Plain, by means of which he measured the shear stress at ground level τ0 ; from it, through the application of Eqs. (6.68)–(6.70), he determined the Karman’s constant:  κ=

  z 2 /z 1 τ0 ln ρ u(z 2 ) − u(z 1 )

(6.77)

where z1 and z2 are the heights at which the mean wind speed had been measured. Thanks to these measurements, Sheppard confirmed that the κ ≈ 0.4 value estimated by Nikuradse for rough pipes [262] could also be applied to the Earth atmosphere under neutral conditions; he also noted that κ decreased under stable conditions and increased under unstable conditions. On this basis, Sheppard reworked Paeschke’s data [255] and other unpublished measurements, providing one of the first classifications of the z0 and cD values for various terrains under neutral atmospheric conditions (Table 6.3). Interestingly, he did not mention the study on this subject carried out by Taylor [199] 30 years earlier (Sect. 6.5). In 1949, Deacon [263] collected numerous measurements of the mean wind speed and of the temperature he himself carried out on the grass in Porton between 1941 and 1945, together with other measurements taken on a desert surface. He first collected the measurements in a neutral regime and placed them in a diagram where the abscissa and the ordinate represented the speed (compared with the speed at 1 m height) and the logarithm of height, respectively. He thus substantiated the logarithmic law, observing

6.7 Wind in the Atmospheric Boundary Layer

409

Table 6.3 z0 and cD parameters according to Sheppard [261] Terrain type

z0 (cm)

cD

Ice or smooth snow

0.0009

2.11 × 10−3

Lawn grass up to 1 cm long

0.10

5.54 × 10−3

Downland; thin grass up to about 10 cm

0.72

1.01 × 10−2

Thick grass up to about 10 cm

2.3

1.60 × 10−2

Thin grass up to about 50 cm

5.0

2.32 × 10−2

Thick grass up to about 50 cm

8.9

3.21 × 10−2

13.9

4.28 × 10−2

Fully grown root crops

cD is referred to the mean speed at the z1 = 2 m height above the ground

Fig. 6.45 Mean speed in neutral regime [263]: a profiles; b roughness length

that the various profiles represented straight lines, whose slope identified the terrain roughness (Fig. 6.45a). On the basis of these results, he proposed a new classification of the roughness length in relation to the roughness typology (Fig. 6.45b), building a scale where he reported, besides the obtained values, the ones gathered from the literature. Deacon noticed that, like earlier reported by Rossby and Montgomery [248] as regards the sea roughness, the roughness of grasslands depended on the mean wind speed. Simultaneously with Sutton [264], he also resumed Eq. (6.75), introduced by Paeschke [255] for smooth terrains, highlighting its effectiveness in terrains with thick and pronounced roughness elements, such as the buildings of a city centre or the trees of a thick wood. Deacon subsequently analysed the variation of the mean wind speed profile in relationship with atmospheric stability by observing deviations from the logarithmic law in stable and unstable regimes. They confirmed the trends in Fig. 6.44, highlighting a dependency from Richardson’s number that satisfied the relationship:

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6 Wind Meteorology, Micrometeorology and Climatology

du = az −β dz

(6.78)

where a is independent from z; β = 1 in neutral regime (Ri = 0), β > 1 in stable regime (Ri > 0), β < 1 in unstable regime (Ri < 0). Deacon observed that the profile near the ground was logarithmic regardless of the thermal stratification. Imposing this condition and integrating Eq. (6.78), he obtained:    z 1−β u 1 = −1 (6.79) u∗ κ(1 − β) z0   1−β having assumed a = u ∗ / κz 0 , so that the profile was logarithmic for Ri = 0. Expanding the right-hand member of Eq. (6.79) in Taylor series, he obtained the result:       1−β 2 z z u 1 + + ... (6.80) ln ln = u∗ κ z0 2! z0 which reproduced the logarithmic profile for β = 1. Deacon thus confirmed the validity of such profile in neutral regime, but expressing the mean wind speed profile as a power law (Eq. 6.79) for β = 1. This justifies the observations of many authors who noticed daily variations of the power law exponent. In the same period, taking their cue from the pioneering concepts of Pagon [243] and from a vast phenomenological literature that appeared in the 1930s and 1940s [265, 266], Queney [167] and Scorer [168] published two papers about the wind over mountains (Sect. 6.4). They originated a vast interest towards this subject, documented by the first state of the art published by Corby [160] in 1954. In 1956, Scorer and Wilkinson [267, 268] studied the wind flow on isolated hills, starting a new series of researches about the wind variation near simple topographic reliefs. In the meantime, from the early 1950s, a new trend flourished in America: the construction of measurement stations on ideal terrains, the acquisition of huge data sets and their processing [269, 270]. The first station was built in Brookhaven, near Long Island, in 1951; the second was installed in O’Neill, Nebraska, in 1953, under Lettau; the third, set up in Cedar Hill, near Dallas, Texas, by the Air Force Cambridge Research Laboratories, made use of an instrumented tower of exceptional height (433 m). These facilities were destined to become benchmark models from the 1960s onwards. In 1953, Robert Sherlock published a state of the art [271] where he transferred the nomenclature and concepts of micrometeorology to engineering. He noted that the variation of the mean speed with the height depended on the pressure gradient, on the eddy viscosity coefficient, on the air density, on the angular speed of the Earth rotation, on the geographic latitude and on the curvature of the wind trajectory; he discussed the role of the wind rotation at the ground level with respect to the

6.7 Wind in the Atmospheric Boundary Layer

411

geostrophic one; he carried out a comparison between the profiles proposed in the literature. The age-old problem of correlating the mean wind speed and its structure with the thermal state was solved in 1954, when Andrey Sergeevich Monin (1921–2007) and Obukhov [272] used the length L defined by Eq. (6.76) and Buckingham’s π theorem to obtain, near the ground, the following expressions: z κz du = ϕm u ∗ dz L  κz dθ z = ϕh θ∗ dz L

(6.81a) (6.81b)

where θ∗ = −w θ /u ∗ , and ϕm and ϕh are universal functions of the ζ = z/L nondimensional ratio. It represents, like Richardson’s numbers (Sect. 6.6) and better than them, being L constant in the inner boundary layer, a fundamental indicator of the thermal stratification. The examination of Eqs. (6.31) and (6.81a, b) proves that the ϕm and ϕh functions are linked by the relationship:   2 z z ϕm z  zL  Ri = ϕm = Rf (6.82) L L ϕh L The atmosphere is neutral for z/L = 0 (Ri = 0), stable for z/L > 0 (Ri > 0), unstable for z/L < 0 (Ri < 0). The integration of Eq. (6.81a) provides the relationship:     z  z + z0 1 − ϕm (6.83) u(z) = u ∗ ln κ z0 L where ϕm (0) = 0 assures that, in neutral regime, Eq. (6.83) reproduces Eq. (6.69). Monin and Obukhov then expressed the ϕm function through the polynomial series: ϕm

z L

= 1 + a1

z L

+ a2

 z 2 L

+ ...

(6.84)

They also proposed, for atmospheric regimes not too far from neutrality, to limit the series to the linear term. They thus obtained the relationship:     z + z0 z 1 + a1 (6.85) U (z) = u ∗ ln κ z0 L With the passing of time, the ϕm (z/L) and ϕh (z/L) functions became the subject of numerous theoretical and experimental researches, which led to various and sometimes conflicting results [273, 274]. In 1955, Charnock [275] resumed Rossby’s and Montgomery’s intuitions [248] noticing that the roughness length z0 of the sea surface increased with the wind speed,

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6 Wind Meteorology, Micrometeorology and Climatology

which increased sea waves. He then expressed the relationship between z0 and u* through the empirical formula: z0 =

αu 2∗ g

(6.86)

where g is the gravity acceleration and α is a non-dimensional parameter that, from this moment on, became the subject of a scientifical and technical debate. In 1958, resuming Jacobs’ work [256], Elliott [276] developed the first mathematical model of the mean wind profile in correspondence with a roughness transition. It originated the growth of an internal boundary layer, whose thickness δ depends on the distance downstream the roughness change:  0.8 δ x =A z 02 z 02

(6.87)

where A = 0.75 − 0.03ln (z01 /z02 ), z01 and z02 are the z0 values before and after the transition. In 1961, Kutzbach [277] provided a new contribution to this subject, carrying out the first full-scale tests. It was the prelude to a vast literature about roughness changes that would especially gain ground in the 1970s. The fundamental paper of this period, a milestone of wind engineering, was published by Alan Garnett Davenport (1932–2009) in 1960 [278]. It transcended the issue of the mean wind speed and, more generally, ranged over the design wind speed (Sect. 9.4). Davenport expressed the profile of the mean wind speed through the power law (Eq. 6.13):  Vz = VG

z zG

1/α (6.88)

where V G is the gradient speed at the gradient height zG . The 1/α exponent assigns the shape of the profile in relation to ground roughness. Davenport noted that in tropical and extra-tropical cyclones, for high wind speeds, the atmosphere is neutral and the profile only depends on roughness. Thunderstorms and frontal winds, conversely, are unstable phenomena; under this condition, 1/α tends to zero and the speed remains invariant with height; the role of surface friction is then almost negligible. On the basis of the data gathered from many bibliographic sources, Davenport first proposed to collect the parameters associated with different ground roughnesses into three categories, whose mean wind velocity profile is shown in Fig. 6.46. Afterwards, basing himself on the pictures of anemometric sites and on some descriptions in The Gazeteer of British Meteorological Stations, he compiled a new table (Fig. 6.47a) with eight roughness categories, which was considered as a reference for many years. Figure 6.47b shows the mean speed profiles associated with the categories in Fig. 6.47a. In parallel with the study of the mean wind speed profile, extensive researches on atmospheric turbulence developed between the late 1920s and the early 1930s. They

6.7 Wind in the Atmospheric Boundary Layer

413

Fig. 6.46 Power law profiles associated with three roughness categories [278]

were originated from, and were related to, the general theories discussed in Sect. 6.6; they also made use of the progress in field measurements. They were initially finalised at speed fluctuations in individual points; the first studies about the correlation and coherence of turbulence at different points appeared in the late 1950s. In 1925, Goldie [279] confirmed Richardson’s pioneering concepts (Sect. 6.6), noting the unstable and decaying nature of the eddies making up turbulence. In 1930, Becker [280] was the first to investigate the isotropy property of turbulence. Scrase [249], Giblett [12] and Best [281] carried out the first measurements of the three atmospheric turbulence components, highlighting the impossibility to adopt the isotropy hypothesis near the ground; they also formulated the convention and the notation that are still adopted. Referring to Fig. 6.38, the longitudinal turbulence u = u1 is the fluctuation parallel to the mean speed and to the ground, the lateral turbulence v = u2 is orthogonal to the mean speed and parallel to the ground, and the vertical turbulence w = u3 is directed upward.

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6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.47 Terrain roughness categories [278]: a parameters; b power law profiles

Scrase [249] noticed that the three turbulence components possessed different intensities. He proved that the longitudinal one (u ) prevailed on the lateral one (v ), which in turn prevailed on the vertical one (w ); he quantified this hierarchy by the σu > σv > σw relationship, where σ is the standard deviation. He also proved that turbulent fluctuations cover a broad spectral domain and are influenced by thermal stratification. The first evaluation of the Reynolds stresses is also attributed to Scrase.30 Giblett [12] experimentally proved that turbulence properties depended on thermal stratification and proposed to classify eddies in relation to their stability. He carried out the first assessments of the autocorrelation and cross-correlation functions of fluctuations (at individual points), representing the energy of eddies with different periods through a spectral function that anticipated, at the conceptual level, the development achieved by Simmons and Salter [221] and by Taylor [222] in 1938, using wind tunnels. He measured the scale of the longitudinal turbulence component in the mean flow direction, estimating such quantity as 120 at 15 m height. Best [281] confirmed the hierarchy of the turbulence components observed by Scrase [249], specifying that near the ground the fluctuations increased with the surface roughness. He noted that such fluctuations have a Gaussian distribution, and that the standard deviation of the turbulence is small in comparison with the mean speed. Best also contributed to consolidate the use of a new parameter, the turbulence intensity:

the isotropy turbulence hypothesis, σu = σv = σw = σ ; u  v  = u  w = v  w = 0. This result is not realistic near the ground.

30 Applying

6.7 Wind in the Atmospheric Boundary Layer

Iε =

σε (ε = u, v, w) u

415

(6.89)

given by the ratio between the standard deviation of the fluctuations and the mean wind speed. In 1935, Pagon [243] and Schmidt [282] understood that the eddies caused by the surface friction spread in the atmospheric boundary layer vertically. Schmidt evaluated the longitudinal turbulence scale in the vertical direction, estimating such parameter as 15 m at 6 m height. In 1939, Calder [283] observed that Reynolds stresses were constant up to approximately 50 m height. In the same year, Lettau [257] published the first book about atmospheric turbulence. The turning point took place between the late 1940s and the first half of the 1950s, thanks to three elements: the progress in the statistical theory of turbulence (Sect. 6.6); the appearance of the first environmental monitoring stations, already mentioned in this paragraph; and the evolution of process theory and signal analysis (Sect. 5.2). These aspects—especially the last one—originated a vast literature [284] about turbulence31 [285], whose foundations were collected in the book by Ralph Beebe Blackman (1904–1990) and John Wilder Tukey (1915–2000) [286] published in 1959. The new concepts that took inspiration from the statistical theory of turbulence to adapt themselves to the atmospheric field were developed thanks to such advancements. Two of them stand out: the generalisation of Taylor’s Eq. (6.41) [217] to determine the Eulerian scale of turbulence and the definition of a compact measure of the wind correlation structure through the nine integral scales: ∞ L αε =

R˜ εε (rα ) drα (α = x, y, z; ε = u, v, w)

(6.90)

0

where R˜ εε (rα ) is the correlation coefficient of two same turbulence components ε at two points r α away in the direction α. The L αu , L αv , L αw lengths are defined, in order, as the integral scales of the longitudinal, lateral and vertical turbulence components in the direction α = x, y, z.32

31 Waiting for the fast Fourier transform (FFT), introduced by Cooley and Tukey [285] in 1965, in the 1950s, the spectral analysis was carried out through four techniques [284]: (a) harmonic analysis; (b) numerical filtering; (c) electrical filtering; (d) Fourier transform of the auto-correlogram of the recording. 32 Applying the isotropy turbulence hypothesis:

∞ L xu = L yv = L zw = L f =

∞ f (r )dr ; L xv = L xw = L yu = L yw = L zu = L zv = L g =

0

g(r )dr 0

where f and g are the functions in Eqs. (6.55) and (6.56). The experimental results prove that these expressions cannot be applied near the ground.

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6 Wind Meteorology, Micrometeorology and Climatology

Shiotani and Yamamoto [287], in 1948, and Sheppard and Omar [288], in 1952, carried out pioneering measurements of the L xu integral scale of turbulence. In 1952, Priestley and Sheppard [289], resuming the principles of the energy cascade stated by Kolmogorov [226, 227] in 1941, clarified in physical terms the energy transfer among different spectral bands of the atmospheric turbulence. In the same year, Gerhardt, Crain and Smith [290] clarified the link between temperature fluctuations and turbulence. In 1953, Shiotani [291] measured the integral scale of the longitudinal turbulence component along three directions, proving that L xu > L zu > L yu .33 In the same year, Ogura [292] showed that Taylor’s hypothesis is valid in a limited range of wavelengths; MacCready [293] experimentally proved that in the inertial sub-range the power spectral density of turbulence is proportional to n–5/3 . In the meantime, the study of the spectral content of turbulence at individual points of the atmosphere gained ground. It evolved along two lines: the first, with a meteorological approach, relied on measurements carried out by anemometric towers; the second, with an aeronautical approach, was based on measurements performed by airplanes in flight (Sect. 7.4). The elements uniting these two lines in the 1950s were the interest for the power spectrum of the vertical turbulence component and the uncertainty about the high-frequency spectral shape. It favoured a wide-ranging diatribe between the supporters of spectral laws consistent with Kolmogorov’s theory, and thus proportional to n– 5/3 , and those who, conversely, preferred “simpler” spectral laws, proportional to n –2 (Sect. 6.6). In 1952, Hans Wolfgang Liepmann (1914–2009) [294] carried out pioneering buffeting analyses (Sect. 7.4) using a power spectrum of the vertical turbulence component w in neutral atmosphere deduced by aeronautical measurements. It is given by the relationship (Fig. 6.48): L 1 + 3(Lω/U )2 Sw (ω) =   2 σw πU 1 + (Lω/U )2 2

(6.91)

where U is the mean wind speed and L is a turbulence scale proportional to the mean size of the eddies. Equation (6.91) belongs to the models according to which, in the high-frequency domain, S(n) ∝ n −2 . The fundamental paper in this sector was published by Panofsky and McCormick in 1954 [295]. Carrying out assessments as sophisticated as never seen before, they analysed wind measurements at eight levels (3, 6, 11, 23, 46, 91, 108 and 125 m) of a tower 125 m high at the Brookhaven National Laboratory in Upton, New York. They obtained the power spectra of the longitudinal (u ) and vertical (w ) components of the fluctuations, S uu (n) and S ww (n). They also obtained the first estimates of the cross-spectrum of u and w at the same point, S uw (n).34 33 Today,

it is well known that L xu > L yu ≈ L zu [238]. the isotropy turbulence hypothesis:

34 Applying

Svv (n) = Sww (n) =

1 n dSuu (n) Suu (n) − ; Suv (n) = Suw (n) = Svw (n) = 0 2 2 dn

6.7 Wind in the Atmospheric Boundary Layer

417

Fig. 6.48 Liepmann power spectrum of the vertical turbulence component [294]

Panofsky and McCormick observed that the harmonic content of turbulence covered a broad spectrum of frequencies; thus, a logarithmic scale abscissa was more appropriate. They also multiplied the ordinate by the frequency, for the purpose of preserving the property according to which the area subtended by the spectrum in the interval between two frequencies is the contribution of the said interval to the variance. This representation, destined to become the reference model, was called “logarithmic spectrum” in this paper. The results proved the diversity of the spectral content of the two components u and w and also that both of them depended on the thermal stratification (Fig. 6.49). The harmonic content of w was translated towards the high frequencies with respect to that of u ; the stable regime suppressed the lowfrequency spectral components, the unstable one enhanced them; high-frequency spectral components were independent from thermal stratification. As regards the power spectrum of w , Panofsky and McCormick proposed two alternative expressions that can be referred to the two above-mentioned model classes: Sw (x) 2x = 2 σw (1 + x)3 Sw (x) 10x = 2 σw 9(1 + x)8/3

(6.92a) (6.92b)

Panofsky’s and McCormick results proved that these expressions are inapplicable near the ground.

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6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.49 Power spectrum of the longitudinal (a) and vertical (b) turbulence component for different thermal stratifications (a: unstable; b: neutral; c: stable) [295]

where x = γf; γ is a parameter independent of the height z above ground, but dependent on thermal stratification, f = nz/U is the reduced frequency. For high-frequency values, Eq. (6.92a) entails S w ∝ n−2 , whereas Eq. (6.92b) entails S w ∝ n−5/3 . As regards the cross-spectrum of u and w , i.e. S uw (n) = C uw (n) + iQuw (n), it was represented through the coherence function: Coh uw (n) =

2 Cuw (n) + Q 2uw (n) Suu (n)Sww (n)

(6.93)

where C uw and Quw are the co-spectrum and the quad-spectrum of u and w , respectively. Figure 6.50 shows that the coherence decreases as the frequency increases. In 1955, Webb [296] examined many time histories of the longitudinal and vertical turbulence components measured by a galvanometer; they were acquired over a 5min period, with a sampling rate of 2–3 s. Webb used a digital analyser to obtain the autocorrelation coefficient, and from the latter, through Eq. (6.48), he obtained the power spectrum. He observed that, because of the finite sampling rate, the spectrum lost significance beyond a threshold indicated by the dotted line in Fig. 6.51a. He then corrected the errors observing that the finite length of the recording reduced the low-frequency harmonic content (Fig. 6.51b). Webb discussed the problem of the turbulence scale as well, expressing pioneering concepts. He observed it can be obtained in three different ways. The first applies Eq. (6.40) using the mean wind speed instead of the square root of the mean quadratic value. The second adopts Eq. (6.50), deriving the scale from the spectral value at the zero frequency. The third uses the relationship: lm =

U 2πn m

(6.94)

where U is the mean speed and nm is the frequency for which the product of n by the power spectrum is the maximum. He also highlighted the uncertainties about the

6.7 Wind in the Atmospheric Boundary Layer

419

Fig. 6.50 Coherence of the longitudinal and vertical turbulence components at the same point [295]

√ assessment of this quantity. He proposed the law L ux ∝ z, which represents the first expression of an integral scale as a function of height. Webb also discussed the problem of the high-frequency spectral shape, without reaching any conclusion. The same subject was resumed and broadened by Harry Press and his co-workers [297] in the aeronautical field; in 1956, they compared the measurements carried out by meteorological towers and by airplanes in flight with the different spectral models of that period. Also, this comparison was unable to resolve the doubt about the high-frequency spectral shape. This was the prelude to Davenport’s 1961 paper [298]. He maintained, recalling the concepts introduced by Liepmann in 1952 [294], that turbulence had to be modelled through stationary series, used a value of the wind speed averaged over an interval from 5 min to one hour, and obtained, in that interval, the power spectrum of the fluctuations. He thus collected three groups of measurements of the longitudinal turbulence component carried out in strong winds, with mean wind speed exceeding 9 m/s, so that the mechanical turbulence prevailed on the convective one. They were carried out: by

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6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.51 Power spectra of the longitudinal turbulence [296]: a unamended diagrams; b diagrams amended depending on the length of the recording

Giblett in 1932 [12], in Cardington, England, with four synchronous anemometers at 15.3 m height; by Deacon in 1955 [299], in Sale, Australia, on a tower equipped with three instruments at 12.2, 64 and 153 m above ground; and by Martin Philip Wax in 1956 [300], in Cranfield, England, at the Windmill Research Station of the Electrical Research Association. The power spectra S(n) were obtained through the autocorrelation functions in the form proposed by Panofsky and McCormick [295].   2 They reported nS(n)/V in the ordinate and ln n/V in the abscissa, being n/V the wave number. They were called “normalised logarithmic spectra” and were plotted by means of a best fitting estimated by eye. Figure 6.52a shows the power spectra obtained from the measurements in Sale. Davenport dwelt on their dependence on the height above ground: he noticed that the shape of the spectrum was approximately independent from z, while energy decreased as z increased, especially at high frequency. He concluded that the energy variation with height is small and comparable with the errors inherent in the method. He then disregarded such dependence and expressed the spectrum as (Fig. 6.52b):   nL nS(n) (6.95) = F 2 V 10 κV 10 where L is a characteristic length, independent of height and terrain roughness, V 10 is the mean speed at 10 m height, and κ is a drag coefficient that depends on the terrain roughness. It is linked to the surface shear stress through the relationship 2 τ0 = κρV 10 , whose analogy with Taylor’s Eq. (6.30) [199] is apparent.

6.7 Wind in the Atmospheric Boundary Layer

421

Fig. 6.52 a Power spectra of the longitudinal turbulence component in Sale [299]: z = 12.2, 64 and 153 m; b normalised logarithmic spectrum [298]

Davenport then studied the shape of the F function in Eq. (6.95). He discussed the uncertainty of the spectrum in the inertial sub-range, recalling the diatribe about the  −5/3  −2 use of S(n) ∝ n/V or S(n) ∝ n/V . He acknowledged that the available data were not sufficient to resolve this doubt, but he came out in favour of the first law, expressing the continuous diagram in Fig. 6.52 as: nS(n) 2 κV 10

4x 2 = 4/3 1 + x2

(6.96)

where x = 1200n/V 10 , with n/V 10 in cycles per minute. By means of Eq. (6.96), Davenport also obtained the variance and the intensity of the longitudinal turbulence: ∞ σv2

=

2

S(n)dn = 6κV 10

(6.97)

√ V 10 √  z −α = 2.46 κ = 2.46 κ 10 V (z) V (z)

(6.98)

0

Iv (z) =

σv

The first is independent of height, and the second derives from Eqs. (6.88) and (6.89). Table 6.4 shows some estimates of κ and α. Equations (6.96)–(6.98) have been cornerstones of wind engineering for many years. The analysis of long-term recordings took roots in 1917, when Hellmann [244] studied the daily variation of the wind speed using three anemometers at 2, 16 and 32 m above ground; he observed the occurrence of two peaks, usually at midday and at midnight, and of two minimums, in the early morning and in the afternoon. Panofsky and Isaac van der Hoven (1923–1995) resumed these assessments between 1955 and 1957, publishing papers [301–303] that were essential for all the sectors of wind engineering, especially as regards wind actions and effects on structures. Making use of the meteorological tower at the Brookhaven National Lab-

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6 Wind Meteorology, Micrometeorology and Climatology

Table 6.4 κ and α parameters according to Davenport [298] Ground surface

κ

α

Open countryside free from obstacles (grassland, arctic tundra, desert)

0.005

0.15

Countryside with obstacles in groups (trees and houses less than 10 m high)

0.015–0.020 0.27–0.31

Built-up city areas with tall buildings

0.050

0.43

oratory and of the advances in the spectral analysis of signals, they carried out many recordings of different lengths and with different sampling rates determining the harmonic content of the wind speed on distinct frequency ranges. High-frequency spectral analysis was carried out using the results obtained by Panofsky and McCormick [295]; the low-frequency spectral analysis was developed for new measurements, over time intervals ranging from 2 h to one week [295]. The composition of the spectra on different harmonic bands was based on methods proposed by the authors themselves [302]. At the end of these researches, van der Hoven [303] obtained the famous spectrum named after him (Fig. 6.53), from which two distinct energy contents emerged. The low-frequency content, with periods ranging from some years to approximately one hour, was called macrometeorological peak and corresponds to macroscale atmospheric motions. Two peaks are recognisable within it: the first, with a period of approximately 4 days, derived from the speed variations due to the passage of large pressure systems at synoptic scale (Sect. 6.3); the second, with a period of nearly 12 h, was linked to the daily variations observed by Hellmann [244]. The high-frequency energy content, with periods ranging from 10 min to a fraction of second, was called micrometeorological peak and corresponds to micro-scale turbulent fluctuations. The two peaks are separated by a harmonic band practically devoid of energy contents, ranging from one hour to 10 min, called spectral gap35 [239]. A principle originated from these observations: it was highlighted by van der Hoven himself [303] and is still fundamental. Expressed in a modern notation, let V be the vector of the wind speed; the mean speed V is defined as the mobile mean of V over a time interval T ranging from 10 min to one hour; it varies so slowly over time that it can be considered constant on successive T intervals. The turbulent fluctuation V of V is the complement of V to V; it quickly varies over time and is treated, in every T interval, as a stationary Gaussian zero-mean process. On the basis of this model, the mean wind speed is considered as a deterministic function of space and a random function of time. The turbulent fluctuation is a random function of space and time. The study of the coherence of atmospheric turbulence originated from two pioneering papers published by Cramer in 1959 [304] and 1960 [305]. He noticed that the literature of that age was rich in single-point measurements of turbulence, but 35 According to Davenport [298], the spectral gap is clear for strong winds, blurred for unstable phenomena.

6.7 Wind in the Atmospheric Boundary Layer

423

Fig. 6.53 Van der Hoven’s power spectrum [303]

there were no studies about its joint statistical properties at distinct points. He also noted, with outstanding shrewdness, that this impaired the knowledge of wind actions on structures (Chap. 9). He thus defined the following function [305] as coherence: Ri j (n, s) =

Si j (n, s) Si (n)S j (n)

(6.99)

where S ij is the cross-power spectrum of the same turbulence components at two distinct points, i and j; S i and S j are the power spectra of the turbulence components in i and j; s is the distance between the points under examination. Making use of the measurements carried out for the Project Prairie Grass, Cramer made many estimates of the coherence related to the longitudinal (u ) and lateral (v ) turbulence components; he examined this quantity dealing with the separation in the along wind and crosswind direction. He observed that the coherence increased with V /n and that in the alongwind direction it was greater than in the crosswind direction. In 1961, in the same paper mentioned with regard to the power spectrum [298], Davenport also expressed fundamental principles and relationships as regards the coherence function. They were based on the simultaneous recordings of the wind speed carried out by Deacon [299] in Sale. Figure 6.54a shows the normalised covariance, i.e. the covariance divided by the square of the mean speed at 12 m height, V 12 , as a function of a so-called equivalent horizontal separation, given by the product of the time lag by V 12 . Like the results obtained by Favre, Gaviglio and Dumas (1957–1958) in a wind tunnel [306, 307], it reached its maximum value for a separation approximately equal to the distance between two stations. From the normalised covariance, Davenport obtained the cross-power spectrum: Si j (n) = Coi j (n) + i Qu i j (n)

(6.100)

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6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.54 a Normalised covariance function; b square root of the coherence function [298]

where Coij and Quij are the co-spectrum and the quad-spectrum, respectively. Finally, he applied Eq. (6.99) and determined the cross-correlation spectrum (defined as coherence by Cramer): Ri j (n) =

Coi j (n) + i Qu i j (n)

Si (n)S j (n)

(6.101)

where S i and S j are the power spectra at the i and j points. The real part is unitary when the wave number is zero and decays like a dampened cosinusoidal function; the imaginary part is zero when the wave number is zero, then initially grows and finally decays. From here, Davenport obtained one of the most famous relationships of micrometeorology and wind engineering. Like Panofsky and McCornick [295], and unlike Cramer [304, 305], he defined the square of the absolute value of the correlation spectrum as “coherence”. Its square root (Fig. 6.54b) is properly approximated by the expression:

√   nk z   (6.102) Coherence = Ri j (n) = exp − V 10 where k ≈ 7.7 is a non-dimensional quantity subsequently called exponential decay coefficient, z = |zi − zj | is the distance between the two points i and j at the zi and zj heights. The different definitions of the coherence provided by Panofsky and McCormick, by Cramer and by Davenport are still present in many papers and books. In parallel with the studies about the mean speed and the turbulence, a third set of studies, which drew its bases from the above-discussed subjects, came to light: the peak wind speed value. This subject aroused great interest in two sectors: micrometeorology and wind actions on structures. A brief review of the researches carried out in the first sector is provided below in this paragraph, whereas Sect. 9.4 deals with the developments associated with the second sector.

6.7 Wind in the Atmospheric Boundary Layer

425

V (T ) is defined here as the mean wind speed over an interval T ranging from 10 min to one hour. V (T, τ) is the mean wind speed over a sub-interval τ of T as short as desired (τ < T ); it randomly varies in relation to the position of τ in the T interval, and then, it is a random variable. V M (T, τ) is a value of V (T, τ) with a small probability of being exceeded; in this period, it was (improperly) called the maximum value of V (T, τ) and was provided by the relationship: V M (T, τ) = G V (T, τ)V (T )

(6.103)

where GV is a non-dimensional coefficient. V M (T, τ) is called gust peak when τ assumes values in the order of a few seconds; in this case, GV takes the name of gust factor. The first evaluations of this quantity were carried out by Giblett [12] in 1932, by Sherlock and Stout [308, 309] in 1932 and in 1937, and by Mattice [310] in 1938; they proved that GV is as greater as τ is smaller. Sherlock and Stout were the first to understand the meaning of the size and duration of the gust peak in relation to wind actions on structures (Sect. 9.5). In 1947 and in 1953, Sherlock [271, 311] resumed Stout’s measurements and discussed the dependence of the gust factor on the mean speed and on the height above ground; assuming τ= 10 s and T = 5 min, he obtained the following profile of GV in an open countryside [271]: G V (T, τ; z) = G V (T, τ; z)

 0.0625 z z

(6.104)

where z = 9.15 m. Starting from Eq. (6.104), Sherlock himself [271] and Deacon [299] proposed to express the profile of the maximum speed by a power law similar to the one used for the mean speed. The fundamental paper was published by Durst [312] in 1960. He reworked Giblett’s measurements [12] on flat ground free from obstacles, noting that V (T, τ) had a Gaussian distribution, being V (T ) the mean value and σV (T, τ) the standard deviation; he also noticed that the ratio σV (T, τ)/V (T ) was practically independent of V (T ) and was as greater as the duration of τ was shorter. He then expressed the maximum speed value as: V M (T, τ) = V (T ) + gV (T, τ)σV (T, τ)

(6.105)

where gV (T, τ) is a non-dimensional parameter now known as the peak coefficient.36 Equating Eq. (6.105) with Eq. (6.103), it follows: G V (T, τ) = 1 + gV (T, τ)

σV (T, τ) V(T )

(6.106)

36 Equation (6.105) does not explicitly appear in [312]; it can however be inferred from the adopted procedure. Moreover, no reference is present to the exceedance probability of V M (T, τ), which defines gV (T, τ).

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6 Wind Meteorology, Micrometeorology and Climatology

Table 6.5 Gust factor GV (T, τ) for T = 1 h according to Durst [312] τ (s)

600

60

30

20

10

5

0.5

σV (T, τ)/V (T )

0.07

0.11

0.13

0.14

0.15

0.16

0.17

gV (T, τ)

0.90

2.10

2.40

2.55

2.80

3.00

3.60

G V (T, τ)

1.06

1.24

1.32

1.36

1.42

1.48

1.61

It is one of the most well-known expressions of wind engineering. Durst himself applied Eq. (6.106) to Giblett’s measurements [12], obtaining the values reported in Table 6.5. He noticed that such values were correct when they were used for terrains similar to those from which they came. Subsequent measurements proved that they actually have a wide domain of validity. The advanced studies that gained ground from the 1970s on this matter do not affect the role of Durst’s estimates; despite all their limits, they are still widely used in many sectors.

6.8 Wind Climatology The evolution of the knowledge about wind configuration (Sect. 6.7) and the acquisition of huge data sets of wind data highlighted the random character of the speed. In the meantime, there was a growing awareness that the knowledge of the probability of occurrence of the speed played an essential role as regards various issues, including the diffusion of atmospheric pollutant (Sect. 8.2), wind energy (Sect. 8.1), and wind actions and effects on structures (Chap. 9). The development of the probability theory (Sect. 5.2) provided solid foundations for the research in this sector, favouring the emergence of a new discipline, known as wind climatology. It mostly dealt with two issues: the first regarded the distribution of the population of the mean wind speed values; the second was concerned with the extreme value distribution of the mean and peak wind speed. These problems were independently approached at first; from the 1960s, they became the subject of increasingly linked analyses. The first assessments about the distribution of the parent population of the mean wind speed were carried out by Hesselberg and Erik Bjorkdal [313] in 1929; they schematised the two orthogonal components of the horizontal wind speed by means of Gaussian distributions. In 1931, Ward Tunte Van Orman (1894–1978) [314] carried out a pioneering study about the wind speed along the Atlantic coast of the USA in order to identify a suitable site to build the Goodyear Zeppelin terminal (Sect. 4.5) and to define its best orientation (Fig. 6.55); it was the precursor of many studies aimed at investigating the local wind climate. In 1945, an electrical engineer of the Federal Power Commission, Percy Thomas, carried out the first probabilistic analyses of the mean wind speed in order to assess the US wind energy potential. The turning point occurred between 1946 and 1950, when Charles Ernest Pelham Brooks (1888–1957), Durst and Carruthers [315, 316] collected the results of the upper air measurements carried out by various Canadian weather stations. Thanks to

6.8 Wind Climatology

427

Fig. 6.55 Wind roses determined by Van Orman [314]

these data, they proposed to represent the two components of the mean wind speed through the bivariate Gaussian isotropic distribution: 

p Vx , Vy



  2  2  Vx − Vx + Vy − Vy 1 = exp − 2πσ 2 2σ 2

(6.107)

where V x and V y are, respectively, the wind speed along parallels (from East to West) and meridians (from North to South), V x and V y are the mean values of V x and V y ,   2 2 1/2 V = Vx + Vy , σ = σx = σy , σx and σy being the standard deviations of V x and V y ; V and σ are defined, respectively, as the mean value and the standard deviation of the vectorial wind speed. Brooks, Durst and Carruthers formulated a detailed procedure based on Eq. (6.107). They collected upper air isobaric charts (Fig. 6.56a) from which they obtained the velocity and direction of the geostrophic wind (Eq. 6.6). From such values, they determined V x and V y as well as the σ standard deviation (Fig. 6.56b). Finally, they obtained the wind roses (Fig. 6.57). Similar maps of the upper air wind were obtained by Henry [317] in 1957. In 1959, Oskar Essenwanger [318] confirmed, through new measurements, that the bivariate Gaussian distribution is an excellent representation of the upper air wind speed. A growing interest towards the distribution of the mean wind speed at ground level developed in parallel with the above-mentioned studies. The most significant exponents of this interest, aimed at wind energy production and at wind actions

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6 Wind Meteorology, Micrometeorology and Climatology

Fig. 6.56 500 mb isobaric surface [316]: a height (in hundreds of feet); b standard deviation of the wind speed (in knots)

6.8 Wind Climatology

429

Fig. 6.57 Wind roses in the upper air [315, 316]

on structures, were Palmer Coslett Putnam (1900–1984) (Sect. 8.1) and Sherlock (Sect. 9.5), respectively. The former published a book [319] in 1948, in which he attributed a type III distribution of the minimum value (Eq. 5.48) to the mean wind speed in non-directional form. The latter expressed the same quantity [320], in 1951, by a Pearson’s distribution. The turning point in this sector, came in 1958, when Gumbel [321] represented the mean wind speed at the ground level by means of the Weibull distribution (Eq. 5.49). The adoption of this model, derived from purely empirical bases (Sect. 5.2), quickly became the reference, still adopted, for the studies about wind energy production and wind actions on structures. The two above-described models of the wind speed in the upper air and at the ground level, independently developed in the 1950s, were then studied in the 1960s to prove their phenomenological and mathematical link. This proved the relationship between the bivariate Gaussian distribution and Rayleigh’s one (Eq. 5.71); the Weibull distribution is a generalisation of the latter [322]. In parallel with these studies, a broad interest arose as regards the extreme value distribution, chiefly aimed at wind actions on structures. They were so strictly linked to the design and verification of structures to discuss this issue in Sect. 9.4. Here, the two main topics of this discussion are anticipated. The first is the need to perform probabilistic extreme value analyses based on homogeneous data; a vast debate originated from here, about issues such as the sites where instruments had to be located, the duration of the interval over which the speed had to be averaged and the methods to transform the measurements associated with different sites and intervals to make the data set homogeneous. The second subject covers the extreme value distribution most suited to represent the maximum speed value; it was oriented towards the type I distribution (Eq. 5.40) and, in part, towards the type II distribution (Eq. 5.44); in this period, there is no trace of papers espousing the use of the type III distribution (Eq. 5.45) and not in the least of the generalised distribution (Eq. 5.43).

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220. Dryden H (1938) Turbulence investigation at the National Bureau of Standards. In: Proceedings of 5th international congress applied mechanics, p 366 221. Simmons LFG, Salter C (1938) An experimental determination of the spectrum of turbulence. Proc Roy Soc Lond A 165:73–89 222. Taylor GI (1938) The spectrum of turbulence. Proc Roy Soc Lond A 164:476–490 223. Solari G (1993) Gust buffeting. I: peak wind velocity and equivalent pressure. J Struct Eng ASCE 119:365–382 224. von Kármán T (1937) The fundamentals of the statistical theory of turbulence. J Aero Sci 4:131 225. von Kármán T, Howarth L (1938) On the statistical theory of isotropic turbulence. Proc Roy Soc Lond. A 164:192–215 226. Kolmogoroff A (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C R Acad Sci URSS 30:301–305 227. Kolmogoroff A (1941) Dissipation of energy in the locally isotropic turbulence. C R Acad Sci URSS 32:16–18 228. Dryden H (1943) A review of the statistical theory of turbulence. Q J Appl Math 1:7–42 229. Batchelor GK (1947) Kolmogoroff’s theory of locally isotropic turbulence. Proc Camb Philos Soc 43:533–559 230. Obukhov AM (1941) On the distribution of energy in the spectrun of turbulent flow. C R Acad Sci URSS 32:19 231. Onsager L (1945) The distribution of energy in turbulence. Phys Rev II(68):286 232. Heisenberg W (1948) Zur statistischen Theorie der Turbulenz. Z Phys 124:628–657 233. von Weizsacker CF (1948) Das spektrum der turbulenz bei grossen Reynoldsschen zahlen. Z Phys 124:614–627 234. Townsend AA (1947) The measurement of double and triple correlation derivatives in isotropic turbulence. Proc Camb Philos Soc 43:560–570 235. Corrsin S (1949) An experimental verification of local isotropy. J Aero Sci 16:757–759 236. von Kármán T (1948) Progress in the statistical theory of turbulence. Proc Nat Acad Sci Wash. 34:530–539 237. Batchelor GK (1949) The role of big eddies in homogeneous turbulence. Proc Roy Soc London A 195:513–532 238. Solari G, Piccardo G (2001) Probabilistic 3-D turbulence modeling for gust buffeting of structures. Prob Eng Mech 16:73–86 239. Batchelor GK (1953) The theory of homogeneous turbulence. Cambridge University Press, U.K. 240. Townsend AA (1956) The structure of turbulent shear flow. Cambridge University Press, U.K. 241. Hinze JO (1959) Turbulence. McGraw Hill, New York 242. Counihan J (1975) Adiabatic atmospheric boundary layers: a review and analysis of data from the period 1880–1972. Atmos Environ 9:871–905 243. Pagon WW (1935) Aerodynamics and the civil engineer—VII. Wind velocity in relation to height above ground. Eng News-Rec 742–745 244. Hellmann G (1917) Über die Bewegung der Luft in den untersten Scichten der Atmosphäre. Zweite Mitteilung, Meteorol Z 34:273–285 245. Chapman EH (1919) The variation of wind velocity with height. Prof. Notes-Met. Office No 6 246. Rossby CG (1932) A generalisation of the theory of the mixing length with applications to atmospheric and oceanic turbulence. Massachusetts Institute of Technology, Meteorological Papers, vol I, no 4, Cambridge, MA 247. Prandtl L (1932) Meteorologische anwedung der strömunglehre. Beiträge zur Physik der Freien Atmosphäre 19:188–202 248. Rossby CG, Montgomery RB (1935) The layer of frictional influence in wind and ocean currents. Papers in Physical Oceanography and Meteorology, M.I.T. and Woods Hole Ocean and Met. Inst., 3, 3

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249. Scrase FJ (1930) Some characteristics of eddy motion in the atmosphere. Met Off Geophys Mem 52 250. Mildner P (1932) Über reibung in einer speziellen luftmasse. Beitr Phys freien Atmosph 19:151–158 251. Ali B (1932) Variation of wind with height. Q J Roy Meteorol Soc 58:285–288 252. Sutton OG (1932) Notes on the variation of wind with height. Q J Roy Meteorol Soc 58:285–288 253. Durst CS (1933) Notes on the variations of the structure of wind over different surfaces. Q J Roy Meteorol Soc 59:361–372 254. Sverdrup HU (1936) Austausch und stabilitat in der untersten luftschict. Meteorol Z 53:10–15 255. Paeschke W (1937) Experimentelle untersuchungen zum rauhigkeits und stabilitätsproblem an der bodernen luftschicht. Beitr Phys Atmos 24:163–189 256. Jacobs W (1939) Unformung eines turbulenten geschwindigkeitsprofiles. Z Angew Math Mech 19:87–100 (English translation N.A.C.A. Tech. Mem. 951) 257. Lettau H (1939) Atmosphaerische turbulenz. Akademische Verlagsgesellschaft, Leipzig 258. Thornthwaite CW, Halstead M (1942) Note on the variation of wind with height in the layer near the ground. Trans Am Geophys Union 23:249–255 259. Thornthwaite CW, Kaser P (1943) Wind gradient observations. Trans Am Geophys Union 1:166–182 260. Obukhov AM (1946) Turbulence in an atmosphere with a non uniform temperature. Tr Akad Nauk SSSR Inst Teoret Geofis No. 1 (translated in Bound-Lay Meteorol, 1971, 2:7–29) 261. Sheppard PA (1947) The aerodynamic drag of the earth’s surface and value of von Karman’s constant in the lower atmosphere. Proc Roy Soc Lond A 188:208–222 262. Prandtl L (1927) Über den Reibungswiderstand strömender Luft. Ergebnisse AVA Göttingen, III Series 263. Deacon EL (1949) Vertical diffusion in the lowest layers of the atmosphere. Q J Roy Meteorol Soc 75:89–103 264. Sutton OG (1949) Atmospheric turbulence. Methuen, London 265. Wurtele MG, Sharman RD, Datta A (1996) Atmospheric lee waves. Annu Rev Fluid Mech 28:429–476 266. Wood N (2000) Wind flow over complex terrain: a historical perspective and the prospect for large-eddy modelling. Bound-Lay Meteorol 96:11–32 267. Scorer RS (1956) Airflow over an isolated hill. Q J Roy Meteorol Soc 82:75–81 268. Scorer RS, Wilkinson M (1956) Waves in the lee of an isolated hill. Q J Roy Meteorol Soc 82:419–427 269. Thuillier RH, Lappe UO (1964) Wind and temperature profile characteristics from observations on a 1400 ft tower. J Appl Meteorol 3:299–306 270. Berman S (1965) Estimating the longitudinal wind spectrum near the ground. Q J Roy Meteorol Soc 91:302–317 271. Sherlock RH (1953) Variation of wind velocity and gusts with height. Trans Am Soc Civil Eng Paper No. 2553, 118:463–488 272. Monin AS, Obukhov AM (1954) Basic laws of turbulent mixing in the ground layer of the atmosphere. Trudy Geofizs Inst An SSSR 2:13 273. Businger JA (1959) A generalization of the mixing-length concept. J Meteorol 16:516–523 274. Swinbank WC (1960) Wind profile in thermally stratified flow. Nature 186:463–464 275. Charnock H (1955) Wind stress on a water surface. Q J Roy Meteorol Soc 81:639–640 276. Elliot WP (1958) The growth of the atmospheric internal boundary layer. Trans Am Geophys Union 39:1048–1054 277. Kutzbach JE (1961) Investigations of the modification of wind profiles by artificially controlled surface roughness. University of Wisconsin, Department of Meteorology, Annual Report, 71 278. Davenport AG (1960) Rationale for determining design wind velocities. J Struct Div ASCE 86:39–68 279. Goldie AHR (1925) Gustiness of wind in particular cases. Q J Roy Meteorol Soc 51:216–357

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280. Becker R (1930) Investigation of the small scale structure of the wind by means of a matrix of wind vanes. Beitre Phys Atmos 16:271 281. Best AC (1935) Transfer of heat and momentum in the lowest layers of the atmosphere. Met. Office Geophys Memoirs, 65 282. Schmidt W (1935) Turbulence near the ground. J Roy Aeronaut Soc 39:335–376 283. Calder KL (1939) A note on the consistency of horizontal turbulent shearing stress in the lowest layers of the atmosphere. Q J Roy Meteorol Soc 65:57–60 284. Pasquill F, Smith FB (1983) Atmospheric diffusion. John Wiley, New York 285. Cooley JW, Tukey JW (1965) An algorithm for the machine calculation or complex Fourier series. Maths Comput 19:297–301 286. Blackman RB, Tukey JW (1959) The measurement of power spectra from the point of view of communications engineering. Dover Publications, New York 287. Shiotani M, Yamamoto G (1948) Atmospheric turbulence over a large city; turbulence in the free atmosphere-2. Geophys Mag 21:2 288. Sheppard PA, Omar T (1952) The wind stress over the ocean form observations in the trades. Q J Roy Meteorol Soc 78:583–589 289. Priestley CHB, Sheppard PA (1952) Turbulence and transfer processes in the atmosphere. Q J Roy Meteorol Soc 78:488–529 290. Gerhardt JR, Crain CM, Smith HW (1952) Fluctuations of atmospheric temperature as a measure of the scale and intensity of turbulence near the earth’s surface. J Meteor 9:299–310 291. Shiotani M (1953) Some notes on the structure of wind in the lowest layers of the atmosphere. J. Meteor. Soc. Jpn 31:327–335 292. Ogura Y (1953) The relation between the space- and time- correlation functions in a turbulent flow. J Meteor Soc Japan 31:355–369 293. MacCready PD (1953) Atmospheric turbulence measurements and analysis. J Meteorol 10:325–337 294. Liepmann HW (1952) On the application of statistical concepts to the buffeting problem. J Aeronaut Sci 19:793–800 295. Panofsky HA, McCormick RA (1954) Properties of spectra of atmospheric turbulence at 100 meters. Q J Roy Meteorol Soc 80:546–564 296. Webb EK (1955) Auto-correlations and energy spectra of atmospheric turbulence. C.S.I.R.O. Division of Meteorological Physics, Technical Paper 5 297. Press H, Meadows MT, Hadlock I (1956) A reevaluation of data on atmospheric turbulence and airplane gust loads for application in spectral calculations. NACA Report 1272 298. Davenport AG (1961) The spectrum of horizontal gustiness near the ground in high winds. Q J Roy Meteorol Soc 87:194–211 299. Deacon EL (1955) Gust variation with height up to 50 m. Q J Roy Meteorol Soc 81:562–573 300. Wax MP (1956) An experimental study of wind structure. Technical Report C/T 114, British Electrical and Allied Industries Research Association 301. Panofsky HA, van der Hoven I (1955) Spectra and cross-spectra of velocity components of the micro-meteorological range. Q J Roy Meteorol Soc 81:603–606 302. Griffith HL, Panofsky HA, van der Hoven I (1956) Power-spectrum analysis over large ranges of frequency. J Meteorol 13:279–282 303. Van der Hoven I (1957) Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour. J Meteorol 14:160–164 304. Cramer HE (1959) Measurements of turbulence structure near the ground within the frequency range from 0.5 to 0.01 cycles sec. In: Advances in geophysics, 6, Atmospheric diffusion and air pollution. New York and London, Academic Press, pp 75–96 305. Cramer HE (1960) Use of power spectra and scales of turbulence in estimating wind loads. Meteor Mon 4:12–18 306. Favre AJ, Gaviglio JJ, Dumas RJ (1957) Space-time double correlations and spectra in a turbulent boundary layer. J Fluid Mech 2:313–342 307. Favre AJ, Gaviglio JJ, Dumas RJ (1958) Further space-time correlations of velocity in a turbulent boundary layer. J Fluid Mech 3:344–356

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308. Sherlock RH, Stout MB (1932) Picturing the structure of the wind. Civil Eng 2:358–363 309. Sherlock RH, Stout MB (1937) Wind structure in winter storms. J Aeronaut Sci 5:53–61 310. Mattice WA (1938) A comparison between wind velocities as recorded by the Dines and Robinson anemometers. Mon Weather Rev 66:238–240 311. Sherlock RH (1947) Gust factors for the design of buildings. International Association for Bridge and Structural Engineering, vol 8, Zurich, Switzerland 312. Durst CS (1960) Wind speeds over short period of time. Meteor Mag, Meteor Office 89, 181–186 313. Hesselberg Th, Bjorkdal E (1929) Uber das verteilungsgesetz der windunruhe. Beitr Phys Atmos 15:121–133 314. Van Orman WT (1931) A preliminary meteorological survey for airship bases on the middle Atlantic seabord. Mon Weather Rev 59:57–65 315. Brooks CEP, Durst CS, Carruthers N (1946) Upper winds over the world—Part I. Q J Roy Meteorol Soc 72:55–73 316. Brooks CEP, Durst CS, Carruthers N, Dewar D, Sawyer JS (1950) Upper winds over the world. Geophys. Memoirs, No. 85, Meteorological Office, H.M.S.O. 317. Henry TJG (1957) Maps of upper winds over Canada. Meteorological Branch, Department of Transport, Toronto 318. Essenwanger OM (1959) Probleme der windstatistik. Meteor Rundsch 12:37–47 319. Putnam PC (1948) Power from the wind. Van Nostrand Reinhold, New York 320. Sherlock RH (1951) Analyzing winds for frequency and duration. Meteor Mon, No 4. American Meteorological Society, pp 72–79 321. Gumbel EJ (1958) Statistics of extremes. Columbia University Press, New York 322. Baynes CJ (1974) The statistic of strong winds for engineering applications. Ph.D. Thesis, The University of Western Ontario, London, Ontario, Canada

Chapter 7

Wind and Aerodynamics

Abstract The knowledge about aerodynamic actions is vitally important in many fields, such as those involving structures and transportation. Facing such issues, This chapter illustrates the experimental techniques that appeared around the end of the nineteenth century to measure aerodynamic actions, first of all the technology that represents the symbol of this discipline: the wind tunnel. It also describes the pioneering stage during which this device was aimed at every type of test, and then, the appearance of facilities specialized in various sectors, first of all those aiming to reproduce the atmospheric boundary layer, then those addressed to aircrafts, sailing boats, road and rail vehicles. The evolution of aerodynamic knowledge is overshadowed by the driving role of aeronautics. Relying on the huge impact of the first flights, it inspired an increasingly stricter relationship between theory and experimentation focusing on the study of wings and originating analytical methods and experimental techniques destined to impact on several sectors, first and above all wind actions and effects on structures and transportation.

When a body is immersed in air and a relative motion exists between the body and the air, the body changes the configuration of the air that, in turn, produces a state of pressure over the body surface. The integration of such pressure generates forces and moments called aerodynamic actions. They are linked to the shape of the body and to the velocity and direction of the relative motion between the body and the air; they also depend on the roughness of the body surface and on the local configuration of the relative motion, e.g. on the mean velocity profile and on the turbulence structure. The knowledge about aerodynamic actions is vitally important in many situations, such as those involving structures and transportation. The former are the best example of fixed bodies in moving air (the wind), without neglecting the situations where the deformation of the structure contributes to the aerodynamic actions (which in this case are called aeroelastic) as well as those where moving structural parts are present (e.g. blades of wind turbines). The latter include aircraft, sailing boats and road and rail vehicles, which share the same role of the aerodynamic actions of still air on the moving vehicle, without neglecting the essential effects induced by the wind. Facing such issues, mankind continued the efforts started in the Renaissance (Sect. 4.2) to provide itself with techniques suited to measure aerodynamic actions © Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_7

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(Sect. 7.1) and with such purpose it attained, at the end of the nineteenth century, the technology that represents the symbol of this discipline: the wind tunnel. Its initial goals were aimed at every type of test (Sect. 7.2), but with the passing of time it specialised towards various sectors; on the one hand, facilities for civil and environmental tests, reproducing the atmospheric boundary layer (Sect. 7.3) made their appearance; on the other hand, the facilities dedicated to vehicles became the subject of increasingly sophisticated research. The latter, in turn, took on different configurations according to whether they were intended for aircrafts (Sect. 7.4), travelling far away from the ground, or for vehicles travelling on the Earth surface, such as sailing boats (Sect. 7.5), road (Sect. 7.6) and rail (Sect. 7.7) vehicles. The evolution of aerodynamic knowledge is overshadowed by the driving role of aeronautics in relation to other sectors. Relying on the huge impact of the first flights, it inspired an increasingly stricter relationship between theory and experimentation; it especially involved the study of wings, originating analytical methods and experimental techniques destined to impact on several sectors, first and above all wind actions and effects on structures. Aeronautics also catalysed the necessity—and even the fad—of giving an aerodynamic shape to a wide range of bodies; this affected road and rail vehicles, which were first inspired to airplanes and then assumed shapes related to the presence of the ground. The relationship between structures and shape is subtler. Windmill blades were designed to maximise energy production (Sect. 8.1). Some structural types, such as cable-suspended bridges (Sect. 9.1) and steel chimneys (Sect. 9.6), often pursued the choice of the shape most suited to minimise wind actions. Other structural types, including buildings (Sect. 9.2), postponed this trend to the twenty first century (Chap. 11); in the age under examination, they only used wind tunnels to evaluate the aerodynamic actions on assigned shapes.

7.1 Advancements in Experimental Aerodynamics Despite the plurality and the development of experimental aerodynamics and hydrodynamics, the study of the resistance of bodies into fluids arrived at the end of the nineteenth century rich in doubts and unsolved problems (Sect. 4.2). This did not discourage experimentation; on the contrary, it favoured—prompted by the increasing request for knowledge on the behaviour of bodies into fluids—more sophisticated measurements. These especially made use of the technological advancements associated with steam machines and electric motors. The analysis of the evolution of this subject from the Renaissance to the end of the nineteenth century (Sect. 4.2) highlights how, in that age, aerodynamics and hydrodynamics were so closely linked to make the enucleation of tests in the air almost impossible. Separate trends, which allowed examination limited to experimental aerodynamics, developed since the late nineteenth century. This involved two main criteria by adopting the pattern proposed by Alexander Gustav Eiffel (1832–1923) [1] in 1910 and the information collected by William Herbert Bixby (1849–1928) [2] in 1895.

7.1 Advancements in Experimental Aerodynamics

443

The first criterion, aligned with tradition and in vogue up to the early twentieth century, consisted in the measurement of aerodynamic actions on moving bodies in still air. It made use of two techniques based on circular motions, accomplished by whirling arms and trolleys, and on straight motions, either vertical, accomplished through free fall, or horizontal, accomplished by locomotives, cars and bicycles. A third technique, associated with pendular motions, soon fell into oblivion. The second criterion, typical of the twentieth century and the harbinger of the developments that opened the door to modern experimental aerodynamics, consisted in the measurement of aerodynamic actions on bodies (mostly, but not necessarily, at rest) immersed in airflow. It identified itself with the natural wind, originating full-scale aerodynamic tests, and with artificial flows obtained through wind tunnels (Sects. 7.2 and 7.3). The whirling arm technology, compared with the devices built by Robins, Rouse, Smeaton and De Borda (Sect. 4.3), showed advances associated with the arm length (L), the revolution speed (V ), the driving mechanism and the measurements instrumentation. Gotthilf Heinrich Ludwig Hagen (1797–1884) [3] used a whirling arm L = 2.5 m long. Saint-Loup (1879) [4] used a steam machine to impart the speed V = 36 m/s to a whirling arm. Thomas Osborne Perry (1847–1927) praised the accuracy of Smeaton’s measurements, but criticised the use of a too short whirling arm; he then built an arm 4.3 m long in a room 11 m wide, 14.6 m long and 5.8 m high; the arm was rotated by means of an 80 HP steam engine and was used (1882–1883) to evaluate the efficiency of windmill blades (Fig. 7.1a) [5]. Henry Allen Hazen (1832–1900) (1986) [2] also criticised the measurements carried out using whirling arms that were too short and built a long arm in Washington. William Henry Dines (1855–1927) [6] used a whirling arm (L = 8.5 m) driven by a steam machine. In 1889, Karl Wilhelm Otto Lilienthal (1846–1896) [7] published the results of experiments started in 1866 with a whirling arm (Fig. 7.1b) similar to Hagen’s one; besides drag, it also measured lift; the results were quantified, for the first time, through force coefficients1 [8]. Between 1887 and 1890, Samuel Pierpont Langley (1834–1906) [9] carried out experiments at the Allegheny Observatory [5]; he first used the longest arm ever built (L = 9.25 m, V = 45 m/s), driven by a steam machine; then he used a whirling trolley. Crosby and Dashiell (1890) [2] used a whirling arm (L = 1.7 m, V = 58 m/s) driven by a steam engine in a room 12 m long, 4–6 wide and 3.7 m high; before the tests, they measured the resistance of the device, then subtracted it from the estimated one when the body was set on the arm; the results were increased by 10% to take into account the effect of the air set in motion by the arm. Von Lössl [10] used a whirling arm (L = 1 m, V = 10 m/s) that was highly regarded in Germany. Between 1895 and 1896, Konstantin Eduardovich Tsiolkovsky (1857–1935) [11] carried out the first Russian experiences with a small whirling arm. Mannesmann (1899) built a whirling arm (L = 49 cm, V = 15 m/s) driven by a dynamo. Reichel [12] used a whirling arm (L = 6.35 m) driven by an electric motor. Finzi and Soldati [13] used   force coefficient is a non-dimensional quantity defined as cF = 2F/ ρV 2 A , where F is the force exerted by a fluid on a body, ρ is the fluid density, V is the relative speed between the body and the fluid and A is the reference surface of the body.

1 The

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7 Wind and Aerodynamics

Fig. 7.1 Perry’s [5] (a) and Lilienthal’s [1] (b) whirling arms

of a whirling arm (L = 6 m, V = 15 m/s) driven by a three-phase motor. Charles Renard (1847–1905) [1] built a dynamometric balance on which an electric motor driving the whirling arm was fitted. Sir Hiram Stevens Maxim (1840–1916) [1] used a whirling arm L = 5.70 m long. The free-fall tests carried out by Galilei and Newton to measure the resistance of bodies in the air were perfected by Louis Paul Cailletet (1832–1913) and Colardeau [14] in 1892. They noticed how a body falling in vacuum was only subject to its weight force; its speed, then, constantly increased. A body falling in the air, instead, met a resistance R that increased with its speed V (Eq. 4.2); the body reached a uniform motion when resistance counterbalanced weight. Equation (4.2), measuring the speed V of the motion and equalling weight with resistance, provided the K drag coefficient. Furthermore, when the body weight was increased by adding ballast without altering its surface and shape, the V speed of the uniform motion increased; by repeating the experience with different weights, therefore, it was possible to obtain K as a function of V. The measurements were carried out on the Eiffel Tower at 120 m height, by means of an unwinding device (Fig. 7.2a). Similar tests were carried out in 1899 by Le Dantec [15] in Paris, using a short falling path (0.50–0.80 m). The surface of the body was crossed by a perpendicular pipe at its centre, which slid along a vertically taut metal wire. The falling height was adjusted through a cursor located on the wire. The Italian engineer Cosimo Canovetti (1857–1932) [16] also carried out freefall tests in Paris from 1899 to 1903. Unlike previous experiments, he had the bodies slide along a 370-m-long inclined plane, with the top at 70-m above ground. Eiffel [1] criticised the test arrangement because the inclined plane was not stiff and the instruments did not allow acquisition suited to obtain resistance. On the other hand, he considered the experiment conception excellent and hoped for a better repetition of this. This was the prelude to the free-fall tests carried out by Eiffel at his tower from 1903 to 1905 [1]. Unlike previous devices, the test plate was connected to a heavy mass by means of calibrated springs making up a dynamometer. The function associating resistance with speed was provided by the solution of a differential equation.

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445

Fig. 7.2 Cailletet’s and Colardeau’s [1] (a) and Eiffel’s [53] (b) devices

The body, together with the measurement device, slid along a vertical cable (Fig. 7.2b) from the second floor of the Tower, along a path 95–115 m long. To avoid wrecking or damaging the device, the fall was stopped by widening the cable diameter and by springs. According to a report of the Commission de l’Académie des Sciences written by Maurice Lévy (1838–1910) and Hippolyte Sébert (1839–1930) in 1908, “the results obtained by M. Eiffel, and put down in writing in his work, today represent the most accurate known values for the measurement of the resistance that air opposes to the straight motion of the surfaces having the size and shapes he indicates, for the displacement speeds falling in the range within which he operated”. Taking inspiration from experiments carried out in towing tanks, pulling boat models, similar tests were carried out in air since the late nineteenth century, pulling models first by means of locomotives and then using cars and bicycles. In 1878, Wellington carried out the first tests of this type near Cleveland [2]. He made use of locomotives speeding along tracks with different slopes. He observed that the measured resistance did not only depend on the pressure of the air on the body, but also on the wake of the train as a whole and on the interference between coaches. In 1885, Ricour [17] built balances and articulated parallelograms that, once installed aboard locomotives, measured the resistance of bodies. Similar tests were carried out by Desdouits [18] in 1886. In 1902, Francis Eugene Nipher (1847–1926) [19] carried out tests on a train car in Illinois recording, instead of the overall resistance of a plate, the pressure distribution on its two faces; he acknowledged that such tests required a lack of wind and it was difficult to quantify the role of the ground [20]. Similar results were provided by tests carried out using cars in the early twentieth century. The tests carried out by Wilbur (1867–1912) and Orville (1871–1948) Wright using bicycles (Sect. 7.4) deserve special mention. They provided poor results, but imparted

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a decisive thrust to wind tunnels and aviation in the twentieth century. Thus, their historical meaning is invaluable. The techniques and devices described above allowed a broad range of tests carried out between the late nineteenth century and the first decade of the twentieth century. They improved the knowledge of subjects already studied in past centuries, chiefly the resistance of thin plates perpendicular or inclined with respect to fluid direction, and opened new research fields, such as the reciprocal screening between adjacent elements and bodies, the position of the aerodynamic centre in inclined plates, the surface distribution of pressure, the resistance of bodies of different shapes and sizes as well as air friction. The measurements of the resistance of thin plates perpendicular to the flow direction (Sect. 4.2) increased with new experiences on square, rectangular and circular surfaces. They were carried out by varying the size and shape of the surface as well as the flow speed. Table 7.1, obtained from the data in [1, 2] through Eq. (4.2), summarises the most prominent experiences. Like Table 4.1, it shows a dispersion greater than the one associated with common measurement uncertainties. An extensive literature about the resistance of inclined plates developed in parallel. It was aimed at determining the Pϕ /P ratio between the Pϕ pressure on the plate, inclined by ϕ angle and the P pressure on the plate perpendicular to the flow (Fig. 4.15). Dines [6] and Langley [9] verified the orthogonality of the resultant of the pressures on inclined plates. Rodolphe Soreau (1865–1935) [21] rejected Newton’s squared-sine law (Eq. 4.4): “Let’s split the V speed (Fig. 7.3a) into two components, one parallel and one perpendicular to the plane. The latter is the only one acting on the plane, and everything takes place like the plane was perpendicular to the V sin(i) speed. Pressure is therefore perpendicular to the surface and its value P = KSV 2 sin2 (i): this is the famous squared-sine law, which perniciously affected aviation. The previous reasoning is false because it does not take into account the actual fluid flow (Fig. 7.3b). The edge projecting in A cuts through the air while an eddy effect takes place on most of the AB plane; the generated pressures and suctions are not equivalent at all to those generated by a flow perpendicular to the plane with speed V sin(i). Actually, the phenomenon is very complex and neither the squared-sine law nor the simple sine law may express it. The conclusion is the following: one has no right to compose or decompose a flow speed. Only experience, therefore, can provide certain data”. Other authors came to the same conclusion carrying out measurements of Pϕ /P. The results were generally compared with those of Duchemin’s Eq. (4.8) [22]: in some cases, they confirmed its correctness [9]; in others, ameliorative expressions were proposed [23]. Figure 7.4 [1] provides a synthesis of the results obtained on square and rectangular plates. The study of the reciprocal screening between adjacent bodies received growing interest, linked to the role of this issue in girder and truss bridges. The presence of beams parallel to the deck edges suggested reducing wind actions on the leeward beam. In 1882, Jules Gaudard (1833–1917) [24] recovered the studies carried out by Thibault in 1826 (Sect. 4.2) about two screens separated by a distance equal to their transversal size: if the pressure on a single screen was equal to 1, the overall one was equal to 1.7. He then examined truss bridges, treating every opening like an orifice;

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447

Table 7.1 Drag coefficients for thin plates (1874–1903) Researcher (year)

Method

Plate

K

G. Hagen (1874)

Whirling arm

Rectangular

1.08 + 0.18pa

M. Ricour (1885)

Square

1.97

M. Desdouits (1886)

Pull with locomotive

H. A. Hazen (1886)

Whirling arm

?

1.25

1.97

S. P. Langley (1888)

Square

1.00–1.47

W. H. Dines (1889)

Rectangular

1.35–1.45

Square

1.26–1.34

Circular

1.25–1.32

S. P. Langley (1890)

Whirling trolley

Square

1.18–1.59

F. von Lössl (1892)

Whirling arm

Rectangular

1.74–1.79

Square

1.62

L. Cailletet and E. Colardeau (1892)

Free fall

M. Le Dantec (1899) O. Mannesmann (1899)

Whirling arm

M. W. Reichel (1901) C. Canovetti (1903)

Free fall

G. Eiffel (1903)

G. Finzi, N. Soldati (1903)

ap

Whirling arm

= plate perimeter in metres

Circular

1.58

Triangular

1.70

Square

1.05–1.09

Circular

1.03

Triangular

1.03

Square

1.23–1.29

Rectangular

1.52

Square

1.43–1.82

Circular

1.17–2.18

Square

1.55–1.64

Circular

1.17–1.55

Rectangular

1.33–1.43

Trapezoidal

1.38

Circular

1.03–1.17

Square

1.06–1.20

Rectangular

1.11–1.14

Square

1.11–1.53

Rectangular

1.23–1.46

Circular

1.15–1.50

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7 Wind and Aerodynamics

Fig. 7.3 Inclined plate [1]: a wind action; b flow field

Fig. 7.4 Pϕ /P [1]: a square plates (I: Eiffel, dihedral; II: Duchemin; III: Eiffel, free-fall device; IV: Dines; V: Langley; VI: Mannesmann; and VII: Lössl); b rectangular plates (I: Stanton; II: Rateau; III: Eiffel; and IV: Langley) Table 7.2 Formulas to evaluate the pressure centre

Author

ρ = x/a

Thiesen

ρ = 0.4 cos ϕ/ (1 + sin ϕ)

Joessel

ρ = 0.6(1 − sin ϕ)

Soreau

ρ = 0.5(1 + 2tgϕ)

from there, he obtained formulae that gave the pressure on the first beam and on all the leeward ones. In the meantime, it became increasingly evident it was necessary to know, besides resistance, the position of the aerodynamic centre of inclined plates, i.e. the point of application of the resultant force that nullified the moment. It was evaluated during tests, the results of which are summarised in Table 7.2 [1], where x is the distance from the plate centre to the aerodynamic centre, defined as positive in the direction of the leading edge, and a is the half-width of the plate. Table 7.3 compares the results of the formulae in Table 7.2 with the ones of Dines’ and Langley’s experiments [9]. The main novelty of such measurements regarded the pressure distribution. In 1890, Dines [25], using a whirling arm and a pressure pipe, determined the “com-

7.1 Advancements in Experimental Aerodynamics

449

Table 7.3 Comparison between formulae and experiments to evaluate the pressure centre Author

Method

ϕ = 10°

ϕ = 20.5°

ϕ = 45°

ϕ = 78°

Joessel

Theoretical

0.495

0.395

0.176

0.043

0.370

0.287

0.166

0.048

0.400

0.250

0.150

0.040

–

0.292

0.166

0.042

Soreau Dines Langley

Experimental

pression and suction” on the upwind and downwind faces of a square plate, with 30 cm side; they were respectively equal to 67 and 33% of the overall resistance for a speed of 26.8 m/s. Dines proved that the suction on the downwind side depends on the shape of the body and on its depth; it was small when the body was shaped as a thin disk and increased when it was elongated. Since the pressure on the upwind face is approximately constant, the same trend, with different proportions, also regards the overall resistance. Similar experiences were carried out by Nipher [19] in 1902, by means of a pull test using a locomotive. He built a receiver consisting of two thin metal disks with sharp edges and diameter of 75 mm; it measured the pressures on the faces of a plate through a pressure gauge linked by pipes. The 90 × 120 cm plate consisted of wood planks inserted into a frame revolving around a vertical rod crossing the roof of a wagon; the lower edge of the plate was 30 cm away from the wagon roof. The plate was orthogonal to the motion direction by means of a spring dynamometer linked to a wind vane before the wagon; it was divided into 108 squares with 10 cm side, each one with a central hole, 1 cm in diameter, closed through a plug matching the upwind side. The pressure and the suction at the centre of every square were measured by removing the plug and introducing the receiver in the hole. A dynamometer simultaneously measured the overall plate resistance. Figure 7.5a shows the pressure on the upwind face, whereas Fig. 7.5b shows the suction on the downwind face. The sum of the partial values is 100; the sum of the values in pressure and suction is, respectively, 56.6 and 43.4. An effective tool to represent these measurements is still missing: the pressure coefficient.2 An extensive literature about the resistance of bodies of various shapes and size developed in parallel with the study of plates. The most famous tests are due to Lilienthal [7], Colonel Renard (1904) [1], Franck [26] and Eiffel [1]. They involved airfoils, curved surfaces, wedges, prisms, pyramids, cones, ogives, cylinders, spheres and hemispheres. Tables for engineering applications were obtained from such tests, the most famous being the ones collected by Lössl [27] in a manual published in Berlin in 1904. The comparison between the results shows amazing differences: by way of example, Renard provided K = 0.20 for a sphere, but according to Lössl K = 0.64.   pressure coefficient is a non-dimensional quantity defined as c p = 2( p − p0 )/ ρV 2 , where p is the pressure at a point of the body surface, p0 is a reference value of p associated to undisturbed conditions, ρ is the fluid density and V is the relative speed between the body and the fluid.

2 The

450

7 Wind and Aerodynamics

Fig. 7.5 Pressure distribution on a rectangular plate [1]: a upwind face; b downwind face

7.1 Advancements in Experimental Aerodynamics

451

It is almost embarrassing to note how this mass of results, produced over the centuries by scholars gifted with outstanding acumen, skill and enthusiasm, was invalidated by the use of techniques suited to outline qualitative trends, but inadequate to provide correct quantitative values. These tests, as well as the results they produced, represent the history of aerodynamics and the foundation of modern conceptions; they were, however, destined to disappear in the early twentieth century, swept away by full-scale measurements and wind tunnel tests. In the wake of the first experiments in the actual wind carried out by Benjamin Baker (1840–1907) during the construction of the Forth Bridge (Sect. 4.9), similar experiences were carried out from 1884 to 1888 in England, at the Bidston Observatory [2], during ten storms. The tests were carried out by means of a plate anemometer with an area of 0.19 m2 . The speed was measured by means of a cup anemometer. In the light of Baker’s results and Langley’s observations (Sect. 6.5), the first provided the peak pressure, the second the mean speed. By applying Eq. (4.2), the plate resistance was quantified by a K parameter ranging from 3.2 to 4.6; no information about the plate inertia is available. In 1887, Thomas Claxton Fidler (1841–1917) summarised the results obtained by Baker (Table 7.4) on the reciprocal screening between two flat circular disks, orthogonal to the wind direction [28]; the overall force ranged from 1 to 1.8 times the force on the individual disk, depending on the ratio between the distance and the diameter. In 1889, Lilienthal [7] investigated variously inclined curved surfaces by means of a plate anemometer and three rudimentary devices (Fig. 7.6): the results could not be accurate [1]. Better experiments were carried out by Thomas Edward Stanton (1865–1931) [29], between 1904 and 1908, at the National Physical Laboratory in Teddington. He first (1903–1904) carried out wind tunnel tests, obtaining the resistance of small plates (Sect. 7.2). He then aimed at measuring the resistance of larger plates, but this was not possible because of the tunnel size, so he installed a steel lattice tower at

Table 7.4 Overall force on two flat circular disks, orthogonal to the wind direction [28]

Fig. 7.6 Lilienthal’s devices [7]

Distance/diameter

1.0

1.5

2.0

3.0

4.0

Force coefficient

1.00

1.25

1.40

1.60

1.80

452

7 Wind and Aerodynamics

Fig. 7.7 a Dines’ anemometric tube [29]; b Stanton’s manometer [29]

the NPL. A vertical rod, supporting a frame manually steered in the wind direction, was fitted at the top of the 15-m-high tower; the frame supported three large-size (3 × 3 m, 3 × 1.5 m and 1.5 × 1.5 m) rectangular plates. The wind speed was initially measured by the Pitot tube used for wind tunnel tests,3 later replaced by a new instrument conceived by Dines (Fig. 7.7a). The resulting pressure on the plates was evaluated through a pressure gauge (Fig. 7.7b), designed and built by Stanton to measure the mean pressure over periods from 1 to 3 s. Stanton obtained values of K ranging from 1.20 to 1.23, nearly independent of the plate size; they were close to those measured by Dines and Langley, in the actual wind, on smaller plates. Stanton thus repudiated Baker’s results: “there appear, therefore, to be good reasons for supposing that the mean intensity of pressure on similar surfaces of area greater than 1 square foot, exposed to the wind, is independent of their actual dimensions”. Between 1911 and 1912 Stanton, who was not convinced by such results, carried out new and more extensive tests, making use of two steel lattice towers at the NPL and of four auxiliary antennas (Fig. 7.8) [30, 31], recording the ratio between the maximum instantaneous pressure averaged along an ideal line more than 100 m long and the pressure due to the local speed peak. This time there were no doubts on the correctness of Baker’s observations: Stanton obtained values from 0.4 to 1. In 1925, he carried out new tests on the Tower Bridge in London [31], proving that the pressure coherence was greater in strong winds. Noticing how structure design depended on such conditions, he concluded that, until new research was carried out, it would have been advisable not to consider the pressure reduction due to the surface size. Such statement does not diminish the value of the researches he carried out and of the results he obtained, but delayed their use for design purposes. Thanks to Stanton, a new measurement technique, full-scale tests, came into being, destined to result in interpretation problems for all those who were to tackle the complexity of the actual wind. On the other hand, it was the sole tool suited to validate the results of model tests. 3 Whereas

the flow in the wind tunnel was uniform, the actual wind showed quick fluctuations that were not detected by the Pitot tube.

7.1 Advancements in Experimental Aerodynamics

453

Fig. 7.8 Anemomentric antennas at the NPL [29]

Wind tunnels are not yet mentioned. The first ones appeared in the late nineteenth century and, from the early twentieth century, were the subject of sensational and still ongoing, advances. The initial stage of such progress was so complex and articulate to require independent treatment (Sects. 7.2 and 7.3).

7.2 The First Wind Tunnels The first experiments in which a stationary object was immersed in an artificial airflow were carried out by Francis Herbert Wenham (1824–1908), an engineer, inventor and aviation pioneer inclined to solve technical problems through experimental tests. On 27 June 1866, during the first meeting of the Royal Aeronautical Society of London, he gave a lecture, On aerial locomotion and the laws by which heavy bodies impelled through air are sustained (Sect. 7.7), in which he summarised his own aerodynamics observations, experiences and studies. He noticed how the wing camber was the key element that guaranteed lift, and that the highest lift occurred near the leading edge; from this, he drew the deduction that wings with large wingspan and small chord, i.e. with a high aspect ratio, guaranteed better performance (Fig. 7.9). He also stressed the importance of equipping aircraft with connected wings arranged on multiple levels. In the meantime, Wenham carried out experiences both on models fitted on a whirling arm and by building full-scale aircrafts. In 1870, disappointed by the results, he proposed to the Aeronautical Society of Great Britain “to try a series of experiments by the aid of an artificial current of air of known strength, and to place the Society in possession of the results” [8]. The Society Council met in May of the same year, acknowledged the lack of data about the resistance of bodies and decided to carry out the experiments. The following month, a committee including Wenham was formed, which decided to build the first wind tunnel in history; it consisted of “a rectangular duct 10 ft long, with a square cross-section 18 in. on a side. The air was driven through the duct by a fan powered by a steam engine”. The flow achieved a speed of 18 m/s [8]. The facility, built in 1871 at the Penn’s Marine Engineering Works in Greenwich, was

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7 Wind and Aerodynamics

Fig. 7.9 Wenham design of different wing structures (1866)

used to evaluate the drag and lift of inclined plates [20, 32]; tests were carried out through a rudimentary spring system in a chaotic flow. The results, divulged in 1874, highlighted two aspects. For small angles of attack, the lift/drag ratio was much greater than that envisaged by the squared-sine law (Sect. 4.2). Moreover, as noted by Wenham eight years before, the aspect ratio played an essential role for lift: a long and slender wing is more efficient than a short and stubby one having the same area. Wenham used these results to design a multiplewing aircraft, a forerunner of biplanes (Sect. 7.4). In 1886, William Cawthorne Unwin (1838–1933) [33] used Wenham’s measurements to evaluate the wind actions on inclined roofs. According to dubious piece of evidence, the first small French wind tunnel was built in 1877 at the French State Airship Factory near Chalais-Meudon. It is likely it, or its evolution, was used or developed by Charles Renard (1847–1905), by 1896, to assess the most efficient shape for aircraft fuselages. In 1880, the English engineer Horatio Frederick Phillips (1845–1924), another member of the Aeronautical Society of Great Britain, criticised Wenham’s measurements and, in 1884, he built the second (or third) wind tunnel in history (Fig. 7.10), where he attempted to avoid the presence of speed fluctuations in the duct. To that end, he installed a “steam injector” and set a chamber, 1.8 m long with square crosssection 43 cm on a side, at its left [8]. He placed a wooden block in the chamber and created a flow choke above it, through which speed reached 18 m/s. The models were installed on a balance, located on a wooden block, which measured the drag and lift of bodies. Unlike Wenham, who only studied flat plates, Phillips studied airfoils with cambered shapes. He published questionable results [34] in a brief paper that appeared in 1895 in a nondescript English magazine [35]. A new technology, which would be subjected to huge developments and would play a leading role in wind engineering, had come into being. With the exceptions of a wind tunnel in Australia and of some facilities in the USA, it especially gained ground in Europe (Table 7.5) [30, 36, 37]. No wind tunnel built before 1910 had a power exceeding 100 HP. All of them produced possibly a uniform flow. In 1890, at the Melbourne University in Australia, William Charles Kernot (1845–1909) [38] produced an airflow in a 25 × 30 cm rectangular channel

7.2 The First Wind Tunnels

455

Fig. 7.10 Phillips’ wind tunnel [8] Table 7.5 First wind tunnels Year

Builder

Location

1871

Francis H. Wenham

Greenwich, UK

1877

Charles Renard

Chalais-Meudon, France

1884

Horatio F. Phillips

Harrow, UK

1890

William C. Kernot

Melbourne, Australia

1891

Nikolai Y. Zhukovsky

Moscow, Russia

1893

Ludwig Mach

Wien, Austria

1893

Johan O.V. Irminger

Copenhagen, Denmark

1894

Hiram S. Maxim

Kent, UK

1896

Albert Wells

Boston, Mass., USA

1896

Paul La Cour

Askov, Denmark

1897

Konstantin E. Tsiolkovsky

Kaluga, Russia

1901

Étienne J. Marey

Paris, France

1901

Wilbur and Orville Wright

Kitty Hawk, USA

1901

Albert F. Zahm

Washington, USA

1903

Thomas E. Stanton

Teddington, UK

1903

Gaetano A. Crocco

Rome, Italy

1904

Dimitri P. Riabouchinsky

Moscow, Russia

1909

Thomas E. Stanton

Teddington, UK

1909

Gustav A. Eiffel

Paris, France

1909

Ludwig Prandtl

Göttingen, Germany

1912

Gustav A. Eiffel

Auteuil, France

1912

Thomas E. Stanton

Teddington, UK

1912

Hugo Junkers

Aachen, Germany

1913

Albert F. Zahm

Washington, USA

1914

Jerome C. Hunsaker

Boston, Mass., USA

1914

Richard Knoller

Wien, Austria

1916

Ludwig Prandtl

Göttingen, Germany

456

7 Wind and Aerodynamics

Fig. 7.11 Kernot’s wind tunnel [33]

(Fig. 7.11). It was generated by a propeller driven by a gas engine. Small-size models were placed on sensitive dynamometric balances at the channel outlet. Kernot studied the resistance of bodies with various shapes—cubes, pyramids and cylinders—and of buildings. He also studied, perhaps for the first time, the interference due to adjacent bodies. The results do not appear to be plausible, in a strict sense, but they are interesting in relative terms [2]. Nikolai Yegorovich Zhukovsky (also mentioned as Joukovsky or Joukowsky, 1847–1921) in 1891 built a small wind tunnel at the Moscow University. He used it to assess the drag and lift of airfoils as a function of the rounded or sharp leading edge, of profile thickness and roundness and of the sharpness of the trailing edge. His lift theory (Sect. 7.4) took its cue and mingled with these experiments. In 1893, Ludwig Mach built a 17.8 × 25.4 cm wind tunnel in Austria, using a suction centrifugal fan. He understood that flow irregularity could be reduced by a metal grid wire at the tunnel inlet. He understood that the observation of the flow around the wings of airplanes would help interpreting flight mechanisms. He then introduced in the flow, at the tunnel inlet, light paper scraps, cigarette smoke, red-hot iron particles and heated smoke currents, taking photographs around the test bodies [39]. In the same year, in Copenhagen, Johan Otto Valdemar Irminger (1848–1938) built a “wind tunnel” destined to have huge repercussions on the aerodynamic tests of structures (Sect. 7.3). This event had its roots in 1880 [40, 41], when Hans Christian Vogt (1848–1928), a Danish engineer unaware, like everybody else, of Cayley’s studies (Sect. 4.5), noted the manoeuvres of albatrosses and perceived they flew by virtue of a strong suction on the upper wing face. This idea, in antithesis to the squared-sine law, improperly attributed to Newton, became Vogt’s obsession. He attempted to substantiate it for nine years, formulating bizarre theories. He even applied to Lord Kelvin, under whom he studied at the Glasgow University, but he was disdainfully dismissed. Between 1888 and 1890, Samuel Pierpont Langley (1834–1906) measured the air loading on a thin inclined plate (Sect. 7.1). As the angle of attack tended to zero, the force on the plate became even twenty times greater than the one envisaged by the

7.2 The First Wind Tunnels

457

Fig. 7.12 Intervention on a chimney at the Copenhagen gas works [40]

squared-sine law. Vogt started a correspondence with Langley to persuade him of the role of the suction on the leeward face. Langley believed Newton could not have failed to notice this and that the test himself carried out had to be somehow wrong [40]. In the same period, Phillips measured a high-pressure drop between the upwind and downwind side of a hill. He then carried out wind tunnel tests on curved surfaces with various shapes [20], finding similar results. When Vogt learned about these measurements, he contacted Phillips and revealed him his theories. Phillips replied that the only way to prove them was carrying out experiments. Vogt followed Phillips’ advice and contacted Irminger, an engineer who was both a friend and countryman of him as well as the director of the Copenhagen gas works [41]. Irminger, fascinated by Vogt’s theories, carried out field tests that turned out to be a failure. He, however, understood, reading Stanton’s works, that probative results could only be obtained by operating within artificial flows [40]. At the gas works, there was a chimney, 33 m high and 1.5 m in diameter, serving many furnaces. In 1893, Irminger made an opening in the chimney and introduced there a rectangular box 1 m long, with 11 and 23 cm sides (Fig. 7.12). He introduced in the box two opposed plates with small holes, by means of which he measured, for the first time [42], a pressure distribution (Fig. 7.13a) instead of a resultant force.4 Starting from this result, and tracing back the resultant force through integration, he validated Vogt’s intuitions [40]. It is said that tests were carried out at night, in secret. What is certain is that almost 30 years were to lapse before these concepts receive any credit. Encouraged by this result, Irminger [43] continued his tests measuring the wind pressures and forces on models of inclined plates, elongated prisms with different cross-sections, pyramids, spheres, cubes, buildings with variously angled sloping roofs and airfoils (Fig. 7.13b). He especially dwelled on the suction due to the “rarefaction” of air on the downwind faces. He noticed the importance of this phenomenon as regards to roofs that had hitherto been subjected—wrongly—to pure 4 Irminger’s

pressure measurements anticipated by a decade similar measurements carried out by Nipher by means of a locomotive (Sect. 7.1).

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7 Wind and Aerodynamics

Fig. 7.13 Irminger’s measures [40]: a pressure on plates; b force on wing and building models

pressure actions. He noticed that, in the case of the sphere, suction accounted for 77% of the overall drag force. In 1894, Sir Hiram Stevens Maxim (1840–1916) [44], an American who became a naturalised British, understood the limitations of the measurements carried out by whirling arms. He then built a wooden duct with square cross-section, 0.52 m on a side, in Kent; it was connected to a larger chamber, 0.61 m on a side, in which two wooden propellers, fastened to the same shaft by cross-arms, rotated (Fig. 7.14). The propellers were divided by means of a screen of thin blades (d). Thin bars, vertical and horizontal, respectively, were fitted in (e) and (f). Two wide and thin boards with sharp edges, arranged as X, were located in (g). This set of devices prevented turbulence. The propellers were driven by a 100 HP engine and produced a smooth flow, achieving speeds up to 22 m/s. The models were supported by a mobile frame governed by levers allowing, with the aid of weights on the balance plate, measuring horizontal and vertical forces. Maxim carried out measurements on propellers and wings, proving that cambered profiles guaranteed maximum lift and minimum drag. In 1896, Albert Wells, a mechanical engineering student preparing his bachelor thesis at MIT (An investigation of wind pressure upon surfaces), built the first American wind tunnel in Boston. He diverted the air from a ventilation duct into a pipe with square cross-section, 0.28 m on a side, where he measured the aerodynamic actions on plates. The ideas and techniques of Vogt and Irminger were resumed by Paul La Cour (1846–1908), a prominent Danish physicist and inventor devoted to produce wind energy (Sect. 8.1). Aiming at improving the efficiency of ancient windmills, he studied blades through aerodynamic model tests. To such purpose, in 1896 he built two wind tunnels with circular cross-section, 0.5 and 1 m in diameter and 2.2 m long, driven by electric fans, in Askov. In 1897, La Cour repeated and extended the tests carried out by Irminger on plates, measuring their drag and lift for various angles of attack. Thanks to these tests, he defined the optimum shape and orientation of blades and formulated new conceptions on windmills (Sect. 8.1). They were steadily used for producing electric energy during the First World War [41].

7.2 The First Wind Tunnels

459

Fig. 7.14 Maxim’s wind tunnel (cross-sections) [1]

Konstantin Eduardovich Tsiolkovsky (1857–1935) [11] founded the Russian astronautical and aeronautical sciences, deriving the first equations about rocket flight. He also became a pioneer of experimental aerodynamics, by acknowledging that any new theory had to be confirmed by experiments. He initially studied the flight of insects and birds, being them references for the flight of airplanes. In 1897, in Kaluga, he built a device with rotating blades that generated an airflow sweeping bodies installed on balances before the mouth of the tunnel. He subsequently enlarged the device, adding a duct with a cross-section four times larger than the original one. Thanks to these devices, Tsiolkovsky carried out tests on surfaces subjected to friction actions, prisms, circular and elliptical cylinders, polyhedrons and spheres, elongated bodies, airfoils, half-cylinders, half-spheres and conical surfaces, dirigibles. He paid attention to the correlation between the resistance of bodies and their shape, varying geometrical ratios and angles of attack; he compared his results with those by Langley, Duchemin and others. He also studied wind actions on inclined plates, analysing the range of validity of the squared-sine law. In 1901, in Paris, Étienne Jules Marey (1830–1904), a French physiologist and inventor studying motion,5 built the “smoke machine” (Fig. 7.15a), a vertical downdraft wind tunnel [39] partially financed by the Smithsonian Institution. Like Mach, 5 Marey

was interested in all forms of motion; he studied the heart cycle, breathing, muscular contraction and motorial coordination. This forced him to invent instruments thanks to which he is considered a pioneer of photography and cinematography. He is famous for his photographic studies about horse gallop, showing for the first time the moment when the horse has its four legs lifted above the ground, and about bird flight, an act described in such detail to become a reference point for aeronautics studies (Sect. 7.4). His books (La machine animale, 1873; Le vol des oiseaux,

460

7 Wind and Aerodynamics

Fig. 7.15 a Marey’s wind tunnel; b visualisation of a flow field

Marey also focused his interest on flow visualisation. He placed 58 small tubes spaced at 6.35 mm intervals at the mouth of the tunnel and introduced smoke filaments through them. The tunnel was placed in a dark environment; the walls of the test chambers were made of glass; a camera equipped with a magnesium flash took clear images (Fig. 7.15b). In the same year (1901), Wilbur (1867–1912) and Orville (1871–1948) Wright [45], two bicycle mechanics in Kitty Hawk, North Carolina, built one of the most famous wind tunnels in history. At the start of that year, fascinated by Marey’s studies, they measured the resistance of airfoils mounted on bicycles. Dissatisfied by results, they built a small wind tunnel, which was completed in October 1901 (Fig. 7.16) [8, 20]. The duct was 1.8 m long; the cross-section was a square, 40.6 cm on a side; and the upper side consisted of a glass plate to allow observing experiments. The device was put on the second floor of the bicycle shop; air was set in motion by means of a fan driven by a diesel engine used in the shop and connected to the tunnel. Despite the use of a rudimentary balance, their measurements changed the history of aviation (Sect. 7.4). In that same year (1901), Albert Francis Zahm (1862–1954) built a huge wind tunnel at the Catholic University in Washington, D.C. It was 12.2 m long with square cross-section, 1.8 m on a side; the instrumentation included a Pitot tube and a pressure gauge; and the tunnel was located in a dedicated building. Zahm built various 1890; and Le mouvement, 1894) will arise the interest of the Wright brothers, giving an essential contribution to aviation.

7.2 The First Wind Tunnels

461

Fig. 7.16 Wright brothers’ wind tunnel [45]

balances, by means of which he measured the resistance of dirigibles, plates and lifting surfaces. He was also the first to notice that friction played an important role as regards to resistance [8]. Unfortunately, the financial backer died, and the facility was closed in 1908. Thomas Edward Stanton (1865–1931), first a student and then a colleague of Reynolds, in 1903 built an updraft wind tunnel at the NPL in Teddington [46]. The device (Fig. 7.17a) used a fan 0,75 m in diameter (A) driven by an adjustable speed electric motor. Air was drawn in a pipe (B) 1.35 m long and 0.60 m in diameter. The test chamber (C) between the pipe and the fan had a square cross-section 1.2 m on a side and 0.375 m deep. It was fitted with glass walls and equipped with a door to introduce the models; a lever that measured the resistance of bodies was put in space (D) beside the test chamber. Flow measurement was accomplished by a pair of Pitot tubes: one measured the flow speed, the other the reference static pressure. Stanton noted that to carry out proper tests the flow speed had to remain constant in the cross-section; thus, he introduced gauze layers in the channel obtaining, excluding the first 2.5 cm away from the edges, a speed variation within 1% of the mean value. Stanton used the new equipment to study the Venturi effect, now known as “blockage”, caused by a plate in the test chamber. It caused an increase in the flow speed near the walls and an increase in the mean pressure P on the plate. He proved that carrying out experiments on plates with diameter D greater than 5 cm, i.e. having an area greater than 0.7% of the channel cross-section area, was not admissible. He then carried out tests on small sized and variously shaped plates, measuring the resistance and the pressure distribution on the windward (Pw ) and leeward (Pl ) face (Fig. 7.17b): he proved that the pressure was maximum at the centre of the windward face, where Pw = ρV 2 /2, and was uniform on the leeward face; in circular plates, on

462

7 Wind and Aerodynamics

Fig. 7.17 a First Stanton’s wind tunnel [46]; b pressure distribution upwind and downwind the faces of circular and rectangular plates [46]

the average, Pw /Pl = 2.1; in rectangular ones, Pw /Pl = 1.5. Stanton also studied the interference between two parallel plates: when they were close, the second was in suction; when they were far, the first did not affect the second one. He finally carried out tests on inclined plates, cylinders and building models, highlighting the suction on leeward surfaces. Gaining momentum from Stanton’s results, NPL started building increasingly improved and powerful wind tunnels. The second one was completed in 1909, had a square cross-section 1.2 m on a side and generated flow speed up to 13.5 m/s. The third one, inaugurated in 1912, had a square cross-section, 2.1 m on a side. They were used during the First World War to study the flutter of airplane wings (Sect. 7.4). These experiences were indeed essential for bridges (Sect. 9.1), placing the NPL, in the mid-twentieth century, at the world forefront for the emerging wind engineering. In 1903, Captain Gaetano Arturo Crocco (1877–1968) built the first Italian wind tunnel in Rome, at the Aeronaut Specialist Brigade of the Military Engineer Corps. The device included a fan 2.5 m in diameter, driven by a 30 HP electric motor. The flow crossed a rest chamber, a kind of tin gas holder 3.5 m high and 5.5 m in diameter that dampened eddy motions. The air then flowed along a square duct, 0.8 m on a side, that ended in the shed where experiments were carried out; here, the speed reached 29 m/s. The bodies subjected to testing, in particular dirigible models, were supported by light mobile frames or suspended to floats that nullified frictions. Propeller tests were carried out through a dynamometric balance that improved the one designed by Renard.

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In 1904, Dimitri Pavlovitch Riabouchinsky (1882–1962) [47] founded the Koutchino Aerodynamics Institute in Moscow, the first European aerodynamics institute. In 1906, at Joukowski’s suggestion, he built there a wind tunnel consisting of a horizontal cylindrical duct 14.5 m long and 1.2 m in diameter (Fig. 7.18a). The facility used a fan 1 m in diameter, driven by an electric motor; the properties of the flow were controlled by means of 2 anemometers, one of them being fixed, the other mobile. Riabouchinsky initially made measurements on propellers with different shapes, with horizontal or vertical axis. The tests proved that their propulsive force increased when the flow was orthogonal to its axis, confirming the results of previous experiences carried out by Joukowski in his wind tunnel and by Maxim by a flying craft. He then carried out measurements on models of windmill blades, studying their shape and inclination. In the course of these tests, he also provided essential contributions to the disruption affecting the air passing around a body subjected to testing, because of the proximity with tunnel walls; if the body size is excessive, it caused an obstruction that distorted results, mainly overestimating pressure values. To quantify this phenomenon, Riabouchinsky put in the wind tunnel disks with different diameters, orthogonal to the duct axis and put on balances. The results suggested to carry out tests on models with an area not exceeding 1% of the duct one. Riabouchinsky also developed a technique to visualise the flow field around a body installed on a metal plate. He introduced lycopodium powder in the fluid and made the plate vibrating by means of a small hammer. The impulse highlighted the streamlines (Fig. 7.18b); the visualisations were called “aerodynamic spectra”. In addition, in 1909 Riabouchinsky invented the hot-wire anemometer (Sect. 6.1), and in 1911, he provided essential contributions to dimensional analysis (Sect. 5.1) and to its use in aerodynamics. Both techniques became distinctive elements of the Koutchino Institute, and from there, they gained ground in the major laboratories worldwide. In 1909, Auguste Camille Edmond Rateau (1863–1930) built a small plant in Paris. The fan was located at the inlet of the divergent. The calm chamber used inlet

Fig. 7.18 a Koutchino wind tunnel [47]; b Riabouchinsky’s “aerodynamic spectrum” [47]

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Fig. 7.19 Eiffel’s wind tunnel, Paris: a photograph [8]; b vertical cross-section [1]

filters and honeycombs at the outlet. The measurements were taken at the outlet of the convergent, outside the tunnel. In the same year (1909), also in Paris, Alexander Gustav Eiffel (1832–1923) realised one of the most famous wind tunnels in history at the Champ de Mars, near the Tower. The plant, of the free jet type, was 3.60 m long, 1.50 m in diameter and attained speeds up to 20 m/s (Fig. 7.19). Eiffel, starting from the blockage issue raised by Riaboucinsky, built an airtight test chamber straddling the flow (Fig. 7.19a). Air was drawn from a hangar (A) through a flow controller (B) separated from the test chamber (C) by means of a cellular diaphragm (Fig. 7.19b) guaranteeing parallel streamlines. On the side opposite to the test chamber, there was the duct for the air (F) delivered to the fan (G). Air was introduced in a corridor (I) linked with the hangar. The fan was 1.75 m in diameter and was driven by a 50 kW dynamo, powered by the generator sets of the Eiffel Tower. The tunnel was fitted with a complete instrumentation [1]. The flow speed was measured by a pressure gauge and a Pitot tube. The test chamber was equipped with a dynamometric balance designed by Eiffel. The measurement of the pressure distribution was accomplished by many properly arranged holes, plugged by small screws that made the surfaces flush. At the measurement point, the screw was replaced by a threaded piece crossed along its axis by a channel 0.5 mm in diameter. On the face to examine, the screw was flushed with the face; on the opposite side, the channel was extended through a small pipe communicating with a pressure gauge. Every test was carried out by checking that the integral of the pressures was equal to the resultant force measured by the balance. Many thin rods, with short and light threads mounted at their ends, could be fitted within the flow. The threads oriented themselves in the direction of the streamlines, implementing a flow visualisation system. Eiffel devoted the first years of this device to the measurement of square, circular and rectangular plates, orthogonal and oblique to the flow, of three-dimensional bodies of various shapes and sizes and of airplane propellers and wings. He proved that the wing lift was chiefly due to the suction on the upper face. He carried out the

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first model tests on complete airplanes (1909) [48]. Here, he coined two terms now in everyday use [8]: “wind tunnel” (Wenham called it “artificial current”, Phillips “delivery tube”, the Wright brothers “the apparatus”, Stanton “channel”; Eiffel used the sentence “ce qu’on appelle la méthode du tunnel”) and “polar diagram” (by which he reported the lift and the drag coefficient for different angles of attack). The wind tunnel at the Champ de Mars was too noisy for the place where it had been built, so Eiffel built another one in Auteuil, in the outskirts of Paris, which was inaugurated on 1 January 1912; he took advantage of this occasion to improve his previous design [8] (the speed now reached 29 m/s, the diameter of the test chamber was 2 m) and to start experiments [49] on 17 1:10 airplane models. The latter turned out to be essential for the purposes of the First World War and for the knowledge on flight stability. In the meantime, wind tunnels based on Eiffel’s patented design were built in other cities in France, Netherlands, Japan and in the USA [50]. Ludwig Prandtl’s (1875–1953) wind tunnel drew inspiration from the ship advances obtained through model tests at towing tanks [51]. Prandtl understood that obtaining similar advances in aerial navigation required measuring resistance to forward motion, stability, manoeuverability, lifting action and propeller efficiency. The critical issue was the reliability of model tests and their check by full-scale measurements. The Göttingen plant was meant to provide answers to the first issue. Prandtl, as a member of a technical committee studying motor airships, proposed building the new plant in January 1907. The construction was approved in September. The building in Göttingen destined to house and the plant was completed in 1908. The wind tunnel, finished and inaugurated in 1909, subverted the conception of all the previous plants. While the latter, from now on called “open-circuit” ones, were straight axis channels where air entered from one end and came out from the opposite end, freely circulating in the space housing the plant, Prandtl’s wind tunnel was the first prototype of the so-called closed-circuit tunnels, where air circulated inside an annular duct. Figure 7.20a shows a vertical cross-section and the layout plan of the plant. The flow was generated by a propeller fan (V), 2 m in diameter, driven by a 30 HP electric motor (E); it produced a maximum speed of 10 m/s. G1 and G2 were the two flow straighteners. The flow ran into a channel with 2 × 2 m cross-section; it formed a continuous loop with four right-angle bends with directional baffle plates (Fig. 7.20b); the latter guided circulation, avoiding separation and vortex wakes. The test chamber, mostly transparent, was on the side opposite to fan. The electric motor control devices, as well as the measurement and control system, were located in the work area before the test chamber; the upper half of the intermediate wall was equipped with glass windows. Flow speed was measured by two Dines pressure tubes, communicating with a pressure gauge. The models—projectiles, propellers and windmill blades—were horizontally suspended by wires that did not disrupt the flow; the wires transmitted tension forces to four levers making up as many balances; the first provided the horizontal component of the aerodynamic action, the second and the third the intensity and the application point of the vertical action and the fourth the torsion. An additional device allowed studying aircraft propellers suspended into the flow.

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Fig. 7.20 a Prandtl’s wind tunnel in Göttingen [51]; b corner baffle plates [51]

In Prandtl’s words [51], “thanks to the many results obtained through this new plant for model tests, a strong desire arose to build everywhere in Germany other plants similar to the one in Göttingen, of increasingly better design, for the purpose of apportioning the huge amount of work among them”. An unstoppable progress was underway. In 1912, Hugo Junkers (1859–1935), a mechanical engineering with a prominent role in aeronautics (Sect. 7.4), built a wind tunnel in Aachen, Germany. In 1913, Zahm built his second wind tunnel at the Washington Navy Yard; it was a closed-circuit one, with square cross-section, 2.4 m on a side; the flow speed reached 71.5 m/s. Jerome Clarke Hunsaker (1886–1984), an American aerodynamics scholar who toured Europe to become acquainted with these plants, built the first important wind tunnel at the MIT in 1914; its cross-section was a square, 1.2 m on a side. In the same year (1912), Richard Knoller (1869–1926) built the second wind tunnel in Wien, at the Aviation and Automobile Engineering Institute; the tunnel was an open-circuit one, with 2.5 m2 cross-section, was equipped with an open test chamber and the flow ran downwards; the return flow crossed the four corners of the building and was propelled by four motors in the basement, with an overall power rating equal to 30 HP; the flow speed reached 80 km/h. In 1916, Prandtl himself built a second closed-circuit wind tunnel in Göttingen (Fig. 7.21), which represented a reference for subsequent plants; the duct gradually

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Fig. 7.21 Second Prandtl’s wind tunnel in Göttingen (1916) [8]

diverged in the flow direction until it reached a calm chamber where turbulence was reduced; after the chamber, a contraction cone accelerated the flow entering the (open) test chamber. The above overview shows that the first wind tunnels were used to carry out a broad range of tests. They included the measurement of aerodynamic actions on ideal bodies, the study of wings, propellers and airplanes, the analysis of civil buildings and the efficiency assessment and optimisation of windmills. As time went by, the field of application of wind tunnels expanded. In parallel, a trend towards specialisation emerged and led to plants increasingly related to the tests carried out there. At first, three plant types gained ground, aimed at civil and environmental (Sect. 7.3), aeronautical (Sect. 7.4) and vehicle (Sect. 7.6) tests. Afterwards, specialisation became so extreme to spawn increasingly specific test equipment.

7.3 Boundary Layer Wind Tunnels The process leading to the implementation of a new type of wind tunnels, purposebuilt for the determination of wind actions and effects on structures and, in general, for civil and environmental tests, started in 1927, when Johan Otto Valdemar Irminger (1848–1938) left the Copenhagen gas company and teamed up with Christian Ditlev Nielsen Nøkkentved (1892–1945) at the Structural Research Laboratory of the Danish Royal Technical College. Between 1930 and 1936, they carried out tests on buildings and other structures, collecting the results in two reports [52, 53] published in 1930 and 1936, respectively. They were the mainstay of the first important code dealing with wind actions on structures (Danish code of wind loading), issued in Denmark in 1945 (Sects. 9.3 and 9.5). The first experiments, mostly carried out by Nøkkentved, qualitatively visualised the flow field around building models laying on a side and fastened to a trolley dragged inside a channel with 60 × 60 cm cross-section, filled with water. Two plates were fastened to the models: one, parallel to the channel bottom, eliminated

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Fig. 7.22 Flow visualisation in a water-filled channel [53]

wall effects, tendentially making the flow bidimensional; the other, vertical in the direction of motion, simulated the presence of the ground. The channel floor was sprinkled with aluminium powder that highlighted the streamlines by spreading into the flow (Fig. 7.22). The tests showed three distinct flow zones: an irrotational portion, an eddy before the upwind face and the vortex wake behind the model. Irminger and Nøkkentved observed how the flow created a pressure on the upwind face, while the downwind face and the downwind pitch of the roof were in suction. As regards to the upwind pitch, there were three different conditions: (a) for great slopes of the upwind pitch, the flow skimmed it, separating from its upper edge; the pitch was subjected to pressure; (b) for lesser values of the upwind pitch slope, the flow separated from its lower edge, then reattached itself again, and in the end, it definitely separated itself from the upper edge: part of the pitch was subjected to pressure, part to suction; (c) for small values of the upwind pitch slope, the flow separated from its lower edge and the roof was integrally subjected to suction. Once this preliminary stage was over, Irminger and Nøkkentved carried out quantitative tests at three different wind tunnels. Most of them were carried out at the Structural Research Laboratory of the Danish Technical College in Copenhagen, in a tunnel with square cross-section, 60 cm on a side (Fig. 7.23), similar to the second NPL wind tunnel. Other tests were carried out in Göttingen, in co-operation with Prandtl. Some more tests were performed at the Flygteknik laboratory of the Royal Technical College in Stockholm, in a closed-circuit tunnel with an open test chamber; the two duct holes opening onto the test chamber were 1.6 m in diameter (Fig. 7.24a). The tests were carried out by placing a plate in the flow direction, on the plane of symmetry, to make the flow bidimensional (Fig. 7.24b). During these experiments, Irminger and Nøkkentved measured the external pressure on buildings (Fig. 7.25) with different shapes and orientations. They made pioneering tests on the internal pressure of non-airtight buildings, discussing the analytical formulae to evaluate it.6 They studied the pressure field and the flow regime 6 According

to Irminger and Nøkkentved, the internal pressure pi in partially open buildings was:

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Fig. 7.23 Wind tunnel at the Technical University of Copenhagen [59]

Fig. 7.24 Royal Technical College in Stockholm [53]: a wind tunnel; b model

on double-pitch or arched roofs. They analysed wind actions on shielding barriers with different shapes and porosity, as well as their screening effect on buildings: this study was part of a co-operation between the Det Danske Hedeselska (Danish Health Society) and the Danmarks Tekniske Hojskole (Danish Technical College). The peculiar element of these researches is the role of the ground, i.e. the tunnel floor. In view of the differences they observed, Irminger and Nøkkentved regarded it as essential. They corroborated this remark by noting that the aerodynamic behaviour of the body varied when the length of the splitter plate in the symmetry plane was changed. 

Aj



p j − pi = 0

j

where Aj is the area of the jth opening, and pj is its external pressure; the sum is extended to all the openings. In comparison with the formula used today to express the quasi-steady mass conservation (Sect. 8.6), the opening shape coefficient is missing. Moreover, the rule about the signs for the emission or introduction of air into the building was not defined.

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Fig. 7.25 Internal and external pressure measurements on buildings [40]

Irminger and Nøkkentved noted that the pressure distribution on bodies with rounded surfaces depended on the Reynolds number. They remembered a treatise in which Eiffel [50] proved that the aerodynamic actions on bodies with sharp edges were not affected by this parameter. They remarked that the situation was different when the body was lying on the ground. In this case, the pressure distribution on the upwind face was affected by the eddy thereabout. The latter depended on the Reynolds number and on the floor roughness; both these parameters were contained in the δ/h ratio, δ being the thickness of the boundary layer at the tunnel floor (Sect. 5.1) and h the model height. Figure 7.26a shows the pressure change (at the point #5 of the building) as a function of δ/h. Figure 7.26b shows the method adopted to define δ: let us consider a diagram with the speed v in the abscissa and the height z in the ordinate; v0 is the value of v reached when the friction exerted by the wall fades away; a segment is then traced, joining the origin with the (v0 , δ) point, δ being the conventional thickness of the boundary layer; it is obtained by equalling the hatched area with the area of the triangle subtended by the segment.7 Irminger and Nøkkentved then came to the revolutionary conclusion that “there is a great variation in the pressure on a building when δ/h varies; for designs or specifications taking wind pressure into account, therefore, it is necessary to determine the value of δ/h in Nature”. Nøkkentved corroborated these concepts in a paper [54] published in 1936. 7 This

definition is different from the one used in fluid dynamics (Sect. 5.1).

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Fig. 7.26 a Wind pressure on buildings as a function of δ/h; b diagram for determining δ [53]

In the same period, Prandtl’s student Otto Flachsbart (1898–1957) came to similar conclusions in Germany. In 1932, he published the results of measurements on models of open and closed buildings (Fig. 7.27), carried out in the Göttingen wind tunnel with two different speed profiles [55]: pressure distributions show remarkable qualitative and quantitative differences. This result initially had limited publicity; Flachsbart will only receive his due recognition at a later time. Between 1930 and 1933, Alfred Bailey [56] carried out at the NPL the first comparison between the pressures measured on a real building in the actual wind and those evaluated in a wind tunnel on a small model; the building was a storage shed for railway passenger cars. The comparison highlighted qualitatively similar but quantitatively very different pressures (Fig. 7.28). Bailey observed that the suction on the downwind face of the real building was much greater than the one evaluated in the wind tunnel; he remembered a similar consideration had appeared in a paper by Stanton [29]. Bailey returned to deal with the reliability of wind tunnel tests in a paper published with Noel David George Vincent [57] in 1943. He wondered whether the results of model tests in artificial flows might be correctly transferred to real structures in actual winds. Bailey and Vincent, remembering the poor quality of previous comparisons [56], examined the causes that could invalidate the tests. These included the ratio between the model size and the cross-section of the test chamber (Sect. 7.2), the properties of the tunnel flow in regard to the roughness of the actual ground, the presence of adjacent buildings and their interference effects. The central point regarded the tunnel floor and the speed profile. Bailey and Vincent recalled that for a long time the model was placed in the centre of the tunnel, ignoring the presence of the boundary. Recently, however, Nøkkentved [54] published an “interesting” work, in which he observed that the tunnel floor caused a boundary layer whose speed profile (“wind-gradient curve”) affected the distribu-

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Fig. 7.27 Building models and pressure taps distribution by Flachsbart [55]

tion and intensity of wind pressures. They were also impressed by Nøkkentved’s consideration stating that8 “the form of the wind-gradient curve in the wind tunnel should correspond to the natural wind-gradient to be expected, on the same scale as that of the model”. On the basis of these remarks, Bailey and Vincent attributed the law indicated by the British Meteorological Office to the mean speed profile of the actual wind [57]. They assumed that the models subjected to tests matched a 1:240 geometric scale and built a very long tunnel at the NPL, scattering on the floor such a series of obstacles that the profile of the artificial wind sufficiently approximated the actual one (Fig. 7.29a). They repeated the model tests carried out by Bailey [56] and obtained a better agreement with full-scale measurements (Fig. 7.29b) [32, 33, 42]. As regards to interference, Bailey and Vincent mentioned Harris (1934) [58] and the Empire State Building (Sect. 9.2), reporting the first wind tunnel tests inspecting 8 This

sentence did not appear, except in a cryptic form, in the original paper by Nøkkentved. So, it represented an anticipation, due to Bailey and Vincent, of the concepts soon to be expressed by Jensen.

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Fig. 7.28 Comparison between full-scale and wind tunnel measurements by Bailey (1930) [33, 56]

Fig. 7.29 a Mean wind speed profiles of the Met Office and in the wind tunnel [57]; b comparison between full-scale and boundary layer wind tunnel tests by Bailey and Vincent [42]

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Fig. 7.30 Measurements carried out by Bailey and Vincent [57]

the effect of adjacent buildings; they remarked that buildings seldom are isolated, took cognizance of the persisting lack of researches on this subject and decided to fill the gap. They built seven models, treating the isolated structure and closely grouped structures (Fig. 7.30). The results proved the essential role played by interference. In the meantime, after the death of Irminger (1938), Nøkkentved continued his researches on the screening role of the shelters, in co-operation with Det Danske Hedeselska, publishing the results of many measurements, both in nature and in the wind tunnel, between 1938 [59] and 1940 [60]. During these researches, he was supported by a young assistant, Martin Jensen (1914–1990), who developed his doctoral thesis [61] on an innovative subject: the role of shelters on microclimate and crops (Sect. 8.5). He thus emphasised his most peculiar aspect: the willingness and skill to “build bridges between different fields of knowledge”9 [62]. By comparing the results of the tests in the nature and in the wind tunnel, Nøkkentved and Jensen highlighted a systematic error: in the wind tunnel, the barriers originated a screening effect much greater than the real one. Nøkkentved understood that the error depended on the fact that the natural wind was more turbulent than the airflow in the wind tunnel. The start of the Second World War and his death (1945) stopped these researches. When Jensen resumed his studies in 1946, he introduced various types of screens in the wind tunnel to simulate the actual turbulence, but he continued to find results differing from reality. One night, while he was tired to think about the shape and size of the screens, a question flashed through his mind: “have you ever thought of how the turbulence is generated in the natural wind?” The answer was simple: “it comes, of course, from the vegetation in the fields, from the trees, houses and all other obstacles”. A few days later, Jensen bought a corrugated paper, laid it on the tunnel floor, measured the screening effect of a shelter and found a better match with

9 In

the mid-1980s, the University of Western Ontario awarded Martin Jensen a Honoris Causa Doctorate with the “Bridge builder” motivation, “in recognition of his achievements (…) in building bridges between different fields of knowledge”. His doctorate thesis on wind sheltering was a bridge between aerodynamics and agriculture. The model law for phenomena in natural wind was a bridge between full-scale and model tests wind effects. His studies on the flight of the locusts were a bridge between aerodynamics and zoology. His book Civil engineering around 1700 (1969) was a bridge between past and present construction methods. What’s more, Jensen was an excellent civil engineer, the builder of many bridges, including the Lillebaelt Bridge.

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reality [40]. In this way, he understood that wind-related phenomena in nature and in the tunnel were governed by the terrain roughness length. Jensen, aiming at proving this principle, started the research programme that led to the “model law”, a mainstay of wind engineering. It was divided into three periods. In the first, from 1946 to 1952, Jensen completed his thesis on the screening role of shelters [61], arriving at the first expression of the model law. In the second and third period, from 1952 to 1957 and from 1957 to 1960, he co-operated with Niels Franck to clarify and validate this law. More precisely, in the second period he studied the screening effect of structures and the dispersion of fumes from chimneys until to fully formulate the model law [63]. In the third period, he applied it to wind actions on structures [64]. The [63, 64] reports appeared in 1963 and 1965, respectively. Before their publication, in 1958, Jensen published his famous paper [65] in which he enunciated the model law, i.e. the fundamental similarity law for civil and environmental wind tunnel tests: “the correct model test with phenomena in the wind must be carried out in a turbulent boundary layer, and the model law requires that this boundary layer be to scale as regards the velocity profile”. The paper summarised the studies carried out up to the mid-third period. Between 1946 and 1952, Jensen [61] continued the experiments started by Nøkkentved on the screening effect of shelters in natural and artificial winds. The measurements in the artificial wind were carried out at the Copenhagen Technical University. The wind tunnel was of an open-circuit type, with a duct 10 m long (Fig. 7.23); the test chamber, with square cross-section 60 cm on a side, consisted of four modules with an overall length of 5.5 m; the flow speed reached 32 m/s. Jensen measured the mean speed profile in various sections, keeping the floor smooth and covering it with corrugated paper: he obtained z0 = 1.1 × 10−3 cm and z0 = 0.09 cm respectively.10 Once the flow properties were identified, Jensen carried out tests on several types of shelters, with smooth and corrugated floor. He also resumed the full-scale measurements carried out by Nøkkentved at the Jyndevad experimental site in Jutland, completing them. The results were illustrated by diagrams reporting the s screening effect11 as a function of x/h, where x is the distance downstream the shelter and h the height of the shelter; s decreases as x/h increases. Postponing the analysis of the results to Sect. 8.5, their main outcome is worth noting here. Excellent agreement between real and artificial wind exists provided that: D d = z0 Z0

(7.1)

where z0 and Z 0 are the roughness length in the tunnel and in nature, respectively; d and D, likewise, are the heights of the shelter. The ratio in Eq. (7.1) is currently recognised as the Jensen number Je. 10 Jensen first evaluated the roughness length through the gradient of the logarithmic scale profile. He then determined the same quantity by comparing the evolution of the measured thickness of the boundary layer with Eq. (5.23), obtaining almost coincident results. 11 s = (v − v)/v , where v is the actual wind speed at a set height z, v is the speed that would 0 0 0 exist at the same location in the absence of the barrier.

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Between 1952 and 1957, Jensen and Franck [63] measured the wind at the Church of Our Saviour in Copenhagen. The profile of the actual wind was determined by 3-cup anemometers. One of them was put at 80 m height, at the top of the spire; the lower ones were fitted at the end of two very stiff and light metal lattice antennas, 12 and 16 m long, respectively. Wind tunnel tests made use of Pitot tubes, pressure gauges and hot-wire anemometers. The artificial roughness on the tunnel floor was created by eight different settings: (1) glazed cardboard; (2) smooth Masonite plates; (3) sandpaper (Fig. 7.31a); (4) corrugated paper (Fig. 7.31b); (5) 2.5 cm fillets; (6) small broken stones (1.5–2 cm) (Fig. 7.31c); (7) large broken stones (3–6 cm); and 8) model of a city (Fig. 7.31d). In some experiments, a turbulence grid was placed at the end of the convergent nozzle of the tunnel. Figure 7.32 compares the logarithmic profiles of the mean wind speed in the wind tunnel (a) and in the natural wind (b). Jensen and Franck noticed how “the wind blowing over the surface of the earth is turbulent. Its mean velocity increases with the height above the surface”. However, “most laboratory experiments curiously enough become invalid because air currents

Fig. 7.31 a Sandpaper; b corrugated paper; c broken stones; and d model of a city [63]

Fig. 7.32 Mean wind speed in the wind tunnel (a) and in the natural wind (b) [63]

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Fig. 7.33 Screening effect in the wind tunnel (dotted lines) and in the natural wind (solid lines) [63]

of an entirely different character are used. Most wind tunnels have a very short working section” in which “it is endeavoured to maintain a constant velocity throughout the cross-section. Besides, everything is being done to keep a low turbulence in the flow of air. Such tunnels are unsuitable for investigations of the phenomena in natural wind at the surface of the ground, and the many experiments made can be used only with great caution”. They also noted that “to have the boundary layers entirely eliminated use has at times been made of the symmetrical double model suspended in the middle of the tunnel. Unfortunately, these efforts (…) lead to serious errors when the results of the model experiments are applied to real objects standing on the ground”. As a confirmation of the results reported in [61], Fig. 7.33 shows new comparisons between the shelter effect in natural and tunnel winds. The continuous curve refers to full-scale tests, with h/z0 = 122. The dotted lines refer to wind tunnel tests; the curve marked with a d refers to the double model suspended at the tunnel centre. When, in the tunnel, h/z0 = 128, the agreement is high. Thus, for a test to be correct, the profiles of the mean speed and of the turbulence in the tunnel should be similar to those in nature; Eq. (7.1), therefore, must hold true. This “requires that it is possible to dress the wind tunnel with rough coverings giving a wide range of roughness parameters, in order to accommodate both variations in roughness parameters and the different scales of models. (…) Furthermore, the experiment must be made in the boundary layer of the tunnel bottom. The boundary layer increases rather slowly, particularly over smooth surfaces, so a considerable length of tunnel will be required”. Starting from this observation, Jensen and Franck studied the dispersion of the fumes from a chimney by extending the tunnel by 2 m and making the test chamber 7.5 m long. Leaving aside any remarks on the results, examined in Sect. 8.2, here it is important to emphasise—one more time—the role of the ground roughness and

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of atmospheric turbulence. The fumes emitted by the chimney spread over a volume the more reduced the smaller is the turbulence related to the roughness length. Between 1957 and 1960, Jensen and Franck [64] studied the correctness of the model law as regards to wind actions on structures, focusing attention on isolated buildings and roofs. They built a house 305 cm long, 105 cm wide and 163 cm high near Albertslund (Fig. 7.34). Pressure measurements on the outer surface were carried out by means of 15 intakes on the symmetry axis (5 upwind, 3 downwind and 3 on each roof pitch). The holes were connected by means of tubes to a pressure gauge that simultaneously measured 15 pressure values. Wind speed was measured by a Pitot tube and 4-cup anemometers fitted on an antenna 6 m high. The ratio between the height of the house and the terrain roughness length was 180. Wind tunnel tests were carried out in the extended chamber, using 8-floor roughness levels; the 1:200 scale plywood model was placed on a revolving plate. When the scale ratio of the roughness length was equal to the scale ratio of the model (Eq. 7.1), the agreement was perfect; otherwise, the deviation may be huge (Fig. 7.34). During the tests, Jensen and Franck also analysed blockage. They built five models, in different scales, of the Albertslund house and evaluated the optimum scale to reproduce reality. The results proved that using a blockage greater than 5% was not acceptable. It is also worth mentioning that Jensen, in the same period he was developing the model law, published a book [66] considered by many as the first wind engineering text. It drew little attention because of the Danish language. The research on the flight of locusts [67–69] he carried out with Torkel Weis-Fogh (1922–1975), a Danish zoologist, gained wider publicity. He proved, in a dozen papers published between the 1950s and the 1960s, that understanding the flight of insects required the study of the properties and motions of their wings. To that end, he carried out wind tunnel tests on the drag and lift of insect wings that represented the grounds of all the subsequent studies about this subject. The enunciation of the model law opened broad horizons to the wind science, even though it generated violent negative repercussions. It proved, in fact, that the equipment used up to the late 1950s could not be directly used for tests on structures and the results it produced were wrong or unreliable. Now, it is bizarre to notice that two years before Jensen’s enunciation, in 1956, the Swiss collected the previously measured pressure and force coefficients in one of the first wind codes [70]. Between 1958 and the acknowledgement of Jensen rule, codes inspired by the Swiss one gained ground in the international field. Many years were required before the tests carried out in the first half of the twentieth century were repeated in boundary layer wind tunnels and the codes of this period were replaced by correct ones. Jensen’s researches were also the starting point, from the late 1950s, of a broad literature aimed at recovering the use, in the civil and environmental field, of the wind tunnels lacking work chambers long enough to naturally create the atmospheric boundary layer. As a consequence, many tools were conceived for the purpose of introducing them in the flow to attribute the real configuration to the wind profile. The first one, built by Owen and Zienkiewicz [71] in 1957, consisted of horizontal bars with variable spacing (Fig. 7.35). The second, installed by Elder [72] in 1959, used

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Fig. 7.34 Pressure coefficients of the Albertslund house (dotted lines refer to full-scale tests; solid lines refer to wind tunnel tests for several h/z0 values) [65]

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Fig. 7.35 Owen’s and Zienkiewicz’s device [71]

Fig. 7.36 Fluid Dynamics and Diffusion Laboratory, Colorado State University [73, 74]

differently thick veils. Both of them showed the limit of these and of the subsequent implementations: they reproduced the desired mean speed profile well enough, but they were not satisfactory as regards to turbulence. The best answer to this issue came from Jack Cermak [73, 74] who, in 1958, designed and built the first large-size meteorological tunnel (Fig. 7.36) to carry out structural and environmental tests. Thermal stratification was accomplished by adjusting the temperatures of the floor and of the flow. The closed circuit guaranteed speed and temperature control. The length of the test chamber allowed the natural formation of a thick boundary layer; it reached 1.2 m height, with a 40 m/s speed.

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7.4 The New Horizons of Aeronautics It is hard, if not impossible, to identify a discipline having, in a short period, such a strong impact on the life of mankind and on scientific advancement as the one caused by aeronautics between the late nineteenth and the early twentieth century. In a few years, a “fools’ pastime” became the “problem of the moment”, accomplishing one of the oldest dreams of mankind, capturing people imagination until it became the reason for exuberant enthusiasm, modelling an unlimited range of daily objects that drew inspiration from the aerodynamic shape of airplanes, originating correlated researches and technologies affecting every aspect of life, reflecting the solutions and advancements of this sector on many scientific areas and also, unfortunately, acquiring a central role in the warfare. Dealing with such reality transcends the aims of the book as well as the author’s capabilities. Here, however, the essential issues of such evolution are stressed, pointing out the scientific and technical knowledge that contributed to the new horizons as well as the innovations that affected wind science and engineering. Most developments taking place in aeronautics between the late nineteenth and the early twentieth century represented an evolution of the pioneering ideas worked out by Cayley between the late eighteenth and the early nineteenth century (Sect. 4.5). They can be framed into three paths: the researches carried out through experimentation, the flight simulations making use of small-scale models, and the experiences of daring aviators on full-size aircraft [75]. The genesis of such trends took place in Europe, thanks to Lilienthal, Phillips, Hargrave, Ader, Maxim and Nyberg, and in America, thanks to Chanute, Lamson, Baden-Powell and Langley. The advent of the Wright brothers represented a turning point. Karl Wilhelm Otto Lilienthal (1848–1896), a mechanical engineer who graduated in Berlin, was a pioneer of the flight with heavier-than-air crafts. From 1866, he carried out experiences, first through a whirling arm, then in the actual wind (Sect. 7.1); he initially measured the lift of thin inclined plates; later, he understood that lift increased by giving thickness and camber to the plates; and finally, he devoted himself to his old interest: the study of the shape of bird wings, intended as lifting tools for flight. Lilienthal published the results of his researches first in Experiments with currents of air, a paper appeared on the English magazine “Engineering” in 1885, and then in Der Vogelflug als Grundlage der Fliegekunst (Bird flight as a basis for the art of flight, 1889) [7], an article in which he analysed and interpreted the shape and the structure of bird wings (Fig. 7.37a) in the prospect of flight [20, 76, 77]. Lilienthal understood that “the sole way that can allow a quick development of human flight was an energetic and systematic practice in real flight experiments”. In 1891, he built his first glider.12 He first jumped from the roofs of houses, and then, he built an artificial hill 15 m high in Grosslichterfelde, near Berlin, with a storage 12 Lilienthal is considered by many as the first man to have lifted himself above the ground on a flying device. Actually, at least five individuals flew before him: the two pilots to whom Cayley entrusted his gliders (Sect. 4.5), the French Jean Marie le Bris (1817–1872) and Louis Pierre Mouillard (1834–1897), and the American John Joseph Montgomery (1858–1911). All of them returned to

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Fig. 7.37 Lilienthal: a study about bird wings; b glider

shed for his aircrafts at the top. Initially, he used sailplanes inspired to the flight of birds, and then, he switched to radial structure aerofoils (Fig. 7.37b); finally, he built biplanes with better handling characteristics. In a few years, he made nearly 2000 flights, arriving to fly 228 m [78–80]. He gained worldwide fame as “the king of gliders” or “the flying man”, but on 9 August 1896 his glider was struck by a sudden gust while it was 17 m high near Gollenburg; the glider stalled and crashed to the ground [76, 81]. Lilienthal died, causing huge bewilderment about the flight safety. Horatio Frederick Phillips (1845–1924) built one of the first wind tunnels in 1884 (Sect. 7.2), using it to carry out experiences on the lift of airfoils. They confirmed some Lilienthal’s concepts, in particular the advantages of thickening and cambering the airfoils, creating a strong suction on the upper side. Phillips first took out two patents (1884, 1891), called “aerocurve” and then built some flying machines called “multi-planes” because of the presence of multiple-wing surfaces, which Phillips called “sustainers”. The first machine, finished in 1893 (Fig. 7.38a), was fitted with 50 wing surfaces that achieved the desired thickness and camber by a double-surface airfoil; it was propelled by a two-blade propeller driven by a steam engine; it ran along a circular track 61 m in diameter and lifted 1 m above the ground at a speed of 64 km/h. Its purpose, therefore, was purely experimental. Lawrence Hargrave (1850–1915), a versatile British engineer, is known for his studies about the shape of the wings of birds and airplanes, for the development of the rotatory engine and, above all, for inventing the box kite. The first model dates back to 1893 (Fig. 7.38b): it had a high lift/drag ratio, was very stiff and guaranteed excellent aerodynamic stability. On 12 November 1894, Hargrave lifted 5 m in the air from Stanwell Park Beach, supported by four kites. His account, published in “Engineering” in 1895, aroused the interest of Abbott Lawrence Rotch (1861–1912), the American meteorologist who founded the Blue Hill observatory; he reproduced Hargrave’s invention to carry meteorological instruments in the upper the ground so scared to refuse any further flying experience; Lilienthal was the first that continued with his attempts, improving his performance [75].

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Fig. 7.38 a Phillips’ flying machine (1893); b Hargrave’s box kites (1893)

air, starting a standard practice that became widespread worldwide (Sect. 6.2). From 1909, Hargrave’s kite became the reference model for most European airplanes. Clement Ader (1841–1925), a French electrical engineer, used the studies about bird flight carried out by Louis Pierre Mouillard (1834–1837) to build Éole, Avion II and Avion III [18, 25]. Éole, completed in 1886, was an airplane equipped with a 4-blade propeller driven by a 20 HP steam engine; the wings were 12.8 m long. On 9 October 1890, in the Armainvilliers Park, Éole made a 50 m leap, lifting 25-cm above ground; according to some, this was the first powered flight in history. It seems Avion II was never completed. Avion III, a kind of giant bat with two engines, a wooden propeller and a rudder, crashed on 14 October 1897 in Satory, struck by a wind gust. Sir Hiram Stevens Maxim (1840–1916), an American engineer that moved to London, became rich by inventing the machine gun and a carousel that simulated flight. He invested his earnings first to build a whirling arm (Sect. 7.1) and a wind tunnel (Sect. 7.2), which he used to measure wing lift, and then in the construction of Leviathan, a huge biplane built between 1889 and 1894. It weighed 4 tons and its wingspan was 31.7 m; it had a pair of propellers, each one of them 5.4 m in diameter, driven by a 180 HP steam engine. It travelled along two 550-m-long rails built in Bexley, which were flanked by a pair of guard rails that allowed the aircraft to lift a few centimetres; its purpose, thus, was to prove its capability to develop lift. On 31 July 1894, it travelled 183 m at 67 km/h, lifted from the groundbreaking through the guard rails and crashed into the ground [26, 47]. Carl Richard Nyberg (1858–1939), a Swede aviation pioneer, worked from 1897 to 1910 to the development of Flugan, an airplane with 5 m wingspan, 13 m2 wing area and an overall weight of 800 N. He built two circular rails using wood (replaced by ice in winter). Because of the low power delivered by the steam engine, the airplane only managed to make some short leaps and Nyberg was ridiculed. It is worth noting, however, the quality of Nyberg’s studies about the shape of wings. He

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Fig. 7.39 a Chanute’s glider; b Langley’s model

first co-operated with Johan Erik Cederblom (1834–1913) at the Royal Institute of Technology, and then, he built his own wind tunnel carrying out pioneering studies. In America, the passion for flight broke out thanks to Octave Chanute (1832–1910), a French civil engineer who emigrated to Chicago where he undertook a brilliant career in the railways. Chanute became interested in flight in 1875, during a trip to Europe, and in 1889 abandoned his profession to devote himself to aerial navigation. Transferring his training to it, in 1894, he published a wonderful history of man’s attempts to fly [35]. In the meantime, he developed an automatic system to control the stability of aircraft and studied the structural strength of the wings, transposing to it his knowledge on bridge decks. Finally, starting in 1896, he became a glider builder: his designs firstly took inspiration from Lilienthal’s, but later models were characterised by a complex arrangement of multiple wings [27]. The first flight attempts, carried out by a young engineer assisting Chanute, Augustus Moore Herring (1867–1926), failed. The ensuing revision process, inspired by Herring, led to a biplane (Fig. 7.39a) that used, as usual by then, a cross-shaped tail with stabilising functions [28]. On his part, Chanute interpreted the wings of the new biplane in the light of his knowledge about the double deck of bridges. He then transferred to his aircraft the principle of joining the wings by side trusses, which originated a strong caisson system (Sect. 4.8) taking inspiration from Pratt’s diagrams (Sect. 4.9). Chanute thus anticipated the first biplanes of the Wright brothers. He also defined Lilienthal’s aircraft dangerous, just before his tragic death [26, 77]. In August 1896, Charles Lamson started new experiments, equipping Hargrave’s box kites with a cell in the rear, by which the pilot controlled the angle of incidence of the wing. The concept, affected by Chanute, of such craft was close to later biplanes. In 1897, Lamson built “aerocurve”, an aircraft that allowed him to remain poised at 15 m height for about half an hour [76]. In the same period, Baden Fletcher Smyth Baden-Powell (1860–1937), the younger brother of the founder of the Boy Scouts, tested increasingly larger kites. Having verified their instability, in 1899 he built “Levitor”, a series of small kites suited to lift a man. He proposed to use it as an observation post in wartime [76].

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In 1887, Samuel Pierpont Langley (1834–1906), one of the most eminent American scientists of the nineteenth century, left his astronomer work, where he was an authority, to throw himself into aerodynamics and aeronautics. He first built a whirling arm (Sect. 7.1), by which he performed, between 1887 and 1890, tests on airfoils and propeller models [7]. Resuming Penaud’s precepts (Sect. 4.5), he also devoted himself to flight simulations by means of large and complex models, driven by miniature steam or gasoline engines (Fig. 7.39b). Langley then built a floating platform, equipped with a launch catapult, on the Potomac River. On 6 May 1896, “Aerodrome No. 5” made two flights and in the better one it covered 1280 m, remaining aloft for 45 s: it was the first powered flight in the history [29]. Prompted by this result, in 1898 the War Department and the Smithsonian Institution provided Langley with funds to build “Aerodrome”, the first real-scale motor aircraft. Langley involved Charles Matthews Manly (1876–1927) as the designer and pilot and built an airplane with two propellers driven by a 50 HP gasoline engine. According to the project, the aircraft, like his models, was to be launched by means of a catapult; moreover, the airplane, which was not very manoeuvrable, was to end its flight in the water. On 7 October 1903, Aerodrome was launched for the first time before a huge crowd; one of the wings hit a wire and the airplane crashed in the sea. Langley repeated the experiment on December 8th, before a still larger crowd. This time, a wing broke and the aircraft crashed, bringing this ill-fated project to an end; the collapse of the Langley’s airplane wing was described by Griffith Brewer (1867–1948) [82] as the first emergence of the torsional divergence.13 Fascinated by the experiments of Lilienthal, Chanute and Langley, and by Marey’s books about animal motion and bird flight (Sect. 7.2), two brothers from Ohio, Wilbur (1867–1912) and Orville (1871–1948) Wright [45], bicycle mechanics by trade, built a biplane glider resembling a kite in 1900. It was inspired to Chanute’s ideas, was designed using Lilienthal’s aerodynamic coefficients and was large enough to carry an individual. It showed the dominant element of the Wright brothers’ works: they paid no peculiar attention to the stability of airplane, an unstable craft by nature, but rather to the fact that a good pilot could control it; it was the principle of the bicycle, a vehicle as much unstable, kept on balance by its driver. The glider, tested in Kill Devil Hills, near Kitty Hawk, North Carolina, lacked lift and was also affected by excessive drag. In 1901, the Wright brothers built their second glider (Fig. 7.40a) offsetting the lack of lift of their first aircraft by increasing the wing surface and camber. They measured the two components of the resulting force on the wings by means of a balance, but the improvement was less than the expected one. They then convinced themselves that their calculations were wrong and understood that, with such uncertainties, flying was hazardous. Accordingly, the Wright brothers questioned the correctness of Lilienthal’s measurements and repeated them through a bizarre test. They fitted on 13 Consider a wing in uniform motion, subjected to an aerodynamic moment countered by an elastic moment. The resisting elastic moment does not depend on the speed, while the aerodynamic moment increases with its square. There is a speed, thus, above which the elastic moment is insufficient to counter the aerodynamic action. It is called critical divergence speed and the associated unstable phenomenon, of a static nature, is called torsional divergence.

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Fig. 7.40 Wright brothers: a second glider (1901); b wing profiles [45]

Fig. 7.41 Wright brothers: a third glider (1902) [81]; b powered flight (17 December 1903)

bicycles a wheel free to rotate in a horizontal plane; they then applied wing models on one side and a control profile on the opposite side. Finally, they penetrated air observing the direction of rotation of the wheel. The results persuaded them that Lilienthal measurements were unreliable and the same was true for bicycle tests. They then applied themselves to build a wind tunnel, completed in October 1901 (Fig. 7.16) [14, 26]. The device, described in Sect. 7.2, was located on the second floor of their shop; air was set in motion by a fan driven by a diesel engine. In two weeks, they carried out drag and lift balance tests on over 200 wing models with different shapes and couplings (Fig. 7.40b). The results, different from Lilienthal’s ones, explained the errors made in the last years. Wilbur and Orville Wright bravely trust the new measurements and, in 1902, built their third glider, implementing the results of wind tunnel tests (Fig. 7.41a). With this aircraft, which used a movable tail operated by the pilot and a wing-warping mechanism, they made more than 800 flights over Kitty Hawk, covering distances up to 180 m. At this point, the only missing item to make flight independent was the engine. The following year, the Wright brothers applied to a mechanic, Charles Edward Taylor (1868–1956), and with his help they built a 4-cylinder, 12 HP internal combustion engine. They also studied the propeller, convincing themselves it was simply a rotating wing; they then selected the most suitable profile among the wings they

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tested in the wind tunnel and built two counter-lifting pusher propellers, coupled to the engine by means of bicycle chains; the whole was fitted in the centre of a biplane labelled “Kitty Hawk Flyer”. The first flight attempt took place on the Kitty Hawk beach on 14 December 1903, six days after Langley’s failure; the airplane, piloted by Wilbur Wright, banked to one side and crashed. Three days later for repairing damage, came the second attempt: at 10:35 A.M. on 17 December 1903, the Kitty Hawk Flyer left the ground and made four legendary flights (Fig. 7.41b): the first one, with Orville as a pilot, covered 37 m in 12 s; the fourth with Wilbur as a pilot, covered 260 m in 1 min.14 In the evening, Orville Wright sent his father a telegram to inform him of the success. The media15 were almost missing, presumably due to the recent Langley’s failure. Encouraged by their results, between 1904 and 1905 the Wright brothers built two new airplanes and put them through flight testing in Huffman Prairie, Ohio. The first, Flyer II, was equipped with a 15 HP engine; in 1904, it made over 100 flights, some of them lasting 5 min. On 5 October 1905, Flyer III flew for 39 min, covering 40 km; in the same year the duration of a flight reached 45 min; the Wright brothers performed various manoeuvres, turning over the airfield time and time again. In 1906, the Scientific American Magazine published an account of their exploits [81]. In the same period, Alexander Graham Bell (1847–1922), the inventor of the telephone, was so fascinated by Hargrave’s kites to define them “the high tide of progress in the nineteenth century”. He then decided to put his mind to aeronautics and in 1898 replaced Hargrave’s square cells with triangular cells that made the structure indeformable. In 1902, he perfected the kites equipped with tetrahedral cells covered with silk cloths. In 1905, he built “Frost King”, a kite formed by 1300 cells. In 1907, he built “Cygnet”, an aggregation of 3393 cells, which supported a passenger (Selfridge) for 7 min up to 51 m height. In 1909, he built “Cygnet II” that also carried, beside the passenger, an engine [76]. On 30 September 1907, Bell founded and took the chair of the Aerial Experiment Association (AEA), surrounding himself with four young brilliant collaborators: Glenn Hammond Curtiss (1878–1930), Thomas Etholen Selfridge16 (1882–1908), Frederick Walker Baldwin (1882–1948) and John Alexander Douglas McCurdy 14 Some bibliographic sources attribute the first powered flight to other aviators [78]. In 1874, a French Navy officer, Félix du Temple de la Croix (1823–1890), put a subordinate of his on an aircraft powered by a steam engine that made small leaps along the slope of a hill. In 1884, Alexander Fedorovich Mozhayskiy (1825–1890), a Russian Navy officer, used a launching ramp near Krasnoye Selo to make a leap approximately 25 m long with a powered aircraft. Gustav Albin Weisskopf (1874–1927), a German emigrated to America, made several powered flights two years before the Wright brothers without any photographic evidence. Another German, Karl Jatho (1873–1933) made some flights with an aircraft with flat wings, a 2-blade propeller and a 10 HP engine; the first flight dates back to 18 August 1903; the longest flight covered a distance of 200 m at 3 m height without any control system. 15 The chronicle from Kitty Hawk dated 18 December 1903 reported: “Mankind wished to fly since the time of Icarus. From yesterday it is a reality. On the beach of Kitty Hawk, North Carolina, two bicycle builders, Wilbur and Orville Wright, made the first powered heavier-than-air craft fly”. 16 Selfridge was the first victim of a powered flight. After having flown on Bell’s airplanes, he flied with the Wright brothers during an exhibition. On 17 September 1908, Flyer, piloted by

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Fig. 7.42 a 14-bis by Alberto Santos-Dumont (1906); b Louis Bleriot’s monoplane

(1886–1961). In 1908, they built four new aircraft, Red Wing, White Wing, June Bug and Silver Dart, to which they transposed Bell’s knowledge on kites. On 12 March 1908, Red Wing, designed by Selfridge and piloted by Baldwin, made the first public flight in North America over Keuka Lake near New York. White Wing was the first airplane to use Bell’s ailerons,17 now customary for any aircraft. On 4 July 1908, June Bug, piloted by Curtiss, flew 1552 m in 1 min and 42 s. On 23 February 1909, Silver Dart, piloted by McCurdy, took off from the frozen runway at the Bras d’Or Lake and made the first Canadian powered flight. In the meantime, in 1908 summer, Baldwin and Bell started devoting themselves to hydroplanes. In 1911, Curtiss built Triad A-1, the first airplane capable of taking off and landing both on land and on water. Bell’s undertakings were only an example, although an important one, of the flight fever that infected the world, originating an unprecedented proliferation of new aviators performing increasingly daring feats aboard increasingly improved airplanes. In 1906, the Brazilian Alberto Santos-Dumont (1873–1932), famous for his exploits on dirigibles, made the first European flights in France. His airplane, “Oiseau de proie” (Fig. 7.42a), resembled a box kite and was fitted with a pusher propeller. On 13 September 1906, it made a 7 m leap in Bagatelle; on 23 October 1906 it flew 60 m in Paris, at a height between 2 and 3 m; on 12 November 1906, it remained airborne 21 s, covering a distance of 220 m. The novel element of these performances was the absence of tracks or catapults to facilitate the take-off stage; for this reason, many view Santos-Dumont as the true father of aviation.18 Meanwhile, Phillips continued the experiments started in 1893 and in 1907 built “Multi-plane”, a flying machine with four batteries of 50 wings each and a proOrville Wright with Selfridge beside him, crashed to the ground: Orville Wright was unharmed, but Selfridge died. 17 The aileron is the moving part of the wing along the trailing edge; it is lifted or lowered to change the lift, especially at the landing stage. 18 The first flights of the Wright brothers, unlike Santos-Dumont’s one, were assisted during the take-off by tail winds or by launch tracks. Their supporters countered that such devices were not used for aerodynamic reasons, but due to the nature of the ground: while the ground at Kitty Hawk and Huffman Prairie was sandy, Santos-Dumont took off from smooth and compact ground.

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peller 2.4 m in diameter; with this aircraft he made the first (uncontrolled) flight in Great Britain, covering a distance of 150 m. On 9 November 1907, Henri Farman (1874–1958), aboard a biplane built by Gabriel Voisin (1880–1973), flew for a minute in Issy-les-Moulineaux, travelling more than 1 km; the following year he made the first flight between two cities, from Châlons to Reims. The first flight in Italian skies took place in Rome, on 28 May 1908, by the French pilot Léon Delagrange (1873–1910). In 1909, Marco Faccioli inaugurated the history of Italian aviation. On July 25th of the same year, the French pilot Louis Bleriot (1872–1936) crossed the English Channel with a monoplane (Fig. 7.42b), taking off from Les Baraques near Calais, in France, and landing near Dover, in England; he covered approximately 37 km, in 35 min and a half. In 1911, the American aviator Calbraith Perry Rodgers (1879–1912) crossed the USA from coast to coast, aboard a Wright machine; he left Sheepshead Bay, in Brooklyn, New York, on September 17th and landed at Long Beach, California, on December 10th, 84 days later; the actual flight time was 3 days, 10 h and 14 min. It was the prelude to huge advancements in aviation, which would receive its greatest stimuli from the imminent outbreak of the First World War. It was, however, clear that such progress could not base itself on the intuitions and courage of daring pilots and creative designers for a long time: it required theoretical and experimental grounds. The heart of the theoretical developments in aeronautics was represented by the formulation of the lift theory for airfoils. It originated between the late nineteenth and the early twentieth century, thanks to the studies independently carried out by Joukowski, Kutta and Lanchester [20]. Their contributions shared a strict link between aerodynamic lift and the circulatory motion of the air around a moving wing. Nikolai Yegorovich Joukovsky (Zhukovsky, 1847–1921) was the first Russian fluid dynamicist of international level. In 1891, he built a small wind tunnel at the Moscow University (Sect. 7.2), where he studied the aerodynamic actions on airfoils with different thickness and camber. Thanks to these experiments, between 1902 and 1909 he formulated the mathematical and physical grounds of the lift theory in bidimensional regime, i.e. for wings with infinite length and constant cross-section. This theory was tied to the interpretation of the Magnus effect provided by Rayleigh [83] in 1878 (Sect. 3.6). Let us consider an airfoil moving in a uniform flow and assume the existence of a circulatory motion of the air around the profile (Fig. 7.43a). On the upper part of the airfoil, the circulatory motion is in agreement with the flow and then the speed increases; on the lower part of the airfoil, the two motions are opposed and the speed decreases. Applying the Bernoulli principle, the pressure decreases in the upper face and increases in the lower one; a pressure gradient, which creates lift, is then originated. Joukowski proved that lift was provided by the relationship: L = ρV 

(7.2)

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Fig. 7.43 a Lift theory [9]; b initial vortex and circulation [20]

ρ being the air density, V the forward movement speed of the airfoil,  a quantity called circulation; it is the integral of the (relative) speed of the flow along a trajectory encompassing the airfoil. Resorting to Karman’s description [20], Joukowski interpreted the circulation by remarking that if an airfoil with a sharp trailing edge was set in motion, it originated a vortex [84], called the starting one (Fig. 7.43b), which remains behind the airfoil while it moves forward. No rotation can exist in a system without a reaction in the opposite direction; in the case of the airfoil, it corresponds to the circulation around the profile and increases until the airfoil emits vorticity. It is then acceptable to admit that “when the starting vortex is swept far away, the circulation has reached its maximum value, as there is no longer a velocity difference between the flows leaving the upper and lower surfaces”. Equation (7.2) can thus be solved by determining “the amount of circulation so that the velocity of the flow leaving the upper surface at the trailing edge is equal to that of the flow leaving the lower surface”. Joukowski also applied a conformal transformation by which he defined the airfoil properties causing the circulation: it must have a rounded leading edge, a double surface guaranteeing it a finite thickness, curved or cambered shape and a sharp trailing edge. His contribution to aeronautics was so important that Vladimir Lenin (1870–1924) called him “father of Russian aviation”. Despite this, his research, published since 1907 in Russian language and venues [85, 86], was unrecognised for years. Similar results were obtained by Martin Wilhelm Kutta (1867–1944), a German mathematician also known for developing, with Carl Runge (1856–1927), a famous method for the numerical solution of differential equations (the Runge–Kutta method). Fascinated by Lilienthal’s experiments, in 1902 Kutta performed the first analytical evaluation of the lift of a horizontal airfoil [87]. Between 1910 and 1911, unaware of Joukowski’s researches, he published two papers [88, 89] in which he obtained Eq. (7.2). This is the reason why the bidimensional wing lift theory is now called “Kutta–Joukowski theory” [20, 90]. By virtue of Kutta’s remarks about the role of the sharp trailing edge in originating circulation, this concept is also known as “Kutta condition”. The solutions by Kutta and Joukowski solved the lift problem for bidimensional wing profiles. Figure 7.44a, b shows the agreement between the theoretical and experimental values of the lift (a) and pressure (b) coefficients. The first diagram

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shows the correctness of the theory when, for small values of the angle of attack, the flow follows the surface of the airfoil. From the second diagram, it is possible to infer how the suction on the upper face of the airfoil contributes to lift in a far greater extent than the pressure on the lower face. Figure 7.44c compares the Kutta–Joukowski’s solution with the squared-sine law (Sect. 4.2); the new theory not only subverted the physical view of lift hitherto acknowledged, but implied that lift increased so high to restore confidence in the possibility of flying. Frederick William Lanchester (1868–1946) was a British engineer and mathematician as well as an aerodynamics scholar, who built cars by profession. While he was crossing the Atlantic travelling to the USA, he was fascinated by the seagulls that flew without flapping their wings, taking advantage of air currents. He then performed measurements on models that led him to develop, between 1891 and 1894, revolutionary ideas on the relationship between lift and circulation, which anticipated the studies by Joukowski and Kutta. Lanchester collected such ideas in a paper, The soaring of birds and the possibilities of mechanical flight, which he submitted to the Physical Society in 1897; it was rejected. He then attempted to develop another idea: the building of an engine with a high power-to-weight ratio, but nobody took him seriously. Lanchester, disheartened, returned to devote himself to cars until he decided to collect his old ideas and some new intuitions in two books, Aerodynamics19 [91] and Aerodonetics [92], published in 1907 and 1908, respectively. In the first book [91], Lanchester did not restrict himself to dealing with the bidimensional issue, but approached the study of the three-dimensional wing, with finite wingspan. He schematised the circulation of the air around the airfoil as a “bound” vortex, i.e. a vortex moving together with the airfoil. Helmholtz [84] proved that a vortex can neither originate nor die or end in the air, but must end against a wall or

Fig. 7.44 Lift (a) and pressure (b) coefficients for airfoils: comparison between theoretical (Kutta–Joukowski) and experimental results; c comparison among the squared-sine law (1) and Rayleigh (2) and Kutta–Joukowski (3) theories [20]

19 Even

though Aerodynamics [91] was a book dedicated to wings, Lanchester described therein a phenomenon, the “aerial turbillon”, associated with cylinders with D-shaped cross-section. When the flat face is orthogonal to a uniform flow, the cylinder developed a steady rotation around its axis, as long as the latter was triggered (Sect. 9.8).

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Fig. 7.45 System of vortices at the wing end [20]

form a closed loop. Lanchester used this principle to schematise the wing as a system including the bound vortex and a pair of free vortices at its end (Fig. 7.45). Thanks to this concept, he was the first to recognise the importance of the aspect ratio, i.e. of the ratio between the wingspan and the mean chord, for lift. He, however, restricted himself to a qualitative view, without being able to translate it into mathematical equations [8, 20, 90]. In the second book [92], which dealt with airplane stability, Lanchester discussed stall20 and introduced new concepts about wing vibration. While Joukowski, Kutta and Lanchester developed these theories, Prandtl also started studying lift. He was impressed by Lanchester’s ideas, and in 1908, he invited him in Göttingen to hold a seminar about his two books; the seminar took place in the presence of Runge, who acted as interpreter, and of the three Prandtl’s students destined to have great influence on aeronautics21 : Betz, Munk and Karman. From this day on, Göttingen became the world centre of the research on wing lift and drag [20, 75, 87]. In 1911 Prandtl formulated a method, the “lifting-line theory”, which reaffirmed the principles by Joukowski, Kutta and Lanchester on circulation, resumed Lanchester’s ideas about the wing aspect ratio and rationalised the treatment, arriving at the first mathematical criterion to evaluate the lift of real (i.e. three-dimensional) wings. This procedure, published in 1913 [93], was based on six assumptions [20]: “(a) the wing is replaced by a lifting line perpendicular to the flight direction; (b) 20 The Kutta–Joukowski theory envisaged that the lift coefficient was a linear function of the angle of attack (Fig. 7.44). When the angle of attack is large, the flow detaches from the wing surface and the theory fails. There is an angle of attack above which lift starts decreasing. This causes stalling. 21 Lanchester was embittered for the appreciation received by Prandtl and the slight recognition to his contribution (reviewed after his death) [20]. In his Wilbur Wright Memorial Lecture at the Royal Aeronautical Society in 1927, Prandtl said that Lanchester “started working on this subject before I did and this undoubtedly led people to believe that Lanchester’s researches, as they had been expressed in 1907 in his work Aerodynamics, suggested me the principles on which the airfoil theory was based. But this was not my case. The basic ideas on which I built that theory, even though those ideas were included in Lanchester’s book, came to my mind before I saw his book. To corroborate this statement, I will point out that actually we, in Germany, were more prepared to understand Lanchester’s book when it appeared than you in England”.

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the lifting line is assumed to consist of a bound vortex with circulation variable in order to account for the fact that the lift may change the span; (c) in accordance with the change in the circulation along the span, free vortices are born and extend downstream; however (d) the flow produced by the vortex system is considered as a small perturbation of the fundamental stream relative to the wing, and therefore (e) it is assumed that the free vortices approximately follow the original direction of the streamlines parallel and opposite to the flight direction, (…); (f) the flow in the immediate neighbourhood of a wing section is determined by the two-dimensional solution given by Kutta and Joukowski”. Thanks to these hypotheses, the lift of every wing element, as well as its overall lift, is a linear function of the angle of attack, just as in the bidimensional theory (Fig. 7.44a); unlike the latter, it decreases as the wing aspect ratio increases; the three-dimensionality of the wing, in other words, decreases its lift. Lift distribution along the wingspan can be obtained, as a function of the wing geometry, solving an integral equation. From this moment, Prandtl, assisted by Albert Betz (1885–1968) and Max Michael Munk (1890–1986), who developed this subject in their doctoral theses, devoted approximately a decade to simplify and clarify his initial treatment. This process led to two articles published in Göttingen in 1918 [94] and in 1919 [95]. Afterwards, thanks in part to his co-operation described later with the newborn US National Advisory Committee for Aeronautics (NACA) [96], Prandtl published some reports [97] that culminated in a 1921 paper [98] that expounded the whole subject with clarity and design purposes. Prandtl also obtained the wing resistance, considering the skin friction due to the formation of the boundary layer as well as the end vortices. He also extended these theories to wing profiles arranged on multiple levels. Thanks to these models, aeronautical engineers were finally able to perform design calculations anticipating the wind tunnel tests. While Prandtl developed these theories, many European countries remained sceptical about circulation. England, the native country of Lanchester, rejected it until the mid-1920s, continuing to interpret lift as a function of the pressure gradient between the face exposed to the wind and the dead air bounded by the discontinuity surface (Fig. 3.20). The situation changed when Hermann Glauert (1892–1934), after visiting Prandtl in 1921, substantiated the worthiness of the new theory and the need to experimentally verify it with his English colleagues. The wind tunnel tests proved circulation [99, 100], and in 1926 Glauert published a book with this view, which became the classic aeronautics text for Anglo-Saxon countries [101]. In 1927, the Royal Aeronautical Society invited Prandtl to deliver the Wilbur Wright Memorial Lecture; it was memorable and a turning point in the history of aerodynamics. In the meantime, Louis Charles Breguet (1880–1955), an aviation industrialist, submitted a paper [102] to the Royal Aeronautical Society of London in which he expressed airplane efficiency as a function of the drag/lift ratio, a quantity he called “fineness”; it must be minimised by the streamlining of the shape of the wings and of any part of the plane. Developing this research, in 1929 Sir Bennett Melvill Jones (1887–1975), an aeronautic engineering professor at the Cambridge University, submitted a paper to the Royal Aeronautical Society [103] where he introduced the idea of a perfectly streamlined airplane; it was the aerodynamic equivalent of the

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7 Wind and Aerodynamics

Fig. 7.46 NACA: a Wind Tunnel No. 1 (1920); b VDT [8]

Carnot’s ideal machine in thermodynamics. Jones drew a diagram proving that all the airplanes of his age were far away from this conceptual limit. The evolution of research in aeronautics received impulse from the First World War, along the axis of a particular co-operation bounding the two most opposed countries, Germany and the USA [75, 96]. In 1913, Zahm and Hunsaker travelled to Europe to visit the leading aeronautical laboratories. The following year, Charles Doolittle Walcott (1850–1927), secretary of the Smithsonian Institution, advocated before the Congress the necessity to set up a national aeronautic laboratory to bring the USA to the European level. The Congress accepted the proposal, and on 3 March 1915, NACA was founded “to supervise and guide the scientific study of flight problems in view of their practical solution”. NACA first sponsored the researches carried out in the wind tunnels at the Washington Navy Yard and at the Stanford University, where William Frederick Durand (1859–1958) performed tests about the optimum shape of propellers. NACA soon understood the need to set up its own laboratory, equipped with an independent wind tunnel, and in 1917, it built the Langley Memorial Aeronautical Laboratory (LMAL) in Tidewater, Virginia. The war, however, created a sense of urgency that did not favour the development of the project and, on the contrary, induced the Navy and the Army to follow their own independent paths. The first trusted Zahm to build (1917) a new open-circuit wind tunnel (taking inspiration from the NPL plants) at the Washington Navy Yard with square cross-section, 1.2 m on a side. The second set up its laboratory at McCook Field near Dayton, where he built a small wind tunnel with circular cross-section, 36 cm in diameter; the flow speed reached 200 m/s. At the end of the war, the NACA resumed its original project, and in 1920, it founded LMAL, setting up a formidable community of engineers, scientists, technicians and pilots that will play a focal role in the history of aeronautics [8, 75, 96, 104, 105]. At the same time, NACA built Wind Tunnel No. 1, an open-circuit wind tunnel with circular cross-section, 1.5 m in diameter (Fig. 7.46a). German aeronautics experienced conflicting moments. In 1915, Prandtl perceived the need to develop aerodynamic experiences for military aviation and founded an

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institute for tests on powered airplane models (Modellversuchsanstalt für Aerodynamik der Motorluftschiff-Studiengesellschaft, MVA) in Göttingen; in this context, in 1917, he built his second closed-circuit wind tunnel (Sect. 7.2). The Versailles Treaty signed in 1919 destroyed these ambitions and obliged the German aeronautic industries to switch to other activities. Prandtl met this requirement transforming MVA in a laboratory with less specific objectives (Aerodynamischen Versuchsanstalt, AVA) including, above all others, aerodynamic tests on cars (Sect. 7.6) and locomotives (Sect. 7.7). America, impressed by the advancements of the European, and especially German, research, sent its emissaries overseas to establish permanent contacts. Before the end of the war, Durand went to Paris, Henry Andrews Bumstead (1870–1920) to London and Samuel Knox to Rome. Between 1919 and 1920, Joseph Sweetman Ames (1864–1943) proposed to found a NACA office in Paris to collect the measurements carried out at the French, English, Italian and German wind tunnels for the purpose of standardising aeronautic equipment and tests. William Knight simultaneously proposed to organise an international aeronautics conference by NACA, to be held Paris; he also travelled to Germany to make the acquaintance of Prandtl and convinced him to write a report describing the Göttingen wind tunnel [106]. Hunsaker himself persuaded Prandtl to write a paper on the theoretical and experimental studies of the Göttingen School; it became one of the most famous reports by Prandtl and NACA [98]. Edward Pearson Warner (1894–1958), another NACA emissary, judged the technology of Prandtl’s wind tunnel astonishingly innovative. The successor to Knight, John Jay Ide (1892–1962), established a harmonious relationship with Prandtl, opening a period in which NACA and Göttingen exchanged reports and achieved the first tangible results in the standardisation process Ames hoped for [107]. The first experimental flights aimed at comparing wind tunnel measurements with the actual behaviour of airplanes were made within this process. The results highlighted a key issue: the scale of the models and the importance of reproducing the Reynolds number. The reality of that period offered two solutions [75]. The first came from Wladimir Margoulis, a Russian aerodynamicist who proposed to introduce carbon dioxide, a substance with density 1.5 times greater than air, in the wind tunnel. The second came from Munk, who proposed to build a wind tunnel inside a pressurised container. NACA, impressed by his ideas and enticed by establishing stricter relations with Prandtl and Göttingen, proposed him to move to the USA to materialise his project. The Versailles Treaty forbade the performance of such activities in Germany, so Munk accepted the invitation and in 1921 started working at NACA. Thanks to Munk’s presence and work, in 1922 NACA built Wind Tunnel No. 2, better known as Variable Density Tunnel (VDT) [108]. VDT was a closed-circuit tunnel (Fig. 7.46b) inside a large pressurised tank shaped like a cylinder with hemispherical sides. The test chamber had a circular cross-section, 1.5 m in diameter. The air inside the chamber reached a density up to 20 times greater than the usual one, with speed up to 23 m/s. These characteristics allowed achieving high Reynolds numbers and VDT became the venue, for about 15 years, of tests on airplane and

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7 Wind and Aerodynamics

Fig. 7.47 NACA: a PRT; b FST

wing models carried out not only by NACA [109] but by universities and companies from all over the world. Munk also showed outstanding ability in the theoretical field, publishing over 40 reports about air navigation, the drag and lift of airfoils, the interference between lifting surfaces, propellers and apparent mass [107]. He had, however, a hellish character that made him unpopular with his assistants [8, 96]; for this reason, in 1926, the NACA transferred him from Washington headquarters to Langley Laboratory; within a few months, the engineers at the centre revolted against him and forced him to resign. The presence of Munk at NACA, even though brief, was a new turning point for aeronautics. Meanwhile, it was noticed how VDT, because of pressurisation, achieved turbulence levels so high they compromised, in some cases, the reliability of tests. NACA then started the design of two new devices, the Propeller Research Tunnel (PRT) and the Full-Scale Tunnel (FST), aimed at realising high Reynolds numbers with high quality flows. PRT, built between 1926 and 1927 under the direction of Fred Ernest Weick (1899–1993), was a closed-circuit wind tunnel; its test chamber was open and 6 m in diameter (Fig. 7.47a); it was driven by two 1000 HP submarine engines and achieved speeds up to 49 m/s; in the test chamber, there was a balance supporting a large-scale airplane model or its full-scale fuselage and propeller. FST, built between 1929 and 1931, was a giant closed-circuit tunnel with a 9 × 18 open test section. The fan consisted of two propellers, 10.7 m in diameter, in two parallel return ducts, driven by as many 4000 HP electric motors; the maximum speed was 54 m/s; the plant housed the first complete large-scale, or even full-scale, airplane models (Fig. 7.47b). In the same period, PRT and FST were built NACA dismantled Wind Tunnel No. 1 and replaced it with two new high-speed tunnels, both completed in 1930. Atmospheric Wind Tunnel (AWT), with its 2.1 × 3 m cross-section, was an evolution of the No.1; it was the first wind tunnel designed for stability and flight control tests. Vertical Wind Tunnel (VWT), with a cross-section 1.5 m in diameter, allowed studying the aircraft spin, one of the causes of plane crashes.

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In parallel to these, increasingly improved plants appeared all over the world. In 1922, the U.S. Army built an open-circuit wind tunnel 1.5 m in diameter at McCook Field; it was chiefly used to study flight stability. In 1929, the NPL started to build a tunnel pressurised at 25 atmospheres; its cross-section was circular, 1.7 m in diameter; the speed reached 27 m/s. Daniel Guggenheim (1856–1930) invested a fortune to develop aeronautics in American universities; the peak of his initiatives was reached in 1930, when he brought Karman in the USA, entrusting him with the direction of Caltech’s Guggenheim Aeronautical Laboratory (GALCIT); it was a new turning point. Soon afterwards, Durand collected the knowledge about this subject in a sixvolume work [110]. The first high-speed tunnel (HST), which produced flows almost reaching the speed of sound, gained ground at the same time. The development of the theoretical and experimental knowledge found an additional drive from an almost endless series of accidents [82] that afflicted the modern aviation as it had happened at the dawning of human flight (Sect. 4.5). They highlighted phenomena, both static and dynamic, which had to be studied and understood in view of further advancements. A circular process then originated, in which evidence suggested researches that, after being carried out, produced advancements that, in turn, triggered new phenomena requiring new studies. It was a reality similar to the one simultaneously experienced by the evolution of cable-supported bridges (Sect. 9.1). The collapse of the wing of Langley’s monoplane, which occurred in 1903 and was classified by Brewer [82] as the first torsional divergence case, as well as the success met by the Wright brothers, made biplanes the preferred design. In the absence of efficient criteria to torsionally stiffen the wings, the double wing with vertical links proved to be an effective choice. This did not rule out, however, severe issues in the tail associated with flutter.22 One of the first documented cases of such phenomena regarded the Handley Page 0/400 bomber, at the start of the First World War. The study of the fuselage and tail vibrations, carried out in 1916 by Lanchester, Leonard Bairstow (1880–1963) and Arthur Fage (1890–1977) [111, 112], highlighted two low-frequency modes. In the first, the right and left elevators vibrated counterphase; in the second, the fuselage vibrated torsionally. The coupling of the two modes caused strong oscillations, which were rectified through a torsionally stiff connection between the elevators. Similar studies were carried out by Blasius [113] in 1918 to explain the collapse of the lower 22 Consider a wing in a tunnel in the absence of wind, a generic disturbance originates a damped oscillation. Assume the introduction of air into the tunnel and a speed increase: the damping initially increases, then decreases. The flutter speed is the one that makes the damping nil. Actually, the wing motion is both bending and torsional. If the wing is only subjected to bending oscillation flutter cannot occur. If it is only subjected to torsional oscillation flutter is possible only if the angle of attack is close to the stall condition (and the flow is separated); this unstable phenomenon is called stall flutter. Excluding it, flutter is only possible in the presence of the coupling of at least two degrees of freedom, generally the bending motion perpendicular to the flow direction and the torsional motion. Both these motions are harmonic ones with the same frequency; all the components of the bending motions are in phase; likewise, all the components of the torsional motion are also in phase; the two components of the motion are out of phase.

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7 Wind and Aerodynamics

wing of an Albatros D3 biplane. Other aircraft types, including the DH-9, were subject to the same phenomenon in the same period, causing severe loss of life. It was the prelude to countless disasters originated by two phenomena peculiar to the 1920s and 1930s. On the one hand, biplanes gave way to monoplanes fitted with wings with insufficient torsional stiffness. On the other, both the speed of aircraft and the possibility of meeting unstable phenomena increased. A sensational case involved one of the first monoplanes, the Fokker D-8. It was assigned to the best pilots, who died one after another in accidents. Initially, army and builders held one another responsible; then, the Fokker company carried out tests that attributed the collapses to high-speed torsional divergence. Another exceptional case, after the war, concerned the aileron flutter of the D-8 wings; the engineers of the American Army Air Corps solved this issue through a static balance technique (1922). Few years later (1925), a report was compiled [114], where the British Aeronautical Research Council described the accidents due to flutter. A peculiar element was represented “by the quick and unusually extensive motion of the wings”, which was made increasingly common by the aircraft speed increase. To avoid this phenomenon, the report recommended that “the vibration of the structures of airplanes is fully studied both theoretically and experimentally, providing the designers with all the data required to calculate and avoid instability”. The report admitted that the investigations showed that this issue was more complex than it had initially been thought. Thus, a large body of the literature flourished, investigating flow–structure interaction as well as critical instability conditions. The autorotation of airplane wings was first investigated in 1918 by Ernest Frederick Relf (1888–1970) and Lavender [115]. They carried out pioneering measurements at the NPL, during which they studied the stall of a wing for angles of attack between 15 and 26.5°. Starting from these tests, Glauert developed a theory [116, 117], valid for any angle of attack, through which he interpreted one of the most common causes of the air crashes in that age. He explained this phenomenon by imposing the balance condition of an airfoil with a single degree of freedom, the transversal displacement, leaving out both rotation and torque. From here, he attributed the instability to the variation of the aerodynamic force as a function of the angle of attack, proving that it can develop under the condition: cD + cL < 0

(7.3)

where cD is the drag coefficient, cL is the lift coefficient and cL is the prime derivative of cL with respect to the angle of attack. He showed that instability is possible in limited domains of the angle of attack and that, for small angles of attack, autorotation only appears in the presence of a small disturbance. He affirmed that it would have been essential to validate this theory by experiments. Equation (7.3), now known as Glauert criterion, is the necessary condition for the occurrence of galloping (Sect. 9.6). Walter Birnbaum (1893–1987) wrote a doctoral thesis in Göttingen (1922), in which he studied the aerodynamic actions on a flat plate harmonically oscillating in

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Fig. 7.48 Wagner (dashed line) and Küssner (solid line) functions

a bidimensional flow. In the same period, using the Prandtl’s boundary layer theory, Walter Ackermann (1899–1978) evaluated the lift of an airfoil in uniform motion. Birnbaum himself generalised this theory to an airfoil harmonically oscillating with small reduced frequency; the results were published between 1923 [118] and 1924 [119]. In 1925 Herbert Alois Wagner (1900–1982) [120] studied the aerodynamic actions on a thin airfoil (in an incompressible fluid and bidimensional conditions) that, starting from rest, suddenly reached (at the time t = 0) a constant speed U. He proved that the L lift is provided by: L(s) = 2πρbU 2 α(s)

(7.4)

where ρ is the density of air, b is the half-span of the airfoil, α is its inclination, s = Ut/b is the reduced time and (s) is a response or admittance indicial function that Wagner obtained in the integral form: ∞ (s) = 1 −



[K 0 (x) − K 1 (x)]2 + π2 [I0 (x) + I1 (x)]2

−1

e−xs x −2 dx (s > 0)

0

(7.5) where K 0 , K 1 and I 0 , I 1 are modified Bessel functions of the second and of the first type, respectively.23 Equation (7.5), drawn by Wagner by points, is now known as Wagner function (Fig. 7.48). In 1926, Hans Jacob Reissner (1874–1967) [121] studied the load distribution on an airfoil and its divergence. In 1929, Glauert [122] applied the Wagner method to evaluate the force and the moment acting on a harmonically oscillating airfoil, providing the first criterion to evaluate flutter. In the same year, Hans Georg Küssner 23 The

modified Bessel functions of the second and of the first type are defined, respectively, as: Iα (x) = i −α Jα (i x);

K α (x) =

π I−α (x) − Iα (x) 2 sin(αx)

where Jα (x) is the Bessel function of the first type (Eq. 7.9a).

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7 Wind and Aerodynamics

[123] extended Birnbaum method to a broad domain of reduced frequencies, clarifying the flutter phenomenon. He also determined the lift variation for an airfoil that, while moving forward horizontally at the uniform speed U, suddenly meets a vertical flow with constant speed w (at s = 0), i.e. orthogonal to the direction of its forward movement; it is provided by: L(s) = 2πρbU w(s) (s > −1)

(7.6)

where  is a response or admittance indicial function now known as Küssner function (Fig. 7.48). Between 1928 and 1931, Robert Alexander Frazer (1891–1959) and Duncan [124, 125] made fundamental advancements towards the knowledge of flutter. In [124], they illustrated qualitative tests carried out at the NPL on a light and flexible cantilever airfoil. They highlighted that: (a) flutter is a form of instability, not of resonance; (b) for every airfoil, there are one or more speed domains where flutter can happen; (c) great airfoil disturbances can trigger flutter even at low speed; (d) flutter is ternary in character, i.e. it involves the bending and torsion of the airfoil and the rotation of the aileron; (e) the critical speeds depend on the mass and stiffness distribution; (f) a suitable positioning of the centre of gravity of the aileron and an effective airfoil–aileron connection ensure that the first critical flutter speed only involves the bending and torsional motions of the airfoil; (g) the use of additional airfoil supports is beneficial; and (h) the changes of the airfoil incidence scantily affect the first critical flutter speed. After stating such premises, Frazer and Duncan developed the flutter theory for the cantilever wing of a monoplane. The wing motion was described by two degrees of freedom related to bending φ and torsion θ; the aileron was treated as a stiff body inclined ξ with respect to the wing. The system, thus, had three degrees of freedom: φ, θ and ξ. The three equations of motion expressed the dynamic balance of the bending and twisting moments on the wing–aileron system and of the moments on the aileron with respect to the hinge. They included inertial, elastic and aerodynamic terms. Every aerodynamic moment is the sum of six terms, proportional to the displacements and to their prime time derivatives; the proportionality coefficients were called (aerodynamic) derivatives. The passage from a stable to an unstable regime due to a continuous speed change can take place in two distinct ways. In the first, the oscillation increases in amplitude over time, passing through an intermediate state in which it is constant and the motion is harmonic; the speed at which it occurs is called critical flutter speed. In the second, a subsident, non-oscillatory motion turns into a diverging condition through a neutral balance state; the speed at which it occurs is called critical divergence speed. The experimental and analytical evaluations of the aerodynamic derivatives represent the core of the problem. Frazer and Duncan compared the evaluated and measured critical speeds, concluding that their theory was adequate to forecast flutter for cantilever wings, provided that accurate data were available. Being such data difficult to obtain for full-scale airplanes, a realistic forecast of the critical flutter

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Fig. 7.49 a Degrees of freedom of the wing–aileron system; b Theodorsen function [127]

speed was difficult. The actual value of the developed theory, therefore, lay in its use to obtain methods suited to prevent flutter. This led the two authors at first to develop a theoretical study of the various forms of instability and then to practical tools to avoid them. Küssner himself and Harold Roxbee Cox (1902–1997) [126] in 1932 provided new rules to prevent flutter. The second report by Frazer and Duncan [125] was an extension of the first one [124] aiming to study flutter in the wings of biplanes and airplane tails. The turning point was due to Theodore Theodorsen (1897–1978), an American physicist and aerodynamicist Ames brought to NACA in 1929. Theodorsen, endowed with exceptional mathematical and experimental abilities, in 1935 [127] obtained the first rigorous analytical solution, valid over an unlimited domain of reduced frequencies, of the lifting and twisting actions on an airfoil–aileron system in harmonic motion. He approached the study observing that, for the occurrence of incipient instability conditions, it was necessary to consider at least two degrees of freedom. This study was approached by assuming the oscillations as infinitely small around the equilibrium configuration and by evaluating the potential of the relative speed of the flow around the airfoil–aileron system. The problem was solved by separately treating the non-circulatory and the circulatory components of the potential flow. The non-circulatory component of the potential flow was tied to the position and speed of the airfoil–aileron system, defined by its vertical displacement h, by the rotation α of the airfoil around its axis of rotation and by the rotation β of the aileron around the hinge constraining it to the wing (Fig. 7.49a); Theodorsen evaluated such potential flow by the classical methods of fluid dynamics, applied the Bernoulli theorem to obtain the pressure distribution and evaluated the lift force on the airfoil–aileron system P , the moment on the airfoil–aileron system Mα around the axis of rotation of the airfoil, and the moment on the aileron Mβ around the hinge. The circulatory component of the potential flow was tied to the discontinuity surface behind the airfoil. Theodorsen evaluated such potential flow by applying the Kutta condition and expressing the force P and the moments Mα and Mβ through a relationship where the following function appeared: C(k) = F(k) + i G(k) =

K 1 (ik) K 0 (ik) + K 1 (ik)

(7.7)

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where: J1 (k)[J1 (k) + Y0 (k)] + Y1 (k)[Y1 (k) − J0 (k)] [J1 (k) + Y0 (k)]2 + [Y1 (k) − J0 (k)]2 Y1 (k)Y0 (k) + J1 (k)J0 (k) G(k) = − [J1 (k) + Y0 (k)]2 + [Y1 (k) − J0 (k)]2 ∞ ∞ sin(kx)dx x cos(kx)dx 2 2 ; J1 (k) = − J0 (k) = √ √ 2 π π x −1 x2 − 1 F(k) =

Y0 (k) = −

2 π

1 ∞

1

cos(kx)dx 2 ; Y1 (k) = − √ 2 π x −1

1 ∞

1

x sin(kx)dx √ x2 − 1

(7.8a) (7.8b)

(7.9a)

(7.9b)

k = ωb/U is the wavelength, i is the imaginary unit, F and G are the real and imaginary part, respectively, of C (Eq. 7.7), shown in Fig. 7.49b as a function of the reduced circular frequency 1/k, b is the half-wingspan, J 0 e J 1 are Bessel functions of the first type, Y 0 e Y 1 are Bessel functions of the second type. Equation (7.7), now known as Theodorsen function, is a mainstay of aeroelasticity. Theodorsen, using such relationships, described the motion through the following system of three linear homogeneous differential equations of the second order in the three unknowns h, α and β:

¨ α + β¨ Iβ + b(c − a)Sβ + h¨ Sα + αCα − Mα = 0 αI

(7.10a)



¨ β + h Sβ + βCβ − Mβ = 0 α¨ Iβ + b(c − a)Sβ + βI

(7.10b)

¨ β + h¨ M + hC h − P = 0 ¨ α + βS αS

(7.10c)

where a and c are geometrical parameters (Fig. 7.49a), m is the wing mass per unit length, S α , S β and I α , I β are the static and inertia moments of the airfoil and of the airfoil–aileron system, C h , C α and C β are the bending and torsional stiffness of the wing and the torsional stiffness of the aileron, P = P  + P  , Mα = Mα + Mα and Mβ = Mβ + Mβ are the total actions induced by the motion; by virtue of the hypothesis of infinitesimal displacements, they are expressed as linear combinations of the three degrees of freedom and of their prime and second time derivatives. Thanks to Eq. (7.10a–c), Theodorsen obtained the occurrence of flutter by imposing the conditions: h = h 0 eiωs ; α = α0 ei(ωs+ϕ1 ) ; β = β0 ei(ωs+ϕ2 )

(7.11)

where h0 , α0 and β0 are the amplitudes of the three degrees of freedom joined by the ω circular frequency; ϕ1 and ϕ2 are the phase angles. Replacing Eq. (7.11) into Eq. (7.10a–c) originated a system of three linear homogeneous algebraic equations in

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the three unknowns h0 , α0 and β0 . This led to an eigenvalue problem that Theodorsen solved both in the case of the system with three degrees of freedom and in the three particular cases of the systems with two degrees of freedom obtained by suppressing one of them at the time. In all cases, Theodorsen obtained the flutter critical speed and its frequency. Theodorsen’s results, which were also destined to play a key role as regards to cable-supported bridges24 [128], represented the starting point for increasingly extensive and varied studies. Placido Cicala (1910–1996) [129] in 1935 and Küssner [130] in 1936 obtained new theoretical solutions of the loading of an airfoil oscillating in a uniform flow. In 1936, Kassner and Fingado [131] proposed a simplified method and a graphic solution for airplane designers, applicable to airfoils without ailerons; they provided the four characteristic quantities of flutter: the circular frequency, the reduced speed, the ratio between the amplitudes of the vertical displacement and torsional rotation and the phase shift between them. In the same year, Edward Garrick [132] applied the Theodorsen equations to determine the drag force, i.e. the propulsion, of a vibrating airfoil–aileron system. In 1938 Karman and Sears [133] resumed the airfoil circulation theory and the mechanisms according to which an airfoil in non-uniform motion 24 Disregarding the aileron, the lift and the moment acting on the wing because of its vertical displacement and of its rotation can be expressed as:

Lh =

  1 2 ˙ h, ¨ α, α, ˙ α¨ ; ρU (2b)CL h, 2

Mα =

  1 2 ˙ h, ¨ α, α, ˙ α¨ ρU (2b)2 CM h, 2

where C L and C M are aerodynamic coefficients that are linear functions of h, α and of their prime and second derivatives with respect to time: 

 h˙ bh¨ bα˙ CL = 2π α + C(k) + ; [1 + C(k)] + U 2U 2U 2 

 h˙ bα˙ b2 α¨ π α+ C(k) − CM = [1 − C(k)] − 2 U 2U 8U 2 Bridge aeroelasticity initially made use of Theodorsen formulas, identifying the deck with a thin plate (Sects. 9.2 and 9.9). This trend continued until Robert Scanlan (1914–2001) unified the analyses (Sect. 11.1). Disregarding the inertial aerodynamic terms, he rewrote the aeroelastic coefficients as: CL = k H1∗ (k)

h˙ h˙ bα˙ bα˙ + k H2∗ (k) + k 2 H3∗ (k)α; CM = k A∗1 (k) + k A∗2 (k) + k 2 A∗3 (k)α U U U U

Hi∗ , Ai∗ (i = 1, 2, 3) being the aerodynamic or flutter derivatives. For a thin plate or an airfoil, they are linked to the Theodorsen function by the relationships:     2πF(k) π 2π kG(k) 2G(k) H1∗ (k) = − ; H2∗ (k) = − 1 + F(k) + ; H3∗ (k) = − 2 F(k) − k k k k 2     kG(k) 2G(k) πF(k) π π 1 − F(k) − ; A∗3 (k) = 2 F(k) − A∗1 (k) = ; A∗2 (k) = − k 2k k k 2 In the case of bridge decks, these expressions have to be obtained through wind tunnel tests [128].

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7 Wind and Aerodynamics

produced a vortex wake; from there, they obtained some simplified expressions of the lift and of the twisting moment, applicable to any type of motion. In the same year (1938), Garrick [134] published the first relationships between the Wagner, Theodorsen and Küssner functions as well as some approximate expressions of the same. He initially noted that Wagner [120] derived his function in integral form (Eq. 7.5) without providing an analytic expression. Küssner [130] obtained the Wagner function in a very complex analytic form. “A fortunate choice by the Author”, conversely, produced the simple formula: (s) ∼ =1−

2 4+s

(7.12)

For 0 < s < ∞ Eq. (7.12) approximates Eq. (7.5) with an error lower than 2%. Afterwards, Garrick obtained the laws linking the Wagner’s Eq. (7.5) and Theodorsen’s Eq. (7.7) as: ∞ C(k) = ik F(k) = k

(s)e−iks ds

0

∞ (s) sin(ks)ds;

G(k) = k

0

2 (s) = π

∞ 0

(7.13)

∞ [(s) − 1] cos(ks)ds 0

2 F(k) sin(ks)dk; (s) = 1 + k π

∞

G(k) cos(ks)dk k

(7.14)

(7.15)

0

He also noted that by replacing Eq. (7.12) into Eq. (7.13), it was possible to obtain the following approximate expression of the Theodorsen function: C(k) ∼ = 1 + 2ike4ik Ei(−4ik)

(7.16)

where Ei(·) is the exponential integral function. Garrick also proved that the Wagner and Küssner functions were linked by the relationships:  σ 1 − s1 1 (s − s1 ) ds1 (−1 < s < 1) (7.17a) (s) = π 1 + s1 −1

1 (s) = π



1 (s − s1 ) −1

1 − s1 ds1 (s > 1) 1 + s1

(7.17b)

where σ = s + 1. Replacing Eq. (7.12) into Eq. (7.17a, b), he obtained the following approximate expression of the Küssner function:  2+σ ∼ − 1 (σ > 2) (7.18a) (σ) = 2 4+σ

7.4 The New Horizons of Aeronautics

505

    2 + σ −1 σ(2 + σ) 1  −1 ∼ sin (σ) = σ(2 − σ) − cos (1 − σ) + 4 (σ < 2) π 4+σ 8 (7.18b) In 1940, Theodorsen and Garrick jointly published a report [135] in which they expounded the 1935 Theodorsen’s theory [127] “in a simpler and exhaustive manner”. They noted that the dissipative actions disregarded by Theodorsen could be recovered by replacing the αC α , βC β and hC h terms in Eq. (7.10a–c) with the αC α (1 + igα ), βC β (1 + igβ ) and hC h (1 + igh ) terms, where gα , gβ and gh are damping coefficients. They discussed the effects of the various parameters on the critical flutter speed. They described approximately 100 experiments carried out on airfoils with and without ailerons. The tests were performed in a high-speed NACA wind tunnel (approximately 2.4 m in diameter) to assess the adaptability of the bidimensional theory to the three-dimensional case. In front of results which were complex to interpret, the authors recommended the introduction, in the bidimensional formulation, of semi-empirical weight functions and of corrective factors dictated by experience. These studies also received impulse and drew interest because of many cases of flutter-related accidents between 1934 and 1937. A tragedy occurred in 1938 stood out: a Junkers four-engine plane with many scientists on board, crashed during a flight test with no survivors. It was then understood that such tests were too dangerous, at least until better knowledge of flutter would be available. As a consequence, a huge development of theoretical studies and wind tunnel tests took place. Actually, the dreaded flutter was not the sole phenomenon endangering airplanes. On 21 July 1930, a Junkers F13 airliner crashed near Meopham in England; the two pilots and four passengers perished in the accident. The news told a loud noise was heard just after the aircraft flew into a cloud and then wreckage rained down on the ground. The unusual circumstances of the accident induced the English and German authorities to start investigations. The British Aeronautical Research Committee [136] carried out wind tunnel tests through which it interpreted the collapse as a phenomenon for which it coined a new term, “buffeting”, which would enter in common use in the aeronautic and civil sectors: “The airplane, flying horizontally at high speed, suddenly entered a region of strong rising gusts; as a result there was a sharp increase in the angle of attack, with the formation of flow separation over the wing. The tail, situated in the wing wake, was subjected to intense forced vibrations caused by the turbulences in the separated flow, which brought about the accident”. The German committee [137] wrote that the accident was likely due to “overstressing of the wing due to high gust or manoeuvering load”. Between 1932 and 1933, Duncan, Ellis and Cristopher (Kit) Scruton25 (1911–1990) [138, 139] carried out wind tunnel tests during which they measured the oscillation of a tail wing, the “detector”, produced by the flow separation from 25 Scruton worked at the Aerodynamics Department of the NPL from 1929. Prompted by the researches carried out by Frazer and Duncan in 1928 [124, 125], he initially devoted himself to study the added mass of the air, tuned mass dampers and flutter derivatives. Transposing his experience in aeronautics to the structural sector, he made an essential contribution to the foundation of wind engineering.

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7 Wind and Aerodynamics

the front wing, for different values of the angle of attack, of the relative speed and of the wing stiffness. The results proved that buffeting severity firstly depended on the angle of attack α that created disturbance: for α = 6° buffeting did not occur; for α = 9.4°, i.e. close to stall, buffeting was moderate; it strongly increased around α = 11.9°. Wind speed was important in relation to the frequency of the wake created by the front wing: buffeting strongly increased under resonance conditions; away from it, it increased with the square of the speed. It became then essential to adopt countermeasures to avoid this phenomenon: the simpler and most effective one consisted of increasing the distance between the two wings so that the second one was outside the region perturbed by the first; the fuselage and tail stiffness must also prevent, under stall conditions, resonant vibrations. With the advent of the Second World War, an increasingly broad range of airplanes was affected by aeroelastic and buffeting troubles. The stiff bidimensional models used to analyse airfoil profiles in the early twentieth century progressively gave way to the stiff three-dimensional models and then, at the end of the 1940s, to the flexible three-dimensional models. The precursor of these models was formulated by William Rees Sears (1913–2002) [140] in 1941; he applied the potential flow theory to evaluate the lift of a wing that, while moving forward horizontally with uniform speed U, meets a vertical turbulence component with w(k, s) = W eiks harmonic law; it was provided by the relationship: L(k, s) = 2πρbU w(k, s)(k)

(7.19)

(k) = [J0 (k) − i J1 (k)]C(k) + i J1 (k)

(7.20)

where:

Equation (7.20), shown in Fig. 7.50, is now known as the Sears function.26 In the same period, the treatment of the aerodynamic and aeroelastic actions on airfoils benefited from the studies by Robert T. Jones (1940) [141] and W. Prichard Jones (1945) [142], who approximated the Wagner, Küssner, Theodorsen and Sears functions through simple analytical expressions [143]:

is given by Eq. (7.6),  being the Küssner function. For any flow path, the lift is given by the convolution:

26 The lift of a wing in a sudden upward flow w

∞ L(s) = 2πρbU

2

    w s − s    s  ds 

0

where  

is the prime derivative of . For an harmonic flow, the lift is given by Eq. (7.19),  being linked with  and   through the relationship [143]:  ∞  ∞ (k) =   (s) exp(−iks)ds = ik (s) exp(−iks)ds 0

0

7.4 The New Horizons of Aeronautics

507

Fig. 7.50 Sears function [140]

(s) ∼ = 1 − 0.165e−0.0455s − 0.33e−0.300s

(7.21)

(s) = 1 − 0.5e−0.15s − 0.5e−s

(7.22)

0.335(ik) 0.165(ik) − ik + 0.0455 ik + 0.30 0.5(ik) 0.5(ik) − (k) = 1 − ik + 0.130 ik + 1

C(k) = 1 −

(7.23) (7.24)

At the same time, also thanks to the publication of the first general books on nonlinear mechanics [144, 145], aeroelasticity achieved its full maturity. It was “defined as a science which studies the mutual interaction between aerodynamic forces and elastic forces, and the influence of this interaction on airplane design. Aeroelastic problems would not exist if airplane structures were perfectly rigid”; since the airplane is a flexible body, deformation and vibration arise that are responsible for additional aerodynamic forces that, in turn, can increase deformation and vibration causing unstable behaviours. Aeroelastic phenomena are defined as dynamic when they involve inertial actions or static if they only depend on aerodynamic and elastic forces. With such premises, in 1946 Arthur Roderick Collar (1908–1986) [146] schematized and classified aeroelastic phenomena by a triangle (Fig. 7.51), the vertices of which were represented by the aerodynamic (A), elastic (E) and inertial (I) forces. The aeroelastic phenomena associated with the three vertices fall within the triangle; those only associated with two vertices lay outside it. The fundamental phenomena are connected to the vertices through continuous lines, the usually less important ones with dotted lines.

508

7 Wind and Aerodynamics

Fig. 7.51 Collar triangle [149]

Collar defined as flutter (F) a dynamic instability occurring at a critical wind speed where the elasticity of the structure plays an essential part in the instability. Buffeting (B) is a vibration due to aerodynamic pulses produced by the wake behind wings, nacelles, fuselage pods or other components of the airplane. Dynamic response (Z) is a vibration of aircraft structural components caused by rapid loads due to gusts, landing, shock waves or other dynamic events. Load distribution (L) is the influence of structural elastic deformations on the distribution of the aerodynamic pressure. Divergence (D) is a static instability of a lifting surface of an aircraft, related to its elasticity, that occurs at a critical speed. Control effectiveness (C) is the influence of structural elastic deformations on the controllability of an airplane. Control system reversal (R) occurs at a critical speed at which the control effects are nullified by structural elastic deformations. DSA and SSA denote the influence of structural elastic deformations respectively on the dynamic and static instability of the aircraft. In the 1950s, Collar’s principles and the advances worked out in half a century of researches were rationally arranged in various books [147–151] that laid the foundations of modern aeroelasticity. The first was the handiwork of Robert Scanlan [147], the man that twenty years later would lay similar foundations in bridge aeroelasticity [128]. The book by Yuan-Cheng Fung (1919–) [148] collected the subjects of the aeroelasticity course the author held since 1948 for the aeronautics students of the California Institute of Technology; it has been reprinted several times and is one of the most classical engineering books. The five-volume NATO handbook [150] provided the state of the art about the knowledge at that time. The two books written by Raymond Bisplinghoff (1917–1985) and Holt Ashley (1922–2006) at an interval of seven years [149, 151] highlighted the scientific evolution in that period: the first one presented the Collar triangle as a model of ingenuity; the second judged it obsolete and too intent on separating phenomena requiring joint treatments.

7.4 The New Horizons of Aeronautics

509

In the same period, thanks to the evolution and diffusion of the probability and process theory (Sect. 5.2), the study of the wing under buffeting actions started making use of random dynamics. The turning point took place in 1952, when Hans Wolfgang Liepmann (1914–2009) [152] published a paper in which he studied the dynamic response of a wing subjected to a lifting action caused by the vertical component of turbulence. From the aerodynamic viewpoint, the wing was schematised as a bidimensional body; from the dynamic viewpoint, it was modelled as a simple linear oscillator. The author acknowledged that most of the concepts used were not new: the power spectrum dated back to Lord Rayleigh [153], the generalised harmonic analysis was the work of Wiener [154], the correlation and turbulence power spectrum were introduced by Taylor [155, 156] and by Karman [157]. The overview through which these concepts were applied, conversely, was revolutionary. Liepmann studied an airfoil in horizontal uniform motion with speed U, in a vertical turbulence field w(t). This is equivalent to assume that the angle of attack varies on time according to the law α(t) = w(t)/U. If w(t) is a harmonic function, the lift L(t) is provided by the Sears’ Eq. (7.19). If, conversely, w(t) is a stationary random process, the power spectrum and the variance of L(t) assume the form: SL (ω) = (2πρbU )2 Sw (ω)|(ω)|2

(7.25)

∞ σL2

=

SL (ω)dω

(7.26)

0

where S w (ω) is the power spectrum of the vertical turbulence. By virtue of Eq. (7.25), the Sears function (ω) (Eq. 7.20) is an aerodynamic admittance, namely a harmonic filter that receives the turbulence spectral content as its input and returns the lift spectral content as its output. Liepmann approximated the square of the module of the Sears function with the formula: |(ω)|2 ∼ =

1 1 + 2πωb/U

(7.27)

that highlights the properties of the aerodynamic admittance: it tends to 1 as the reduced frequency k = ωb/U tends to zero; it tends to zero for k tending to infinity. Liepmann also expressed the power spectrum of w by Eq. (6.91), where L = L w is the scale of the vertical turbulence. Besides, by applying Eqs. (7.27) and (6.91), he proved that Eq. (7.26) could be solved in closed form and studied the dependence of σL2 on η = b/L: σL2 is maximum for η tending to 0, i.e. when the width b of the wing is small with respect to L = L w ; σL2 tends to zero for η tending to infinity, i.e. when b is large with respect to L w . Equation (7.27) is still in use for bridges. Being the lift power spectrum known, Liepmann expressed the power spectrum and the variance of the vertical displacement y of the airfoil as: S y (ω) = SL (ω)|H (ω)|2

(7.28)

510

7 Wind and Aerodynamics

Fig. 7.52 General scheme of buffeting

∞ σ2y

=

S y (ω)dω

(7.29)

0

where H(ω) is the airfoil complex frequency response function, i.e. a harmonic filter that receives the lift spectral content as its input and returns the displacement spectral content as its output. Figure 7.52 summarises the relationship between Eqs. (7.25) and (7.28), highlighting the essence of buffeting. In 1955, Liepmann [158] resumed his previous theory [152], limited to the bidimensional wing, proceeding to examine the three-dimensional case. For this aim, modelling turbulence through the mere power spectrum was no longer enough; it was necessary to take into consideration the flow correlation structure. Liepmann dealt with the problem by passing from the frequency domain to the time domain and using the indicial approach; he schematised turbulence through a process that was stationary in time and homogeneous in space; he expressed the correlation tensor in the now classical form (Sect. 6.5) enunciated by Batchelor in 1953 [159]; he obtained an aerodynamic admittance depending on the wing length and that, unlike Eq. (7.27), in closed form, required the solution of a double integral in the space domain; he proved that, in the bidimensional case, the solution reproduced the previous one [152]. The passage to the time domain and the use of the correlation tensor are likely due to the fact that, when Liepmann wrote his second paper, the turbulence coherence concept had not yet appeared; this would occur, in embryonic form, thanks to Cramer [160, 161], between 1959 and 1960 (Sect. 6.7). In the wake of the pioneering works by Liepmann [152, 158], a vast literature that applied the spectral method to determine the dynamic response to turbulence of airplanes and missiles [162–164] appeared since the mid-1950s. It used the threshold crossing theory formulated by Rice [165, 166] between 1944 and 1945 (Sect. 5.2) and the new capabilities provided by computers (Sect. 5.3). In 1961, Alan Garnett Davenport (1932–2009) transferred these concepts to the wind actions on structures [167] (Sect. 9.6), opening the doors to wind engineering (Sect. 11.1).

7.5 Aerodynamics of Sailing With the end of the nineteenth century the epic of merchant and military sailing ships came to an end (Sect. 4.4) and the age of technological and scientific research to improve the performance of yachts [168, 169] came into being. It took its drive from some tragedies that caused sensation and, above all, from the increasing interest

7.5 Aerodynamics of Sailing

511

Fig. 7.53 a Mohawk; b Oona [169]

about sailing competitions. The evolution of the capabilities in the aeronautics sector played a key role (Sect. 7.4). The two tragedies that originated renewed interest for the safety of pleasure boats struck the most typical American and British yachts, the sloop and the cutter. In 1876, Mohawk (Fig. 7.53a), a classical wide and flat American sloop, capsized for a wind gust while it was weighing anchor; all the passengers perished. In 1886, Oona (Fig. 7.53b), a classical narrow and deep British cutter, lost her keel because of the stresses it was subjected to; also in this case, all the passengers perished. Sailing competitions evolved around three poles that had a focal role for research: America’s Cup, the offshore races and, to a lesser extent, the Olympic Games. America’s Cup started in 1851, when John Cox Stevens (1787–1857) brought the Hundred Guinea Cup, won by the yacht America in the waters of Cowes (Sect. 4.4), at the New York Yacht Club and promised a return match in American waters to British; it was the beginning of a series of competitions (Table 7.6) carried out at the frontiers of technology and science, which kept this trophy in the USA until 1983; the races initially were held in the Long Island Sound (New York) on windward–leeward courses (1870–1895), then they adopted a triangle course (1899–1920), and finally came to Rhode Island (1930–1983). Offshore races also acquired increasing importance for the progress of sailing; some of them—the Bermuda Race since 1906, the Fastnet Race since 1925, the Sydney Hobart Race since 1945 and the Admiral Cup since 1957—became references. Sailing was included among Olympic sports from the 1896 first edition in Athens. Taking into account the evolution of sail types, towards the end of the nineteenth century the use of the spinnaker (from “spin maker”, motion creator) became widespread; it was a foresail that assured thrust when sailing before the wind (Fig. 7.54a). In the early twentieth century, the gaff disappeared and the gaff-sail, which became triangular, was labelled Bermuda or Marconi (in Europe) because of the mast resembling a radio antenna (Fig. 7.54b). A large jib, the Genoa (Fig. 7.54c) or the Olympic jib (Fig. 7.54d), was rigged near the bow; it covered the gaff-sail and led to removing the bowsprit; it replaced the three jibs used until then and provided

512

7 Wind and Aerodynamics

Table 7.6 America’s Cup challenges from 1851 to 1958 Challenge

Year

Defender (country)

1

1870

Magic (USA)

Challenger (country) Cambria (UK)

2

1871

Columbia, Sappho (USA)

Livonia (UK)

3

1876

Madeleine (USA)

Countess of Dufferin (Canada)

4

1881

Mischief (USA)

Atalanta (Canada)

5

1885

Puritan (USA)

Genesta (UK)

6

1885

Mayflower (USA)

Galatea (UK)

7

1887

Volunteer (USA)

Thistle (UK)

8

1893

Vigilant (USA)

Valkyrie II (UK)

9

1895

Defender (USA)

Valkyrie III (UK)

10

1899

Columbia (USA)

Shamrock (UK)

11

1901

Columbia (USA)

Shamrock II (UK)

12

1903

Reliance (USA)

Shamrock III (UK)

13

1920

Resolute (USA)

Shamrock IV (UK)

14

1930

Enterprise (USA)

Shamrock V (UK)

15

1934

Rainbow (USA)

Endeavour (UK)

16

1937

Ranger (USA)

Endeavour II (UK)

17

1958

Columbia (USA)

Sceptre (UK)

Fig. 7.54 a Spinnaker; b Bermuda or Marconi gaff-sail; c Genoa; and d Olympic jib

the boat with better aerodynamic efficiency. Finally, many mechanical devices for manoeuvre of the sails made their appearance. Passing to examining the main technological and scientific advances in sailing races, the late nineteenth and the early twentieth century were dominated by the legendary figure of an American naval engineer-architect, Nathanael Greene Herreshoff (1848–1938), the first designer of yachts taking inspiration from advanced and innovative concepts.27 Herreshoff, known as the “Bristol wizard”, built Gloriana (1891), the first modern racing yacht, Dilemma (1891), the first fin keel yacht, and Alpha 27 Herreshoff brought grace, beauty, speed and design innovations into yachting. He literally is to yachting as Einstein is to science and Picasso to art.

7.5 Aerodynamics of Sailing

513

(1892), the first centreboard in yachting. Afterwards, he designed the six America’s Cup defenders that kept the trophy in the USA from 1893 to 1920, the “age of Herreshoff”. Each one of them made use of technological innovations; Vigilant (1893) used a welded steel structure; Defender (1895) used an aluminium alloy fairing; Reliance (1903) was an extreme boat, drawing inspiration from aeronautic design. These boats shattered the dream of Sir Thomas Johnstone Lipton (1848–1931), the tea tycoon dubbed “the grocer”, who outfitted the British challenger five times (1899–1930) in the hope of bringing America’s Cup back to Britain; even though the British were always defeated, Lipton had the merit of entrusting gifted designers that introduced many technological innovations in the conservative British yachting. One of these was emblematic. In 1901 George Lennox Watson (1851–1904), a Scottish naval architect, carried out the first towing tank tests on a yacht model, Shamrock II, the challenger of Columbia (Table 7.6). After defeat, Watson expressed his disappointment affirming: “I wished Herreshoff also had a towing tank”. After the period of the First World War, the sailing sector was filled with renewed scientific fervour. On the one hand, huge advances were made in the hydrodynamic study of the hulls, which had been the focus of research in the nineteenth century (Sect. 4.4). On the other hand, the aerodynamic study of the sails broke out. The two trends, interacting and inspired to research in aeronautics (Sect. 7.4), used model tests in towing tanks and wind tunnels (Sect. 7.2) and also full-scale tests. The symbol of the aeronautic influence on sailing was the research carried out by Max Michael Munk (1890–1986) at the NACA between 1919 and 1923. Munk [170] formulated several theorems, known as stagger theorems, about the interference and the aerodynamic actions on complex systems of wing surfaces. Even though they were intended for airplanes fitted with multiple wings, especially biplanes, they also entered in common use for the evaluation of the aerodynamic actions on sails. In the same period, Edward Pearson Warner (1894–1958) and Ober Shatswell (1894–1985) carried out the first full-scale and wind tunnel tests on the aerodynamic behaviour of sails, transferring into this sector the experience gained at NACA and MIT in aeronautics. The tests started in 1923 and were published in 1925 [171]; actually, as documented by the authors themselves, the MIT was involved in the performance of tunnel tests on sails from 1915. Full-scale tests were carried out on an S-class yacht named Papoose, equipped with a Marconi sail and with a jib near the bow; they were aimed at evaluating the pressure distribution on the sail surfaces as well as the flow field; they availed themselves of the collaboration of William Starling Burgess (1878–1947), one of the most charismatic figures of the twentieth century in the sailing field. Pressure measurements were carried out by perforating the sail and by connecting the pressure taps to a manometer through rubber tubes. Pressure was measured by taking photographs of the liquid level in the tubes. The problem was that in the sail there was no space where to “hide” the measurement equipment. Thus, only the surface side on which the measurements were carried out was made smooth and undisturbed. At first, a single horizontal row of pressure taps was used, extending from the luff to the leech, in parallel with the boom. Afterwards, four parallel rows of pressure taps were created; one of them, consisting of six taps, was positioned on the

514

7 Wind and Aerodynamics

Fig. 7.55 a Papoose (1923); b airflow around the sails [171]

jib. As it was usual for aeronautic measurements, pressure taps were concentrated near the edge of the sails (Fig. 7.55a). The tests, carried out on the full sail system and in the absence of the jib, proved that: (1) the suction on the downwind face was much greater, in absolute value, than the pressure on the upwind face; (2) the pressure reached its maximum value near the luff just as, for airplane wings, it reached its maximum near the leading edge; (3) the mast, if not streamlined, disrupted sail efficiency; thus, it was necessary to reduce its influence; (4) the jib, in proportion to its surface, was much more important than the mainsail as regards to the overall force on the sail system; and (5) a twisting moment, partially mitigated by the jib, acted on the sail; this action had to be minimised. The study of the flow near the sails was carried out by comparing the results of deductions inferred from the pressure field with those provided by visualisations (Fig. 7.55b). They were carried out by introducing in the air fumes produced by candles on poles before the sails. The results were recorded by shooting carried out by Papoose and by other nearby boats. The jib played an essential role since it directed air on the mainsail and prevented flow separation. Model tests were carried out on the smallest of the wind tunnels at MIT. A single boat model and five types of sail, with different chambers, were used (Fig. 7.56a); every sail was reproduced using a steel sheet nearly 0.4 mm thick. The resultant force was decomposed into its drag and lift components, i.e. those parallel and perpendicular to the wind direction, as well as the driving and heeling ones, i.e. those parallel and perpendicular to the boat axis (Fig. 7.56b). The objective was not to determine

7.5 Aerodynamics of Sailing

515

the absolute value of the aerodynamic actions, but to compare the actions due to different solutions. Simultaneously with the studies carried out by Warner and Shatswell in the U.S., a German physicist son of American parents, Manfred Curry (1899–1953), provided a great scientific contribution to the study of sails. Curry, a famous yachtsman and aerodynamics scholar, understood that the absence of vortex wakes increased the efficiency of the sail equipment. He then devoted himself to build sails and masts that reduced parasite wakes; for this reason, he studied sail shapes drawing inspiration from bird wings (Fig. 7.57a). He also studied the experiments on cambered surfaces by Lilienthal using the whirling arm (Sect. 7.1), but he did not deem the results reliable. In 1923, Hugo Junkers (1859–1935) (Sects. 7.1 and 7.4), impressed by Curry’s studies and by his ideas, invited him to carry out tests at the wind tunnel in Dessau (Fig. 7.57b). Air entered the duct through a wide intake; the fan was at the opposite end, so it sucked air to guarantee a uniform flow. The tests took place in an open chamber; the flow speed could reach 35 m/s. Curry and Junkers prepared various models of sails and masts (Fig. 7.57c), reproducing the rigging used by Curry in his races. The sails were arranged in different positions for different angles of attack of the wind. The tests were carried out by introducing the equivalence between the action of the actual wind on the moving boat and that of the apparent (or relative) wind, with speed equal to the vectorial

Fig. 7.56 a Cross-section of sails; b decomposition of the resultant force [171]

Fig. 7.57 a Comparison between sails and bird wings; b Dessau wind tunnel; and c models of sails and masts tested by Junkers and Curry [172]

516

7 Wind and Aerodynamics

Fig. 7.58 a Flow lines on the upwind side of a sail; b correlation between the drag of the sail (in the abscissa) and the wind lateral pressure (in the ordinate) [172]

difference between the speed of the actual wind and that of the boat, applied to the motionless boat. The flow field (Fig. 7.58a) and the pressure distribution were measured on both the faces of the sails; the resultant forces were also determined. Figure 7.58b shows the aerodynamic behaviour of eight configurations of Marconi sails. In 1925, Curry published a book, Yachts racing, reporting the results obtained in the wind tunnel and during his races. The volume, updated and reprinted many times [172], became a reference text for this sector and the first work dealing with sail aerodynamics on modern grounds. Curry also first discussed, based on his sailing experience, competition strategies in relation to wind and rigging. For this reason, the book became a sort of Bible for yachtsmen. Kenneth S. M. Davidson (1848–1958), an American engineer working at the Stevens Institute of Technology (Sect. 4.4), was the most scientifically and technically reputable figure, in the sailing and naval field, of the first half of the twentieth century. He was greatly proficient in fluid dynamics, had a passion for sailing, was in the crew of important boats and had been an aviation pilot. Davidson understood the contradiction between Watson’s mistrust towards towing tank tests on a yacht model and its success for steamship models; he also became aware of the advancements made in aeronautics as regards to wind tunnel tests on airplane models. He remarked that the first towing tank tests did not take into account the boundary layer and the production of turbulence inside it (Sect. 5.1). He noticed that all the previous tests were carried out in huge towing tanks, conceived for large models, on a small number of cases. He then came to the conclusion that the future resided in the use of small models, but their proper use would have required a remarkable improvement in experimentation.

7.5 Aerodynamics of Sailing

517

Fig. 7.59 a Swimming pool of the Stevens campus outfitted as a towing tank [173]; b Gimcrack

Accordingly, in 1931 Davidson outfitted the swimming pool at the Stevens campus as a towing tank (Fig. 7.59a) [173]. The following year he started tests to reproduce in scale the boundary layer on the hull, “that sort of water envelope the boat drags with her and that increases both her weight and drag”. The most effective technique was the application of a strip of coarse-grain sand below the hull. It produced the transition to turbulence for Reynolds numbers much smaller than the ones corresponding to the smooth hull [174]. The comparison between the results of these tests and the full-scale tests on Gimcrack (Fig. 7.59b), a sloop 7.25 m long at the waterline and with a sail area of 40.3 m2 , showed excellent concordance; the tests were carried out in smooth waters, with no heeling. In 1934, a new 6-m boat, Jack, proved itself clearly inferior to the old boat, Jill. To understand the reasons, the two boats repeatedly exchanged their sails and crews, but the result did not change. Davidson carried out drag tests on models in smooth waters and with no heeling, but the results did not justify the actual difference between the two boats. He then deduced that a boat hardly sailed upright on smooth waters. On the contrary, when the boat sails closed to the wind it is impossible for her not to heel. Thence originated the intuition that the heel, leeway and trim angles (Fig. 7.60), could play an essential role in the performance of a boat. To develop this concept, in 1935 Davidson founded the homonymous laboratory, equipping it with an important towing tank by means of which he carried out studies, published in 1936 [175], whose results represent a milestone. Davidson schematised a sailboat under way in steady conditions as a balanced rigid body subjected to three actions: the gravity force W applied in the centre of gravity G, the aerodynamic actions on the sails and the hydrodynamic actions on the hull. The aerodynamic actions were traced to a concentrated force F in the aerodynamic centre. The vectorial combination of W and F originated a resultant force R. It was balanced by the resultant of the hydrodynamic actions, applied along the line of action of R with the opposite direction.

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Fig. 7.60 Heel, leeway and trim angles

Since the weight force was known and the equipment to measure hydrodynamic actions in the towing tank was available, should the aerodynamic actions on sails be available it would be possible, by suitable similarity criteria, to systematise the three Cartesian components of the balance equation and to directly obtain the speed as well as the heel and leeway angles of the boat. Unfortunately, the data about the aerodynamic actions on the sails were too incomplete and uncertain. Davidson then proposed an indirect procedure by means of which the boat model was subjected to measurements in the towing tank for different values of the speed, heel, leeway and trim. From them, he obtained the aerodynamic actions guaranteeing balance and even deduced new information about such actions. The first application of this method was carried out on a small model of Gimcrack (Fig. 7.59b) in the towing tank. It confirmed the impossibility of judging the efficiency of a boat on the basis of the drag only, stressing the role of the heel angle. Intersecting the results of towing tank tests with the data recorded on Gimrack at sea, Davidson found the aerodynamic coefficients of the sails, namely the drag C D , lift C L , heel C H and propulsion C R coefficients as a function of the heel angle (Fig. 7.61a). Davidson then returned to a direct procedure. Knowing the hydrodynamic actions, evaluated on the model, and the aerodynamic actions, deduced from the Gimcrack coefficients, he obtained the speed, heel and leeway of the boat from their balance; finally, he determined the relative speed and the “made good” speed, i.e. the projection of the speed at which the boat sailed up the wind (Fig. 7.61b). During subsequent evaluations, Davidson proved that the shape and size of the sail had little influence on the Gimcrack coefficients. The latter could then be generalised to any boat. He repeated the study of Jill and Jack using this principle, explaining the reason for the superiority of the former. It was the first time the tests on small models explained the relative performance between two racing boats. This gave confidence to designers who from then on, for over forty years, would adopt this procedure.

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Fig. 7.61 a Aerodynamic coefficients of Gimcrack; b boat, wind, relative wind and “made good” speed [175]

The new hydrodynamic and aerodynamic culture developing between the two World Wars had remarkable impacts on boats and on sailing competitions, especially on America’s Cup challenges from 1930 to 1937 and on offshore races. The first adopted J-class yachts, monstrous boats that could only be used in sheltered waters. The second received a huge stimulus by the limits of America’s Cup boats and by the desire to build yachts suited for any situation. The man who gave the greatest boost to the transfer of the new concepts to the racing sector was Olin Stephens (1908–2008), a legend among the yacht designers of the twentieth century. He started his career as an assistant of Davidson, then passed on to the design of yachts for offshore races, building epoch-making and invisible boats, including Dorade (1932), Stormy Weather (1935) and Vim (1939). With Dorade, winner of the 1932 Bermuda Race, Stephens achieved the highest evolution within traditional canons. Stormy Weather was a revolutionary boat, which many people consider the first yacht of the modern age: it was neither narrow and deep like the English cutters, nor wide and flat like the American ones; it came into existence from their compromise on theoretical and experimental grounds. Vim (Fig. 7.62a) had a nimble and powerful shape and introduced the use of a light alloy mast and of rigging consisting of streamlined rods; the utmost care for details, implemented for the first time, anticipated one of the characteristics of all modern sporting competitions. In the same years, Harold Stirling “Mike” Vanderbilt (1884–1970), shipowner and skipper of the American defenders in America’s Cup challenge of the 1930s (Table 7.6), transferred to his crews the organisation of his shipping and railroad empire (Sect. 7.6). In 1930, he steered Enterprise to an easy defence of America’s

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Fig. 7.62 a Vim (1939); b Endeavour (1934) [169]

Cup. The situation changed in 1934 when Vanderbilt faced the British challenger Endeavour (Fig. 7.62b) with Rainbow, a not especially evolved boat. Endeavour, instead, was an outstanding boat, whose spinnaker, with central openings, reduced turbulence and improved stability. Endeavour, the sole British challenger considered better than the American defender, lost because of a regulatory technicality. Vanderbilt, disturbed by the near defeat, was convinced by Stephens of the need to adopt, even for this race, boats designed according to scientific principles; he then decided to have Burgess, the designer of Rainbow, flanked by Stephens to design the defender of the Cup in 1937. Stephens, destined to design again 5 of the next 6 winnings US defenders, invited Davidson to apply his calculation procedure [175] with the support of hydrodynamic and aerodynamic tests at the Stevens Institute of Technology. Such efforts originated Ranger, the best J class in history, which triumphed in the duel with Endeavour II. The Second World War disrupted and exhausted yachting. Ballast lead was used to make bullets; the larger boats were transformed into cargo, hospital and troop ships; the huge spinnakers of the sail races were used to make shirts, tents and parachutes; yacht designers were diverted towards amphibious crafts and torpedoes. Davidson’s towing tank became the core of the strategic projects of the US Navy. They highlighted the need for more sophisticated equipment. Davidson took advantage of this situation to obtain funding from the National Defense Research Council (1939), through which he built a new and larger towing tank (1942) and a huge whirling

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arm (1945). This arm, 10 m long and capable of accomplishing six revolutions per minute, only apparently was the evolution on a large scale of the devices described in Sects. 4.2 and 7.1. Whereas the latter used circular motion as a makeshift replacement for straight motion, Davidson’s whirling arm subjected the models to angular speeds to verify the stability and manoeuvrability of boats in non-straight motion. The post-war years saw the start of a “democratisation” process of sailing. The idea that this elite sport could only spread provided boat cost was reduced by mass production processes gained ground. Starting from this principle, Jean Jacques Herbulot (1909–1997) designed and built on industrial scale Vaurien and Coursier, two small sailing boats that quickly became popular. Philippe Viannay (1917–1986) founded the Glénans sailing school, catering to the youth that wished to practise a no-frills, sporting and popular yachting. A fair implementation of such ideas started in the 1960s. In the early 1950s, the sailing competitions resumed, with a novelty: the reduced size of boats. Yachts not exceeding 20 m in length took part in offshore races; Carina, a magnificent boat designed by Olin and Roderick Stephens (1909–1995) stood out from the others. America’s Cup abandoned the J Class so as to use yachts in other, especially offshore, races. The principle, due to the British, of using pure racing yachts, beautiful and unmistakable, however, remained; for this reason, the 12-m international rating was adopted. This type of boat appeared in America’s Cup from the first post-war challenge, in 1958, between Sceptre and Columbia. The British designed eight different solutions for the challenger; they made a model of each one of them and selected the most effective boat by comparative towing tank tests. The American also compared many solutions; unlike the British, however, they built their yachts in full-scale, selecting the best boat over nearly one hundred races. A now standard procedure was born: the design and testing of multiple alternatives, through which the optimal solution was selected on comparative grounds. The first theoretical studies about the data obtained in wind tunnel tests [176] gained ground at the same time; they determined the aerodynamic actions on the sail equipment by the application, like in aeronautics (Sect. 7.4) and structural engineering (Sect. 9.6), of the drag and lift coefficients, and of their directional derivatives, in correspondence with the relative wind speed. In parallel with the development of sails in yachting, new sporting activities that used sails in different ways, as propulsion or lifting means, gained ground. Windsurfing is the sport where the athlete stands on a board (the surfboard) fitted with a sail propelled by wind on the surface of water; the sail is rigged on a mast articulated at its base, supported and controlled by the yachtsman with the only aid of the boom; probably this is one of the most revolutionary inventions among pleasure craft: by minimising hull size without sacrificing sail area, it allows achieving high speeds, nimble manoeuvres and acrobatic performance. Windsurfing dates back to 1935 and is an evolution of the old surf28 ; it appeared on a postcard (Fig. 7.63a) 28 The first historical source of surfing is contained in the log of James Cook (1728–1779), the man who discovered Hawaii islands; he told the feats of the Polynesians, described as people who enjoyed being carried by waves riding on wood boards. The surfing, banned in the age of

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Fig. 7.63 a 1935 postcard depicting the first windsurf; b Harper’s Bazaar Magazine (1878)

considered a historical evidence by those who practise this sport; the wording on its back read: “A Young woman poses for a publicity photo on what could well be the first windsurfing device as created by famed surf innovator Tom Blake”. It shows a sail on a perforated board used by Blake for a competition off Waikiki, Hawai, in 1935; Blake himself described the device in a book, Hawaiian surfboard (1935). The first models were produced in 1940. Modern windsurf development started in 1964. Ice boating or ice yachting, the use of sailing boats fitted with sled skids to slide over ice [177], originated more than 4000 years ago among the Finns and the Lapps. Since the eighteenth century, the Dutch used sail sleds to carry loads and passengers along frozen canals. From Holland, like yachts (Sect. 4.4) and windmills (Sect. 4.6), ice boating reached the Hudson River valley; from there, it spread throughout the USA, where frozen rivers and lakes were common in winter; in Michigan and Wisconsin (Fig. 7.63b) it became a popular sport in the late nineteenth century. In 1913, the Northwest Ice Yacht Association was founded in Madison: every year it organised a race; in 1921, the Four Lakes Ice Yacht Club came into being, with its associated annual race; on the Geneva Lake, the Skeeter Ice Boat Club was founded. The use of modern ice boats dates back to the 1930s. In 1933, Walter Beauvois built BeauSkeeter in Wisconsin. In 1937, the Detroit News sponsored the first competition for the best racing ice boat; it was won by Blue Streak 60, designed by Archie Arroll, a Scotsman, Joseph Lodge and Norman Jarrait. From then on, ice boating became an agonistic sport in many parts of the world. Hang gliding, also known as sailplaning, is a pleasure or sporting flight system, the only one in which the aircraft is guided only through the displacement of the colonisation by Calvinist missionaries because of the exposed naked bodies, made its comeback in the late nineteenth century. The credit for its diffusion goes to Duke Paoa Kahinu Mokoe Hulikohola Kahanamoku (1890–1968), a swimming champion who toured the world for swimming and surfing exhibitions. Thomas Edward Blake (1902–1994) met Kahanamoku in 1920 and was fascinated by him. He first devoted himself to surfing in Santa Monica, and then, he moved to Hawai Islands, in Waikiki. Here, in 1931, Blake conceived the idea of equipping his board with a sail; he first used an umbrella, then implemented the 1935 solution.

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pilot weight. It is almost impossible to indicate the period of its origin. According to some, it dates back to the first silly attempts at human flight using wings and kites (Sect. 2.6). According to others, its history began with Lilienthal in 1874 (Sect. 7.4). The man who gave the greatest boost to hang-glider, in the modern meaning of this term, was Francis Melvin Rogallo (1912–2009), an American aeronautic engineer of Sicilian descent. Rogallo graduated in 1935, and from 1936, he worked at the wind tunnel of the NACA Langley Research Center in Hampton, Virginia; there, he had the idea of building a flexible aerofoil, lifted by the wind. Since he could not devote

Fig. 7.64 Rogallo’s patent (1951)

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himself to the project during his work hours, he built a small wind tunnel at home, where he carried out tests, assisted by his wife Gertrude Rogallo (1914–2008); they performed the first flight experiences in North Carolina where half a century before the Wright brothers began their adventure (Sect. 7.4). Rogallo attempted involving the Langley Research Laboratory in the use of his sails to develop a simple and cheap recreational flight system. He then renounced this possibility and in 1948 he privately obtained, with Gertude, his first patent for the flexible wing. Three years later, he obtained the second patent for “flexikite” or “flexiwing” (Fig. 7.64), a sort of kite with diamond-shaped flexible wings. Despite many attempts, Rogallo failed to draw the public attention to his aircraft. The situation changed in 1957 when NACA, that in the meantime had become NASA, took interest in the Rogallo wing: since it combined the lightness of parachutes with the manoeuvrability of other aircraft, it was considered as an effective system for the recovery of Gemini space capsules. Wind tunnel tests were started from the following year at the Langley Research Laboratory to study the Rogallo wing, renamed “parawing”, with different shapes and stiffness properties. The tests did not lead to its use in the aerospace sector, but gained it such great popularity that, from the 1960s onwards, the recreational and sporting use of the hang-glider pursued by Rogallo flourished all over the world.

7.6 Aerodynamics of Road Vehicles The technological progress between the late nineteenth and the early twentieth century brought into being a generation of road vehicles—cars, buses, lorries and motorcycles—that, just like airplanes (Sect. 7.4) and sailboats (Sect. 7.5), originated issues in relation to the fluid (air) into which they were immersed and that subjected them to aerodynamic actions. On the one hand, this started the scientific and technological research for determining the most suitable and pleasant shapes to achieve effective operational and efficiency conditions. On the other hand, the culture of the risk to which these means of transport were exposed because of wind came to maturity. The solution of the two issues, like in the sailing sector, drew its inspiration from the aerodynamic concepts that took shape in aeronautics. The first attempts to design cars based on aerodynamic principles led to torpedoes and airplanes equipped with wheels. They had less drag than the first cars; they were not successful, however, because the ground disrupted the aerodynamic properties of the undisturbed flow. Moreover, in a period when roads were very bad and engines delivered little power, the use of streamlined shapes not only did not produce any peculiar benefits but also generated a sense of mistrust. The first streamlined vehicles were built for a competition organised at the end of the nineteenth century by the French magazine La France Automobile, to set the official speed record. It was first achieved by the Count Gaston de Chasseloup-Laubat (1867–1903), who, on 18 December 1898 reached the speed of 63.13 km/h in Achères in Yvelines; he used a car powered by an electric motor, Jeantaud (Fig. 7.65a), built by the French manufacturer Charles Jeantaud; the car had a vaguely streamlined

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Fig. 7.65 a Jeantaud and Chasseloup-Laubat (1898); b Jenatzy’s Jamaise Content (1899)

Fig. 7.66 a Edge’s Napier (1907); b Audi-Alpensieger (1913) [178]

shape. Camille Jenatzy (1868–1913), a Belgian builder of racing cars that he piloted by himself with the nickname of “Le diable rougue”, engaged a duel with Gaston de Chasseloup-Laubat during which the two competitors repeatedly took the record away from each other until, on 29 April 1899, Jenatzy broke for the first the 100 km/h barrier, pushing Jamaise Content (Fig. 7.65b), a torpedo-shaped car powered by an electric motor, to 105.88 km/h. In both cases, the presence of the pilot and of the wheels disrupted the attempt to make the vehicle streamlined. The first estimate of the resistance of a car in the air was carried out in 1910 by Eiffel [1], based on the experiments performed in 1907 by Selwyn Francis Edge (1868–1940) on the Brooklands circuit in England. Edge, driving the Napier (Fig. 7.66a) he used to win, in that same year, the 24 h of Brooklands, first reached 127 km/h29 ; he then installed on the car screens of increasing size: with a 1.10 m2 screen on board, speed dropped to 100 km/h; applying a 2.80 m2 screen, speed fell to 79 km/h. Eiffel, interpolating these results, observed that the drag coefficient of the car was a little greater than 1. The Audi-Alpensieger (Fig. 7.66b), a car that only had its rear streamlined, was built in 1913; since the flow detached in the front part but did not reattach in the rear, streamlining only had a stylistic effect. Something similar occurred for the Mercedes used by Christian Friedrich Lautenschlager (1877–1954) to win the 1914 Grand Prix 29 Since Edge’s Napier was faster than Jenatzy’s Jamaise Content, both Chasseloup-Laubat and Jenatzy records were little related to car aerodynamics.

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Fig. 7.67 a Mercedes with pointed radiator (1914); b vehicle of Count Ricotti (1914) [178]

of France (Fig. 7.67a); it had a pointed radiator inspired to aerodynamic principles; the unsheltered wheels and the driver, however, produced negative effects greater than the advantages provided by the shape of the radiator. The situation was better for the 40–60 HP Aerodinamica (Fig. 7.67b) realised in 1914 by the Count Marco Ricotti using the chassis of an Alfa Romeo. The car, called “Siluro Ricotti” made use of a fairing inspired by the shape of dirigibles that enclosed the engine compartment and the driver, even though the radiator, the lights and the wheels remained exposed. The rounded shape of the windscreen, and the pointed one of the rear, also stood out as peculiar features. The common denominator of these cars, poorly effective with respect to the hopes of their builders and pilots, was that their shapes were conceived on purely intuitive grounds [178, 179]. Once this pioneering stage was over and the First World War had ended, the situation changed [178, 179]. Many studies carried out before the war [180, 181] clarified the role of the resistance opposed by air to car penetration. Eiffel, Prandtl and other scholars gave a huge boost to aerodynamics culture and to the use of wind tunnels (Sect. 7.2); the knowledge of aeronautics was gradually understood and adapted to the automotive field; the power delivered by engines increased; the quality of the roads improved and in the late 1920s the first motorways made their appearance. The Austrian Edmund Rumpler (1872–1940), initially an airplane designer and builder, changed his business because the Versailles Treaty barred Germans from engaging in any aeronautical activity. Since 1917, he devoted himself to design cars and in 1919 he presented his teardrop car. Seen from above, it had the shape of an airplane wing (Fig. 7.68) [182] and aroused interest in Germany on account of the use of aerodynamic principles in the automotive sector; this drove Rumpler to carry out, in 1922, the first wind tunnel tests on cars. The tests, carried out on various models in 1:7.5 scale at the second Prandtl’s wind tunnel in Göttingen (Sect. 7.4) proved that the drag coefficient of the teardrop car was nearly 1/3 of that of the contemporary cars; Rumpler’s car, moreover, raised much less dust than other cars.

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Fig. 7.68 Rumpler’s teardrop car (1919) [178]

Fig. 7.69 a Rumpler’s Tropfenwagen (1922); b Bugatti at the Grand Prix de Strasbourg (1923)

The Tropfenwagen (Fig. 7.69a) produced by Benz from 1922, derived from these studies. The Bugatti Type 32 tank that raced at the 1923 Grand Prix de Strasbourg (Fig. 7.69b) also had aerodynamic properties. The flat sides had poor efficiency, but the forward and rear shapes were excellent; the latter was also true, the first time, as regards to the placement of wheels. Unfortunately, the unsheltered presence of the pilot disrupted the tail aerodynamics. Both the Rumpler’s teardrop car and the Bugatti Type 32 tank highlighted a characteristic of the aerodynamic design of this period: the use of shapes drawing inspiration from bidimensional concepts. Rumpler’s car, even though fitted with a slightly curved roof [178], had bidimensional properties in the horizontal plane; the Bugatti shared the same concept, but in the vertical plane. Paul Jaray (1889–1974), an Austrian aeronautical engineer, devoted himself to floatplanes until 1914, and then, he moved to the Luftschiffbau Zeppelin, in Friedrichshafen, Germany, to work on dirigibles. Here, he was entrusted with the

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Fig. 7.70 a Drag coefficient cD of the half-body car by Klemperer and Jaray (1922); b composition of wing profiles according to Jaray [178]

design of the largest European wind tunnel, built between 1919 and 1920. Thanks to it, he studied the best shape for dirigibles, favouring the birth of the Zeppelin LZ 120, a jewel with a low drag coefficient that represented a reference model even for subsequent Zeppelins. He also took part, together with Michael Max Munk (1890–1986) and Wolfgang Benjamin Klemperer (1893–1965), in studies according to which the difference between a body fully immersed in a flow, e.g. an aircraft, and a body resting on the ground, e.g. a car, was experimentally and theoretically clarified. During these studies Jaray introduced the “streamlined car” concept, a term coined in 1922 [183]. In the same year, Klemperer [184] carried out tests in Jaray’s wind tunnel; thanks to them he introduced the “half-body car” (Fig. 7.70a) concept. He started from the examination of a wing body with slenderness ratio equal to 5: its drag coefficient away from the ground was cD = 0.045 (A). The proximity of the ground originated a perturbation that increased cD ; if only half of the body in contact with the ground was considered, however, the flow tended to become symmetrical with respect to the specularity plane, a fact that decreased cD (B). Klemperer also proved that cD increased moving the body away from the ground, decreased making its front edge rounded (C), and increased adding the wheels (D). In comparison with the drag coefficients of that age, which were averagely equal to 0.70, obtaining cD = 0.15 was a success. During the same researches, Klemperer [184] pointed out the issues related to the transversal wind action on vehicles. He observed that vehicle drag increased with the inclination of the wind and this effect was the less pronounced the more the car was

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Fig. 7.71 a Audi (1930) [178]; b Tatra 87 (1937)

streamlined. He wrote that, for great angles of attack of the wind, “the vehicle body behaves like the sail of a ship difficult to control when sailing close to the wind”. Actually, since the boundary layer only remained adherent to the surface with moderate adverse pressure gradients, to avoid the flow separation from half-body cars required very long tails. Jaray had the intuition of conceiving a car whose shape derived from the composition of a pair of wing profiles (Fig. 7.70b): the lower one was horizontal, and the upper one had different shapes in the two 192130 and 1930 proposals. They were covered by patents through the work of Reinhard KoenigFachsenfeld (1899–1994), a builder, pilot and aerodynamics scholar who carried out theoretical and practical tests in the wind tunnel and on the road. Jaray’s concepts were put into practice by Ley, Audi (Fig. 7.71a) and Dixi since 1922; in 1928, they were used by Chrysler; in 1933, Pierre Mauboussin (1900–1984) [185] applied them to Mistral, a “Voiture aérodynamique”; in 1937 the wind tunnel tests carried out by Koenig-Fachsenfeld [186] led to the Tatra 87 (Fig. 7.71b). In the same year, Lange [187] described the measurements carried out at the AVA in Göttingen under Prandtl’s leadership: starting from Jaray’s double-wing profile and smoothing its irregularities, it arrived at an ideal car, the Lange car, with a drag coefficient cD = 0.15; its shape still inspires many Porsche models. In 1938, Karl Schlör (1911–1997) [188] carried out tests in Göttingen by means of which he proved that the Lange’s car was far from perfect. He then introduced some changes through which he achieved cD = 0.125. An interesting aspect of these tests was their systematic repetition in different scales at different laboratories; the results, when compared, showed excellent agreement (Fig. 7.72a); they also highlighted the drag reduction obtained by moving the car bottom away from the ground. Schlör’s Schlörwagen was presented to the public in 1939 (Fig. 7.72b). It is also worth noticing how this period saw the consolidation of the vogue for speed records obtained by vehicles designed and built for this aim. Opel Rak 2 was a 30 The base of the body is shaped like a wing profile; a volume, the “windshield cockpit” rested over it; and the cockpit copied the shape of a dirigible, with the difference of being located on the upper side.

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Fig. 7.72 a Drag coefficient of the Lange’s car as modified by Schlör [178]; b Schlör’s Schlörwagen (1939)

torpedo with horizontal wings (reverse with respect to those of airplanes) producing a negative lift to increase the adherence to the ground; in 1928, it achieved the speed of 238 km/h. Golden Arrow by Sir Henry O’Neil de Hane Segrave (1896–1930), the car that in 1929 set the new speed record by reaching 372.456 km/h,31 had a streamlined shape, with the addition of a vertical fin in the rear to increase longitudinal stability.32 Actually, all the previously mentioned designers made the same mistake [178]. They started from shapes developed in the aeronautics field and adapted them to cars with just some little changes. All of them aimed at achieving a drag coefficient cD = 0.15, overlooking the fact that the cars of this period had cD ranging from 0.7 to 1.0. Nobody gave a thought about gradually reducing drag without radical changes. This led to a clear distinction between normal, relatively ugly, cars and streamlined cars, having such peculiar shapes as to be rejected by the public. This distinction lessened when car designers started to busy themselves with the aerodynamics of their products. This occurred in the USA thanks to Walter Edwin Lay (1889–1974), a professor at the University of Michigan, and in Germany thanks to Wunibald Kamm (1893–1966), a professor at the Stuttgart Technical University and the director of the Research Institute for road vehicles and engines. Lay was the first to carry out wind tunnel tests during which he modified the shape of vehicles, evaluating their drag coefficient (Fig. 7.73). The results, published in 1933 [189], showed the interaction between the airflow in the front and rear part 31 Segrave repeatedly beat the speed records on land and on water. He was the sole pilot that simultaneously held the two records. In 1926, he reached 245.149 km/h aboard “Ladybird”. In 1927 he reached 327.97 km/h aboard “Mystery”. In 1929, in Daytona Beach, he reached 372.46 km/h aboard “Golden Arrow”. In 1930 he won the water record. In the same year, he beat his own record a few seconds before overturning and losing his life. 32 In 1939 the Mercedes-Benz T80 used, for the first time, vertical fins and horizontal wings with negative lift. In the same year, Josef Mickl patented a system of wings offsetting side actions. Kamm developed aerodynamic solutions to achieve car stability at high speeds. In 1947, John Rhodes Cobb (1899–1952) set the record of 634.39 km/h with Railton Mobil Special. Few years later, he died on Loch Ness while attempting to beat Segraves record on water.

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Fig. 7.73 Drag coefficient according to Lay [189]

of the car; they also showed that an accurate design of the rear part was effective if the flow did not separate in the front one. These results remained unnoticed for a long time because of an unhappy choice: the implementation of cars with flat sides and edges that created vortex streets. Only a few noticed a great discovery: the drag of a vehicle with a blunted rear is only a little greater than the one achieved using an elongated shape. The same concept was expounded by Kamm, who conceived a car vertically truncated before the area where flow separation would take place. The reduced crosssection at that point created a moderate wake and little drag. This arrangement is now known as Kamm-back or K-back. Actually, the debate on the paternity of the idea is still ongoing. Kamm introduced it in a 1934 paper [190] and developed it in 1939 [191]. Von Koenig-Fachsenfeld published the results of measurements on bus models with truncated tails in 1936 [192]. It is undeniable, however, that many prototypes of truncated tail, which had great impact on the automotive sector, were developed under Kamm’s leadership. The first, and the most innovative one, was built in 1938 in co-operation with the BMW; it was named K1 and had a drag coefficient cD = 0.21. K1 was followed by K2 and K3 (Fig. 7.74), built on a Mercedes chassis, and by K4, on a BMW one. The common element was the rationality of their design. Every car was first studied in the wind tunnel by means of tests on a 1:5 scale model. The final solution was subjected to road tests during which stabilisers were fitted to evaluate the behaviour of the car with side winds.

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Fig. 7.74 Kamm’s truncated tail car: tests in the Volkswagen AG wind tunnel (1930) [178]

While Europe developed the aerodynamic design of cars based on scientific grounds, a new trend came to light in the USA. Until the mid-1920s, the American society was satisfied with sturdy and cheap cars. At the start of the 1930s, the customers faced the problem of replacing their old cars with new models with an already consumeristic attitude. The companies, thus, created products of everyday use, but with lines capable of arousing an idea of novelty and modernity. This translated into cars with streamlined shapes not so much to reach high speeds, but to implement aesthetically pleasant lines, while also aiming at energy savings. With such premises, some figures from the world of design and architecture, like Bel Geddes, Stout and Fuller, established themselves on the automotive scene. In most cases, they replaced the wind tunnel with their inspiration. In 1927, Norman Melancton Bel Geddes (1893–1956), industrial designer, theatre scenographer and director, became a consultant for the Graham-Paige car factory. Captivated by the tests carried out by the aeronautical engineer Glenn Hammond Curtiss (1878–1930), he immersed himself in creating new streamlined shapes for cars. The October 1929 stock market crash caused the suspension of this work. From 1932, then, Bel Geddes devoted himself to publish Horizons, an industrial design magazine where he proposed various objects, including airplanes, trains, ships, household appliances, buildings and cars, in futuristic manner. Motor Car Number 8 (Fig. 7.75a) was an eight-seat vehicle that became a reference for future vans; it had a rear fin ensuring better stability with side winds. The next Motor Car Number 9 introduced radical solutions: the drop-shaped body was made of aluminium sheet with load-bearing function; large, spherically rounded windows, smoothly fitting in the body, highlighted the aerodynamic effect. Some of Bel Geddes‘ sketches even showed variants equipped with spoilers. William Bushnell Stout (1880–1955) started his designer and builder career in aeronautics; he then went on to build locomotives and finally came to the automotive sector, designing his most famous work in 1932: the Scarab car (Fig. 7.75b). As a consequence of Stout experience in aircraft design, it had an aluminium body consisting of a load-bearing shell formed by a skeleton of pipes. According to Stout,

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Fig. 7.75 a Motor Car Number 8 by Bel Geddes (1932); b Stout’s Scarab (1932)

its streamlined shape was not aimed at reducing drag, but rather at meeting the changing wind conditions; the all-rounded body also made the car safer in case of crash. Only nine Scarabs were produced, but this car is still an Art Deco icon. Richard Buckminster Fuller (1895–1983), a futurist architect, designer and inventor, tied his career to an existential question: “has humankind a possibility to successfully survive for a long time on the planet Earth? And if the answer is yes, how?” He devoted his life to answer it, taking mankind improvement on himself by initiatives and projects that were only partially implemented (Sect. 8.6). He interpreted this mission giving utmost importance to sustainability, to renewable energy sources (especially solar and wind power) and to the feeding, housing and mobility of the Earth population. The projects of Dymaxion33 Car and Dymaxion House (Sect. 8.6) were consistent with this scenario. Dymaxion Car, a “streamlined and safe” car, was the evolution of a 1927 project by Fuller, Auto-Airplane, which operated as both an airplane and a car; the wings and the rear fin were pneumatic structures that were inflated and stretched or folded, depending on their use in the air or on the ground; the load-bearing structure consisted of a triangular latticework; four so-called liquid air turbines drove three wheels or the propeller; the fin above the rear wheel served to guide the vehicle like a boat rudder. In 1932 Fuller illustrated a new proposal in which his vehicle, which by then had become a car, lost its wings and had the two large forward wheels moved back; a small guiding wheel remained on the bottom of the fuselage. Fuller then involved the sculptor Isamu Noguchi (1904–1988) to prepare plaster models for wind tunnel tests, so as to improve the streamlined shape. Finally, he presented Dymaxion Car at the 1933 New Yorker Automobile Show, arousing huge interest and obtaining funds to build the first prototypes. Fuller then teamed up with the yacht builder Stirling Burgess (Sect. 7.5) to build the first Dymaxion Car (Fig. 7.76a). The car could hold 11 people and could make U-turns in place thanks to the small rear wheel. The latter, however, made the car very difficult to control at high speed with side winds. The consequences were tragic: in the same year it was built, Dymaxion car had an accident that caused the death of the driver. Fuller built two other cars, but its fate was decided.

33 “Dymaxion” was the acronym of “DYnamic MAXimum tensION”. It indicated any project aimed

at improving the living conditions of mankind.

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Fig. 7.76 a Dymaxion car by Buckminster Fuller (1933); b Chrysler Airflow (1934)

In the same period, the Chrysler Corporation started the development of a car integrally inspired by streamlining. The project, started in 1930, was assigned to Carl Breer (1883–1970) an engineer who, assisted by Orville Wright, carried out wind tunnel tests to determine the most efficient shape created by nature among those that could be transferred to a car. Chrysler built its wind tunnel near Highland Park: over 50 cars with different shapes were subjected to tests. They originated the Chrysler Airflow (Fig. 7.76b), a car that was put on the market in 1934. According to many, it was the greatest failure in the history of the automotive sector. Chrysler was unprepared to build a radically new car and amassed endless mistakes and delays. The public, in turn, was unprepared to accept a so futuristic product. The production was discontinued in 1937. The car remains an icon of its age. In the meantime, the speed of vehicles increased thanks to the first motorways, to the average improvement of road surfaces, to the use of more powerful engines and to the first benefits due to the new aerodynamic concepts. This aggravated the stability issue for cars subjected to side wind actions, increased the number of accidents and favoured the start of researches about this subject. In the wake of the pioneering observations carried out by Klemperer [184] in 1922, in the early 1930s it was clear that the resultant V of the vehicle and wind speed produced six action components on the moving vehicle, three forces (D, L, Y ) and three moments (M, R, N) (Fig. 7.77a), none of which could be disregarded in advance. They were quantified by three drag (cD ), lift (cL ) and side (cY ) force coefficients and by three pitching (cM ), rolling (cR ) and yawing (cN ) moment coefficients: 2D 2L 2Y ; cL = ; cY = ρV 2 A ρV 2 A ρV 2 A 2M 2R 2N cM = ; cR = ; cN = ρV 2 Ad ρV 2 Ad ρV 2 Ad cD =

(7.30a) (7.30b)

The measurements of these parameters (Fig. 7.77b) and the study of the methods to calibrate their values became the subject of wind tunnel tests [193]. They highlighted, as Kamm remarked [194], that a vehicle in an airstream is the less stable the better its shape is suited for low drag. The same result was confirmed by Hansen e Schlör [195] and by the accident that, on 28 January 1938, caused the death of the German pilot Bernd Rosemeyer (1909–1938) during a test to set a new speed record. His

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Fig. 7.77 a Aerodynamic actions on vehicles; b aerodynamic coefficients [123]

vehicle, fine-tuned down to the last detail to reduce drag, crashed into a tree because of a wind gust. This episode impressed the public and mobilised the scientific interest against wind actions on cars, creating an indissoluble tie, from then on, between vehicle aerodynamics and micrometeorology (Sects. 6.5 and 6.7). The risks associated with crosswind gusts, caused by turbulent and chaotic flows, by the presence of alternating obstacles, like trees and houses, that produced a succession of calm and impact states on the vehicle, emerged in the research about this issue [178]. The first data collections about the accidents caused by this phenomenon proved that their number increased in winter when the wind was stronger and the road surface more slippery [178]. A new research sector, aimed at studying air circulation inside the vehicles, came into being in the same period. Klemperer studied the flow crossing the radiator, proving that it increased drag [178]. Fiedler and Kamm [196] studied some devices to reduce this effect. Kamm himself studied the internal ventilation of vehicles to improve the comfort for passengers [178]; this accomplished an ideal link with the research about the natural ventilation of buildings that developed since the 1950s (Sect. 8.6). After the Second World War was over, the automotive production in the USA and in Europe once again followed different paths [178, 197]. Europe restarted from the concepts devised before the war. America developed concepts that led to a threevolume car (one for the engine, one for passengers and one for the baggage) called pontoon-body. Initially, it did not leave space for aerodynamic aspects, and then, it improved in this respect. The enthusiasm towards the aerodynamic innovation of cars was fading away. It would gain new strength in the 1970s, on different grounds. The technological advancement of vehicles, instead of being managed by individuals as it happened in the first part of the twentieth century, became a primary field for large corporations [178]. The use of aerodynamic criteria in the bus and lorry design started in the 1930s, prompted by the construction of the first motorways and high-speed roads. Buses first followed the development of cars, with length and size being the sole distinguishing features. The situation changed in 1936, when the Gaubschat company

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Fig. 7.78 a Gaubschat tramway bus (1936); b bus with Kamm-back (1936) [178]

Fig. 7.79 a Volkswagen lorry by Möller (1951); b cab spoiler by Sherwood (1953) [178]

built a tramway bus (Fig. 7.78a) with a rounded front and a tapered rear. The first bus making use of the Kamm-back was built in the same year; it allowed the placement of an additional row of seats in its end part (Fig. 7.78b). The most important advancement in the aerodynamic evolution of lorries was accomplished by Möller [198] in 1951. Volkswagen (Fig. 7.79a) put it into practice by entailing a rounded front that favoured the formation in the body rear of a narrow wake that reduced the drag. Two years later Wes Sherwood [199] invented, at the University of Maryland, the cab spoiler (Fig. 7.79b), a streamlined element above the cab preventing the flow separation between the cab itself and the container. The aerodynamic design of motorcycles appeared in 1929, when Ernest Jakob Henne (1904–2005) set the first documented speed record, 215 km/h, with a BMW 750 cc; the aerodynamic aspects did not relate to the motorcycle, but to the pilot helmet and the funnel-shaped appendix behind his back (Fig. 7.80a). The first attempts to equip motorcycles with streamlined fairings dates back to 1931–1932 and involved two British vehicles, Excelsior and Brough Superior (Fig. 7.80b); most efforts were dedicated to the vehicle rear. In 1937 Henne broke his own speed record bringing it to 280 km/h, with a BMW R5 500 cc motorcycle enclosed within an aluminium fairing (Fig. 7.81a). Actually, most streamlined motorcycles showed stability issues to transversal wind [200–202]; builders attempted solving this by enclosing the pilot within a fairing, but the results were poor and the driving posture was too uncomfortable. The situation improved in the 1950s, when partially streamlined motorcycles

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Fig. 7.80 a Henne driving a BMW 750 cc motorcycle (1930); b Brough Superior (1932) [178]

Fig. 7.81 a BMW R5 500 cc (1937) [178]; b NSU 250 cc Rennmax (1953)

gained ground; the 1953 NSU 250 cc Rennmax had a carefully designed streamlined front and partially streamlined wheel (Fig. 7.81b); it was the prototype of the most common motorcycles still in use.

7.7 Aerodynamics of Trains The origins of the aerodynamic study of trains are at least as old as the corresponding researches about road vehicles. The problems concerning this subject however are, if at all possible, even more wide, diversified and complex. In the late nineteenth and in the early twentieth century, they regarded the train drag, the overturning action of transversal winds and the return of the smoke emitted by locomotives in the passenger coaches and in the driver’s cab. Afterwards, on increasing train speeds, they also involved the shock wave at tunnel mouths, the effects of air displacement near tracks, during station crossings and on railway signals, as well as pantograph aerodynamics. The first examples of locomotives built to mitigate drag appeared in France towards the end of the nineteenth century and were labelled “machines coupe-vent” and “locomotives à bec”. Their front was pointed to cut through air like the bow

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Fig. 7.82 a N. 2072 locomotive by Ricour (1883); b N. 8001 locomotive by Heilmann (1897)

of ships cleaved the waves; they had, therefore, a shape very different from the aerodynamic concept that would lead, in the 1930s to the famous streamliner and streamlined locomotives [203]. The first coupe-vent machines, the locomotives N. 2071 (Orléans A 2-4-0) and N. 2072 (120 2-4-0) (Fig. 7.82a), were built by François Ricour in 1883 for the Compagnie du Chemins de Fer. They had pointed shapes at their front and before the steam intake of the driver’s cab. The spaces between the spokes of their wheels were filled with wood elements that anticipated the lenticular wheels of modern racing bicycles. According to Ricour, in the 13 months between June 1884 and June 1885 these devices involved 10–12% fuel savings. In 1890, Jean Jacques Heilmann (1822–1859), the owner of Société Industrielle de Moteurs Électriques et à Vapeur in Le Havre, patented the first steam–electric locomotive; it used a steam engine to drive a generator that produced electricity to move the train with no need for external power lines. The prototype of the new locomotive, called “le fusée electrique”, was built in 1892 and tested in 1893 on the Le Havre-Beuzville line. Engines and generators were housed in a large cab of metal plates with a pointed shape to reduce drag. From 1894 it entered in regular service for the Compagnie des Chemins de Fer de l’Ouest from Paris St-Lazare to Nantes (Fig. 7.82b). The first contribution to the study of train aerodynamics dates back to 1895, when Ernest Deharme (1838–1916) and A. Pulin published a book about railway consists [204] that highlighted the importance of the penetration into the air. They observed that the relationship that expressed the drag in proportion to the square of the train speed gave exaggerated estimates for speeds higher than 15 m/s. They also remarked that experiences carried out by various railway companies proved that traditional drag coefficients were too high. They came to the conclusion, therefore, that the uncertainties were too large and recommended the performance of new and more accurate experimental researches. It is worth noticing that Deharme and Pulin wrote about the machines coupe-vent of the Compagnie du Chemins de Fer Paris-Lyon-Mediterranee, mentioning, besides the “thin plates arranged before the machine to realise the shape of a ship’s bow”, the plates between the locomotive and the first coach to seal the intermediate space and to avoid air suction. Additional statements on the locomotives à bec date back to 1897,

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539

Fig. 7.83 a Locomotives à bec: Encloitre (1897); b Thuile locomotive (1900)

when four locomotives, Loun, Encloitre (Fig. 7.83a), Villefagnan and Boursay 4-4-0 of the 220 class (N. 2751-2754), came into service, and to 1900, when the Thuile 4-4-6 locomotive (Fig. 7.83b) was displayed at the Paris Universal Exhibition. Germany showed interest in aerodynamic locomotives since 1899 when feasibility studies about fast interurban trains were started. In 1901, the Siemens & Halske Company carried out full-scale tests about the drag of trains [1] by means of a locomotive that travelled along the 23-km strategic track from Zossen to Berlin, reaching a speed of 160 km/h; the vehicle was fitted with pressure taps on the front face and on the side walls, connected to water manometers by means of pressure tubes. Similar locomotives, built by the AEG and UEG companies in 1903, reached speeds in excess of 210 km/h, the record of that age for any ground vehicle. Such high speeds put the German industries building steam locomotives in the position of using devices to increase the speed. In 1902 the Verein Deutscher Ingenieure (VDI) announced a competition for developing steam locomotives capable of hauling a 180-ton train at a speed of 150 km/h. It originated several wind-splitter machines similar to the French ones. Standing out among these there were the Altona 561 class S9 locomotive of the Kuhn-Wittfeld type and the T16 locomotive (Fig. 7.84a), built by the Prussian State Railways in 1904, the Maffei’sche Riesenlokomotive (Fig. 7.84b) and the giant S 2/6 locomotive built by Maffei company, designed by Anton Hammel (1857–1925) in 1905, which was put into service the following year. Almost simultaneously, similar studies and projects gained ground in the USA. In 1891, William Freeman Myrith Goss (1859–1928) built the first plant for locomotive tests [205] at Purdue University; it was initially aimed at studying the flow in the smokebox and the power delivered by the machine. Afterwards, between 1895 and 1898, Goss carried out the first wind tunnel tests concerning locomotive drag [206]; they were highlighted in his 1907 book [207]. Goss’ tests made use of an open-circuit wind tunnel with square cross-section, 51 cm on a side, 18.3 m long. A fan was located at one end of the tunnel that produced a flow whose speed could reach 44.7 m/s. It was measured through Pitot tubes, which detected a decrease near the walls. The drag of wagons, either individual or in series, was measured by dynamometric balances. The models were built in 1:32 scale. Every model wagon was 30.6 cm long, 8.6 cm wide and 11.4 cm high. Initially, the tests

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Fig. 7.84 a T16 locomotive (1904); b Maffei’sche Riesenlokomotive (1906)

were carried out on single wagons; afterwards the drag of the train as a whole was also measured. The study of individual wagons proved that the drag was the sum of three contributions: the pressure on the front face, the friction on the side walls and the suction on the rear face. Their sum was approximately equal to half the drag calculated through the multiplication of the velocity pressure of the flow (or the train advancement pressure) by its front area; the drag coefficient was then cD  0.50. Goss declared himself amazed that such value was less than 1. The presence of a pair of wagons changed the situation: the first one was subjected to a drag lower than that of the isolated case (cD = 0.40) since suction was not present; the second was subjected to the suction due to the first one (cD = 0.14). The overall drag (cD = 0.54) was then only a little greater than the drag of a single wagon. Measurements with 3, 4 and 5 wagons were also carried out, whereas no evaluation was made about the transversal wind action. In 1900, the author and inventor Frederick Upham Adams (1859–1921) persuaded the Baltimore and Ohio Railroad Company to build the Windsplitter (Fig. 7.85), an aerodynamic train that reached a speed of 137 km/h by reducing drag. The front of the steam locomotive was shaped like the bow of a ship. The passenger coaches were cylinder-shaped. The traditional bellows between the coaches were replaced by almost continuous connections. The tender was fitted with a cover that smoothly connected the locomotive cab with the first coach. The windows were sealed to contain parasite drag. An internal ventilation system was adopted: air entered the tender through dedicated openings and was distributed inside the coaches through a duct. Later on, full-scale tests were carried out, installing plates that made up different shapes of the locomotive bow and simulating a fishtail at the end of the train. In 1904, the Electric Railway Test Commission of St. Louis carried out the first full-scale train drag measurements in America. The tests, documented by Charles Ashley Carus-Wilson (1860–1942) in 1907 [208], used an instrumented coach to measure the total drag and its components: the friction of the side faces and on the roof was quantified by a friction coefficient ranging from 0.0025 and 0.0044; the friction under the locomotive depended on the shape of the surface and on the size of the bogies. Frames with different shapes were applied to the coach front. The box-

7.7 Aerodynamics of Trains

541

Fig. 7.85 Adams’ Windsplitter (1900)

shaped frame made the drag coefficient the highest (cD = 0.95); the parabolic-shaped frame minimised it (cD = 0.28). The construction of aerodynamic locomotives and trains subsided with the advent of the First World War, then resumed with no enthusiasms in the 1920s to break later in the 1930s [209, 210]. On the one hand, the interest towards the studies on train drag increased. On the other hand, two different trends came into being, leading to the so-called streamliner and streamlined locomotives. The former had a streamlined shape from the beginning; the latter achieved this prerogative through frames affixed to the first coach. They originated the so-called “flying” trains. The turning point in the study of drag took place in 1926 when W. J. Davis Jr. published a paper [211] in which he expressed train drag in proportion to the square of its speed. This expression, initially limited to freight and electric trains and to speeds not exceeding 64 km/h, was named after him in a short time and became the subject of many researches to improve its accuracy and to extend its range of application [212]. The desire to achieve increasingly higher speeds originated from at least two reasons. First, it translated the willingness of railway companies to remain competitive with airplanes and cars. Second, it was the answer through which the companies using steam locomotives defended themselves from the competition of the new electric and diesel locomotives: before their highest power, steam trains reduced their drag, looking at streamlining shapes to create a suggestive appearance to attract passengers. In reality, the aerodynamic shape was almost always restricted to the locomotive, with no attention paid to the rest of the train; this limited the technical advantage of this intervention. Another reason contributing to the success of the aerodynamic shapes of steam locomotives was the smoke getting into the driver’s cab, limiting the machinist’s

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view. This problem was made more severe by the increasing number of bridges and tunnels which led to shorter chimneys. The aerodynamic design of the locomotives allowed not only speed increases, but also a rational disposal of the exhaust fumes. Besides these technical and economical reasons, style and image aspects assumed a focal role. Taking cue from the aerodynamic shapes of aviation and road transportation, and, in turn, providing inspiration for such progress, locomotives and trains did not escape the widespread fad that attributed aerodynamic shapes to any object, from radios to coffee grinders. The railway companies made the aerodynamic and stylistic aspects almost inseparable. The stylistic aspect often outweighed the technical reasons that inspired this trend. It did not even stop before model and full-scale tests proving the poor effectiveness of these shapes at limited speeds and the problems involved in the maintenance work on rolling stock enclosed in frames made smooth by the almost complete absence of joints and connections. The outbreak of the aerodynamic trains started in Germany in 1929, when a German engineer coming from the aviation industry, Franz Friedrich Kruckenberg (1882–1965), designed Schienenzeppelin (Fig. 7.86a). The train, built in 1930, consisted of a single experimental coach that took the shape of the Zeppelin dirigibles. It was driven by a wooden propeller at the rear of the railcar, powered by a BMW 12-cylinder gasoline engine. The propeller shaft was tilted by seven degrees to create a downward thrust ensuring adhesion to rails. The maiden run took place on 25 September 1930 on the Braunschweig-Paderborn line, between Kreiensen and Altenbeken. On 10 May 1931, the train came close to a speed of 200 km/h. On 21 June 1931, it set the new world speed record on rail, travelling at 230 km/h on the Karstädt-Dergenthin section of the Berlin-Hamburg line. The Schienenzeppelin was a very fast train but it was also fraught with problems. The propeller generated noise and air currents was dangerous during station crossings and allowed travelling in one direction. Thus, in 1932 Kruckenberg designed and built a new version of the Schienenzeppelin with no propeller. The gasoline engine drove the railcar by a hydraulic system and new streamlined fairings were fitted at the front and rear ends. The prototype retained many problems and the Deutsche Reichsbahn-Gesellschaft developed a new diesel–electric train, DRG SVT

Fig. 7.86 a Schienenzeppelin (1930); b Fliegender Hamburger (1933)

7.7 Aerodynamics of Trains

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Fig. 7.87 a Bugatti Express (1935); b Silver Jubilee (1935) [209]

877 Fliegender Hamburger (Fig. 7.86b), based on experiences and concepts developed by Kruckenberg for the Schienenzeppelin. The Fliegender Hamburger was built in 1933 and reached 160 km/h, the highest speed for a train in passenger service. Its development, between 1934 and 1935, led to DRG SVT 137, a diesel–hydraulic train that reached 205 km/h in 1936 and 215 km/h in 1938. In both cases, it was the new world speed record for diesel trains. In the same period, the French railcars, known as Autorails, also entered the age of streamlining originating trains with high speeds and suggestive shapes. Standing out among these there were the Micheline and Renault diesel trains, used since 1932 and 1935 respectively, and the Bugatti Express (Fig. 7.87a) gasoline trains, in service on the Paris-Le Havre and Paris-Lyon-Mediterranee lines since 1933. The railcars, which had the typical bidimensional streamlined shape of the homonymous cars (Fig. 7.69b), where built with aluminium bodies fastened to metal underframes by vibration-dampening couplings. The space between coaches was sealed by rubber elements that preserved the streamlined shape of the train. The trains were equipped with sophisticated air-conditioning systems. The use of aerodynamic locomotives in England was mainly due to the London and Northern Railway (LNER) company and to the engineer heading its mechanical sector, Sir Herbert Nigel Gresley (1876–1941). During a period he spent in Germany in 1933, he travelled aboard Fliegender Hamburger and was impressed by the potential of streamlining. He also initially used diesel trains in England, then he realised that the application of streamlined fairings on suitably modified LNER steam locomotives of the A1 and A3 classes would have allowed the implementation of high-speed trains with 8–9 coaches. This idea introduced a great innovation with respect to Germany and France, where streamlining was mostly adopted on railcars or trains consisting of a locomotive and few coaches. On the basis of these concepts, Gresley studied a streamlined solution for the P2 2-8-2 Mikado A3 class locomotive, to be used for the passenger express train running over the Edinburgh-Aberdeen line; the wind tunnel tests led to changes in the position and shape of the smoke deflector plates and to introduce V-shaped fairing on the cab front; the train entered service in June 1935. In parallel, Gresley carried out tests

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Fig. 7.88 a ETR 200 (1937); b Confederation 6400 (1936)

during which the A1 class Flying Scotsman reached 160 km/h, while the A3 class Papyrus attained speeds with peaks up to 174 km/h. The results were so encouraging to induce Gresley and LNER to use the same principles for the A4 Express Pacific, the most prestigious LNER locomotive; this led to Silver Jubilee (Fig. 7.87b), the English symbol of luxury and fascination. All the elements making up the Silver Jubilee—locomotive, coaches and connections between coaches—were streamlined. The relatively flat sides drew their inspiration from the Bugatti Express (Fig. 7.87a). The details of the shape were selected among many alternatives subjected to wind tunnel tests at the NPL. It is said that the fine-tuning of the smoke deflectors, one of the main features of the locomotive, was originated by a small plasticine bump applied to the model by mistake: it solved, as if by magic, all the issues that were studied for a long time without ever finding a convincing solution. The train entered service in 1935, reaching 181 km/h. In 1938, the original locomotive was replaced by the Nr. 4468 Mallard that, reaching 202 km/h set the new world speed record34 for steam trains. Italy joined the boom of streamliner trains with the ETR 200 electric train (Fig. 7.88a) of its State Railways. The train was subject to aerodynamic tests at the wind tunnel of the Turin Polytechnic and was built by the Società Italiana Ernesto Breda in 1936. It entered service in 1937, achieving a speed of 201 km/h between Campoleone and Cisterna on the Rome-Naples line. It exceeded itself in 1939, reaching 203 km/h. In this period, it was considered the fastest and most comfortable European train. In Canada, the study of aerodynamic locomotives started in 1931, when the Canadian National Railway (CNR) understood the increasingly higher risks associated with smoke entering the driver’s cab. In this period, the National Research Council (NRC) inaugurated one of the most famous wind tunnels of this era in Ottawa. It was then natural for CNR to entrust NRC with the study about fumes. The diffusion of streamlining concepts directed it towards more appropriate locomotive shapes. The 34 The previous record had been set in 1936 by a Deutsche Reichsbahn Class 05 4-6-4, which was the first locomotive to reach the speed of 200 km/h. Pennsylvania Railroad maintained its S1 steam locomotive reached a speed of 225 km/h; this possible record, however, was not documented enough.

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study not only solved the smoke issue; it also provided elements to reduce drag by 33%. The results were so brilliant that CNR approved the design criteria indicated by NRC and entrusted Montreal Locomotive Works with the construction of the new 6400-6404 (4-8-4) locomotives. Defined as semi-streamlined, they entered service in 1936, were named Confederation (Fig. 7.88b) and became the reference for other Canadian and foreign railway companies. Canadian Pacific Railway (CPR) took their style and concepts as a model for its two new locomotives, the Jubilees and Royal Hudsons, which entered service in 1936 and 1937 respectively. There is no doubt, however, that the boom of the streamliner and streamlined trains mainly took place in the USA, where it was an epoch-making and society event. It was affected by the previously discussed factors and also assumed some aspects typical of the American reality. The companies that survived the 1929 Wall Street Crash needed increasing sales and beating competition. This led to the industrial design, intended as a tool to attract the public towards the purchase or use of products able to strike fantasy and to revive the enthusiasm subdued by the Great Depression. Also thanks to charismatic figures like William Bushnell Stout (1880–1955), Norman Melancton Bel Geddes (1893–1956), Richard Buckminster Fuller (1895–1983), Raymond Loewy (1893–1986) and Henry Dreyfuss (1904–1972), streamlining became synonymous with American design [213]. The railway sector was more affected by this reality than others, due to the competition among companies that served different links and attempted to beat the competitors by offering shorter travel times and more luxurious trains: the streamlining met both these requirements. The age of the American aerodynamic trains started with Pullman Railplane, an experimental railcar designed by Stout and built by Pullman-Standard in 1933. It was powered by a gasoline engine, had an aluminium body and reached 145 km/h. It was displayed at the 1934 Chicago World Exhibition. Simultaneously, a competition broke out between the Chicago Burlington and Quincy (CB&Q) and Union Pacific (UP) railways to build the first passenger train of the new generation. Both decided to create a light, aerodynamic train powered by a diesel–electric engine. UP entrusted the University of Michigan with wind tunnel tests, CB&Q assigned them to MIT. Both applied to General Motors for the engine, but involved different companies to build the cars: UP asked Pullman to build aluminium coaches like the Railplane; CB&Q anticipated its competitor, entrusting Budd Manufacturing with the construction of stainless steel coaches. UP replied abandoning the diesel–electric engine in favour of the quicker construction of an engine using a gasoline distillate similar to kerosene. Thanks to it, UP won the competition, putting into service M-10000, the first streamliner train in the U.S., on 25 February 1934. Two months later the Burlington Zephyr of CB&Q, the second American streamliner train made its first travel from Denver to the Century of Progress Exhibition in Chicago. Both trains were enthusiastically met by the public. The construction of UP M-10000 (Fig. 7.89a) (also known as “Tin Worm” or “Little Zip” or “City of Salina”) was followed (1934) by UP M-10001 (also known as “City of Portland”), the diesel–electric version of the original gasoline distillate locomotive. The style of both versions was the work of the Pullman engineer Martin

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Fig. 7.89 Union Pacific M-10000 (1934): a front; b streamlined tail

Petrus Frederik Blomberg (1888–1966). The wagons were designed as streamlined, ultra-stiff, tubular beams, this allowing remarkable material savings and the construction of a light train. The tail of the train was the subject of detailed wind tunnel studies (Fig. 7.89b). The train used a sophisticated internal ventilation system; the windows were sealed to optimise passenger comfort and to reduce parasite drag. Before being put into service, the train travelled over 20,000 km with any type of weather: it was tested against wind, snow, rain and sand storms. The Burlington Zephyr35 (Fig. 7.90a), considered by many superior to its predecessor, was the outcome of the aerodynamic studies carried out by the aeronautic engineer Albert Gardner Dean, who designed the front part of the locomotive, by the architect John Frederick Harbeson (1888–1986) and by the industrial designer Paul Philippe Cret (1876–1945), who improved the appearance of the sides. The train tail was inspired by aerodynamic criteria (Fig. 7.90b), arriving at a result different from that of UP M-10000. In 1936 an improved version of the train was renamed “Pioneer Zephyr” or “Twin Cities Zephir”. In 1937 the CB&Q 3002 steam locomotive was equipped with a streamlined fairing inspired to Zephyr and denominated “Aeolus” 4000. The roots of the second competition that stirred the American railway sector were even older than those of the one leading to the construction of the UP M-10000 and Burlington Zephyr. The New York Central (NYC) Lines and the Pennsylvania Railroad (PRR) operated different lines linking New York and Chicago: the first relied on its Twentieth Century Limited express train, the second used Broadway Limited. Towards the mid-1930s the two companies attempted to outweigh each other by equipping their locomotives with streamlined fairings.

35 Ralph Budd (1879–1962), president of CB&Q, attributed great importance to the train name. He demanded that such name started with the Z letter so that the train was considered “the last word” in railway service. Unfortunately, he did not find the last two words of the American dictionary—zyzzle and zymurgy—attractive whereas he was impressed by The Canterbury tales and their description of “Zephyrus”, the “delicate and nourishing” west wind.

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Fig. 7.90 Burlington Zephyr (1934): a front; b aerodynamic tail

Fig. 7.91 a Commodore Vanderbilt (1934); b Super Hudson (1938)

The NYC Twentieth Century Limited, inaugurated in 1902, was a “national institution” and “the most famous train in the world”. In the mid-1920s, it used a steam locomotive called Hudson 4-6-4 to haul this train; it was built by the ALCO Company and entered service in 1927. In the early 1930s, a project came into being, aimed at covering the locomotive with a cladding, the “shroud”, that exalted its modernity. This project was given to a NYC technician, Carl Kantola, flanked by the specialists of the Cleveland Case School of Applied Science; the wind tunnel tests were carried out by Norman Zapf (1911–1974). The result was welcomed and led to the first streamlined locomotive in the USA. It was put in service in 1934 and was called “Commodore Vanderbilt” (Fig. 7.91a) to honour the NYC founder. In 1935, NYC entrusted the industrial designer Henry Dreyfuss36 with the design of a streamliner passenger train to link the central–western cities. The new train, denominated “Mercury”, introduced outstanding stylistic innovations: it drew inspiration from Art Deco and represented the first example of global design, from the shape of the locomotive to the interiors of coaches and services. The use of a rounded tail, inspired to aerodynamics, to create the observation car, a sophisticated and exclusive space, stood out. The train, inaugurated in 1936, was so appreciated to induce 36 Henry Dreyfuss, initially an apprentice of Bel Geddes, rejected a merely stylistic view of design, imprinting his projects through choices inspired to technical and functional aspects. Besides its locomotives, he was known for the Bell phones that invaded the USA.

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Fig. 7.92 a S-1 and Raymond Loewy (1938); b Comet (1935)

NYC to entrust Dreyfuss with the design of a renewed image for the Twentieth Century Limited. In 1938 the Commodore Vanderbilt was then replaced by the “Super Hudson” or “Restyled Hudson” or “Dreyfuss Hudson” (Fig. 7.91b), judged by many as the most beautiful and famous train ever built. The PRR Broadway Limited, inaugurated in 1912, was the evolution of Pennsylvania Special, a train that entered service in 1902. Since 1914 it was hauled by K4 4-6-2, a successful steam locomotive. Starting in 1934 PRR built new electric locomotives called GG-1, entrusting Raymond Loewy,37 “the man who shaped America”, with the task of improving their appearance; Loewy, considered by many as a promoter of streamlining as a stylistic rather than a technical matter, gave the locomotive rounded shapes and replaced riveted joints with welds. The result was so successful that Loewy became the designer of all the streamlined PRR locomotives. The cladding of the K-4 (1936), S-1 (Fig. 7.92a) (1939) and T-1 (1942) locomotives stood out, but, like for all other streamlined locomotives, it was an endless source of troubles, especially for maintenance work; shrouds were then gradually removed. Gaining momentum from the competitions between UP and CB&Q and between NYC and PRR, since 1935 the American railway sector went wild with an unprecedented race towards fast, beautiful and luxurious trains: streamlining was their common denominator. In 1935, the Chicago, Milwaukee, St. Paul and Pacific Railroad built Hiawatha, a light steam train whose aerodynamic design was managed by Otto Kuhler (1894–1977); its integrated design of the shape of the interiors of the train, as well as the beaver tail observation car stood out. Almost simultaneously, the Baltimore & Ohio Railroad put into service the “Abraham Lincoln” diesel train, Chicago & North Western Railroad built “The 400”, subsequently renamed as the “Twin Cities 400”, the Maine Central Railroad and the Boston & Maine Corporation built the “Flying Yankee” diesel streamliner train. 37 Besides locomotives, Raymond Loewy also tied his name to indelible images of cigarette packs, refrigerators, cars, helicopters, ships and logos (e.g. for Exxon and Shell), inspired to his motto, “beauty through function and simplification”. He was the designer of the Air France Concorde and of the Air Force One. At the peak of his career, over 75% of the American citizens came into contact, at least once in a day, with one of his products.

7.7 Aerodynamics of Trains

549

Still in 1935, New York, New Haven & Hartford Railway Company put into service “Comet” (Fig. 7.92b), a diesel–electric streamliner train built by the GoodyearZeppelin Corporation through an aeronautic approach. For the first time, aerodynamic studies made use of tests at two distinct wind tunnels: the laboratories of the Columbia University and of the David Guggenheim Airship Institute in Akron, Ohio. Since the train could travel in both directions, its front and tail were identical. Zeppelin Corporation also took advantage of its expertise with dirigibles to reduce the weight of the coaches: each one of them consisted of a rigid tubular frame; an aluminium shell strengthened by the frames of the end doors and of side windows was fastened to such frame. The train was devoid of sharp edges; all the finishing details were inserted in the shell that enclosed the coaches. The Second World War being imminent, the meteor of the streamliner and streamlined trains, was about to fade away, leaving the memory of a frenzied brief era. In wartime, the streamlining shrouds of locomotives were a hindrance to maintenance works and were removed. In many countries, the shrouds were used for war purposes. In any case, the conditions to develop streamlined trains did not exist anymore. When the war was over, the USA abandoned their streamlined trains because of the popularity of cars and airplanes. Europe, conversely, turned back, using the experience of the 1930s to build a high-speed communication network. This trend was subjected to a new breakthrough on 1 October 1964 when the 0 series of the Shinkansen trains entered service in Japan, just before the Tokyo Olympics. It originated researches about the issues of pantograph aerodynamics, the shock waves generated by trains and the danger of overturning due to the transversal wind action. The studies on pantographs proved they were subjected to upward and downward aerodynamic actions that were responsible for wear and lack of contact. It became essential, therefore, to test this train component in wind tunnels and to equip it with small wings to nullify aerodynamic actions. There was, however, a second cause for concern deriving from transversal wind actions that caused damage at the contact point between the pantograph and the overhead power line at high train speed as well as strong oscillations of the conductors. The effects of train shock waves on the structures adjacent to the lines were studied by Walter Tollmien (1900–1968) in 1927 using potential flow theory [214]. In 1935, the first breaking of window glasses because of the passage of a train occurred in Le Havre. The first wind tunnel tests aimed at examining this phenomenon were carried out in Derby, England, in the same year; more sophisticated tests were carried out in Japan from 1962 [215]. The risk due to transversal wind actions was a consequence of train evolution: it implied the speed increase and weight reduction, two adverse effects as regards to train stability. The resultant of the train and wind speed produced three force and three moment components on the moving vehicle, just like it did for road vehicles (Sect. 7.6) The moment in the plane perpendicular to the railway line caused an overturning action as much higher as the speed; it was only opposed by the stabilising action of the train weight.

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Fig. 7.93 1935 railway accident on the Owencarrow Viaduct, Ireland [217]

Actually, the problem of tranversal wind actions appeared since the construction of the first railways. The first accidents date back to the late nineteenth century and occurred in Japan [216] and in Europe [217]. They were almost always associated with the passage of trains over viaducts or embankments, where an increase in the wind speed takes place. From 1872 to 1960, in Japan 22 railway accidents occurred because of the wind; the highest number was concentrated between 1920 and 1930 when an uncontrolled increase in railway traffic was not met with specific safety regulations. In 1869, the wind caused the derailment of a French train with seven coaches. In 1903, a storm overturned a passenger train on the Leven Viaduct, at the north end of Morecambe Bay in England. The most emblematic accident happened in 1925 on the Owencarrow Viaduct in Ireland; the line section where the derailment took place consisted of a viaduct and an arc bridge, connected by an embankment (Fig. 7.93); the train overturned on the embankment where, at the same height above the ground, the flow was accelerated by the embankment slope. Unfortunately, the number of accidents caused by the wind was higher, even though it was attributable to a different cause: the collapse of the bridges, especially the truss structure ones, during the passage of trains. The most famous occurred in 1879 on the Tay Bridge and caused the death of 76 people (Sect. 4.9). Similar accidents, due to the inadequacies of bridges as regards wind actions, took place in many European countries and in the USA between the late nineteenth and the early twentieth century, causing great loss of life. On passing the time, the growing culture of the wind actions on structures (Chap. 9) reduced this phenomenon; the raising train speed, however, increased the derailment risk so much that it made transversal wind a focal issue for the safety of the railway lines.

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144. Kryloff N, Bogoliuboff N (1943) Introduction to non-linear mechanics (trans: Russian by Lefschetz S). Princeton University Press 145. Minorsky N (1947) Introduction to non-linear mechanics. J.W. Edwards, Ann Arbor, MI 146. Collar AR (1946) The expanding domain of aeroelasticity. J R Aeronaut Soc L 613–636 147. Scanlan RH, Rosenbaum R (1951) Introduction to the study of aircraft vibration and flutter. Macmillan, New York 148. Fung YC (1955) An introduction to the theory of aeroelaticity. Wiley, New York 149. Bisplinghoff RL, Ashley H, Halfman RL (1955) Aeroelasticity. Addison-Wesley, Cambridge, MA 150. (1959). Manual on aeroelasticity. NATO Advisory Group for Aeronautical Research and Development 151. Bisplinghoff RL, Ashley H (1962) Principles of aeroelasticity. Wiley, New York 152. Liepmann HW (1952) On the application of statistical concepts to the buffeting problem. J Aeronaut Sci 19:793–800 153. Rayleigh Lord (1945) Theory of sound. Dover Publications, New York 154. Wiener N (1930) Generalized harmonic analysis. Acta Math 55:117–258 155. Taylor GI (1921) Diffusion by continuous movements. Proc Lond Math Soc 20:196–212 156. Taylor GI (1938) The spectrum of turbulence. Proc R Soc Lond A 164:476–490 157. von Kármán T (1948) Progress in the statistical theory of turbulence. Proc Natl Acad Sci Wash 34:530–539 158. Liepmann HW (1955) Extension of the statistical approach to buffeting and gust response of wings of finite span. J Aeronat Sci 22:197–200 159. Batchelor GK (1953) The theory of homogeneous turbulence. Cambridge University Press, UK 160. Cramer HE (1959) Measurements of turbulence structure near the ground within the frequency range from 0.5 to 0.01 cycles sec. In: Advances in geophysics, 6, Atmospheric diffusion and air pollution. Academic Press, New York and London, pp 75–96 161. Cramer HE (1960) Use of power spectra and scales of turbulence in estimating wind loads. Meteor Mon 4:12–18 162. Press H, Meadows MT, Hadlock I (1956) A reevaluation of data on atmospheric turbulence and airplane gust loads for application in spectral calculations. NACA report 1272 163. Press H, Houbolt JC (1955) Some applications of generalized harmonic analysis to gust loads on airplanes. J Aeronaut Sci 22:17–26 164. Thorson KR, Bohne QR (1959) Application of power spectral methods in airplane and missile design. Institute Aerospace Science, report 59-42 165. Rice SO (1944) Mathematical analysis of random noise. Bell Syst Tech J 23:282–332 166. Rice SO (1945) Mathematical analysis of random noise. Bell Syst Tech J 24:46–156 167. Davenport AG (1961) The application of statistical concepts to the wind loading of structures. Proc Inst Civil Eng 19:449–472 168. Sciarrelli C (1970) Lo yacht: origine ed evoluzione del veliero da diporto. Mursia, Milan 169. Giorgetti F (2003) Storia ed evoluzione degli yacht da regata. White Star, Vercelli, Italy 170. Munk MM (1923) The minimum induced drag of aerofoils. NACA report 121 171. Warner EP, Shatswell O (1925) The aerodynamics of yacht sails. Trans Soc Naval Architects Mar Eng 33:207–232 172. Curry M (1948) Yacht racing: the aerodynamics of sails and racing tactics, 5th edn. Charles Scribner’s Sons, New York 173. DeBord F Jr, Kirkman K, Savitsky D (2004) The evolving role of the to wing tank for grand prix sailing yacht design. In: Proceedings of 27th American towing tank conference, Newfoundland and Labrador, Canada 174. Taylor DW (1933) Speed and power of ships. Ransdell 175. Davidson KSM (1936) Some experimental studies of the sailing yacht. Trans Soc Naval Architects Mar Eng 44:288–334 176. Herreshoff HC (1964) Hydrodynamics and aerodynamics of the sailing yacht. Trans Soc Naval Architects Mar Eng 72:445–492

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177. Melaragno MG (1982) Wind in architectural and environmental design. Van Nostrand Reinhold, New York 178. Hucho WH (ed) (1998) Aerodynamics of road vehicles. Society of Automotive Engineers, Warrendale, PA 179. Hucho WH, Sovran G (1993) Aerodynamics of road vehicles. Annu Rev Fluid Mech 25:485–537 180. Riedler A (1911) Wissenschaftliche automobilbewertung. Oldenburg, Berlin 181. Aston WG (1911) Body design and wind resistance. The Autocar 364–366 (August) 182. Rumpler E (1924) Das Auto in Luftstrom. Z Flugtech Motorluftschiffahrt 15:22–25 183. Jaray P (1922) Der stromlinienwagen - Eine neue form der automobilkarosserie. Der Motorwagen 17:333–336 184. Klemperer W (1922) Luftwiderstandsuntersuchungen an automodellen. Z Flugtech Motorluftschiffahrt 13:201–206 185. Mouboussin P (1933) Voitures aérodynamiques. L’Aéronautique 239–245 (November) 186. Koenig-Fachsenfeld R (1941) Luftwiderstandsmessungen an einem Modell des TatraWagens Typ 87. ATZ 44:286–287 187. Lange A (1937) Vergleichende Windkanalversuche an Fahrzeugmodellen. Berichte Deutscher Kraftfahrzeugforschung im Auftrag des RVM 31 188. Schlör K (1938) Entwicklung und bau einer luftwiderstandsarmen karosserie auf einem 1,7Ltr-Heckmotor-Mercedes-Benz-Fahrgestell. Deutsche Kraftfahrforschung, Zwischenbericht 48 189. Lay WE (1933) Is 50 miles per gallon possible with correct streamlining? SAE J 32:144–156, 177–186 190. Kamm W, Schmid C, Riekert P, Huber L (1934) Einfluss der Autobahnen auf die Gestaltung der Kraftfahrzeugen. Automobiltech Z 37:341–354 191. Kamm W (1939) Der Weg zum wirtschaftlichen autobahn- und straentüchtigen Fahrzeug. Strae 6:104–109 192. Koenig-Fachsenfeld RV, Ruehle D, Eckert A, Zeuner M (1936) Windkanalmessungen an Omnibusmodellen. Automobiltech Z 39:143–149 193. Heald RH (1933) Aerodynamic characteristics of automobile models. US Department of Commerce, Bureau of Standards, RP 591, 285–291 194. Kamm W (1933) Anforderungen an kraftwagen bei dauerfahrten. Z Ver Dtsch Ing 77:1129–1133 195. Hansen M, Schlör K (1938) Aerodynamische modellmessungen an veschiedenen kraftwagenformen und verhalten des wirklichen fahrzeugs bei seitenwind. Deutsche Kraftfahrtforschung, Zwischenbericht 63 196. Fiedler F, Kamm W (1940) Steigerung der wirtschaftlichkeit des personenwagens. Z Ver Dtsch Ing 84:485–491 197. Kieselbach RJF (1986) Streamlining vehicles 1945-1965. A historical review. J Wind Eng Ind Aerodyn 22:105–113 198. Möller E (1951) Luftwiderstandsmessungen am VW-Lieferwagen. Automobiltechnische Zeitschrift 53:153–156 199. Sherwood AW (1953) Wind tunnel test of trailmobile trailers. University of Maryland, Wind Tunnel report 35 200. Scholz N (1951) Windkanaluntersuchungen am NSU-Weltrekordmotorrad. Die Umschau 51:691–692 201. Scholz N (1953) Windkanaluntersuchungen an motorradmodellen. Z Ver Dtsch Ing 95:17 202. Schlichting H (1953) Aerodynamische untersuchungen an kraftfahrzeugen. Kassel, Hochschultag 203. Vilain LM (1967) L’évolution du matériel moteur et roulant des chemins defer de l’Etat. Vincent, Paris 204. Deharme E, Pulin A (1895) Chemins de fer, matériel roulant, résistance des trains, traction. Gauthier-Villards, Paris 205. Goss WFM (1891) An experimental locomotive. Railroad Eng J 65:549

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206. Goss WFM (1898) Atmospheric resistance to the motion of railway trains. The Engineer, 12 August, 164–166 207. Goss WFM (1907) Locomotive performance: the result of a series of researches conducted by the Engineering Laboratory of Purdue University. Wiley, New York 208. Carus-Wilson CA (1907) The predetermination of train resistance. In: Minutes of proceedings, Institution of Civil Engineers, CXLVII, pp 227–265 209. Riley CJ (2002) The encyclopedia of trains & locomotives. Metro Books, New York 210. Schafer M, Welsh J (2002) Streamliners: history of a railroad icon. Motorbooks, St. Paul, MN 211. Davis WJ Jr (1926) The tractive resistance of electric locomotives and cars. Gen Electr Rev 29:685–707 212. Gawthorpe RG (1978) Aerodynamics of trains in the open air. Railway Eng Int 3:7–12 213. Giedion S (1948) Mechanization takes command. Norton, New York 214. Tollmien W (1927) Air resistance and pressure zones around train in railway tunnels. Z Ver Dtsch Ing 71:199–203 215. Hara T, Okushi J (1962) Model tests on the aerodynamical phenomena of high speed trains entering a tunnel. Quarterly report of RTRI, vol 3, pp 6–10 216. Fujii T, Maeda T, Ishida H, Imai T, Tanemoto K, Suzuki M (1999) Wind-induced accidents of train/vehicles and their measures in Japan. Quarterly report of RTRI, vol 40, pp 50–55 217. Gawthorpe RG (1994) Wind effects on ground transportation. J Wind Eng Ind Aerodyn 52:73–92

Chapter 8

Wind, Environment and Territory

Abstract This chapter provides a fairly consistent picture of the unlimited range of actions and effects induced by the wind on the environment and territory. Accordingly, it describes the transition from ancient windmills to modern wind turbines. It deals with the role of the wind in the transport and diffusion of minute materials, highlighting three issues: the diffusion of pollutants introduced in the air during combustion processes, soil erosion, a phenomenon able of changing the geomorphological features of nature and of making soil dry up with devastating consequences, and the snow drift that causes severe problems for road and rail traffic as well as for built areas. The chapter also deals with natural and artificial barriers and their manifold uses, first of all, the protection of crops. Finally, it continues the description of the efforts mankind carried out since ancient times to build settlements and dwellings taking inspiration from bioclimatic principles; in this framework, city planning and architecture came into contact with environmental and climatic issues reassessed on scientific grounds.

Wind exerts an unlimited range of actions and effects on the environment and territory. This chapter attempts to provide a fairly consistent picture of them, knowing that making such picture exhaustive represents a demanding task, at least for the author. With the advent of the Industrial Revolution, mankind’s long-standing ambition to use wind as an energy source (Sects. 2.7 and 4.6) enters a new age, during which ancient windmill turns into modern wind turbines (Sect. 8.1). This transition is characterised by the increasing demand for electric energy, by the invention of the dynamo and, above all, by two motivations that will henceforth influence the use of wind energy: the political willingness and economical advantages. It was by no accident that from the mid-twentieth century, this subject followed different paths in different countries. The second subject dealt with is the role of the wind in the transport and diffusion of minute materials. Three issues stand out. The first one, which mankind noticed since ancient times (Sect. 4.1), is the diffusion of pollutants (Sect. 8.2) introduced in the air during combustion processes; it involves severe risks for the health of mankind and, more in general, of the animal and plant worlds; it also affects the preservation of the built. The second issue is soil erosion and transport (Sect. 8.3), able to change © Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_8

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the geomorphological features of nature and to make soil dry up, with devastating consequences for agriculture and for those living on this resource; the accumulation of soil shifted by the wind also has adverse effects on road and rail traffic. The third issue regards snow drift (Sect. 8.4); like soil transport, it causes severe problems for road and rail traffic; it can also paralyse airports as well as air traffic, cause disruption to any activity and subject building roofs to severe risks. In the first half of the nineteenth century, the consequences of the transport and accumulation of soil and snow led to developing large-scale research about natural and artificial barriers. Their role went beyond such phenomena and became especially crucial to protect crops (Sect. 8.5). The primary effect of the barriers is the reduction of the wind speed; their secondary effect, i.e. the alteration of the local microclimate according to trends favourable to crop growth, is, however, essential. The last paragraph (Sect. 8.6) continues the description of the efforts mankind carried out since ancient times to build settlements and dwellings taking inspiration from bioclimatic principles (Sect. 2.8). At first, they were dictated by intuition and experience. Afterwards, around the mid-nineteenth century, they took increasingly inspiration from field measurements and wind tunnel tests. City planning and architecture came into contact and interacted with environmental and climatic issues, reassessed from a scientific viewpoint. The common denominators of these subjects are their territorial scale and the scientific ground for their treatment: wind measurement instruments (Sects. 6.1 and 6.2), micrometeorology (Sects. 6.5 and 6.7) climatology (Sect. 6.8), aerodynamics (Sect. 7.1) and wind tunnels (Sect. 7.2).

8.1 From Windmills to Wind Turbines With the advent of the Industrial Revolution and the steam engine, Europe gradually lost interest in wind energy. It even seems that in this continent the golden age of windmills was approaching its end. The situation was the opposite in the USA, where the use of windmills to pump underground water aroused widespread interest that increased their production [1]. The origin of this trend has been historically set in 1854, when Daniel Halladay (1826–1916), a New England engineer, obtained the first American patent for a windmill featuring highly autonomous operation: it automatically oriented itself in the wind direction; the speed of the rotor was almost constant, thanks to a device that changed blade pitch in relation to the wind speed and protected the blades during storms (Fig. 8.1). In 1857, Halladay founded the U.S. Wind Engine & Pump Company, the first American firm for the production of wind machines to pump water from the underground. Their success increased in 1860, when a rich Texan wrote on the Scientific American Magazine: “The great want of Texas is water. (…) There is a million dollars lying waiting for the first man who will bring us a windmill strong, durable, and controllable”. This announcement unleashed the creativity of the American builders and inventors, who designed and built various types of machines.

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Fig. 8.1 Halladay’s windmill (1854)

What in Europe represented a brake for wind energy, in the USA was an incentive to its use. With the proliferation of railways, Americans migrated west after 1865. Steam locomotives used coal and needed at least 2000 gallons of water every 20 miles. Railway builders set up windmills along their route, creating an indissoluble tie between railroads and wind rotors (Fig. 8.2a). The latter also became common in farms (Fig. 8.2b), both to provide water and for other uses, and in gold mines, where the salt used to preserve meat and to treat ore was extracted from the water pumped from underground. Taking their cue from the European evolution (Sect. 4.6), the American windmills of the 1860s used annular rotors with six or eight blades and were 2–5 m in diameter; smaller rotors were fitted with wooden blades, larger ones with iron frames covered by cloth sails; the towers were usually made of wood. The use of these materials

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Fig. 8.2 Windmills [1]: a railroad depot in Laramie, Wyoming; b Nebraska Farm

made construction and repair simpler. As early as the late 1870s, the use of iron and steel for both blades and towers became increasingly common. The turning point took place in the early 1880s, when Thomas Osborn Perry (1847–1927), an engineer of the Daniel Halladay’s U.S. Wind Engine and Pump Company, carried out the first American scientific studies about windmills [2]. He fitted a whirling arm1 (Sect. 7.1), more advanced than Smeaton’s one (Sects. 4.2 and 4.6), in a large room. By means of this between 1 June 1882 and 15 September 1883, he carried out over 5000 tests on models of wheels with blades of varying shape, size and pitch (Fig. 8.3a); he also examined several combinations of wind speed and rotor revolving speed. Perry strove after a configuration allowing the mill to efficiently operate in both low and high wind speeds: the best solution was to use suitably inclined cambered metal blades that guaranteed higher efficiency than the flat wooden blades adopted until then. He submitted this proposal to the board of directors of his company, which rejected it. He then contacted La Verne Noyes (1849–1919), and with him, he founded a new company, Aermotor Windmill Company,2 which produced Perry’s windmill (Fig. 8.3b). Because of its scientific origin, it was called the “mathematical windmill”. As a consequence, America saw the foundation of many companies manufacturing windmills; 77 companies, united by the proliferation of interests and objectives, were active in 1887. In 1893, during the World’s Columbian Exhibition, windmills represented a major attraction (Fig. 8.4a). In 1904, the Kansas City Star wrote: “The prairie land is fairly alive with them. (…) The windmill has taken the place of the old town pump, and no Western town is complete in its public comforts without a mill supplying water to man and beast by the energy of the wind”.

1 Many

references mistakenly credit Perry with the construction of a wind tunnel, mentioning the plant in this paragraph as an “enclosed wind tunnel”. 2 Thanks to Perry’s mathematical windmill, Aermotor became the leading American windmill manufacturing company. From 1888, a year when it sold 48 windmills, in 1900, it arrived to sell 800,000 windmills, i.e. 50% of the American production in this sector.

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Fig. 8.3 a Wheels tested by Perry on the whirling arm [2]; b mathematical mill [1]

Fig. 8.4 a Chicago Exhibition, 1893 [1]; b wind turbine by Brush [1]

While America experienced this moment of excitement for windmills, an event changed their history in Europe. In 1871, a Belgian, Zènobe-Théophile Gramme (1826–1901), invented the dynamo, a machine converting the mechanical work of rotors into continuous electric current. It was the start of the process that transformed the ancient windmill into the modern wind turbine [1, 3, 4]. It restored enthusiasm and trust in wind energy in Europe, and forced the USA to face new prospects and problems.

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Fig. 8.5 La Cour: a experimental windmill (1891); b participants to training course (1904)

In 1887, a French, Duc de La Peltrie, built the first European windmill generating electric energy. In 1888, Charles Francis Brush (1849–1929) built the first American windmill generating electric energy in Cleveland, Ohio (Fig. 8.4b). Brush set up a large room in its basement, where he placed 408 battery cells, similar to glass jars and filled with chemical substances, to store the generated electric energy. Through this device, he produced the energy required by the 350 light fixtures of his villa. The cost and size of the equipment were huge and the invention did not arouse interest in the USA. Great interest, conversely, was aroused by Poul La Cour (1846–1908), a prominent Danish physicist and inventor who, fascinated by the unsuccessful Dutch attempts to obtain electric energy from wind energy, understood that the reason lied in the poor aerodynamic efficiency of windmills and in the way energy was stored. In 1891, thanks to funding from the Danish government, La Cour founded a centre for studying windmills in Askov. He simultaneously built an experimental windmill (Fig. 8.5a) that drove an electric energy generator: it produced a constant amount of energy through a blade speed differential governor; energy was accumulated by electrolysis, making electricity pass through water. La Cour’s researches obtained great publicity in 1894, when the Norwegian explorer Fridtjof Nansen (1861–1930) undertook an expedition in the Arctic Ocean aimed at finding the exact position of the North Pole; during the long winter night, his ship was imprisoned by ice and Nansen used the electricity produced by a small windmill coupled to a generator of the type invented by La Cour. This result and its echoes prompted La Cour to carry out more detailed researches in the aerodynamics

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field. The latter were performed in collaboration with Vogt and Irminger and used two new wind tunnels (Sect. 7.2) designed and built in 1896 to improve the aerodynamic efficiency of Danish windmills and to increase energy production. Thanks to wind tunnel tests, La Cour achieved a result, still accepted nowadays, which overturned the knowledge of that age: for the same blade area, energy production was highest if the number of blades was small, if their pitch was minimal and if the rotor speed was high. La Cour later improved his tests3 and confirmed Perry’s discovery: the blades with cambered cross-section were more efficient than the flat ones. La Cour also built new experimental windmills, by means of which he proved the correctness of his measurements and the advancements that could be obtained through the new concepts. Building on the momentum of his results, La Cour proposed his new technology to the Danish government. Acknowledging the permanent national shortage of energy resources and fossil fuels, the Danish government accepted this proposal and in 1903 founded the Danish Wind Electricity Company that promoted electric energy generation through windmills. A relentless process thus came into being. In 1904, La Cour ran the first training course for agricultural electricians (Fig. 8.5b) in Askov. In the same year, he published the first issue of “Tidsskrift for vind ellektrisitet” (Journal of Wind Electricity), of which he became the publisher and main author [5]. In 1905, he coupled two dynamos, rated at 9 KW each, to a four-blade rotor and built a wind generator that produced energy and became the prototype used to formulate the first theories about this subject. In 1908, Denmark had 72 wind turbines designed by La Cour, with power ratings up to 30 KW. In 1910, their number increased to several hundreds. The advent of the First World War and the lack of fossil fuels gave an additional stimulus to wind energy production. Taking advantage of the advancements in aeronautics (Sect. 7.4), many French (Gustav Eiffel and Adrian Constantin), German (Ludwig Prandtl and Albert Betz), British (Hermann Glauert) and Russian [Nikolai Joukovski and Valer’yan Ivanovich Krassovsky (1907–1993)] scientists carried out increasingly accurate wind tunnel tests and developed the first aerodynamic theories about blades and the efficiency of wind turbines. Albert Betz (1885–1968) proved that a wind turbine could not convert into mechanical energy more than 16/27 (59.3%) of the wind velocity energy. A book he wrote in 1926 [6] provided a valuable state of the art about this subject. In this period, Europe did not actually show much interest in extracting electricity from the wind. Only Denmark showed how it understood the value of this technology as an alternative source and an integration of traditional energy sources. It then developed the production of wind turbines that, at the end of the war, covered approximately one quarter of its overall national energy production. The situation was different in America, especially in great western plains, where electric energy was almost unknown up to the 1920s. In this period, the invention of 3 In

1899, La Cour noticed that the speed was not uniform in the cross-section of his tunnels: at the centre, it was two times the speed near the walls. He then repeated his measurements on small-size models, in the tunnel portion where the flow speed was approximately constant.

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the radio fascinated American families; its use, however, required electricity, which did not reach most farms. The farmers then tried to generate it by windmills hitherto used to pump water, but the blade rotated too slowly to generate current. They then replaced the old rotors with airplane propellers, producing current by means of car generators and accumulating it in storage batteries. This crude technique aroused the interest of many inventors, who devoted themselves to its development. The most enterprising among them founded the first companies manufacturing wind turbines. Marcellus Jacobs (1903–1985), one of the first to follow this path in the early 1920s, designed a three-blade wood propeller coupled to a generator he invented and sold to many farms in Montana. His product was successful, and, in the mid-1920s, he founded the Jacobs Wind Electric Company with his brother Joseph. In 1931, this company moved to Minneapolis, Minnesota, where it built a modern plant for manufacturing wind turbines suited to the needs of the most isolated farms and of settlements in remote areas. In a short time, the Jacobs Company produced and sold thousands of machines capable of meeting the energy requirements of the radio, of the lighting and of all the electric tools used in a farm. They adopted an efficient control system that adjusted blade pitch to protect them from the strongest winds; this also meant they did require almost no maintenance.4 Actually, the situation of American wind energy was more complex and articulate. Because of the 1929 stock market crash, thousands of companies went bankrupt and millions of people lost their jobs. President Franklin Delano Roosevelt (1882–1945) launched a reconstruction plan to bring the USA out of The Great Depression. It provided jobs for unemployed people by several public works projects. One of the most important ones, started in 1935 through the foundation of the Rural Electrification Administration (REA), was aimed at electrifying rural areas bringing power to the most remote farms, with free connection and minimal costs. It did not go as far as decreeing the end for small-size wind turbines, but put a brake on their development. While this socially significant process took place, an American engineer, Palmer Cosslett Putnam (1910–1986), persuaded himself that the wind was an outstanding tool for large-scale electric energy generation; the subject, however, required exhaustive studies. In 1939, he presented the results of his studies to the Morgan Smith Company in York, Pennsylvania. The company was so impressed to set up a team formed by experts in electricity, aerodynamics, engineering and meteorology, including Karman as well as many M.I.T. professors; this group came to the conclusion that only large-size machines could make the cost of wind-generated energy competitive. The design and construction of the “Smith–Putnam wind turbine”, the largest and most powerful wind turbine ever built, stemmed from there. First, topographical tests were carried out in the wind tunnel of the Guggenheim Aeronautical Institute in Akron, Ohio, under the supervision of Karman; they reproduced Mount Washington (1917 m), Mount Glastenbury (1170 m), East Mountain (671 m) and Pound Mountain (429 m) by means of a model 1.2 m in diameter, in a 1:5280 geometric scale. The selection of the most suitable site was carried out 4 In

1933, Richard Evelyn Byrd (1888–1957) installed a Jacobs machine in Little Antartica, at the top of a radio tower 21 m high. In 1955, his son found it still working and in excellent condition.

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Fig. 8.6 a Anemometric mast on Grandpa’s Knob [7]; b Smith–Putnam turbine construction [7]

through many field measurements. A 56-m-high antenna, shaped like a Christmas tree [7] (Fig. 8.6a), was erected on a hill called Grandpa’s Knob near Rutland, Vermont; it was fitted with many anemometers, heated to prevent ice formation, which provided an exhaustive view of the horizontal and vertical wind configuration. The turbine (Fig. 8.6b), completed in 1941, consisted of a tower 34 m high and of a rotor 57 m in diameter; the latter was formed by two stainless steel blades with NACA 4418 wing profile. Blade pitch was controlled by an automatic device guaranteeing their uniform rotation at 28.7 radians per minute for wind speeds ranging from 13 to 32 m/s; at higher wind speeds, the machine stopped. The rotor drove an asynchronous generator with a power rating equal to 1250 KW. The machine steadily worked for 18 months, supplying power to the Central Vermont Public Service Corporation. In 1943, the wind turbine suffered a local collapse and the plant was closed for two years. Under such conditions, the blades were subjected to strong oscillations due to wind actions, which caused widespread damage (Fig. 8.7a). Despite the advice of technicians that insisted on the need to repair it, the turbine was restarted in 1945 without performing any work. Three weeks later, a blade broke and fell down to the ground (Fig. 8.7b). The company did not have enough funds to repair the machine and resume its operation; the plant was definitively closed. Despite this disaster, the construction of the Smith–Putnam turbine had significant effects. Thanks to the accrued experience, Putnam wrote the first book that fully and

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Fig. 8.7 Smith–Putnam turbine: a damaged blade [1]; b collapse (26 March 1945) [7]

systematically dealt with the production of wind energy; it was published in 1948 [7] and still remains a reference text today. Another Federal Power Commission engineer, Percy Holbrook Thomas, examined the information collected during the turbine service and analysed the issue of wind potential as an energy source. The results were contained in four reports, published between 1945 and 1954 [8–11]. Thomas started his researches by studying which wind was most suitable to produce energy. He selected 31 years of measurements collected by the U.S. Weather Bureau at 50 weather stations. He discovered that wind was a persisting phenomenon: the monthly average was seldom less than 50% of the yearly average, and it often ranged between 1 and 10% of the daily average; the yearly average was seldom lower than 10–15% of the average over a 30-year period. Thomas designed two large-size machines, rated at 6500 and 7500 KW; the former was recognisable through its tower 145 m high and its two rotors, each one 61 m in diameter. During these projects, Thomas understood that the most effective way to produce wind energy was to connect the wind turbine to an existing electric grid. It became persuaded, in particular, that in this way, it was possible to extract from wind 20% of the country energy requirement, and in 1945, he recommended to start a research programme with such goal. The idea was accepted by the Federal Power Commission and by the Department of Interior, which funded the project. In 1951, this project disappeared when the House of Representatives diverted its appropriation of funds to the war in Korea. Actually, this event, so negative for wind energy, was not an isolated case. In the 1950s, the American government launched the project to produce nuclear energy. In the 1960s, the REA set up a programme to provide farms with electricity at low cost. Many American companies in the wind turbine manufacturing sector replied to these political decisions by reconverting themselves to other activities. The situation was similar in Europe and in other countries worldwide. Social contingencies and political decisions played an increasingly important role in energy exploitation technologies. The evolution and diffusion of wind turbines could not therefore leave this situation aside and then required an analysis aimed at individual

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Fig. 8.8 a Baden-Baden ship (1925) [7]; b Madaras’ experimental rotor (1933) [7]

countries [4, 12–15]. This goes beyond the objectives of this paragraph, which ends providing the essential elements of the most important European accomplishments. Three tendencies arose [7]. The first, inspired by Flettner and Madaras, was based on Magnus effect. The second, accountable to Savonius, consisted of using S-shaped, vertical axis rotors. The third, from which large-size turbines with high-speed propulsors derived in the 1950s [12], included Kumme and Bilau in Germany, Darrieus in France and the Central Wind Energy Institute in Moscow among its precursors. The Magnus effect (Sect. 3.6) was first used as an energy source by Anton Flettner (1885–1961), a German aeronautical engineer and inventor who designed and built a ship that tapped wind by means of a pair of vertical axis revolving cylinders; the ship steered making use of the reverse rotation of cylinders. The vessel, called BadenBaden (Fig. 8.8a), was inaugurated in 1925 for an Atlantic crossing from Hamburg to New York 5 [12]. In 1926, Flettner used this principle to build a windmill with four blades consisting of as many tapered revolving cylinders, driven by electric motors; each cylinder was 5 m long with external diameter of 90 cm and internal diameter of 70 cm; the tower was 33 m high.6 Between 1929 and 1934, Julius Madaras, an inventor of Hungarian descent, studied a new use of the Magnus effect. He designed a circular track with 460 m in diameter, over which a 18-car train ran; every car was fitted with a vertical axis revolving cylinder, 27 m high and 6.8 m in diameter, driven by an electric motor; if the component of the orthogonal wind was strong enough, the lifting action moved the cars along the track. The produced power, estimated in 18 MW (with the vehicles moving at 8.9 m/s in a 13 m/s wind), was extracted by electric generators applied to the wheel axles. The system was never built because of its excessive losses and of 5 After

six years of experimental operation, Baden-Baden was destroyed by a storm in 1931. use of Magnus effect as a sailing propulsion device was criticised by Einstein in an article on Science in 1936. An equally negative opinion was formulated by Karman. On the other hand, Marco Todeschini (1899–1988), a controversial Italian scientist, affirmed that Magnus effect was one of the most powerful dynamic phenomena of the nature, no less than the element propelling universe (Teoria delle apparenze (1949) and Psicobiofisica (1978)).

6 The

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Fig. 8.9 Savonius turbines [7]

the difficulty of placing it on hills where the wind was stronger. In 1933, Madaras put a rotor into service near West Burlington, New Jersey; it was fitted with a single revolving cylinder (Fig. 8.8b): the results were not encouraging. In 1922, the Finnish engineer Sigurd Johannes Savonius (1884–1931) invented a vertical axis turbine now known as Savonius turbine or rotor [16]. In its most elementary form, it consisted of the translation of the two parts of a cylinder with circular cross-section, cut in half in the plane of its axis (Fig. 8.9a); each cylinder half was subjected to a pressure on its front face and to a suction on the back face; since the resultants of such actions were different, the rotor was subjected to a twisting moment that made it rotate around its axis. Another configuration consisted of a set of two sections with concave cross-section, A and B (Fig. 8.9b), where A was propelled by the flow coming from B. More complex shapes were created by setting various parts of a cylindrical body around a vertical axis.7 The most typical element of the Savonius turbine was its operation, based on drag rather than on lift. It provided sufficiently satisfying performance, especially for small plants. The production of large-size wind turbines in Europe was started in 1920 by Rolf Kumme in Germany. He built a wind turbine fitted with six blades connected by stays, which was not so profitable from the economic viewpoint [7]. In 1925, Kurt Bilau (1872–1941), at the Göttingen Institute of Aerodynamics, developed a turbine, called “aerodynamo”, which generated twice the power than other contemporary machines. Its four blades, consisting of a pair of airplane propellers, took advantage of the suction downwind the blades. The first prototype was a reinforced concrete, cable-stayed tower 12 m high; each blade was 7.6 m long. The tower top, which supported the rotor and the dynamo, was mounted on ball supports; thanks to the

7 The

first sample of a machine similar to the Savonius’ one dates back to the eighteenth century; it was a horizontal axis type conceived by Johann Ernst Elias Bessler (1680–1745), a German known for his studies of machines for producing perpetual motion. Bessler died while he was building this machine near Furstenburg, in Germany, in 1745. The machine then remained unfinished.

8.1 From Windmills to Wind Turbines

571

Fig. 8.10 a Darrieus rotor (1931 patent); b H-Darrieus rotor

latter, the blades automatically oriented themselves in the wind direction. The dinamo was connected to batteries that stored the generated energy. In 1927, a French aeronautical engineer, Georges Jean Marie Darrieus (1888–1979), patented in France a vertical axis turbine that operated regardless the wind direction. It included the machine shaped like a egg beater (Fig. 8.10a), now known as Darrieus rotor, and giromill or H-Darrieus rotor (Fig. 8.10b), a machine equipped with wing profile vertical blades connected to the central shaft by horizontal supports. Their operation was similar: when the blades rotated, a relative flow between them and the air was originated; its speed was the vectorial composition of the blade and wind speeds; this was equivalent to the motion of a wing profile with a small angle of attack. A lifting force, skewed with respect to the rotor axis, was generated on every blade; it determined a twisting moment that fed the initial motion. The Darrieus rotor, therefore, had to be started after every shutdown; on the other hand, it did not require being oriented in the wind direction; the current generator and the control systems could be located at the ground level near the rotor shaft. Its first implementation was initiated by the Compagnie Electro-Mécanique; in 1929, it erected a Darrieus rotor in Bourget, France, consisting of a tower 20 m high and of two blades 20 m in diameter.8 In 1931, after two years of measurements, the Central Wind Power Institute of Moscow built a pilot plant for the production of wind energy in Balaklava, near Yalta, on the Black Sea. It made use of a 100 KW machine (Fig. 8.11a); the tower was 23 m high; the rotor consisted of two blades, 30.5 m in diameter. The machine was characterised by a diagonal lattice element that absorbed the wind force: the base ran over a circular rail to follow the rotor that oriented itself in the wind direction. In 1933, Hermann Honnef (1878–1961) designed a turbine for producing 50 MW in Berlin. The design took advantage from the wind increase with height: the tower was 305 m high and supported five rotors, each one of them 40 m in diameter, by 8 The

Darrieus rotor, widely criticised after the first prototypes and almost fallen into disuse, has recently become the subject of remarkable development.

572

8 Wind, Environment and Territory

Fig. 8.11 a Balaclava turbine [13]; b Honnef’s turbine (1933) [7]; c Gedser turbine [13]

means of a light frame (Fig. 8.11b). The project was clearly unrealistic; it predicted, however, the development of increasingly larger and powerful machines. Between 1941 and 1942, the Danish company F. L. Smidth built two machines equipped with blades using wing profiles drawing inspiration from aerodynamic concepts; many consider them as the precursors of modern wind turbines. After the war, the Danish Johannes Juul (1887–1969), a student of the Askov School, coupled the blades to an asynchronous motor. His first machine (Fig. 8.11c) was built by the Gedser company in 1957 and remained operational until 1968.9 The tower was 26 m high, the rotor was 24 m in diameter, and the generator was put at the tower top. The machine had a power rating 200 KW with a wind speed of 15 m/s; on the average, it produced 400,000 KWh per year. Between the late 1940s and the early 1950s, the British understood the importance of detailed information about the wind to select the sites most suited to host turbines. They collected the data from 100 anemometric stations spread on their territory, obtaining a unique description of the windiness of the country. In 1950, the North Scotland Hydro-Electric Board placed an order with the John Brown Company for the construction of a 100 KW turbine on Costa Head in the Orkney Islands; it started operating in 1955 (Fig. 8.12a). In the same period, the Enfield Cables company built in Saint Albans, Hertfordshire, an innovative machine designed by the French Jon Andreau (Fig. 8.12b). The tower was hollow and was 30 m high; likewise, the two blades—which made up a rotor 24 m in diameter—were also hollow. When the blades rotated, the centrifugal forces sucked air from the blade ends through the tower. A rotor driving an electricity generator was located at the base of the tower. The machine power rating was 100 KW. In 1957, the Czech engineer Ulrich Hütter (1910–1990) designed a turbine that was built in the early 1960s (Fig. 8.12c). It consisted of a cable-stayed tower and of a 9 The

Gedser turbine was stopped in 1968, when Denmark judged wind energy economically disadvantageous and turned to nuclear energy.

8.1 From Windmills to Wind Turbines

573

Fig. 8.12 a Capo Costa turbine [13]; b Enfield-Andreau turbine [4]; c Hütter’s turbine

pair of fibreglass blades put downwind the tower; the rotor was 35 m in diameter; the blade pitch was adjusted through an automatic control system that kept their revolving speed constant. The machine was efficient, since it developed 100 KW power with 8 m/s wind speed, much less than the speeds that produced similar amounts of power at that age. It also was very light and resistant to fatigue.

8.2 The Atmospheric Diffusion of Pollutants Air contamination due to gaseous substances from emission sources created by mankind is one of the main causes of atmospheric pollution. These substances are almost always harmful for the health and well-being of living creatures, corrode construction materials, reduce visibility and are often foul-smelling. Atmospheric pollution represents, since ancient times, one of the most concerning issues [17]. It was described by Seneca in ancient Rome and documented from the Middle Ages in the London area (Sect. 2.8); it relentlessly evolved during the Industrial Revolution and in the early twentieth century. The development of metropolitan areas and the growth of industrialisation, the combustion processes and treatments taking place in factories, in quarries, in mines, in agriculture, in the production of new energy sources and in transportation systems were all responsible for such evolution. The essential elements determining this phenomenon are, besides the properties of the polluting sources, the thermal stability regime and the wind [18–21]. In the troposphere, temperature decreases with height; its reference profile takes place under neutral conditions when air particles adiabatically rise and expand (Sect. 6.5). When the temperature decreases with height quicker than the reference profile, the air particles are in an unstable regime and tend to raise fast, also originat-

574

8 Wind, Environment and Territory

ing strong updrafts; this favours the dispersion of pollutants and their dilution at high altitude. When, conversely, the temperature decreases with height slower than the adiabatic profile or even increases until it causes temperature inversion, the air particles are in a stable regime and are restrained to lift, since they are cooler and heavier than those of the overhanging air; this favours the accumulation and stagnation of pollutants. In highly built-up areas, heat accumulation at ground level grows because of the emissions from vehicles, industrial plants and heating systems. The group effect of buildings prevents the wind to blow as in the open areas outside cities, limiting the recirculation and cooling of the air at ground level. In built-up areas, moreover, the ratio between the horizontal and vertical surfaces is smaller, preventing heat dissipation through irradiation. All these phenomena, as a whole, alter the local microclimate and favour the stagnation of pollutants. This reality, highlighted by Luke Howard (1772–1864) [22] and Emilien Renou (1815–1902) [23] in the nineteenth century (Sect. 4.1), was studied by Wilhelm Schmidt (1883–1936), between 1917 and 1930 [24–26], by fitting instruments on vehicles moving in cities. In 1937, Albert Kratzer (1908–1975) collected a state of the art and published the first scientific book on this subject [27], devoting a whole chapter to urban planning (Sect. 8.6); the second edition of the book, published in 1956 [28], provided a measure of the evolution of such studies. The “urban heat island” expression was first used in 1958 [29]. A large collection of data, as well as of case studies of great interest, were gathered thanks to these investigations [30]. Surveys carried out in London [31], Paris [32], Tokyo (Fig. 8.13) [33] and in various American cities [34] highlighted the increase in urban temperatures. Horst Dronia [35], collecting data worldwide, estimated an average temperature increase of 0.008 °C per year from 1871 to 1960. The heat difference between the city centre and the adjacent countryside was sharp by night but much less pronounced by day, especially with clear and sunny skies. Extreme temperature inversion phenomena in densely built-up areas caused dramatic events (Table 8.1) [17, 21, 30, 36–38]. The first severe pollution phenomenon documented in detail occurred in the Meuse River Valley, Belgium, in 1930; a thick smog bank fell on the valley between Lieges and Huy and remained there 5 days, causing 63 deaths and 6000 cases of disease. In October 1948, Donora, Pennsylvania, in the Monongahela Valley, was shrouded by the dirt of the houses and streets heated by air [39] (Fig. 8.14a): 21 people died and over 6000 residents, almost 50% of the city population, were affected by severe respiratory system ailments; many animals were killed. The most tragic event struck London in December 1952 [40]; the city was stifled by a pall of smog that hanged over it for 5 days (Fig. 8.14b): 4000 (12,000 according to some sources) people died, especially older individuals affected by respiratory and heart troubles. This event stimulated the first air purification interventions and the start of researches aimed at cataloguing past events and

8.2 The Atmospheric Diffusion of Pollutants

575

Fig. 8.13 Evolution of the yearly average temperature in Tokyo (1901–2000) [33]

Fig. 8.14 a Donora, Pennsylvania, 29 October 1948 [17]; b London, December 1952: daily death rate (dotted line) and SO2 concentration (solid line)

at formulating forecasting criteria [41]; the latter revealed that similar situations had already repeatedly struck London since 1873.10

10 In 1843, a committee to collect information about pollution was set up in London. From then on, the bills aimed at limiting noxious emissions came one after another. The first, launched in 1863, remained unapplied for many years. The first American law dealing with atmospheric pollution dates back to 1869 and was an ordnance of the city of Pittsburgh that was never enforced. Similar unused laws were issued in Cincinnati and Chicago in 1881. The first actually enforced law about pollution appeared in St Louis in 1893. In 1910, Massachusetts promulgated the first state law about pollution [17].

576

8 Wind, Environment and Territory

Table 8.1 Major catastrophes due to atmospheric pollution (1873–1962) Year

Period

Location

Dead

Diseased

1879

December

London, UK

270–700

?

1880

January–February

London, UK

700–1100

?

1892

December

London, UK

4000

?

1909

Fall

Glasgow and Edinburgh, Scotland

1000

?

1930

December

Meuse River Valley, Belgium

63

6000

1948

October

Donora, Pennsylvania, USA

21

5900

1948

November

London, UK

300

?

1952

December

London, UK

4000

?

1953

October

New Orleans, USA

2

200

1953

November

New York City, USA

250

?

1956

January

London, UK

480–100

?

1957

December

London, UK

300–800

?

1962

December

London, UK

340–700

?

The presence of wind alters the problem. It carries and scatters pollutants causing, depending on its direction, on the weather conditions and on the involved areas, beneficial or detrimental situations. The studies about the scattering of pollutants due to the wind started between 1915 and 1921. In 1915, Geoffrey Ingram Taylor (1886–1975) [42] generalised the heat propagation law in a solid medium (Eq. 3.30) (Sect. 3.7), developed by Fourier in 1822, to a turbulent flow (Eq. 6.24) (Sect. 6.5). In 1921, Taylor himself [43] extended the heat propagation to any property diffusible in a fluid, schematising turbulence as a stationary Gaussian random process. Taylor considered the fluid incompressible, assumed that its mean speed u was directed along x, and placed himself in a Lagrangian context to formulate the theorem (Eq. 6.33) thanks to which he would subsequently define the link between the Eulerian and Lagrangian views, expressed the variance of the x(t) displacement of a fluid particle as a function of the variance of the flow longitudinal speed u(t), being t the time. He linked the turbulent motion of the particle with a generic property diffused in the flow, e.g. temperature, content of smoke, dyes or other substances identifiable with the particle. On the basis of these tools, Taylor considered a particle emitted by a source in x = 0 for t = 0 and proved that if the time t elapsed from the emission of the particle was short, the standard deviation of its x displacement was proportional to t (Eq. 6.34); if t was long, the standard deviation of x was proportional to the square root of t (Eq. 6.35). He also noted that his results agreed with previous observations by Richardson and by Dobson about smoke emission: they observed that, near the source, the space containing the fumes was conical in shape; at greater distances, it became a paraboloid.

8.2 The Atmospheric Diffusion of Pollutants

577

In parallel with Taylor’s theoretical studies, the first measurements were also carried out. They were linked to the researches performed during the First World War about the propagation of explosive processes and the diffusion of toxic gases. Such activities received a boost by the British government that, in 1916, created the Royal Engineers Experimental Station, an experimental chemical warfare centre near Porton, in the Salisbury plain. After the war was ended, the government decided to continue these studies, entrusting them to civil scientists. The first experiment aimed at measuring the concentration of tracer elements introduced in the air was carried out in 1923. It consisted in the release of harmless fumes generated by candles and in the estimation of their concentration in the air by means of a physical–chemical technique devised by Scrase. It was the beginning of a series of tests carried out in Porton, which from then on were used to verify and calibrate the theoretical models of the atmospheric diffusion of pollutants. In 1923, Roberts [44] formulated the method that represented the sole alternative to the statistical theory for the whole first half of the twentieth century. Known as the gradient or source transfer method, it consisted in the solution of the equations introduced in 1855 by the German physiologist Adolf Eugen Fick (1829–1901). They described the concentration of the materials into which diffusion processes were taking place; in the monodimensional case11 : ∂χ ∂z

(8.1)

∂χ ∂ 2χ =K 2 ∂t ∂z

(8.2)

J = −K

where J is the diffusion flow, i.e. the amount of substance diffused through a unit surface in the unit time, χ is the substance concentration, i.e. the mass per unit volume, K is the diffusivity coefficient assumed as constant, and z is the co-ordinate in the direction of the diffusion. They are similar to Eqs. (3.29) and (3.30) introduced by Fourier in 1822 to describe heat propagation in solid media. Drawing inspiration from Taylor’s pioneering 1915 paper [42], Roberts generalised Eq. (8.2) to the case of diffusion in an isotropic turbulent flow. It assumed the form: ∂ 2χ ∂χ = KT 2 ∂t ∂z

(8.3)

where K T is the eddy diffusivity coefficient. Roberts himself [44] extended Eq. (8.3) to the turbulent, anisotropic and three-dimensional flows in the form:

11 Equation

(8.1) postulates that the diffusion took place from the high- to the low-concentration region, in a quantity proportional to the concentration gradient (from which the gradient transfer denomination was derived). Equation (8.2) is obtained by combining Eq. (8.1) with the continuity equation.

578

8 Wind, Environment and Territory

u

      ∂ ∂ ∂ ∂χ ∂χ ∂χ ∂χ = Kx + Ky + Kz ∂x ∂x ∂x ∂y ∂y ∂z ∂z

(8.4)

where u is the mean speed of the flow in the x-direction, and K x , K y and K z are the three eddy diffusivity coefficients (omitting, for the sake of simplicity, the T index) along the x-, y- and z-axes. With such premises, Roberts assumed that the surface of the ground coincided with the x, y plane that the z-axis was directed upwards, that the emissive source was on the ground and that u, K x , K y and K z did not depend on z. He associated the continuity equation to Eq. (8.4) and solved the set of the differential equations at the partial derivatives by imposing boundary conditions consistent with the properties of the examined sources. He then solved the problem in four cases concerning instantaneous and continuous sources over time, as well as punctiform (in x = y = z = 0) and linear (in x = z = 0, and then orthogonal to the wind direction) sources over space. In the case of the continuous punctiform source, the concentration in x, y, z was provided by:    u y2 z2 Q  exp − + χ(x, y, z)  4x K y Kz 4πx K y K z

(8.5)

where Q is the substance mass emitted by the source in the unit time; the distribution of the concentration is a Gaussian one along z. In the case of the continuous linear source, the concentration was:   q uz 2 χ(x, z)  √ exp − 4K z x 2πK z x

(8.6)

where q is the substance mass emitted by the source in the unit time per unit length; even in this case, the distribution of the concentration is a Gaussian one along z. The concentration, in accordance with the assigned boundary conditions, is infinite at the source and nil at infinite distance away from it. In the case of the punctiform source, the concentration in y = z = 0 decays with a trend proportional to x −1 . In the case of the linear source, the concentration in z = 0 decays with a trend proportional to x −1/2 . In both cases, at the distance x from the source, it assumes a Gaussian trend in both the horizontal (Fig. 8.15) and vertical plane. The assessment of the diffusion caused by multiple punctiform sources and by lines or continuous areas can be performed by means of sums or integrations of the results associated with the elementary solutions. In 1926, Lewis Fry Richardson (1881–1953) [45] studied the instantaneous emission of a particle cluster through a method referable to the gradient transfer. He praised the elegance of Taylor’s statistical theory, but maintained that it was more accurate to study the distance l between two particles rather than the position of each one of them. He then resumed Fick’s equations and, carrying out complex mathematical developments, came to the relationship:

8.2 The Atmospheric Diffusion of Pollutants

579

Fig. 8.15 Concentration as a function of the distance from the source [44]

  ∂p ∂q ∂ = 2K T ∂t ∂l ∂l

(8.7)

where p is the density function of the separation l between two particles at the time t, and K T is the Taylor’s eddy diffusivity coefficient (without mentioning Roberts’ contributions). Richardson measured and collected many data on diffusion problems. They regarded acetylene particles, cigarette smoke, balloons and ashes from volcano eruptions. The experiment Richardson carried out by releasing 10,000 balloons in the sky of London on a windy day is well known; every balloon carried a note that invited who found it to report the time and the location where the balloon had landed. Thanks to this information, he constructed a bilogarithmic scale diagram (Fig. 8.16a) through which he proved that K T is an increasing function of l described by the relationship: K T = 0.2 l 4/3

(8.8)

It is valid for values of l ranging from 1 m to 10 km.12 Richardson then replaced Eq. (8.8) into Eq. (8.7) and obtained the solution: 

4εt p(l, t) = A 9

−3/2



9l 2/3 exp − 4εt

 (8.9)

where A and ε are model parameters. Equation (8.9) is the Richardson’s non-Gaussian (pointed) density function, opposed to the Gaussian functions by Taylor and Roberts. Figure 8.16b shows some diagrams of Eq. (8.9): for t = 0, q(l) = δ(l), δ being the

12 Richardson

affirmed that Eq. (8.8) derived from uncertain data and that in the future, with new instruments, it would be remarkably improved.

580

8 Wind, Environment and Territory

Fig. 8.16 a K T as a function of l; b density functions of q(l, t) [45]

Dirac function; as t increases, the height of the peak in l = 0 decreases and the density function widens; as a consequence, the variance of l increases. Richardson also determined the statistical moments and proved that the variances of the separation l between two particles and of the pollutant concentration χ were both proportional to t 3 ; this result is known as the t 3 Richardson’s law. He also noticed that Dobson, Roberts and he himself previously proposed a law according to which the diffusion variance was proportional to t. Such law, on the other hand, had been obtained for small values of l; the t 3 law, conversely, was also valid for large values. In 1948, Henry Melson Stommel (1920–1992), an oceanographer, provided evidence of the correctness of the t 3 law observing some turnips floating in the water of a lake in Scotland [46]. Between 1932 [47] and 1934 [48], Oliver Graham Sutton (1903–1977) provided a fundamental contribution to the application of the statistical theory of turbulence to diffusion. He started from the consideration that the study of diffusion imposed a Lagrangian treatment to follow the motion of the diffused particles. Adopting Taylor’s Eq. (6.33) [43] and assuming that the diffused particles behaved like all of the other particles in the air, he expressed the variance of the distance travelled by particles in the direction x, y, z in the form: x/u t σ2x

=

x/u t RuL (ξ)dξdt;

2σu2 0

0

σ2y

=

RvL (ξ)dξdt;

2σv2 0

0

x/u t σ2z = 2σw2

RwL (ξ)dξdt 0

0

(8.10)

8.2 The Atmospheric Diffusion of Pollutants

581

where x is the distance from the source in the direction of the diffusion; u is the mean wind speed; σu , σv , and σw are the standard deviations of the three turbulence components u , v , and w ; RuL , RvL and RwL are the Lagrangian correlation coefficients of the u , v , and w fluctuations of a same particle at the times t and t + ξ; Sutton attributed them the form: n ν ; ν + ξσu2 n  ν L Rw (ξ) = ν + ξσw2 

RuL (ξ) =

 RvL (ξ) =

ν ν + ξσv2

n ; (8.11)

where ν is the kinematic viscosity of the air and n is a non-dimensional parameter. Replacing Eq. (8.11) into Eq. (8.10): σ2x =

1 2 1 1 C x (ut)2−n ; σ2y = C y2 (ut)2−n ; σ2z = C z2 (ut)2−n 2 2 2

(8.12)

where C x , C y and C z are generalised turbulent diffusion coefficients:  2 1−n σu 4νn (1 − n)(2 − n)u n u 2  2 1−n σv 4νn C y2 = n (1 − n)(2 − n)u u 2  2 1−n σw 4νn 2 Cz = n (1 − n)(2 − n)u u 2 C x2 =

(8.13a) (8.13b) (8.13c)

Applying the above equations, the concentrations of the substance diffused by a punctiform and by a linear continuous source result: 

 Q 1 z2 y2 χ(x, y, z)  exp − 2−n + 2 πC y C z ux 2−n x C y2 Cz 

 1 y2 z2 Q exp − + = (8.14) 2π σ y σz u 2 σ2y σ2z     q 1 z2 1 z2 q = (8.15) exp − exp − χ(x, z)  √ √ x 2−n C z2 2 σ2z πC z ux 1−n/2 2πσz u Equations (8.14) and (8.15) confirm that the distribution of the concentration is a Gaussian one along both y and z; moreover, they coincide with Eqs. (8.5) and (8.6) for n = 1 and: C x2 =

4K y 4K x 4K z ; C y2 = ; C z2 = u u u

(8.16)

582

8 Wind, Environment and Territory

Fig. 8.17 a Method of images [36]; b concentration along y = z = 0 of a chimney emission [88]

Sutton’s equations, being able to graduate n, are more general than Roberts’ equations. Sutton also noted how n assumed values from 0 to 1 and n = 1 corresponded to Einstein’s equation about Brownian motion (σ2 ∝ t). He also carried out several experiments, thanks to which he observed that n depended on thermal stratification; he recommended, on the other hand, using n = 0.25 (σ2 ∝ t 7/4 ). Subsequent studies proved that n = 0.25 in a neutral atmosphere; in an unstable one, n = 0 − 0.25; in a stable one, n = 0.25 − 1 [49]. Advanced expressions of Eq. (8.10) were provided by the French mathematician Marie-Joseph Kampé de Fériet (1893–1982) in 1939 [50]. In 1947, Sutton [51] rearranged his previous evaluations [47, 48] in the light of the results provided by measurements carried out in Porton from 1932 to 1938. Among many other results, Eqs. (8.14) and (8.15) were rewritten as: 

 1 z2 y2 2Q exp − 2−n + 2 χ(x, y, z)  πC y C z ux 2−n x C y2 Cz 

 1 y2 z2 Q exp − + = (8.17) π σ y σz u 2 σ2y σ2z     2q 1 z2 1 z2 2q = (8.18) exp − exp − χ(x, z)  √ √ x 2−n C z2 2 σ2z πC z ux 1−n/2 2πσz u where the 2 factor that multiplies Q and q takes account of the reflection properties of the ground. All the previous relationships dealt with ground-level sources. Most of them, however, were well above the ground, e.g. in chimneys. Sutton solved this problem in 1947 [52] by a technique known as the “method of images”. It assumed the existence of a second source below the ground, identical to the first one and specular to it (Fig. 8.17a). For every particle crossing the ground in one direction, another one would cross the ground in the opposite direction. The surface where this exchange takes place identifies the pollutant fallout zone. With this principle, Eq. (8.17) assumes the form:

8.2 The Atmospheric Diffusion of Pollutants

583



  1 (z − h)2 Q 1 y2 exp − χ(x, y, z) = exp − πC y C z ux 2−n x 2−n C y2 x 2−n C z2   1 (z + h)2 (8.19) + exp − 2−n x C z2 where h is the height of the source. For h = 0, Eq. (8.19) coincides with Eq. (8.17). For x = y = 0 and z = h, Eq. (8.19) gives an infinite concentration, like Eq. (8.17), for x = y = z = 0. For very large values of x/h, Eq. (8.19) coincides with Eq. (8.17). Figure 8.17b shows the concentration in y = z = 0. At the foot of the chimney, it is nil and initially it remains low; it then increases up to a relative maximum; finally, it tends to zero. The maximum value of the concentration at ground level and its position is given by: χm =

2QC z ; xm = πeuC y h 2



h Cz

2/(2−n) (8.20)

where e ∼ = 2, 72 is Euler number. This result highlighted, like Bosanquet and Pearson already observed in 1936 [53], that the maximum concentration at the ground level is inversely proportional to the square of the chimney height; increasing it is then advantageous for the people living near it. Under neutral thermal conditions (n ∼ = 0.25),the distance from the chimney where the maximum concentration occurs increased almost proportionally to h (xm ∝ h 1.14 ); in the presence of a temperature inversion (n ∼ = 1), it increased more quickly (xm ∝ h 2 ); in other words, the night inversion provides relief to the people living near the pollution source. Sutton observed that the above situation takes place when the temperature of the smoke and of the surrounding area is equal. Since smoke is usually hotter, it tends to raise with respect to what forecasted by the mathematical solution. This is equivalent to raise the chimney top and then to decrease the maximum concentration and to move the maximum concentration position away; this latter property is corroborated by the fact that the C y and C z parameters decrease with the height above the ground [52]. In 1949, Sutton himself [54] improved Eq. (8.13a–c) by replacing the kinematic viscosity with the term N + v ∼ = N , where N is a parameter of turbulent nature called kinematic macroviscosity or kinematic eddy viscosity. In the same year (1949), Phil E. Church [55] classified the vertical distribution of pollutants into three families linked to atmosphere stability (Fig. 8.18). They were indicated as looping under unstable conditions, coning in approximately neutral conditions and fanning under stable conditions. Two mixed forms also existed, called lofting, when the atmosphere was unstable at the top and stable at the bottom and fumigation in the opposite case. These conditions were first associated with the thermal gradient, then with the Richardson number and finally with the Obukhov length. Thanks also to this work, it became commonplace to consider the emission of pollutants from chimneys as a turbulence and stability indicator [56] (Fig. 8.19). Under conditions of moderate wind and clear sky, atmospheric stability evolves over

584

8 Wind, Environment and Territory

Fig. 8.18 Emission families [21]

the day: (A) when the sun is high, the temperature profile is superadiabatic, weather conditions are unstable, the atmosphere is turbulent, and the smoke is twisting; (B) at sunset, the temperature profile tendentially remains subadiabatic, the inversion phenomenon starts taking place, weather conditions near the ground become stable, and the smoke assumes the shape of a bulbous cone; (C) during the night, inversion is well developed, the atmosphere is very stable with no turbulence, and the smoke is threadlike and horizontal; (D) early in the morning, weather conditions become unstable again, the turbulence arises all over again and fumigation develops near the ground. In parallel with the formulation of the theoretical foundations of the subject, a vast experimental literature was developed: it was based on wind tunnel tests and full-scale experiments. The former started in the 1940s, the latter showed rapid development from the 1950s. The first wind tunnel tests about the diffusion of pollutants in the atmosphere were carried out by Sherlock and Stalker in the 1930s and were published in 1941 [57], without making provisions to properly simulate wind speed and temperature profiles. They regarded the fallout mechanisms of the fumes emitted by the chimneys of the Crawford Power Station in Chicago. The tests, carried out in the closed-circuit wind tunnel of the University of Michigan, used two models: the first one reproduced the whole complex in 1:300 scale (Fig. 8.20a), the second only the chimney in a small scale (Fig. 8.20b). The chimney emitted sulphuretted hydrogen. The ground was painted with a lead acetate mixture. When gas settled on the mixture, a reaction produced a dark brown colour. The tests were repeated varying the wind speed and direction; the speed and temperature of the emitted fumes were also varied. The results proved that the phenomenon was governed by the ratio between the wind speed and the emission speed of the fumes. Similar experiments were carried out to visualise the smoke plume due to the Riverside Power Station in Baltimora, with the

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Fig. 8.19 Evolution of temperature profile, stability regime, and chimney emission over a day with moderate wind and clear sky: a high sun; b sunset; c full night; d early morning

Fig. 8.20 Model of the Crawford Power Station in Chicago [57]: a full plant; b chimney model

aim of mitigating their interference with the airplanes landing and taking off from the nearby airport [58]. The first quantitative measurements of the pollutant diffusion in a wind tunnel were carried out to analyse the emissions from a chimney 77 m high in a built-up area in New York near the Brooklyn–Battery tunnel [59]. They made use of two models in 1/200 and 1/400 scale to study the concentration within a 150 m radius and were carried out varying the emission and the wind speed. Even in this case, no attempt was made to reproduce the atmospheric boundary layer. Towards the end of the Second World War and in the ensuing period, Kalinske, Jensen and Schadt [60, 61] and Rouse [62] carried out tests at the Iowa University to

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evaluate the concentration of the gases diffused by the wind following the explosion of a bomb in a Japanese urban area. The tests were carried out on an 1:72 model in a tunnel 2 m wide, 1.3 m high and 6 m long. The floor was covered with buildings to simulate the urban area; the gases were emitted from holes on the floor. The distribution of the concentration was measured and compared with the results of full-scale tests carried out in a Japanese village at the Dugway Proving Ground, Utah. The orders of magnitudes were in agreement. In the same period, the first European tests were carried out at the National Physical Laboratory in Teddington. The most famous ones regarded the emissions from the chimneys of thermoelectric power plants [63–65]. In most cases, the evaluation of the fume trajectories and dispersion was of the visual type, unsuited to provide probative results. In the 1950s, research activities at the American universities prevailed. In 1950, at the Colorado State University, Cermak [66] built a wind tunnel 2.7 m wide and high, and 7.9 m long, in which he developed a turbulent boundary layer to simulate the evaporation from Hefner Lake; the tests were carried out on an 1:2000 scale model. Between 1952 and 1954, Strom and Halitsky [67] studied the diffusion of pollutants building the first wind tunnel capable of simulating turbulent boundary layers with any thermal stratification at the New York University. The tunnel, 2.1 m wide, 1.1 m high and 9.2 m long, was equipped with elements that heated the flow and with screens near its mouth to adapt the profile. They thus brought to their conclusion the pioneering researches carried out by Prandtl and Reichardt in 1934 [68]. The turning point occurred in 1958, when Cermak built the first wind tunnel with a truly developed boundary layer [69] (Fig. 7.36) (Sect. 7.3) at the Fluid Dynamics and Diffusion Laboratory of the Colorado State University. It was used to perform diffusion tests regarding public buildings, complex terrains, coastal sites, valleys, islands and woods. The first tests on the infiltration of pollution into buildings and on the pollution in urban canyons were also carried out there. In the same period, during the studies on the model law (Sect. 7.3), Jensen and Franck [70] carried out tests about the dispersion of fumes from chimneys. The emission was produced through a Venturi tube, and the plumes were subsequently photographed (Fig. 8.21a). The tests were carried out by changing the shape of the emission outlet, the fume emission speed, the ground roughness and the turbulence: the results proved that the plume increased its size when passing from low to high turbulence. Other tests were carried out on the fallout of fumes and their concentration near houses in the wake of isolated chimneys. Finally, in 1960, the Tuborg Brewery applied to Copenhagen laboratories to measure the effects of the emission of its own fumes. Since the tunnel was being used by Jensen for testing the model law, a new and larger tunnel, with 1.15 × 1.15 m cross-section, was built in Tuborg to perform 1:500 scale tests (Fig. 8.21b) [71]. It was one of the first examples of wind tunnels just built for one experiment. Full-scale tests used three techniques [21]: optical tracking, the observation of the trajectories of marked particles and the measurement of the concentration of tracer elements introduced into the air.

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587

Fig. 8.21 Dispersion of fumes: a from a chimney [70]; b from the Tuborg Brewery [71]

Optical tracking methods were the simplest and cheapest. They consisted in taking pictures of the smoke emission and tracing its contours. The average emission status was identified by pictures with longer exposure times or by overlaying multiple instantaneous images [44, 47, 72]. The observation of the trajectories of marked particles represents the perfect technique. It was, however, difficult to select tracers suited to Lagrangian observations. Soap bubbles and fluff were used for short-term observations; long-term observations were carried out by constant height balloons [73]. The measurement of the concentration of tracer elements introduced into the air made use of physical and chemical techniques. After the tests carried out in Porton since 1923, similar experiments were carried out in Cardington in 1931, using a tower downwind a transversal line of smoke generators. It was concluded that effective results could only be achieved through toxic fumes. The situation changed in the 1950s, thanks to the use of fluorescent tracer particles [74] and of advanced air sampling techniques [75]. These technological advancements originated new experiments carried out, like the previous ones, through sources at ground level. The most famous were performed between 1954 and 1956 by the M.I.T. near the Round Hill Field Station. Similar tests were carried out in 1956 within the Prairie Grass project in O’Neill, Nebraska; they used sulphur dioxide as a tracer; new instruments were also used to measure the lateral and vertical fluctuations of the wind speed and to correlate the concentration of pollutants with the statistical properties of turbulence [76, 77]. The first experiments about the dispersion from elevated sources, such as chimneys, were made in the same period. In 1957, Hay and Frank Pasquill (1914–1994) [78] carried out measurements using lycopodium spores; in 1958, Hilst and Simpson [79] used fluorescent pigments; in 1961, Islitzer [80] performed the first measurements of the pollutant concentration at ground level. These tests, as a whole, provided an exhaustive picture of the diffusion patterns. Figure 8.22a shows the plan distribution of the concentration of a pollutant emit-

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Fig. 8.22 Pollution concentration from a ground source [21]: plan (a) and height (b) distribution

ted by a continuous punctiform source at ground level, highlighting the difference between the average and instantaneous distribution; the instantaneous distribution (with sampling period shorter than or equal to 1 s) randomly evolved on space and time, with a narrow and pointed shape; the average distribution (over intervals ranging from a few minutes to an hour) enveloped instantaneous distributions, and its shape was more scattered. The vertical distribution of the concentration highlights a less clear difference between the average and the instantaneous distributions and the importance of the boundary represented by the ground (Fig. 8.22b). The essential role of temperature and gravity came to light. The diffusion can be characterised by significant ascents, in the case of hot gases emitted by factory chimneys, or by quick fallouts, in case of large and heavy particles. The ascent of hot gases emitted by factories and chimneys is due to the buoyant force governed by the laws of thermodynamics [19, 20]. Some observations are reported in [81–83]. The deposition of heavy particles can occur through three mechanisms: particle sedimentation, ground retention through stagnation and absorption processes, and the fall of rain and other substances. Sedimentation experiences for particles with freefall speed higher than the usual vertical turbulence speed, governed by gravitational deposition, were reported in [84–86]. The ground retention of particles with low deposition speed in comparison with the vertical turbulence speed was studied in [87]. Raindrops impacting on suspended particles and carrying them to the ground were considered in [75]. In parallel, theories more consistent with the physics of the phenomenon were developed thanks to these measurements and observations. Sutton provided a state of the art about this subject in his 1953 book, Micrometeorology [88], which is still a milestone. He discussed the new models of the diffusion coefficients in relation to the height above the ground, taking into account the atmospheric stability and the gravitational force. In the same book, Sutton reworked the measurements carried out in Porton between 1923 and 1924, generalising the concentration transversal distribution model by the relationship:   χ(y) = χ0y exp −ay r

(8.21)

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589

where r = 2 identifies Eq. (8.21) with the Gaussian model. A series of new tests carried out in Porton in 1959, using fluorescent fumes and lycopodium spores, showed that r approximately changed from 1.5 to 2.5; the use of the Gaussian model, therefore, represented a reasonable approximation. Similar studies were carried out by Elliott [89] in 1961, reprocessing the measurements from Porton (1923), from Cardington (1931) and from the Prairie Grass project (1956). They led to the following generalised model of the concentration vertical distribution:   χ(z) = χ0z exp −bz s

(8.22)

Unlike transversal distribution, s assumed values from 1.15 to 1.5; thus, the exponential distribution (s = 1) appeared more suited than the Gaussian one (s = 2). Other measurements and interpretations proved that s ≈ 1 in unstable atmosphere, s ≈ 1.35 in neutral atmosphere, s ≈ 2 in very stable conditions. In the same period, the lack of data suited to adequately provide the σy and σz parameters in Eqs. (8.13a–c)–(8.15) and in the subsequent models implementing Eqs. (8.21) and (8.22) became clear. This dramatically appeared in 1957, following an accident that caused the release of radioactive materials from the Windscale reactor in Cumbria [90, 91]. The British Meteorological Office, consulted to provide such parameters, relied on the procedure published by Pasquill [92] in 1961. Pasquill considered a continuous punctiform source at ground level (x = y = z = 0), assumed that the mean wind speed u did not depend on the height z and the concentration distribution was Gaussian both transversally and vertically; he expressed this concentration at the ground level (y = z = 0) as: χ0 =

γQ uxθδ

(8.23)

where γ is a scale parameter, x is the distance from the source, θ is the angle in the x, y plane within with the concentration diffuses up to 1/10 of the maximum χ0 along the centre line; δ is the height at which the concentration in the x, z is equal to 1/10 of the one on the ground. The laws expressing θ and δ as a function of x, assigned by diagrams (Fig. 8.23), depend on the atmospheric stratification. Pasquill identified six classes, indicated by A–F, destined to become a cornerstone of micrometeorology. A, B, and C corresponded to unstable regimes, D to the neutral regime, E, F to stable regimes (Table 8.2). Pasquill also provided a method to extend the treatment to the case of a source raised above the ground, as well as various calculation examples. In the same year (1961), Frank A. Gifford [93] applied the Pasquill’s model as well as some of his results [94, 95] to express δ and θ as a function of x, σy and σz :   2.15 σ y θ = (8.24) δ = 2.15 σz ; tg 2 x

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Fig. 8.23 Horizontal angle and height of fumes as a function of their distance from the source [92]

The above relationships, applied against Pasquill’s diagrams (Fig. 8.23), originated two new diagrams, known as Pasquill-Gifford model, which provided the horizontal and vertical dispersion as a function of the distance from the source (Fig. 8.24). In parallel with these developments, focused on the classic statistical theory and on the gradient transfer method, a third procedure, based on similarity (Sect. 6.7), came into being; it identified the essential physical parameters and developed the diffusion laws on dimensional grounds. It appeared in a 1959 paper by Andrey Sergeevich Monin (1921–2007) [96] and was elucidated and developed by George Keith Batchelor (1920–2000) between 1959 and 1964 [97] under neutral conditions and by Gifford [98] in 1962 for stratified flows. The basic principle of the Lagrangian similitude consists in admitting that the statistical properties of the particle speed depend on the same parameters used to determine the Eulerian turbulence properties, i.e. the friction speed u* and the heat flow H combined in the Obukhov length L. By way of example, considering a source at the height z = 0, the mean values of the transversal y and vertical z displacement of a pollutant particle at the time t are given by:

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Table 8.2 Stability classes according to Pasquill Speed at 10 m height (m/s)

Insolation Strong

Moderate

Weak

4/8 cloud cover

Night 3/8 cloud cover

6

C

D

D

D

D

Fig. 8.24 Horizontal (a) and vertical (b) dispersion as a function of distance from source [93]

  dy z dz = u(a z); = bu ∗  dt dt L

(8.25)

where a and b are universal constants, u is the mean wind speed in the direction x, and  is an universal function such that  = 1 in neutral atmosphere. At the time, it was an embryonal approach, but it was destined to be very successful, especially since the 1970s. Finally, three significant phenomena deserve to be mentioned, at least briefly: acid rains, linked with large-scale diffusion phenomena, the greenhouse effect, associated with the warming of the Earth surface, and the carriage of small organisms. Acid rains are a pollution phenomenon that causes the contamination of rainwater by toxic substances, mainly sulphur and carbon dioxides, in the atmosphere. They attack structures and monuments (corroding facades and transforming limestone into gypsum), forests (reducing photosynthesis and slowing their growth), the tissues of the most delicate organisms (e.g. flowers), the human body (especially the mucosae

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of the initial respiratory tract) and farmlands (altering the chemical composition of soil). The corrosive effect of pollution on London buildings was noticed by John Evelin (1620–1706) in the seventeenth century. In 1872, Robert Angus Smith (1817–1884), a Scottish chemist now known as the father of acid rains,13 studied the effects of the pollution caused by English and Scottish factories on areas far away from them, examining the rain to determine the concentration of acid substances [99]. The first estimate of the effects of a long-distance diffusive phenomenon goes back to the tests carried out by Richardson and Proctor [100] in 1925 and reworked by Sutton [47] in 1932; they regarded the destination of balloons launched during public competitions held in Brighton and in Regent Park. Some measures of the diffusion of pollutants over a distance approximately equal to 100 km were carried out in 1952, at the New Mexico Institute of Mining and Technology, by means of tracking techniques based on the use of fluorescent pigments [101]. Similar analyses were performed in Australia by Crozier and Seely [102] in 1955 and in Porton by Pasquill [103] in 1956. They highlighted how the polluted area increased with the distance from the source. The greenhouse effect is a phenomenon due to the fact that Earth atmosphere is transparent to short wave solar radiation, while it is opaque to the long wave radiation from the Earth surface due to the warming caused by sunrays. Its discovery dates back to 1824, when Jean Baptiste Joseph Fourier (1768–1830), during his studies about heat transmission, realised that the energy irradiated by the Earth towards the space was less than the one it received from the sun; accordingly, the Earth should have been colder than the planet it was if warmed by only oncoming solar radiation. The turning point occurred in the early twentieth century, when the Swedish Svante August Arrhenius (1859-1927), Nobel Prize for chemistry in 1903, understood that the natural greenhouse effect was intensified by the warming of the Earth surface due to the anthropic introduction of carbon dioxide related to industrial processes.14 This consideration pointed out the risks associated with the diffusion of pollutants in the atmosphere. The carriage of small organisms is, even with all its peculiarities [104], a phenomenon similar to the carriage of pollutants. It is important if the carried organisms are infesting (e.g. for agriculture) or harmful for human health. The wind plays an essential role because without it such organisms could not move and would be at the mercy of environmental changes. Since the wind follows recurring or privileged paths, biological evolution may be related to the meteorological properties of the atmosphere. 13 After

Smith’s studies, almost a century elapsed before experiments carried out in Scandinavia in the 1960s confirmed that acid rains could pollute areas several hundreds or thousand kilometres away from the source [21]. The “acid rain” term dates back to 1972. 14 Arrhenius first approached the “doubling problem” of carbon dioxide in the atmosphere: he calculated that if its concentration increased by 50%, the temperature would have increased by 4.1 °C on the land and by 3.3 °C over oceans. “Such increase would have been beneficial for northern countries”.

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The dissemination of microscopic organisms, such as fungi, spores, pollen or small non-winged insects,15 takes places over distances of continental magnitude [105]. The most famous example is the Puccinia graminis, a cause of wheat enfeeblement that distresses plant pathologists since the early twentieth century. Every spring, these spores, picked up from Mexican plantations, reach the Great Plains and the American Prairies causing disasters. The evolution of the knowledge about the diffusion of pollutants opened new perspectives to study such phenomena. In 1935, the Russian Stepanov [106] released microscopic spores in the wind, observing their diffusion. Philip Herries Gregory (1907–1986), the pioneer of aerobiology, used these experiences to prove that the diffusion theory accurately described the carriage of microscopic pathogens [87]: the concentration of the spores in the air decreased with the distance from the source. From this moment on, the experimental verifications on the field and in wind tunnels became countless. Gregory himself, in 1951, carried out model tests [21] studying the deposition of lycopodium spores on the plates of a microscope as a function of the flow speed. The results of these and of many other studies were collected in a book published by Gregory in 1961 [107]. A fundamental concept came to light: being the wind structure and the position of the source introducing the spores in the air known, the statistical theory of turbulence and the gradient transfer theory represented appropriate tools to assess the concentration of organisms over space and time.16

8.3 Soil Erosion and Transport Erosion is the combination of the physical and chemical natural processes that alter and take away rocks and soil. It is caused by the joint activity of many factors: temperature, water and wind are the most important. In some cases, the role of wind is easily recognisable. In others it is difficult, if not impossible, to separate the different causes of erosion. The erosion of rocks starts with the physical crumbling of their matrix. In the most arid climates, it is mainly caused by the exposure of the rocky surfaces to sunrays; if the rock consists of different materials, they expand at different rates, causing 15 The situation is different for winged insects that use wind as a means of transportation [104]. The flight takes place through take-off, carriage and deposition. The simultaneous take-off of a swarm is determined by biological and meteorological conditions. Once they come to contact with each other, they learn to associate. When they reach the flow, they use it as a means of transport. Finally, they play an active role at the deposition, identifying any suitable site to lay their eggs. Often, when they arrive at destination, they note that the ground is unsuitable and take off again until they find a better place. 16 Gregory’s theory does not solve the problem of the dispersion of organism over long distances. Applying his theory to the flight of the Puccinia graminis from Mexico to the America Great Plains and prairies, the end concentration is faint, but the problem is documented. Gregory attempted explaining this by hypothesising that only a few organisms reach their destination, but they find environmental conditions favouring their quick reproduction.

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internal stresses that create cracks on a microscopic scale; the material produced by the crumbling is washed away by water (as rain or surface watercourses) and carried away by wind by means of an abrasive process called corrasion. Soil erosion by wind occurs in the areas where the ground surface includes a high proportion of mud and fine sand, in unobstructed lands exposed to strong winds and in the deserts with little or no vegetation. In such cases, the wind captures and carries away the finest grains, leaving the larger ones on site. This can go as far as causing exceptionally important phenomena, such as the drying up of lands. The first report about the erosion caused by the wind was probably written by the American explorer Zebulon Montgomery Pike (1779–1813) in 1807; in the journal through which he documented his expeditions, he described the “sand hills” in the current Great Sand Dunes National Park in Colorado [108]. In 1890, the Dodge City region in Kansas was struck by a dust storm [109]. The issue of farmland erosion was first discussed by King [110] in 1894, with reference to Wisconsin. In 1910, Edward Elway Free (1883–1939), one of the first scholars of the soil science, and Westgate [111] illustrated the first protective measures against wind erosion. During the First World War, the lands of North America were subjected to substantial evolution. Farmers exasperated the exploitation of soil well beyond its natural limits, cultivating even unsuitable lands. This led to unwise agricultural use of pastures, to intensive farming and to the lack of crop rotation. The lands of the Great Plains were exposed to deep ploughing that destroyed grass ensuring their hydration. It was the beginning of a period of drought that assumed dramatic proportions in the so-called Dust Bowl, the region that became desertic in the 1930s: it was centred around Morton County, Kansas, and included 13 states in the Great Plains, from Texas to North Dakota, as far as Canada [109]. The consequences were catastrophic. The soil, dried and turned into dust, was lifted by the westerly wind in large black clouds, the terrible dust storms that struck central USA and part of Canada, especially between 1931 and 1939. Frederic Edward Clements (1874–1945), the pioneer of vegetal ecology, wrote many storms lasted more than 10 h [112]. The storm on 11 May 1934 removed a huge amount of soil from the Great Plains, dropping the equivalent of 1.8 kg of debris per inhabitant on Chicago. On 14 April 1935, the “Black Sunday”, the day was as dark as night (Fig. 8.25a). The U.S. Department of Agriculture reported that, in 1935 only, the wind took away approximately 850 million tons of soil from southern plains. Because of such events, more than 500,000 people became homeless; many others abandoned their now sterile lands, starting a westward migration [113]. The most eminent American scholar about this subject was Hugh Hammond Bennett (1881–1960). Starting in 1903, he carried out researches in the USA and in other countries, through which he proved that soil erosion was an issue of planetary importance and extent. In 1928, before the terrible events of the 1930s, Bennet published a prophetic report about these dangers [114]. It was the prelude to a series of papers [115–118] that reached their peak with his 1939 book [119], in which he laid the grounds of a discipline—soil conservation—destined to play a central role for agriculture (Sect. 8.5).

8.3 Soil Erosion and Transport

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Fig. 8.25 a Dust storm, Stratford, Texas, 18 April 1935; b Bennett at an experimental station

Taking advantage of his popularity and of the willingness of Franklin Delano Roosevelt (1882–1945) to implement programmes to restore the ecological balance of the nation, in 1933, Bennett founded and became the director of the Soil Erosion Service, a federal agency of the Department of Interior that in 1935 passed under the Department of Agriculture with the name of Soil Conservation Service. In this position, he carried out a political awareness work that created the conditions for the US parliament to examine the implementation of soil preservation measures. He recommended the creation of a belt of forests across the USA capable of providing a screen against wind and to protect soil from erosion [113]. This plan turned out to be too expensive, difficult and uncertain; the government attention was then turned to local remedies, such as soil treatment and the use of shelterbelts (Sect. 8.5). Bennett also played a key role in this field, promoting the construction of many experimental stations studying soil erosion (Fig. 8.25b); the first one, the Coon Creek Watershed Project, was set up in Wisconsin in 1933. Thanks to experiences carried out at these stations, Bennett provided a decisive contribution to transforming the way of thinking of American farmers, helping them to understand and implement new farming and soil defence techniques. In 1935 the US government passed an act, Soil Conservation and Domestic Allotment Act, which granted subsidies to farmers applying such measures. With such boundary conditions, the research was pervaded with widespread interest towards the issue: the first wind tunnels conceived to study soil erosion and transport made their appearance, the first field measurements were performed, and the publications and scientific bulletins about erosion and its control proliferated. It is bizarre how, against a crucial problem especially concerning the USA, the most important scientific contribution of that time came from a British military engineer, Ralph Alger Bagnold (1896–1990), famous as an explorer and an expert about the Libyan Desert. Between 1935 and 1936, Bagnold built the first wind tunnel specifically conceived to study soil erosion at the Imperial College of Science and Technology in London (Fig. 8.26a). The duct had a square cross-section, 0.3 m on a side; the floor and the ceiling were made of plywood, with glass walls; air was sucked from the A inlet by the B fan (0.46 m in diameter) up to the C box, where the carried sand was collected

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Fig. 8.26 Bagnold’s wind tunnel: a transport of sand [120]; b visualisation [123]

and then deposited in D. The visualisation of the transport took place thanks to the light that penetrated in the darkened tunnel from the ceiling (Fig. 8.26b). After completing these experiments, in 1938, Bagnold carried out a campaign of full-scale tests in the Libyan Desert, funded by the Royal Society. They were aimed at measuring wind speed by Pitot tubes fitted on vertical antennas and connected to a pressure gauge, as well as the sand transport, by means of two collectors, one for the sand away from the ground, the other for that near the surface. Bagnold collected the results of these experiences and their theoretical motivation in a 1941 book [120], destined to be a cornerstone. It provided the first physical— mathematical interpretation of the erosion and transport of solid particles into fluids, wind actions on snow, wind effects on desert sands, dust and sand storms, sand ripples, dunes and seas. In 1946, a new turning point took place. The US government passed a new act, Research and Marketing Act, destined to affect the studies in agriculture. It appropriated large sums to set up research programmes about wind erosion. This led to establish, in 1947, the Wind Erosion Project, headquartered at the Kansas State Agricultural College in Manhattan, Kansas. The project was co-ordinated (until 1953) by an agricultural engineer, Austin Wesley Zingg (1906–1959). The most eminent individual involved in this activity was William Stephen Chepil (1904–1963), project director since 1953 and founder of the High Plains Wind Erosion Laboratory (1948). He co-ordinated experimental and theoretical researches about the mechanisms of erosion: he built a wind tunnel to measure erosion effects, formulated the wind erosion equation, analysed the factors affecting erosion and proposed methods to counter it. Chepil’s wind tunnel (Fig. 8.27a) was equipped with modern instruments. It also had the property of being transportable, so that it could be used to carry out open chamber field measurements on actual crops (Fig. 8.27b) [121]. The wind erosion equation (WEQ) expressed the erosive potential of the soil as a function of the parameters governing it. On Chepil’s death, it had the form [122, 123]: E = f (I, C, K , L , V )

(8.26)

8.3 Soil Erosion and Transport

597

Fig. 8.27 Chepil’s wind tunnel: a laboratory; b field measurements

Fig. 8.28 Ground and its roughness [122]

where E is the average amount of soil eroded by the wind in a year per unit area, I is a factor expressing the erodibility of the ground, C is a local climatic factor, K is a factor depending on the soil roughness, L = Df − Db is the equivalent length of the field under examination, i.e. the maximum unsheltered distance in the prevailing wind direction, Df is the overall length and Db is the length protected from erosion by means of shelterbelts, V = RSK 0 is the equivalent amount of vegetation cover, R is the weight of the vegetation over the ground, S is a factor depending on vegetation type, and K 0 is a factor depending on the orientation of the vegetation. Equation (8.26) is still the subject of developments. The methods to contrast erosion can be classified into four families. The first consisted in the use of vegetation and other types of surface covers; it was one of the cheapest and most effective methods; the use of resin, asphalt and other emulsion layers increased protection but was more expensive. The second used clods and soil protrusions, obtained through ploughing, that increased soil roughness and reduced the surface wind speed; it was a temporary but effective solution, especially if accom-

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plished by non-erodible and stable materials. The third alternated strips of crop to be protected with erosion-resistant strips; it was a solution to be used together with other measures. The fourth used natural or artificial barriers (Sect. 8.5). The results of this activity were collected in a series of papers published between 1941 and 1965 [122–132]; they reached their apex with the fundamental article by Chepil, published with Neil P. Woodruff in 1963 [122], that provided a synthesis of the researches carried out in this period. Mainly thanks to the studies by Bagnold and Chepil, in the late 1950s, it was known that ground grains were eroded and set in motion by the wind through three mechanisms: saltation, creeping and suspension; creeping and suspension derived from saltation that represented, thus, the fundamental phenomenon triggering soil motion. Saltation affects intermediate size particles, such as quartz sand grains approximately 0.05–0.5 mm in diameter. The eroded particles glide, leap bounce and advance, keeping close to the ground surface. On this account, they are influenced by the properties of the wind in contact with the soil, i.e. from that part of the flow that is usually ignored or the subject of faint interest (Sects. 6.4 and 6.6). On the basis of such concepts, Bagnold [120] was the first to study the profile of the mean wind speed near the ground, using language and symbolism different from those in the micrometeorological and aerodynamic fields. Retaining this language and its symbolism, the profile of the mean wind speed V near the ground satisfies the logarithmic law by Prandtl and Karman17 in the form (Eq. 6.75): z (8.27) V (z) = 5.75 V∗ log k where z is the height above an ideal plane, the mean aerodynamic surface, at the height √ Z 0 above the mean ground surface (Fig. 8.27); V∗ = τ/ρ is the shear velocity, where τ is the shear stress and ρ is the air density; k is the height above Z 0 of an ideal plane, the aerodynamic surface, where V = 0. In the lands without vegetation [120], Z 0  0 and k  d/30, where d is the average diameter of the surface grains and stones. In the terrains covered with vegetation [123], Z 0 is as greater as the vegetation is higher and thick; however, because of vegetation √ porosity, V > 0 even below Z 0 (dotted line in Fig. 8.29); moreover, [133] V∗ = τ/(aρ), where a is a coefficient depending on the vegetation type and height. The wind flow above and below Z 0 is, respectively, defined as free and restricted (Fig. 8.28). Equation (8.29) corresponds to the case in which the soil is at rest, i.e. when the wind does not cause erosion. When the wind erodes the soil, the surface grains lift in saltation and pervade the free flow. This determines a local flow slowdown, which is matched by the varied mean wind speed profile: z V (z) = 5.75 V∗ log  + Vt (8.28) k 17 According to Bagnold and Chepil, the power law properly approximated the logarithmic law away from ground. It was not applicable near the ground.

8.3 Soil Erosion and Transport

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Fig. 8.29 Mean wind speed profiles [122]: a decimal ordinate; b logarithmic ordinate

V∗ is the shear velocity relative to the eroded ground, k’ is the height where V = Vt regardless of the shear velocity; this height is greater than k but much smaller than the average saltation height of grains. The above speed profiles cause different aerodynamic actions on individual grains, according to whether the latter lie on the ground or are lifted above it [122]. In the case of grains lying on the ground, the wind exerts three types of actions [130, 134, 135]: (1) the positive pressure on the upwind face (impact or velocity pressure), matched by an action called form drag; (2) the negative pressure on the downwind face (viscosity pressure), matched by an action called skin friction drag; (3) the upwards action, due to the pressure gradient between the upper and the lower face (static isotropic or internal pressure). The resultant of the first two contributions originates the drag force F c ; the third contribution corresponds to the upward lift force L c (Fig. 8.30a). Assuming that the grain is spherical in shape, Chepil [131] proved that the shear stress causing the incipient motion is given by: τc = 0.66g Dρ η tan φ(1 + 0.75 tan φ)T

(8.29)

where g is the gravity acceleration, D is the diameter of the grain, ρ is the immersed density, i.e. the difference between the grain and air density, η is the closeness of packing, i.e. a parameter that expresses the compactness of the grain, φ is the rest

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Fig. 8.30 Wind actions on grains: a lying on ground, b as a function of height [122]

angle of the grains, i.e. the maximum slope of a cluster of grains that guarantees stability; T is a parameter depending on turbulence.18 In the case of the grains lifted above the ground, the drag and lift forces are different. The lift, associated with the gradient of the mean wind speed at the ground level, quickly increases with height and becomes faint at a height equal to a few grain diameters; the drag, which is linked to the mean wind speed profile, increases in relation to the height above ground (Fig. 8.30b) [132]. Lacking aerodynamic lift, a grain lifted above the ground is subjected to the drag force and to the gravity force, and then, it tends to fall down. Since the drag force is much greater than the gravity force, the descent takes place with a small slope, 10° on the average. When the grain reaches the ground, it impacts with other grains and, for geometrical reasons, it bounces almost vertically (Fig. 8.31); this is favoured by the lift that, near the ground, returns to prevail on the drag. Saltation, thus, takes place through almost vertical ascents and almost horizontal descents. The impact of grains involved in saltation on those lying on the ground causes a bombardment that determines two consequences. On the one hand, the ground texture is disrupted, and this exposes other grains to erosion. On the other hand, two new types of motion appear: creeping and suspension. Surface creeping takes place through slipping and rolling phenomena involving the largest grains (with diameter approximately equal to 0.5 mm). Suspension occurs through the turbulent diffusion of the lightest and tiniest particles (less than approximately 0.05 mm in size) such as dusts, volcano ashes and fine sands, which are lifted by large-scale vortices at heights up to 3000–4000 m; under such conditions, the suspended materials are carried long distances by wind without ever touching ground. The studies carried out by Chepil [125] in 1945 proved that, on the average, 50–75% of the erosion takes place by saltation, 5–25% by creeping, and 3–40% by suspension. In the light of these concepts, the increase or decrease in erosion depends on three factors—local climatic conditions, the properties of soil, and vegetation—and their link [123]. The main climatic factors are the wind speed, the temperature and 18 Without turbulence, T = 1. With turbulence, T is the ratio between the maximum and average wind force on a grain; since the 1960s, its expression is the subject of probabilistic treatments.

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Fig. 8.31 Saltation: grain trajectories [120]

the precipitations: an increase in the wind speed enhances the erosive potential; high-temperature values dry up lands, exposing them to the collection of materials; heavy precipitation can compact or disrupt the ground, improving or worsening its cohesion. Terrain properties play an essential role as regards the presence of stable or unstable aggregates in the presence of water, to the geometrical and mechanical properties of its texture and to the composition and granulometric distribution of its surface crust: a not excessively wet terrain is less erodible; a flat and smooth terrain is more erodible than a rough and irregular one; the increase of cohesion and weight is beneficial; vegetal soils, with possible clayey and silty components, are more resistant to erosion than loose soils; a loose aggregate with variable granulometry minimises hollows and is heavier than a terrain with uniform granulometry; the presence of organic materials in the soil produces a binding effect. The presence, or absence, of vegetation represents the fundamental aspect: it binds soil by its roots, reduces the wind speed at the ground level and is a screen against grain motion (Sect. 8.5).

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The importance of mankind, for ill or good, stands out. The man plays a devastating role when he interferes in the delicate balance among climate, soil and vegetation, favouring fires, deforestation and excessive growth of pastures and farming. He is the protector of his lands when he effectively intervenes to preserve and stabilise them. In this spirit, two alternative or integrative strategies against wind erosion came into being: windbreaks and soil treatment [122, 123]. Windbreaks, which made their appearance in the agricultural sector in the 1930s and 1940s, over time became increasingly important in various areas. Soil treatment followed two separate paths [136]. The first used surface vegetation to bind terrain by its roots and to reduce the local wind speed by increasing the surface roughness. The second envisaged ploughing techniques aimed at creating rational roughness and irregularity patterns as well as advanced protective measures based on the use of resin, asphalt, lubricant and other emulsion layers. Many of these topics are the subject of Sect. 8.5. The erosive effects of the wind and the phenomena associated with the transport and deposition of eroded grains, called Aeolian processes, produce exceptionally important effects, the study of which proceeded, since the 1940s, in parallel with the search for effective protective measures. They include dust and sand storms, the drying up of lands and the implementation of deflation forms, the accumulation of the carried materials and corrasion. Such phenomena, depending on different situations, affect the same area from which the material is picked up, the neighbouring areas and, sometimes, faraway lands.19 Their consequences can be immediate, deferred or can take place over long periods of time.20 According to Bagnold [120], dust and sand storms were different phenomena. The first often had devastating polluting effects: they developed in arid countries swept by winds and on alluvial soils with little deposited sand; the dust lifted in thick clouds up to heights of several kilometres, saturating air and obscuring sun. The second is related to the deserts of erosive nature, where wind removed fine rock particles and scattered them near the ground, creating remarkable accumulations of materials. This clear-cut distinction was gradually replaced by a view in which the part of the atmosphere pervaded by the dispersion is inversely proportional to the size and weight of the carried grains and is all the same affected by the thermal stratification and by the type of wind triggering the phenomenon. Besides the Dust Bowl that shocked America in the 1930s, there are other areas—the Sahara Desert,21 Ethiopia,22 the Arabian Peninsula, Iraq, Palestine, Israel, 19 In some dust storms, the eroded material is carried from a continent to another. Sometimes, air swollen with dust makes a full revolution of our planet. 20 The dusts coming from the 1883 Krakatoa eruption remained in suspension in the higher atmosphere layers for many years [113]. 21 The sirocco that blows over Sahara carries a huge amount of sand over the Mediterranean and to Europe. In 1901, over 2 million tons of sand arrived in Europe from Sahara [137]. The sand mixed with rain or snow causes the blood showers. In 582 the inhabitants of Paris were terrified by this phenomenon [137]. 22 Herodotus (484–425 BC) told that an army sent by the Persian king Cambise II (559–522 BC) to attack Ethiopia was swallowed by sirocco in the Nubian Desert. The desperate soldiers went as far as to eat each other [137].

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Fig. 8.32 a Drying up of the Dust Bowl; b Palmira, Syrian Desert

Syria, Jordan and, in part, Iran, Pakistan and India—which are subject to dust or sand storms. Known winds causing such phenomena include the simoom, a dry, local wind that is the harbinger of strong dust and sand storm in the Sahara desert, and the haboob, a stormy wind that induces massive carriages of sands in Sudan near Khartoum. Their consequences are often severe, both in social and economical terms.23 They damage agriculture, eroding fertile soil layers, removing organic materials and light particles rich in nourishment for the soil, and exerting abrasive effects on crops. They cause problems for transportation, covering roads, railroads and airports with dust and reducing visibility. They harm the respiratory system undermining human health. The drying up of the soil is often caused by wind erosion, which removes the finer and lighter materials, leaving the thicker and heavier ones in site. The severity of this phenomenon was clear in the Dust Bowl (Fig. 8.32a). In addition to what has already been said, studies carried out after the events of the 1930s proved that, in western Kansas and eastern Colorado, the 1954 and 1955 sandstorms carried away, on the average, 10,000 tons of materials per hour per square kilometre [129]. The overall duration of these storms in Dodge City was estimated in 435 h. In two years, then, 2.5 mm of soil was eroded. As a consequence, 3 cm of soil was carried away from 1922 to 1961. There is an area in Kansas where, in 20 years, 23 cm of soil was eroded [127]. There are fascinating theories maintaining that the sand carried by desert winds often wiped out entire civilisations [119, 137, 138]. According to Howard Crosby Butler (1872–1922), archaeologist and architecture history professor at the Princeton University, there is a 20,000 square miles area in the Syrian Desert, which was densely populated in the past and is now scattered with sand-covered ruins. Palmira (Fig. 8.32b), an almost ruined Syrian city, was the Palm city, inhabited by 200,000 people and called “the Desert Bride”. Ur, the main Babylonian city, populated by 500,000 inhabitants in ancient times, is now almost a ghost town, where sand obscures the sun 6 or 7 weeks per year. Nigeria, an area of dust and sand storms, is scattered 23 Sand storms may provide beneficial effects. The forests of Central and South America receive nutrient minerals required for their survival from Sahara.

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Fig. 8.33 a Dunes in Mojave Desert, California; b elementary dunes: (A) longitudinal; (B) transversal; (C) barchan; (D) parabolic ones

with ruins of ancient cities. Some historians hypothesised the decline of Greek and Roman civilisation derived from soil erosion [123]. Deflation is an ultimate effect of erosion carried out by wind over the Millenia. In some areas, it comes to remove such a large amount of material to originate broad and deep basins, called deflation basins. Sometimes, they were originated by tectonics and deflation modelled their shape. According to some theories, almost half the deserts on the Earth were originated by deflation. There are two forms of accumulation of the materials eroded and carried away by the wind: the first, small-scale one is represented by dunes [120]; the second, large-scale one is represented by loess. Dune formation is associated with strong wind conditions near the ground (Fig. 8.33a). This occurs in areas characterised by minimal roughness, such as deserts and seashores. In such cases, dunes are, respectively, called desert and coastal dunes. Dunes form through three mechanisms. The first is due to sudden changes in wind speed, which cause forms of accumulation in casual areas. The second takes place when the carried material deposits itself near vegetation or other obstacles. The third occurs when the wind meets a roughness increase that reduces its speed; the most typical example takes place when the wind coming from the sea meets the shore and originates the coastal dunes. Dunes sometimes reach a height of approximately 100 m; they evolve in both shape and position, moving up to 30 m in a year; they generally appear in groups. The shape of the individual dunes can be tracked down to four types (Fig. 8.33b): longitudinal, transversal, barchans and parabolic dunes. Longitudinal dunes are arranged in parallel with the wind direction, which attains its maximum speed in corridors and the minimum speed near ridges. Transversal dunes are orthogonal to the wind direction, are comparable to sea waves in size and are associated with the flow periodicity; in coastal areas, they are usually parallel to shore; in desert areas, they assume the shapes of ridges (Fig. 8.34a) or ripples. Barchans are sickle-shaped, with the convex side exposed to the wind. Parabolic dunes are specular to barchans and expose their concave side to the wind.

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Fig. 8.34 a Ridge-shaped dunes in the Libyan Desert; b Egyptian sand sea [120]

Fig. 8.35 Accumulation near obstacles and close to channelling [120]

Complex dunes are formed by groups of elementary dunes. Barchans and parabolic dunes often join in groups, forming meandering transversal dunes. Nonorganised formations are found in the great erg, or sand seas (Fig. 8.34b), where the wind creates articulated shapes; some dune deserts in North Africa, in the Arabian Peninsula and in Central Asia are classic examples of such arrangements. The presence of obstacles, like houses or barriers, alters the phenomenon (Fig. 8.35) [120] originating two zones, separated by a discontinuity surface (the dotted line in a), where the flow has different properties. In the outer area, it is not affected by the obstacle and is devoid of vorticity. In the inner area, an alternation of eddy layers and stale air layer is generated that favours deposition along the wake (b, c, d, e) and in front of the obstacle (f). The phenomenon changes when pairs of close obstacles originate channelling phenomena. The flow speed increases in the narrow area and then decreases when the accelerated air merges with the free flow; the deposition takes place in this area (g, h). The loess is a form of accumulation that takes place over the millennia. This term indicates a fine material, consisting of sharp-cornered granules 0.01–0.05 mm in size. It covers nearly 10% of the world’s land surface, especially steppes and prairies at the peripheral areas of deserts. Loess reaches its maximum amplitude in the Yellow

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Fig. 8.36 a Loess plateau, Yellow River; b Finger of God near Asab, Namibia

River basin in China (Fig. 8.36a). In Europe and North America, it seldom exceeds 20–30 m of thickness and dates back to the cold phases of the Pleistocene. Corrasion is the physical phenomenon by which the wind erodes coherent rocks and models them in peculiar shapes. It takes place by means of the sand granules that, after being picked up by the wind erosive action and carried out by saltation, carve the rock with an abrasive action. A remarkable situation occurs when the rock consists of materials with different consistency: in this case, corrasion is selective and produces pits, recesses, ridges and protruding layers. There are two forms of corrasion: the small-scale one carves small rocks; the large-scale one involves great expanses of land. Among the most typical forms of small-scale corrasion, it is worth mentioning the sculptures in the Vila Velha Reserve in Brazil, on Kimolos Island in the Aegean Sea, in the Nambung National Park in Western Australia, at Timna, in the Negev Desert in Israel and on Bolivian Plateau. The Finger of God, near Asab in Namibia (Fig. 8.36b), was a sandstone rock pinnacle 35 m high; it formed in the course of erosive processes during 500 million years, but collapsed because of the wind action (and perhaps of an earthquake) on 8 December 1988 [139]. The rock arches in Utah (Fig. 8.37a) and the tafoni of Gallura in Sardinia (Fig. 8.37b) are the result of the erosive action of wind and water. Yardangs are the most typical form of large-scale corrasion; they are rock ridges stretching out in the wind direction, generated by deflation and corrasion over the millennia. In the Lut, in eastern Iran, they cover a 150 by 170 km area, achieving heights up to 100 m (Fig. 8.38a); their orientation matches the direction of the strongest winds that blow in the summer for two or three months (Fig. 8.38b). Similar, but smaller, corrasion forms are found in Sahara, south of the Tibesti massif, carved in the Palaeozoic sandstones of the ancient Chad basin; the ridges are 0.5–4 m high and a few metres to some kilometres long; they are oriented from north-west to south-east, with the trade winds direction. The Ischigualasto Provincial Park in the

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Fig. 8.37 a Rainbow Bridge, Utah; b Bear Rock, Palau, Sardinia

Fig. 8.38 Yardang del Lut, Iran: a close view; b overall view

province of San Juan, Argentina, covers an area approximately equal to 50,000 ha; it is known as the Moon Valley because of its affinity with moonscapes; its rocky structures are the result of corrasion by winds and of corrosion by rain.

8.4 Snow Drift Wind erodes, carries and accumulates snow [120, 123] just like soil (Sect. 8.3). Soil accumulation, however, is virtually permanent, while the snow drift usually melts and turns into water, often with remarkable consequences. The wind carries snow during its fall or takes it away from the ground regardless of the presence of snowfall. A snowstorm is defined as a strong wind phenomenon entailing the carriage of a large amount of snow either coming from snowfalls or

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Fig. 8.39 Effects of the blizzard

eroded from the ground. A blizzard (Fig. 8.39) is a snowstorm causing low temperatures, high wind speed and heavy carriage of snow.24 Snow drift takes place, like that of dust and sand, at those places where wind speed decreases. This can occur in casual areas, associated with terrain configuration, or in the presence of obstacles or barriers, either natural or artificial, slowing down the airflow. Such an event, if not kept under control, usually causes great troubles, especially in areas exposed to heavy snowfall and strong winds. Uncontrolled snow drift can cause problems to road and rail traffic, blocking them or making them dangerous and also paralyzing airports and air traffic. It hinders travel within the cities, causing disruption for schools and work activities. It exposes building roofs and trees to weights so heavy to cause their collapse. The costs associated with snow removal and damage repair are often considerable. The Great Plains of North America requires peculiar considerations. Since they are characterised by summer dryness and plentiful winter snowfall, in this area it would be important to accumulate and store the winter snow falling on the ground as long as possible, to favour the growth of summer crops. Unfortunately, the wind takes the snow away from the fields and carries it over cities and farms, along roads 24 The conditions causing the blizzard change from a country to another. The Canada Environmental Service states that a blizzard exists when wind speed exceeds 40 km/h, the snow transport reduces visibility to less than 150 m, wind-chill temperature (Sect. 8.6) is less than −25 °C, and such conditions continue for at least 4 h. The U.S. National Weather Service defines as a blizzard an atmospheric state, in which wind speed exceeds 56 km/h, and the transport of snow reduces visibility to less than 150 m and that continues for at least 3 h; no temperature thresholds are set. The British weather office defines a blizzard as an event in which wind speed exceeds 48 km/h and snow carriage reduces visibility to less than 200 m.

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Fig. 8.40 Snow drift at a barrier 3 m high, with slats spaced by 2.5 cm [140]

and railroads, originating accumulations near obstacles. The snow remaining on the fields, in addition, is unlikely to be uniform; it accumulates near stockades, fences and vegetation. When melting occurs, then the beneficial role of the water concentrates on a few areas. Snow drift, just like soil erosion, can be controlled through natural or artificial measures or by resorting to ground treatments. Both systems aim at preventing accumulations or at locating them at intended zones. Since ancient times, mankind attempted to defend itself from the snow drift making use of barriers or of other measures dictated by experience and tradition. In a famous passage from his autobiography (It’s a good deal), Jeremy Triefenbach, a nineteenth-century German explorer, recounted how he remained trapped in a snow drift and survived thirteen days feeding on snow. The first technical–scientific report about this subject was published in 1852 by Johnson [140], a retired road maintenance inspector, who explained the effects of snow drift along Norwegian roads and railroads. He described the accumulation at fences (Fig. 8.40), buildings and trenches along communication lines. Soviet literature mentioned the Russian engineer V. A. Titov as the one who invented the snow barriers between 1860 and 1870. In 1887, Schubert [141] described the effectiveness of a new type of barriers along some roads in Northern Germany; he subsequently illustrated the experimental tests carried out in 1901 [142] on many types of barriers to identify the most effective ones; in the same article, he described the snow drift forms produced by barriers. In 1902, Vaughan Cornish (1862–1948), a British geographer, travelled to Canada to study snow and surface waves causing its carriage [143]. He gave an account of his observations between 15 December 1901 and 4 March 1902, travelling 3000 miles aboard the Canadian Pacific Railway trains through almost entirely snow-covered territories. In the first part of his paper, Cornish described erosion and accumulation, comparing them with the similar ones associated with sand. He noticed how snow erosion and accumulation forms were very sensitive to local climatic conditions, making snow wet or dry. He described snow mushrooms, i.e. the spheroidal aggregations that formed over pedestals during the fall of wet snow in calm air conditions. He also noticed that wind actions on the dry snow originated ridges and barchans similar to sand dunes. In the second part of his paper, Cornish described the snow drift near obstacles. Examining the fences, he noticed how accumulation on a single side (Fig. 8.41a)

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Fig. 8.41 Snow drift [143] on one side a and two sides b of a fence and around a building: c plan; d centreline longitudinal cross-section; e transversal cross-section downwind the building

Fig. 8.42 Typical shape of a snow drift (a) and specular complement (b) [143]

indicated uniform wind direction coming from the opposite side; accumulation on both sides (Fig. 8.41b) was typical of wind with variable direction. Accumulation around buildings showed a horseshoe-shaped layout (Fig. 8.41c); the longitudinal (Fig. 8.41d) and transversal (Fig. 8.41e) cross-sections show areas free from accumulations adhering to the building. Similar observations were made for single trees and tree rows. Cornish remarked that the accumulation took place in the eddy zone created by an obstacle and assumed the shape shown in Fig. 8.42a, with its rounded edge exposed to the wind. The contour matched an ichthyoid that, when specularly turned over, assumed the shape of a fish (Fig. 8.42b), i.e. the one providing less resistance. Interpreting this observation and some statements by Cornish in view of the knowledge that was about to blossom, the formation of this accumulation pattern precluded both wake separation and vortex shedding, preventing the development of additional accumulations. The advent of the twentieth century and the ongoing technological evolution led to the growth of road and rail networks. Mankind became increasingly dependent on transportation and felt the need to always have them at its disposal. The necessity of keeping roads and railroads free from snow made controlling its accumulations a priority and gave a stimulus to the scientific and technological research pervading universities as well as highway and railroad companies. In 1909, a committee analysed the qualities and faults of various measures to protect railroads from snow drift [144]. Six points were discussed: (1) protective barriers; (2) the enlargement of trenches; (3) the devices applied to the front end of locomotives to remove snow from the tracks; (4) the use of salt to prevent ice formation; (5) snow sheds; (6) the sites through which the railroads run. Some concepts, quite advanced for this age, stood out. The committee suggested to make the

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slopes of trench sides gentler, in order to avoid the formation of eddies and the snow drift. It also maintained that a solid barrier created eddies and accumulation before its upwind face, while a porous barrier shifted it on the downwind side (Sect. 8.5); in both cases, the barrier must be set up far away from the railroad. Also, thanks to these guidelines, a vast literature originated about the effectiveness of artificial and natural screens [145–151], first of all tree rows used as protective devices against the snow drift. Many projects to improve the practicability of road and rail networks were developed in parallel. Between 1905 and 1916, the Great Northern Railway Company planted tree rows along its railroads in North Dakota. In 1914, the Minneapolis, St. Paul and Sault Ste. Marie Railway Company started experiments about the effectiveness of trees as barriers in North Dakota and Montana. In 1916, the Canadian Pacific Railway Company started a programme of tree planting along its railroads; the adopted criteria were described in a manual, Tree planting for snow control. In Pennsylvania, the planting and care of anti-snow vegetation were regulated by the Nr. 481 Act, dated 7 May 1929; it authorised the Pennsylvania State Highway Department to keep the tree rows near the roads in good shape. The project that imparted the major change was started in 1925 by the Michigan State Highway Department, in cooperation with the Civil Engineering Department and Engineering Experiment Station at the Michigan State College. It involved the planting of several types of trees in different patterns to evaluate their qualities and faults as well as wind tunnel tests to define the most effective snow control strategies. Trees were planted from 1928. Shortly afterwards, the construction of a small closedcircuit wind tunnel (Fig. 8.43) was started at the Michigan State College. Its crosssection was 0.6 m2 , and it was 3 m long; the wind achieved a speed of 22.35 m/s; the interior was lighted for visualisation tests; coarse sandpaper was placed on the floor to simulate the effect of the ground; snow was reproduced by means of flake mica and balsa sawdust. The results appeared in three reports by E. A. Finney, which represent milestones, published in 1934 [152], 1937 [153] and 1939 [154]. They contained a state of the art on the studies carried out until then and about the US practices to protect highways and railroads, summarised the results collected during measurements and observations both on the field and in the wind tunnel, formulated proposals about protection measures aimed at guaranteeing the continuity of transportation, and indicated three methods to prevent and counter snow drift: (1) artificial barriers, consisting of screens and fences [152]; (2) natural barriers, consisting of tree and plants [153]; (3) the design of new communication routes and of their cross-section as well as the improvement of the existing ones [154]. The study of artificial barriers [152] was based on field and wind tunnel tests; in the latter case, models can be tracked down to three types: horizontal slat (Fig. 8.44a), vertical slat (Fig. 8.44b) and solid fences. Fences, in 1:12 scale, occupied the whole width of the tunnel. For every type of fence, the tests analysed the role of several parameters: the height of the fence and of its lower edge, the wind speed and the eddy near the fence, the size and spacing of slats, the inclination of the fence with

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Fig. 8.43 Wind tunnel at the Michigan State College [153]

Fig. 8.44 Typical stockades with horizontal (a) and vertical (b) slats [152]

respect to the wind direction and to the vertical over the ground and the density of the snow drift. Figure 8.45a shows the eddy created by a fence with horizontal slats: in A, air moves quickly, preventing deposition; in B, air slows down originating a deposit shaped like the zone of air where wake separation takes place; in C, before the fence, a small eddy forms, but it causes a deposit only if the wind is prevented from flowing below the fence (e.g. for the presence of grass or other elements). In any case, the snow drift is independent from the wind speed. Figure 8.45b shows the eddy created by a fence with vertical slats; its characteristics are similar to the ones mentioned above. In both cases, the snow drift occurs downwind the fence and takes the shape illustrated by Cornish (Fig. 8.42a) [143]. The situation is different for solid fences (Fig. 8.45c). In the A zone upwind the fence, a small eddy originates and causes deposition. In the downwind area, three different zones are created: in B, a small eddy, rotating counterclockwise, occurs; in D, a large eddy, rotating clockwise, occurs; both carry the snow in C, originating

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Fig. 8.45 Eddy near horizontal slat (a), vertical slat (b) and solid (c) fences [152]

Fig. 8.46 Wind tunnel tests on single (a) and multiple (b) tree rows [153]

a deposit. The extent of the deposits depends on the wind speed. For low wind speeds, the upwind deposit is plentiful, while the downwind deposit is limited. At high wind speeds, the snow goes beyond the fence: the upwind deposit decreases, and the downwind deposit increases. According to these studies, the link between the fence height H and the length L of the snow drift zone is properly approximated by the linear relationship L = K H [152], where K is a coefficient varying between 10 and 25 in relation to the fence porosity. Assuming that the fence must prevent snow drift on the roadbed, L is the minimum distance from the fence to the roadside as a function of the fence type. Finney also remarked that using multiple parallel fences was beneficial, as long as they were spaced enough to prevent overlapped snow drift zones. In every case, the effective control of snow drift requires wide spaces near the road. It is also worth mentioning that the inclination of the fence with respect to the vertical (Fig. 8.44) deflects downwind air and reduces the upwind snow drift. The oblique incidence of wind reduces the effectiveness of solid fences; their use, therefore, is advisable only in case of winds with almost constant direction. Considering that such fences are expensive and not so functional, a clear indication emerged towards the use of fences with an intermediate porosity level. The study of natural barriers [153], like that of artificial barriers [152], was based on field and wind tunnel tests; tree models in 1:12 scale were built with the materials used to manufacture brushes (Fig. 8.46). Finney started remarking that the use of tree rows was suited for locations where wide spaces were available and permanent barriers could be used. It was also suitable from the landscaping viewpoint and for environmental inclusion. He then divided the vegetation suited to be used as a snow barrier into three classes: conifers, deciduous trees and brushes.

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Conifers are suited for this purpose and were reviewed by Finney in relationship with the requirements needed to make effective use of them. Trees must be available on site and capable of quick growth. The ideal tree is symmetrical with a thick and compact crown and branches reaching down to the ground. Both the tree and its branches must also be able to withstand wind actions. On such premises, Finney classified the conifers into three categories: flame-, pike- and heart-shaped. He noticed that the growth of the tree did not alter its shape and that its effectiveness depends on the ratio between the effective area (in contact with the wind) and the crown area (enclosed within its perimeter); this parameter ranged from 0.66 to 0.85; the most effective trees have the higher ratio. Deciduous trees and brushes are suitable for use in the prairies, where the climatic conditions are too severe for conifers. The tree has to develop thick branches from its base to the top. It has to possess strong branches, to withstand wind actions and the weight of snow and ice. It has to quickly grow even in adverse climates and to be able to withstand such conditions. After such premises, Finney examined the advantages and disadvantages of various row types. Planting trees on multiple (3–5) and staggered rows kept the snow within the barrier; this technique was used, as an example, by the Michigan State Highway Department and by the Great Northern Railway. Narrow planting, with a double row of trees, like the one used by the Pennsylvania State Highway Department, caused snow drift downwind the second tree row; it was an effective technique when trees were fully grown. The characteristics of the single row barrier are similar to those of the double row barrier, as long as the tree crowns are thick and close to each other. Finney noted that the design of a barrier was defined by the spacing between the trees of every row and by the position of the barrier with respect to the roadbed. Starting from the assumption that, in an effective row, the crown of adjacent trees came into contact, tree spacing in every row was, in turn, a function of the crown diameter S, and then of the tree age A. He then introduced the relationship S = k A, where k is a spacing index provided by tables depending on the tree type. As regards the length L of the downwind snow drift zone, the model tests carried out by Finney proved that, in the case of a single row barrier with thick crowns touching each other, it was, on the average, equal to 15 times the height H of the trees. Passing to multiple rows, the snow drift zone grew larger. Finney [154] remarked that few highways (and railroads) were designed taking into account the snow drift; he then hoped for a change, motivated by the prohibitive yearly costs incurred to remove the snow. He also remarked that a growing political and technical awareness towards snow issues had developed in the 1920s and 1930s. He then approached the subject of the design of new highways by submitting a questionnaire to American states, to collect the most common strategies. The replies indicated that the measures adopted were building roads raised above the land, avoiding road sections with deep excavations, paying attention to the shape of trench and embankments, adopting limited slopes and rounded edges, using broadside shoulders and deep ditches and avoiding guard rails.

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Fig. 8.47 Typical Colorado road cross-section [154]

Finney studied the main causes of snow drift and criteria to counter it. Snow accumulated over roads because of four reasons: (1) right-of-ways fences, tall grass and weeds, brushes, trees and hedges, debris; (2) low-grade line, detected road and cut sections with unsuitable excavations and exceedingly steep slopes, highway appurtenances such as guard rails; (3) poor inclusion of the road within the local topography; (4) buildings, billboards and other similar obstructions near the roadbed. Issue (1) involves old roads and can be removed by eliminating easement restraints or requiring the cooperation of owners of adjacent lands. The snow drift causes under point (2) can be eliminated by better design procedures for new roads: the grade line has to be raised above the height of the snow blanket; the side shoulders of embankments and trenches have to be wide, with slopes not exceeding 1:4; rounded edges and streamlined cross-sections have to be used; wide ditches and cut sections have to be envisaged (Fig. 8.47); guard rails causing eddies have to be avoided. As regards point (3), roads running along valleys and crossing woods are usually sheltered; it is important to avoid downwind slopes, while upwind slopes and high altitude routes are favourable; any deep excavations of the slope are unfavourable when the road is orthogonal to prevailing winds. Buildings, billboards and other obstacles near the road (point 4) have to be avoided, leaving broad free side spaces where grass and scrubs are mowed at regular intervals. On the basis of these considerations, Finney carried out new wind tunnel tests, in 1:12 scale, by which he examined the relationship between the shape of the road cross-section and the snow drift. Finney first studied an embankment with vertical walls, discovering results similar to those for solid barriers [153] (Fig. 8.45c). The length of the separation zone was approximately equal to 6.5 times the embankment height. The separation zone was characterised by three parts (Fig. 8.48): in A, air was in counterclockwise circular motion; in C, it was in clockwise circular motion, and snow was carried towards the embankment and accumulated in B. The amount of snow drift in B increased with wind speed. The size of recirculation and accumulation zones was independent from wind speed. The situation changed giving a slope variable between 1:1 and 1:6 to the downwind side of the embankment (Fig. 8.49). The limit of the downwind separation zone remained almost unchanged, but the snow drift was subjected to gradual changes.

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Fig. 8.48 Wake separation and accumulation behind a cut section with vertical walls [154]

Fig. 8.49 Wake separation and snow drift behind an embankment with 1:1 to 1:6 slope [154]

Initially, the A zone disappeared and the snow drift spreads along the embankment shoulder. Once the 1:4 ratio was exceeded, the snow drift almost fully disappeared. The 1:6 ratio was the best, because it eliminated the phenomenon. The rounding of the embankment top shifted the snow drift zone towards the embankment base, improving the situation. The rounding of the embankment base played a marginal role. Two years after Finney’s triptych of papers, in 1941, Bagnold [120] published his book about the erosion and carriage of solid particles performed by fluids, including the erosion, carriage and accumulation of soil (Sect. 8.3) and snow. Thanks to this work, it became clear that snow, like soil, was put in motion by wind through three mechanisms: creeping, saltation and suspension (Fig. 8.50). Creeping regards the heaviest particles and takes place within the first millimetres in contact with ground. Saltation takes place between 10 cm and 1 m away from ground; intermediate particles are involved, i.e. the ones too heavy for suspension and too light for creeping; they represent the prevailing amount of snow carried by wind. Suspension regards

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Fig. 8.50 Snow saltation, creeping and suspension

Fig. 8.51 a Carriage of snow in suspension; b Mirny Russian Antarctic Station

the finest and lightest particles; their carriage starts by saltation and develops in a layer whose top lies between 10 and 100 m above ground (Fig. 8.51a). Finney’s papers and Bagnold’s book established solid foundation for a subject, snow drift, which had become essential in many countries all over the world. They found an unexpected sounding board in the early twentieth century that assumed strategic importance in the second half of the 1940s: the establishment of Antarctic bases 25 (Fig. 8.51b). These bases, erected at sites lashed by strong katabatic winds26 (Sect. 6.4) and characterised by minimal ground roughness (ice), highlighted, besides the classic snow drift problems, new issues ranging from entering or leaving buildings to abandoning them when they were covered or invaded by snow. 25 The first Antarctic bases, Orcadas Base and Macquarie Island Station were established by Argentina in 1904 and by Australia in 1911, respectively. On 14 December 1911, the Norwegian explorer Roald Engelbregt Gravning Amundsen (1872–1928) was the first to reach the South Pole, beating the British expedition lead by Robert Falcon Scott (1868–1912) by 35 days. The realisation of Antarctic bases resumed in 1947, when Chile established Captain Arturo Prat Base. From that time on, the institution of new bases for scientific reasons was continuous. 26 The katabatic winds coming down the slopes of the central ridge in Antarctica often reach higher speeds than hurricanes.

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With such premises, in the 1940s and 1950s, the study of snow drift showed an overwhelming evolution based on the cross-use of field tests, wind tunnel experiments and theoretical analyses. Thanks to these tools, a renewed culture developed and affected classical subjects, like snow carriage and protective barriers, as well as innovative issues, such as snow drift near buildings and city planning under aggressive climatic conditions (Sect. 8.6). Many papers on these subjects were written in Russian or in Scandinavian languages, and only in a few cases, translation is available [155]. Nøkkentved first understood the importance of this trend, publishing two papers, in 1939 [156] and in 1940 [157], which illustrated field and wind tunnel tests; he suggested that the maximum area of the snow cross-section deposited behind an artificial barrier in a vertical plane in the wind direction was A = KH 2 , where H is the barrier height and K a coefficient depending on its shape. He noted that barrier effectiveness increased if slats were rough and irregular rather than smooth and streamlined. In 1943, the Swedish Sten Hallberg (1905–1982) published five papers [158] that described field tests, carried out between 1941 and 1942 at the Mälaren Lake, during which he measured wind speed and snow drift as well as the mechanical strength of 27 types of artificial barriers, divided into collection (to create a local snow drift) and deflection (to direct the snow drift elsewhere) barriers; each group was divided into permanent or mobile barriers and into open or closed ones. The tests confirmed that the most effective barriers had a density nearly 50% and used rough and irregular slats. The best effectiveness of fences with density from 40 to 50% was confirmed by two papers published by Pugh [159] in 1950 and by Bekker [160] in 1951. Bekker parametrised the results by expressing the downwind snow drift length (in m) as L = 860(2.2 + H )/(22.1 + d), where H is the fence height (in m) an d is its density (in %). He proposed, allowing for uncertainties, to place the fence L + 5 m away from the area to protect. The most significant contribution in this period was provided by Pugh and Price [161] in 1954. They collected the results of their experiences, including researches carried out in Antarctica, as well as various trends, elaborating a synthesis of the properties and of the most effective use of fences. In the first part of the paper, Pugh and Price, elaborating Hallberg’s classification [158], defined a collecting fence, regardless of density, as a shelter that slowed down wind causing local accumulation; a leading fence is a solid shelter, perpendicular to the ground and oblique to the wind, which diverted snow aside to collect it into holes dug to serve as tanks; a blower fence is a shelter inclined with respect to the vertical on the ground, which accelerated wind so that the snow drift zone formed elsewhere. In the second part of the paper, Pugh and Price, also making use of the data collected in [159], reviewed fences adopted in various countries. Besides, the traditional ones authors wrote about fences to install in emergency situations, like the ones put together using vertical wooden poles and horizontal iron wires, with interposed branches and vegetation. In the third and most original part of the work, Pugh and Price observed that collecting fences were effective if arranged perpendicularly to the wind direction on regular ground. Being the direction of the snow-carrying winds often variable

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Fig. 8.52 Fence arrangement [161]: a in parallel; b staggered; c winged

and the ground to protect often rough, it was difficult to put in practice principles deduced under ideal conditions and fence arrangement required resorting to experience. Examining fences laid out along roads and railroads, they were identified and classified as parallel, staggered and wing arrangements (Fig. 8.52). In case of winds with variable direction, the authors recommended mixed continuous-staggered systems. Arrangements were also proposed for areas near curves or at the edge of woods. New studies on artificial and natural fences were published in the late 1950s by Masao Shiotani and Hideo Arai [162] in Japan, by Dyunin and Komarov in Russia, later translated in Canada [163–168], by Kreutz and Walter [169] in Germany and by Martin Jensen [170] in Denmark. The studies by Dyunin and Komarov established a general theory on the flow of a granular material in a fluid—snow in the wind, in the case in point—[166] before field and wind tunnel tests. The snow flux q is the weight of the snow carried in the unit time through a unit area orthogonal to the wind direction. The overall snow flux Qh is the integral of q between the ground and the h height. The measurements of this quantity, carried out since 1927 at the Vodenyapino Experimental Station of the Central Research Institute of the Russian Ministry of Communications, proved that Qh depended on the wind speed v and that snow carriage concentrated in the first 2 m above the ground. Dyunin [166] used these measurements and dimensional analysis [163] to obtain the relationship:  3 Q 2 = ψ2 v1 − v1

(8.30)

where ψ2 is a coefficient with an average value 0.255, v1 is the mean wind speed 1 m above the ground, and v1 = 2.71 m/s is the critical value of v1 . The comparison with measurements was excellent. On the basis of Eq. (8.30), Dyunin e Komarov [167] expressed the amount of snow drift near a fence as the difference between the overall flux upwind and downwind the fence. It is given by:  3  3  (8.31) Q H = ψH v1 − v1 − u 1 − v1

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where v1 and u1 are the mean wind speeds 1 m above the ground, upstream and downstream the fence, respectively. Defining the wind speed attenuation law downstream the fence, u1 = f (v1 ), provided the snow drift. The problem was theoretically solved for ideal cases, using the results of field and model tests. A second approach extended to snow the turbulent transport introduced by Taylor between 1915 [42] and 1921 [43]. Shiotani and Arai [171] in 1953, Frederick Fritz Loewe (1901–1988) [172] in 1956 and M. Mellor and Uwe Radok [173] in 1960 focused on snow particles in suspension carried by the wind through the diffusive processes caused by eddies in the atmosphere. Admitting the w snowfall speed as constant, and imposing the steady-state condition, they deduced the differential equation: wη(z) +

A(z) ∂η(z) =0 ρ ∂z

(8.32)

where η is the snow concentration, i.e. the snow mass in a unit mass of air, z is the height above the ground, ρ is the air density, and A is the turbulent exchange coefficient. They also assumed that the mean wind speed profile at the ground level was logarithmic, and, using experimental data, they defined: A(z) = κu ∗ ρz

(8.33)

 z − κuw ∗ η(z) = η(h) h

(8.34)

They then obtained:

where h is a reference height, κ is the Karman constant, and u ∗ is the shear velocity. Equation (8.34) proved that the air depth where transport in suspension takes place depends on the wind and snowfall speed. The concentration increases when, for the same amount of snow, wind speed increases; it decreases when, at the same wind speed, the fall speed increases. This equation drastically underestimates the transport near the ground, since it neglects creeping and saltation. The snow drift takes place when wind speed decreases and snow particles do not remain in suspension. This occurs, for instance, near obstacles. In 1961, Dingle and Radok [174] analysed the mean wind speed and the snow concentration, measured at the Wilkes Antarctic base in 1959, to experimentally validate the new theory. The agreement was fairly good but not satisfactory. The authors remarked that attributing the logarithmic profile to the speed of katabatic winds was approximate; they also noted that assuming the snowfall speed as constant was not realistic: snow particles have a broad range of size and fall with a broad range of speeds. Accordingly, they started theoretical and experimental researches leading to formidable advancements from the early 1960s. Besides the development of the first mathematical models of snow drift, the other novelty of this period was the first assessments of snow drift near buildings. The first

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Fig. 8.53 Wind tunnel tests [176]: a raised building; b group of tanks

contribution dates back to 1942, but it went almost unnoticed due to the Japanese language. Kimura and Yoshisaka [175] simulated the snow using dust and studied snow drift around six buildings, including one with square plan, a shed roof tilted by 30° and another with rectangular plan and a pavilion roof; they remarked that snow accumulated before the upwind face, while downwind accumulation was very limited. The turning point occurred in 1961, when Robert Wallace Gerdel (1901–1987) and Gordon H. Strom [176] published the results of a research funded by the U.S. Army Snow Ice and Permafrost Research Establishment to identify the best methods and materials to simulate snow in wind tunnels. They defined the non-dimensional parameters to be reproduced, as well as those having higher priority for simulation. They noticed that the best way to model snow in a 1:10–1:50 scale was using borax particles. They performed wind tunnel tests at the New York University,27 visualising and measuring snow drift near buildings (Fig. 8.53a) raised from the ground through columns used as protection against excessive accumulation and near tanks (Fig. 8.53b). Both were tested individually and in groups, highlighting that snow drift zones depended on wind direction and snow erosion at the structure base. The latter caused differential settlements that impaired the stability of structures, especially of those resting on the snow blanket. Gerdel and Strom also noticed the beneficial use of deep poles. Finally, a paper published by Ernest Frederick Roots (1923–2016) and Charles Winthrop Molesworth Swithinbank (1926–2014) [177] in 1955 is worth noting. Taking advantage of experience acquired during the Norwegian–British–Swedish Antarctic Expedition (1949–1952) about the planning and management of the Maudheim base, they stressed the importance of the planning and orientation of the buildings of a settlement exposed to extreme climatic conditions as regards accumulation and burial phenomena due to wind and snow. This issue lies at the interface between snow drift and bioclimatic city planning and architecture (Sect. 8.6). 27 The wind

tunnel was 1 m high, 2 m wide and 9 m long. During the tests by Gerdel and Strom, no boundary layer was developed.

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Roots and Swithinbank maintained that planning an Antarctic base, it is necessary to distinguish between bodies that can be covered with snow and those that must be kept free as long as possible. Free bodies must be accessible, anchored, sheltered and thermally insulated. Bodies that can be submerged need access excavations and communication tunnels under the snow blanket; they must be grouped, keeping in mind that snow drift is quick if there are high bodies on the upwind front; to avoid excessive snow drift, then grouped bodies must be low and streamlined in shape; faces exposed to wind should be smoothed and rounded. Free bodies, conversely, must be spaced to prevent interference between each snow drift zone; raised platforms prevent accumulation by favouring wind acceleration below them; the platform and the bodies resting on them must be anchored; it is necessary to avoid exceedingly large platforms. The use of distributed fences to deflect snow is extremely useful.

8.5 Windbreaks, Shelterbelts and Crops Surface roughness produces shear stresses; the profile and intensity of the mean speed and atmospheric turbulence depend on them (Sects. 6.5 and 6.7). The wind shear plays also a key role in three phenomena regarding soil behaviour: the erosion and transport of the finest sand grains and, in part, of rocks (Sect. 8.3), the snow drift (Sect. 8.4) and the crops (the subject of this paragraph). At first, mankind endured wind effects on soil passively. It then attempted to protect its land by wind barriers, either natural or artificial, based on experience and tradition. From the early twentieth century, it understood the importance of these effects and trusted science to study and counter them. Widespread interest towards barriers was then originated that established a solid knowledge base. It represents the premise for the assessments and intervention that, since the 1960s, became systematic. The study and the implementation of wind barriers are the common denominator of the researches carried out to protect crops and to mitigate the consequence of sand transport and snow drift. At first, specialists in various sectors operated independently. Afterwards, the experiences gained in different fields were used in similar sectors; the barriers then became the subject of intersector studies. Finally, their use extended to many applications, such as the protection and comfort of urban spaces (Sect. 8.6), the screening of equipment sensitive to wind effects and noise reduction. The first observations about the wind barriers were carried out by Paul La Cour (1846–1908) in 1872. He noticed that natural barriers caused an increase in day temperature and a drop of the night temperature. La Cour also observed how barriers affected evaporation, reducing it in different ways on their upwind and downwind sides; this result does not appear reliable, but has a historical value. The first scientific studies about the effects of natural barriers on microclimate and crops were published by Carlos G. Bates (1885–1949) [178] in 1911 and by N. Esbjerg [179] in 1917.

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Bates carried out experiments in the Great Plains of the USA, during which he measured the air temperature 1.2 m above the ground and the soil temperature at 50 cm depth. These tests confirmed La Cour’s observations, proving that air temperature near the windbreaks increases by day and drops by night; this effect was significant when the screen was effective against wind, especially in the soil ranging from 2 to 5 times the height of the windbreak. As regards soil temperature, near windbreaks, it was nearly 3.5 °C lower than air temperature. Bates also noticed that soil was warmed by downward heat conduction and that this was favoured by humidity; evaporation, then, tended to cool soil; the windbreaks mitigated this effect for a distance at least 10 times their height. On the other hand, they reduced humidity if the extension of their roots was excessive. In Denmark, between 1913 and 1915, Esbjerg carried out humidity and evaporation measures 50 cm above the ground, at various distances away from a vegetal windbreak 2.5 m high and for various wind speeds. Evaporation mitigation extended approximately 20 times the windbreak height on the upwind side and approximately 24 times on the downwind side. The study of plant transpiration started in 1920 with a paper by Oskar Eric Gustav Bernbeck [180]. In 1929, Maximov [181] noted that an increase in wind speed deprived plants of water and favoured their wilting. This led to the closure of stomata and delayed the assimilation of CO2 ; even so, the plant continued breathing and soon died. Windbreaks were effective: by reducing wind speed, they favoured the assimilation of the carbon dioxide essential for the crop growth. The 1930s were dominated by the disaster of the soil erosion in the Dust Bowl and by Hugh Hammond Bennett (1881–1960) (Sect. 8.3). He established the foundations of soil conservation in a series of papers culminating in his 1939 book [119], founded the Soil Erosion Service and the Soil Conservation Service, played a central role in making the American politicians aware of this issue and promoted the establishment of many experimental stations, the first of which was set up in 1933. Thanks to Bennet, America was pervaded by a passion for studies. Raphael Zon (1874–1956) [182], in 1935, and Daniel Den Uyl [183], in 1936, proved that the drop in wind speed takes place for a distance from 10 to 30 times the height of trees forming the windbreak. Pilot projects for establishing experimental stations started in parallel. The most famous were set up between 1935 and 1940 in Conquest and Aneroid, Saskatchewan, in Lyleton, Manitoba and in Indian Head. Between 1944 and 1945, Bates [184] identified the wind speed drop due to windbreaks as the primary factor from which three secondary aspects derived: the reduction of the mechanical wind action on plants, the limitation of soil erosion and the alteration of the local microclimate. As regards the third aspect, Bates noted that the wind dried up the soil; the windbreaks opposed this phenomenon by preserving humidity and reducing evaporation by up to 65%. During the day, thanks to windbreaks, temperature increased downwind, originating a positive effect; by night, temperature dropped, causing negative effects in case of frost; however, by night the crops rest, so the beneficial effect is prevailing. Bates also remarked that natural windbreaks could also be disadvantageous: their roots subtracted humidity and nitrogen to cultivations and their foliage subtracted light to crops. It was advis-

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Fig. 8.54 Effects of a shelter as regards the wind [185]

able, thus, to interpose a space equal to one or two times the height of trees between windbreaks and crops. Bates reported the results of tests in Nebraska, Kansas, Iowa and Minnesota, showing a clear predominance of advantages on disadvantages. He noted that the snow drift in the wake of windbreaks, if present, preserved terrain humidity and increased it when it melted. He studied the effectiveness of windbreak orthogonal to the wind direction and recommended various measures to take in case of variable wind direction. In 1951, Charles Ernest Pelham Brooks (1888–1957) published a book [185] where he identified four zones where wind was altered by a windbreak (Fig. 8.54). In the upwind zone (A), the speed started decreasing from nearly six times the windbreak height. Behind the barrier (B), the speed dropped to 15–40% of the undisturbed value; the maximum reduction occurred at a distance 3–4 times the windbreak height. From 6 to 12 times the obstacle height (C), the wind speed grew up to 75–80% of its initial value; here, the wind was turbulent in inverse proportion to the screen porosity. The wind assumed its undisturbed condition again (D) at 24–30 times the obstacle height. These estimates were almost independent from the windbreak height and from the wind speed. Other studies started in 1949 at the Lake States Forest Experiment Station, Nebraska [186], and in 1952 at the Kansas Agricultural Experiment Station, the centre headed by Chepil (Sect. 8.3). During these researches, field and wind tunnel tests were carried out to assess the effectiveness of natural and artificial windbreaks used to protect crops [187] and houses [188] (Sect. 8.6). They proved that solid barriers reduced the mean wind speed, but created harmful eddy formations; exceedingly, porous barriers were not effective; the size of protected area depended on the barrier height. The rows of tree with adequate foliage represented an excellent protection [189].

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625

While these researches were carried out in the USA, many European countries understood the role of wind on agriculture and the effectiveness of windbreaks to improve the microclimate. In 1935, Paul Otto Rudolf and Suren Rubeniam Gevorkiantz [190] published the measurements carried out in Russia, remarking that windbreaks reduced evaporation and increased harvests by up to 30%. In 1936, Bodrov [191] noted that a solid barrier was less effective in reducing evaporation than a porous one, since the turbulent stirring behind it carried the water vapour away from the screened area. In 1938, Woelfle [192] stated that, all other parameters being equal, evaporation was nearly proportional to the square of the wind speed; this correlation was less marked near the most effective barriers. In that same year, Wilhelm Kreutz [193] confirmed that the temperature was higher near barriers; he also noticed that the humidity increase in the fields protected by artificial barriers was higher than the one due to natural barriers. In 1941, Gorshenin [194] carried out field and laboratory tests in Russia through which he confirmed the beneficial role of barriers to preserve humidity; he also proved that the stagnation of night air was the cause of freezing near edges. Between 1942 and 1943, the Swiss Nägeli [195, 196] carried out tests about the wind speed reduction due to solid and porous windbreaks (Fig. 8.55), observing that such effect was effective in terms of evaporation. Irminger and Nøkkentved (Sect. 7.3) published two reports, in 1930 [197] and in 1936 [198], in which they studied the screening effect of many shelters of different shape and porosity on the buildings located in their wake. Nøkkentved continued these researches, publishing two new papers in 1939 [156] and 1940 [157]. The first one showed the signs of his cooperation with Irminger (who died in 1938). The second, in cooperation with the Det Danske Hedeselskab (Danish Health Society) was linked, since 1939, to Martin Jensen, one of his students, who studied for his doctorate the role of shelters on microclimate and crops. Nøkkentved and Jensen noted that the screening effect in the wind tunnel was systematically greater than the real one. Nøkkentved was the first to understand that this error was due to the fact that the natural wind was more turbulent than the artificial one (Sect. 7.3). The research was interrupted, because of the Second World War and of Nøkkentved’s death (1945). Jensen resumed his studies in 1946 and continued them until 1954, when he completed his thesis [199]. It included utterly innovative results: Parts I and II laid the foundations of the model law (Sect. 7.3); Parts III and IV provided a decisive contribution to the knowledge of wind in agriculture. Jensen illustrated the state of the art in the first half of the twentieth century, identifying and discussing the five elements governing the growth of crops: temperature, humidity, carbon dioxide, light and soil. Above all, he carried out famous field and wind tunnel tests. In Part III of his thesis, Jensen illustrated the field tests carried out in Jyndevad, Jutland; a more limited series of measurements was carried out in Ugerup, near Kristianstad, Sweden. Tests were carried out by creating almost identical experimental conditions, in order to study three different situations: unscreened, weakly screened and strongly screened wind. Four measurement zones, each one of them with an area of 80 m2 , were created; every area was divided into three zones to evaluate the

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Fig. 8.55 Wind speed reduction by porous (a) and solid (b) shelters, in relationship with the shelter height and with the ratio between the distance of the examined point and the shelter height [200]

variability of the recordings. The Jyndevad tests were carried out using two types of shelters, sharing the same shape but with different density; Fig. 8.56 shows the more porous solution. Shelters were erected in May 1949, and tests were carried out over 3 years and 6 harvests. The measurements regarded wind speed and direction, temperature (through thermometers at 20 cm depth) as well as air humidity, rain, soil humidity and crop growth. The Ugerup tests started in 1950. To investigate the effect of the temperature increase regardless of other climatic changes, specific experiments

8.5 Windbreaks, Shelterbelts and Crops

627

Fig. 8.56 Reduced porosity shelters, installed by Jensen in Jyndevad, Jutland [199]

were carried out in Jyndevad, heating 9 m2 of soil with a grid of wires crossed by electricity, located 2 cm below the ground surface.28 In 1950, in cooperation with the Royal Veterinary and Agricultural College of Copenhagen, Jensen carried out wind new tunnel tests creating water, light and flow similar to the natural ones. Vegetation samples with different water content were placed in the wind tunnel in an area 60 cm wide and 80 cm long. The tunnel roof was made of glass and was lighted by lamps reproducing the harmonic content of solar radiation. They turned on and off, simulating the evolution of the day. Wind was only present when it actually blew in the field. Despite this accuracy, the tests were affected by uncertainties and difficult to interpret. In any case, the study proved that improvements due to shelters were linked to temperature increase and to the reduction of water consumption. The six harvests highlighted a production increase proportional to the screening of the shelters. Jensen started Part IV of his thesis by stating that shelters included any object reducing wind speed and could be classified into eight types: (1) hedgerows, i.e. trees planted in one or more rows; (2) screens, i.e. solid or perforated elongated bodies; (3) earth embankments and walls; (4) hedgerow systems, i.e. rows of parallel hedgerows; (5) systems of parallel screens; (6) shelterbelts, consisting of trees and shrubs; (7) woods and tree plantations; (8) landscapes, i.e. areas scattered with objects having protective purposes. Aerodynamic tests were performed for every type (Fig. 8.57), using smooth or corrugated floor, analysing the effect of the parameters on which the physical phenomenon depended, especially screen porosity and turbulence; the results were almost independent from the shape of the porosity. Every time the scale ratios of the roughness length and shelter size were similar, the results of wind tunnel tests reproduced full-scale measurements (Sect. 7.3). 28 The initial idea to heat soil using lamps was discarded because of the shadows created by lamps and of the difficulty of accomplishing a harmonic band of radiations similar to those coming from the sun.

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Fig. 8.57 Shelters subjected to aerodynamic tests by Jensen [199]

Jensen also illustrated a study of the sheltering effect of woods and plantations (Fig. 8.58). He assumed that the mean wind speed profile in a was in equilibrium with the terrain upstream the wood. In b, the speed was nil in the wood but, because of the continuity equation, it increased above it. Passing from b to d, an inner boundary layer developed; its growing thickness was related to the roughness of the upper surface of the wood. In d, four distinct portions of the profile existed: in 1, wind was absent; in 2, the profile was in equilibrium with the upper surface of the wood and the thickness of the boundary layer depended on the distance from d to b; in 3, the transition between 2 and 4 took place, with a speed increase due to the continuity law; in 4, the profile coincided with the one in a. At the end of the wood, there was a sheltered zone where the flow was locally separated; a new inner boundary layer grew, and, at great distance, it tended to reproduce a in f. The sheltering occurred in the area from d to f. These concepts were consistent with the current knowledge about transition profiles. Finally, Jensen studied the wind speed in open or wooded landscapes. He first carried out tests in Jutland along two lines: line 1 crossed an area with scattered hedges and woods; line 2 passed through hedges, woods and plantations. He then reproduced these conditions in the wind tunnel. Results proved that along line 1, the speed of the wind from the sea at 2 m above the ground was reduced by 20% in 10 km; along line 2, the reduction was 50% in 20–30 km. New studies were carried out by James Maurice Caborn [200] at the Department of Forestry of the University of Edinburgh in the mid-1950s. He analysed the effect of the tree and wood shelterbelts on wind speed, temperature, atmosphere humidity, evaporation, transpiration and soil humidity by wind tunnel and field tests. Model tests, carried out at the Imperial College, studied natural shelters with different depths

8.5 Windbreaks, Shelterbelts and Crops

629

Fig. 8.58 Effect of woods on the wind configuration [199]

(in the along wind direction), shapes and permeability, paying attention to the scale of the physical parameters. Caborn noted that, with equal permeability, the less deep tree shelterbelts were more effective; any permeability lower than 20% made shelterbelts ineffective. He also remarked the importance of the slope of the upwind side–and, in part, of the downwind side–of the tree crown; a positive 10° upwind slope deflected the flow upward, reducing wind penetration into the vegetation but reducing also the downwind sheltered area; thus, it was favourable for the wood but unfavourable for crops lying in its wake. Finally, Caborn studied the evolution of the vegetation over time and the need to preserve desired conditions through targeted interventions. Field tests were carried out for some tree shelterbelts near Edinburgh. The comparison between model and full-scale tests was satisfactory. The studies by Jensen and Caborn originated correlated researches [201] that will be subject to exponential growth starting from the 1960s.

8.6 Bioclimatic City Planning and Architecture Section 2.8 illustrates the efforts made by man, since ancient times, to build settlements and buildings drawing inspiration from bioclimatic principles. Initially, he relied on intuition and experience, applying rules and concepts handed down from father to son; afterwards, even thanks to Vitruvius, Alberti and Palladio, he acquired the knowledge of techniques and notions ensuring increasingly higher life standards. Towards the end of the nineteenth century and in the first half of the twentieth century, the bioclimatic culture in the city planning and architectural field showed an exponential growth. With the advent of the Industrial Revolution, cities were subject to uncontrolled growth that highlighted the need to operate by greater concern for the environment and human comfort; here originated the social and political willingness to realise projects drawing inspiration from bioclimatic principles, to ensure better living conditions. Many city planners and architects of the twentieth century

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Fig. 8.59 Howard [204]: a Three magnets; b Garden City

embraced this trend, turning it into an ideological banner. A drive aimed at studying new bioclimatic concepts on scientific grounds developed in parallel. A circular process derived: the willingness to build projects based on bioclimatic premises offered endless ideas to research. The research, in turn, provided rational answers to problems that in the past were approached through experience and tradition, indicating innovative and effective solutions. Wind played an essential role within this context. In 1870, Nuremberg introduced the first urban plan laws on the natural light required for every home. In 1874, Sweden issued a law stating that city plans had to guarantee light and air in accordance with housing standards. Around 1900, the Wien city plan made use of a study about the direction of the prevailing winds, so that the fumes emitted by factories were driven away from the city [202]. In the meantime, Sir Ebenezer Howard (1850–1928), a British city planner interested in social issues, pursued the idea of a cooperative city where land speculation would be eliminated and the ideal condition of urban and rural life came true [203]. Drawing inspiration from an utopian tale by Edward Bellamy (1850–1898), Looking backward (1888), Howard expressed his thought in a 1898 book, To-morrow: A peaceful path to real reform (reprinted in 1902, Garden cities of to-morrow [204]). In 1899, he founded the Garden Cities Association, the oldest British environmental organisation. His Three magnets drawing (Fig. 8.59a) posed a key question: “Where are people going?” Howard identified three choices—the city, the country and the city-country—namely the three magnets; this was the origin of the garden city concept (Fig. 8.59b), i.e. suburban cities surrounded by permanent belts of agricultural land. Letchworth (Fig. 8.60a), the first garden city inspired to Howard’s concepts; was designed by Barry Parker (1867–1947) and Raymond Unwin (1863–1940) for 35,000 inhabitants; it stands in Hertfordshire, 50 km away from London, and its construction started in 1904. The second garden city drawing inspiration from Howard, Welwyn (Fig. 8.60b), was designed in 1919 by Louis de Savoie-Carignan (Louis de Soissons, 1890–1962) 30 km away from London. Both Letchworth and Welwyn had their

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Fig. 8.60 a Letchworth [205]; b Welwyn

industrial areas located to the east, so that the prevailing winds carried the polluting fumes away from the city [205]. They were the reference model for all the subsequent garden cities 29 [203]. Nikolaj Aleksandroviˇc Miljutin (1889–1942), Russian architect, urbanist and Finance Minister, designed Stalingrad and Magnitogorsk on economic grounds, in accordance with a linear pattern [206]. Magnitogorsk stands in the south-western Siberian Russia; it was founded in 1929 and was the seat of one of the greatest Russian steel mills and of many industrial plants manufacturing machinery, cement, coke, chemicals and glass. Like Howard, Mlijutin studied the location of the industrial and residential zones in accordance with the direction of the prevailing winds [205, 207]. In the same period, three architecture masters—Frank Lloyd Wright (1867–1959), Richard Buckminster Fuller (1895–1983) and Charles-Edouard Jeanneret (Le Corbusier, 1887–1965)—left an unforgettable mark on bioclimatic design. Wright, an American architect and a pioneer of the Modern Movement, supported an “organic” and “functionalist” architecture opposing the neoclassic and Victorian ornamentalism, advocating a concept where aesthetics is less important than practicality: “form comes after function” (1901). He maintained that the building, a unit whose parts integrate into a balanced whole, must blend with the surrounding environment up to become part of it. The architectural form must be determined 29 The German architect Hermann Muthesius (1861–1927), inspired by Howard and Letchworth, gave an essential contribution to Hellerau (1909), the first garden city in Germany. After the Second World War, the British government favoured the construction of over 30 communities based on Howard’s principles between Letchworth and Welwyn: the first was Stevenage in Hertfordshire, the last and largest was Milton Keynes in Buckinghamshire. Howard’s ideas also provided inspiration for Canberra, the Australian capital, and for Epcot, Florida, the Walt Disney’s (1901–1966) amusement park.

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Fig. 8.61 Frank Lloyd Wright: a Larkin Building, Buffalo; b Robie House, Chicago

in relation to the specific use of the building, the environment including it and the materials used. Wright paid special care to the internal air circulation, using both forced and natural ventilation [206, 208]. The Larkin Administration Building, built in Buffalo in 1904 (Fig. 8.61a), was one of the first office buildings using air conditioning. It was built in masonry with double glass windows and was hermetically sealed to protect internal volumes from the noxious gases of trains at the New York Central Station and from the pollution of factory chimneys. The external air was drawn in the upper part of the building, above the height of pollution; from there, it was blown down to the basements, where it was cleaned and heated; finally, it was blown upward through ducts made of holed bricks and distributed at the various floors. Wright used similar principles for the Isabel Roberts House in River Forest (1908) and for the Frank J. Baker House in Wilmette, Illinois (1909). In the Robie House in Chicago (1909) (Fig. 8.61b), one of his famous “prairie houses”, Wright heated the interior by means of hot water. This opened the building to air and light, creating one of the most successful examples of climatised house. The courtyard, on the north side sheltered from freezing winter winds, was cool and shaded in the summer; the ground floor, which was also sheltered, was a cool air reservoir even when no wind was present. The layout of the windows at the living floor created an effective natural cross-ventilation system. Fuller, an American architect, inventor and writer [208–210], influenced many generations of architects and engineers with his optimistic view of a world that could be improved through the use of technology for peaceful purposes: “Don’t try to fight forces with forces: use them”. He gave strategic importance to sustainability (Sect. 7.6), to the production of renewable energy and to a link between architecture and environment that led him to the environmental design concept. He remarked that solar radiation originated wind, the melting of glaciers, the photosynthesis of the plants; mankind could take part in these processes altering every form of metamorphosis. In 1927, Fuller conceived “The air ocean world plan”, a project involving ten residential towers in unsettled and unaccessible areas (including the Arctic Polar Circle, the Alaska Coast, Greenland, the Siberian coast, the Sahara desert and north-

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Fig. 8.62 Buckminster Fuller [209]: a “multiple deck 4D house”; b its streamlined version

ern Amazzonia), linked by airlines; it interpreted the planet city concept, devised to deal with the rush of building concentrations. The individual tower was called “multiple deck 4D house”; its weight was so low it could be transported by Zeppelin dirigibles (Fig. 8.62a). Its more revolutionary, and impressive version was enclosed in a transparent streamlined shroud (Fig. 8.62b) that rotated around the building, automatically arranging itself in the direction offering lesser resistance to the wind; by so doing, it reduced the internal stresses at the tower base, limiting its weight and making transportation by air easier. He was, therefore, a forerunner of aerodynamic control, which is nowadays increasingly used for towers and skyscrapers [211–214]. Between 1927 and 1929, Fuller designed and patented the “Dymaxion House”, a self-contained, transportable residential unit based on bioclimatic ideas. The building was made of light aluminium, was easy to move and assemble and was suited for windy climates. It had a hexagonal plant around a central column that housed the technological systems; at its top, there was an air intake that favoured the natural ventilation of internal rooms by convection.30 It accomplished “a perfect balance between the atmosphere and the needs of man”. Fuller resumed the design of Dymaxion House in 1945, making several changes. The hexagonal building became circular and assumed the shape of a flattened bell (Fig. 8.63a); at its top, there was a circular structure that, by revolving around a central antenna, used wind as natural means of ventilation and to cool air inside

30 Fuller’s ventilation system took its cue from the Siberian grain silos using the dome effect. Placing a single opening at the dome top and many smaller perimetral openings at a lower level, a circulation is originated inside the dome that draws cold air downward.

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Fig. 8.63 Buckminster Fuller: a Dymaxion House (1945); b geodetic dome for New York City

the house. Despite some requests, only two prototypes of this building were built, “Barwise House” and “Danbury House”. In the meantime, Fuller shifted his researches from the single building to the ecosystem. Aiming at the construction of light and easily transportable buildings, he conceived his geodetic dome between 1945 and 1949. The dome was intended as an energising valve between external and internal environments and the ideal tool to organise human activities in accordance with environmental standards. Fuller understood the severity of the urban pollution issue and admonished: “We soon will have to rename our planet ‘Poluto’ and to promote the hypothesis of environmental control system on a city scale”. Dwelling about the pollution rate in New York, he designed a utopian dome, two miles in diameter, which enclosed a large part of Manhattan (Fig. 8.63b). Le Corbusier, a Swiss-born naturalised French architect, urbanist, painter and essayist, exerted a strong influence on modern architecture. His theories, formulated between 1920 and 1925, reached their peak with his concept of an ideal house as “dwelling machine”. As a confirmed functionalist, he looked for a style suitable to the twentieth century, based on the use of new materials and on the need to give concrete answers to contemporary requirements, starting with urban planning and with the design of buildings with high housing standards. Aiming at such objectives, Le Corbusier lavished interest towards the environmental factors [208], introducing the use of the “climatic grid” (Fig. 8.64), a “material visualisation tool that allows listing, co-ordinating and analysing the climatic data of a given location, with the aim of directing architectural research towards solutions in accordance with human biology”. The grid was divided into four horizontal belts corresponding to the four climatic parameters—temperature, air humidity, wind speed and direction, thermal radiation—and into three vertical sectors, corresponding to the design stages, that identified environmental conditions, the variants introduced to ensure comfort, and architectural solution. The drawings were the architect’s answer to the problem under study and formed the “booklet enclosed with the grid”. The Sarabhai House in Ahmadabad, India (1955), was a product of this criterion; it was

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Fig. 8.64 Climatic grid by Le Corbusier [208]

Fig. 8.65 Chandigarh [222]: a original plan by Mayer; b final plan by Le Corbusier

located in a tropical environment and was exposed to the monsoon two months every year, but it ensured effective natural ventilation by means of a roof fitted with vaults oriented to favour the channelling of the prevailing south-westerly winds. In the meantime, a team of architects including Albert Mayer (1897–1981), Julian Hill Wittlesey (1905–1995), Clarence Samuel Stein (1882–1975) and Maciej Nowicki (1910–1950) formulated the city planning design for Chandigarh, the capital city of the state of Punjab in Northern India [215]. When Nowicki died, Le Corbusier joined the design staff and co-ordinated an international committee supervising the construction. Even though he retained many principles of the initial plan, he changed various aspects, including the layout of the urban fabric and construction materials. Starting from the curvilinear grid of Mayer’s plan (Fig. 8.65a), Le Corbusier developed a grid of orthogonal roads that created rectangular blocks of buildings (Fig. 8.65b). The individual buildings, with approximately rectangular plan and immersed in the greenery of parks and gardens, made use of exposed brickwork and stone. The work on Chandigarh started in 1951, and it was inaugurated in 1953; it is a brilliant example of city planning on bioclimatic grounds [202, 203, 216]. Making use of counselling by the climatologist Helmut Erich Landsberg (1906–1985), Le Corbusier oriented the city road grid in relation to the direction of the prevailing winds and to sun exposure (Fig. 8.66a). The study proved that the

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Fig. 8.66 a Orientation of city roads [202]; b Four season chamber, Nijo Castle, Kyoto

role of the wind prevailed on that of the sun; the main roads were then arranged in accordance with the direction of the prevailing winds, from north-west to southeast. Landsberg’s study also proved that a perfect alignment between wind and main roads was not essential: deviations of less than 20° did not compromise the quality of results; an appropriate arrangement of building blocks and the widening of roadbeds made deviations up to 30° acceptable. A research about the layout of building blocks and the urban comfort related to night breezes was also carried out. The industrial areas were located in the south-west part of the city to prevent day breezes from carrying noxious fumes over residential areas. The natural ventilation of buildings was favoured by the orientation of the road grid, by ventilation intakes on the roofs, by openings on the opposing sides and by sliding internal partitions. Similar partitions, conceived by the architects Antonin Raymond (1888–1976) and Ladislav Leland Rado (1909–1993) [202], were widely used in Far Eastern and Japanese houses, where they were the key element for internal ventilation [205]. The Nijo Castle, built in Kyoto on several stages from 1602, is a wonderful example of the artistic and functional use of these partitions (Fig. 8.66b). Analogous bioclimatic principles inspired the activity of Vasco Vieira da Costa (1911–1982), Paul Lester Wiener (1895–1967) and Josep Lluis Sert i López (1902–1983). Da Costa, an architect born in Angola, studied in Portugal, worked with Le Corbusier (1945–1948) and returned to Angola in 1950, becoming one of the leading exponents of the tropical version of the Modern Movement. Da Costa, a competent professional responsive to the environmental aspects and to the wind, affirmed the importance of orienting the building with regard to natural ventilation, maintaining that the main facades had to be perpendicular to the direction of the prevailing winds in the warmest periods of the year. He suggested criteria for the most effective orientation of the buildings in the cases where the study of the wind and of the sun led

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Fig. 8.67 a Cidade dos Motores [202]; b Breathing wall [202]

to contradicting choices. He provided the first rules about how far buildings must be spaced to ensure their ventilation. Wiener and Sert realised many bioclimatic interventions in Medellin, Cali, Bogotà and Tumarco in Colombia, Chimbote and Lima in Perù, Cidade dos Motores in Brazil. In Medellin, where prevailing winds came from the north, the industrial area was put in the south. The same principle was adopted in Tumaco, where all the buildings used natural ventilation. In Chimbote and in Cidade dos Motores (Fig. 8.67a), buildings were oriented in the direction of prevailing winds, and covered passages were built between blocks to shelter the inhabitants from sun and to ensure natural ventilation. A common element of the architecture of Da Costa, Wiener and Sert was a sort of screen, called “breathing wall” (Fig. 8.67b), which was placed on the building front to favour the air circulation and to protect the house from sun and oblique rain. The dormitory towns in New Jersey, built in the 1950s for those who worked in New York, drew their inspiration from similar concepts (Fig. 8.68a). Thick rows of evergreen plants formed wind-breaking barriers that sheltered inhabitants from cold winter north-westerly winds and favoured the channelling of cool summer southeasterly breezes [205, 217]. Ralph Erskine (1914–2005) started his career as an architect and city planner working at the design of Welwyn, under the supervision of Louis de Soissons, developing a style making reference to functionalism and to local building traditions. He moved to Sweden in 1939, and there he acquired great experience about Arctic areas, which brought him to approach and solve issues associated with extreme climatic conditions. Aiming at this goal, Erskine introduced the elements characterising his designs.

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Fig. 8.68 a Dormitory town in New Jersey [205]; b vaulted roof, Barberaren, Sandviken

The perimetral wall that sheltered the urban space from the cold northern winds was the most famous element of the residential centres designed by Erskine, such as Brittgérden (1959), Kiruna (1961) and Svappavaara (1961). The same concept was implemented in Barberaren, the most important area of the city of Sandviken, designed by Erskine around 1960 and built between 1962 and 1982. The complex consists of three blocks of elongated buildings, with huge copper vaulted roofs (Fig. 8.68b). As a whole, they formed a barrier against cold winds from the north. They also created a sheltered space facing south that reproduced, on a large scale, the residential courtyards. The vaulted roof was the second distinctive element of Erskine’s architecture [218, 219]. It could metaphorically be traced back to umbrella and was the fulcrum of the building protective strategies in terms of energy and insolation. The roof, paired with the perimetral wall, also formed a baffle that sheltered the areas facing south from northerly winds. It was part of a group of elements with aeronautical shapes, conceived to “pilot” the wind. With this aim, in Kiruna and Svappavaara Erskine built towers with rounded edges (especially Växjö towers in Kiruna), undulated roofs, shielding walls of variable porosity and building layouts drawing inspiration from wings. These design solutions, like Fuller’s shrouds (Fig. 8.67b), were forerunners of the aerodynamic control [211–214]. The research oriented towards bioclimatic aspects related to wind on scientific grounds followed two paths, aimed at the internal and external spaces of the buildings. The study of the internal spaces had a priority relation with the wind, especially as regards natural ventilation. Applying Baruch Givoni’s conception [220], it implied three problems: ventilation requirements, the physical mechanisms governing it and the design parameters affecting it. Building ventilation must guarantee health and improve the comfort of inhabitants, keeping air quality high; it is essential to continuously replace air made stale by life processes. The first researches on this subject date back to 1925, when an American bacteriologist, Charles-Edward Amory Winslow (1877–1957) [221], published a state of the art on the physiological role of air quality, proving that the effects

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harmful for health started when oxygen dropped below 16–18% and carbon oxide reached 1–2%. In 1937, Constantin Prodromos Yaglou (1897–1960) and William N. Witheridge [222] studied ventilation in relation to smells and fumes in the homes, correlating such requirements with population density. In 1947, William V. Consolazio and Louis J. Pecora [223] studied the link between natural ventilation and smells inside buildings; they availed themselves of 45 individuals that remained into a room for 17 days, 20 h a day, expressing a judgement, referred to a scale, on the perceived smell level; it was correlated with ventilation. This was the prelude to studies, between the late 1950s and the 1960s, made more significant by the assessment of new parameters, such as the body heat variation and the thermal gradient between the interior and the outside environment [220]. The study of the physical mechanisms and design parameters governing natural ventilation started in 1903, when Sir William Napier Shaw (1854–1945) held a cycle of lectures about air currents and ventilation at the Cambridge University [224]. In the 1947–1948 winter, J. B. Dick [225] carried out full-scale tests near Abbots Langley, Herts, U.K., by means of which he studied various heating systems in relation to the physiological needs of residents. It was essential to determine the amount of heat lost due to natural ventilation, i.e. because of the motion of the air crossing rooms and of the distribution of the external and internal pressure due to the wind. The tests, carried out with both open and closed doors and windows, highlighted the role of the pressure gradient due to the wind and of the thermal gradient caused by chimney effect: the former derived from the openings on surfaces subjected to different external pressures, like the leeward and windward sides of a building; the latter was originated by the different exposure to sun or by openings at different heights. The results of the full-scale measurements were compared with the model tests carried out by Irminger and Nøkkentved [197, 198] and by Bailey and Vincent [226]. In 1950, Dick resumed Shaw’s assessments and his own previous measurements, providing the first organic picture of the mechanisms and laws governing the natural ventilation [227]. He noticed that the airflow moving across a building depends on the external and internal openings. The former were, in general, doors, windows, chimneys and ventilation ducts. Neglecting cracks around windows and doors was never acceptable; they were essential for the building permeability. Taking into examination the ventilation due to the pressure gradient caused by wind actions, using a modern notation, Dick expressed the airflow crossing an opening as:  Q = CA

2p ρ

(8.35)

where C is the coefficient of discharge, A is the area of the opening, p is the pressure gradient through the opening, and ρ is the air density. Based on measurements on small openings, Dick found C ~ 0.65.

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Fig. 8.69 Airflow due to pressure (a) and temperature (b) gradient; A1 = 2A, A2 = 6A [227]

If N openings exist on the same face of the building, each one of them with area Ai (i = 1, 2, …, N) and all of them are subjected to the same pressure gradient p; they are said to be in parallel. The overall airflow Q is then the sum of the partial flows Qi crossing the individual openings. Equation (8.35) remains therefore valid, as long as: A=

N 

Ai

(8.36)

i=1

Two or more openings crossed by air in sequence are said to be in series. The most typical case involves two openings: the first, with area A1 , on the windward face; the second, with area A2 , on the leeward one; p1 and p2 are the pressure gradients of the two openings, p = p1 + p2 = pw − pl is the difference between the pressure on the windward face pw and the (negative) suction on the leeward face pl ; the incoming and outgoing flows are the same, Q = Q1 = Q2 ; A1 and A2 represent the overall areas of the windward and leeward openings. Dick proved that Eq. (8.35) remains valid as long as: A= 

A1 A2

(8.37)

A21 + A22

So, being known the external pressure p (Sect. 7.3), proportional to the square of the wind speed V, and the area of the openings, it is possible to obtain the airflow crossing the building. Even though this problem is not explicitly considered by Dick, his equations can be applied to determine the internal pressure pi of the building (Sects. 7.3 and 9.5). Considering again the case of the two openings (Fig. 8.69a), the use of Eqs. (8.35) and (8.37) provides the relationship:

8.6 Bioclimatic City Planning and Architecture

pi =

641

A21 pw + A22 pl A21 + A22

(8.38)

As regards to the chimney effect, i.e. the difference T = T i − T e between the temperatures of the internal and external air, using a modern notation Dick expressed the pressure gradient as: p = ρ g h

T Ti

(8.39)

where ρ is the air density, g is the gravity acceleration, h is the distance between the two openings through which the chimney effect takes place. In two-storey buildings (Fig. 8.69b), it is significant only if the wind speed is low 31 ; otherwise, the aerodynamic gradient prevails. Replacing Eq. (8.39) into Eq. (8.35), the airflow is given by:  Q = CA

2 g h T Ti

(8.40)

Figure 8.70 shows some measurements carried out by the Building Research Station. In the (a) diagram, corresponding to the absence of wind, the airflow Q is an approximately linear function of the root of the thermal gradient T (Eq. 8.40). In the (b) diagram, for small values of the wind speed V, Q is constant and is a function of T; as V increases, Q tends to an approximately linear function of V and then of the root of the pressure gradient p (Eq. 8.35). The most influential tests were carried out in the USA, at the Texas Engineering Experiment Station (TEES), and in Sydney, Australia, at the Commonwealth Experimental Building Station (CEBS). In 1945, TEES developed a pioneering research [228] on the better arrangement of trees, hedges and shelters around buildings aimed at favouring natural ventilation and improving environmental conditions in internal spaces (Fig. 8.71). Between 1951 and 1954, the same centre carried out full-scale and wind tunnel tests [229–233] that clarified the role of the parameters affecting natural ventilation [205, 234]. The fullscale tests were carried out on residential buildings and schools. The wind tunnel tests made use of plexiglas models; streamlines were visualised by means of kerosene fumes.32 The measurements proved that a single opening was not sufficient to create air circulation within a building (Fig. 8.72a). When air entered from small openings and went out through larger ones (Fig. 8.73a), a Venturi effect occurred that increased 31 Dick’s

remark was only valid for low buildings. In the case of tall buildings, both h and T can assume values so high to make the pressure gradient high. This situation became dangerous in skyscrapers, for openings at low and high floors, connected through the stair or lift well. 32 No speed measurements were carried out during the tests; the closely grouped streamlines pointed out high speed values.

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Fig. 8.70 Experimental measurements of Q as a function of [227]: a T 1/2 ; b V

Fig. 8.71 Effects of the greenery layout on the airflow [217]

ventilation; the opposed was ineffective (Fig. 8.72b). Any opening on orthogonal walls (Fig. 8.72c) as well as internal partitions (Fig. 8.72d) caused vortex airflows. External barriers (Fig. 8.73b), baffles (Fig. 8.73c) and grates (Fig. 8.73d) near the windward openings altered the airflow. Natural ventilation was really effective for inhabitants if the openings were located no more than 2 m above the ground level. Between 1954 and 1956, CEBS carried out wind tunnel tests [235, 236] that first approached the effect of tall buildings on the neighbouring microclimate. The measurement carried out on industrial buildings in the wake of a structure showed

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Fig. 8.72 Plan view of the airflow for different types of openings [217]

that as higher the latter, as greater was the flow inside the industrial building, in the direction opposed to the wind direction (Fig. 8.74). In 1957, Wannenburg and Van Straaten [237] studied natural ventilation through model tests on double pitch school buildings, carried out in South Africa in the wind tunnel of the National Mechanical Engineering Research Institute; they focused on the distribution of the external pressure as a function of the building shape and on the position and size of the openings. The coefficients of discharge of large openings were measured. Similar tests were carried out in Pretoria in 1960 [238]. Like the study about the climatic conditions of building interior spaces, even the one associated with external spaces had a priority relationship with the wind. It originated two correlated approaches, concerning the environmental behaviour of the human body and the physical mechanisms determining the environmental condition in open spaces. The study of the environmental behaviour of the human body was started in 1935 by Gold [239] who associated physiological comfort with the heat lost by the body due to wind and temperature. The turning point came in 1945, when Paul Allman Siple (1908–1968), an American explorer and Antarctic geographer, and Charles Passel [240] introduced the “wind-chill” concept. During an experiment in Antarctica in the winter of 1941, Siple and Passel measured how much time elapsed before a wet cloth froze, discovering that it depended on the wind speed. This originated the idea of transposing the concept to the human

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Fig. 8.73 Vertical cross-section of the airflow for different types of openings [217]

Fig. 8.74 Airflow in the wake of a structure [234]

body, observing that a body lost heat because of evaporation and convection at a rate that was proportional to the wind speed grazing its surface. For a lifeless object, this phenomenon, called wind-chill, reduced the temperature of the body until it reached the ambient one. A biological organism, conversely, attempted to oppose the phenomenon by keeping its temperature; this caused a feeling of cold and discomfort that depended on the temperature and on the wind speed. Siple and Passel quantified

8.6 Bioclimatic City Planning and Architecture Table 8.3 “Wind-chill index” by Siple and Passel (1945)

645

Class

WCI

Description

1

Higher than 10

No particular discomfort

2

From 10 to −1

Slight discomfort condition

3

From −1 to −10

Discomfort condition

4

From −10 to −18

Severe discomfort condition

5

From −18 to −29

Possible frostbite following prolonged exposure

6

From −29 to −50

Frostbite following prolonged exposure

7

Lower than −50

Quick frostbite even for short exposure

this concept by means of an index, called wind-chill index (WCI), which provided a measure of the heat rate lost by the body; it is given by the expression:   √ WCI = 33 − (33 − T ) 0.474 + 0.454 V − 0.0454V (8.41) where T is the temperature of the air in °C, V is the wind speed in m/s. Equation (8.41) is valid for T < 11 °C and V between 2 and 24 m/s. Siple and Passel introduced the classification reported in Table 8.3. In the 1960s, the original wind-chill index was transformed into the wind-chill equivalent temperature (WCET), i.e. the perceived temperature in the presence of wind. Little by little, this parameter became famous and was used both for scientific purposes and in media reports. The study of the physical mechanisms determining environmental conditions and the wind flow in open spaces was started by two pioneering studies carried out by the Texas Engineering Experiment Station in 1945 [239] and in 1957 [241]. The wind field due to various layouts of buildings was studied during a campaign of full-scale and wind tunnel tests. The arrangement in rows parallel to the wind direction created different conditions in relation to the transversal distribution of the buildings. When buildings were located one behind the other in aligned rows (Fig. 8.75a), at a distance less than 6 times their height, they were mutually sheltered and determined a vast volume of stagnating air between successive blocks; a staggered arrangement (Fig. 8.75b) made them more exposed to wind actions. The first distribution is therefore better suited to deal with cold winter winds, the second to deal with pleasant summer breezes. In the same period, Jensen e Franck [70] studied the sheltering effects produced by five 1- or 2-storey schools in rural areas. Analyses were carried out through wind tunnel tests in 1:200 scale. The aim was to determine the environmental conditions

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Fig. 8.75 Wind regimes in different building layouts [217]: a aligned rows; b staggered rows

Fig. 8.76 Sheltering effect created by a two-wing building [70]

due to wind in playgrounds and in the gardens of schools. The sheltering effect was defined by the parameter s = (vo − vs )/vo , where vo and vs are the wind speeds without and with shelters, respectively. Jensen and Franck provided many diagrams (Fig. 8.76) for isolated and grouped buildings and for various wind directions. Judging the cases where s is less than 50% of scarce interest, the diagrams reported curves joining points with equal values of s higher than 50%; the hachures with increasing density identified areas where the sheltering effect was increasing. The sheltering effect due to buildings was less prominent than the one created by porous natural or artificial barriers. Buildings provided sheltered areas of limited size; they originated eddy formations near the edges (s < 0); their effects were influenced by the wind direction. A new research line was born: from then on, it would be called pedestrian wind environment. It went through formidable development starting in the 1960s [242, 243], especially in relation to the appearance of an increasing number of tall buildings within the urban fabric.

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Chapter 9

Wind Actions and Effects on Structures

Abstract This chapter deals with the studies on wind actions and effects on structures carried out between the late nineteenth and the mid-twentieth centuries. It starts speaking of the developments associated with the evolution and failure of suspension bridges, as well as with the new issue about the behaviour of towers and skyscrapers in the wind. It then passes to examine the renewed culture spanning the whole range of structures that came to maturity in this period; it gained ground through state of the arts and textbooks representing milestones of a discipline that is herein organised along four conceptually sequential topics: design wind speed, building aerodynamics, dynamic response to turbulent wind and aeroelastic phenomena. The presentation of the design wind speed addresses the mean and peak profiles, the time–space structure of turbulence and their probability of occurrence. Building aerodynamics is illustrated with special regard to the growing use and potential of wind tunnel facilities. The dynamic response to the turbulent wind is examined with reference to the transition from deterministic to random dynamics. Aeroelastic phenomena are discussed mainly with regard to vortex shedding, galloping and flutter.

Wind actions and effects on structures represent the cornerstones of the studies carried out between the late nineteenth and the mid-twentieth centuries. They provided continuity with the nineteenth-century research about cable-suspended, girder and truss (Sects. 4.8 and 4.9) bridges, showing developments related to the evolution and failures of suspension bridges (Sect. 9.1). A new culture about the behaviour of towers and skyscrapers in windy conditions (Sect. 9.2) gained ground in parallel, whose origins can somehow be traced back to the pioneering evaluations on the Eiffel Tower (Sect. 4.7). Suspension bridges, towers and skyscrapers are the icons of the structures vulnerable to wind; a renewed culture spanning the whole range of structures (Sect. 9.3) came, however, to maturity in this period; it gained ground from 1887 to 1961, through state of the arts and texts representing the milestones of a discipline that was organised along four conceptually sequential topics: the design wind speed, building aerodynamics, the dynamic response to the turbulent wind and aeroelastic phenomena. © Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_9

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The design wind speed study (Sect. 9.4) finalised the arguments approached in Chap. 6 to structures. It dealt with the mean and peak speed profile, with the time–space structure of turbulence and with their probability of occurrence. Building aerodynamics (Sect. 9.5) made use of the advancements in fluid dynamics (Sects. 3.6 and 5.1) and in the measurements of pressures and forces on bluff bodies (Sects. 7.1–7.3). It determined the rules that express, by means of parameters called aerodynamic coefficients, the static wind actions on structures considered as indeformable. The dynamic response to the turbulent wind (Sect. 9.6) dealt with the vibrations due to speed fluctuations on the basis of the advancements made by structural dynamics and by the theory of random processes (Sect. 5.2) in the early twentieth century. The knowledge transfer from the aeronautics sector (Sect. 7.4) to the structural sector around the mid-twentieth century played an essential role. The aeroelastic phenomena involve the situations in which the oscillations of structures, or of their elements, are so large as to change the wind field in which they take place. This originates wind–structure interaction phenomena that often stray into devastating forms of instability. The construction of a new generation of increasingly flexible, light and low-damped structures originated an unlimited range of phenomena traced back here, for the sake of simplicity, to the vortex shedding, galloping and flutter. The vortex shedding (Sect. 5.1) is relevant when it occurs with a frequency close to a natural frequency of the structure, causing a resonance phenomenon (Sect. 9.7). When the structural mass and/or the damping are small, it degenerates into a form of aeroelastic instability called lock-in. In this period, it chiefly appeared in chimneys and cables. Galloping (Sect. 9.8) takes place through vibrations of unstable nature, mostly orthogonal to the wind direction. They may develop when the prime derivative of the lift coefficient with respect to the wind angle of attack is negative. In this period, they mostly affected ice-covered cables. Their study was carried out in parallel with that concerning the autorotation of airplane wings (Sect. 7.4). Flutter (Sect. 9.9) is an aeroelastic instability usually involving two degrees of freedom, the cross-wind displacement and the torsional rotation. It was studied as a consequence of the Tacoma Bridge collapse, borrowing concepts and methods developed in aeronautics (Sect. 7.4). The whole range of the subjects covered in this chapter highlights complex phenomena whose study required the joint use of advanced experimental and mathematical tools. They planted the seeds of the evolution that took place from the second half of the twentieth century also thanks to the advent of the electronic computer (Sect. 5.3). The grounds of these topics, however, were already present in this pioneering and founding age.

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9.1 The Evolution of Suspension Bridges Between the late nineteenth and the early twentieth centuries, engineers became aware that only suspension bridges could allow crossing long spans. Within this context, more and more calculation theories made their appearance; they were applied and verified on increasingly long and sleek bridges, giving rise to a lively cooperation between researchers and engineers [1–4]. Starting from the Rankine theory, the Swiss Wilhelm Ritter (1847–1906) in 1883 [5] and the French Maurice Lévy (1838–1910) in 1886 [6] developed elastic theory [2]. Like the Rankine theory, it assumed the cable as parabolic under both the permanent distributed load and the variable concentrated load. It, however, associated the strength in the hangers to the concentrated load, taking account of the flexural stiffness of the deck and of the axial stiffness of the cables. It thus attributed less flexural stiffness to the deck than the Rankine theory and, as a consequence, transferred more strength to cables through hangers. Ritter, in contrast with the use of very sophisticated mathematical analyses, insisted on carrying out simple measurements, on performing full-scale tests and on striving for aesthetic excellence [7]. The Williamsburg Bridge (Fig. 9.1a), completed in New York by Gustav Lindenthal (1850–1935) in 1903, was the first suspension bridge designed in accordance with this theory. It resumed the concept of two stacked and connected road levels. Its centre span was 488 m long, 2 m longer than the Brooklyn Bridge’s (Sect. 4.8). In comparison with the Brooklyn Bridge, the span was almost twice as thick and was hinged at its ends. The absence of the stay cables used by Roebling was linked to the little trust the engineer of that age had in them and on the impossibility of evaluating their effects by elastic theory. Such theory, on the other hand, did not lead to clear critical states [8]. The turning point took place in 1888, when the Austrian engineer Josef Melan (1854–1941), resuming some ideas developed by Ritter in 1877 [9] and by Augustus Jay Du Bois (1849–1915) in 1882 [10], formulated in Wien the flexural theory [11], the first calculation method for suspension bridges taking account of the second-order effects. Unlike the elastic theory, it considered the change in the cable shape due to

Fig. 9.1 a Williamsburg Bridge (1903); b Manhattan Bridge (1909)

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the concentrated load. He thus attributed to cable stiffness a role more important than that of deck stiffness [12]. Leon Solomon Moisseiff (1872–1943) applied the flexural theory to the Manhattan Bridge (Fig. 9.1b), a light bridge with a 448 m span, designed by Lindenthal and opened to traffic in 1909. The flexural theory, like the Navier, Rankine and elastic theories, continued to overlook the vertical and torsional wind actions on the deck. The engineers, however, clearly believed a suitably stiff deck made examining wind effects a meaningless proposition. Charles Walker Raymond (1842–1913), William Herbert Bixby (1849–1928) and Edward Burr wrote, in 1894 [13]: “to consider upward wind pressures is hardly required for long, modern and properly stiffened bridges, since observations show that they are of a small order magnitude, with the exception of the ones peculiar to gorges or occurring during cyclones and tornadoes”. In 1913 David Bernard Steinman (1886–1960) published the English translation of the Melan theory [14], from which he derived his treatise on suspension bridges [15], enlarged in the 1929s edition [16]. It had great influence on the development of this structural typology in the USA, not least because, by allowing to reduce deck stiffness, it brought about significant savings. Moisseiff used such advantages to design the Bear Mountain Bridge (1924, L = 497 m), the Delaware River Bridge, then named Benjamin Franklin Bridge (1926, L = 533 m) and the Ambassador Bridge (1929, L = 564 m) (Fig. 9.2a). At the time of their construction, each one of them was the longest in the world. It is especially worth mentioning the evolution of the ratio between the span length L and the deck thickness D, which passed from 60 in the Manhattan Bridge to 84 in the Ambassador Bridge. In 1931, Othmar Ammann (1879–1965), using the same theory, designed the George Washington Bridge (Fig. 9.2b), a bridge on the Hudson River with a L = 1066 m span, the first bridge exceeding the threshold of the one-kilometre span. The ratio L/B = 33 between the length and width (B) of the deck, as well as the increase in length in comparison with other bridges of this era were amazing; the span of the George Washington Bridge was almost twice as long than the one of the Ambassador Bridge.

Fig. 9.2 a Ambassador Bridge (1929); b George Washington Bridge (1931)

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The original project for the George Washington Bridge envisaged two levels: an upper highway level and a lower railroad level. Afterwards, it was decided to drop the railway level and to avoid the connecting truss.1 The bridge, however, was so heavy it initially properly withstood wind actions. Amman, applying the flexural theory, even went as far as to prove that, for long and heavy bridges, the importance of deck stiffness tended to disappear. These concepts, as well as the bridge behaviour, provided engineers with a false sense of confidence, going a long way towards the obliteration of the experience accumulated thanks to Telford’s and Roebling’s teachings. Some theoretical developments provided an additional contribution to the trend towards the reduction of the deck stiffness, placing reliance in the cables. In 1933, Moisseif and Frederick Lienhard published a paper [17] in which they attributed the possibility of absorbing the horizontal wind forces to the cable stiffness. The joint use of this criterion and of the flexural theory allowed designers to almost eliminate deck stiffness. Moisseiff made use of this approach to design the San Francisco-Oakland Bay Bridge, a bridge with continuous spans L = 704 m long; its construction started in 1933 and ended in 1936. The same criteria inspired the Golden Gate Bridge (1937, L = 1280 m), the Thousand Islands Bridge (1938, L = 240 m), the Deer Island Bridge (1938, L = 329 m) and the Bronx–Whitestone Bridge (1939, L = 701 m). The Golden Gate Bridge (Fig. 9.3a), Joseph Baermann Strauss’ (1870–1938) masterpiece, was the new longest bridge in the world. It consisted of three truss girders: the horizontal one supported the road level and accomplished the stiffening as regards to horizontal wind forces; the two vertical ones were arranged sideways at the deck intrados. The bridge, then, had a shape like an inverted U, which possessed limited torsional stiffness. The L/B = 47 and L/D = 168 ratios were sensational. The Deer Island Bridge, designed by Steinman, and the Bronx–Whitestone Bridge, designed by Amman, were the first bridges with solid wall stiffening vertical girders; they offered an aesthetically innovative image. The Bronx–Whitestone Bridge (Fig. 9.3b) had a thickness D = 3.40 m and a L/D = 206 ratio, even greater than the Golden Gate Bridge. When achieving greater ratios appeared impossible, they were further increased in the project of the Tacoma Narrows Bridge (Fig. 9.4a). In its original version, developed by Clark Eldridge (1896–1990) in 1938, the bridge was a suspended lattice frame; it had a central span L = 792 m long and two side spans, each of them 396 m long; the deck was B = 12 m wide and D = 7.60 m thick. The work was so formidable that Eldridge requested advice by Moisseiff. The latter overrode the assignment he was entrusted to and radically altered the project until he reduced its cost from 11 to 6.4 million USD: to achieve this, he carried his theory to extreme limits [18]. Moisseiff increased the length of the central span to L = 854 m, shortening the side spans to 355 m; the deck was B = 11.90 m wide and was stiffened through a to its single deck level, in Washington Bridge L/D = 350; previous bridges reached, at most, L/D = 84.

1 Thanks

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Fig. 9.3 a Golden Gate Bridge (1937) [18]; b Bronx–Whitestone Bridge (1939)

Fig. 9.4 Tacoma Narrows Bridge: a 1940; b static model in 1:100 scale [22]

pair of solid wall I-beams with height D = 2.44 m. Therefore, L/B = 72 and L/D = 350. Moisseiff also reduced the height of the towers to 130 m; as a consequence, he reduced the sag f of the cables up to f /L = 1/12, when the usual values fell within the f /L = 1/11–1/9 range; according to Moisseiff this alteration would have increased the stiffness of the suspension system, partially offsetting the reduced stiffness of the deck. The bridge was very light; its weight was approximately 1/5 when compared to the George Washington Bridge. The design of the Tacoma Narrows Bridge [19, 20], following the practice of that time and using the fully developed knowledge about similarity theory [21], made use of a 1:100 scale static model (Fig. 9.4b). It was used to calibrate the parameters of the mathematical model and to study the structural behaviour at the various executive stages [22, 23]. Thanks to this approach, calculations were outstanding in terms of road loads. The bridge was perfectly dimensioned for a 200 kgf/m2 horizontal static force, corresponding to a 55 m/s wind speed, i.e. almost 200 km/h. The project,

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Fig. 9.5 Tacoma Bridge [22]: symmetrical (a) and anti-symmetrical (b) modes

like all of that age, considered neither the vertical and torsional wind actions, nor evaluations of dynamic type. The Tacoma Narrows Bridge, inaugurated on 1 July 1940, showed vertical oscillations right from the construction stage. It started vibrating when the wind reached 2 m/s (7 km/h). On increasing the speed, the motion changed, involving vertical modes at higher frequency2 (Fig. 9.5). At a 14 m/s speed (50 km/h), it vibrated on the seventh anti-symmetrical mode at the frequency of 0.5 Hz with amplitude equal to 75 cm, i.e. 1.5 m peak-to-peak. Cars travelling over it disappeared in the valleys created by the undulations and then appeared again at the crests. For locals, crossing it became a fashion, observing it a curiosity. It was dubbed “Galloping Gertie”. The Washington Toll Bridge Authority, confronting with bridge large oscillations even before its opening, strengthened the structure by stiffening cables, hydraulic dampers and diagonal cables. The stiffening cables, in the centre, were advantageous for side spans but useless for the central one. The hydraulic dampers, put between the towers and the deck to counter longitudinal motions, were ineffective. The diagonal cables initially restrained vertical and torsional motions but were subject to fatigue failure. The other measures taken into consideration did not appear to be reliable enough and were discarded. Once the construction was over, targets were fitted to measure oscillations through theodolites. Two alternative theories were formulated to interpret bridge oscillations. The first attributed them to atmospheric turbulence, assuming it produced a periodic 2 Waiting for computers and finite elements methods, free vibration analyses were usually performed

by the Rayleigh-Ritz method. Friedrich Bleich used the first two terms of the Fourier series. Steinman obtained simplified formulas of the characteristic frequencies and shapes.

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Fig. 9.6 Static sectional models in the wind tunnel of the Washington University [22]

lift variation near an eigenfrequency. The second, known as autorotation theory, explained oscillations as an incipient galloping condition due to the negative slope of the lift coefficient (Sect. 9.8). The monitoring of the bridge,3 the first ever performed, led to abandon the first theory; the research continued by carrying out pioneering wind tunnel tests (in a 2.4 × 3.6 m cross-section), coordinated by Frederick Burt Farquharson (1895–1970) at the Washington University in Seattle, aimed at validating the deck autorotation hypothesis and at redressing it. Borrowing classical analyses for airplane wings, four static models, marked as A, B, C and D in Fig. 9.6 and from now on defined sectional models, were built: the A model reproduced the actual cross-section of the deck; the B and C models represented the deck shape with different B/D aspect ratios; the D model was a flat plate with rounded edges. The A model showed negative slope of the lift coefficient and autorotation for angles of attack between −5° and +3°; it was attributed to the large flat surface of the stiffening beams near the leading deck edge. Several variants of the deck shapes were then studied to mitigate its vibrations (Fig. 9.7). Similar tests were carried out on the B, C and D models. At the same time, it was decided to modify the static model (in 1:100 scale) to make it suitable to represent dynamic phenomena. It was the first attempt to realise a dynamic model. It was set into vibration either manually or by electric pulses. The presence of excessive friction damped the motion to such extent as to make any conclusions meaningless. Thus, only static tests enjoyed any credit. The sectional model tests provided results that clarified the importance of the D/B aspect ratio, of the end-plates placed orthogonally to the model axis to eliminate border effects and of implementing drastic changes in the bridge deck aerodynamic behaviour through the alteration of its details. The researchers came to the conclusion of altering the deck shape to eliminate the negative slope of the lift coefficient. To 3 Oscillations were detected by means of theodolites through targets on lamps and sights on towers.

Movie shootings were also performed. The wind speed was measured by an anemometer conceived for ventilation purposes, so they were little more than estimates. In this period, only vertical modes were activated.

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Fig. 9.7 Lift coefficient of the A model and of its variations; AA indicates the original model [22]

achieve this, various measures were examined, including the use of curved shrouds, of inclined plates playing the role of flow baffles and of boring the webs of longitudinal beams.4 Baffles were considered the best solution since their installation would have been reversible and were then selected: they were quickly built and were ready in late October 1940. Their installation was delayed because of a possible oncoming storm. This decision turned out to be dramatically wrong [24]. On 7 November 1940, at 3:30 A.M., an employee of the Washington Toll Bridge Authority reported noises coming from mooring cables; at 5:00 A.M. he observed a slight stretching of cables. At 8:30 A.M. Eldridge crossed the bridge, but the oscillations he perceived were smaller than previous ones. At 9:00 A.M. the wind speed reached 18 m/s (65 km/h); the bridge oscillated on the eighth vertical mode at the frequency of 0.62 Hz; the deck showed a displacement approximately equal to 60 cm. At 9:45 A.M. Farquharson started filming bridge oscillations; this footage, now famous even outside the structural sector, was to play a key role in the interpretation of the collapse. At 10:00 A.M. some suspension cables broke and the bridge showed the limited torsional stiffness of its deck: from the eighth vertical mode, it oscillated on the first two-wave anti-symmetrical torsional mode, with the central point of the span at rest (Fig. 9.8a); the motion frequency dropped from 0.62 to 0.23 Hz; at intervals, the node disappeared and the deck oscillated with a single wave. At 10:30 A.M. the slab developed cracks and the frequency dropped from 0.23 to 0.2 Hz; the deck was subjected to torsional rotations approximately equal to plus or minus 35°; the deflections at the deck edge reached 4 m, i.e. 8 m peak-to-peak. At 11:00 A.M., with 4 The diagram of the twisting motion coefficients in relationship with the angle of attack proved that

the negative slope of the deck changed into positive slope for any examined measure. Since only vertical motions were observed, this result received scant attention.

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Fig. 9.8 Tacoma Bridge: a torsional vibrations [36]; b new wind tunnel cross-section [31]

a mean wind speed of 18.8 m/s, a stiffening beam became unstable, some hangers collapsed and a concrete slab element broke. The Tacoma Narrows Bridge fell into the water and most engineers’ certainties [25, 26] went to the bottom along with it. The Tacoma Narrows Bridge failure represented a historical turning point in the knowledge of the wind [26–28], giving a stimulus to the aeroelasticity studies already well known in aeronautics [29], which from then on became essential also in civil engineering [30]. It was the start of an age in which theoretical researches, wind tunnel tests and full-scale measurements accomplished a symbiosis with the studies aiming to interpret critical states, to restore existing bridges and to design new ones. The study of the causes of the collapse, assigned to Farquharson, Frederick Charnley Smith and George Sylvester Vincent at the Washington University in Seattle, was documented in five reports, published between 1949 and 1954 [22, 23, 31–33], which represent milestones. The first two reports [22, 23] examined the bridge design and the interventions attempted during its brief operational life; the third [31] interpreted the reasons of the collapse by means of experimental tests; the fourth [32] described the project for the reconstruction of the Tacoma Bridge; the fifth [33] discussed the dynamic response of suspension bridges in the light of new theories and of many available case studies. Examining the third report [31], it described the design and construction of a full dynamic model in 1:50 scale and of a new wind tunnel specifically built to perform the tests. As usual by then for many wind tunnels conceived to perform aeroelastic tests on bridges, it was equipped with a test chamber whose width (30 m) was much greater than the other dimensions. Figure 9.8b shows a cross-section, where I is the engine, J is the line shaft, B is the fan (10 parallel ones), C is a metal wire mesh, D is the tab-equipped jet that controls flow direction (angle of attack), E is the model, F is its support. The dynamic model of the Tacoma Bridge (Fig. 9.9a) was among the first ones, and the very first of this size, built taking into account the similarity principles of the fluid–structure interaction [34]. Except for the oscillations on the eighth mode (Fig. 9.6), it reproduced the bridge vibrations (Fig. 9.9b), emphasising the sequence

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Fig. 9.9 Tacoma Bridge [31]: a dynamic model in 1:50 scale; b dynamic response

of the vertical modes that activated as the wind speed increased. It also highlighted an aerodynamic instability form that from then on would be called flutter. The first dynamic tests on sectional models of the deck [31] were carried out simultaneously with the dynamic tests on the full model. They were carried out by extracting a deck quoin 152 cm long from the full model. The quoin was supported by three types of suspension systems, called torsional, vertical and free-spring mounts by Farquharson. Such tests were less taxing and simpler than the ones carried out on the full bridge, and allowed easily repeating the measurement after making alterations to the initial deck. They provided information with a meaning that went beyond the specific case for which they had been conceived. Similar tests were carried out in 1941 by Fritz Stüssi (1901–1981) and Jakob Ackeret (1898–1981) [31, 35] in Switzerland, at the Zurich Aerodynamic Institute, and in 1943 by Theodore von Karman (1881–1963) [31, 36] and Louis Dunn (1908–1979), at the Guggenheim Aeronautical Laboratory of the California Institute of Technology. On 21 November 1941, Ackeret wrote Farquharson a letter explaining the advantages, especially as regards to torsional motion, produced by a wide opening at the centre of the deck and parallel to its axis (Fig. 9.10). It originated aerodynamic damping actions that stabilised the oscillations. Ackeret’s plan anticipated by over half a century the cross-sections consisting of independent caissons linked by rigid cross-beams, which were destined to have wide publicity with the Messina Strait Bridge project [37]. Karman used two sectional models, in 1:90 (Fig. 9.11a) and 1:30 (Fig. 9.11b) scale, with regard to dynamic and static tests, paying particular attention to vortex shedding. The former, carried out by restraining the models through rigid springs, confirmed the linearity of the Strouhal law (Eq. 5.1) (Fig. 9.12a). The latter showed how, once the critical speeds that put the bridge into resonance were reached, vortex shedding was controlled by large deck oscillations in a neighbourhood of the critical speed value subsequently called self-control or synchronisation or lock-in domain; Karman noticed that its lower limit coincided with the critical speed value, while the

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Fig. 9.10 Effects of the opening along the deck axis suggested by Ackeret [31]

Fig. 9.11 Sectional models of the Tacoma Bridge by Karman in 1:90 (a) and 1:30 (b) scale [31]

Fig. 9.12 Vortex shedding from the Tacoma Bridge deck [31]: static (a) and dynamic (b) tests

upper limit was not clearly defined (Fig. 9.12b). 25 years still had to go by before Scruton clarified the parameters on which the amplitude of the domain where the Strouhal law was violated depended (Sect. 9.7). The committee tasked with the investigation on the causes of the collapse, made up of Amman, Karman and Glenn Woodruff, delivered its report on 28 March 1941,

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affirming the project had been carried out in the best possible way, but the effects the limited stiffness of the deck would have had on its aeroelastic behaviour had been overlooked. Analyses confirmed the scarce contribution of the deck to the overall stiffness that the stiffening effect of suspension cables had been overestimated and that mooring cables had no influence. The report ended claiming that “the current state of knowledge about the aerodynamic forces acting on suspension bridges and about those indirectly generated by the oscillatory motion of such structures provides a partial solution of the excessive motion and of the collapse of this bridge, but a complete quantitative analysis requires additional experiments and theoretical studies”. In 1967, Karman [25] reaffirmed the role of dynamics in cable-suspended bridges and its poor knowledge at the time of the collapse: “I hadn’t reckoned on the depth and long standing of the prejudices of the bridge engineers. Their thinking was still largely influenced by the consideration of ‘static forces’ like weight and pressure which create no motion instead of ‘dynamic forces’ which produced motion or changes of motion. Bridges had been observed to oscillate in the wind before, but nobody had thought such motion is important. Bridge failures were usually blamed on other things”. In parallel with, and by virtue of, the evolution in the experimental field, the first mathematical models about the aeroelastic instability of suspension bridges came into being. They were mainly stated by Hirai, Reissner, Steinmann, Pinney, Bleich and Selberg (Sect. 9.9) and schematised the deck as a system with two degrees of freedom (2 DOF), vertical displacement and torsional rotation, evaluating the uncoupled and coupled instability of the two motion components. The link to the theories developed in the aeronautics sector (Sect. 7.4) was one of the mainstays of the new formulation. Even though still far from current methods, many concepts behind such methods came into being in this period. The reality of that age offered an unlimited range of applications [4, 26, 38, 39]. The Fyksesund Bridge, designed by Arne Selberg (1910–1989) and opened to traffic in 1937, was very sensitive to wind. With a length L = 237 m and a crosssection similar to the Tacoma Bridge, it had L/D = 511 and L/B = 36 ratios; unlike the Tacoma Bridge, the side spans rested on piers instead of being suspended. The deck developed twice vertical oscillations that reached a peak-to-peak value equal to 160 cm and damaged the towers. They were first confirmed by wind tunnel tests; afterwards, in 1947, they were countered through stays linking the deck intrados to the base of the pier. The Thousand Islands Bridge, fitted with stiffening beams and built in 1938, showed peak-to-peak oscillations of 61 cm on the first vertical mode right from its completion; they decreased to 38 cm after the addition of stabilising cables. The Deer Island Bridge, a bridge with stiffening beams (L = 329 m, B = 7.6 m, L/D = 166) designed by Steinman through flexural theory, showed 15–25 cm motions on the first anti-symmetrical vertical mode from its construction. It was strengthened by cables and on 2 December 1942, in a 116 km/h wind, miraculously survived selfexcited vibrations with vertical displacements over 2 m [26]. It was then subjected to a second intervention that implemented a full system of stiffening cables.

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Fig. 9.13 a Bronx–Whitestone Bridge (1943) [4]; b George Washington Bridge (1962) [4]

The Bronx–Whitestone Bridge (Fig. 9.3b), built in New York in 1939 (L = 701 m), was subjected to self-excited vertical vibrations, for weak winds, during its construction. The design was modified before the inauguration with the addition of eight inclined cables running from the top of the towers to the deck stiffening beams; a damping system was used to mitigate torsional vibrations. Thanks to such measures, its oscillations did not exceed 40 cm for wind speeds ranging from 18 to 27 m/s. Even so, it was the subject of great concern: first, the similarity between its deck and that of the Tacoma Bridge was apparent; the wind tunnel tests at the Washington University showed that the critical wind speed was too small, nearly 20 m/s. Even though this estimate was in contrast with reality, in 1943 Amman took advantage of the addition of two new lanes to face the traffic increase to widen the deck and to place two truss beams, 4.30 m high, beside it5 (Fig. 9.13a) [39]. The design of the George Washington Bridge involved two running levels, one for the highway and the other for the railroad, connected by two wall truss braces arranged to form a caisson deck. For many reasons, only the upper level was built (Fig. 9.2b) and the bridge, also because of the war, was almost without torsional stiffness for over 20 years. It survived to several problems by virtue of the weight of the reinforced concrete deck and of the oversizing of cables, designed to support two running levels [2]. In 1962, when the second level was completed (Fig. 9.13b), it achieved required stability. The greatest concerns came from the Golden Gate Bridge (Fig. 9.3a) [39, 40]. Right from its construction, it was subjected to oscillations, not very extensive but alarming in view of the end of the Tacoma Bridge. They led to monitoring the bridge. The first anemometer was installed in January 1942. In March of the same year, an accelerometer was fitted to measure the horizontal components of the motion. In 1945, 10 accelerometers were installed to measure vertical motions. In this period, the wind speed was limited and vertical oscillations remained within such limits that no potentially catastrophical conditions were predicted. At the same time, the first 5 The persistent oscillation of this bridge led, in 1986, to the fitting of tuned mass dampers. In 2003,

the truss beam was replaced with flow baffles.

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Fig. 9.14 Golden Gate Bridge: measurements on December 1951 [40]

wind tunnel tests on sectional models of a real bridge were carried out. They revealed the torsional instability of the deck for a critical wind speed of nearly 100 km/h. This result was received with scepticism, and no measures were taken. On 6 June 1950, the mean wind speed reached 17 m/s (61 km/h), with direction orthogonal to the bridge axis; the bridge vertically oscillated, with 114 cm peak-to-peak displacements at the span centre. On 1 December 1951, the mean wind speed was 20 m/s (72 km/h) and its direction was again orthogonal to the bridge axis; between 17:50 and 18:00 a speed peak equal to 111 km/h occurred: the deck motion became an anti-symmetrical torsional one and the peak-to-peak vertical displacement at 1/4 of the span was 368 cm (Fig. 9.14). In 1953, the monitoring system was integrated by instruments to also detect torsional motions. In 1954, the torsional stiffness of the deck was increased by means of a truss brace at its intrados; it completed the inverted U shape of the deck, turning it into a caisson system. Summarising the knowledge accumulated in this period [33, 41] suspension bridges with stiffening beam deck displayed, above given wind speed thresholds, broad vertical and/or torsional oscillations in relationship with their D/B ratio. The thinner structures, like the Tacoma Bridge (D/B = 0.2), were sensitive to torsional motions. The thicker structures, like the Deer Isle Bridge (D/B = 0.28), were subjected to vertical motions. The separation between the two behaviours corresponded to D/B = 0.20–0.25. The situation improved by using truss decks or placing stiff truss beams beside the deck plane. Twin-level bridges with decks connected by side truss beams implemented a closed cross-section characterised by high torsional stiffness. In all these cases, the critical flutter speed significantly increased. This sum of knowledge received a formidable stimulus by the reconstruction of the Tacoma Bridge after the end of the Second World War. The project, by Dexter R. Smith (1891–1973), retained the towers, suitably stiffened, and nearly 2/3 of the anchor blocks. The deck, 10 m high and 18.3 m wide, consisted of four truss planes

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Fig. 9.15 Second Tacoma Bridge: a deck cross-section [24]; b dynamic model [32]

forming a box-like cross-section (Fig. 9.15a), retained enough transparency to offer a limited area to the wind force, was weighted to increase its stability and made use of dampers consisting of hydraulic cylinders. The bridge was inaugurated on 14 October 1950. The aerodynamic tests were carried out by Farquharson at the Washington University [32]. The cooperation between Smith and Farquharson was a dominant aspect of this construction and, from then on, a benchmark for large engineering works. At first, a full dynamic model in 1:50 scale (Fig. 9.15b) was built, comparing theoretical and experimental vibration modes. A deck quoin was extracted from the full model and used for tests on six different sectional models (Fig. 9.16). Each configuration was studied for angles of attack from −5° to +5°, showing high stability. Noticeable torsional oscillations, however, developed for angles of attack from +6° to +8°. They were eliminated by locally altering the shape of the leading edges and introducing longitudinal grating in the deck to allow the passage of air [24]. Once the best deck shape was selected, the full bridge model was updated and subjected to new tests, the results of which were compared with those of sectional model tests. A procedure close to the one currently used for the most important structures had come into being. In the same years, the USA discovered aeroelastic instability, England found new interest towards suspension bridges when, after the Second World War, it decided to improve the road links with Wales and Scotland’s east coast, building long-span bridges over the Severn and the Forth [28]. The Tacoma Bridge collapse, however, gave cause for concern. It was then decided to cautiously proceed with the study of the Severn Bridge only. For the first time, a bridge made use of the wind tunnel as a design tool. The analyses, assigned to Robert Alexander Frazer (1891–1959) and Christopher (Kit) Scruton (1911–1990) [42] at the NPL in Teddington, were carried out from 1946 to 1951. Such analyses were obviously related to the planned bridge, but they were carried out also with the aim of developing procedures and obtaining results that could be generalised to any suspension bridge [43, 44]. At first, four sectional models in scale 1:100 were built, matching the bridge configurations studied at design level (Fig. 9.17); tests were carried out in a wind tunnel with cross-section 1.2 × 1 m. The results indicated the best cross-section (Fig. 9.17d).

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Fig. 9.16 Configurations of the six sectional models examined for the second Tacoma Bridge [32]

At the same time, a full aeroelastic model in 1:100 scale, 15.2 m long (Fig. 9.18a) was built. This required the construction of a large temporary tunnel, near Thurleigh in Bedfordshire, with a test cross-section 18.3 m wide and 2.1 m high (Fig. 9.18b) [45, 46]. Other tests were carried out on sectional models in 1:32 scale fitted on springs. The comparison between different results confirmed the effectiveness of sectional models. Afterwards, once the bridge design was defined, analyses were repeated on a sectional model in 1:32 scale representing structural details with greater accuracy; this decision derived from the observation that in 1:100 scale any small alteration in the bridge shape entailed significant changes in the results [47]. In 1952, it was decided to use the Severn bridge project to build, without relevant alterations, the bridge over the Forth; the construction of the Severn Bridge was deferred to 1960. This led to wind tunnel tests on the towers of the Forth Bridge6 [48] and to study new structural solutions for the Severn Bridge. The designers of the new Severn Bridge at first suggested to stiffen the truss deck; this required new tests on a sectional model in 1:48 scale. Later (1959), being subjected to pressure to build a thin deck entailing savings, they developed two alternative solutions: a thin truss deck and, for the first time, a flat caisson deck. The second solution met strong hostility: it would have required new tests and sounded too be revolutionary. 6 The

study highlighted the importance of increasing the stiffness of the towers during the construction to balance the lack of the stabilising effect of the cables. This principle turned out to be fundamental in 1964, when the towers of the Forth Bridge exhibited large oscillations due to vortex shedding.

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Fig. 9.17 1:100 sectional models of the Severn Bridge [47]

Fig. 9.18 Severn Bridge [45]: a aeroelastic model in 1:100 scale; b wind tunnel

Kit Scruton supported the latter proposal; its selection, however, was due to an accidental event [49, 50]. A sectional model of the traditional cross-section was built in 1:37 scale. During the tests, a connection broke, the model was blown away and was destroyed by the fan blades. It was then decided to build a new model and Kit Scruton took advantage of this to carry out, with Denish Walshe, tests on the novel solution. They proved that a rectangular-shaped cross-section with the flat face exposed to the wind and perpendicular to the flow caused unstable phenomena. Scruton, drawing on his experience with airplane wings, studied a deck endowed with stylistic elegance and aerodynamic efficiency, carrying out new tests to identify the most suitable shape (Fig. 9.19a). The tests, in 1:48 scale, proved that the most stable shape was fitted with sharp edges and side footways (Fig. 9.19b). They also proved this solution had a safety margin much higher than the traditional one in terms of flutter and vortex shedding. The engineers acknowledged that the new shape required 2/3 of the steel required by the traditional solution and perfected the design starting from Scruton’s configuration. New tests were carried out to investigate the deck behaviour for various rotations

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Fig. 9.19 Cross-sections of the Severn Bridge decks subjected to wind tunnel tests [49]

and different traffic conditions. The results highlighted strengths and weaknesses. The former included optimisation of the use of materials, low drag to the wind and aeroelastic stability. The sensitivity to shape changes and the limited structural damping stood out among the latter. The first issue required wind tunnel tests that were reassuring for rotations up to 5°; torsional instability, however, developed for greater rotations; the influence of the Reynolds number was studied in a compressed air tunnel. The second issue was countered by means of inclined hangers that increased damping. It was the start of a new era for bridges.7 The studies started in 1955 to build Watako Bridge, the first long suspension bridge in Japan, are worth mentioning. They were assigned to Atsushi Hirai (1908–1993), the first scholar to develop a theoretical explanation of the Tacoma Bridge collapse (Sect. 9.9). The Watako Bridge centre span was just 367 m long; when it was inaugurated in 1962, it was the longest suspension bridge in the East.

9.2 The Evolution of Towers and Skyscrapers The construction of longer, lighter and bolder bridges forced engineers and builders to deal with the wind culture and issues since the early nineteenth century (Sects. 4.8, 4.9 and 9.1). The construction of tall buildings and towers [51, 52] followed a different path; until the late nineteenth century, they were almost exclusively built in masonry and were so heavy and rigid to be almost insensitive to wind (Sect. 2.9). The situation changed in the late nineteenth century, when the iron became the primary element of a new generation of towers and of a new building typology—the skyscraper—which gained ground in Chicago and New York. The engineers, unprepared before a sudden 7 The Severn Bridge, started in 1961 and finished in 1966, was built [50] transporting the floating deck quoins. Once they were positioned, they were hoisted by means of cables. Pioneering tests in 1:32 scale were carried out to evaluate wind actions and effects on the quoins during the hoisting stage. The results proved the dangerousness of this operation and identified the cable configuration that guaranteed the utmost stability.

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change, relied on a technique that from then on became more and more common: full-scale measurements [25]. The turning point occurred in 1889, on the occasion of the Paris International Exhibition, when the Eiffel Tower (Fig. 4.44a), reaching a height of 301.75 m, became the tallest structure in the world.8 Alexander Gustave Eiffel (1832–1923) realised it was a unique tool to carry out hitherto unprecedented scientific experiments. Besides his studies on wind (Sect. 6.5) and aerodynamics (Sect. 7.1), he carried out structural tests that were to become a milestone. Eiffel evaluated the displacement trajectories of the structure through a mirror and a theodolite. The mirror was placed on the terrace and was marked with concentric rings, divided into eight sectors to observe the displacement direction. The theodolite was fastened to a masonry block at the tower base and pointed at the mirror centre in the absence of wind and sun, at a temperature of 10 °C. Displacement trajectories were reported by hand on a diagram that reproduced the mirror on a reduced scale. Three daily readings were performed at 7:00 A.M., at noon and at 7:00 P.M. Additional readings were carried out in case of high temperature or wind speed. They proved that the tower, because of wind, moved along ellipses whose major axis was oriented in the wind direction.9 Eiffel reported that the maximum displacement took place on 20 December 1893, between 11:30 A.M. and 12:00 P.M., with a mean wind speed equal to 3.18 m/s and instantaneous peaks up to 44 m/s; the axes of the ellipse in the alongwind and in the cross-wind direction were 10 and 6 cm respectively (Fig. 9.20a). Eiffel noticed that the displacements were smaller than those envisaged, deducing that the calculation criteria in use overestimated reality (Sect. 9.6). He also noted that in sunny days the amplitude of the deformations caused by thermal effects was much greater than those due to wind. He recorded that on 15 and 16 August 1894, the thermal-induced displacements had been greater by 15 cm, with ranges in the order of 25 cm (Fig. 9.20b) [53]. Taking advantage of the tower height, he also measured the Coriolis force by means of a Foucault pendulum hanging from the top. While the Eiffel Tower became an icon of structural engineering, Chicago became the world capital of modern architecture. In 1879, William Le Baron Jenney (1832–1907) designed the Leiter Building, whose interior, consisting of wood-iron floors resting on cast iron columns, was independent from the self-bearing outer walls, dominated by large windows; it was the first example of the skeleton system. In 1881, Jenney designed the Home Insurance Building, a ten-storey skeleton building with a masonry shell and an internal metal frame, which was the first to be named a skyscraper; its height reached 55 m, making it the highest multi-storey building in the world. In 1889, Jenney designed its main piece of work, the Leiter Building 8 From

2520 BC, when the Pharaohs built the Great Pyramid, 146 m high, to 1884, the year the George Washington Monument, a 169-m-high stone stele designed by Robert Mills (1781–1855), was completed, mankind undertook a competition to build increasingly higher structures. Using stone and wood, over 4 millennia it improved by 23 m. With his steel tower, Eiffel made a 133-m jump upwards. 9 Today, it is well known that this is the result of the composition of two harmonic motions with the same period in two orthogonal planes; it is also known that lattice towers give rise to alongwind and cross-wind displacements of comparable amplitude.

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Fig. 9.20 Trajectories of the displacement at the top of the Eiffel Tower [53]

II, the first example of the cage system: all the vertical weights were supported by a metal frame, the outer walls providing a stiffening contribution against horizontal loads. With Jenney, the Chicago School came into being, leaving an indelible mark on the twentieth-century engineering and architecture. In this spirit, the Loop (the city business district) became populated with outstanding works—the Montauk Building (1882, 10 floors), the Rookery Building (1886, 12 floors) and the Tacoma Building (1889, 13 floors)—which increased the tallest building to 60 m height. The Tacoma Building lost this record in 1891, on completion of the Monadnock Building, a 17storey, 66-m-tall masonry building; this was the last time masonry stood comparison with iron. In the same year, the record went back to a metal building in neo-Gothic style, the Masonic Temple (1891, 20 floors), 83.5 m high. It was the last time, for many years, Chicago held this record. In 1892, George Browne Post (1837–1913) built the Pulitzer Building in Manhattan, a skeleton structure 94 m high. It represented the image of a different principle: in Chicago, the skyscraper was a huge, solid block; in New York, the soaring tower prevailed. According to Paul Goldberger (1950–), there was a proportion “as an elephant to a giraffe”. Corydon Tyler Purdy (1859–1944), considered the father of the skyscraper because of his contribution to the design of many tall buildings, symbolised the passing, from Chicago to New York, of the leadership in this structural typology. In the 1890s he assumed a key role in the debate between those who maintained that the metal frame had to be designed to integrally withstand the wind lateral action and those who believed that walls and partitions contributed to convey part of the loads towards the ground. Purdy published a series of papers [54] in which he insisted on the uselessness of assigning the resultant shear force at the base to the metal frame, since “the dead weight of the structure itself acts to some extent to counteract the distorting effect due to lateral force”.

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Fig. 9.21 a Metropolitan Life Tower, New York [52]; b Monadnock Building, Chicago

The architects were unprepared to deal with the capabilities offered by iron and steel. Engineers took advantage of this situation to rise to a prominent role; on the one hand, they developed increasingly evolved analysis methods, constructive details and structural systems; on the other hand, they used every component of the structure to guarantee its safety without altering its architecture, or arranging the most suitable alterations with architects. Purdy was the leader of this trend. In 1904, he presented a paper [55] at the national congress of the American Institute of Architects destined to become a cornerstone. A few years later, in 1910, in cooperation with Napoleon Eugene Charles Henry Le Brun (1821–1901), he built his masterpiece in New York: the Metropolitan Life Tower (Fig. 9.21a), the new tallest building in the world (213 m), second only to the Eiffel Tower in height. In 1894, the first measurements of the dynamic response of buildings to wind actions were carried out in Chicago, on the Monadnock Building (Fig. 9.21b) and on the Pontiac Building [25, 56]. The tests on the Monadnock Building used a plumb line sent down the stairwell from the roof. In witness of an age characterised by rigid structures, during a storm with gusts at over 130 km/h the maximum measured displacement was equal to 1 cm. Today, a glance would be enough to realise that everything could cause troubles to this building, except wind. At that time, this was not taken for granted. In 1910, Cyrus Alan Melick (1883–1953) carried out new measurements of the vibrations of a 17-storey office building built in 1901. During the tests, the max-

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imum wind speed reached 71 km/h and the building showed displacements that just exceeded 1 cm. Melick commented that walls and internal partitions probably reduced the displacement by 40% [57]. The most effective tests in this time were carried out in Italy by Father Guido Alfani (1876–1940), who, between 28 March and 9 May 1903, studied the vibrations of the Palazzo Vecchio tower10 in Florence (Fig. 9.22a). The Tower, Alfani wrote [58], “caused great concern (…) at a time when every Italian, repository of its art treasures, grieved over the sudden demise of the Campanile di San Marco11 in Venice (Fig. 9.22b). The governors of the Municipality of Florence wondered, therefore, if the daily shock caused by the gun shot announcing noon could not, over time, damage it. This represented the occasion and the reason for this work (…). To that end, and before carrying more complex and delicate machines up there, I made use of an artificial horizon in mercury; the latter, as everybody knows, ripples very easily, detecting the existence of a vibratory phenomenon.” Alfani discovered that vibrations really existed, but they were caused by the bell sound and by wind actions, not by the gun rumbling. “At the end of the preliminary experiences with the artificial horizon, and having undoubtedly determined that the tower was subjected to vibrations and oscillations due to various causes, (…) I thought about placing a recording device (a microseismograph) so that a visible track of the various phenomena under examination remained. (…) I must however remind that on [April] 8th a very strong N–E wind got up: it left on the tape (…) a very important diagram I reproduce here, with the warning that, given it excessive amplitude, almost a fourth of it is missing because of the insufficient width of the tape. The maximum hemi-amplitude of the recorded range is 42 mm. The wind speed was approximately 20 m/s.” Such words documented the approach to a phenomenon—the wind—hitherto mostly unknown. The vibration issue, conversely, appeared to be well understood: “The device I used in the first stages of the research—wrote Alfani—(…) was a small pendulum, even though with a fairly heavy mass, with a vertical amplifying lever, so that the two orthogonal movements were simultaneously recorded and translated into a curve of variable amplitude and regularity. A more exhaustive study of this complex phenomenon required a device capable of providing me with separate data about the three components, or at least about the two horizontal ones. I then built a new instrument I called trepidometer and during its construction I introduced some peculiarities that allowed me to easily change the elements of the machine. In fact, it stands to reason that, if the pendulum period is long, it will not affect the recording. If, conversely, the pendulum period is short and undulations with a long period have to be recorded, the peculiar vibrations of the pendulum will not significantly affect the sinusoid of the undulations.”

10 The Palazzo Vecchio tower is 94 m high above the square floor and 45.3 m higher than the tip of the palace. Its sides vary from 6.34 to 8.69 m. 11 The Campanile di San Marco, completed between 1156 and 1173, suddenly collapsed in 1902, after being repeatedly struck by lightning.

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Fig. 9.22 a Palazzo Vecchio, Florence [51]; b collapse of the Campanile di San Marco, Venice

The American debate about the contribution of walls to the resistance to wind actions continued in the 1920s, enriched by often conflicting opinions. An editorial in The Canadian Engineer on a hurricane that stroke Florida in 1926 affirmed that an examination of building walls in Miami showed that the frame started being put to test by wind only after the walls reached their ultimate resistant capacity. When this happened, the frame had to be able to absorb the whole wind forces by itself. Under such viewpoint, to distribute the horizontal forces between the fragile walls and the metal frame was wrong. In a 1929 paper [59], conversely, David Albert Molitor (1866–1939) maintained that tall buildings without the walls, partitions and floors, would show oscillations much greater than the highlighted ones. “A steel building frame—he said—is an engineering structure only so long as the frame is bare; but when clothed with architectural coverings of stone, brick and concrete, with concrete floors, tile partitions, etc., it becomes a composite structure the nature of which cannot be appraised in terms of mathematics.” According to Molitor, the architectural cladding increased frame stiffness by over 300–400%.

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Fig. 9.23 Vibration measurements carried out by Coyle [61]

The main contribution came from David Cushman Coyle (1887–1969), an engineer from New York who carried out the monitoring of several buildings [60, 61] between 1929 and 1931. In support of this issue, he wrote: “we know that there have been no spectacular collapses of high towers, but we know very little else in the way of definite check of current design practices. The large crop of new theories for wind design indicates that the profession is conscious of the fact that we have out-grown the old approximate methods; but it is not always apparent that we yet realise the extent of our ignorance in regard to the factors which should be taken into account”. Probably this is the first time someone insisted on the need to quantify calculation uncertainties to acquire knowledge about the actual safety margin of structures. To solve this problem, Coyle built a portable seismographic horizontal pendulum by means of which he measured, in the winter of 1930, the vibrations of the Metropolitan Life Insurance Tower12 (Fig. 9.21a). He simultaneously carried out similar experiences on the Ritz Tower, a more flexible and lighter 41-storey skyscraper. He discovered height was not the decisive parameter of the vibratory phenomenon. In fact, while the higher Metropolitan Tower displayed imperceptible motions, the lighter Ritz Tower showed vibrations that were not in the least negligible (Fig. 9.23) [25]. He then wrote: “As a rule the bracing of tall buildings has been regarded as a problem in safety. As less and less bracing is used, and they do not blow over, the feeling grows that the heavy construction of the past was unnecessary. (…) But the old towers, which were designed to be safe according to a theory which was perhaps ultra-conservative, achieved incidentally a result which was of more immediate importance. Their vibration in time of storm is slight (…). They are not only safe, but they are on the safe side of the motion which most people can feel (…). Some of most recent towers, on the other hand, have two or three times as 12 After

the Pulitzer Building (1892, 94 m) brought the record of the tallest building to New York, in that same city this record was broken by the St. Paul Building (1896, 95 m) by George Browne Post (1837–1913), by the Park Row Building (1898, 117.5 m) by Robert Henderson Robertson (1849–1919), by the Singer Tower (1907, 187 m) by Ernest Flagg (1857–1947), by the Metropolitan Life Insurance Company Tower (1909, 206 m) by Napoleon Eugene Charles Henry Le Brun (1821–1901) and Purdy, and by the Woolworth Building (1913, 242 m) by Cass Gilbert (1859–1934).

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Fig. 9.24 Bracings [56]: a sway-rod type; b latticed girder type; c portals; d knee type

much swing and are therefore, by that much, closer to the ‘threshold of sensation’ of the average man or woman. (…) In the case of high buildings the frame must be designed to resist wind pressure with sufficient stiffness to keep the vibration caused by the wind within limits that inspire the occupants with confidence in the strength of the structure.” The engineers of that age listened to his words with scepticism. The value of Coyle and of his intuitions was not understood until the 1970s, when macroscopic vibrations occurred. Two books published in 1930, by Fleming [56] and Spurr [62], offered a picture of the knowledge about skyscrapers at that time. Fleming’s book went beyond the boundaries of wind actions on buildings (Sect. 9.3). He approached this subject, which remains the core of his book, discussing three subjects: the typologies of resistant frames, structural calculation methods and constructive details. Fleming noted that the architects who designed the first tall office buildings made use of four types of braces (Fig. 9.24) described by Joseph Kendall Freitag (1869–1931) in 1901 [63]. Vertical sway-rod-type braces (a) were simple to make and did not create moments on the columns (Masonic Temple, Chicago, 1890). Latticed girder-type braces (b) entailed the difficulty of transferring horizontal forces among the columns only through storeys (Reliance Building, Chicago, 1894). Portal-type braces (c) were expensive but very effective for wide openings between the columns (Old Colony Building, Chicago, 1894). Knee-brace type (d) guaranteed high frame stiffness; they were a creation by William Le Baron Jenney, described by Frank Eugene Kidder (1859–1905) and Thomas Nolan (1857–1926) in 1921 [64]. These systems, with the partial exception of the knee-brace type, were gradually abandoned in favour of the gusset-plate type made of riveted, bolted, welded or mixed plates that joined girders and columns; this technique was expensive, did not achieve the stiffness of the previously described systems and originated large horizontal displacements because of wind actions; on the other hand, it guaranteed the maximum utilisation of the space.

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The gusset-plate type of wind bracing made the use of effective calculation methods necessary. They were developed in the first 30 years of the twentieth century, along two lines: the theoretical, or exact, methods and the engineering, or approximate, methods. The most famous exact methods are attributed to Johnson [65], Smith [66], Wilbur M. Wilson (1881–1958) and George Alfred Maney (1888–1947) [67], Clyde Tucker Morris (1877–1965) and Ross [68]; without numerical tools to solve systems of linear equations with many unknowns, they were complex and bothersome. The approximate methods can be traced to two families: the cantilever method, developed by Wilson [69], and the portal method, formulated with contributions by Fleming himself [70]; none of them could be applied to complex frames. Constructive details played an essential role as regards to wind. Fleming [70] described them by many pictures. He dwelt on the restraints of supported, continuous and clamped beams, on the stiffening of beams, columns and connections, on the use of rivets, bolts and welds. He emphasised the selection of connections, also in relationship to the freedom allowed for architectural choices. Spurr [62] resumed the concept of the structural layout evolution that led to a decrease in stiffness and to an increase in wind-induced displacements and vibrations. In the past, displacements received little consideration because the designer had great confidence in constructive systems. Now, it was necessary to carefully study them and to formulate criteria to reduce their excesses. Spurr proposed to limit the displacement between two floors to 1/1000th of the floor height and the displacement of the building top to 1/500th of its height. Spurr focused on the vibrations caused by wind. They were complicated by the undetermined nature of the pressures themselves and by the variability of the building size, shape, height and site. He emphasised some aspects usable by engineers: (1) the oscillation period is independent of the amplitude of the vibrations; (2) decreasing the building stiffness, the amplitude of the vibrations increases; (3) the frequency of the vibrations is proportional to the square root of the stiffness and inversely proportional to the square root of the mass. Spurr remarked that wind never caused the collapse of tall buildings. For buildings under construction, conversely, being subjected to damage was common: by way of example, the Myerkeyser Building (Fig. 9.25a), during the hurricane that struck Miami in 1926, was subjected to the breaking of windows and shutters and its residents perceived strong oscillations. As regards to people discomfort, according to Spurr acceleration is the main parameter, but displacement is just as important for tenants. Large accelerations coupled with small displacements are unnoticed; large displacements have little effect if they occur slowly and gradually. Experiments were to clarify such aspects. Following these developments, the American Society of Civil Engineers (ASCE) instructed the Sub-Committee 31 to prepare a report about the bracings of metal buildings. After five partial reports (1931, 1932 [71], 1933, 1936 and 1939), the final one was issued in 1940 [72]. It provided an overview of the knowledge of buildings concerning wind actions, bracing types and the distribution of horizontal forces in their members, methods for bracing calculation, secondary stresses and

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Fig. 9.25 a Myerkeyser Building (1926) [62]; b Torre del Parco, Milan (1933) [75]

torsional effects, the role of displacements13 and vibrations, and the overall strength and stability. The report affirmed that “only experience can clarify the relationship existing between the displacement and tenant comfort”. This proves that the ASCE Committee was unaware of Cesare Chiodi (1885–1969), an Italian engineer who in 1933 signed the structural design of the Torre del Parco in Milan, a lattice tower 110 m high (Fig. 9.25b), unique at that time. The tower, characterised by exceptional slenderness, supported a restaurant and a belvedere at its top [73–75]. The writings by Chiodi witness how wind action was a matter of concern in his time, his awareness he was dealing with a mostly unknown issue (“experience will prove if these calculation forecasts will be confirmed in reality”) and the willingness to set the problem within a correct physical frame to achieve realistic, but very cautious, engineering assessments (“the assumed wind pressure values can then be considered as highly conservative”).

13 The ASCE report remarked it was impossible to assess the contribution of secondary elements to stiffness and damping. It then proposed to express stiffness through the deflection index, namely the ratio between the top displacement of the load-bearing frame and its height. The building behaviour was satisfactory if the index was smaller than 1/500; in particular cases, indices as low as 1/250 or 1/200 were considered acceptable.

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Chiodi, making comments on his static analyses, wrote: “applying the usual methods for the determination of the elastic displacement f, considering the structure as clamped at its base, we obtain, in the hypothesis of the maximum wind pressure considered in calculations, f = 0.39 m. At the height of the restaurant floor (97.00 m) the displacement decreases to approximately 0.32 m. Except that (…) it is difficult that (…) such displacements really develop, it must also be taken into account that public will access the tower in relatively calm weather (…). The maximum deflection of the tower in the presence of the public will then decrease to less than 2 cm”. Today, this opinion arouses scepticism: a 39-cm displacement at the top, equal to 1/276th of the height, appears to be large even though by action of the design wind speed. It was probably the first time, however, an engineer stated the advisability of using differentiated actions and verifications in relation to the ultimate and serviceability limit states. Chiodi also maintained that “knowing the maximum acceleration assumed by the back-and-forth motion can be a matter of interest, since it is the acceleration with which the displacement occurs, rather than the displacement in itself, to make the phenomenon perceptible by people at the top of the tower”. Starting from this concept, he calculated its intensity using wrong expressions. By sheer luck, he estimated, for the displacement f = 0.019 m, an acceleration a = 0.335 m/s2 , astonishingly close to reality. He concluded that this value was “perfectly perceptible, but not in such a way to be annoying”. The studies carried out since the 1970s (Chap. 11) agreed on defining such an acceleration as higher than the discomfort threshold. In other words, Chiodi’s assertion was an explicit forecast that the physiological tolerability limit [75] will be exceeded, as confirmed by the tower closure. Despite this, it was the first time structural reliability was judged in relation to acceleration only. With his statement, which went unnoticed, Chiodi perfected the intuitions of Coyle and Spurr without knowing them, anticipating by 40 years the understanding of physical phenomena destined to become essential for tall buildings. In the meantime, the USA went through the skyscraper boom, which reached its peak in 1931, when the Empire State Building (Fig. 9.26a) took the world’s tallest structure record away from the Eiffel Tower,14 reaching 381 m. Like the Eiffel Tower, this structure was the subject of fundamental studies. 14 The highest building record, established by the Woolworth Building in 1913 with 242 m, was broken, between 1930 and 1931, by three of the four New York giants: the Manhattan Tower, the Chrysler Building, the Empire State Building and the RCA Building. William van Alen (1883–1954) and Craig Severance (1879–1941) were tasked with the design of two skyscrapers on behalf of the Chrysler Corporation and of the Bank of Manhattan, respectively. They both decided to build the highest skyscraper in the world. Severance’s project overtopped the Woolworth Building by a few metres. Alen designed a 282-m-high Chrysler Building. Severance discovered this and modified the Manhattan Tower raising it to 283 m. Alen, informed of Severance’s variant, corrected his project during the construction, raising the Chrysler Building (1931) to 319 m: it was not only the highest building in the world, but also exceeded 300 m and 1000 (1046) ft. By just 3 m, it did not reach the Eiffel Tower that retained, for a few days, the absolute record, which was broken, in that same year (1931) by the Empire State Building. The latter, designed by William Frederick Lamb (1893–1952), 381 m high, surmounted by an antenna reaching 449 m, overwhelmed the Chrysler Building and the Eiffel Tower, bringing the height record to a stratospheric height. It also was the first building

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Fig. 9.26 Empire State Building: a New York, 1931 [52]; b wind tunnel model [76]

In 1933, Hugh Latimer Dryden (1898–1965) and George C. Hill carried out wind tunnel tests [76] to compare their results with those of the full-scale tests planned later. A wood and aluminium model in 1:250 scale (Fig. 9.26b) was built and installed in a homogeneous flow wind tunnel with circular cross-section 3 m in diameter. Pressure taps were placed at three levels (A, B and C) corresponding to the 36th, 55th and 75th floors, where full-scale measurements were envisaged (Fig. 9.27a); 34 measurement stations were fitted at each level. The model was fitted on a circular metal plate that could be rotated with respect to an underlying square metal plate fastened to a wooden platform. The plates and the platform were perforated to allow the passage of 51 pressure tubes. Figure 9.27b shows the pressure coefficients for two wind directions. Base along wind and cross-wind overturning moments were also measured by means of balances. The moments were used to obtain the force coefficients in the two directions. According to authors, the comparison between the measured overturning moments and those obtained from pressure measurements was not accurate because of the lack of measurements at the top and of the speed reduction in the lowest part of the model. with more than 100 floors (102) and the first building holding the absolute record for the highest structure.

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Fig. 9.27 Model tests on the Empire State Building [76]: a cross-section heights of the pressure taps; pressure coefficients for wind parallel (b) and orthogonal (c) to the long side; upper diagram for A, lower for B (solid line) and C (dashed line) sections

Afterwards, Rathbun [77] undertook, between 1938 and 1940, the greatest campaign of full-scale measurements ever carried out until then. He performed the monitoring of the Empire State Building by installing an anemometer, a plumb line, a telescope sight and a target, 22 strain gauges, 30 pressure gauges and 28 cine-cameras (Fig. 9.28a). The anemometer was a 32-blade rotor, 4.6 m above the building top. The measurements proved that the wind speed at this height was much higher than the one recorded by nearby stations at lower heights. The measurement of the building displacement was favoured by a continuous stairwell from the 6th to the 86th floor and made use of two techniques. The first adopted a plumb line hanging from the 86th floor; the wire was 295 m long and supported a 15.88 kg concrete cylinder (Fig. 9.28b). The second used a vertical axis sight at the 6th floor and a target at the 86th floor. The strain gauges were applied to the pillars of the 24th floor. The measures proved that, despite the heaviness and stiffness of the building, oscillations were not negligible. They also proved that the building had natural periods equal to 8.2 and 5.3 s [25] in the NS and EW directions, respectively (Fig. 9.29). Thirty pressure gauges were placed, 10 on each floor, at the 36th, 55th and 75th floors (Fig. 9.30). Rathbun stated that his measurements provided results different from those obtained by Dryden and Hill in a wind tunnel [25, 78]. He received a harsh judgment: “wind configuration is too complex to measure pressures on a building with a view to obtain probative answers”. Rathbun’s measurements, conversely, were accurate, unlike those carried out in a wind tunnel unsuitable for such tests. When, in 1943, they were repeated by Alfred Bailey and Noel David George Vincent

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Fig. 9.28 Empire State Building [77]: a sensor layout; b, c oscillation measurements

(1910–1996) in a boundary layer wind tunnel, the pressure distribution was fairly in agreement with full-scale tests [25, 27, 79]. While the Empire State Building became one of the most admired images of mankind’s boldness and building expertise, in 1938 Constantin Brancusi (1876–1957), the father of modern sculpture, created a less famous but no less outstanding work in his home town, Targu-Jiu, Romania: the Endless Column [80]. He cooperated with an engineer, Stefan Georgescu Gorjan (1905–1985), with whom he accomplished one of the greatest masterpieces of symbiosis between sculpture and engineering. The 29.35-m-high column (Fig. 9.31a) consisted of an iron spine (Fig. 9.31b) that supported 15 hollow modules, the beads, plus two half-modules, one at the base and one at the top. Every module is made of iron and is coated with a brass layer that gives it a golden-yellow hue and meets Brancusi’s idea of the harmony of the dimensions: the overall height of a bead (180 cm) is 2 times its longer side (90 cm) and 4 times its shorter side (45 cm). The column, with respect to its smallest cross-section size, has an exceptional slenderness equal to 66. It resumes the idea of the axis mundi that supported the heavenly vault and linked earth and sky, a symbol of ascension and transcendence. Through it man uplifts his spirit, reaches absolute freedom and blissfulness, rejects any conditioning. According to art critics, it is “the most radical sculpture in the history of classic modernism”. Under a structural viewpoint, the capability to withstand wind actions by such a slender structure is puzzling, despite its long existence. When reviewed in the light

9.2 The Evolution of Towers and Skyscrapers

687

Fig. 9.29 Empire State Building [77]: plumb line and floor displacements

of modern knowledge, the Endless Column showed a dynamic and aerodynamic conception of outstanding skilfulness [81]. The hollow elements stacked along the load-bearing spine guarantee high damping. Thanks to its undulated edges, it offers small resistance to wind and causes an irregular vortex shedding; it then eludes possible forms of instability and synchronisation (Sect. 9.7). It is difficult to believe that Brancusi had perceived concepts so complex and sophisticated. On the other hand, there is no denying he conceived an architectural shape and a constructive system not just magnificent, but also astonishingly effective in relation to wind. Anticipating current concepts, it can be said that the perfection of its shape identifies itself with the maximum aerodynamic efficiency. Finally, it is worth mentioning the problems suffered, because of wind actions, by two great works of the Italian engineering and architecture, both designed by Alessandro Antonelli (1798–1888): the dome of the Basilica of San Gaudenzio and the Mole Antonelliana [82].

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Fig. 9.30 Empire state building [77]: pressure in pounds per square foot

Fig. 9.31 Brancusi endless column: a construction stage; b completed structure

9.2 The Evolution of Towers and Skyscrapers

689

Fig. 9.32 a Basilica of San Gaudenzio; b spire of the Mole Antonelliana [82]

The dome of the Basilica of San Gaudenzio, built in Novara between 1844 and 1878, was made in masonry, with the exception of the small dome, made of granite with metal belts (Fig. 9.32a). It is 122 m high, and the diameter at its base is approximately 20 m. Between 1882 and 1883, some cracks appeared at the base of the cupola [82]. Antonelli himself carried out the monitoring and reinforcement of the structure, completed in 1885. This aroused the first doubts about his work. They grew at the end of the nineteenth century, when small cracks appeared in the joints of the granite masonry of the small dome. The cracks got worse until 1922, when they appeared in the higher columns. In March 1927, the situation became alarming. The Fabbrica Lapidea, the organisation that administered the basilica, verified the progress of the cracks and turned to Arturo Danusso (1880–1968) to repair them. He attributed the damage to the oscillations of the dome top due to the wind and to the alternation of freezing and thawing in masonry. At first, he suggested that the monument was kept under observation but then, having ascertained the disastrous state of the spire, between 1931 and 1932 he demolished and rebuilt the spire, strengthening the underlying structure and the columns at the base of the small dome by means of reinforced concrete works. In 1934, new cracks appeared in some capitals of the columns of the small dome. Between 1934 and 1935, they expanded and spread to almost all capitals. In 1936, Danusso submitted a new project—which was accepted—envisaging an internal reinforced concrete structure in correspondence with the small dome. In September 1937, during the works, new cracks appeared in the arches at the base of the dome. Danusso

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suggested to complete the works and to install strain gauges and deflectometers to detect deformations. On 29 October 1937, two days after they had been installed, an announcement that invited the residents living within a 90 m radius from the basilica to leave their homes was issued. Danusso carried out some urgent interventions: the arches at the base of the basilica were shored up by wooden structures and the columns supporting the arches were encircled with metal rings. In the meantime, (1937–1938) new damage appeared. Danusso attributed them to Antonelli’s boldness, to the poor quality of the foundation and to the demolition of parts of the structure to introduce a stairway. In 1939, the Fabbrica Lapidea stated that, even though Danusso’s expertise was unquestionable, “it does not appear advisable to saddle a single man with such a heavy burden of responsibilities”. The harshest attacks came from Arialdo Daverio (1909–1990), tasked with reading the measurements. In 1940, he wrote a book [83] that documented what had happened, judged Danusso’s instruments and interventions unreliable and offered a precious assertion for the not yet born wind engineering. According to Daverio, the alarm launched in 1937 was unjustified and the shorings were only a monument to fear. Before the interventions, the centre of gravity of the weights was shifted downward; the structure was then light and flexible and properly absorbed wind actions. He also resumed the studies by Father Alfani about Palazzo Vecchio and quoted some words written by Gustavo Colonnetti (1886–1968) in 1939: “a dynamics of structures barely exists; little or nothing definable as systematical or complete has been done. We know little or nothing about the law observed by pressures exerted by wind. (…) Structural engineering is anchored to statics and nature, conversely, is nothing but dynamics”. Daverio wrote passages [83] that ooze with the need to dynamically interpret wind action and took cognisance of the lack of knowledge in this field: “The structure of the Antonellian dome—he said—is an elastic, continuous and sprung complex, resting on the elastic support of the arch system, of the ramming wings and of the foundation ground. (…) Under wind action, the whole Antonellian structure is pervaded by complex oscillatory motions, which are transmitted through elastic deformations of materials. (…) When alterations are introduced in a part of an elastic and harmonic structure, changing its nature, the oscillatory motions, as a consequence, are forced to solve a new dynamic balance. (…) The Antonellian small dome was almost a sensitive and delicate antenna, suited to feel the air blow in the first instants and, perhaps, to gradually prepare the lower trunk of the structure to the dynamic balance required to stand the wind. Just like nature does in trees. (…) Today, conversely, the structure of the little dome, because of its stiffness, refuses to deform itself. (…) The impact of the wind, which is immediately transmitted to the underlying structure, tends to discharge itself in the restraints of the system of internal fulcrums over which the little dome is set. (…) The Antonellian little dome reacted to wind action in its fibres through a deformation work. Now, instead, the more inert (because of the increased mass) little dome, resting on the more elastic support of the lower structure, transmits the reaction work to the latter. (…) In the nature, whether we like it or not, Wind still exists”.

9.2 The Evolution of Towers and Skyscrapers

691

The Mole Antonelliana, started in 1863 and intended as a synagogue, was later destined for the National Museum of the Italian Risorgimento and completed in 1889. At that time, its height (167.5 m) made it the second tallest structure in the world after the George Washington Monument. The evening of 23 May 1953, a storm broke the spire 47 m below its top (Fig. 9.32b), causing one of the most famous collapses due to the wind.15 Following it, wind tunnel tests were carried out at the Polytechnic of Turin [84] in 1954 on a wooden model in 1:50 scale. It provided a drag coefficient for the spire, cD ≈ 1.15 that explained collapse only for a wind speed (165 km/h) far greater than the maximum value recorded by the Statistical Office of the Municipality of Turin (100 km/h). The spire restoration project, by Giuseppe Albenga (1882–1957) and Danusso [84], made up for the lack of resistance to wind through a metal tube put inside the spire for a height approximately equal to 55 m from the top. Its base was rooted in the existing building, between the four triangular gables of the Tempietto and the squarebased dome. This area was strengthened by means of a strongly reinforced concrete ring. The analyses took advantage of the experiences carried out on a reinforced concrete model in 1:4 scale. The vertical load was accomplished by means of eight jacks at the base of the model. Wind actions were simulated through a metal stay applied to the metal tube. The measurements were carried out by means of strain gauges. The reconstruction works were completed on 31 January 1961.

9.3 Wind Actions and Effects on Structures With the advent of the twentieth century, a new culture about wind actions and effects on structures came into existence. It took its stimuli from the knowledge acquired building and studying bridges (Sect. 9.1) and towers (Sect. 9.2). It spanned, however, all the structural typologies. Engineers understood that wind exerted dynamic actions on structures. Often, their study can be simplified by bringing the problem back to static analyses. In other cases, this is unacceptable and distorts the interpretation and evaluation of the phenomenon. Going back over the evolution of this matter is an intricate task, unless the presentation is divided into thousands little trickles. A series of state of the arts and books published between 1887 and 1961, however, are milestones that allow establishing clear terms of reference. In 1887, Thomas Claxton Fidler (1841–1917) published a state of the art about wind actions on bridges [85]. Its content transcended this structural typology, discussing some concepts that anticipated issues among the most debated by wind engineering. Fidler remarked that: “in designing bridges (…), a correct estimate of wind forces is quite as important as a correct estimate of the load; but it must be confessed that the knowledge we actually possess upon this subject is at present very 15 The collapse of the spire was not the first catastrophic event that struck the Mole Antonelliana. In 1904, during a thunderstorm, a lightning knocked down the statue of the winged genius at its top. It was replaced by a five-pointed star, over 4 m in diameter, designed by Ernesto Ghiotti (1847–1938).

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small, and totally inadequate to the requirements of modern engineering”. He divided the assessment of the wind actions on bridges into three parts: (1) “to estimate the violence of the greatest windstorm that has to be resisted, and to express it either by some maximum velocity or by the pressure exerted upon” the bridge; (2) the forces acting on the bridge; (3) the dynamic effects of wind gusts. Fidler maintained that evaluating wind speed was difficult even if many measures existed; the uncertainties were originated not by a lack of data, but by ignorance preventing an appropriate analysis of such data. He noticed that wind pressure on long-span bridges could hardly assume its maximum value on the whole span at the same time; he then suggested to statically apply half such pressure on the whole bridge and to distribute the remaining half on limited portions of the spans. He maintained that wind gusts followed each other with periods that could equal the bridge own periods, causing such dynamic amplifications to double the static load; this led to actions comparable to the maximum values of the local pressures. Fidler concluded that the existing data were insufficient even for ordinary bridges, which mostly relied on experience. Lately, engineers had designed bridges of increasing size, perceiving the need of carrying out accurate calculations. Before this problem, they felt the weight of the uncertainties. It was a concept that anticipated, by over three quarters of century, an essential passage in engineering: with the advent of electronic computers in the 1960s and with the proliferation of more and more innovative works, the experience acquired over the centuries failed; a new vision of safety came then into being, probabilistically taking into account the uncertainties in external actions and material resistances. In 1895, William Herbert Bixby (1849–1928), a captain of the US Army Corps of Engineers, published a state of the art about wind pressure on structures [86], which summarised the work produced in the nineteenth century (Sects. 4.2 and 7.1). In 1910, Alexander Gustav Eiffel (1832–1923) wrote a book, Wind resistance, an explanation of formulae and experiments, in which he collected, besides the results of his researches, a synthesis of knowledge in his time. He observed how wind resistance, by then an essential issue for aviation, had become increasingly important in various sectors of civil engineering, especially for large metal structures. Eiffel emphasised three unsolved problems: the correlation between pressure and the swept surface, wind actions on inclined surfaces and the position of the pressure centre [87]. In 1930, Robins Fleming published a book [56] on wind effects on buildings (Sect. 9.2). Even in this case, the book went beyond this structural typology, providing a picture of the knowledge about wind. It started (part I) with a call to the necessity, for engineers, to acquire knowledge about the wind through basic meteorology and atmospheric physics. It continued with a classification of winds (part II), based on their speed and phenomenologic properties. Part III covered tornadoes and hurricanes, providing a description of their effects on structures. Part IV discussed the evolution of the knowledge about wind speed in contact with the ground and the transformation of such speed into aerodynamic actions. Parts V and VI, which represented the core of the book, covered wind actions on low-rise and tall buildings (Sect. 9.2), paying attention to structural schemes and construction details.

9.3 Wind Actions and Effects on Structures

693

Fig. 9.33 a Dynamic damper by Frahm; b elementary tuned mass damper

The years from 1930 to 1935 were dominated by the figure of Otto Heinrich Georg Flachsbart (1898–1957), one of the most eminent students of Prandtl. Flachsbart published a series of papers [88–98] on the aerodynamics of structures (Sect. 9.6), which lacked the extensiveness of other works mentioned in this paragraph but deserves a special mention in the foundation of wind engineering. Flachsbart built a wind tunnel where he measured the aerodynamic coefficients of almost any structural typology. He explained the results with outstanding clarity. He studied buildings, highlighting the essential role played by a boundary layer complying with the principles of similarity with the reality (Sect. 7.3). He carried out tests on solid and truss beams, in a homogeneous smooth flow, so accurate that their results still appear in most international standards. The study, diffusion and application of dynamics and of the structural response to wind actions received a decisive stimulus in 1934, when Jacob Pieter Den Hartog (1901–1989) collected, in the first edition of his book [99], his lessons at the Harvard School of Engineering. The subsequent editions, published in 1940, 1947 and 1956, marked the major advances of a matter with an impressive growth gradient. Den Hartog himself pointed out that whereas the first edition of his book illustrated subjects for few individuals, the fourth edition reported knowledge by then indispensable for modern engineers. From this point of view, he provided an exhaustive picture of the knowledge at that time and divulged a pioneering vision of two major subjects in many branches of engineering: vibration damping and isolation and self-excited vibrations due to fluid–structure interaction. As regards to the first subject, Den Hartog resumed the studies on vibration dampers carried out by Hermann Frahm (1867–1939) [100] in 1909 in the naval sector (Fig. 9.33a), introducing novel concepts with great engineering impact on tuned mass dampers (Fig. 9.33b) [101]. Within the second subject, Den Hartog formulated fundamental principles. He discussed the vortex shedding from cables, chimneys and suspension bridges, observing that this phenomenon started when the mean wind speed reached a critical threshold; increasing such speed the shedding frequency remained unchanged up to an

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upper speed limit, for which the Strouhal law was again in force; within this interval, the structure controlled the vortex shedding (Sect. 9.7). He provided a definition of the conditions causing galloping—“a section is dynamically unstable if the negative slope of the lift curve is greater than the ordinate of the drag curve”—stressing its dangerousness for ice-coated transmission lines (Sect. 9.8). He treated flutter as an aeroelastic instability mainly concerning aircraft wings and suspension bridges; it took into account, in the 1940 edition and even more in the 1956 one, the theoretical developments introduced by Theodorsen [102] in 1935 (Sect. 7.4). Between 1934 and 1935, William Watters Pagon (1885–1973) made an essential contribution to wind actions on structures. He started from the assumption that aerodynamic engineers had developed many experimental tests and theoretical studies towards which civil engineers were grossly unaware and amazingly indifferent: they practically never advanced beyond the results obtained by Duchemin almost a century before. Since Pagon was a civil engineer who always operated in contact with the aerodynamic sector, he felt the moral obligation to transfer the new knowledge to his colleagues. He did so by publishing eight papers titled Aerodynamics and the civil engineer [103–110] on the Engineering News-Record, in which he transposed the aerodynamic and meteorological culture to the civil sector. In his first paper [103], Pagon recalled similarity, the motion of fluids and aerodynamic actions. He started from examining ideal fluids, mentioning the Bernoulli theorem and its limits (Fig. 9.34). He then examined real fluids and the formation of vortices beyond the bodies with curved surfaces; for this aim, he mentioned the Karman’s vortex wake, Prandtl’s boundary layer, the variation of fluid properties and the drag of bodies with the Reynolds number; he interpreted the drag variation in cylinders and spheres through the surface pressure diagrams obtained by Arthur Fage (1890–1977) at the NPL. He discussed the separation of the boundary layer near the edges, recalling Rayleigh’s discontinuity surface; he examined the drag of plates, mentioning the assortment of results obtained from Duchemin to Eiffel for circular, square and rectangular plates; he observed that the drag depends on the size and shape of the plate and is proportional to the square of the speed, but does not depend on the Reynolds number. He discussed the pressure distribution over plates and the effects of their inclination, reporting the results of Eiffel’s experiences as well as Duchemin formula. He wrote about the twisting moment on inclined plates and on the drag of cylindrical bodies as a function of their aspect ratio. In the second paper [104] (Sect. 9.7), Pagon discussed the techniques aimed at mitigating chimney vibrations making use of full-scale tests. In the third paper [105] (Sect. 9.5), he examined the wind tunnel tests on the truss beams of bridges, providing a vast literature and a critical analysis of code provisions. In the fourth paper [106] (Sect. 9.5), he illustrated the distribution of the internal and external pressures of buildings through a digression of historical nature. In the fifth paper [107], Pagon returned to the fundamentals of aerodynamics, discussing the concepts of streamline, shear, vortex, laminar and turbulent boundary layer, the pressure distribution on cylindrical surfaces, the role of surface roughness (Fig. 9.35) on the basis of the experiences carried out by Fage and Warsap [111]. He discussed the meaning of eddy mentioning theories about tornadoes and cyclones.

9.3 Wind Actions and Effects on Structures

695

Fig. 9.34 Aerodynamic actions of ideal fluids [103]

He analysed turbulence as the result of eddies produced by what lies on Earth surface, such as structures and vegetation, or in a wind tunnel, such as honeycombs and grates. In the sixth paper [108] (Sect. 6.4), Pagon analysed the atmospheric circulation, evaluating wind measurements in relationship with the definition of the design wind speed. In the seventh paper [109] (Sect. 6.7), he provided a state of the art on the wind structure in the atmospheric boundary layer; especially, he discussed the power law, through which he expressed the mean speed profile, and its matching with the speed in undisturbed atmosphere (Fig. 6.42). In the eighth and last paper [110], Pagon summed up the previous concepts through practical rules for the evaluation of wind actions on structures like plates, bridges, truss beams, buildings, cables and transmission lines, chimneys and tanks; he focused on the ratio between the wind speed and the external and internal pressures, providing several examples of calculation with great design worth. In 1936, Giovannozzi [112] made a new contribution to wind actions on structures. In comparison with Pagon, he wrote a state of the art limited to aerodynamic actions; he, however, broadly covered this subject and substantiated his data through a vast bibliography. The paper was divided into three parts: the first provided the basic rules to evaluate the design actions on structures, discussing the difference between static

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Fig. 9.35 Drag coefficient of cylinders versus Reynolds number and surface roughness [107]

and dynamic loads; the second and third parts, respectively, dealt with truss and solid wall structures. The paper made a remarkable impact on the diffusion of the wind culture in the Italian civil engineering. Likewise, a paper published by Blanjean [113] in 1949 favoured the spread of this culture in France. In 1948, the Societe des Ingenieurs Civils de France published a conference of Theodore von Karman (1881–1963) [114], dealing with aerodynamic issues in various branches of industry. According to the author, they could be traced to three trends: the first included external flows and was divided into three sub-themes: the air drag on aircraft and vehicles (Sects. 7.4, 7.6 and 7.7); aeroelastic phenomena; the erosion caused by wind (Sect. 8.3). The second covered internal flows and included two sub-themes: air channelling and ventilation; internal flow machines, namely fans, compressors and turbines. The third studied aerothermodynamics and aerochemistry; it covered heat transfer, the diffusion and mixture of gaseous flows, the aerodynamic effects in combustion and in other chemical reactions. The site where the conference was held induced Karman to approach only the first subject, but he did so with such extensiveness to originate the first consistent picture of many subjects making up the core of wind engineering. As regards to wind actions on structures, Karman differentiated the static problems from the dynamic ones. Dealing with the former, he placed emphasis on codes, observing that aerodynamic coefficients consistent with the results of wind tunnel tests were only prescribed after the war; they were limited to classic structures with usual shapes; in case of large-size or unusually shaped structures, it was necessary to carry out tests to evaluate pressure distribution. Passing to dynamic problems, Karman maintained that in most tall buildings, towers, transmission lines, chimneys and suspension

9.3 Wind Actions and Effects on Structures

697

bridges16 oscillations played an essential role; he then went on to differentiate such problems into resonance and self-vibration. Karman defined resonance as the coincidence of the natural frequency of a mechanical system and of an external periodic force. He remarked that the resonance due to aerodynamic actions did not exactly match this definition: wind speed is variable in intensity and direction, so it lacks “its own periodicity”. The situation changes when the body generated an alternate turbulence, the vortex wake Karman “was honoured to be named after”, organised in a periodic flow to which, for a definite value of the wind speed, corresponds a resonant force with a frequency of the structure. Unlike resonance at distinct speed values, self-vibration, or dynamic instability, was usually extended to speeds exceeding critical thresholds; this took place when the structural response, instead of damping vibrations, amplifies them. A similar phenomenon could also occur in the static field, in particular for flattened bridges subjected to aerodynamic torsion; generally, the twisting moment negates deck rotation, causing a “positive” response; there were, however, cases in which the twisting motion for a given wind direction increased rotation, originating a “negative” response similar to static instability. In 1955, Yuan-Cheng Fung (1919–) [115] published the first edition of a book where he collected the subjects of the aeroelasticity course he ran since 1948 for the aeronautical engineering students of the California Institute of Technology. It offered a complete and original view of the discipline, depicting the phenomenological aspects and the mathematical bases of a broad range of phenomena: “Trees sway in the wind; so may smokestacks. Flags and sails flutter; so may airplane wings and suspension bridges. The wind played ancient aeolian harps; so it plays the electric transmission lines, making them sing or even gallop.” Like Den Hartog’s book, the subsequent editions of Fung’s book (1969, 1983, 1993) also represented milestones. In 1958, ASCE published six linked papers [116–121] thanks to which it summarised, correlated and discussed various trends contributing to the state of the art about wind forces on structures [122]. The first paper, by Biggs [116], illustrated the evolution of the subject. The second paper, by Sherlock [117], classified and described wind types. Sherlock, recalling the studies he himself carried out (Sects. 6.7 and 6.8), illustrated a wind model for codification uses, similar to the one adopted by modern wind engineering (Sect. 9.4). The third paper, by Woodruff and Kozak [118], discussed the general aspects of wind actions on structures. They are the sum of two contributions, called aerostatic and aerodynamic. The aerostatic contribution induces drag, lift and twist actions that, even though, strictly speaking, of a dynamic type, can be treated as static ones. They are obtained from the product of three terms: velocity pressure; a reference size; aerodynamic coefficients called drag, lift and twisting moment coefficients, 16 According to Karman [114] “many excellent bridge builders were alarmed because our actual knowledge was not sufficient to predict aerodynamic instability without model tests. In the US Government Board of Inquiry about the Tacoma Narrows Bridge, a bridge builder told me: ‘You would not seriously think that, from now on, if we build a large suspension bridge we will have to test a model in a wind tunnel?’—‘This is exactly what I intend to propose’, I replied.”

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whose values depend on the shape of the structure, on the presence of sheltering bodies, on air friction on the structure surface and on its size. The aerodynamic contribution causes harmonic actions, fundamental for flexible structures. It these cases, three conditions are crucial: the synchronisation of the oscillations due to vortex shedding, the negative slope of the lift coefficient and galloping, and flutter. The fourth and fifth papers, by Singell [119] and Pagon [120], discussed wind actions in relation to speed and aerodynamic coefficients. Singell summarised, classified and discussed the aerodynamic coefficients of structures enclosed by surfaces, starting from the data reported in 1940 in the final report of the ASCE Sub-Committee 31 [72]. He integrated such data with shape coefficients assigned by the 1948 Danish standard [123] and by the 1956 Swiss standard [124], a broad collection of available measurements. Pagon, in turn, provided a state of the art about the aerodynamic coefficients of lattice structures, divided into two families: flat beams and large surfaces; frames and truss girders, both flat and spatial, made up by elements whose cross-section size was small with respect to their length and variously shaped. Their behaviour depended on the Reynolds number, on their aspect and solidity ratios, on the inclination of the oncoming wind and on the mutual sheltering of the component elements. The sixth and last paper, by Farquharson [121], maintained that wind actions on structures were dynamic; treating them statically was admissible for certain values of the eigenfrequencies. Farquharson, resuming Woodruff and Kozak’s classification [118], discussed three phenomena: the synchronisation of the oscillations due to vortex shedding, especially dangerous for chimneys, suspended pipes, power transmission lines, suspension elements of arch bridges and decks of suspension bridges; the negative slope of the lift and moment coefficients and the related galloping phenomena (Sect. 9.8) affecting ice-covered transmission lines and suspension bridges with flat plate decks; and flutter (Sect. 9.9), affecting flattened structures, such as the decks of suspension bridges, large cantilever roofs, signs and billboards as well as the elements loosely connected in the assembly stage. Fìnally, starting from tests carried out since 1940 at the NPL, Christopher Scruton (1911–1990) [45] in 1960 classified experiments into three classes: the study of the emission of fumes from ground (chimney) and marine (ship) sources (Fig. 9.36), the measurement of forces and pressure induced by wind on buildings and other rigid structures (bridges, radio, TV and radar antennas), the vibration tests on flexible structures (suspension bridges, chimneys, TV towers, tube bundles in heat exchangers).

9.4 Design Wind Speed The chronological interpretation of the studies carried out between the late nineteenth and the early twentieth centuries on the wind in the atmospheric boundary layer (Sects. 6.5, 6.7 and 6.8) highlights a development into four stages. Between 1880 and 1925 the studies about the mean speed profile [125, 126], the peak wind speed

9.4 Design Wind Speed

699

Fig. 9.36 Emission of fumes from marine sources [45]

[53, 127], Ekman’s spiral [128–130] and atmospheric turbulence [131–133] gained ground on experimental, theoretical and empirical grounds. Between 1925 and 1935, favoured by the developments in probability theory (Sect. 5.2), analyses about the distribution of the parent population of the mean wind speed [134, 135] and its extreme values [71, 108] were started. Between 1935 and 1945, thanks to new theories and instrumentations, research on atmospheric stability [136–138] and roughness transition [139] was born. Based on the advancements in process theory and spectral analysis (Sect. 5.2), the first models of turbulence [140, 141] and long-term wind speed [142, 143] power spectral density were formulated from 1955; the turbulence coherence concept [144, 145] also appeared at that time. Thus, in the early 1960s the basic knowledge of the wind can be defined as homogenous and well developed. While this knowledge became the mainstay of micrometeorology, climatology and atmospheric physics, civil engineering drew from a minimal portion of it to formulate, in the 1930s, the first models of the wind actions on structures. They exploited the knowledge acquired in three fields only: the mean wind speed profile, the transformation of the mean speed into the peak through the gust factor (Sect. 6.7) and the distribution of the mean wind speed extreme values (Sects. 5.2 and 6.8). This trend remained deep-rooted up to 1961, when Davenport [146] stated the first method for the dynamic response of structures to wind that, using all the above-mentioned concepts, created an indissoluble link between the wind models in the atmospheric boundary layer and the aerodynamic actions on structures. The first contributions to the wind representation in relationship with its actions on structures were made by S. P. Wing, William Watters Pagon (1885–1973) and Robert Henry Sherlock. Between 1931 and 1940, the ASCE Sub-Committee 31 compiled six reports about the bracings of metal buildings [72]. In the second report (1932) [71], Wing gave the Committee, in which he sat, credit for the importance of having approached a subject

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neglected in the past; he was, however, critical towards many aspects of the document and discussed them through arguments that subverted deep-rooted concepts. He remarked that the design wind speed had been the subject of a debate at first inspired by observations and experience, then by measurements; it was anyway set within a deterministic view. Wing maintained the need to rationalise this assessment through the statistic analysis of extreme wind speeds. Accordingly, he developed prophetic remarks on the quality and the homogeneity of data. Wing criticised the measurements carried out by the Weather Bureau by means of Robinson-type cup anemometers fitted on antennas at the top of buildings: they were affected by the wake of the body where they were installed and of the adjacent ones; they suffered the constructions that grew over the years and slowed the wind down; thus, their information was affected by severe uncertainties. He was also critical on using a single speed profile for USA and Canada. He gathered the yearly maximum value of the mean wind speed over 5 min in several American cities and statistically processed them using criteria similar to those adopted to study water course floods; the analyses highlighted huge variations from one site to another and the need to assign diversified values of the design wind speed. Wing remarked that the profiles proposed by the Committee were not realistic, since they were affected by local obstacles; it would have been better to assign a profile associated with a reference site in open countryside, and then to correct it to take the local roughness into account. He also dissociated himself from assigning gust peaks 1.25 times the mean wind speed over 5 min; he stressed that the ratio between the peak and the mean speed increased at low heights and low speeds and decreased at high heights and high speeds; as a rule, it was equal to 1.50 at ground level and to 1.13 at 365 m height. Finally, Wing discussed load combination; he pointed out that the Committee, paraphrasing the rules for bridges, allowed high stresses for the simultaneous action of the self-weight, of the imposed loads and of the wind; this was a realistic assumption for bridges, where the passage of a train was rare enough to make its occurrence simultaneous with the maximum wind an improbable event; it was, conversely, dangerous for buildings, where the maximum wind speed could occur even with high overloads. The final version of the document compiled by ASCE in 1940 [72] almost completely ignored these considerations, which were perhaps too advanced for that time. In 1935, Pagon [108] resumed Wing’s concepts [107] about the statistical analysis of extreme wind speeds. He also returned to the quality of data, focusing on the Weather Bureau choice to discard the Robinson 4-cup anemometers it used up to 1927 and to switch to 3-cup anemometers from 1928: this made the data set nonhomogeneous and invalidated the results of the statistical analyses. Sherlock contributed to the definition of the design wind speed by means of four papers published in 1932 [147], 1937 [148], 1947 [149] and 1952 [150]. The first two papers, written with Stout [147, 148], illustrated a research, initially founded by the National Electric Light Association, aiming to assess wind actions on transmission lines. The research studied the duration, intensity and magnitude of the gusts affecting the conductors. A lattice tower 76 m high and a series of poles

9.4 Design Wind Speed

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15 m high, evenly spaced by 18 m, were erected along a directrix orthogonal to the prevailing winds. Suitable instruments were installed on the top of the poles and on the tower at 15 m steps, to measure the peak wind speed. Sherlock and Stout acknowledged that commercial anemometers were unsuitable, since they provided reasonable measures only for speeds averaged over approximately 10 s. For this reason, they built new pressure instruments consisting of a 23 × 20 cm plate, by means of which they measured mean speed values over 0.25 s. The acquisitions were carried out on 28 April 1931 and on 19 January 1933. The results were represented by isovelocity maps (Fig. 9.37) that showed discrete eddy structures of various sizes, causing non-simultaneous peaks. Wind actions on structures, therefore, could not disregard gusts with a size commensurate with that of the structure. In the third paper [149], Sherlock introduced a new term: the gust factor. For the time being, it was defined as the ratio between the gust peak and the mean speed, over five minutes in this case. Sherlock formulated two fundamental concepts. Firstly, the peak randomly changed from a recording to another; he then proposed to represent the speed population (in his paper, the mean values over intervals from ½ to 10 s) through a “primary” Pearson type III distribution; he associated with the latter a “secondary” distribution of the maximum characterised by a mean value, called the “maximally probable value”, expressed as the sum of the mean value of the population and of its standard deviation multiplied by a non-dimensional parameter subsequently called peak factor (Fig. 9.38); the ratio between the mean peak value and the mean speed value usually ranged from 1.2 to 1.5. Secondly, Sherlock suggested that wind actions were determined for a design wind speed obtained from the product of the mean wind speed by a gust factor related to the smallest size of the structure or element under examination; also, he thought that the size of the effective gust was associated with its duration and that the gust duration most suitable for low-rise buildings was 3 s, with a corresponding gust factor 1.385. For large-size structures, the duration of the effective gust increased and, as a consequence, the gust factor decreased. In the fourth paper [150], Sherlock developed a design wind speed model nearly like the one adopted by modern wind engineering. The windiness of a region was defined by the mean wind speed over 5–10 min at 30 ft height, in an open flat countryside called the reference site. In this site, the mean wind speed variation as a function of height was described by a power law with exponent 1/7. The designer was tasked with modifying such profile with regard to the local roughness. The transformation could be pursued by attributing an exponent of the power law to the local roughness and by imposing that the power laws at the structure and at the reference site match at 1000 ft height, i.e. at a conventional height where the effect of earth surface frictions disappeared. The designer was also tasked with correcting the mean wind speed in relationship with local topography. The profile of the design wind speed V is the product of the mean wind speed by a gust factor ranging from 1 to 1.5 in relation to the size of the structure and of its response time to wind. The velocity pressure q associated with V is given by: q=

1 2 ρV 2

(9.1)

9 Wind Actions and Effects on Structures

Fig. 9.37 Isovelocity maps [148]

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9.4 Design Wind Speed

703

Fig. 9.38 Density functions of the speed population values and peaks [149]

where ρ is the air density, assumed as constant with height. The design pressure is the product of the velocity pressure by an aerodynamic coefficient (Sect. 9.5). The criterion to assign the design wind speed, however, was still missing. It was provided by Court [151] in 1953, in a paper concerning mobile structures. He actually formulated a general criterion that originated a turning point. Court first discussed, like Wing and Pagon, the issue with non-homogeneous data. He remarked that in 1947 the International Meteorological Organisation established that mean wind speed values were to be standardised over a 20-min period; on the other hand, the U.S. Weather Bureau, which in the past recorded mean values over 5 min, now recorded means over 1 min where pressure anemometers were operating, or over 5 min in stations equipped with traditional rotating anemometers. The situation was even more chaotic for maximum values: depending on the instruments used by each station, the USA had maximum values averaged over 5 min, V , or the fastest mile wind speed,17 V f , or the peak value, V , actually averaged over a few seconds. Court quoted studies [152] according to which V  1.4V f  1.5V , and gave a strategic role to the familiarity with the anemometer: if the instrument was known, data must be made homogeneous; otherwise, the statistical estimates led to misleading results. Court, applying his conversion method, transformed the maximum measured values, initially heterogeneous, into a homogeneous set of data averaged over 5 min and reconstructed, for 25 stations in the USA, as many homogeneous databases from 1912 to 1948. He also processed the data, representing them, for the first time, through an asymptotic type I distribution (Eq. 5.40) (Fig. 9.39). Court recommended that the design speed was assigned through a pair of values: the mean over 5 min and the maximum value, assumed a 1.5 times the mean value. They had to possess at least a 10% probability of not being exceeded during the structure life time L. For a mobile structure with L = 2 years, the return period R had to be at least equal to 20 years; for a temporary structure with L = 5 years, R = 47 years; for a semi-permanent structure with L = 10 years, R = 95 years. For the 



17 The

fastest mile wind speed V f is the mean speed associated with the passage of a mile of wind, i.e. the mean wind speed over a period T f equal to the ratio between one mile and V f .

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9 Wind Actions and Effects on Structures

Fig. 9.39 Type I distributions of the yearly maximum of the mean speed over 5 min [151]

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first time, a definition of the wind loads based on probabilistic criteria was proposed and applied. Court also analysed the data about American tornadoes [153–155] concluding that the probability that a tornado struck a 1-square mile area in a year was approximately equal to 1/5000; it was so small it could be excluded for mobile and common structures. In 1954, Thom [156] collected the yearly maximum values of the fastest mile wind speed measured at 131 airport stations and at 165 city stations in the USA over a 9-year average period. He transformed such values at the 10 ft reference height through a power law with exponent 1/n = 1/7. He then represented them by a type II distribution (Eq. 5.44), regressing its parameters by the maximum likelihood method. Thom justified his choice by exclusion: the type I distribution (Eq. 5.40) was defined for speeds from minus to plus infinite, then it admitted a non-null probability for negative speeds; the type III distribution (Eq. 5.45) was defined for speeds between minus infinite and an unjustified upper limit; the type II distribution covered speeds greater than zero (setting ε = 0 in Eq. 5.44, with an upper limit “defined only from the smallness of the probability”). In 1960, Thom [157] took cognisance of the scarce reliability of the measurements in areas with different roughness. He acknowledged that the recordings in urban areas were not so representative and, taking advantage of the time elapsed and of the installation of new sensors, collected the measures acquired by 131 airport stations, plus 10 at open sites, over an average period of 15 years. He repeated his previous study, continuing to use the type II distribution, and defended his choice mentioning a study carried out in Russia in 1958 [158]; he thus started a still ongoing heated debate on the distribution most suited for extreme values. Thom also compiled the first extreme wind maps of the USA, in relation to the fastest mile wind speed, with yearly probability of exceeding the maximum value p = 0.01 (R = 100 years), p = 0.02 (R = 50 years) (Fig. 9.40) and p = 0.5 (R = 2 years). In the same period (1958–1962), Shellard [159, 160] carried out the first statistical study on the extreme wind speed in Great Britain. He made use of the measurements carried out by 56 stations over many years—often, up to 50—with the Dines pressure tube anemograph and, more recently, with the electric cup anemograph; both were sensitive to wind speed changes, providing reliable estimates of the mean value over 5 s (and significant ones up to 3 s). Shellard noted that these instruments were generally located in open country; where this was not true, he corrected and made homogeneous the data through the power law in relationship with the instrument height and with the local roughness. He then represented the yearly maximum values by the type I distribution and regressed its parameters through order statistics (Fig. 9.41a). He compiled wind maps, with R = 50 years, for the mean wind speed over an hour and for the gust peak (Fig. 9.41b); the bracketed values refer to stations with less than 15 years of data. In 1958, Sherlock [117] published the second of six papers [116–121] through which ASCE outlined a state of the art on wind actions (Sect. 9.3). He maintained that the basic value of the reference speed had to be the fastest mile wind speed with R = 40–50 years and that the design wind speed had to be increased near promontories

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Fig. 9.40 Yearly maximum value of the fastest mile wind speed with a 50-year return period [157]

Fig. 9.41 Yearly maximum value [160]: a type I distribution; b 50-year return period gust peak

9.4 Design Wind Speed

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and in the areas subject to hurricanes. He divided the reference speeds into two categories: those lower than 34 m/s were due to extra-tropical cyclones; the higher ones were due to tropical cyclones. In the reference site, the former were associated with mean speed profiles with a power law exponent 1/7; the latter originated profiles involving the greatest between the value provided by the power law related to the 34 m/s basic speed and the basic speed at the site, greater than or equal to 34 m/s, assumed as independent of height. The gust factor depended on the period over which the peak wind speed was averaged and was commensurated to the size and response time of the structure: it was 1.3 for gusts lasting approximately 1 s; 1.1 for peaks averaged over 10 s. In 1959, Barstein (1959) [161] published a paper on the wind-excited response of structures (Sect. 9.6) in which he described the state of the art of the design wind speed in the Soviet Union. Barstein remarked that the determination of the wind load on structures required distinguishing the mean wind speed, from which the design value of the velocity pressure was derived, from the maximum wind speed associated with gusts, whose contribution must be considered separately. The detection of these values entailed relevant difficulties. At most weather stations in the USSR, measurements were carried out by Wild anemometers (Sect. 3.2), and the wind speed was assessed according to the average position of the foil in 2 min; for high speeds errors reached ±6 m/s and depended on the judgment of an observer; besides, Wild anemometers equipped with light foils could not measure speeds exceeding 20 m/s and only the anemometers with heavy foils were capable of measuring higher speeds. The first zoning of the velocity pressure in the USSR dates back to 1935 and was based on measurements carried out by Wild anemometers. The uncertainties, therefore, did not allow draw up a detailed map; USSR was then divided into three areas, whose design velocity pressure at the anemometer height, were 400, 700 and 1000 N/m2 . This zoning remained unchanged until 1955. Facing the need to improve such information, the Central Geophysical Observatory carried out a statistical analysis of the data measured by approximately 500 stations in the last 20 years. This led to a new zoning, in which the USSR was divided into seven regions [162]; the mean wind speed was provided in relationship with the return period R for each one of them. The design speed was referred to a mean value over 2 min with R = 5 years. For residential, public and industrial buildings, R = 10–15 years. For tall buildings, towers and antennas, R = 20 years. As regards to the relationship between the mean wind speed and the height, the 1935 standard used a power law with exponent 1/4. The 1955 standard, drawing inspiration from the researches by Mikhail Ivanovich Budyko (1920–2001) [163, 164], passed to the logarithmic law; the mean wind speed was assigned at the height of the anemometers, z = 10 m, and referred to the roughness length z0 = 0.05 m; the speed profile at the reference site thus tended to the power law with exponent 1/7 [162]. Being the mean wind speed profile as a function of R known, the maximum wind speed profile was given by the product of the mean speed by a gust factor. It was determined assuming that both the speed and the velocity pressure (Eq. 9.1) have an

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9 Wind Actions and Effects on Structures

“absolutely random character” described by “the Gauss normal distribution law”.18 The maximum velocity pressure was then given by:   σq q p = (1 + m)q = 1 + α q (9.2) q where q and σq are the mean value and the standard deviation of the velocity pressure, m = ασq /q is the velocity pressure pulse coefficient, α = 2–3 is the number of standard deviations separating the mean from the maximum. To estimate the involved parameters, the speed graphs of strong winds recorded in Neftjanye Kamni, on the Caspian Sea, in Antarctica and on the Markhotskij pass were examined. Statistics indicated that σq /q = 0.12 − 0.16. Here came into being code provisions according to which, for heights below 20 m, m = m20 = 0.25–0.35 (α = 2–2.5); for heights higher than 20 m, m(z) = m20 (20/z)1/n with z expressed in m and n = 8–12. The 1960 Davenport’s paper [165] was a milestone (Sect. 6.7). It affirmed the advisability of assigning the design wind speed through the mean value rather than the peak one. The former, unlike the latter, depended neither on the structure size nor on the anemometer and structure response. It was also necessary to apply laws that transferred the mean wind speed, assessed according to statistical grounds at weather stations, to sites with different roughness and at any height above ground. Davenport used the power law he expressed through Eq. (6.88). The starting point of any transformation was the measurements at anemometer stations mostly located in open countryside. Davenport recommended to represent such measurements through the type I distribution (Eq. 5.40) and to obtain the a and u model parameters for every anemometer. Let’s assume zA is the height of an anemometer; 1/α and zG are the power law parameters associated with its site roughness (Sect. 6.7). The parameters of the type I distribution at the gradient height19 are a  = a/kA , u  = ukA , where kA = VG /VA = (z G /z A )1/α . The gradient speed, therefore, is given by:     1 1 + u VG =  − ln − ln 1 − (9.3) a R R being the return period. The design wind speed profile at a site characterised by the 1/α and zG parameters is obtained by replacing Eq. (9.3) into Eq. (6.88). Davenport applied this method to the British design wind speed. Starting from the a and u values estimated by Shellard [159, 160] through anemometers at ground level, he obtained the a and u values at the gradient height and compiled their map.

18 Despite

an outstanding knowledge of probability and process theories, it is odd how Barstein attributed the normal distribution to the speed and its square. 19 If there are multiple anemometers representative of the same zone at the gradient height, a and u can be obtained through weighting factors in relation to the number of the available years (objective criterion) and the quality of stations and measurements (subjective criterion).

9.5 Building Aerodynamics

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9.5 Building Aerodynamics Despite, or perhaps because of, the performance of many full-scale tests, in the early twentieth century the idea that direct experiences on structures were difficult and not so representative took shape: the former were considered useful to verify the results of wind tunnel tests, the only ones that could offer reliable aerodynamic actions [112]. As a result, a vast body of literature centred on model tests flourished: it was traceable to three subjects: building enclosed within surfaces, slender elements and lattice beams. The pressure on buildings enclosed within surfaces is given by the relationship20 : p = cpq

(9.4)

q being the wind velocity pressure (Eq. 9.1), cp a non-dimensional parameter called pressure coefficient. This assessment can be classified according to two aspects: the structure typology and the tunnel used. As regards to the first aspect, it is divided into four subjects: buildings with sharp edges, buildings with round edges, internal pressure and interference [106, 112, 114, 119]. The second aspect entails a distinction between the tests carried out in homogeneous flow and in boundary layer wind tunnels (Sect. 7.3). The former were used for all the tests performed until the mid-1930s and for most of those carried out between the mid-1930s and the late 1950s; the latter gained ground, slowly, from the mid-1930s. Aerodynamic studies, from Newton’s times (Sect. 4.2) to the early twentieth century (Sects. 7.1 and 7.2), were dominated by measurements on plates with various shapes and inclination. Often, the wind actions on buildings with sharp edges were estimated by applying the results of such measurements to upwind faces. This led to an unjustified use of the Duchemin formula (Sect. 4.2) on the upwind slope of the roofs and to ignore depression on the faces where the flow was separated [114]. In 1886, Raymond Unwin (1863–1940) [166] published a book about wind actions on sloped roofs where he used the results obtained by Wenham on inclined plates [27, 167, 168]. In 1890, William Charls Kernot (1845–1909) [169] carried out the first force balance wind tunnel tests, measuring the overall resistance of buildings. The first measurements of the pressure distribution on buildings with sloped roofs were carried out Johan Otto Valdemar Irminger (1848–1938) [170, 171] in 1893; they highlighted the importance of the suction on downwind faces. Similar tests were carried out by Thomas Edward Stanton (1865–1931) [172] in 1903 and by Alexander Gustave Eiffel (1832–1923) [173] in 1907. Eiffel measured the pressure distribution on buildings with various shapes, integrated the pressure field to evaluate its resultant and obtained it also through balance tests, achieving a fair agreement; he proved that, unlike buildings with rounded surfaces, in buildings with sharp edges the Reynolds number played a negligible role. Hugh Latimer Dryden (1898–1965) and Hill [78] (Fig. 9.42) in 1926, Coupard [174] in 1927, Bounkin and Tcheremoukhin [175] in 20 Actually,

the pressure p should be replaced by p–p0 , p0 being the environmental pressure of the undisturbed flow.

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9 Wind Actions and Effects on Structures

Fig. 9.42 Pressure coefficients for a parallelepiped building [78]: a upwind A, downwind C and side B, D faces for wind perpendicular to a face; flat roof for wind perpendicular to a face (b) and diagonal (c)

1928, Richard Leonard Arnold Schoemaker (1886–1942) and Wouters [176] in 1932, Harold Mac Tavish Sylvester in 1932 [177] and in 1936 [178], and Vanderperre [179] in 1934 continued this trend. Between 1930 and 1933, Bailey [180] carried out the first comparison between model and full-scale measurements of a shed, noticing huge discrepancies. The discussion about the suction on downwind faces developed in the structural design sector. It was brought up by Nielsen [181] in 1903 and by Arthur William

9.5 Building Aerodynamics

711

Brightmore, who in 1908 titled a paragraph of his book [182]: “Stresses due to wind pressure and depression”. Between 1911 and 1914 Alfred Smith [183–185] debated the importance of rationalising the design of low-rise buildings by applying the pressure on the upwind face and pitch and the depression on the downwind face and pitch; he made use of tests on models of hangars with a double-pitch roof.21 Andrews [186] in 1913, Milo Ketchum (1872–1934) [187] in 1921, George Fillmore Swain (1857–1931) [188] in 1927, and Charles Milton Spofford (1871–1959) [189] in 1928, criticised the tendency to neglect the suction on downwind faces, emphasising the importance of sizing roof anchorage to counter uplifting. What Fleming [56] wrote in 1930 was symptomatic. Even though he showed great skill on the wind (Sect. 9.3), he estimated that, considering the weights involved, taking account of depression was unnecessary; he added that, considering the uncertainties about the distribution and size of openings, avoiding the reduction of vertical loads by ignoring depression was a good practice on the safe side. At least, he recognised the importance of strong anchorages. Giovannozzi [112] (1936) replied that direct wind actions caused pressure coefficients cp ≤ 1 whereas suction originated cp values that could be lower than −2.5; they were not usually important for the overall actions, but they were essential for the local ones. As explained by Karman [114], the codification sector was affected by this situation, being very slow to reach a suitable attitude. The 1928 French regulations still made use of the Duchemin formula, considering only wind actions on the front face and on the upwind slope. The 1936 German regulations first introduced depression on downwind faces. The French regulations conformed to this evolution from 1939. In 1940, the ASCE Sub-Committee 31 provided new recommendations on wind actions on metal buildings [72]; they were inadequate for the design speed [71] but, if only qualitatively, correct in terms of pressure distribution. Some of them stand out: the pressure on the upwind slope is a function of its inclination, the pressure on building surfaces was the resultant of external and internal pressures, torsional effects have to be considered for asymmetrical buildings. The measurements in the early twentieth century about curved surfaces mostly involved hangar roofs. The first were carried out by Giulio Costanzi (1875–1965) [190] in 1912 and by Albert Smith between 1913 and 1914 [184, 185]. Unlike the measurements on buildings with sharp edges, they highlighted the dependency on the Reynolds number and on construction details. In 1914, Eiffel [191] carried out tests on a hangar in Belfort with inclined and curved slopes; the pressure on the upwind edge was positive, but it became negative half-way through the slope; the downwind slope was subjected to depression. New measurements were carried out by Sylvester [177], in 1929, and by Karl Arnstein (1887–1974) and Wolfgang Benjamin Klemperer (1893–1965) [192], who, between 1928 and the early 1930s, compared the results of full-scale and model tests on a hangar near Akron. Pagon [106] (1934) made a similar comparison between the measures carried out on sloped and curved roofs (Fig. 9.43). In 1940, ASCE [72] divided the roof into three areas: the first 21 The tests were not carried out in a wind tunnel. Large hangar models were used, simulating the application of the aerodynamic forces.

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9 Wind Actions and Effects on Structures

quarter, the central half and the last quarter; the pressure on each area depended on the ratio between the roof height and width and on its height above ground. The first wind tunnel tests on spheres were carried out in 1912, by Eiffel in Paris and by Prandtl in Göttingen (Sect. 5.1), in 1913 by Rayleigh [193] and in 1914 by Carl Wieselsberger (1887–1941) [194]. The first tests on gasometers and chimneys were carried out at the AVA in Göttingen (Sect. 7.4). In 1927, Seitfert [195] measured the pressure distribution on a gasometer with smooth surfaces. In 1930, Dryden and Hill [196] published the results of wind tunnel tests on circular cylinders and of previous unpublished full-scale measurements22 on chimneys. They reported pressure coefficients as a function of the Reynolds number, and from the former they obtained drag coefficients per unit length. Full-scale measurements were carried out as a consequence of the difficulties and uncertainties inherent in wind tunnel tests for high Reynolds numbers; they turned out to even more difficult and of dubious interpretation, but highlighted interesting results: besides the Reynolds number, pressure also depended on the height/diameter ratio and on surface roughness; local pressure could reach high values and could represent a problem for chimneys with thin walls. In 1931, Flachsbart [91] measured the wind pressure on chimneys; the following year [92], he measured the drag and the distribution of the radial pressure on a sphere, highlighting its dependence on the Reynolds number. He also carried out pressure measurements on a gasometer [94], whose metal sheets were stiffened by angle bars (with height 1/30 of the diameter) along the generatrices. He used a model 580 mm high and 300 mm in diameter (Fig. 9.44a). Figure 9.44b shows the distribution of the

Fig. 9.43 Wind pressure on curved and pitched roofs [106] 22 Measurements were carried out on an experimental chimney built on the roof of a building at the National Bureau; it was 3 m in diameter and 9 m high; 24 pressure taps were arranged along a circumference. Taking advantage of the construction of a chimney at the power plant of the Bureau of Standards, other tests were carried out; the chimney was 3 m in diameter and soared 36 m above the roof; 24 pressure taps were installed along a circumference.

9.5 Building Aerodynamics

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Fig. 9.44 Flachsbart’s gasometer [94]: a model; b radial pressure

radial pressure at 11 levels. The comparison with Seitfert’s measures [195] proved that the angle bars reduced the suction due to wake separation. At all events, the issue of the meaningfulness of tests came to light. They hardly reproduced the actual Reynolds number. Thus, their results were qualitatively interesting but quantitatively unreliable. The turning point was the appearance of boundary layer wind tunnels (Sect. 7.3). The first to perceive their importance were Irminger and Nøkkentved in Denmark and Flachsbart in Göttingen. Irminger and Nøkkentved [197, 198] carried out pioneering experiments between 1930 and 1936. At first, they performed flow visualisation tests showing that the upwind face was subject to pressure, while the downwind face, the side faces and the downwind slope were subject to depression; the upwind slope was subjected to pressure or depression depending on its inclination. Afterwards, they carried out pressure measurements for various building shapes and wind directions, highlighting the importance of the ratios between width, depth and height. The study of curved roofs and of circular-shaped buildings confirmed the role of the Reynolds number. Other tests were carried out to study the sheltering effect of buildings on structures in their wake. Reproducing in scale the wind profile was always essential. Similar tests were performed by Flachsbart [88, 89, 93] from 1930 to 1932. His measurements of the pressure on the surfaces of buildings, sheds and hangars were milestones (Sect. 7.3). His remarks about interference also stood out. While the measurements carried out by Harris [199] on a model of the Empire State Building surrounded by buildings exhibited sheltering effects, Flachsbart maintained that

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9 Wind Actions and Effects on Structures

Fig. 9.45 Pressure coefficients on building facades (a) and flat roofs (b) [201]

peculiar layout arrangements could originate channelisations capable of enhancing wind actions. This was confirmed by the studies of Bailey and Vincent [79] in 1943. Martin Jensen (1914–1990) [200–202] completed this course between 1946 and 1958, formulating the model law (Sect. 7.3), validating it through comparisons and producing data of great design importance. He remarked that the pressure coefficient may be referred to the velocity pressure of the undisturbed flow at the measurement height or at a reference height; in this case, he suggested to use the building top. He carried out tests on seven building models, showing that the maximum overturning moment occurred when the wind was orthogonal to a wall; the pressures on the upwind and downwind faces were maximum for low turbulence; strong depressions were present near the edges of the upwind face and in depression zones; as the surfaces increased, both pressure and depression decreased. He stated that flat roofs were mostly subjected to suction; the suction was at its maximum near the edges of the upwind face; if wind was orthogonal to a face, the suction decreased starting from the upwind edge; if the flow was inclined, suction was the highest in the corner swept by the wind. Jensen also reported measurements on buildings (Fig. 9.45a) with flat (Fig. 9.45b), single-slope, double-slope and four-slope roofs. He measured wind actions on isolated single- (Fig. 9.46a) and double-slope (Fig. 9.46b) canopies, providing the pressure distribution as well as the resultant force and its point of application.

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Fig. 9.46 Pressure coefficients on single (a) and double (b) slope isolated canopies [201]

Unfortunately, when Jensen provided such contributions, the codification sector was already pervaded by rules based on measurements carried out without reproducing the atmospheric boundary layer, i.e. inherently wrong. The state of the art by Thomas W. Singell (1958) [119] was symptomatic. He mentioned the 1940 ASCE document [72], which collected the measurements available until 1936 and, without ever mentioning Jensen [202], made it more substantial with the data introduced in the 1948 Danish standard [123] and in the 1956 Swiss standard [124] (Fig. 9.47), considered the most extensive collections of information on wind actions. He concluded affirming that the available information was then sufficient to obtain reliable assessments. To have reliable data at its disposal, the design sector had to wait for the construction of the first boundary layer wind tunnels in the 1960s, the repetition of the tests carried out without meeting the requirements of the model law and the gradual replacement, in the codification sector, of the old pressure coefficients by the new values. There is still a fundamental issue to discuss for structures enclosed by walls: internal pressure. The first measurements on non-airtight structures were carried out by Bounkhin and Tcheremoukhin [175] in 1928; they assumed that openings were uniformly spread, that the speed of the air crossing the openings was proportional to the square root of the difference between external and internal pressure, that the air mass passing through the building did not change its volume and that

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9 Wind Actions and Effects on Structures

Fig. 9.47 1956 Swiss standard [124]: low (a) and tall (b) buildings

internal pressure was constant; they proved that the internal pressure coefficient was cp = −0.25. Between 1930 and 1936, Irminger and Nøkkentved [197, 198] carried out new measurements of the internal pressure of uniformly porous buildings, confirming Bounkhin’s and Tcheremoukhin’s results and obtaining internal pressure coefficient values from −0.05 to −0.41.23 Similar measurements were carried out by Flachsbart [88, 89, 93] between 1930 and 1932. Giovannozzi [112] (1936) examined previous measurements and noticed that if buildings were not permeable their internal pressure would be the one existing at the time they were last opened or built. Actually, there were many paths through which air could flow (doors, windows, dormers, skylights, …). He then expressed doubts about results obtained with homogeneous openings. He observed that the knowledge of his age was still far from clarifying the internal pressure issue; while waiting for better assessments, he proposed, on the safe side, cp = −0.30/−0.35; in other words, he ruled out the possibility that internal pressure could be positive. The 1940 ASCE paper [72] provided indications close to current ones. It remarked that, even when the structure was apparently airtight, there were distributed cracks that created internal pressure. The pressure coefficient ranged from cp = + 0.25, when the upwind opening prevailed, to cp = −0.35, when the downwind ones prevailed. Internal pressure increased when large openings were present. The most important contribution to this subject came from Dick [203]. In the 1947–1948 winter, he carried out full-scale tests, near Abbots Langley, Herts, UK, to study the heating techniques in relation to the physiology of inhabitants (Sect. 8.6). He determined the heat lost because of natural ventilation as well as the distribution of external and internal pressures. The tests highlighted the role of the pressure gradient due to openings on surfaces with different values of the external pressure, e.g. the downwind and upwind faces. The results were compared with those of the model tests carried out by Irminger and Nøkkentved [197, 198] and by Bayley and Vincent [79]. Dick resumed his tests in 1950, giving a consistent picture of the mechanisms 23 According to Irminger and Nøkkentved, the copper roof of a Danish cathedral with many holes since ancient times was replaced by an airtight roof. During the first storm the roof was eradicated by wind, highlighting the role of holes, i.e. to counter the uplift taking advantage of the internal depression. Restoring the holes, the roof came through subsequent storms undamaged.

9.5 Building Aerodynamics

717

and laws governing natural ventilation [204]. Even though this was not envisaged by the author, his equations also provided internal pressure (Sect. 8.6). The assessment of the aerodynamic coefficients of slender elements and lattice beams is relatively simpler than the analogous assessment for buildings enclosed by walls. It does not require pressure taps, but dynamometric balances. Reproducing the atmospheric boundary layer was usually not necessary. Then, the assessment of wind actions on these structures or elements in the early twentieth century was already close to the current ones. In many cases, the aerodynamic coefficients in use date back to this period. Slender elements with the z-axis orthogonal to the wind direction are subjected to aerodynamic actions per unit length, defined through two alternative conventions. The first convention expresses the actions by means of a drag D, a lift L and a twisting motion M given by: D = cD ql;

L = cL ql;

M = cM ql 2

(9.5)

where cD , cL and cM are drag, lift and twisting moment coefficients (Fig. 9.48a). Retaining the definition of M in Eq. (9.5), the second convention defines a couple of forces, f x and f y , referred to two fixed axes, x and y, which make up an orthogonal triad with z. The aerodynamic actions are then given by: f x = cx ql;

f y = c y ql;

M = cM ql 2

(9.6)

where cx = cD cos β − cL sin β and c y = cD sin β + cL cos β are force coefficients, β is the angle of attack (Fig. 9.48a). In both cases, l is a characteristic size of the cross-section. The aerodynamic coefficients are the product of the same coefficients for an ideal monodimensional element of infinite length (with index 0) by an aspect ratio factor ψλ that takes end effects into account: cD = cD0 ψλ ; cL = cL0 ψλ ; cx = cx0 ψλ ; c y = c y0 ψλ ; cM = cM0 ψλ

(9.7)

The literature of the first half of the twentieth century is rich in the former but lacking in the latter. The aerodynamic coefficients of the ideal monodimensional elements can be divided into two families including sharp-edged and rounded elements. The former did not depend on the Reynolds number Re and on the surface roughness. In the latter, these quantities play an essential role. The first measurements on sharp-edged elements were carried out by Irminger (1893) [170, 171], by Stanton (1903) [172] and by Nagel (1927) [205]. Nagel measured wind actions on isolated elements and composite beams, expressing the results through Eq. (9.6); the x(n) and y(t) axes were normal to two orthogonal faces of the element, l was the normal projection of the cross-section on an axis parallel to the face with the largest area; cx = cn and cy = ct reached their maximum values when the wind was normal to the faces of the elements and assumed values between 1.8

718

9 Wind Actions and Effects on Structures

Fig. 9.48 a Aerodynamic actions on slender elements; b drag and lift coefficients for metal elements [97]

and 2.2; changing the wind direction, the aerodynamic coefficients often changed their sign, showing steep gradients. The most known and reliable measurements of the force coefficients of sharpedged elements were carried out by Flachsbart [97] in 1934. He performed tests on rectangular, caisson-type, L-shaped, T-shaped and H-shaped cross-sections (Fig. 9.48b). The first measurements on elements with rounded surfaces were carried out by Konstantin Eduardovich Tsiolkovsky (1857–1935) [206] in 1897, on cylinders with circular and elliptical cross-section. In 1929, Arthur Fage (1890–1997) and Warsap [111] studied how the drag of the cylinders depended on turbulence and surface roughness. They noticed that there was a domain of the Re values for which the flow around a smooth cylinder was subjected to a change, with a corresponding decrease of the drag coefficient cD (k D ) from 0.6 to 0.2; it was due turbulence and surface roughness. The artificial turbulence was produced through a wire mesh before the model; the tests were carried out on varying the distance S from the mesh to the cylinder for Re = 40,000–230,000. On decreasing S, the turbulence increased but the diagram shape did not change. The surface roughness produced local turbulence; the experiments were carried out wrapping the cylinder with paper of different roughness. Figure 9.35 shows that as roughness increased, the cD drop took place for smaller Re values. Roughness was more effective when it was located near the separation points. Other researches were carried out arranging local rather than diffuse roughness: wires were placed along the generatrices θ = ±65°; their diameter was so small to be contained within the wall

9.5 Building Aerodynamics

719

Fig. 9.49 a Drag coefficient cD (k D ) as a function of Re and of the wire diameter [111]; b radial pressure for a cylinder without and with wires

boundary layer; Fig. 9.49a shows the withdrawal of the cD diagram on increasing the wire diameter; Fig. 9.49b shows the diagram of the radial pressure in relationship with the wind speed, for a cylinder without and with wires. The wires with diameter so great to protrude from the boundary layer were ineffective if they were moved away from the separation zone. In 1936, Giovannozzi [112] collected measurements carried out on elements with circular cross-section; they included classical slender cylinders, gasometers, chimneys, transmission line poles and cables. He constructed two tables: Table 9.1 provided the drag coefficient of an infinitely long cylinder, cD0 , as a function of Re; Table 9.2 reported the aspect ratio factor, ψλ , as a function of the aspect ratio λ (i.e. the ratio between the cylinder length and its diameter), for Re = 80,000. In the hypercritical regime, uncertainties were huge because of the scarce confidence of wind tunnel tests. Unfortunately, real structures often have Reynolds numbers much greater than the ones used for tests. Giovannozzi believed it was reasonable that cD , beyond the critical regime, tended to an asymptote. For smooth surfaces, he recommended cD = 0.4 for λ < 15; for chimneys, cD = 0.67.

720

9 Wind Actions and Effects on Structures

Table 9.1 Drag coefficient cD0 as a function of Re

Table 9.2 Aspect ratio coefficient ψλ as a function of λ for Re = 80,000

Regime

Re

cD0

Hypocritical

103 –105.5

1.2–1

Critical

105.5 –105.7

1–0.3

Hypercritical

>105.7

Increasing

λ

ψλ

3

0.75

5

0.74

10

0.83

20

0.92

40

1.00

∞

1.20

On truss beams, or on their parts, the aerodynamic actions can be traced to the three Cartesian components of the force F and of the moment M. They were defined by: Fα = cFα q l 2 ;

Mα = cMα q l 3 (α = x, y, z)

(9.8)

where cFα and cMα are force and moment coefficients; l is a characteristic length. Assuming that the x-axis is oriented in the wind direction, the drag force F x generally is the major aerodynamic action, and often it is the only one taken into consideration. As regards to aerodynamic coefficients, lattice beams were classified into three families: flat, isolated or parallel; truss girders; lattice structures and bridges. The first measurements on lattice beams were carried out by Eiffel [191] in 1914 and in Rome, in 1924, at the Experimental Aeronautical Institute of the Pali Committee [112]; they proved that the aerodynamic actions on structures made of sharp-edged elements do not depend on the Reynolds number. Similar results were obtained by Albert Betz (1885–1968) [207] in 1927, by Baes [208] in 1931, by Betz and Peterson [209] in 1932, and by Vanderperre [179] in 1934 for a lattice beam, either isolated or sheltered by an identical beam located upwind. The most famous measurements of the aerodynamic coefficients of isolated lattice beams were carried out by Flachsbart between 1932 [95] and 1934 [97]. He analysed the case of wind orthogonal to the plane of a beam with height h and infinite length, made up by sharp-edged elements, expressing the drag coefficient cn = cn∞ in relationship with the solidity ratio ϕ = F r /F, where F r was the net area of the exposed elements, F was the gross area of the beam, considering the empty spaces as solid ones. He then measured the drag coefficient cn of a beam with length l, expressing the cn /cn∞ ratio as a function of the solidity ϕ and of the aspect ratio λ = h/l (Fig. 9.50a). He studied the influence of the shape and layout of the elements making up the lattice beams and the effects of the gusset plates. He also examined the wind inclined by the

9.5 Building Aerodynamics

721

angle α (Fig. 9.50b) and expressed the normal N and tangent T force (in relationship to the beam plane) through a pair of aerodynamic coefficients, cn and ct . In 1935, Flachsbart and Winter [98] studied two parallel identical beams. In the case of wind orthogonal to them, the force coefficients of each beam depended on ϕ and λ and on the d/h ratio, where d was the distance between the beams. The tests led to diagrams of the ψI = cnI /cn and ψII = cnII /cn ratios, where the I and II indices indicate the upwind and downwind beam, respectively (Fig. 9.51). With inclined wind, most of the sheltering effect provided by the upwind beam on the downwind one was lost. In the same 1935 paper, Flachsbart and Winter [98] studied the wind actions on lattice masts, in particular on lattice towers with square cross-section. Wind tunnel tests were carried out on sectional and full models. In the case of wind orthogonal to a face, authors expressed the drag coefficient through the results obtained for the beam pair, ignoring the elements parallel to the wind direction; they took account of the speed and solidity changes with the height, dividing the structure into vertical trunks and considering the wind uniform on each one of them. The problem became more complex when the wind was oblique; it caused the most severe actions. According to Baes [208], the worst angle of incidence was α = 20°; according to Katzmayr and Seitz [210], α = 25°; according to Flachsbart and Winter, α = 45°. The differences were small and showed that, assuming ξ = S max /S, being S max the maximum force with oblique wind and S the force with wind orthogonal to a face, ξ = 1.1–1.2. Flachsbart and Winter recommended ξ= 1.15. New tests were carried out at the NPL in 1954 on television antennas [211] and cranes [212].

Fig. 9.50 Aerodynamic actions on flat truss beams [97]: a ratio between the drag coefficients of beams (orthogonal to wind direction) with finite and infinite length; b inclined wind direction

722

9 Wind Actions and Effects on Structures

Fig. 9.51 ψI and ψII sheltering coefficients [98]

In 1957, Cohen and Perrin [213] approached wind actions on cable-stayed towers. Because of the evolution of telecommunication systems, they were increasingly higher and sensitive to wind. Generally, they were lattice masts with triangular or square cross-section; some had triangular- or square-shaped tubular cross-section. Cohen and Perrin started from the assessment of the drag and lift on individual variously shaped elements [68, 95, 98, 113] (Fig. 9.52). They noticed the overall force could not be calculated as the sum of the forces on the individual elements; they then collected in a diagram (Fig. 9.53) data [95, 98, 191, 210, 214] concerning towers with square or triangular cross-section, made up of sharp-edged or circular elements. They advised designers to take account of the aerodynamic actions on the elements supported by the tower (e.g. dishes and antennas) ignoring, on the safe side, their sheltering effects. They also provided the first criteria to assess wind actions on cable stays. The most discussed subject in this period was the wind action on truss bridges (Sect. 9.1). In 1887, Thomas Claxton Fidler (1841–1917) [85] observed that, when the wind was orthogonal to the vertical truss beams along the bridge axis, the first beam sheltered the other ones. A small inclination in the wind direction was enough to deprive the back beams of the sheltering effect; in any case, the overall pressure was smaller than the sum of the pressures on the individual beams. Even though the overall force was intermediate between the one on the front beam and that on all the beams dealt with as isolated, the interval between these conditions was large and there were no elements to choose an intermediate value. It was then reasonable to assume that the sheltered beams were subjected to forces equal to the force acting on the first beam multiplied by a factor smaller than 1 and that this factor depended on the distance between the beams, on the shape of the elements and on the overall shape of the truss. The assessment of this factor was to represent a key subject of the research in the first half of the twentieth century.

9.5 Building Aerodynamics

723

Fig. 9.52 Aerodynamic coefficients of individual elements [205]

In the same period, a debate about the wind pressure on truss bridges developed in the design sector. Charles Shaler Smith (1836–1886) in 1881 [215], John Alexander Low Waddell (1854–1938) in 1884 [216], in 1898 [217] and in 1916 [218], and Theodore Cooper (1839–1919) in 1905 [219] proposed a pressure range so broad (1.20–2.40 kPa) it once more showed the uncertainties about wind actions. Such values highlighted, however, the dependence on the span length, pointing out the increasingly familiar concept of the non-simultaneous occurrence of the maximum actions at different positions. The first studies about this subject were carried out in Göttingen by Betz (1935) [207], and by Flachsbart and Winter (1935) [98]. They built the models of five isolated truss beams (Fig. 9.54a) and performed measurements changing wind intensity and inclination. The tests were repeated coupling the beams to assess their sheltering effect. Wind actions on a full bridge were determined by arranging two beams in parallel, with an interposed deck (Fig. 9.54b). Seven different elements were used for every truss beam. The overall aerodynamic coefficients measured in the longitudinal, transversal and vertical directions highlighted the role of the solidity ratio. Flachsbart remarked that the wind action on two parallel beams approximated the case when a deck was interposed between the beams. This derived from the fact that wind was essentially horizontal and tangential actions were negligible; the deck then offered a drag commensurated to its thickness, which was small in comparison with the height of the beams. Such results confirmed Betz’s ones [207].

724

9 Wind Actions and Effects on Structures

Fig. 9.53 Aerodynamic coefficients of lattice towers [213]

Fig. 9.54 Prandtl’s and Betz’s truss beams for bridge decks [105]: a models; b results

9.5 Building Aerodynamics

725

Fig. 9.55 Biggs’ railway bridge model [220]: a disassembled beams; b overall bridge

Pagon [105] appreciated them hoping that they could change the design trend to apply wind pressure on exposed surfaces, multiplying it by 1.5 or 2 to take the sheltered elements into account. New tests on models of truss bridges were carried out by Biggs [220] in 1954. He built two dismountable models of railroad truss bridges (Fig. 9.55a) and measured wind actions on beam pairs with and without an interposed horizontal truss beam; he then replaced the latter with a solid plate, carrying out new tests on models of highway bridges. The railway bridge model in 1:120 scale consisted of two parallel Warren truss beams, closed by a truss beam above and by the railway floor below (Fig. 9.55b); the deck, therefore, was of the closed cross-section type. The highway bridge model, in 1:40 scale, was used to simulate two positions of the deck. The tests were carried out in four stages. In the first stage, the analysis of a single beam confirmed that the drag coefficient for sharp-edged elements mostly depended on solidity. In the second stage, two parallel unconnected beams were studied, changing the angle of attack. The third and fourth stages were concerned with the whole bridge: the railway floor did not increase the drag because the upwind beam sheltered it; on the contrary, it reduced the drag because the floor sheltered the downwind beam; the floor, then, only contributed to the friction force. During the tests, the lift and moment coefficients were assessed for the first time, considering the wind direction and the height of the bridge above ground: when the wind was horizontal, the lift was small and the torsion was almost equal to the drag multiplied by the distance from its point of application to the shear centre; when the wind was inclined on the horizontal, lift and torsion increased. New measurements on bridge models were carried out by Biggs et al. [221] in 1956. Nearly all the railway bridge typologies were analysed whereas only the most common road bridges were studied (Fig. 9.56). Since bridges were sensitive to the deck thickness/width ratio, 24 models were built, reproducing a wide range of values of this parameter. The tests were carried out in Cambridge at the M.I.T., on sectional models in scales between 1:32 and 1:25. Edge effects were avoided by means of end-plates or making use of a pair of disconnected side models. Various values were used for the Reynolds number, the angle of attack and the yaw angle in the horizontal plane. The measurements of the drag, lift and twisting moment proved that the third quantity was correlated with the second but not with the first.

726

9 Wind Actions and Effects on Structures

Fig. 9.56 Aerodynamic coefficients of various railway and road bridges [221]

9.6 Dynamic Response to Turbulent Wind Unlike vortex shedding (Sect. 9.7), galloping (Sect. 9.8), divergence and flutter (Sect. 9.9), which in the early twentieth century were already treated on conceptual and mathematical grounds close to the current ones, the dynamic response of structures to the turbulent wind had difficulty to suitably develop, relying for a long time on patterns and models detached from reality and that have fallen into disuse. The reason is clear: while aeroelastic phenomena are deterministic in nature, turbulent wind is a random field and its properties and effects cannot elude a probabilistic framework (Sect. 5.2). In 1887, Thomas Claxton Fidler (1841–1917) [85] studied for the first this subject in a qualitatively appreciable manner. He noted that, if after a period of calm, a sudden pressure increase p occurred, the stresses due to such change were equivalent to the static application of 2p. Likewise, if after a period with constant pressure p a sudden pressure increase up to p + p occurred, the stress assumed a value equal to the one due to the static action of p + 2p. In any case, even if pressure increased gradually, the maximum stress was greater than the one caused by the static application of the maximum pressure pmax . Such stress was then equal to the one due to the static application of the pressure: σ = pmax + η( pmax − p)

(9.9)

where η is a coefficient smaller than 1. In 1933, Rausch [222] developed the most famous and applied theory in the first half of the twentieth century. According to him, the dynamic wind action depended

9.6 Dynamic Response to Turbulent Wind

727

on its continuous variation in time and space; it produced dynamic effects greater than the static effects due to the maximum action. This occurred because of the link between the pressure fluctuations and the inertial actions due to structure oscillations. Assuming as known the relationship that links, at every instant t, the wind pressure and speed, Rausch schematised the gusts through a pressure diagram as a function of t. He expressed the pressure p as the sum of the constant mean value p0 and of the fluctuation p1 ; the latter consisted of a sequence of segments (Fig. 9.57a): the first increased with a linear law (A); the second was constant, with fluctuation p1 (and overall value p = p0 + p1 ) (B); the third decreased with a linear law (C); and so on. Based on this model, Rausch evaluated the static response x s of the structure to the maximum pressure p. He expressed the maximum dynamic response through the relationship x d = x 1 + x 2 , where x 1 is the static response to the mean pressure p0 , x 2 is the maximum dynamic response to the pressure fluctuation. This term was determined by the equation of the undamped forced oscillations for the increasing segment (A) of the pressure; in the subsequent constant segment (B) the equation of the damped free oscillations was applied, with initial displacement and velocity values equal to the final values of the segment (A). This procedure is still in use to evaluate the dynamic response to short duration actions. Rausch afterwards schematised the previous polygonal chain with a sinusoid and obtained the γ = x d /x s ratio in closed form. This quantity was called dynamic coefficient and was given by (Fig. 9.57b): γ=1+β

(9.10)



π ω α ; α= 1 + α2 − 2α sin β= 2 α −1 2α λ

(9.11)

where

ω is the frequency of the wind sinusoid, λ is the eigenfrequency of the structure. In other words, a gust with maximum pressure p produces stresses 1 + β times greater than those due to p if it were constant. Since for λ tending to infinity α and β tend to zero and γ tends to 1, while for λ tending to 0 α tends to infinity, β tends to 1 and γ tends to 2, flexible structures are more sensitive to wind than rigid structures.

Fig. 9.57 Rausch model [222]: a wind pressure; b dynamic coefficient

728 Table 9.3 T fundamental period and β parameter for various structural typologies

9 Wind Actions and Effects on Structures

Typology

T (s)

β

Chimneys

2–3

0.30–0.70

Radio antennas

1–4

0.15–0.70

Lattice masts for power lines

9.5, −k a is negative, so the aerodynamic damping is positive and increases the structural damping, mitigating the vibrations. Figure 9.72b, associated with the case in Fig. 9.72a, shows −k a as a function of η0 for V r = 5. Since −k a is positive, δa is negative; its absolute value decreases as the motion amplitude increases; the motion amplitude due to vortex shedding synchronisation, or lock-in, cannot then indefinitely grow, but tends to the finite limit η0 = η0L . It decreases in so far as, because of the mechanical nonlinearity, δs increases as η0L increases (Fig. 9.73). The box in Fig. 9.72b shows a diagram of −k a for V r = 3; −k a is positive for small values of η0 whereas it is negative as the displacement amplitude increases. There are still to make some comments about the most sore point: the dependence of −k a on the Reynolds number for elements with rounded surfaces. Many measurements in the sub-critical regime were available, but there were none in the super-critical regime of real structures. Scruton [45] tried to bypass this problem by creating a dummy roughness on the surface of the model; it was obtained using titanium oxide in suspension in paraffin and was increased until the laminar boundary layer causing the wake separation in the forward part of the cylinder turned into a turbulent boundary layer that separated in the rear part. This technique improved the tests but did not settle the doubts; despite a massive effort developed over the years to obtain −k a through tests on real structures, they are still mostly unsolved. The above mathematical framework clarified the properties of the instability domains introduced by Scruton. Figure 9.74 shows two examples for elements with circular (a) and square (b) cross-section; in the abscissa there is the k s coefficient (Eq. 9.58, unless a 2 factor), in the ordinate the reduced speed V r . The solid line is the so-called instability domain, i.e. the locus of the points where the equality in Eq. (9.62) is valid: outside this domain, in the stability region, the positive structural damping prevails on the negative aerodynamic damping and the oscillations damp down; inside the domain, in the instability region, the negative aerodynamic damping prevails on the positive structural damping and the oscillations diverge. Figure 9.74a, referred to the circular cross-section, shows an instability form caused by vortex shedding. It starts for a wind speed V just lower than the critical value

752

9 Wind Actions and Effects on Structures

Fig. 9.72 k a for a circular cylinder (Re < 105 ) [254]: a η0 = 0.011; b V r = 5

9.7 Vortex Shedding

753

Fig. 9.73 Critical instability condition and limit value of the reduced displacement

Fig. 9.74 Instability domain for elements with circular (a) and square (b) cross-section [254]

V cr corresponding to V r = 5; in a neighbourhood of this value, in the lock-in domain, the structural damping required to counter instability increases; subsequently, past this domain, it decreases again. Figure 9.74b, referred to the square cross-section, shows a different behaviour. The instability due to vortex shedding occurs in a neighbourhood of V r = 6.6. Past this first critical region, at first the phenomenon damps down, then a second critical region, related to galloping (Sect. 9.8), appears. It starts for Vr ∼ = 14; as V r increases, the structural damping required to counter the instability linearly increases and the phenomenon gradually becomes uncontrollable.

754

9 Wind Actions and Effects on Structures

Fig. 9.75 Dynamic response to vortex shedding of a tapered chimney [45]

In parallel with the basic research on the elements with circular and square crosssection,28 many other studies about the vortex shedding from real elements and structures were carried out at the NPL. They proved that this phenomenon was critical for a broad variety of structures. The case of the tapered chimneys is explanatory. Figure 9.75 shows some results of tests on an aeroelastic model in 1:50 scale, highlighting three critical speeds. The first concerns the fundamental mode and occurs when the vortex shedding is critical at the top; with the same diameter, vibrations are as strong as those of the chimneys with constant cross-section; since tapering reduces the diameter at the top, vibrations occurred at a lower critical speed; consequently, being the excitation proportional to the square of the speed, they are less strong. The second and third critical speeds correspond to the vortex shedding in resonance with the second mode: the second occurs for resonance at the top; the third is associated with a greater diameter at a lower height, that of the relative maximum of the second mode. Another interesting aspect involves the elements applied to structures, e.g. antennas and dishes on telecommunication towers. It seemed possible they disrupt the wake until its effects are mitigated. The experimental tests on the Jonsknuten television tower in Norvegia proved that this was not true. A mention must also be made of the contribution of the NPL to the aerodynamic measures to suppress vortex shedding [249, 253, 256]. 28 The measurements were carried out at the NPL on regular polygons with 6, 8 and 12 sides. Vortex shedding was always present, but its intensity varied in relationship with the number of sides; it was maximum for the square and minimum for the hexagon; in both cases, the worst situation took place with the wind perpendicular to a face. Other tests were carried out on L- and H-shaped cross-sections elements.

9.7 Vortex Shedding

755

Fig. 9.76 Helical strakes: a on a cylinder [256]; b response of a tapered chimney [257]

In 1957, Scruton and Walshe [256] introduced the helical strakes, i.e. helices coiled up around chimneys or tubular elements to prevent the formation of an organised vortex wake. The wind tunnel tests were carried out with three helices (Fig. 9.76a). Every helix completed its revolution along 15 cylinder diameters. The optimum height of the helix depended on the structural damping. This remedy was also advantageous to mitigate ovalisation. In 1959, Woodgate and Mabrey [257] proved that the most effective configuration was accomplished by means of three helices, with height 0.09 times the cylinder diameter, coiled with an inclination between 30° and 40° (Fig. 9.76b). They were, for many years, the classical technique to suppress the vibrations due to vortex shedding. On the other hand, likewise the shroud, they greatly increased the drag. In 1959, William Weaver [258] remarked that vortex shedding was dangerous also for the tubular elements of metal frames and truss beams. Because of this phenomenon, the elements supporting radar antennas suffered collapses due to fatigue.29 To analyse such occurrences, static and dynamic tests were carried out in the wind tunnel of the M.I.T. Aeroelastic Laboratory. At first, the tests were carried out to obtain the Strouhal number, the wake lift coefficient and the vibration amplitude in relationship with the Reynolds number. They were subsequently repeated with helical spoilers consisting of flexible pipes made of plastics, in different diameters. The results proved their validity under restrictive conditions.

29 Collapses due to vortex shedding from tubular elements of radar antenna frames were observed at

the M.I.T. Lincoln Laboratory, where an element of a dish 8.5 m in diameter broke. Other collapses involved a reflector 25 m in diameter. An element of a similar structure widely vibrated in Boston, MA.

756

9 Wind Actions and Effects on Structures

9.8 Galloping From the early twentieth century, the conductors of transmission lines showed wide oscillations attributable to the wind [240]. They moved along elliptical orbits with their major axis in upright position, causing either electric, when they came into contact along a span, or mechanical failures, when fatigue broke them near suspension clamps. Such phenomena caused alarm for electrical companies as well as technical and scientific interest. A vast literature aimed at explaining and countering them developed from the late 1920s. Varney [242], noticing that oscillations were resonant, attributed them to vortex shedding. Others interpreted them through the Magnus effect, or attributed them to the vibrations of the wooden poles supporting the cables, or thought they were due “to the pulsating action of the wind”. A. E. Davison (1930) [259] considered such interpretations respectable but insufficient to explain the motion of conductors. Davison quoted what reported by Archer, a member of the Hydro-Electric Power Commission, on the vibrations observed in 1927 in Whitby and near the Niagara Falls. They took place in different weather with different characteristics. The former appeared in a hot day, with strong wind, but did not compromise the line operation. The latter occurred in a cold day with light rain and moderate wind; a cable span vibrated, like it was “possessed”, but the adjacent ones didn’t. Archer observed that the cable, of the strand type, was coated with ice on the face exposed to wind. He also noted that vibrations decreased when the cable was also coated with ice on its downwind face. The second Davison’s remark regarded the pictures taken by Muehleman, another member of the Hydro-Electric Power Commission, during strong vibrations of the conductors of the line crossing Hamilton, Niagara. Even in this case they were partially iced. In some cases, vibrations involved two adjacent spans, in others only a single span. Following such phenomena, Davison carried out wind tunnel tests at the Toronto University. He took a section of a strand-type conductor, smoothing and painting half of its circumference. Figure 9.77a shows that its lift was subjected to large variations, arriving to reverse its direction for small variations in the angle of attack. Since conductors were sensitive to the alternation of the forces, even if the latter were small in comparison with their weight, Davison concluded that the partial formation of ice on the surface of cables was sufficient to explain their oscillations. In December 1929, a storm bringing wind, sleet and frozen rain occurred in the New York and Ontario districts. Davison was in Allanburg, at the centre of this phenomenon, and observed many power lines. The cables were fully covered by ice with variable thickness and shape, due to multiple depositions and stratifications. A conductor line vibrated with light wind, inclined by 75° with respect to the line. Vibrations were irregular, with 6–8 m amplitudes. In some parts of the line, the vibration took place in a single span, along its whole length. In other spans, a kind of gallop appeared: the vibration started on the side third of the span, vertically, then moved to the central zone and so on, like the propagation of a wave. The phenomenon continued for many hours, until the wind changed.

9.8 Galloping

757

Davison then decided to carry out new wind tunnel tests, using cable sections covered by irregular ice formations (Fig. 9.77b). In comparison with the previous case, lift increased and its variation concentrated in small ranges of the angle of attack. The examination of cables fully covered by ice, but with more regular shape, led to similar situations. Davison concluded that the only measures to avoid the crisis of power lines were either to prevent ice formation by electrically heating conductors or to space out the cables to avoid that, when subjected to vibrations, they could come into contact, thus interrupting the line; he was sceptical about the use of dampers. Taking his cue from these studies, between 1932 [260] and 1934 [99], Jacob Pieter Den Hartog (1901–1989) formulated the quasi-steady theory of the SDOF galloping. In his first fundamental paper [260], he maintained that conductor oscillations were, by then, partially understood: they vibrated at high frequencies for low wind speeds because of Karman wake; they conversely vibrated at low frequency for high wind speeds when a coat of ice had formed. Recalling the paper in which Davison proved that, because of the change in shape of the conductor coated by ice, the lift force changed its intensity until it exceeded the weight of the cable, Den Hartog remarked that this did not explain the vibrations, and then Davison’s treatment was incomplete. Towards this aim, Den Hartog examined a unit length cable in a horizontal wind with speed V. Assuming that the cable oscillated vertically with speed v = y˙ (Fig. 9.78) it “felt”, besides V, a vertical component of the speed; it could then be treated as a stationary element subjected to the relative speed: Vr =



V 2 + y˙ 2

(9.63)

When the cable moved with speed v = y˙ upwards, the relative wind was inclined downward by the angle (of attack):

Fig. 9.77 Lift of a conductor [259]: a smoothed and painted on half circumference; b covered by irregular ice

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9 Wind Actions and Effects on Structures

 α = arctg

y˙ V

 (9.64)

Since the cable speed changed, the direction of the relative wind also changed. If the cable cross-section was circular, it was only subjected to drag D, regardless of the relative direction; otherwise, a lift L was also originated. Figure 9.79a shows the drag and lift on an ellipse-shaped element as a function of the angle of attack: for α between 0° and 90° lift acts upward; for α between 90° and 180° lift acts downward. For α = 0°, when it moves upward, V r is inclined downward, α < 0°, and lift is negative; when it moves downward V r is inclined upward, α > 0°, and lift is positive; in both cases, the motion is damped by the wind and the element is stable. For α = 90°, when it moves upward V r is inclined downward, α < 0°, and lift is positive; when it moves downward V r is inclined upward, α > 0°, and lift is negative; in both cases, the motion is amplified by the wind and the element is unstable. This derives from the negative slope of the lift diagram and is valid for small displacements in a neighbourhood of the initial configuration. Figure 9.79b shows the role of drag, by way of example for α = 90°. The vertical component of lift amplifies the element motion. The vertical component of drag is opposed to lift and damps the motion down. As a consequence “instability develops when the effect of the negative slope of lift is greater than the damping action due to drag”. With these premises, Den Hartog introduced the hypothesis of small oscillations in the form:

Fig. 9.78 Wind speed and direction on a circular cable [260]

Fig. 9.79 Drag and lift of an elliptical element [260]: a wind direction changes; b components

9.8 Galloping

759

Fig. 9.80 a Aerial tourbillon by Lanchester [261]; b Den Hartog’s experiment [99]

y˙ ; Vr ∼ =V V  dL  ∼ ∼ D = D0 ; L = L 0 + α dα 0 α∼ =

(9.65) (9.66)

where the 0 index indicates quantities evaluated for the initial angle of attack α = α0 . Referring to Fig. 9.79b, the element is subjected to the following vertical force per unit length:    dL  ∼ (9.67) F = L0 + − D0 α dα 0 The first addend of the right-hand side is the static lift, i.e. the lift independent of time and not affecting instability. The second addend is a dissipative force of viscous type, which erodes mechanical dissipation if opposed to the latter; the motion is potentially unstable if:  dL  − D0 < 0 (9.68) dα 0 Den Hartog remarked that in order to apply Eq. (9.68) it was sufficient to make static sectional model tests providing lift and drag as a function of the wind direction. He also noted that this phenomenon was based on the same principle of the aerial tourbillon described by Lanchester30 (Fig. 9.80a) in 1908 [261]. In the second contribution by Den Hartog about galloping, which appeared in the first edition of his book [99], he went back to the self-excited nature of the phenomenon, remarking that it developed with an oscillation frequency close to that of the ice-covered conductor. “The fact that, once started, the disturbance is very persistent and continues sometimes for 24 h with great violence makes an explanation on the basis of “forced” vibration quite improbable. Such an explanation would imply

30 Lanchester illustrated the aerial tourbillon, a clear case of autorotation, and then of galloping, like a game. It consisted of a bar with the semi-circular cross-section fitted on an axis perpendicular to the flat face orthogonal to the wind. When a rotatory motion was applied, it continued over time.

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9 Wind Actions and Effects on Structures

Fig. 9.81 a Relative wind speed; b force decomposition into drag and lift [99]

gusts in the wind having a frequency equal to the natural frequency of the line to a miraculous degree of precision”. Den Hartog subsequently examined which were the dynamically stable (the circle) and unstable cross-sections: “this brings us into the domain of aerodynamics, a science which unfortunately is still very little developed” [99]. He maintained that the most unstable cross-section was the D-shaped with its flat face exposed to wind. This fact was highlighted through an experiment: a semi-circular bar made of light wood (5 cm in diameter and 38 cm long) was suspended by four springs (Fig. 9.80b); the bar, with a limited damping, developed vertical vibrations whose amplitude exceeded its diameter. Finally, Den Hartog introduced a reference system (Fig. 9.81) different from the one used in his first paper (Figs. 9.78 and 9.79b) [260]. He then repeated the analyses, proving that “a section is dynamically unstable if the negative slope of the lift curve is greater than the ordinate of the drag curve”, dL/dα + D < 0. This statement, rewritten in modern form, results: cD + cL < 0

(9.69)

where cD is the drag coefficient and cL is the prime derivative of the lift coefficient cL with respect to the angle of attack. Equation (9.69) obtained by Den Hartog for ice-covered cables is the same (Eq. 7.3) obtained in 1919 by Glauert [262] in the aeronautics field (Sect. 7.4). It was subsequently called “Glauert-Den Hartog necessary condition”, and it is the mainstay of the lift coefficient negative slope, or galloping, theory. Den Hartog acknowledged this phenomenon depended on mass and damping, but he did not provide an expression of the critical speed that caused instability. In the meantime, setting up on-site experimental stations to analyse the vibrations of power line conductors became a common practice. Stations used operating lines or appropriately installed cables, under suitable climatic conditions. One of the first stations dates back to 1930 and was set up by the Alcoa company in Rojse City, Texas, to continue laboratory tests on span models. The first tests with artificial ice were carried out in the state of Niagara in 1937 [263], on a span 32 m long.

9.8 Galloping

761

Fig. 9.82 Experiments by Tornquist and Becker [264]: a laboratory; b experimental span

In 1947, Tornquist and Becker [264] carried out wind tunnel and on-site tests. Wind tunnel tests were carried out with equipment similar to the one used by Den Hartog (Fig. 9.80b); it turned out to be too flexible and new equipment based on the same principles was adopted (Fig. 9.82a). Approximately 30 models, with different shape, length, diameter and surface finish, were studied with frequencies from 2 to 6 Hz; tests were carried out on varying the angle of attack and the wind speed. On-site tests were carried out on a rubber tube 1.5 m long, restrained by springs at its ends (Fig. 9.82b); the tube was partially covered with clay to simulate variable shape cross-sections. Afterwards, an experimental span 75 m long was built; the cable was covered with different shapes set in rotation; the tests were carried out for 40 days: the oscillation amplitude in this period reached 75 cm. Finally, a new experimental line was built: it consisted of four spans and shapes were fitted on one conductor. During the tests on a single span Tornquist and Becker observed, together with vertical oscillations, coupled torsional motions that disappeared in the tests involving the four-span experimental line. From then on, the coupling of motion components became a crucial subject. Taking their cue from these and similar observations, Ruedy [243] in 1948 and Cheers [265] in 1950 carried out new researches about the galloping of ice-covered cables. Such researches, carried out at the National Research Council of Canada, originated a generalised negative slope theory that, making use of measurements of the twisting moment (Fig. 9.83), also considered longitudinal motion and torsional rotation, besides vertical motion. Ruedy proved that torsion was an integral part of galloping and it was its coupling with vertical motion that caused wide oscillations. Cheers emphasised that torsion was important to start the motion; at this stage, even the longitudinal motion coupled with the vertical one and with torsional rotation was not negligible.

762

9 Wind Actions and Effects on Structures

Fig. 9.83 Aerodynamic coefficients of an ice-covered cable [265]

Fig. 9.84 Semi-circular cross-section tests [265]: a scheme; b drag, lift and twisting moment

Cheers at first carried out wind tunnel tests at the National Research Council in Ottawa, for sectional models of ice-covered cables with eight different shapes. He measured the drag D, the lift L and the twisting moment M (Fig. 9.84a) varying the angle of attack α in 10° steps: using smaller steps would have been useful, but he believed his tests gave an idea of the aerodynamic actions. Figure 9.84b shows the diagrams of D, L and M for the D-shaped cross-section. Cheers subsequently developed a theory based on the assumption that the galloping of an ice-covered conductor started with small oscillations that slowly increased in amplitude; he then assumed that limiting the search for the (incipient) instability to the domain of small oscillations was reasonable. The analysis was carried out ignoring the effects of side spans and the role of horizontal oscillations. Assuming that η and θ are the vertical displacement and the angular rotation with respect to the static equilibrium position, respectively, the equations of motion took on the form:

9.8 Galloping

763

  2 ∂ η ∂ 2η 1 ∂ 4η ∂η T 2 − EJ 4 − P + Fa = ∂t 2 m ∂s ∂s ∂t   ∂ 2θ 1 ∂ 2θ ∂θ + Ma = S 2 −R 2 ∂t I ∂s ∂t

(9.70a) (9.70b)

where m and I are the mass and the mass rotatory moment of inertia per unit length respectively, E is the elastic modulus, J is the moment of inertia, S is the torsional stiffness, T is the cable stress in the equilibrium position, P and R are damping coefficients, F a and M a are the vertical force and the twisting moment caused by the cable displacement with respect to the equilibrium position:   ∂L ∂L 1 ∂η 1 ∂η = θ− +D (9.71a) Fa = (L − L 0 ) − D V ∂t ∂α ∂α V ∂t   1 ∂η ∂M Ma = (M − M0 ) = θ− (9.71b) ∂α V ∂t D0 , L 0 and M 0 are the values of D, L and M for α = 0; V is the wind speed. Assuming that the vertical and torsional oscillations occur as sinusoidal waves with components η = η0 sin(aπs/l) and θ = θ0 sin(bπs/l), η0 and θ0 being the motion amplitudes, l the cable length, s the spatial coordinate measured from a cable end, and replacing Eq. (9.71) into Eq. (9.70), it follows: ∂η0 1 ∂L ∂ 2 η0 + f 1 η0 = θ0 +A 2 ∂t ∂t m ∂α   ∂ 2 θ0 ∂θ0 1 ∂M 1 ∂ M ∂η0 + f θ0 = − + B − 2 2 ∂t ∂t I ∂α V I ∂α ∂t

(9.72a) (9.72b)

being:    1 1 ∂L R A= P+ +D ; B= m V ∂α I     

aπ 4 aπ 2 1 S bπ 2 f1 = ; f2 = T + EJ m l l I l

(9.73a) (9.73b)

Cheers contemplated three cases: free oscillations without wind; vertical oscillations due to wind, ignoring torsional motion; vertical and torsional oscillations due to wind. The equations of the free oscillations of the cable, deduced from Eq. (9.72), assume the form: ∂η0 ∂ 2 η0 +A + f 1 η0 = 0 2 ∂t ∂t

(9.74a)

764

9 Wind Actions and Effects on Structures

∂ 2 θ0 ∂θ0 + f 2 θ0 = 0 +B ∂t 2 ∂t

(9.74b)

If damping √ is small, the vertical and torsional circular frequencies are ω1 = and ω2 = f 2 . The equation of the vertical oscillations due to wind assumes the form: ∂ 2 η0 ∂η0 + f 1 η0 = 0 +A 2 ∂t ∂t

√

f1

(9.75)

The oscillation stability then depends on the quantity A in Eq. (9.73a), which includes the Den Hartog’s term dL/dα + D. From Eq. (9.72), the equation of the coupled vertical and torsional motion becomes: ∂ 4 η0 ∂ 3 η0 ∂ 2 η0 ∂η0 + λ4 η0 = 0 + λ + λ + λ3 1 2 4 3 2 ∂t ∂t ∂t ∂t

(9.76)

1 ∂M λ1 = A + B; λ2 = f 1 + f 2 − + AB; I ∂α   1 ∂L 1 ∂M A− λ3 = f 1 B + f 2 A − I ∂α V m ∂α   1 ∂M λ4 = f 1 f 2 − ; λ5 = λ1 λ2 λ3 − λ23 − λ21 λ4 I ∂α

(9.77a)

where

(9.77b)

The motion is asymptotically stable if the five parameters λ are all positive; λ4 = to a stable 0 corresponds to the torsional divergence threshold; λ5 = 0 corresponds √ motion threshold (neutral oscillation) with circular frequency ω = λ3 /λ1 . Cheers examined the reliability of his model through two checks based on Dshaped conductors. The former used the data measured by the Hydro-Electric Power Commission of Ontario during tests on experimental spans that missed some mechanical parameters. The latter concerned dynamic wind tunnel tests on sectional models free to perform vertical and angular oscillations: they indicated that the motion started on a mode, then transferred to another mode with increased frequency. The theory agreed quite well with tests for low critical speeds, much less for high speeds. In all the cases in which the model galloped, torsional rotation was small and difficult to perceive visually. Cheers concluded that the suppression of the torsional motion, if possible, could prevent many cases of galloping. To this end, increasing the torsional damping was handy but not essential; increasing the torsional circular frequency ω2 to separate it from the flexural circular frequency ω1 , conversely, would have been helpful. The considerations by Ruedy and Cheers were experimentally confirmed by A. T. Edwards and A. Madeyski in 1956 [266, 267], by means of two series of tests carried

9.8 Galloping

765

out at the Research Division of the Hydro-Electric Power Commission of Ontario. The former was carried out between 1953 and 1954, at various power transmission lines equipped with wooden targets on conductors to measure the three motion components; the motion was filmed and analysed one frame at a time; frequency was measured by means of a clock; an anemometer recorded the speed at which galloping set in. The latter was made on a seven-span transmission line, built in real-scale in Port Credit; the measurements were carried out on a conductor of a 125-m-long span, covered with D-shaped wood profiles; a dynamometer, an accelerometer and an anemometer were used to measure stress, motion and speed, respectively; a torsion detector was also present; the angle of attack was changed by rotating the profile on the conductor; tests were carried out by modifying the (mechanical) stress and the torsional frequency of the cable. The results proved that the vertical motion was harmonic and prevailing. The horizontal motion was small with amplitudes equal to 10% of the vertical ones.31 Torsion was important to trigger the phenomenon, then decreased; it was anyway important to assess the angle of attack. The vertical motion was self-excited; the torsional one was forced and coupled with translation because of inertial forces, of the asymmetry of ice cover and of aerodynamic coupling; even when the vertical and torsional eigenfrequencies were different, the coupling of motions took place at the same frequency. The phase shift between motions took on several forms; in most cases they were either in phase or out of phase. Galloping in the absence of ice was also mentioned: it was due to non-symmetrical atmospheric corrosion and to corona discharge32 [266]. In 1959, during the construction of the power transmission line crossing the Severn and Wye rivers in England (Fig. 9.85) [268, 269], oscillations developed in five pilot cables installed to check operation. They oscillated and collided, interrupting the electrical link, in 24 days between July 1959 and the 1960–1961 winter. Laboratory and on-site tests were carried out in autumn 1960. Wind tunnel tests were performed at the Aeronautics Department of the Bristol University, at the NPL and at the Imperial College of Science and Technology. On-site monitoring used cup anemometers, TV cameras and strain gauges. The results showed a behaviour of the strand-type conductor different from that of the circular cylinder, as well as its galloping even without ice. Different oscillation regimes also occurred, according as the wind was perpendicular or inclined with respect to the vertical plane of the cable. This phenomenon was explained remarking that in the second case the wind “saw” an elliptical cross-section. Three measures were devised to mitigate vibrations. The first, based on electrical alterations, gave poor results. The second made use of mechanical interventions, e.g. by transversally linking the cables, to increase damping. The third consisted of aerodynamic alterations aimed at reducing the slope of the lift coefficient, wrapping 31 In

the rare cases in which the horizontal motion was comparable with the vertical one, the conductor moved along a clearly perceivable elliptical orbit. 32 Corona discharge is a process by which a current flows from an electrode (cable) with high potential in a neutral fluid (air); the latter ionises the fluid and creates a plasma region around the source.

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9 Wind Actions and Effects on Structures

Fig. 9.85 Power line crossing the Severn and Wye rivers in England [268]

Fig. 9.86 Classification of various ice formations [268]

conductors in P.V.C. adhesive tape to make their surface smoother. The last solution was the best: the conductors wrapped in tape did not show appreciable motions; the others continued to oscillate. Similar studies were carried out between 1960 and 1963 by Richardson et al. [270] at the M.I.T., on behalf of the Edison Electric Institute. At first, a classification of ice formations was formulated (Fig. 9.86). Static wind tunnel tests were carried out for each one of them, to assess drag, lift and twisting moment coefficients in relationship with the angle of attack (Fig. 9.87). Later on, theoretical models were developed to forecast instability with 1, 2 and 3 DOF (horizontal and vertical displacements, torsional rotation), either independent or coupled in different patterns. The 3 DOF system, i.e. including the torsional DOF, proved that, at the galloping critical speed, the motion occurred with the same circular frequency in the three directions. The critical speed and the motion circular frequency were provided by the solution of a complex cubic equation. The examined models were unstable for many angles of attack; the instability modes involved different combinations of the three DOF. The most unstable situation regarded the 2 DOF system, with vertical and horizontal anti-symmetrical motion. The possibility of stabilising the system by acting on parameters did not provide encouraging results. The sole effective intervention was to add damping. A damper was then designed, built and tested for this purpose. In the meantime, aeroelastic wind tunnel tests were carried out, using an aluminium bar fitted with balsa wood sections with various shapes. The bar had 1, 2 or 3 DOF, with adjustable frequencies (Fig. 9.88a) and stood across the whole wind tunnel width (Fig. 9.88b); the angle of attack, the minimum speed, the frequency and the galloping oscillation modes were determined for each model. Full-scale tests, carried out in 1960, focused on the torsional properties of conductors. The com-

9.8 Galloping

767

Fig. 9.87 Aerodynamic coefficients of two ice-covered cables [205]

Fig. 9.88 Dynamic wind tunnel tests [268]

parisons between theoretical results based on static measurements and experimental tests were fairly good. The studies by Richardson, Martuccelli and Price, like those by Cheers, proved that a cable can show torsional divergence. For this to occur, it is necessary that:  cM >0

(9.78)

and also that the wind speed reaches or exceeds the critical value: Vcr =

μrα2 ωα d  cM

(9.79)

768

9 Wind Actions and Effects on Structures

where μ = 2 m/pρ2 , r α is the non-dimensional radius of gyration with respect to the shear centre, ω2 is the torsional circular frequency, d is the reference size of the cross-section. Unlike Cheers, Richardson, Martuccelli and Price observed that when  > 0, the conductor tended to diverge and the angle of attack α0 was such that cM rotate, altering the angle of attack; generally, the new angle of attack made cL < 0 and  < 0, no divergence favoured galloping. When the angle of attack was such that cM was originated and the angle of attack did not change; generally, it corresponded to  , tend to gallop. cL < 0. In other words conductors, regardless of cM While these researches occurred, between the late 1950s and the early 1960s Scruton, at the NPL, and Geoffrey Varnon Parkinson (1924–2005), at the Mechanical Engineering Department of the University of British Columbia, formulated two mathematical models destined to become reference points. Scruton’s model [254, 255] (Sect. 9.7) unified the treatment of the cross-wind vibrations induced by vortex shedding and galloping. To illustrate it, let’s take into consideration again Eq. (9.54) and express F through Den Hartog’s Eq. (9.67) [260]. Ignoring the static part of the force, which does not affect instability, Eq. (9.56a) is obtained, with n = n0 , in which the logarithmic damping decrement and the aerodynamic damping parameter are, respectively, provided by the expressions:

ρV d cD + cL δa = (9.80) 4mn 0

V cD + cL ka = (9.81) 2n 0 d which represent the equivalent for galloping of Eqs. (9.57) and (9.59) for vortex shedding. Replacing Eqs. (9.80) and (9.81) into Eq. (9.56), the critical galloping wind speed is provided by the relationship: Vcr = −

4mn 0 δs 2n 0 dks

=−  cD + cL ρd cD + cL

(9.82)

from which emerges, once again, the essential role of k s (Eq. 9.58): the greater it is, the higher the galloping critical speed is. The comparison between Eqs. (9.57) and (9.59) for vortex shedding and Eqs. (9.80) and (9.81) for galloping highlights both the analogy between these phenomena and their conceptual diversity. Vortex shedding is resonant with the structure when the wind speed V assumes the critical value V cr given by Eq. (5.2); in this case, the reduced amplitude of the oscillations η0 may increase up to the limit value η0L ; past the V cr speed, η0 remains high within a speed interval V (Fig. 9.12), called lockin, which is as much wide as k s is smaller; past such interval η0 decreases. Galloping develops when the wind speed V reaches the critical value V cr given by Eq. (9.82); for such speed η0 increases indefinitely; this derives, as proven by Parkinson, from the linearity of Den Hartog’s and Scruton’s theories.

9.8 Galloping

769

Fig. 9.89 Parkinson’s drag and lift components on a square element [271]

Scruton observed three important aspects. First, the literature of galloping had been developed for ice-covered cables, but there were many other situations in which structures, or elements, suffered it. A remarkable case was represented by regular polygons with 4, 6, 8 and 12 sides: galloping developed for small angles of attack with respect to the side axis; it tended to disappear as the number of sides grew and was almost absent for a 12-side polygon. Another remarkable case was represented by metal carpentry elements, either isolated or belonging to truss frames or beams. Second, the quasi-steady theory was reasonable only if the critical reduced galloping speed was greater enough than the vortex shedding speed. Third, the treatment of a SDOF system, linked to tests on sectional models limited to cross-wind movements, was a simplification of the real cases involving multiple DOF; it could happen that individually positively damped DOF or motion components were unstable because of their coupling. Parkinson acknowledged that some forms of galloping required combined motions with 2 or 3 DOF [265], while others required inclined wind [268]. Most galloping phenomena, however, took place with a SDOF, transversal to the wind and to the element [267]. He also remarked that the amplitude of the oscillations caused by galloping did not indefinitely increase, but tended to a finite limit. He then defined galloping “as the self-excited oscillation of an elastic cylinder in a uniform transverse flow, in which the shape of the cylinder cross-section and its attitude to the incident stream cause flow separation and the formation of a broad wake, and the resulting fluid forces and/or moments on the cylinder produce instability to small lateral or torsional displacements. Energy is extracted from the flow, and the oscillation amplitude grows until an energy balance over the oscillation cycle is reached”. Thanks to such concepts Parkinson [271–273] applied the quasi-steady theory to extend Den Hartog’s formulation for the 1 DOF galloping from the linear domain of small displacements to the nonlinear domain of large displacements. In the first of three famous papers (1961), Parkinson [271] studied a cylinder, symmetrical in the wind direction (Fig. 9.89) and expressed the equation of motion in the form:

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9 Wind Actions and Effects on Structures

m y¨ (t) + c y˙ (t) + ky(t) = F(t) =

1 2 ρV cF y d 2

(9.83)

where cF y is the force coefficient in y direction: cF y = −(cL + cD tgα) sec α

(9.84)

cD and cL are the drag and lift coefficients, respectively, approximated through thirdand fourth-degree polynomials,33 d is the reference size of the cross-section (in this case, the width of the cross-section exposed to wind); V r and α are the relative speed and the angle of attack, expressed in the nonlinear form typical of large displacements (Eqs. 9.63 and 9.64). Thus:  cF y = A1

y˙ V



 + A3

y˙ V



3 + · · · + AN

y˙ V

N (9.85)

with N = 5. For small values of α, A1 = dcFy /dα = −(cL +cD ). Replacing Eq. (9.85) into Eq. (9.83), the equation of motion becomes:

Y  − ε 1 − PY  2 − QY  4 Y  + Y = 0

(9.86)

where T = ω0 t is the non-dimensional time, (·) = d(·)/dT, Y = y/d is the nondimensional displacement, P and Q are the parameters: P=

A3 ; A1 U (U − U0 )

Q=

A1

A5 3 U (U − U

0)

(9.87)

U and U 0 are the reduced speed and the U value for which galloping starts, respectively: U=

δs ks V ; U0 = = ω0 d πn A1 πA1

πc ρd 2 ; ε = n A1 (U − U0 ) δs = √ ; n = 2m km

(9.88) (9.89)

δs is the logarithmic decrement of the structural damping, k s is the non-dimensional structural damping parameter defined by Eq. (9.58), and n is a mass parameter. If , P and Q are all positive, the oscillation starts from rest and increases up to a stationary amplitude. If , P and Q are all negative, any oscillation damps down. If U > U 0 , i.e. if the aerodynamic forces are greater than the dissipative ones, stability depends on A1 . If the motion is small, the instability necessary condition is given by 33 In

the expansion of cL and cD , the polynomial terms with even and odd exponents are missing since cL and cD are odd and even functions of α being the cylinder symmetrical with respect to the wind direction.

9.8 Galloping

771

the Den Hartog’s equation (9.69), whereas the critical galloping velocity is provided by Eq. (9.82).34 For  small, Eq. (9.86) can be solved through the method by Nikolay Mitrofanovich Krylov (1879–1955) and Nikolay Nikolayevich Bogolyubov (1909–1992) [274], assuming: Y = Y sin(T + ϑ)

(9.90)

where Y is the amplitude of Y and ϑ is a phase angle weakly depending on T. Solving the problem: ⎡ 2

⎢Y εT = ln⎣ 2 Y0 ⎡



2 Ys 2 Ys

−Y −

3A3 2 2 Y s , Y i = U 2 ⎣− ± 5A5

2



2 Yi 2 2 Y s −Y i



2 Y0



2

Y − 2 Y0

3A3 5A5

2

−

2 Yi 2 Yi



2 −Y s 2 2 Y s −Y i

⎤ ⎥ ⎦

⎤   U0 ⎦ 8A1 1− + 5A5 U

(9.91)

(9.92)

Equation (9.91) provides Y as a function of T. Y 0 is the initial value of Y (Y 0 = 0 when the motion starts from the rest condition). Equation (9.92) provides Y s to which Y tends when the energy balance gives rise to a limit cycle. By convention, the motion reaches the limit cycle after T = T s such that Y = 0.99Y s . Wind tunnel tests supporting this theory were carried at the Mechanical Engineering Department of the University of British Columbia; it was 2.6 m long, 0.9 m wide and 0.7 m high. The aerodynamic coefficients were obtained by integrating the pressure coefficients measured on a fixed cylinder with b = 5 cm; aeroelastic tests were carried out on a balsa cylinder suspended by means of four springs. Figure 9.90a shows the experimental values of cF y for cylinders with various crosssections. Figure 9.90b shows the theoretical values of Y s as a function of U, highlighting the U = U 0 value for which galloping starts; in any case, this occurs from the rest condition Y = Y 0 = 0. Parkinson observed that theoretical results were satisfactory, even though experimental tests were carried out on models with low structural damping. For this reason, with the exception of the D-shaped cross-section cylinders, the U = U 0 incipient galloping values were close to the U = U R values related to the resonant vortex shedding35 : UR =

1 2πS

(9.93)

that for small values of α, A1 = −(cD + cL ), the replacement of the second into the first Eq. (9.88) provides Eq. (9.82). 35 Eq. (9.93) derives from replacing Eq. (5.1) into the first Eq. (9.88). 34 Remembering

772

9 Wind Actions and Effects on Structures

S being the Strouhal number. For cylinders with D-shaped cross-section, the motion started for U 0 equal to approximately half the value of U R ; the motion amplitude was maximum for U = U R . In the second paper (1962), Parkinson [272] dwelt on the cylinder with square cross-section, remarking that the diagram of cF y as a function of α showed an inflection (Fig. 9.91a) that could not be captured by a fifth-degree polynomial (Eq. 9.85, N = 5). For this reason, he extended the polynomial to the seventh order (Fig. 9.91a), obtaining unexpected results. The fifth-degree polynomial led to a motion law that predicted the start of the oscillation from the rest condition up to a stationary cycle when the wind speed exceeded a critical value correlated with the structural damping; in this case, the oscillator was a soft one, with a stable limit cycle. The seventh-degree polynomial (Eq. 9.85, N = 7) originated a nonlinear damping of the type discussed by Francis Clauser (1913–2013) [275]; thus, there were two stable limit cycles (solid lines), separated by an unstable limit cycle (dashed line), corresponding to it (Fig. 9.91b); in other words, there was a speed interval within which the oscillation could be stable with two different amplitudes. It was also confirmed that, for small displacements, the system was potentially unstable for A1 > 0. Resuming the problems not solved in [271], Parkinson repeated the tests for various damping ratios β = δs /2π (Fig. 9.91b). The increase in damping shifted the triggering of the galloping towards a higher reduced speed, so the resonant vortex shedding did not coexist. Parkinson noted that measurements with small β values [271] presumably did not highlight three limit cycles because of the interaction with vortex shedding. They were clear for medium β values, while they tended to disappear for large β values. According to Parkinson, this depended on the difficulty to set the model with high damping into vibration. The improvement of the theoreti-

Fig. 9.90 Cylinders [272]: a transversal force coefficients; b amplitude of the limit cycles

9.8 Galloping

773

Fig. 9.91 Square cross-section cylinder [272]: a approximation of cFy through a seventh-order polynomial expansion; b amplitude of the limit cycles

cal estimates confirmed that quasi-steady theory was correct for high U values, in particular for those much greater than U R . In his third paper (1963) Parkinson [273] collected, summarised and interpreted the results of the experimental tests performed and of the theoretical results achieved. The tests involved cylinders with D-shaped cross-section and their flat face exposed to wind as well as square and rectangular cross-section elements with side ratio b/h = 0.375–6, where b is the width of the face exposed to the wind and h the depth of the cylinder. Figure 9.92a, referred to square cross-section cylinders, corresponds to Fig. 9.91b. Unlike the latter, the abscissa U and the ordinate Y s were multiplied by nA1 /2β = 1/U 0 ; the abscissa is then the ratio between U and the U = U 0 value that causes incipient galloping. In this way, all the curves coincided with a single curve that tended, for large U values, to an asymptote passing through the origin. Experimental measurements for different damping values agreed with theory. The two stable configurations with different amplitude were reached by starting from the rest condition and from amplitudes larger than the theoretical one, respectively. The curve was far away from the resonant vortex shedding (U = U R ). Figure 9.92b is referred to D-shaped cross-section cylinders. Parkinson observed that tests failed to create galloping from rest because cF y = 0 for α < 25°. The quasi-steady theory predicted this behaviour as long as seventh-order polynomial was used (as for the square cross-section). In this case, the oscillator was a hard one, with two limit cycles, a stable one with large amplitude and an unstable one with smaller amplitude; galloping was only triggered starting from an oscillation amplitude larger than that of the unstable limit cycle. The comparison with tests was satisfactory, even if partially confused by the fact that U 0 is close to U R . It is not by chance that the comparison between theory and measurements improved for great U values. Parkinson emphasised the complexity of the behaviour of the D-shaped crosssection even in the light of on-site observations [259, 264, 266]. The latter showed

774

9 Wind Actions and Effects on Structures

Fig. 9.92 Amplitude of the limit cycles: a square; b D-shaped cross-section [273]

that this cross-section also developed galloping for wind inclined by 22°–65° with respect to the power line. In many cases, vertical oscillations coupled with torsional ones, with rotations from 30° to 90°. According to Parkinson, the change in direction could create flow reattachments affecting galloping. The behaviour of cylinders with rectangular cross-section depended on the b/h ratio, i.e. from the size of their rear body. According as it was short or elongated, galloping did not occur or occurred from rest. In the case b/h = 2, the seventhdegree polynomial fairly approximated the force coefficients. The theory showed two limit cycles, a stable one and an unstable one. Galloping was triggered from rest for large U values or from remarkably smaller U values, as long as a motion existed. The experimental tests provided different results for low U values: they showed that galloping started for U = U R , and then in resonance with vortex shedding; the agreement with theory only became satisfactory for U > 10. Both measurements and theory agreed that, for this particular cross-shape, damping had little effect.

9.9 Flutter Flutter is an aeroelastic instability phenomenon usually involving 2 DOF: cross-wind displacement and torsional rotation. In the aeronautics sector (Sect. 7.4), the turning point occurred in 1935, when Theodore Theodorsen (1897–1978) published his famous theory [102]. In the structural sector, the turning point was the Tacoma Bridge collapse, occurred in 1940 (Sect. 9.1). It highlighted the risks of cable-supported bridges in relation to wind, establishing a link between flutter and this structural typology. It originated the development of an unlimited range of wind tunnel tests

9.9 Flutter

775

(Sect. 9.1) and of theoretical methods, which are the subject of this paragraph. A common aspect of the papers that dealt with this methods is the complexity of the language used and of the formulations provided. Atsushi Hirai (1908–1993) was so struck by the projection of the movie of the bridge collapse to start a research on this subject. It led to two papers in Japanese language, published in 1942 and 1947, which provided the first theoretical interpretation of the instability of suspension bridges subjected to torsional oscillations. The international divulgation of these papers took place between 1955 and 1956, when Hirai published his theories in English [276, 277]. Hirai’s formulation was based on seven hypotheses: (1) the bridge had a single span, with length l; (2) the wind direction was horizontal and perpendicular to bridge axis; (3) the presence of towers and side spans was ignored; (4) the distance between the cables was equal to the deck width b; (5) the flexural and torsional stiffness of the deck were constant; (6) the structure was elastic; (7) the deck cross-section was H-shaped, and the slab was at half the height of the stiffening beams. The deck had 3 DOF—the horizontal and vertical displacements, u and v, and the torsional rotation, ϕ—and was subjected to forced oscillations due to harmonic aerodynamic actions. The torsional fundamental frequency of the deck depended on the wind speed V. The critical speed V k causing torsional instability was given by the expressions: 

Vk Nϕ b

2



√ m 128 1 1− ρb2 μcD h √ 128 cL 1+ 4π2 cD

2r = b 

μ=

2

(9.94)

(9.95)

where N ϕ is the torsional fundamental frequency in the absence of wind, r is the radius of gyration, m is the deck mass per unit length, cD is the drag coefficient, cL is the prime derivative of the lift coefficient with respect to the angle of attack, h is a parameter provided by experimental tests. Hirai’s analyses proved that the torsional and flexural stiffness of the deck greatly affected the critical speed; they also proved that increasing the deck weight had a beneficial effect on stability. As regards to the shape of the deck cross-section, Hirai noticed that a small μ value increased the critical speed; moreover, it was advisable to adopt a cross-section that caused a limited vortex shedding, a positive lift curve for positive angles of attack, a small and negative moment coefficient cM for positive angles of attack and a prime derivative of cM with respect to the angle of attack close to zero. In 1943, the German aeronautical engineer Hans Jacob Reissner (1874–1967) [278] developed the equation of the undamped motion of suspension bridges in relation to the vertical displacements of the edge beams; they described both the torsional and flexural motions. Reissner used his equations to obtain the natural frequencies and the mode shapes. He subsequently added the dissipative term and formulated an innovative theory of self-excited vibrations, expressing the overall damping as the sum of a structural part and an aerodynamic part, on which stability depended; the structural damping chiefly occurred in the deck and was independent

776

9 Wind Actions and Effects on Structures

of the wind speed; making use of the reports about the Tacoma Bridge collapse [36], the aerodynamic damping decreased as the reduced speed increased, until it became negative. So, as the wind speed increased, the overall damping changed from positive to negative. The speed determining such transition and causing instability was defined as critical. The solution obtained highlighted that the increase of the structural damping and of the deck width increased the critical speed. A proper selection of these parameters, therefore, made the critical speed greater than the design speed. In the same year, David Bernard Steinman (1886–1960) [279] studied the vertical and torsional oscillations of suspension bridges, interpreting their instability in terms similar to galloping (Sect. 9.8). As regards to vertical oscillations, the composition of the horizontal wind speed V with the relative speed of the deck −v was equivalent to a variation of the angle of attack α = −v/V; when the deck moved downwards, then, the relative speed was inclined upwards and vice versa (Fig. 9.78). The variation of α caused a variation of the lift per unit length that was given by the expression:

1 L = − ρV b cD + cL v 2

(9.96)

If, in correspondence with α, (cD + cL ) < 0 (Eq. 9.69), L is concordant with v and the deck is unstable. Moreover, since L is resonant with the vertical harmonic motion and is out of phase by 90°, it produces an increase in energy for every oscillation cycle. A negative aerodynamic damping proportional to V and to (cD + cL ) is then originated. Steinman noticed that the amplitude of the oscillations self-excited because of the negative aerodynamic damping was not unlimited: as the motion amplitude increased, α increased until (cD + cL ) became positive. The appearance of a negative aerodynamic damping made the structural damping crucial. Its logarithmic decrement assumed values ranging from 0.002 to 0.130 and depended on the deck stiffness, since its deformation was the primary cause of dissipation, while cables played a secondary role. According to Steinman, the structural damping also depended on the motion amplitude in relation to the hysteresis of the oscillation cycles. Other dissipation sources were due to secondary vibrations, to the deformation of the roadway and to the frictions in the connections. The instability of the bridge developed when the wind speed reached the critical value that would void the overall damping given by the sum of the structural part and of the aerodynamic part; this value was as smaller as the structural damping was smaller and the absolute value of (cD + cL ) (negative) was higher. The increase of the structural damping with the motion amplitude reduced the amplitude of the oscillation limit value and delayed instability. The above provided concepts drawing inspiration from quasi-steady theory. Steinman modified it by introducing a corrective factor β, a multiplier of (cD + cL ), which took account of the shift in the propagation of aerodynamic actions from the deck leading edge through the width of its cross-section. Since β could be negative at low speeds, this coefficient could make unstable a section judged stable according to

9.9 Flutter

777

(cD + cL ). This fact was important because, without taking β into account, the theory provided high critical speeds; the presence of β also created instability conditions at low wind speeds. The prevailing element of torsional oscillations was the behaviour of the leading edge; it caused flow deviation and separation, originating vortex shedding. As previously stated for vertical oscillations, the composition of the horizontal wind speed V with the relative speed of the leading edge −v was equivalent to a variation of the angle of attack α = −v/V; when the leading edge moved downwards, then, the relative speed of the flow was inclined upwards and vice versa. The α variation determined a variation of the twisting motion per unit length of the deck given by the expression: 1  v M = − ρV b2 βM cM 2

(9.97)

where ßM is a corrective factor, similar to ß, which takes account of the shift in the propagation of aerodynamic actions through the deck cross-section. If in cor < 0, M produced a rotation concordant with the respondence with α, βM cM direction of v and the bridge was unstable. Moreover, since M was resonant with the torsional harmonic motion and is out of phase by 90°, it produced an increase in energy for every oscillation cycle. A negative aerodynamic damping, linked to tor was then originated. Steinman sional oscillations and proportional to V and to βM cM remarked that, even in this case, the amplitude of the oscillations self-excited because of the negative aerodynamic damping was not unlimited: as the motion amplitude  became positive. increased, α increased until βM cM Steinman also remarked that, because of the rotation θ of the deck, a variation of the twisting moment originated; it was given by the expression:   1 2 2  (9.98) ρb V cM θ M = 2 This had the effect of changing the torsional eigenfrequency of the bridge, which became:  1 Nt = 2π

 K t − 21 ρV 2 b2 cM 2r 2 m

(9.99)

where K t is the torsional stiffness coefficient [279], r is the radius of gyration of the  was negative N t increased to a negligible deck mass m. Steinman noticed that if cM  was positive N t decreased and extent. He did not dwell, instead, on the fact that if cM this produced, at the limit, torsional divergence. Steinman concluded his paper asserting that, by then, it was possible to inexpensively design suspension bridges of any length, ensuring them the appropriate aerodynamic stability. Actually, both his and Reissner’s theories [278] were still far away from properly interpreting the unstable phenomena of cable-suspended bridges.

778

9 Wind Actions and Effects on Structures

In 1948, Edmund Joy Pinney (1917–2000) [280] treated the vertical and torsional oscillations of suspension bridges in coupled form. He formulated the concept that deck oscillations produced, on the deck itself, aeroelastic or self-excited actions expressed as a linear combination of vertical displacement and torsional rotation; the coefficients of the combination were of the type introduced by Theodorsen for flat plates. As in previous theories, Pinney also ignored the vortex shedding. Pinney assumed that the bridge was 2a long and 2b wide. In the X, Y, Z reference system, Y was vertical and positive upwards, Z was parallel to the bridge axis; the wind blew towards X. The motion was described by the vertical displacement h of the centreline, positive downwards, and by the α torsional rotation; the rotation angle was measured from the positive direction of X to the negative direction of Y. The equations of motion were formulated in energy terms, ignoring dissipative actions and considering the virtual work δL of the inertial and elastic actions in the deck, in the towers and in the cables, and of the external actions. Omitting the dependence on Z and t for sake of simplicity: a δL =

"

 E I  h iv − 2T0 h  + ρ0 h¨ − L + gρ0 σ δh

−a

 #

 + − C  + 2b2 T0 α + I  α¨ − M + gρ0 bτ δα dZ = 0

(9.100)

where E is the elastic modulus of the material, I  is the moment of inertia of the deck cross-section, T 0 is the horizontal component of the cable stress when the bridge is at rest, ρ0 is the deck mass per unit length, g is the gravity acceleration, C  is the torsional stiffness of the deck, I  is the mass rotatory inertia moment of the deck per unit length, σ and τ are symbols described in [280], L and M are the aeroelastic lift and twisting moment per unit length concordant with h and α. Since the virtual δh and δα variations are independent, two equations of motion derived from Eq. (9.100), in the h and α unknowns: E I  h iv − 2T0 h  + ρ0 h¨ − L + gρ0 σ = 0

(9.101a)



− C  + 2b2 T0 α + I  α¨ − M + gρ0 bτ = 0

(9.101b)

Pinney obtained the flexural and torsional vibration modes in the absence of wind by removing the aeroelastic actions L and M, and imposing that the oscillations in the h and α directions occurred with their circular frequencies ωh and ωα . He then expressed the vertical displacement and torsional rotation as: g H f h (Z ) ω2h gρ0 b α(Z , t) =  2 A f α (Z ) I ωα h(Z , t) =

(9.102a) (9.102b)

9.9 Flutter

779

H and A being quantities discussed in [280]; f h and f α are the vibration modes in the h and α directions. The flutter was studied assuming that the vibration modes retained their shape in the absence of wind and that the deck vertically and torsionally oscillated with the same circular frequency ω. Replacing these statements into Eq. (9.100), it followed: a −a a

 2

 ρ0 ω − ω2h h(Z , t) + L(Z , t) f h (Z )dZ = 0

(9.103a)

  2

 I ω − ω2α α(Z , t) + M(Z , t) f α (Z )dZ = 0

(9.103b)

−a

where, as anticipated, the aeroelastic actions were expressed as linear combinations of h and α:   L(Z , t) = πρb2 ω2 L h h(Z , t) + bL α α(Z , t)

(9.104a)

  M(Z , t) = πρb3 ω2 M h h(Z , t) + bM α α(Z , t)

(9.104b)

L h , L α , M h , M α being the coefficients of the combination. Replacing Eq. (9.104) into Eq. (9.103), applying Eq. (9.102) and taking into account the structural damping, hitherto ignored, by replacing 1/ω2 with the term (1 + iδ/2π)/ω2 , δ being the logarithmic decrement of the damping, it followed:  a  a ω2h ρ 2 ρ 2 2 f h (Z )d Z +Bbπ b L α f h (Z ) f α (Z ) dZ = 0 H 1 − 2  + π b Lh ωα ρ0 ρ0 −a

−a

(9.105a) Hπ

ρ 2 b Mh ρ0



a f h (Z ) f α (Z ) d Z + Bb −a

=

 ω2α 1 ω2

I2 ρ (1 − ) + π b2 M α 2 2 ρ0 ρ0 b

 δ +i ; 2π

 a f α2 (Z )dZ = 0 −a

(9.105b) B=

Aρ0 bω2h I  ω2α

(9.106)

It is worth noting that the aeroelastic actions coupled the vertical and torsional motions, which in their absence were independent. Equation (9.105) is a system of two homogeneous algebraic equations in the H and B unknowns. To obtain meaningful solutions, it was then necessary to make the determinant of the coefficient matrix null by assuming:



2 − L h + Mα  + L h Mα − L α Mh = 0

(9.107)

780

9 Wind Actions and Effects on Structures

where L h

  ρ 2 ω2α = 2 1 + π b Lh ; ρ0 ωh

Mh = μ

ρ20 b2 ρ 2 π b Mh ; I  2 ρ0

L α =

ω2α ρ 2 π b Lα ω2h ρ0

(9.108a)

ρ20 b2 ρ 2 π b Mα I  2 ρ0

(9.108b)

Mα = 1 + μ

Since in the case of flutter f h (Z) and f α (Z) are similar, μ ≈ 1 [280]. Pinney admitted that the deck behaved like a thin flat plate and that the aeroelastic actions on an elementary cross-section inclined by α were the same that would occur if the whole deck was inclined by the same angle; the flow was thus treated as a bidimensional one and the L h , L α , M h , M α parameters were given by the relationships:   i 2 2i i (9.109a) + 2 C(k) L h = 1 − C(k); L α = − − k k k k   i i 1 i 1 + + 2 C(k) M h = C(k) ; M α = − (9.109b) k 8 2k 2k k where C(k) is the Theodorsen’s complex function, Eq. (7.7), and k is the reduced circular frequency: k=

ωb V

(9.110)

ω being the flutter circular frequency.36 Solving Eq. (9.107), it is possible to obtain  and then ω and δ as a function of k. From here, through Eq. (9.110), it is possible to obtain V as a function of k; so, using k as a parameter, δ can be plotted as a function of V. The smaller value of V corresponding to the maximum allowable value of δ is the critical flutter speed. Figure 9.93 shows the diagrams referred to the Tacoma Bridge; the results were fairly consistent with reality. Pinney noticed that the weak point of his formulation was the thin flat plate hypothesis, which could provide useful indications at the predesign stage but did not represent the actual shape of the deck. At the final design stage, then, it was necessary to resort to tests on sectional models. In 1949, Hans Friedrich Bleich (1909–1985) [281] formulated a new theory. The paper started with analysing the properties of the two most common structural types: the girder-stiffened bridge, e.g. with H-shaped cross-section, and the truss-stiffened bridge, usually of closed type, with stiffened roadway. Girder-stiffened bridges were more vulnerable to wind than truss-stiffened bridges. They were most excited when the angle of attack was approximately nil.

36 Pinney

provided modified expressions of L h , L α , M h , M α to take account of the openings in the roadway, a widespread oscillation mitigation technique.

9.9 Flutter

781

Fig. 9.93 Structural damping versus wind speed [280]: asymmetrical modes of the central span without (a) and with (b) central connecting elements; c symmetrical modes

Their stability depended on the d/(2b) ratio, where d is the thickness and b the halfwidth of the deck. Generally, the motion derived from the vortex shedding from the upper and lower sides of the leading edge. At the critical speed, resonance generated increasing vertical or torsional oscillations of self-excited type; they had the same frequency of the excited mode. The potential instability at the critical speed depended on the cross-section shape. The vertical motion was not catastrophic, except for the case d/(2b) > 0.2. The wind speed at which torsional excitation developed increased when d/(2b) decreased. In the thinner decks, with d/(2b) < 0.06, vortex shedding became weaker until it disappeared and decks tended to behave like thin flat plates. Truss-stiffened bridges with continuous roadway had their maximum stability when the angle of attack was approximately nil. Their aerodynamic behaviour was similar to that of thin flat plates. Self-excited vibrations could become catastrophic only if they coupled the vertical and torsional motions; in this case, the motion frequency was different from that of the two excited modes and was slightly lower than the torsional frequency. This phenomenon, known as flutter, was similar to that of airplane wings. The classic definition of flutter, however, was not sufficient to explain the aeroelastic behaviour of these bridges. The horizontal plate of the roadway was not fully streamlined, since it had a leading edge that favoured vortex shedding. Aeroelastic stability was then affected by the shape of the roadway cross-section near the leading edge. Bleich idealised the floor structure as a thin plate with two shallow chords on both edges (Fig. 9.94a). Thanks to this model, the plate was subjected to a force distributed across its surface, which could be evaluated through Theodorsen’s equations [102], and to an alternating lift force F v along the leading edge, which was a function of the edge shape and could be evaluated through wind tunnel tests. Bleich thus formulated a general theory for truss and girder bridges, as long as the latter was thin. At first, Bleich treated the deck as a flat thin plate, ignoring the force F v . Unlike Pinney [280], who expressed the self-excited actions as a linear combination of vertical displacement and torsional rotation (Eq. 9.104), Bleich expressed such actions as a linear combination of three terms: the prime derivative of the vertical displacement

782

9 Wind Actions and Effects on Structures

Fig. 9.94 Bleich model [281]: a cross-section; b degrees of freedom of the deck

(with respect to time), torsional rotation and its prime derivative. He looked for these actions under the condition they kept the bridge oscillations stable. This occurred for a critical wind speed at which vertical and torsional motions had the same frequency but different phases; the flutter frequency was an intermediate one between vertical and torsional eigenfrequencies. The self-excited actions on the thin flat plate were expressed through Theodorsen’s formulation, using two simplifications: (1) the aileron terms were omitted; (2) the inertial actions on the air cylinder with 2b diameter enveloping the plate were omitted; they were comparable to the inertial actions for an airplane wing, but were negligible for a bridge deck. The “resultant lift force” and the “resultant lift moment” per unit length, therefore, were given by:     ˙ ηb b φ˙ + [1 + C(k)] FL = −2πρbv2 C(k) φ + v 2v     ˙ ηb b φ˙ 2 2 + [1 − C(k)] ML = πρb v C(k) φ + v 2v

(9.111a) (9.111b)

where η = η/b is the non-dimensional vertical displacement; η is the downward positive vertical displacement, φ is the clockwise positive torsional rotation (Fig. 9.94b); C(k) is defined by Eq. (7.7); k is the reduced circular frequency. Accordingly, Eq. (9.111) can be rewritten as:     b b FL = −sv2 f 1 φ + η˙ + f 2 φ˙ (9.112a) v 2v     b b sbv2 f 1 φ + η˙ − f 3 φ˙ ML = (9.112b) 2 v 2v where f 1 = C(k), f 2 = 1 + C(k), f 3 = 1 − C(k), s = 2πρb. Bleich determined the natural frequencies and the mode shapes through the Ritz method, and expressed the motion by Lagrange equations ignoring dissipative terms. He then applied modal analysis taking account of a single vertical and torsional mode: η = q 1 1 ; φ = q 2 2

(9.113)

9.9 Flutter

783

q1 and q2 being the principal coordinates; 1 and 2 are the normalised modes. Since flutter involves similar vertical and torsional mode shapes, the equations of motion resulted as follows:     b sbv2 b f 1 q2 + q˙1 + f 2 q˙2 = 0 q¨1 + + mb2 v 2v     2 b sbv b 2 q¨2 + ω2 q2 − f 1 q2 + q˙1 − f 3 q˙2 = 0 2mr 2 v 2v ω21 q1

(9.114a) (9.114b)

where ω1 and ω2 are the circular frequencies, m is the mass per unit length, r is the mass radius of gyration. Equation (9.114) is identical to that of a bridge cross-section with unit length. Therefore, when the shape of the vertical and torsional motion is the same, flutter can be studied through a sectional model free to vertically and torsionally oscillate. Since the incipient flutter condition involves harmonic vertical and torsional motions with constant amplitude and with the same frequency, they can then be expressed as: q1 = u 1 eiωt ; q2 = u 2 eiωt

(9.115)

u1 and u2 being complex non-dimensional amplitudes. Replacing Eq. (9.115) into Eq. (9.114), it follows:     f1 f1 f2 −1 + Z + μ i u 1 + μ 2 + i Du 2 = 0 (9.116a) k k 2k    f1 ω22 f1 f3 −μ i Du 1 + −κ + κ 2 Z − μ 2 − i u 2 = 0 (9.116b) k k 2k ω1 where μ=

2r 2 sb ; κ= 2 ; m b

Z=

ω21 ω2

(9.117)

Equation (9.116) is a homogeneous linear algebraic set of two equations in the u1 and u2 unknowns. It provides a not trivial solution when the  determinant of the coefficient matrix is nil. The equation  = 1 + i2 = 0 is called stability condition. Two equations, 1 = 0 and 2 = 0, derive from it, whose solution provides k = k c and Z. The flutter circular frequency ωc and the critical flutter speed vc are then given by: ω1 ω = ωc = √ Z ωc b v = vc = kc

(9.118) (9.119)

784

9 Wind Actions and Effects on Structures

The replacement of Eqs. (9.118) and (9.119) into Eq. (9.116) provides the u1 /u2 complex ratio. From the latter, it is possible to obtain the ratio between the real amplitudes as well as the phase shift between the motion components. Bleich provided a procedure to analytically solve this problem. The above formulation regards decks that could be tracked down to thin plates. This model is not realistic for most suspension bridges, in which vortex shedding takes place near the leading edge. Bleich took it into account by overlapping to Theodorsen’s actions a periodic lift force F v (Fig. 9.94a). He assumed that the vortex shedding frequency is controlled by the frequency with which the deck oscillates and that F v is proportional to torsional rotation and to the prime derivative of the vertical displacement. Bleich admitted that vortex shedding had limited effects in comparison with Theodorsen’s actions, except for girder bridges in which F v played a dominant role. In this case, F v takes the form:   ˙ ηb (9.120) Fv = sv2 f 4 φ + v where f 4 is a non-dimensional parameter depending on the shape of the cross-section and on the reduced frequency k, which can be assessed through sectional model tests. Since the transport of F v on the deck axis causes a moment bF v , the lift force and the twisting motion per unit length (Eq. 9.112) become:      b b b ˙ 2 (9.121a) FL = −sv f 1 φ + η˙ + f 2 φ + f 4 φ + η˙ v 2v v      b b b sbv2 ML = f 1 φ + η˙ − f 3 φ˙ + 2 f 4 φ + η˙ (9.121b) 2 v 2v v Likewise, Eq. (9.114) becomes:      b sbv2 b b q¨1 + f 1 q2 D + q˙1 + f 2 q˙2 D + f 4 q2 D + q˙1 =0 + mb2 v 2v v (9.122a)    2   b sbv b b q¨2 + ω22 q2 − f 1 q2 + D q˙1 − f 3 q˙2 + 2 f 4 q2 + D q˙1 =0 2 2mr v 2v v (9.122b) ω21 q1

From then on, the search for flutter continued like in the case of the flat plate. When F v increased, vc decreased and ωc increased and came close to the torsional circular frequency. In fact, a conceptually and technically essential change occurred. When only Theodorsen’s actions were present, flutter instability could develop for no less than two coupled degrees of freedom. As a consequence, without the F v force no instability could arise for a bridge oscillating in a purely vertical or torsional manner. The presence of the F v force could cause the instability of 1 DOF.

9.9 Flutter

785

The case of pure torsional instability is known as stall flutter. For this purpose, consider Eq. (9.122b) and nullify the q1 principal coordinate associated with vertical displacement. It follows that: q¨2 +

ω22 q2

sbv2 − 2mr 2



b f 1 q2 − f 3 q˙2 + 2 f 4 q2 2v

 =0

(9.123)

Expressing the torsional motion as q2 = eiωt , it follows that:   μ f4 ω22 μ f1 f3 −1 + 2 − − i −2 =0 ω κ k2 2k κ k2

(9.124)

Two equations, in the real and imaginary parts, can be deduced from Eq. (9.124); from them, it is possible to obtain ω= ωc and k = k c ; from the latter, it is possible to obtain vc (Eq. 9.119). Even in this case, the motion circular frequency ωi is smaller than the natural torsional circular frequency ω2 . Bleich concluded his paper by applying his method to the Tacoma Bridge and to the Golden Gate Bridge. In the first case, the thin flat plate theory predicted the oscillations fairly well; in the second case, it was necessary to consider an experimentally evaluated force due to vortex shedding. In the same year Bleich formulated his method (1949), Steinman [282] went beyond the disjoint approach to vertical and torsional instability that was behind his previous 1943 paper [279] and some subsequent developments [283], formulating a procedure that contemplated the coupled vertical and torsional motion. Like Bleich [281], the lift and twisting self-excited actions were linear combinations of three terms: the prime derivative of vertical displacement, torsional rotation and its prime derivative. Unlike Bleich, Steinman stated that the coefficients of the combination could not be obtained from Theodorsen’s theory, but required wind tunnel tests on static sectional models. By virtue of the relativity principle, according to Steinman the motion of a crosssection in a flow could be tracked down to a relative inclination or distortion of the streamlines, or to an opposing inclination or distortion of the cross-section [284]. The vertical motion with the v speed downwards (Fig. 9.95a) was equivalent to an upward rotation of the streamlines by the v/V angle; it was likewise equivalent to rotating the cross-section downwards by the same angle. The angular speed of the cross-section was equivalent to attributing to streamlines a concentrical and circular shape with downward convexity (Fig. 9.95b); it was likewise equivalent to curve the model cross-section in a equal and opposed way; the slope at the leading edge was β = v/V; the radius of curvature was bV /(2v). The straight inclined model represented the effect of the angular rotation α and of the vertical speed v; in the aerodynamic equations, the two effects were interchangeable assuming α = −v/V. The curved model, conversely, only represented the ˙ the conversion factor was β = −v/V = −bα/(2V ˙ effect of the angular speed α; ). Figure 9.96 shows the lift and twisting motion coefficients for a bridge whose crosssection is similar to that of the Tacoma Bridge; the passage from the straight model

786

9 Wind Actions and Effects on Structures

Fig. 9.95 Aerodynamic equivalence [282]: a vertical motion; b torsional rotation

Fig. 9.96 Straight and curved sectional models [282]: lift (a) and twisting moment (b) coefficients

to the curved one halved the slope of the lift coefficient but doubled the slope of the twisting moment coefficient.37 The aerodynamic actions on an oscillating cross-section were expressed by the relationships: ˙ + L(α) ˙ + L(η) ¨ + L(α) ¨ L = L i + L(α) + L(η)

(9.125a)

˙ + M(α) ˙ + M(η) ¨ + M(α) ¨ M = Mi + M(α) + M(η)

(9.125b)

where L i and M i are the static actions for the angle of attack αi corresponding to the section at rest; α is the deck rotation, measured from αi , η is the vertical displacement; 37 Without tests on curved models, the effect of the angular velocity was previously studied through

graphs of the static torsion obtained by rotating a non-curved model. Assuming α = β, the results should qualitatively coincide, since the dominant effect is the inclination near the leading edge. Quantitatively, the passage from the straight to the curved model made torsional stability worse.

9.9 Flutter

787

L(γ) and M(γ) are the contributions to lift and twisting moment due to the motion ˙ η, ¨ α, α, ˙ α. ¨ Applying relativity principles: γ = η, η,      η˙ bα˙ 1 ¨ − C 3 s3 + m α (V α˙ − η) L = L i + ρV 2 b C1 s1 α − (9.126a) 2 V 2V      η˙ bα˙ 1 − C 4 s4 − Iα α¨ M = Mi + ρV 2 b2 C2 s2 α˙ − (9.126b) 2 V 2V where b is the deck width, V is the wind speed, mα = πρr 1 b2 /4 is the mass of the air cylinder enveloping the cross-section, I α is the associated rotatory moment of inertia, r 1 is a function of the cross-section shape [282], s1 = ∂cL /∂α, s2 = ∂cM /∂α, s3 = ∂cL /∂β, s4 = ∂cM /∂β; s1 and s2 are the slopes of cL and cM obtained from tests on straight models; s3 and s4 are the slopes of cL and cM obtained from tests on curved models. C1 , C 2 , C 3 and C 4 are correction factors that take account of the phase shift due to the time delay between motion and pressure changes throughout the deck cross-section. In the case of harmonic vibrations, they are functions of the reduced speed or circular frequency, assume the form C k = F k − iGk (k = 1, 2, 3, 4) and can be obtained from the pressure distribution on the cross-section contour [282]; F 1 , F 2 , G1 and G2 correspond to straight models; F 3 , F 4 , G3 and G4 to curved models. Steinman expressed the equations of motion of a deck with 2 DOF (η and α) as: m η¨ + c1 η˙ + k1 η = L

(9.127a)

I α¨ + c2 α˙ + k2 α = M

(9.127b)

where m and I are the mass and the mass rotatory moment of inertia; c1 , c2 , k 1 and k 2 are the dampings and stiffnesses in the vertical and angular directions, respectively; L and M are the aerodynamic actions defined by Eq. (9.126). Steinman assumed that motion is governed by the equations: η = η0 eiωt ; α = α0 eiωt

(9.128)

where η0 and α0 are the amplitudes, ω is the circular frequency. Moreover: ω1 =

c1 k1 δ1 ; g1 = = ; ω2 = m π mω



c2 k2 δ2 ; g2 = = I π Iω

(9.129)

ω1 and ω2 being the natural circular frequencies; g1 , g2 , δ1 and δ2 are damping coefficients. The instability condition is evaluated by replacing Eqs. (9.126), (9.128) and (9.129) into Eq. (9.127), ignoring the inertial actions associated with the air mass enveloping the cross-section, and removing the external actions L i and M i . He obtained:

788

9 Wind Actions and Effects on Structures

    1 i 4 ω1 2 2η0 2η0 i = 2 C 1 s 1 α0 − C 1 s 1 + (πr1 − C3 s3 )α0 + ig1 − 1 μ ω b k k b k (9.130a)      2 2a1 ω2 i 2η0 1 i − C 4 s 4 α0 (9.130b) + ig2 − 1 α0 = 2 C2 s2 α0 − C2 s2 μ ω k k b k where ρ b2 4r 2 ; a1 = 2 ; r = μ= m b



I m

(9.131)

Steinman used Eq. (9.130) to first assess the 1 DOF vertical and torsional instability conditions [282], and then the instability conditions for the 2 DOF coupled system. This analysis was carried out introducing the following quantities:     4 ω1 2 2a1 ω2 2 X1 = − 1 ; X2 = −1 (9.132a) μs1 ω μs2 ω s3 s4 q3 = ; q4 = (9.132b) s1 s2 by means of which Eq. (9.130) assumed the form:      2η0 i i πr1 1 X 1 + id1 + C1 α0 = 0 + − 2 C 1 + q3 C 3 − k b k k s3     2η0 i 1 i C2 + X 2 + id2 − 2 C2 + q4 C4 α0 = 0 k b k k

(9.133a) (9.133b)

where C k = F k − iGk (k = 1, 2, 3, 4). Equation (9.133) is an homogeneous linear algebraic system of two equations in the η0 and α0 unknowns. It has a non-trivial solution provided that the determinant  = r + ii of the coefficient matrix is nil, and then r = i = 0. This implies: X 2 = H2 − H1 X 1 2X 1 = −H3 ±



H32 − 4H4

(9.134a) (9.134b)

where H 1 , H 2 , H 3 and H 4 are parameters depending on k [282]. Assuming a2 = a1 (ω2 /ω1 )2 , from Eqs. (9.132) and (9.133) it follows that:   1 1 (9.135a) s2 X 2 − a 2 s1 X 1 μ a2 − a1 = 2 4

ω 2

ω 2 πs1 πs2 1 2 X1 ; =1+ =1+ X2 (9.135b) ω 4 ω 2a1

9.9 Flutter

789

ω 2 1

ω

=

2 as21 + 4 Hs11 + μH2 2 as22 + 4 Hs11

(9.135c)

The solution of Eq. (9.135) provides k, X 1 , X 2 and ω. Being k and ω known, the flutter speed is: Vc =

ωb 2k

(9.136)

Steinman concluded his paper stating that the proposed model was the first aerodynamic theory applicable to any oscillating cross-sections regardless of their shape. He maintained that this theory was the most complete and general one among those developed until then. He submitted it to the sector so that “a revision and a constructive discussion can further develop the solution of the problem towards the definitive completeness and finality”. Considered it in the light of current knowledge, Steinman’s model, like Bleich’s one, had robust foundations. Vertical and torsional vibrations were coupled through motion-induced actions, expressed as linear combinations of the prime derivative of the vertical displacement, of the torsional rotation and of its prime derivative. The critical flutter speed was looked for imposing that the vertical and torsional motions had the same frequency, solving an eigenvalue problem. Steinman’s and Bleich’s models were lacking, conversely, as to the coefficients of the linear combination linking aeroelastic actions with motion. It was necessary to wait over twenty years (Sect. 11.1) before Robert Scanlan (1914–2001) [285] formulated the appropriate procedure to evaluate these coefficients. In 1950, the activity started in 1942 by the Bureau of Public Roads through the establishment of the Advisory Board on the Investigation of Suspension Bridges came to an end [286]. The Board pursued three goals: (1) to determine the causes of the vibrations of suspension bridges; (2) to correlate the behaviours observed on models and real structures to develop a rational theory explaining vibrations; (3) to produce design calculation methods preventing dangerous motions and applicable to existing bridges requiring remedies. From the theoretical viewpoint, the book [286] was greatly influenced by the presence of Bleich among the authors [281]. From the design viewpoint, it offered an overall summarising picture. The authors observed that suspension bridges were usually built with two stiffening side truss beams and a horizontal truss girder under the roadway; they then had a torsional stiffness only provided by the flexural strength of cables, i.e. negligible. Torsional modes were identical to vertical ones, with the cables vibrating out of phase; torsional frequencies just higher than vertical ones favoured flutter. The double-level horizontal bracing created a tubular structure with high torsional stiffness. The connection of the tubular structure with suspension cables increased torsional eigenfrequencies for symmetrical and anti-symmetrical modes. The towers, hinged or clamped at their base, had little effects on eigenfrequencies. The increase in the torsional stiffness of towers had a limited beneficial effect on torsional eigenfrequencies. The diagonal cables connecting the tower top to side truss beams had little

790

9 Wind Actions and Effects on Structures

effect on symmetrical modes, whereas they were favourable for anti-symmetrical modes. The authors unanimously considered the determination of the flutter critical speed by Bleich’s method [281] exceedingly arduous in relationship with the k and Z parameters (Eq. 9.116). They then developed a design method that, through tables, allowed to approximately perform such calculation. The authors remarked that the proposed method could turn out to be essential not only to calculate the critical speed of a given bridge, but also to design a deck section guaranteeing the utmost stability. In 1955, the ASCE compiled a new state of the art on the aerodynamic stability of suspension bridges [287]. The most critical and uncertain aspect remained the relationship linking aerodynamic actions to structural motion. There was, however, plenty of evidence about the conditions that favour aerodynamic stability. They could be summarised as follows: (1) a stiffened truss cross-section was more favourable than a stiffened girder one; (2) openings in the deck and other measures breaking the uniformity of wind actions were favourable; (3) the use of two side truss beams and two horizontal top and bottom slabs originated a closed truss beam that increased torsional frequencies and drew the critical flutter speed away; (4) the increase of the eigenfrequencies was favourable for any cross-section; (5) at most sites the wind was not uniform along the bridge axis and turbulence increased with the mean speed; this did not favour the growth of aeroelastic oscillations; (6) an increment in stiffness due to an increment in weight increased the time required to increase the amplitude of the oscillations. Between 1961 and 1963, the Norwegian Arne Selberg (1910–1989) [288, 289] observed that the evaluation of the critical flutter speed developed by Bleich implied complex and boring calculations [281] or an inaccurate interpolation between tabulated data [286]. He then developed a very successful relationship, now known as the Selberg formula. It expressed the critical flutter speed in the form: VC = K VF

(9.137)

where V F is the critical flutter speed of a thin flat plate in a flow parallel to its plane, K is a factor that quantifies the critical speed reduction of an actual bridge in comparison with that of a thin flat plate. The critical flutter speed of the thin plate was provided by the empirical formula: $   %√   ν ωV 2  (9.138) 1− VF = 0, 44 ωT b ωT μ where b is the width of the deck, ωV and ωT are the natural vertical and torsional circular frequencies, ν = 8 r 2 /b2 and μ = πρb2 /4m, r being the radius of gyration of the mass, ρ the air density, m the mass per unit length. The error made using Eq. (9.138) decreased with ωV /ωT : for ωV /ωT  0.7, the error was 4%; for ωV /ωT  0.5, the error was 1.5%. The flutter speed increased with the deck width and with its

9.9 Flutter

791

torsional circular frequency. The flutter circular frequency associated with V F was given by: ωF =

2K C VF b

(9.139)

where K C is a coefficient provided by diagrams as a function of ωV /ωT , ν and μ for various deck cross-sections; its simplicity does not impair the correctness of evaluations. The tests carried out between 1954 and 1958 on models of existing and new bridges proved that the effect of open lattice structures, railings and other details was minimal. The parametric study leading to the Selberg formula was then carried out on simplified models. Also the K parameter in Eq. (9.137) was provided by diagrams depending on the deck type, on the angle of attack α and on the criticality level of the speed. According to Selberg there were three levels of critical speed, V C1 , V C2 , V C3 , and three corresponding values of K, namely K 1 , K 2 and K 3 : at the first level (1) oscillations are felt by traffic but are not dangerous for the bridge; at the second level (2) a properly built bridge can withstand oscillations for many hours; at the third level (3) oscillations destroy the bridge in a few hours. V C1 , V C2 and V C3 were the maximum wind speeds for which stable or decreasing oscillations respectively equal to 0.01, 0.1 and 0.2 radians occur. On increasing d/b, the oscillations change from coupled to mostly torsional ones. Under pure torsion conditions, Eqs. (9.137) and (9.138) become: √ VC = K T VT ; VT = 0, 44 ωT b

ν μ

(9.140)

where K T is a non-dimensional coefficient. As regards to vertical oscillations, they are usually less important. Even though they have been observed several times, they are not known to have caused or contributed to any disaster. In this case, Eqs. (9.137) and (9.138) become: VC = K V VV ; VV = ωV b

(9.141)

where K V is also given from diagrams.

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Chapter 10

Wind Hazard, Vulnerability and Risk

Abstract With the onset of the twentieth century, mankind grew a renewed awareness about the risks affecting whole areas exposed to wind phenomena of devastating strength, such as tropical cyclones, tornadoes and thunderstorms. This chapter deals with this issue pointing out the trend, which gained ground in this period, aimed at collecting the data concerning the location, recurrence and intensity of wind storms, the relationships between the intensity of calamitous phenomena, the characteristics of structures and of their elements, and the damage they suffered, the consequences of such damage and the strategies to mitigate losses through the attenuation of hazard and vulnerability.

With the onset of the twentieth century, engineers woke up to the importance of understanding and evaluating the physical phenomena through which the wind acts on structures according to their geometrical and mechanical properties. They realised that light, flexible and low-damped structures were the most sensitive to wind effects. As a consequence, they learnt to take precautions against them by developing effective technologies to improve existing structures, as well as appropriate analytical and experimental procedures to design the new ones (Chap. 9). At the same time, mankind grew a renewed awareness about the risks affecting whole areas exposed to wind phenomena of devastating strength, such as tropical cyclones (Sect. 10.1), tornadoes and thunderstorms (Sect. 10.2). In this period, concepts such as hazard, vulnerability and risk, even though codified within a probabilistic context,1 were still vague and undetermined. A trend, however, gained ground aimed at collecting the data concerning the location, recurrence and intensity of storms (hazard), the relations between the intensity of the calamitous phenomena, the characteristics of the structures and of their elements and the damage suffered (vulnerability), the consequences of such damage in relationship to those experiencing it (risk) and the strategies to mitigate losses through the attenuation of 1 The hazard of a system (a structure, a city, a land area, a nation, …) is the probability of occurrence

of an event, in this case of windy nature, with a given intensity. The vulnerability of a system is the probability this system is subjected to a given damage (natural, anthropic, …) for a given event intensity. The risk is the probability the system is subjected to a given loss (of human lives, economical, functional, …) for a given damage. © Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_10

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hazard and vulnerability. Such activities were not exactly set in a scientific context. However, they led to bountiful collections of information, data and knowledge that laid the foundations for the systematic evaluations that blossomed from the second half of the twentieth century.

10.1 Tropical Cyclones Even though tropical cyclones are phenomena dreaded and studied since ancient times (Sects. 4.1 and 6.4), both the knowledge about them and the analysis and interpretation of their consequences were subjected to significant evolution only between the late nineteenth and the early twentieth centuries. Tropical cyclones are cyclonic formations with intertropical origin that draw their energy from the latent heat released by water vapour condensation.2 They mostly develop in the geographical areas indicated in Fig. 10.1 [1]: in the oceans of the northern hemisphere they mostly proceed from south-east towards north-west (Fig. 10.2); in the oceans of the southern hemisphere, their direction is specular with respect to the equator; it is interesting to remark the almost absence of tropical cyclones in the Southern Atlantic Ocean.

Fig. 10.1 Geographical areas where tropical cyclones develop and their directions [1]

2 To

feed its thermal mechanism, a tropical cyclone must remain over warm waters providing the humidity required by the atmosphere. Some scientists estimated that the thermal energy released by a hurricane ranges between 50 and 200 trillion Watt, approximately equal to the energy released by the explosion of a 10-megaton atomic bomb every 20 min.

10.1 Tropical Cyclones

805

Fig. 10.2 Hurricane trajectories between 16 and 30 September from 1874 to 1933 [1]

Table 10.1 shows the most devastating events striking the Earth until 1960 [2–7]; because of the lack of information about older events, the list mostly includes data referring to twentieth century events. Tropical cyclones, when compared with extra-tropical cyclones typical of middle latitudes, are usually characterised by a smaller extension, with diameters not exceeding a few hundred kilometres, and by much higher wind speeds. In America, those causing wind speeds exceeding 120 km/h are called hurricanes.3 The same phenomena are called typhoons in the Far East and cyclones in Australia and in the Indian Ocean. They take place in August and September in the northern hemisphere and in February and March in the southern one. For many centuries, the hurricanes of the West Indies were called with the name of the Catholic saint of the day in which they occurred. Between the late nineteenth and the early twentieth centuries, the Australian meteorologist Clement Lindley Wragge (1852–1922) gave them the names of his friends, politicians and historical and mythological figures. Later, they were identified by the coordinates of their latitude and longitude. After the Second World War, military meteorologists indicated hurricanes with female names. From 1950, names with initials in alphabetic order were adopted. From 1979, following the protests of the feminist movement, male names were also used, in accordance with rules established by the World Meteorological Organization (WMO). 3 The

term hurricane derives from an ancient tribe of Central America aboriginals, the Trainos; according to this tribe, hurricane was the God of Evil [2].

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Table 10.1 List of the most devastating tropical cyclones until 1960 Date

Location

Casualties

7 October 1737

Calcutta, India

300,000

October 1780

Barbados, Guadeloupe, Martinique

24,000

June 1822

Bakarganj, Bangladesh, India

50,000

5 October 1864

Calcutta, India

50,000

October 1876

Bakarganj, Bangladesh, India

215,000

8 October 1881

Haiphong, Vietnam

300,000

June 1882

Mumbai, India

100,000

8 September 1900

Galveston, Texas, USA

6000

1906

Hong Kong

10,000

1919

Florida Keys; Corpus Christi, Texas, USA

600–900

12–17 September 1928

West Indies, Florida, USA

1800–4000

3 September 1930

San Domingo

2000

10–22 September 1938

New England, USA

600

15–16 October 1942

Bangladesh, India

11,000–61,000

25–27 September 1953

Vietnam and Japan

1300

27 September 1954

Japan

1218

17–19 September 1959

Far East

2000

26–27 September 1959

Honshu, Japan

4600–5100

Applying the criterion introduced by José Algue (1856–1930) in a work published in Spanish in 1897 and translated in English in 1904 [8], tropical cyclones lash the land by three main mechanisms: the wind force, the storm surge and the torrential rains.4 The sum of these concurrent causes brings about damage and loss of human life not commensurable with any other natural phenomena. Wind force causes extensive damage through the direct actions associated with the speed field and the indirect actions due to the impact of debris. In 1882, Bender [9] recounted that in February 1818, in the Mauritius Islands, a hurricane displaced by 1.5 m, over its foundations, a 16 by 10 m, 10 m high, nearly built wing of a theatre, covered with heavy wood. During the hurricane that struck Guadalupe in 1825, a wood piece with 50 cm2 cross section, 4.5 m long, was hurled by the wind and penetrated almost 1 m into a bar. In 1868, two contiguous spans of the Mauritius Railway viaduct over the Grand River, weighing 30,000 N/m and 35 m long each, were lifted and swept away from piers.

4 Sometimes hurricanes also produce devastations through tornadoes that represent one of their con-

sequences. A theory developed by Charles Franklin Brooks (1891–1958) and by some Japanese seismologists states that tropical cyclones cause favourable conditions for the occurrence of earthquakes; according to it, the pressure drop caused by the storm can put the Earth crust through exceptionally strong stress conditions [1].

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807

Table 10.2 Some of the highest wind speeds recorded during tropical cyclones until 1950 Speed (km/h)

Location

Date

299

Mount Washington, New Hampshire

21 September 1938

282

Chetumal, Mexico

27–28 September 1955

262

Havana, Cuba

18 October 1944

249

Hillsboro Lighthouse, Florida

17 September 1947

241

San Juan, Puerto Rico

13 September 1928

212

Jupiter Lighthouse, Florida

26 August 1949

206

Miami Beach, Florida

18 September 1926

195

Milton, Massachusetts

21 September 1938

Such events gave rise to remarkable consequences on 21 and 22 September 1938 (Table 10.1) during the Long Island Express, a hurricane that, according to the forecasts, should have faded out in the high-pressure area off the U.S. East Coast. It actually changed its trajectory, swept Long Island and continued its deadly and devastating course through New England along the Connecticut Valley (Fig. 10.3a), between Boston and New York, and finally went out in the cold Canadian forest, over 520 km away from the coast. On the slopes of Mount Washington, New Hampshire, it originated a wind speed equal to 299 km/h, the highest measured during a hurricane5 (Table 10.2) [10]. Besides 600 casualties, the effects of its passage included 60,000 left homeless and the destruction of 26,000 cars, 75% of the pleasure craft moored at Long Island (Fig. 10.3b) and 32,000 km of transmission lines; in New England only, 250 million trees were uprooted. The overall damage, assessed at the time, amounted to 330 million USD [11].

Fig. 10.3 Connecticut, September 1938 [11]: a Boston–Stonington train; b boats destroyed 5 Curiously,

the maximum measured speed of this period is associated with a wind event of extratropical origin. It is equal to 302 km/h, with gust peaks up to 368 km/h and dates back to 12 April 1934; it was recorded at the Mount Washington Observatory in New Hampshire [10].

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10 Wind Hazard, Vulnerability and Risk

Fig. 10.4 San Felipe hurricane, Puerto Rico, September 1928: a pressure, wind speed, temperature and rainfall in San Juan [1]; b pinewood beam (3 m × 7.6 cm × 2.5 cm) embedded in a palm tree [3]

The wind actions associated with the San Felipe hurricane, which travelled across the Caribbean Sea on 13 and 14 September 1928, were just as devastating. Its passage on San Juan, Puerto Rico (Fig. 10.4a), is remembered for the effects caused by roof fragments, tree branches, building walls and other objects, strongly hurled in every direction (Fig. 10.4b). They caused the death of 300 people, plus 1836 casualties caused by the same hurricane as it passed through Florida. The storm surge is a swift increase of the sea level, driven by the wind strength, caused by the pressure drop in the eye of the storm [12] (Fig. 10.5a). In open seas, the water level raises by no more than one metre; near the shore, it grows up to 4 m; inside bays or closed channels, it can reach 10–20 m height6,7 (Figs. 10.5b and 10.6). Devastating effects caused by this phenomenon occurred in Galveston, Texas, which was razed to the ground (Fig. 10.7) by the storm surge due to a hurricane on 6 The

first data about the effects of the storm surge date back to the early Second Millennium and concerned Northern Europe [7]. In January 1281 and in November 1421, IJsselmeer, in the Netherlands, was swept by two waves that caused 80,000 and 100,000 deaths, respectively. In December 1287 and in January 1362, the shores of the German North Sea were lashed by two waves that killed 50,000 and 100,000 people, respectively. The greatest catastrophe in ancient times occurred on 7 October 1737 at the mouth of the Hooghly River, in the Bay of Bengal: the wave reached 12 m height and killed 300,000 people. In 1970, the situation will be much worse, when the surge of a tropical typhoon caused 500,000 deaths in Bangladesh. 7 In the Philippines, tropical cyclones are called “bagiuos”, a name deriving from the city of Baguio, flooded by waters in 1911 [2].

10.1 Tropical Cyclones

809

Fig. 10.5 a Pressure at sea level (in inches) during the hurricane that crossed West Palm Beach, Florida, on 1928 [1]; b storm surge caused by the hurricane that struck Miami Beach in 1926 [2]

Fig. 10.6 a Providence, Rhode Island, flooded by the storm surge, September 1938 [11]; b a ship settled on the Connecticut shore, September 1938 [1]

8 September 1900 (Table 10.1). Here, a different spirit came into being. To protect themselves from new hurricanes, the citizens studied and applied the first measures aimed at defending their land. From 1902 to 1904, they built a reinforced concrete wall over 5 km long, 5.2 m high and 4.9 m wide at its base; boulders were placed before the wall to mitigate the force of the waves (Fig. 10.8a); the wall bore the brunt of a new fierce hurricane that struck Galveston 11 years later. In the meantime, many buildings were raised at least 2 m above ground level (Fig. 10.8b) to reduce the damage caused by future storm surges; in 1910, over 2000 buildings had been raised. This was a message that was upheld at conceptual and operational levels in different parts of the world. In 1925, Stephen Sargent Visher (1887–1967) [13] examined the effects of the cyclones in the Pacific and set out a principle that is still valid: “Obviously loss of property and life from severe tropical cyclones cannot be entirely prevented, but it certainly can be reduced”. He then continued by illustrating two construction recommendations aimed at mitigating the effects of the wind force, of the storm surge and of torrential rains: (1) buildings should be located so as to avoid

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10 Wind Hazard, Vulnerability and Risk

Fig. 10.7 Galveston hurricane, 1900: a devastation; b search for survivors

Fig. 10.8 Galveston, defences against storm surges [11]: a wall and boulders; b raised buildings

hurricane waves and floods; if possible, they should be at least 20 feet above sea level or valley bottom; (2) buildings should be constructed to withstand the wind. Examining the damage caused by the hurricane that struck the Bahamas and Florida in September 1926, Schmitt [14] published new guidelines for residential and ordinary buildings. He maintained that “wooden shutters would prove to be a wonderful safeguard to residences. In wood-frame buildings, it is important to take particular care that the rafters are spiked securely to the sidewalls and the ends of all partitions are well spiked to the walls. Such buildings should also be anchored to their foundations and should not have to depend on weight alone to resist being turned over or shoved off their base. Tile and cement block construction for residences, small stores and apartment buildings should be laid up in cement mortar”. It was

10.1 Tropical Cyclones

811

Table 10.3 Some of the most intense rainfalls recorded during tropical cyclones until 1950 Water (cm)

Days Location

Date

245

4

Silver Hill, Jamaica

November 1909

224

4

Baguio, Philippines

July 1911

207

3

Funkike, Formosa

18–20 July 1913

160

3

Mount Malloy, Queensland, Australia

?

119

7

Reunion, Mauritius

15–21 February 1896

117

–

Baguio, Philippine Islands

July 1911

104

7

La Marie, Tamarind Falls and L’Etoile, Mauritius

15–21 February 1896

Fig. 10.9 Rainfalls (in inches) caused by hurricanes on Puerto Rico [1]: a August 1899; b September 1928

the start of a literary production aimed at defining good construction practices in the areas exposed to tropical cyclones. Actually, many years will pass before mankind got ready, especially in the rich and advanced countries, to counter tropical cyclones. In 1961, by way of example, the floods due to the storm surge caused by the Muroto II typhoon killed 32 people in Osaka, flooding the city for the sixth time in the last 30 years8 [15]. This prompted the start of studies that lead to the construction, in 16 years, of the barrages completed in 1981. Torrential rains, often referred to as cloudbursts because of their intensity, can produce up to 2.5 m of water in local areas (Table 10.3; Fig. 10.9) [10]. Unlike the actions of winds and storm surges, whose effects are limited to a narrow coastal belt, rains produce the flooding of coastal areas for a depth that can reach several hundred kilometres, causing devastating effects in hill and mountain areas, or downstream of them, because of the landslides and floods due to the overflowing of rivers and lakes. Torrential rains, on the other hand, represent, for many areas subject to droughts, irreplaceable irrigation tools which agriculture cannot do without [16, 17]. Figure 10.10a shows the trajectories of nine tropical cyclones that produced, from 1928 to 1955, rains sufficient to put an end to droughts on areas extending over 26,000 km2 (Fig. 10.10b); this implied, of course, a high price in casualties and devastations [16]. 8 Osaka

suffered terrible devastation from 753, when the storm surge killed 560 people [15].

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10 Wind Hazard, Vulnerability and Risk

Fig. 10.10 Nine tropical cyclones that produced (1928–1955) enough rainfall to end droughts on areas exceeding 10,000 square miles [16]: a trajectories; b affected area and consequences

The onset of the 1940s brought substantial changes. On the one hand, research showed a renewed interest in modelling and forecasting tropical cyclones (Sects. 4.1 and 6.3). On the other hand, the acknowledgement of the terrible consequences of these phenomena fuelled the opinion that it was necessary to implement wide-ranging projects to mitigate hazard, vulnerability and losses in the most exposed areas. One of these projects, started in 1940 by the instrumental division of the U.S. Weather Bureau, created experimental automated stations that transmitted information about barometric pressure and wind speed and direction by radio, without personnel. The first three stations became operational in 1943, proving themselves essential for hurricane sighting. Two stations were set up on the Orange Cay and Dog Rock island, in the Bahamas; the third one, located in Flamingo, Florida, was not initially equipped with a radio and recordings where physically collected. A fourth automated station was installed in Naples, Florida, in the late 1940s. At the start of the 1950s, similar stations proliferated in areas exposed to hurricanes; they transmitted radio messages every 3 h. As in other sectors, even in this context the turning point was motivated by a terrible accident. In December 1944, an American fleet commanded by Admiral William Frederick Hasley (1882–1959) was sent to the Philippines to support the invasion of those islands, which were occupied by the Japanese. On December, George Kosco, the chief meteorologist of the expedition, located the Cobra typhoon. Kosco forecasted its evolution, indicating the course to avoid it. It is said that the Admiral was not convinced by Kosco’s explanations and put up with them on sufferance. On 18th the fleet entered the hurricane, which travelled in the direction opposed to the forecasted one (Fig. 10.11a). It was a massacre of men, ships and aircraft (Fig. 10.11b); there were 82 survivors out of 872 expedition members. The Admiral, like the designer for structures, was held responsible for the incident, even though he followed an authoritative opinion [11].

10.1 Tropical Cyclones

813

Fig. 10.11 Philippine Sea, Cobra typhoon, 1944 [11]: a trajectory forecast (black line), actual trajectory (light blue line), Halsey’s course (orange line); b the day after the typhoon (colour figure online)

The U.S. Army Air Force (Fig. 10.12a), already involved in flights in the eye of the storms, started on 27 July 1943 by Colonel Joseph Duckworth9,10 (1902–1964) (Fig. 10.12b), multiplied the reconnaissance flights and, since 1945, fitted its aircraft with the first onboard radars. The U.S. Navy, involved in the hunt for Atlantic and Caribbean hurricanes under the aegis of a centre headquartered in Miami, established in 1944 as a joint operation between the Weather Bureau and the armed forces, developed the warning stations in the Pacific. Within the end of 1945, the U.S. Army and the U.S. Navy collected a huge amount of data. They also accurately located hurricanes and followed their evolution, giving prompt alerts to the endangered population, which was then able to reach safe places. The use of hurricane alerts, the improvement of buildings and the spread of coastal barrages entailed huge advantages: in 1925, a hurricane that caused 10 million USD of damage resulted in, on the average, 160 casualties; in 1946, the same damage level implied an average of approximately 4 victims [11]. Unfortunately, often there was no way to remedy economical damage, especially to crops, which became increasingly extensive (Fig. 10.13). In the meantime, Irwing Langmuir (1881–1957), Vincent Joseph Schaefer (1906–1993) and Bernard Vonnegut (1914–1997) wrote a new chapter in the history of wind: weather control [11]. In 1890, the U.S. Congress funded an experiment aimed at causing rain, conceived by General Robert Saint George Dyrenforth (1844–1910), which consisted of firing artillery guns under a clear sky. During the Civil War, the General noted that after the battles rain almost always began to fall. He then felt that rain was caused by the noise of artillery fire: of course, experiments carried out in Texas failed.

9 Many claim the first flight in the eye of a storm was carried out in 1933, near Norfolk, Virginia, by an

aerodynamicist working at the NACA Langley Research Center, Eastman N. Jacobs (1902–1987). Unlike Duckworth, however, there is no objective evidence of his flight. 10 Duckworth, penetrating into the eye of a hurricane near Galveston, proved that such practice was not too risky. Even though these reconnaissance flights proliferated, only one aircraft loss was recorded, on 1 October 1945 in a typhoon over the China Sea, with one meteorologist and six crewmembers on board [11].

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10 Wind Hazard, Vulnerability and Risk

Fig. 10.12 a Hurricane hunters; b a weather aircraft flies over a hurricane [11]

Fig. 10.13 Evolution of the damage and casualties caused by hurricanes in the USA [2]

10.1 Tropical Cyclones

815

Fig. 10.14 Hail cannons

A similar technique gained ground in Europe between the late nineteenth and the early twentieth centuries [18]. The idea was to build cannons (Fig. 10.14) that, when pointing to storm clouds, would have broken hailstones and caused downpours of fine and beneficial rain. The cannons were loaded with gunpowder, weighed approximately 10 tons and were almost 10 m high; they produced a deafening noise and a smoke ring that raised up to 300 m height. In Austria, they were used for two years for experimental purposes. No hail-producing events occurred in the experimental area during this period; in the surrounding areas, conversely, many devastating hailstorms occurred. This was interpreted as a proof of the effectiveness of hail cannons and their use spread across the whole Europe, especially in the areas where valuable crops were present. In 1899, over 2000 cannons were in operation in Italy only. After approximately a decade of experiments, they turned out to be absolutely useless. The scientific study of this subject matter started in 1911, at embryo level, in a paper by Alfred Lothar Wegener (1880–1930) in which he formulated a theory of precipitations called the ice germ theory [19]. In 1928, it was developed and fully exposed by Tor Harold Percival Bergeron (1891–1977) [20]. At the Assembly of the International Geophysical and Geodetical Union, held in Lisbon in 1933, Bergeron explained that when damp air cools down below a given limit, water vapour condenses into tiny droplets with negligible falling speed and that, as a consequence, it does not cause rainfall. If small ice crystals (germs) are present, however, the droplets evaporate for the benefit of the crystals, which enlarge until they acquire a falling

816

10 Wind Hazard, Vulnerability and Risk

Fig. 10.15 a Schaefer’s laboratory [11]; b seeded area of a cloud, 1947 [11]

speed that is no longer negligible. If, during their fall, they cross for a sufficiently long-time atmosphere layers with temperature higher than 0 °C, the snowflakes reach the ground as rain drops. This theory, developed between 1937 and 1938 by Theodor Robert Walter Findeisen (1909–1945) [21] through experimental and theoretical works, is still known as the Bergeron–Findeisen theory. In the same years, Langmuir, a physicist and chemist working at the General Electric Research Laboratory in Schenectady, New York, who won the 1932 Nobel Prize for his studies about particle chemistry, decided to devote the rest of his life to atmospherical and meteorological sciences [22]; he immersed himself, flanked by Schaefer, in the study of methods to favour rainfall; they were part of warfare researches. In the summer of 1946, during a laboratory experiment at the Mount Washington Observatory (Fig. 10.15a), Schaefer [23] discovered that at temperatures below −40 °C, the super-cooled water vapour particles solidified even if no condensation cores were present. This result was made possible through the introduction of dry ice (solid carbon dioxide at a temperature equal to approximately −78 °C) in the freeze room used for the tests. On 13 November 1946, encouraged by Langmuir, Schaefer rented a small airplane, reached 4500 m height over the Berkshire Mountains, leaned out the window and seeded a stratiform cloud with 3 kg of finely ground dry ice (Fig. 10.15b). In a few instants, the super-cooled droplets condensed and turned into snowflakes; the snowfall was limited to an atmospheric layer approximately 600 m deep, within which the snow melted and evaporated. Despite failure, Langmuir considered Schaefer’s attempt a memorable one and urged him to make another attempt. Schaefer repeated the experiment, with some changes, on 20 December 1946. This time the snow did not evaporate and fell on the states of New York and Vermont, paralysing traffic and causing severe inconveniences to the population. In the meantime, on 14 November 1946, Vonnegut [24] carried out an experiment at the General Electric laboratories through which he proved that silver iodide can

10.1 Tropical Cyclones

817

turn super-cooled droplets into ice crystals at temperatures below −4 °C. He proved that 90 kg of this material could be enough to cover the whole Earth with snow. Many contested the experiments carried out by Schaefer, Langmuir and Vonnegut. Others were fascinated by the perspective of weather control and asked to produce water and snow, by artificial means, in different parts of the world. Langmuir took advantage of this situation to obtain funds from the U.S. Air Force and Navy. Thanks to such funding, he set up the Cirrus Project, aimed at mitigating the strength of hurricanes by seeding them. The first attempt within this project was carried out on 13 October 1947. 40 kg of dry ice were jettisoned into the eye of a hurricane moving seawards, 600 km off the Florida coast. The storm, which was at a decreasing strength stage, gained new strength, changed its direction and hit Georgia causing dramatic consequences. The experiments were discontinued and banned [11, 25–27]. The situation changed between 1954 and 1955, when the USA were struck by six hurricanes (Carol, Edna, Hazel, Connie, Diane, Ione), which killed 400 people and caused a huge amount of damage. The Congress decided to intervene11 and the Weather Bureau founded the National Hurricane Research Project, appointing Robert Homer Simpson12 (1912–2014) as its head. In 1959, this body merged with the hurricane forecast Centre based in Miami, originating the National Hurricane Centre. It aimed at three objectives: the physical and mechanical interpretation, the forecasting and the alteration of hurricanes. The studies about hurricane behaviour improved the understanding of its energy cycle, highlighting the role of the sea surface as a thermal source. The researches aimed at forecasting hurricane evolution were once more unsuccessful. The attempts to alter storms were the subject of renewed interest. On 27 August 1959, the Daisy hurricane was bombed four times with silver iodide, but the failure of the monitoring system did not allow assessing the effects of the intervention. On 16 September 1961, with fully operational instruments, an aircraft seeded the wall of the eye of the Esther hurricane with eight silver iodide canisters, north of Puerto Rico. The hurricane, which was in an increasing strength stage, from then on kept its strength at a constant level; near the walls of the storm eye, its strength even decreased. The next day the aircraft repeated the operation, but the canisters fell out of the eyewall without causing consequences. Even in view of these experiments, the idea that the effects of such interventions depended on the point of the hurricane where they were carried out gained ground [11].

11 In 1953, the US government set up the Weather Control Agency. In 1957, a committee of this agency claimed “weather changes could turn out to be a weapon more important than the atom bomb”. In 1958, Howard Thomas Orville (1901–1960), the Agency director, stated that “ways to alter climate using an electronic beam to ionize or de-ionize the atmosphere above a given areas” were under study. Senator and future President of the USA, Lyndon Baines Johnson (1908–1973), declared “from space, it would be possible to control the weather on the Earth, to cause droughts and floods, to change tides and to raise sea level, to turn temperate climates into freezing ones”. 12 Simpson is also known as the author, together with Herbert Seymour Saffir (1917–2007), of the Saffir–Simpson hurricane intensity scale.

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10 Wind Hazard, Vulnerability and Risk

This interpretation was accepted by the Weather Bureau and by the U.S. Navy, which in 1962 jointly engaged in the Stormfury project [26], led by Simpson, with the aim of formulating theoretical models for the selection of the area where seeding was to be performed. The new principles were applied in August 1963 on the Beulah hurricane, in the middle of the Atlantic Ocean. The operation shattered the storm eye, extended the area of the storm and reduced wind speed by 14%. The result was temporary, and there was no proof that the strength reduction depended on the seeding process.13

10.2 Tornadoes and Thunderstorms In parallel with the formation of the culture of tropical cyclones and of the criteria to face their devastation, a similar culture came into existence, aimed at thunderstorm events and at their most destructive form: tornadoes (Sects. 4.1 and 6.4). They are tight columns of air with upward spiral run, which move at speeds ranging from 30 to 100 km/h along trajectories usually a few dozen kilometres long. Their formation takes place in atmospheric zones characterised by strong instability, in particular along the cold fronts of cyclonic formations. Among the wind events, they are the ones that reach the highest speed, over 700 and perhaps 1000 km/h. The modern study of this subject started at the end of the nineteenth century. The first drawings and engravings about the damage caused by tornadoes date back to 1865 (Fig. 10.16) [11]. The first photographs of these events date back to 1884 (Fig. 10.17) [28]. In 1882, John Park Finley (1854–1943) published a pioneering report [29] that included the Scientific resumé of tornado characteristics. Reprinted and extended between 1882 and 1887, it provided various images of tornadoes (Fig. 10.18a) and of the damage they caused (Fig. 10.18b), the first map of the tornadoes that struck America from 1760 to 1885 (Fig. 10.19), as well as a descrip-

13 In 1965, it was decided to seed the Betsy hurricane, but the seeding was aborted when the storm came too close to the shore; by mistake, the information did not reach the public opinion and the Congress. Betsy destroyed Southern Florida, stirring up people and politicians against seeding. Much time was required to persuade anyone, after this event, that the disasters they suffered were not the consequences of experiments. The subsequent attempt occurred on 1 August 1969 during the Debbie hurricane. After five seedings in eight hours, the maximum wind speed dropped by 30%, from 180 to 125 km/h. After 24 h, Debbie recovered, stronger than before. Additional seeding reduced wind speed by 15%. It became clear that the interventions only caused temporary consequences. The day after, while the seeding was suspended, Debbie regained strength and reached 182 km/h. A new seeding was performed, and the wind speed dropped to 154 km/h [11]. Paradoxically, the age of seeding was coming to an end. The countries interested in the problem stood on different positions and imposed insurmountable vetoes. The government of the People’s Republic of China, afraid that seeding could possibly change the trajectory of typhoons, made clear it would not accept any intervention that could cause damage to its coastal areas. Japan also was contrary, considering storms indispensable for its water supplies [16]. Mankind and engineering lost a potentially formidable risk mitigation tool [11].

10.2 Tornadoes and Thunderstorms

819

Fig. 10.16 Ancient engravings concerning a tornado in Viroqua, Wisconsin, June 1865 [11]

Fig. 10.17 Tornadoes [28]: a Garnett, April 1884; b Howard, South Dakota, August 1884

tion of their characteristics, of the conditions under which they formed and of their warning signs. According to Finley, there were 14 characteristic main elements of tornadoes: (1) the direction of rotation, almost always counterclockwise; (2) the lightning zone, especially in the cloud above the tornado; (3) the width of the destructive path, 400 m on the average; (4) the length of the trace, 40 km on the average; (5) the forward progress speed, 67 km/h on the average; (6) the time the tornado remained in the same place, 74 s on the average; (7) the occurrence of thunderstorms, especially before the tornado; (8) the hour, usually between 3:30 P.M. and 5:00 P.M.; (9) the states where their frequency was higher: Missouri first and then Kansas and Georgia; (10) the months during which more tornadoes occurred, usually April, May and June; (11) the month with the highest number of days in which tornadoes occurred, May; (12)

820

10 Wind Hazard, Vulnerability and Risk

Fig. 10.18 a Tornado in Ercildoun, Pennsylvania, July 1877; b damage caused by the tornado in Grinnel, Iowa, June 1882 [29]

Fig. 10.19 Map of the tornadoes striking America from 1760 [29]

10.2 Tornadoes and Thunderstorms

821

Fig. 10.20 Underground tornado shelters [29]

the prevailing direction of forward movement, towards north-east; (13) the time rain was heavier; (14) the time when hail was heavier. Finley also reported tables summarising the phenomena occurred until then and a classification of the damage produced. He discussed the defensive procedures against tornadoes and reported the first images of underground shelters (Fig. 10.20). Thanks to this information, in 1890 Henry Allen Hazen (1849–1900) [30, 31] published the first tornado scale, the ancestor of many subsequent classifications14 [32–34]. For this purpose, he analysed 2221 tornadoes occurred from 1873 to 1888 and defined nine categories, with degrees ranging from +3 and −1, based on the overall economic damage caused by the event.

14 In 1945, Seelye [32] analyzed the damage caused by tornadoes in New Zealand, classifying their

intensity through a scale with classes from 0 to 5; the class 5 corresponded to the destruction of strong buildings; the class 3 occurred when the external parts of buildings (e.g. canopies and verandas) were wiped out; class 0 tornadoes did not cause damage since the vortex did not come into contact with ground. The peak of such scales was reached in 1971, when Tetsuya Theodore Fujita (1920–1998) and Allen Pearson (1925) developed the Fujita–Pearson scale [33, 34]; it envisaged six degrees, from F0 to F5: the F0 degree indicates “light” damage, the F5 degree corresponds to “incredible” damage.

822

10 Wind Hazard, Vulnerability and Risk

Fig. 10.21 Tri-State Tornado, 1925: a photograph; b Longfellow School, Murphysboro, Illinois

From the late nineteenth century, an increasing number of reports about the damage caused by tornadoes was published [35–38]. Their availability increased the possibility of drawing up more complete diagrams about the zones and frequency of occurrence of tornadoes, the characteristics of such phenomena and their consequences. During the First World War, they spread to America, Japan, Australia, New Zealand and Europe. In 1916, the U.S. Weather Bureau inaugurated a monthly information collection about the tornadoes striking the USA. It was a regularly feature of the Monthly Weather Review, together with annual statistics and summarising tables. From such information, it was possible to infer that the USA were struck by 5204 documented tornadoes from 1915 to 1950, with an average of approximately 140 tornadoes per year; they caused 7961 deaths, i.e. 220 per year on the average, and injured approximately 100,000 people. The overall damage amounted to approximately 500 million USD. The greatest devastation was produced by the Tri-State Tornado; (Fig. 10.21) on 18 March 1925, travelling 352 km across Missouri, Illinois e Indiana with an uncommon speed that reached 117 km/h, it caused 689 deaths and injured 1980 people. According to [39], it gave rise to the highest death count in America, from 1900 to 1969, by a single phenomenon of this type. The event that struck Tokyo on 1 September 1923 greatly exceeded such statistics; after a very strong earthquake, the city was subjected to fires that originated smoke and hot air that formed a cloud that loomed over Tokyo for the whole day following the earthquake. The cloud originated 120 tornadoes that struck a devastated area, contributing to an overall final balance of 142,000 victims [34]. In 1917, Alfred Lothar Wegener (1880–1930) [40] published a catalogue of European tornadoes, based on the data collected from 1650 to 1916. It highlighted the limits of the available information, showing an unrealistic growth with the passing of time (Fig. 10.22a) due to the progressive increase of data; it was also distorted by the nationality of the author (Fig. 10.22b), who tended to collect more data about his own country and the neighbouring ones. The first trend disappeared from the 1960s; the second still represents an issue. Wegener visited the Estonian meteorologist Johannes Peter Letzmann (1885–1971) in 1918 and encouraged him to continue with his researches. Letzmann [41], impressed by Wegener’s studies and results, collected data about many

10.2 Tornadoes and Thunderstorms

823

Fig. 10.22 European tornadoes from 1650 to 1916 [40]: time (a) and b geographical distribution

Baltic tornadoes, cataloguing observations and measurements at ground level and at in the upper air, photographs, drawings as well as the damage they caused; on the basis of such information, he published an annual report in which he interpreted the characteristics of these phenomena. One of the main aspects of his researches was the study of the wind field associated with a moving vortex [42–44]. It was originated by the overlapping of a rotational and a translational field and was preferable to various categories (Fig. 10.23) characterised by two parameters: the G ratio between the maximum rotation speed and its translation component, and the distance between the rotational and the circular motion, caused by the flows coming into or out the vortex (Fig. 10.24). Letzmann schematized this situation through a modified Rankine vortex, providing a diagram of the damage field (Fig. 10.25) [42, 45]. He also carried out several laboratory tornado simulations15 [46–48], both in water and in air, proving that the vortex was guided from above. Finally, in 1937, he published his famous guidelines about how to study tornadoes [49]; this work, a pioneering one in its time, is now almost completely outdated [50]. The outbreak of the Second World War favoured the development of the research about storms [51, 52]. In the USA, the Weather Bureau and the War Advisory Committee on Meteorology jointly set up various strategic networks of volunteers who scanned the skies and reported the formation of storms, by phone, to the police and to radio and television stations; in the strategic areas—e.g. near weapons factories and associated facilities, airports and training grounds—the observation points were spaced by 80–120 km; they were integrated at local level by radars and control towers. Thanks to such collection, Joseph Lloyd in 1942 [53] and Albert Showalter and Joe Fulks in 1943 [54] published pioneering papers about storm forecasting. Showalter and Fulks discussed the synoptic conditions at ground level and in the upper air that favoured the formation of tornadoes. Despite this, storm forecasts remained scant and ineffective. The observation networks, on the other hand, turned out to be so important that, after the war was over, they were improved in many states. The age of modern tornado forecasting started under fortuitous circumstances [51, 52]. In the evening of March twentieth 1948, Major Ernest Fawbush (1915–1982) 15 In his memories, Letzmann mentioned the first attempts to simulate a vortex in a laboratory, carried out by the Swedish physicist Johan Carl Wilcke (1732–1796) between 1780 and 1785.

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Fig. 10.23 Letzmann model of the tornado [41]; the passage from type I to type IV corresponds to increasing values of G; α is the counterclockwise angle from the vector towards the centre of the vortex to the vector of its horizontal relative speed: α = 0° is a radial flow towards the centre; α = −90° is a tangential counterclockwise flow; α = −30°, −60° is a flow with radial and tangential components

and Captain Robert Miller (1920–1998), meteorologists of the U.S. Air Force at the Tinker Air Force Base (AFB) in Oklahoma, observed a tornado that devastated the Tinker AFB and the surrounding area (Fig. 10.26a) causing injuries to many people and damage amounting to over 10 million USD. In the afternoon of 25 March, the same officers observed, through a radar (conventional), atmospheric conditions similar to those of five days before. Fawbush and Miller, encouraged by their commander, General Frederick Borum (1892–1978), formulated an unprecedented forecast, announcing that a second tornado could possibly strike Tinker AFB within the end of the day. Almost unbelievably, it occurred in the evening. Thanks to this forecast and to the ensuing state of alert, no casualties were inflicted and the damage (Fig. 10.26b) was more limited than the previous time. Fawbush and Miller became national heroes. Building on the momentum of this forecast, in 1951, Fawbush et al. [55] collected and analysed, at the U.S. Air Force and Air Weather Service, the synoptic charts associated with the occurrence of tornadoes in the USA between 1940 and 1951. Thanks to this study, they maintained that tornadoes could only develop when six coded conditions existed in the same area and at the same time: (1) a thin layer of damp air near the ground is surmounted by a thick layer of dry air, with a strong temperature drop as the height increases; (2) the horizontal distribution of humidity in the damp air layer reaches its maximum along a relatively thin band; (3) the

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Fig. 10.24 Flow (dashed) and isotach (continuous) lines [41]

horizontal distribution of the wind in the upper air reaches its maximum, higher than 35 knots, along a relatively thin band between 3000 and 6000 m height; (4) the vertical projection of the band where the upper air wind is at its maximum meets the band where humidity at ground level is at its maximum; (5) the column of air joining these bands has a vertical temperature distribution that configures a high instability condition; (6) the top surface of the damp air layer is skimmed by an upper cold air front. From this layout, they deduced that tornadoes could be forecasted by identifying a meteorological evolution concentrating such conditions [56, 57]. In the same year, the cooperation between the U.S. Weather Bureau and Air Weather Service led to the establishment of a network consisting of 135 ground stations in Kansas, Oklahoma and Missouri. The personnel, all of them volunteers, was equipped with microbarographs, sometimes with hygro-thermographs and with instruments to measure wind speed and direction. The acquired data were integrated by the upper air measurements carried out by the Omaha, Nebraska, Columbia, Missouri and Little Rock, Arkansas by means of radio-equipped probes. They were completed through the images obtained by the radars in the area. In early 1952, the president of the U.S. Weather Bureau, Francis Reichelderfer (1895–1983), formed, within the Weather Bureau Analysis (WBAN) Centre in Washington, DC, the severe weather unit (SWU), a special group tasked with storm

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Fig. 10.25 Damage fields associated with different angle α values [41]

Fig. 10.26 Tinker Air Force Base: a 20 March 1948; b 25 March 1948

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forecasting and alert issuance. The first alert was issued in early March 1952 and involved a wide area. People liked the initiative, took such information seriously and kept ready to flee. The first successes came shortly afterwards: the first was the early alert about the tornado that struck six southern states on 21 and 22 March 1952; the second referred to the tornado that wrecked Oklahoma on April 21st 1952. In 1953, the Severe Weather Unit was redesignated as the Severe Local Storm Warning Service (SELS); the following year it moved from Washington, DC, to Kansas City, Missouri. From this moment, the pace of innovation became frantic. In 1955, the Radar Report and Warning Coordination (RAWARC) was created: it was a teleprinter circuit that received and issued radar observation in real time. In 1956, the Radar Analysis and Development Unit (RADU) was inaugurated to take advantage of the data provided by the RAWARC network. In the same year, the SELS absorbed the Severe Weather Warning Centre (SWWC). In the meantime, the first scientific criteria for tornado forecasting were proposed and applied. In the late 1940s, Herbert L. Jones developed a new method to spot tornadoes at the Oklahoma Agricultural and Mechanical College in Stillwater [58]. It consisted in detecting large electrical charges through a cathode ray oscilloscope. According to Jones, the lightnings during the tornado were much stronger than in any other thunderstorm and their colour was different; thus, they were recognizable. The first applications of this method were promising and led to the detection of two tornadoes near Norman, on 30 April 1949, and Stillwater, on 2 June 1949. In 1950, Morris Tepper (1916–2009) [59, 60] developed a new theory on the formation of tornadoes, the pressure-jump theory. According to it, the tornado was originated by the instability conditions along the plane of intersection of atmospheric pressure planes with a strong gradient. To validate this theory, in 1951 Tepper established the Tornado Project, with the help of Harry Wexler (1911–1962), setting up a meso-scale network of stations equipped with instruments including microbarographs. The analysis of the measurements disproved Tepper’s theory; his network, however, played an important role in the understanding of the phenomena originating convective storms. Two years later (1953), Snowden Dwight Flora (1879–1957) collected the whole of these data and knowledge in a book [58]. It discussed the conditions under which the tornado developed, the causes producing it and its configuration, its destructive strength, the forecasts and alerts, how to protect oneself from tornadoes and the disasters caused by this phenomenon in the USA. It also reported data associated with the tornadoes occurring in other parts of the world, especially in Canada, Great Britain, France, Netherlands, Germany, Hungary, Italy, Australia, India, Russia, China, Japan, Bermuda and Fiji Islands. By virtue of this information about the tornado and its consequences, the three fundamental mechanisms through which it strikes the land were focused on: the pressure drop, wind actions and the impact by debris [60, 61]. The passage of the tornadoes produces a sudden decrease in the atmospheric pressure, which drops up to 80–90% of its initial value (Fig. 10.27a). In airtight structures, this phenomenon causes forces from inside (where pressure remains unchanged)

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Fig. 10.27 a Weather Bureau barographic recording, Wold-Chamberlain airport, Minneapolis, June 1951 tornado [58]; b Tri-State Tornado, Baptist Church in Murphysboro, Illinois, March 1925

towards the outside (where the pressure drop takes place) that can make them explode (Fig. 10.27b). William Watters Pagon (1885–1973) [62] recalled a situation mentioned by Irminger and Nokkentved, reporting the description of a tornado in 1838 according to which “a sudden drop in external air pressure caused so powerful an internal pressure that the building blew up and fragments of clothes were found jammed into cracks in the walls”. Flora, describing the tornado that struck St. Louis on 27 May 1896 [58], documented a 10% decrease in the barometric pressure; in this situation, the roof of a 36-m airtight structure with walls 3 m high was subjected to a 400 KN lift, while the side walls were subjected to 200 KN outward forces. It is said [25] that a pilot, flying over Waco, Texas, during a tornado, saw “windows with glass panes, on both sides of Main Street, to swell outward in progressive waves, opposed brick walls coming into contact before collapsing on the lanes full of slow-moving cars and roofs falling into the interiors, by then without walls, of warehouses. A theatre and a six-storey warehouse swelled making their joints fail, like slow-motion bombs and then collapsed shortly afterwards, forming heaps of twisted wreckage”. The belief that the pressure gradient could be the main cause of the damage caused by tornadoes came into being. The theory now reappraised that during a tornado, it was advisable to open doors and windows to equalise internal and external pressures also spread out. Even though the dangerousness of this phenomenon was acknowledged, it became increasingly clear that most damage caused by tornadoes must be attributed to the direct wind actions, in particular to the exceptional strength of the horizontal component of its speed, due to the vortex translation and, above all, to its rotation (Fig. 10.28). Fleming [63] remarked that when a tornado originated 600–700 km/h speeds, no structure could reasonably withstand them; if all structures were designed to effectively withstand the wind actions provided by codes, however, the damage caused by tornadoes would be reduced to less than one quarter. The ascending component of the air vortex also appeared dangerous. On 18 March 1925, the Tri-State

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Fig. 10.28 Tri-State Tornado, Murphysboro, Illinois, March 1925

Tornado uprooted a railroad bridge from its foundations. In 1931, during a thunderstorm over Minnesota, a tornado struck the Empire Builder, a train travelling at 100 km/h, lifting five passenger cars (each of them weighing 700 KN) and dropping them 25 m away from the tracks; another vortex produced by the same thunderstorm uprooted the spire of a steeple, carrying it 24 km away. Flora [58] made use, for the first time, of the damage assessment to obtain the wind speed; the study of the Texas Panhandle tornado on 6 April 1947 proved it reached 730 km/h; there is other evidence about tornadoes that reached speeds between 725 and 800 km/h.16 In 1955, Van Tassel [64] obtained the wind speed by examining the vortex tracks on the ground; he applied this method to the tornado hitting the North Platte Valley, Nebraska, on 27 June 1955, estimating a speed value equal to 780 km/h. Another technique made use of the early movie shooting; Hoecker [65] studied the speed of the tornado that struck Dallas, Texas, on 2 April 1957 by examining the speed of debris. The third cause of damage, the impact of debris, is often prominent in the balance of the casualties and economic losses caused by tornadoes. The consequences depend on the characteristics of the affected site first. If the tornado travels across countryside and rural areas, it first grabs and then hurls away in every direction earth, sand, stones as well as many types of vegetation. If, conversely, it moves through settled areas, it seizes cars (Fig. 10.29a) and motorcycles, billboards and signs, poles and street lights, phone booths and shelters (Fig. 10.29b); in this case, the presence of vulnerable structures is essential: they are first damaged and then destroyed by the pressure drop 16 In 1961, using this procedure, the ASCE Task Committee on Wind Forces affirmed that tornadoes originated wind speeds routinely exceeding 500 km/h.

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Fig. 10.29 Tornadoes: a Leedey, Oklahoma, May 1947 [58]; b Omaha, Nebraska, March 1913

Fig. 10.30 a Tri-State Tornado, debris; b tornado in Westboro, Massachussets, June 1923 [74]

and by wind actions; doors and windows, roof, wall and eave fragments, wooden or iron beams (Fig. 10.30a) as well as furniture then become deadly projectiles. It is said that in 1931, in Minnesota, a 3 KN ice box was hurled 5 km away. To make up so much ferocity and destructive capability, the tornado is, thankfully, a rare phenomenon with limited extension: generally, its diameter ranges from 100 m to 1 km; the length of its trace does not exceed 500 km.17 It then causes devastations limited to the swept area (Fig. 10.30b), characterised by a clear separation between heaps of rubble and almost intact structures. Thus, on the one hand, the tornado is the most destructive individual wind event; on the other hand, it has the lowest probability of occurrence. This explains why the casualties and damage caused by tornadoes are a tiny percentage of those caused by tropical cyclones. The second half of the 1950s brought to light many significant innovations. First, storm (in particular, tornado) chasers made their appearance. They were intrepid individuals who faced the strength of the wind by moving as close as possible to storms to collect data useful to understand them. Roger Jensen (1933–2001) was the first to photograph a tornado in 1953. In 1956, David Hoadley (1938–) shot the first footage of a tornado in North Dakota. Neil Burgher Ward (1914–1972), an American meteorologist, was the first storm chaser operating on a scientific basis; 17 The longest continuous trace for tornadoes striking the USA in the first half of the twentieth century was 471 km long and occurred in Mattoon, Illinois, on 26 May 1917 [59].

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he developed thunderstorm and tornado models, as well as forecasting and detection criteria; his studies contributed to gain institutional status for storm chasers. The second aspect worth mentioning regards the impact of technological evolution, especially of radars (Sect. 6.2), in the study of storms. The increasing use of (conventional) radars entailed advantages but did not represent a turning point as far as the detection of storm motion was involved. The switch to doppler radars was a very important event because of its consequences on the safeguard of human lives. The first successful attempt to spot a tornado by means of a Doppler radar was carried out in 1958, when Robert L. Smith and David Holmes detected a tornado near El Dorado, Kansas [66]; they used a continuous wave Doppler radar (Fig. 6.12) with a 3 cm wavelength; the radar set, provided by the U.S. Navy, was modified to spot tornadoes by James Brantley (1927–1961) at the Cornell Aeronautical Laboratory [67, 68]. It is interesting to notice that computers, which became increasingly common at the end of the 1950s (Sect. 5.3), were a formidable tool to analyse and forecast synoptic events; the first storm and tornado forecasts, i.e. meso-scale phenomena, made use of graphical and manual assessments within the numeric context of large-scale assessments. In 1953, Horace Robert Byers (1906–1998) (Sect. 6.4) invited to Chicago, as the third important element, a Japanese meteorologist, Tetsuya Theodore Fujita (1920–1998), who became the undisputed master of tornadoes and downbursts. Fujita applied the analytical tools he developed in Japan to the data collected by the first meso-scale networks; this led to the formulation of a conceptual model of the structure and evolution of convective systems, destined to become a milestone [69–71]. Fujita also introduced new techniques for the quantitative analysis of storm pictures and footage. His studies about the tornado occurred in Fargo, North Dakota, on 20 June 1957 were so complete and innovative they represented a reference [72]; thanks to them, Fujita formulated the first modern conceptual model of the tornado. In parallel with the culture of tornado detection and forecasting, the protection of human lives saw the addition of new strategies. Shortly after the devastating tornado that hit Omaha, Nebraska on 23 March 1913, Colonel W. H. Nelson built some tornado-resistant buildings (Fig. 10.31a) in Kansas City. The connections between elements were accomplished by means of riveted plates. The vertical elements were anchored to the foundation. Every building was fitted with a pair of high chimneys that stiffened its structure and equalised the internal and external pressure. The roof slopes were short and connected to the walls to prevent unroofing. Unfortunately, or thankfully, none of these building was struck by a tornado, so there was no way to verify their performance. They became, however, the model providing inspiration for the requirements the Weather Bureau adopted to guarantee the safety of the structures swept by tornadoes. In 1928, Teesdale [73] published one of the first reports about the safety of the structures exposed to tornadoes, in which he proposed the introduction of automated venting systems in side walls and roofs. He acknowledged, however, that “there may be some question as to whether any automatic vents would act quickly enough to save a building”.

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Fig. 10.31 a Nelson’s tornado-resistant building, Kansas City; b cyclone cellar or storm cave [58]

Actually, the opinion that any building well-designed in accordance with reliable standards was relatively safe became widespread; the same did not occur for churches and schools, characterised by wide halls and less partitions; in any case, the secondary elements of facades and roofs were vulnerable [74]. This was confirmed by the iron and reinforced concrete structures swept by the tornado that moved across St. Louis, Missouri, on 29 September 1927. The same can be said of the tornado striking the Gordon Hotel in Albany, Georgia, on 10 February 1940; the building, made of steel and reinforced concrete, had its windows completely destroyed without suffering any damage to its structural parts. It was clear, on the other hand, that events so sporadic and limited like tornadoes implied, as regards structures, a probability of occurrence so little it made a design aimed at withstanding them not very justifiable under the economical point of view. In the wake of the techniques illustrated by Finley, at the end of the nineteenth century the idea of building shelters, either inside or outside the buildings, allowing their inhabitants to stay safe progressed and became a trend. The most typical external shelter, built near the rural houses in the Middle West, was known as cyclone cellar or storm cave (Fig. 10.31b). It was obtained by digging a hole into the ground, covered by a frame that was subsequently covered with earth or garbage. More accurate rules and criteria were established by the U.S. Red Cross, which recommended the building of concrete-lined pit, 2.4 m long, 1.8 m wide and 2.1 m high, suited to house 8 people for a short time. It must be connected to the basement of the adjacent house through a tunnel. In case the latter was not present, the pit must be located north-east of the south-western side of the house—in the USA, tornadoes usually come from south-west and hurl debris towards north-east—and covered with earth. It must not be too close to the house to avoid impacts from debris. The door must be made of strong wood, with a lock capable of withstanding the depression. A reinforced concrete room inside the house represented an equally safe shelter. If the latter was not present, it was suggested to inhabitants to assemble themselves in the south-west corner of the basement. Finally, it is worth mentioning that in the 1950s, the opinion that the effects of tornadoes on structures were similar to those of nuclear explosions emerged.

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A literature [75] aimed at designing and strengthening strategic structures against tornadoes then came into being. In parallel, attention was paid to the construction of shelters taking inspiration from more advanced principles. Even though tornadoes are the most destructive and conspicuous consequence of thunderstorm phenomena, there are over 16,000,000 thunderstorms on Earth each year, i.e. 45,000 per day, on the average; at any given time, at least 2000 thunderstorm cells are active [76], but they only originate tornadoes under particular conditions. This aspect is essential because thunderstorms, as a whole, cause phenomena—wind, rain, hail and lightning18 [77]—that often are of limited magnitude taken individually but that, as a whole, are much more substantial than those due to tornadoes considered as stand-alone events. Within such phenomena, governed by complex electrical, thermodynamical and fluid dynamical mechanisms (Sect. 6.4), enucleating the direct and indirect consequences of wind does not represent an easy task. Mankind understood the extreme dangerousness of thunderstorm phenomena as early as the 1920s, as a consequence of the development of aviation (Sect. 7.4). In 1925, Simpson [78] studied the risks to which airplanes were exposed within thunderstorms, especially because of vertical updrafts and downdrafts. In the same year, a disaster that dramatically highlighted this problem occurred [11]. On 3 September 1925, the Shenandoah dirigible, a descendant of the German Zeppelin and the pride of the U.S. Navy, left Lakehurst bound for Detroit under the command of Captain Zachary Lansdowne (1888–1925); as fate would have it, he was writing a manual about the necessity to avoid thunderstorms for rigid dirigibles. The day after, at 4:30 A.M. the dirigible entered a thunderstorm and crashed (Fig. 10.32), causing the death of 6 people; 29 survivors managed to land aboard portions of the aircraft.19 This episode cast an indelible shadow over the safety of dirigibles and flight inside thunderstorms. In the 1940s, air traffic increased and so did the number of accidents in thunderstorms [79]. To reduce them, between 1939 and 1941 Germany set up the first network for the detection and control of storm lines, the Lindenberger Böennetz, 20 km east–south-east from Berlin [80]. In 1940, Japan created a thunderstorm reporting network, the Maebashi Raiu Kansokumo, 100 km north-west of Tokyo [81]. The advent of the Second World War spurred the researches about thunderstorms. The governments and military organizations of many countries acknowledged the strategic importance of flight safety within thunderstorms; in order to achieve this 18 Lightning, unlike rain and hail, is a deadly event. They often play a marginal role in the news because they usually kill one or two victims at a time. Actually, the overall number of the victims of lightning strikes is far from negligible. In the USA, they cause an average of 100 deaths and 250 injuries, a number close to those due to tornadoes. Lightning strikes also cause heavy damage to structures and woodlands; in the USA, such losses are estimated to amount to 40 million USD per year. 19 The Shenandoah dirigible replaced the German use of highly flammable hydrogen with helium, a rare and light gas found in Texas and Kansas. The airship was 200 m long, 25 m in diameter and was propelled by six 300 HP engines. It made her maiden flight on 4 September 1923. The inquiry following the crash concluded, two years later, that if the dirigible had been filled with hydrogen, it would have exploded, killing everyone on board.

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Fig. 10.32 September 1925, Shenandoah dirigible crash [11]

objective, better understanding of such phenomena was required. The use of radar developed playing the dual role of an instrument suited to locate airplanes and ships as well as the secrets of storms. Within this context, the Thunderstorm Project, operational in Florida from 1946 and in Ohio from 1947 [82], came into existence: it was the turning point in the study and understanding of thunderstorm phenomena (Sect. 6.4). Among many other results, it proved that a properly designed airplane with appropriately trained pilots could safely fly into thunderstorms [74]. The process to reach this goal, however, was still long and daunting. In 1959, 31 people died in an accident over Maryland caused by a lightning that struck the tanks of an airplane, causing its explosion. As a consequence of this and other events, in 1961 the USA created the National Severe Storms Project (NSSP), headquartered in Kansas City, Missouri, appointing Clayton Van Thullenar (1863–1959) as president and Chester Newton as scientific director [51]. Within the NSSP, the Project Rough Rider was implemented: thanks to it, the use of instrument-equipped aircraft flying into storms to collect data was increased. The data were then compared with the observations of ground radars. Finally, it is worth noting that the great attention paid in this period to the safety of the flight in the thunderstorm and above all in its downdraft tended to cover another great problem associated with them: the actions and effects of the thunderstorms and its outflows on structures. Between the end of the twentieth century and the beginning of the third millennium, having overcome most of the risks associated with flying, this topic will become a central theme of the modern wind science and engineering.

References

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65. Hoecker WH (1960) Wind speed and air flow patterns in the Dallas Tornado of April 2, 1957. Mon Weather Rev 88:167–180 66. Smith RL, Holmes DW (1961) Use of Doppler radar in meteorological observations. Mon Weather Rev 89:1–7 67. Rogers RR (1990) The early years of Doppler radar in meteorology. In: Atlas D (ed) Radar in meteorology. American Meteorological Society, pp 122–129 68. Brown RA, Lewis JM (2005) Path to NEXRAD: Doppler radar development at the National severe storms laboratory. Bull Am Meteorol Soc 86:1459–1470 69. Fujita TT (1955) Results of detailed synoptic studies of squall lines. Tellus 7:405–436 70. Fujita TT, Newstein H, Tepper M (1956) Mesoanalysis: an important scale in the analysis of weather data. USWB Research Paper 39, Washington, D.C. 71. Fujita TT (1963) Analytical mesometeorology: a review. Severe Local Storms Meteor. Monogr 27, Am Meteorol Soc, pp 77–125 72. Fujita TT (1960) A detailed analysis of the Fargo tornadoes of June 20, 1957. USWB Research Paper 42, Washington, D.C. 73. Teesdale LV (1928) Tornado-resistant construction and building possible by venting. Madison Forest Products Laboratory Branch, Wisconsin 74. Battan LJ (1961) The nature of violent storms. Doubleday, New York 75. Reynolds GW (1958) Venting and other building practices as practical means of reducing damage from tornado low pressures. Bull Am Meteorol Soc 39:14–20 76. Wood RA (1985) A dangerous family: the thunderstorm and its offspring. Weatherwise 38:131–151 77. White GF, Haas JE (1975) Assessment of research on natural hazards. The MIT Press, Cambridge, MA 78. Simpson CC (1925) Thunderstorms and aviation. J R Aeronaut Soc 29:24–46 79. Fujita TT (1981) Tornadoes and downbursts in the context of generalized planetary scales. J Atmos Sci 38:1511–1534 80. Koschmieder H (1955) Ergebnisse der deutchen böenmessungen 1939/41. Friedrich Vieweg, Braunschweig 81. Fujiwara S (1943) Report of thunderstorm observation project. Japan Meteor, Agency, Tokyo 82. Byers HR, Braharn RR (1949) The thunderstorm. U.S. Department of Commerce, Weather Bureau, Washington, D.C.

Part IV

Advancements: From the Mid-Twentieth Century to the Third Millennium

Chapter 11

Advancements in Wind Science and Engineering

Abstract This chapter addresses the outburst of research and applications that, since the early 1960s, has given rise to the transition from a set of varied and often independent subjects to an organic and unitary vision of the phenomena that revolve around the wind and its effects on men, buildings, territory and environment. This evolution is organised according to three successive phases. In the first phase, from 1963 to 1978, the study of wind actions and effects on structures determined an unprecedented aggregation of interests around wind modelling, bluff-body aerodynamics and wind-excited response of structures. In the second phase, from 1979 to 1998, the scientific community involved in wind and of its effects on structures felt the need to broaden its horizons and to give life to a new cultural aggregation called Wind Engineering. In the third phase, since 1999, a new transformation has been taking place according to which Wind Engineering, more and more often labelled as Wind Science and Engineering, shows a bursting development aiming to enlarge engineering boundaries towards a renewed vision that embraces most sectors of science and penetrates into society through scientific, technical and educational initiatives that are increasingly numerous, ramified and incisive.

Since the early 1960s, there has been an outburst of research and applications that have determined the transition from a set of varied and often independent subjects to an organic and unitary vision of the phenomena that revolve around the wind and its effects on men, buildings, territory and environment. This evolution may be divided into three successive phases. In the first phase (Sect. 11.1), from 1963 to 1978, the study of wind actions and effects on structures determined an unprecedented aggregation of interests around wind modelling, bluff-body aerodynamics, the wind-excited response of structures and aeroelasticity. It manifested itself through a series of meetings on Wind Effects on Building and Structures, which laid the foundations of the new discipline. In the second phase (Sect. 11.2), from 1979 to 1998, the scientific community that studied the wind and its effects on buildings felt the need to broaden its horizons and gave life to a new cultural aggregation that ranged from the single construction to the territory and environment. In this framework, a new body came into being, the International Association for Wind Engineering, which planned the activities © Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3_11

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of the new discipline. Among several other initiatives, it organised a new series of meetings, the International Conferences on Wind Engineering, which marked the times and directions of its evolution. In the third phase (Sect. 11.3), since 1999, a new transformation has been taking place thanks to which Wind Engineering, more and more often labelled as Wind Science and Engineering, exhibits a bursting development aiming to enlarge its engineering boundaries towards a renewed viewpoint that embraces most sectors of science and penetrates into the life of the society through scientific, technical and educational initiatives that are increasingly numerous, ramified and incisive. On the whole, this process is consolidating an integrated and homogeneous viewpoint of the wind. On the other hand, some sectors such as climatology, meteorology, aerodynamics, atmospheric pollution and wind energy have been tending to follow independent paths even though they continue to cultivate the liaisons with Wind Engineering. In this context, the intersectoral and interdisciplinary vision that today represents a fundamental pillar of large cooperative projects is becoming more and more strategic. Reconstructing and illustrating this evolution with the detail of the previous chapters is very difficult, if not impossible, for a single author. In front of a now almost contemporary knowledge, it would be arduous to see from above and organically a myriad of specialised rivulets that would require each one a new book. In any case, this approach would go beyond the objectives set by this work and the knowledge of the author. An alternative way is then followed: it aims at reconstructing and illustrating this evolution at a general level, giving also due importance to the associations, conferences, journals, books and initiatives that represent dominant aspects of the pulsating soul of this sector. In this spirit, entering into the details is avoided, pursuing a comprehensive picture of the literature that can direct the reader to the topics that mostly arouse his/her interest, without losing sight of the overall vision.

11.1 Wind Effects on Buildings and Structures In 1961, Davenport [1] published the celebrated paper (Sect. 9.6) in which the basic concepts of meteorology, micrometeorology, climatology, aerodynamics, wind loading, structural dynamics, and probability theory, referred to as the “Davenport chain” (Fig. 11.1) later depicted in [2], were first integrated into a homogeneous framework of the wind-excited response of structures; this paper opened new and unlimited prospects to the design and investigation of wind-sensitive structures creating a growing interest in engineering towards this topic [3]. Two years later, in 1963, Kit Scruton and his research group organised a symposium about Wind Effects on Buildings and Structures [4] in Teddington, UK, which represented a milestone. It was held under the auspices of the Aerodynamics Division of the National Physical Laboratory (NPL), in cooperation with the Building Research Station, the Institution of Civil Engineers and the Institution of Structural

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Fig. 11.1 Davenport chain [2]

Engineers. During that symposium, attended by 300 participants from 20 countries, 24 papers were presented in six plenary sessions concerning: (1) design wind speed, wind structure, wind loads on full-scale buildings; (2) experimental determination of wind loads in wind tunnels, wind clauses in codes and the response of structures to gusts; (3) aerodynamic oscillation of suspension bridges; (4) wind-excited oscillations of transmission lines, towers, stacks, and masts. The content of many papers has already been partly illustrated in Chap. 9 since they provided an overview and a state of the art for the research conducted in the years preceding that symposium. The percentage of these papers that still represent cornerstones is amazing [5]. Scrolling the index of the proceedings, Shellard [6] discussed the design wind speed, used the type I extreme distribution and order statistics to regress yearly maxima, and drew the first UK wind maps (Sect. 9.4); it is worth noticing that in a framework clearly devoted to synoptic winds, he provided without any comment one of the first pictures of a transient gust front (Fig. 11.2). Davenport [7] described the properties of the turbulent atmospheric boundary layer (ABL) for synoptic winds and neutral conditions, giving special regard to the relationships linking the surface wind speed with the gradient speed and the power law with the logarithmic profile. Newberry [8] discussed the requirements for proper full-scale measurements of the wind pressure on buildings, illustrating the pilot study carried out for the State House, Holborn (Fig. 11.3); he concluded “that the natural wind movements are not at all like those in a wind tunnel”. Douglas Baines [9] showed pictures of the flow field around models and of the pressure distribution on the walls of rectangularblock buildings as measured in a wind tunnel both in an artificially produced velocity gradient and in a constant velocity field (Fig. 11.4); he noted distinct phenomena only

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Fig. 11.2 Record of the wind speed and direction at Tiree, UK, 26 February 1961 [6]

on the front surfaces. Whitbread [10] sets out “the similarity requirements which need to be observed in order that the results of tests carried out in a wind tunnel may be used to predict the behaviour of the full-scale prototype in the natural wind”. Davenport [11] traced some evolutions of his recent approach to the loading of structures by gusts [1] (Sect. 9.6), describing field experiments aiming to inspect the aerodynamic response of structures to fluctuating turbulent flows (Fig. 11.5) and to extend his original applications to a variety of structures including long-span cables, suspension bridges, tall masts and skyscrapers. Selberg [12] reported his formula for the flutter wind speed of suspension bridges (Sect. 9.9). Walshe [13] described the investigations conducted at the NPL with reference to the design of the proposed long-span suspension bridges over the River Severn and Firth of Forth (Sect. 9.1) Hogg and Edwards [14], Parkinson [15], Richardson et al. [16] and Richards [17] summarised the previous studies and provided new advances on the galloping (Sect. 9.8) of slender elements studied by experimental and theoretical methods,

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Fig. 11.3 State House: a picture; b wind-pressure gauge in a window [8]

Fig. 11.4 Pressure coefficients of a cube: constant (a) and boundary layer (b) velocity field [9]

linear and nonlinear approaches and single- and multi-DOF models. Nakagawa et al. [18] proposed a random excitation model of the vortex shedding and discussed the efficacy of single helical strakes in various arrangements to mitigate vortex-induced vibrations (Sect. 9.7). Scruton [19] provided a general and unitary framework of aeroelastic phenomena (Sects. 9.7–9.9) and similarity criteria to reproduce them correctly using wind tunnel model tests. At the close of the Teddington symposium, an International Study Group on Wind effects on buildings and structures was constituted, with four aims [4]: (a) to produce a bibliography of wind effects on structures; (b) to keep a record of the research in

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Fig. 11.5 Square board and anemometer mounted in an open field [11]

progress; (c) to work for a standardization of symbols and nomenclature, and to bring together codes of practice; (d) to ensure that a further international conference was held. This last aim led to a series of international meetings (Table 11.1), the second, third and fourth of which were promoted by the International Study Group. In a period in which the tradition of publishing, the most relevant papers in the international journals had not yet become customary in this field, the proceedings of these conferences still offer today an extraordinarily valuable insight of the new tendencies that were gradually maturing and of the contributors who provided these tendencies with fundamental or pioneering advances. Even when, with the passage of time, the conferences will become more and more the occasion for the meeting of scholars and their proceedings will progressively lose importance in front of the pressing role of journals, the international conferences in Table 11.1 remain the proof of the appearance of new trends and of the major scientific and technical progress. The second conference on Wind Effects on Buildings and Structures, called International Research Seminar, was held in Ottawa, Canada, in 1967, and was chaired by Schriever [20]. It was organised by the Division of Building Research of the National Research Council of Canada with the support of Canada’s National Aeronautical Establishment, the Universities of Western Ontario and Toronto, and the Meteorological Service of Canada. The presence of 100 participants from 15 countries, compared to the 300 of the first conference, reflected the fact that this seminar was attended by invitation only. A total of 37 papers were presented, framed within four themes:

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Table 11.1 Wind Engineering International Conferences Number

Year

City

Country

Chair

1

1963

Teddington

UK

C. Scruton

2

1967

Ottawa

Canada

W. R. Schriever

3

1971

Tokyo

Japan

A. Hirai

4

1975

London

UK

K. J. Eaton

5

1979

Fort Collins

Colorado, USA

J. E. Cermak

6

1983

Gold Coast and Auckland

Australia and New Zealand

W. H. Melbourne

7

1987

Aachen

Germany

C. Kramer

8

1991

London

Canada

A. G. Davenport

9

1995

New Delhi

India

P. Krishna

10

1999

Copenhagen

Denmark

A. Damsgaard

11

2003

Lubbock

Texas, USA

K. C. Mehta

12

2007

Cairns

Australia

J. Cheung

13

2011

Amsterdam

The Netherlands

C. Geurts

14

2015

Porto Alegre

Brazil

A. Loredo Souza

15

2019

Beijing

China

Y. Ge & Q. Yang

(1) prediction and nature of wind near ground: climatic factors and boundary-layer characteristics; (2) determination of aerodynamic forces due to wind: wind tunnel modelling, theoretical modelling, and full-scale tests; (3) performance and response of particular structures: buildings, towers and chimneys, suspension bridges, simple geometric shapes, cables, shell roofs and others; (4) criteria for design against wind: performance criteria, acceleration, deflection, fatigue, etc., and code presentation. The conference opened with a keynote lecture by Jensen [21], who narrated the birth of the model law giving prominence to the human and personal sides of this discovery (Sect. 7.3). Davenport [22] discussed the dependence of wind loads on meteorological parameters, providing an impressive number of pioneering remarks. He started with a prophetic recommendation towards the performance-based design of structures, giving prominence to design limitations accounting for fatigue and deflection, to serviceability concepts and to the prediction of the statistical distributions of the response. He also dealt with the Van der Hoven spectrum (Sect. 6.7) summarising the properties of a suitable averaging period for defining the mean wind speed: (1) it should minimise non-stationarities within the period; (2) it should be short enough to reflect the maximum effect of a relatively short duration wind storm; (3) it should be long enough to allow the steady-state response of structure; (4) it should conform to standard meteorological observations. These remarks led him to conclude that the best choice was a period of 10–15 min. In addition, Davenport stated that wind should be studied with regard to its structure and statistics: the former referred to the mean wind velocity profile and atmospheric turbulence; the latter involved wind climate

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Fig. 11.6 Validation of the Weibull model of the parent wind speed in different sites [22]

analyses concerning the statistics of the wind speed population (Fig. 11.6) and of extreme wind speed. Davenport also studied the relationship between the distribution of the extreme wind speed and the parent distribution, noting that the Weibull tail inferred a type I distribution. He observed that difficulty in using this approach was due to the extreme value theory that assumed sample values independent of one another. Thus, he proposed to consider the wind speed as a random process, the parent distribution of which is a Rayleigh one, and derived a closed form solution of the type I parameters as a function of the power spectral density (PSD) of the macro-meteorological peak wind speed. Davenport concluded this paper with another prophetic viewpoint on intense local storms: “In formulating wind statistics—we wrote—the question has been posed as to whether intense local storms including tornadoes and thunderstorms conform to the wind structure of large-scale storms. Tornado probability is an order of magnitude different from other storm winds. A design approach based on fail-safe concepts is indicated. The question of thunderstorms is less clear cut. In certain parts of the

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world (…), a significant proportion of maximum gusts arise from thunderstorms. Whittingham [23], in his analysis of Australian wind conditions, shows that as much as 50% of maximum winds occur in thunderstorms. These storms may last 5–10 min and subside rapidly during which time severe convective turbulence may induce strong gusts. From the design point of view, the question is probably best treated by adopting an approach in which the mean velocities are obtained for intervals short enough to reflect the higher winds prevalent in the thunderstorm and assume turbulence response characteristic of other major storms. Eventually, it may be possible to treat thunderstorms separately and (…) prove important design accordingly”. This view anticipated the state-of-the-art by 30 years. Shiotani and Arai [24] performed simultaneous measurements of the wind speed by means of “five anemometers mounted on top of towers which are 40 m in height and were located at 0, 12, 35, 80 and 190 m points along the coastal line”, to determine the PSD, cross-PSDs, coherence functions and correlation coefficients of gusts. Singer et al. [25] noted that “in spite of a tremendous increase in the number of workers studying the meteorology of the lower part of the earth’s boundary layer, our knowledge about the characteristics and governing parameters of atmospheric turbulence is still limited due to the complex nature of the turbulent flow field. One of the cornerstones of the description of the structure of atmospheric turbulence is the Monin-Obukhov similarity hypothesis. (…) The insight already gained”, however, “is not fully applied to practical problems such as structural design. Most probably this is a result of the lack of communication between the atmospheric scientists and other disciplines”. Starting from asserting that “the present paper is educational in nature”, Authors discussed the mean wind velocity profile in neutral, unstable and stable conditions, the link between the Obukhov length and the Richardson number, the shear velocity, the turbulence spectra, covariance functions and integral length scales. They also provided many measurements and a huge literature on the evolution of atmospheric sciences in the period 1955–1967. It highlighted a systematic recourse to the publication of books and journal papers (e.g. the Journal of Geophysical Research, the Journal of Atmospheric Sciences and the Quarterly Journal of the Royal Meteorological Society), a custom not yet familiar to the community of this conference. Thom [26] employed the II type distribution for fitting the extreme wind speed, a choice that will not find consensus in the following years. In the same paper, he also highlighted that different phenomena such as extra-tropical cyclones, tropical cyclones and thunderstorms normally imply different extreme distributions: “this results in the annual extreme wind population being a mixture of extreme winds giving the mixed extreme value distribution function”. Dalgliesh et al. [27] described wind pressure measurements on a full-scale highrise office building in downtown Montreal (Fig. 11.7a), “to obtain basic information on the actual wind loading on buildings, to check the applicability of wind tunnel test results and to supply information on the fluctuating pressures”. Davenport and Isyumov [28] discussed the use of boundary-layer wind tunnels for the prediction of wind loading. First, they described four techniques aiming to modelling the natural wind through the model law: “(1) curved screens and grids of horizontal rods placed at varying spacing to model the structure of the mean wind speed; (2) coarse grids

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Fig. 11.7 a Full-scale pressure measurements on a building [27]; b boundary-layer wind tunnel, University of Western Ontario [28]

to produce large-scale turbulence superimposed on a uniform wind stream; (3) grids of flat plates with added turbulence and vortex generators, to model both the mean and the turbulence; (4) turbulent boundary-layer tunnels”. They also illustrated the new facility at the University of Western Ontario (Fig. 11.7b): the working section was 24-m long, 2.4-m large and adjustable in height between 1.7 and 2.3 m; the maximum wind velocity was 15 m/s. Scruton [29] classified the recent research on wind effects on buildings and structures under three headings: (1) the time-averaged wind loads and pressures, considering the effects of Reynolds number, the slenderness ratio, the velocity profile, the turbulence and the grouping effects; (2) the response to fluctuating forces due to atmospheric turbulence; and (3) the oscillatory and divergent instabilities due to wind, namely: (a) vortex shedding; (b) galloping excitation; (c) stalling flutter; (d) interference and buffeting effects; (e) classical flutter. Vickery and Davenport [30] presented a paper in which the “theoretical estimates of the loads acting on elastic structures and the response of these structures in turbulent flow are compared with model and full-scale observations. (…) In view of the extreme difficulty of obtaining accurate and reliable field data, the overall agreement between theory and observation can be regarded as satisfactory. The results obtained indicated clearly the importance of aerodynamic damping”. Wardlaw [31] analysed the wind-excited vibrations of slender elements with angle cross-sections, showing the importance of the coupled galloping in two directions. Hirai et al. [32] studied the critical wind velocity for suspension bridges by means of wind tunnel tests at the Department of Civil Engineering of the University of Tokyo (Fig. 11.8). The wind inclination could be varied by rotating deflectors over a range of ±10°. The tests demonstrated that the stability of bridges against wind loads depended not only on self-excited oscillations but also on the excessive lateral deflection or on the lateral buckling of their stiffening frames. The smallest velocity that gave rise to one of these three phenomena was the critical one. Melbourne’s and Styles’ [33] paper was a sort of singularity in a conference mainly focused on structural problems. At the same time, it was a forerunner of future wind engineering conferences aimed at embracing a wider range of wind issues. It described wind tunnel tests (Fig. 11.9) “on a model of the proposed new station near Wilkes (Antarctica) with a view to establishing a building layout and configuration

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Fig. 11.8 Wind tunnel tests at the University of Tokyo [32]

Fig. 11.9 Velocity profiles under and behind a 2D model of a rectangular hut with and without a semi-circular leading edge [33]

which would retain a maximum ground-level wind velocity over the area”, so as “to reduce the fall-out and consequent accumulation of wind-borne drift snow, and in critical areas under and near the main buildings to prevent it as completely as possible” (Sect. 8.4). A wide discussion occurred at the end of this conference, where delegates stressed the need to increase international cooperation, the dissemination of results to practicing engineers and the publicity of the Study Group. Others pointed out the advisability that the Study Group be associated with an international body such as the International Association of Bridge and Structural Engineering or the Comité Européan du Béton and Conseil International du Bâtiment. Though no formal decision was taken and the Study Group retained its informal status, a wide consensus was growing on the necessity of promoting better organisation and more liaisons.

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The next of these meetings [34], the Third International Conference on Wind Effects on Buildings and Structures, was held in Tokyo, Japan, in 1971, under the chairmanship of Atsushi Hirai. It was characterised by an impressive growth of the number of participants, approximately 215 from more than 20 countries, and of presented papers, over 100. These papers were framed into four groups: (1) characteristics of wind; (2) wind force and wind pressure; (3) design criteria, damage due to wind and static structural analysis; (4) dynamic behaviour of structures. Even in this case, the set of the presented papers provided a synthesis of the advances in this discipline. Some of these papers are milestones in wind engineering. Others were the forerunners of new lines of research. Trying to select the most relevant and innovative contributions, Melbourne and Joubert [35] discussed why tall buildings, when erected in a city or suburban environment, often brought severe wind problems to pedestrians at their base (Fig. 11.10); tentative criteria were developed for defining unacceptable wind velocities. Chang [36] illustrated a laboratory model of a tornado-like vortex (Fig. 11.11a) at the Catholic University of America [37]; it was used as an indirect tool to investigate tornado wind effects on buildings and structures. Cermak and Sadeh [38] carried out boundary-layer wind tunnel tests on a smallscale building model with emphasis on the local pressure fluctuations; they noted a striking similarity between the oncoming turbulent energy spectra and the surface pressure fluctuation spectra on the upwind face of a bluff-body (Fig. 11.11b). Standen et al. [39] described a method to simulate the natural wind boundary layer in a conventional, short working section; this approach was used to measure the wind pressure on a model of the CBC Building in Montreal; the same measurements were repeated using the long roughness fetch technique and the results were compared within an extensive programme of full-scale measurements.

Fig. 11.10 Flow field around a large building [35]

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Fig. 11.11 a Sectional view of a laboratory tornado funnel [36]; b turbulence and pressure fluctuation spectra on the upwind face of a building [38]

Wen and Shinozuka [40] described a Monte Carlo method for the simulation of multivariate and multidimensional homogeneous random processes [41]; it was used for evaluating the maximum structural response of a nonlinear plate excited by a random wind load. Khan and Parmalee [42] noted that the sway motion of a tall building in a turbulent wind [43], if perceptible, may produce psychological effects which rendered the building uncomfortable for the occupants; the reduction of such motion to acceptable levels thus became an important criterion in the design of tall buildings. Wyatt and May [44] studied the accumulation of plastic deformation and the ultimate load behaviour of simple inelastic structures under wind loading. Ang and Amin [45] formulated a comprehensive probabilistic method for wind-resistant design based on acceptable risk. Cooper and Wardlaw [46] studied, through wind tunnel and full-scale tests, the aeroelastic instabilities due to wake interference in groups or arrays of parallel slender structures. Yamaguchi et al. [47] inspected the vibrations caused by vortex shedding on slender bridge members and their countermeasures. Laneville and Parkinson [48] investigated turbulence effects on the galloping of bluff cylinders in a wind tunnel and by quasi-steady theory: increasing the turbulence intensity made square, rectangular and D-section elements less unstable; quasi-steady theory correctly predicted these trends. Novak [49] analysed the galloping and vortex-induced oscillations of prismatic bodies (Fig. 11.12); he showed that galloping oscillations could arise with

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Fig. 11.12 Lateral response of a tall building model with side ratio b/h = 2 in a smooth flow [49]

cross-sections that were aerodynamically unstable and also with those that were stable, provided that an initial amplitude triggered the vibration [50]. Okubo et al. [51] carried out wind tunnel tests of the Kanmon suspension bridge girder deck with reference to 22 cross-section designs, in order to find a solution that satisfied the provisions of design criteria. Wardlaw [52] investigated the edge modifications of a recently completed Canadian cable-stayed bridge that was observed to vibrate; they were installed on the real bridge preventing further motion. Scanlan’s paper [53] was a milestone and proposed a novel “basic analytical model for bridge flutter”, using the corresponding problem for airfoils “as an invaluable guide towards”. With this aim, Scanlan considered a bridge deck sectional model with 2 DOF, h and α (Fig. 11.13a), and expressed the equations of motion as:     ˙ α, ˙ α m h¨ + 2ξh ωh h˙ + ω2h h = L h h,

(11.1a)

    ˙ α, ˙ α I α¨ + 2ξα ωα α˙ + ω2α α = Mα h,

(11.1b)

where m and I are the mass and the torsional mass moment of inertia, respectively, ωh and ωα are the vertical and torsional fundamental circular frequencies, respectively, ξh and ξα are the corresponding damping ratios, L h and Mα are the self-excited lift force and torsional moment given by:   ˙  1 2 ˙ ∗h ∗ bα 2 ∗ ˙ ˙ α = ρv (2b) k H1 + k H2 + k H3 α L h h, α, 2 v v     1   bα˙ h˙ ˙ α, ˙ α = ρv2 2b2 k A∗1 + k A∗2 + k 2 A∗3 α Mα h, 2 v v 

(11.2a) (11.2b)

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Fig. 11.13 Bridge deck aerodynamics [53]: a 2 DOF system; b deck cross-sections; c nondimensional aerodynamic coefficients

where k = ω b/v is the reduced frequency, b is the half-deck width, ω is the circular frequency, v is the wind velocity, Hi∗ , Ai∗ (i = 1, 2, 3) are non-dimensional aerodynamic coefficients depending on k, namely the flutter derivatives, shown in Fig. 11.13c for various deck cross-section shapes (Fig. 11.13b). Scanlan pointed out that Eqs. (11.1) and (11.2) were expressed in real form, whereas most previous authors preferred the complex form corresponding to Theodorsen’s theory (Sects. 7.4 and 9.9). He also stressed that flutter aerodynamic actions had to be determined by experimental tests: on the one hand, he noted the clear distinction between airfoil results and those for the several deck types; on the other, he stated that “the fundamental reason for the failure of the airfoil theory in application to bridge flutter was that most bridge decks are bluff bodies for which the flow separates, creating complex events in the wake”. He also commented that “fixed model tests or steadyflow theory are also inadequate to the problem since primary roles are played by the aerodynamic damping terms” and discussed “the relative merits of obtaining experimental aerodynamic coefficients by the driven model [54, 58] versus the free oscillation [55–57] type of testing”. Saffir [59] described the Hurricane Camille that hit the Gulf Coast of the USA, providing extensive meteorological data (Fig. 11.14a) and damage survey (Fig. 11.14b). Similarly, Chang [60] described the giant Lubbock Tornado and its damage (Fig. 11.15); preliminary criteria on tornado-resisting building and new concepts of city-storm-preparedness were also outlined. During this conference, important decisions were taken by the International Study Group [34]: (1) after the three conferences held in the European and African Region (Teddington, UK, 1963), in the American Region (Ottawa, Canada, 1967), and in the Asian and Australasian Region (Tokyo, Japan, 1971), this rotation of conference venues had to continue; (2) Newberry, Schriever and Ito were appointed for EuropeAfrica, North and South America, and Asia-Australasia, to update the list of the

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Fig. 11.14 Hurricane Camille [59]: a meteorological data; b damage survey

Fig. 11.15 Lubbock Tornado [60]: a pattern; b damage to First National Bank & Gas Building

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members of the International Study Group, and to find a suitable host for the next conference; (3) despite a long discussion, it was agreed that the time was not yet ripe for the setting-up of an International Association for Wind Effects on Buildings and Structures; (4) it was stressed the importance that a greater use might be made of the Journal of Industrial Aerodynamic Abstracts, as a medium for communicating current developments and research; and, (5) an offer made by the Japanese Secretariat, aimed at publishing a collection of national codes of practice and specification relating to wind resistant design of structures, was accepted. Following this decision, in 1975, a Japanese committee, chaired by Hisada, published a book [61] that collected the regulations of 29 countries. In the same year, the first issue of the Journal of Industrial Aerodynamics was published, edited by Ian Raymond Harris, who wrote: this “seems to be a good place to set out the background to the new journal and what it aims to achieve in future” [62]. Harris pointed out that “in European usage the term industrial aerodynamics could strictly mean any non-aeronautical aerodynamics, which, in theory, could cover an enormous range of subjects. However, many non-aeronautical flow studies (…) are already well-established as branches of Mechanical Engineering, and by common consent industrial aerodynamics has come to mean the study of the large class of topics associated with natural wind flows. For this reason, in North America the term ‘wind engineering’ is commonly used as an equivalent to the European usage of industrial aerodynamics”. “Experimental work has been undertaken in the form of full-scale measurements of wind and wind effects, and in the form of model studies in wind tunnels. It is now known that some of these studies, particularly those using standard aeronautics wind tunnels which were unsuitable for the purpose, gave misleading results. On the other hand, some of the early full-scale studies can now be seen as really remarkable feats of experiments, given the limitations of the instrumentation, recording techniques and data processing methods then available”. “In the last 20 years, industrial aerodynamics has developed very rapidly indeed. The post-war boom in construction and changes in construction methods have, in many cases, changed the role of wind effects from a subsidiary consideration to a major design parameter. Advances in instrumentation, recording and data processing technology have made large full-scale experiments a practical proposition, and many such experiments have been undertaken. During the same period, effective methods of simulating in a wind tunnel, the relevant features of flow in the earth’s boundary layer have been developed, and wind tunnels, especially suited to this purpose have been built and used for a wide range of experiments. Finally, the availability of large, fast digit computers has enabled more progress to be made in the theoretical treatment of problems”. “Industrial aerodynamics involves a very wide range of disciplines including meteorology, instrumentation technology, classical aerodynamics and fluid mechanics, turbulence, random vibration and structural dynamics, and civil and structural engineering. In the absence of a specialist journal for industrial aerodynamics, papers have been published in one of the journals devoted to constituent disciplines, or have been contributed to one of the numerous symposia which have been held. As a result,

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much of the work is relatively inaccessible. The aim of the new Journal is to provide a convenient place where work can be published and will therefore be accessible in the future.” Accordingly, the content of the first issue of the Journal of Industrial Aerodynamic looks like a declaration of the new potentialities in instrumentation and wind monitoring of structures. In particular, Davenport [63] “discusses the historical role that full-scale observations have played in the development of engineering approaches to wind effects. These observations have not only provided vital clues for successful theories but also provided the verification needed before a theory can be proclaimed successful”. However, “many difficulties and uncertainties associated with individual full-scale experiments make it desirable to view full-scale experiments in a collective manner”. Dalgliesh [64] compared full-scale and wind-tunnel tests on the Commerce Court Tower in Toronto, exhibiting satisfactory agreement; large pressure fluctuations occurred on the windward and side walls, whereas they were less important on the leeward wall (Fig. 11.7a). Eaton and Mayne [65] described the first extensive full-scale tests on a low-rise building at Aylesbury, 65 km north-west of London; tests were made for a variety of wind speeds and directions, and for several roof pitches between 5° and 45° (Fig. 11.16). Isyumov and Davenport [66] compared full-scale and boundary-layer wind tunnel tests on a plaza in a built-up urban environment, showing encouraging agreement (Fig. 11.17). Muller and Nieser [67] illustrated measurements of the wind velocity and structure vibration made on a concrete chimney 180-m high in south Germany; theory agreed with measurements if the cross-correlation of the wind velocity was taken into account (Fig. 11.18). Deaves [68] described a numerical approach to evaluate the wind speed over hills; the results for some particular hill shapes agreed fairly well with experimental and theoretical data [69, 70]. The Fourth International Conference on Wind Effects on Buildings and Structures, held in London, in 1975, under the chairmanship of Keith Eaton [71], was attended by 200 delegates from 26 different countries. It included eight sessions: four of the classic type, dealing with wind structure, static and dynamic loading, and dynamic response, two novel sessions about environmental effects and measurement techniques, and two sessions discussing practical applications and design relevance, aiming to strengthen the link between scholars and practitioners. An associated sym-

Fig. 11.16 Two-storey Aylesbury house with three roof pitches: a 5°; b 22.5°; c 45° [65]

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Fig. 11.17 Wind speed in a plaza located in a built-up urban terrain [66]: a plan of measuring sensors; b measurements for several wind directions

Fig. 11.18 Oscillation amplitude of a reinforced concrete chimney versus wind speed [67]

posium, Designing for Wind, was also held on the last day and was joined by 100 additional delegates. Among the most relevant or new contributions, Duchène-Marullaz [72] described the wind measurements made by means of three 60-m high masts at the Centre Scientifique et Technique du Bâtiment (CSTB) on the outskirts of Nantes, France. Taking a cue from [70], Jackson [73] illustrated an analytical theory for a turbulent boundary-layer flow on low two-dimensional humps with a small slope; escarpments were examined in detail (Fig. 11.19). Gandemer [74] noted that buildings, with their shapes or settings, could cause unpleasant high speeds or vortices in pedestrian areas; model tests in the CSTB. wind tunnel were carried out with reference to 12 situations for which full-scale measurements were also developed (Fig. 11.20). Lawson and Penwarden [75] examined the mechanical and thermal effects of wind on the people in the vicinity of buildings, proposing remedial actions and probabilistic acceptability criteria.

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Fig. 11.19 Velocity deficit over an escarpment [73]

Fig. 11.20 Pedestrian areas [74]: a Venturi effect; b downwash vortex at the foot of buildings

Whitbread [76] pointed out that the studies of non-steady wind loading on building models were mainly concentrated on the wind-pressure distribution; dynamic forces and deflections were measured using more complex aeroelastic models to a much lesser extent; “the approach adopted (…) is that of measuring the quasi-static force spectrum which is independent of the frequency and damping of the model” by a force balance at the base of the building model (Fig. 11.21); “it is then proposed that in-wind dynamic-force spectra for particular buildings may be predicted with reasonable accuracy using calculated mechanical admittance function”. Taking a cue from the recent advances in the dynamic alongwind response of structures [77–82], Simiu [83] illustrated a numerical procedure that incorporated new issues about the logarithmic velocity profile, the dependence of the longitudinal wind velocity spectrum upon the height above ground, the cross-correlation of fluctuating pressures on the windward and leeward faces, the role of higher modes of vibration, and the acceleration; a simplified version of this procedure was illustrated for practical engineering use. Melbourne [84] discussed the cross-wind forcing mechanisms, dividing them into categories associated with the wake, the incident turbulence and the crosswind motion. Konishi et al. [85] expressed the aerodynamic

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Fig. 11.21 a Complete model assembly; b general arrangement of the balance [76]

Fig. 11.22 Tornado risk evaluation [88]

admittance of trussed bridge sections by means of the Sears, Wagner and Kussner functions. Sfintesco and Wyatt [86] described a proposed European code of practice developed by the European Convention for Constructional Steelwork (ECCS) that incorporated stochastic process analysis [87]. Wen and Ang [88] proposed a model of the wind field in a tornado vortex from which drag and inertial forces were determined, evaluated the structural elastic and inelastic response to tornadic winds, performed risk analyses and the probability of severe wind effects was inspected considering structural size and layout geometry (Fig. 11.22). Kind [89] carried out wind tunnel tests to find the wind speeds that caused the scouring and blow-off of rooftop gravel; he noted the occurrence of a vortex pair along the front edges of the roof when the flow was diagonal. Saffir [90] examined the effects of high winds on glass and curtainwall (Fig. 11.14), stressing the necessity of developing appropriate design criteria. As regards to organisational aspects, crucial decisions were taken for the future of wind engineering. The Steering Committee Meeting of the International Study Group

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Table 11.2 IAWE regional secretaries and coordinators Period

America

Asia and Australasia

1971–1975

W. R. Schriever

M. Ito

Europe and Africa C. W. Newberry

1975–1979

R. Parmalee

W. H. Melbourne

H. Van Koten

1979–1983

R. Parmalee

G. R. Walker

H. Van Koten

1983–1987

J. E. Cermak

P. Krishna

H. Van Koten

1987–1991

J. E. Cermak

T. F. Sun

D. Sfintesco

1991–1995

J. E. Cermak

T. F. Sun

N. J. Cook

1995–1999

A. Kareem

S. Murakami

G. Solari

1999–2003

A. Kareem

J. D. Holmes

G. Solari

2003–2005

A. Kareem

J. D. Holmes

C. J. Baker

2005–2009

A. Kareem

K. Kwok

C. J. Baker

2009–2013

L.S. Cochran

K. Kwok

R. Hoffer

2013–2017

L. S. Cochran

Y. Ge

R. Hoffer

2017–2021

J. Galsworthy

You-Lin Xu

G. Bartoli

decided [71]: (a) to regularly update the international collection of wind resistant design regulations [61], appointing Ito as the chairman of the Japanese Committee in charge to prepare its first issue; (b) to found the International Association for Wind Engineering (IAWE), aiming to widen the field of the topics initially concerning wind effects on buildings and structures; (c) that next meetings should be called International Conferences on Wind Engineering (ICWE); (d) that IAWE Chairman should also be the next ICWE Chairman; and, (e) the appointment, in the previous tradition, of three Regional Secretaries for the Europe-African, American, and AsiaPacific regions (Table 11.2). Despite a long discussion and the proposals raised by Sfintesco on the opportunity of giving the IAWE a formal organisation, no action was agreed in such direction. The decisions ripened at the London conference laid the foundations of the organisation of wind engineering up to the end of the second millennium, giving rise to a major turning point: wind engineering, born around the study of wind effects on buildings and structures, came to embrace a wider set of issues and, therefore, a wider community. This new reality was testified by a growing number of events that took place in the period 1963–1978 and were the roots of a growth destined to become irrepressible in a short time. The first national wind engineering bodies were founded in the 1970s, like the US Wind Engineering Research Council (1970), the Canadian Wind Engineering Association (1976) and the Japan Association for Wind Engineering (1976). Besides the international conferences, many meetings were held on specific topics, e.g. The Seminar on Modern design of wind-sensitive structures, organised by the Construction Industry Research and Information Association (CIRIA) in London, (1970), chaired by A. J. Harris, the first Japanese National Symposium on Wind engineering (1970) and the first US National Conference on Wind engineering (1970), the first Collo-

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quia on Industrial aerodynamics in Aachen, Germany (1974, 1976, 1978), chaired by Carl Kramer and Hans-Juergen Gerhardt, the Symposium on Full-scale measurements of wind effects on tall buildings and other structures, in London, Ontario (1974), chaired by Alan Davenport, the Symposium on Tornadoes assessment of knowledge and implications for man, in Lubbock, Texas (1976), chaired by Abbey Jr. and Kishor Mehta. The first wind engineering books were published in this period by Sachs [91], Ghiocel and Lungu [92], Houghton and Carruthers [93], Aynsley et al. [94], Simiu and Scanlan [95]; the first edition of the latter, a milestone of wind engineering was issued in 1978. At the same time, many other books were published which, although not strictly related to wind engineering, provided such support to its evolution to rapidly become irreplaceable cornerstones of this matter. The books by Papoulis [96] on probability theory and random processes, by Gordon [97] and Holton [98] on dynamic meteorology, by Lumley [99] and Tennekes and Lumley [100] on turbulence, by Rae and Pope [101] on wind tunnel testing, by Crandall and Mark [102] and Lin [103] on random dynamics, and by Blevins [104], on flow-induced vibrations, stand out among them. Lumley’s book [99] also represented a milestone for proper orthogonal decomposition (POD)1 [105–107]. In the same period, some reports that still retain the role of reference points [108–113] were also issued. The reports issued by the Engineering Sciences Data Unit (ESDU) in the Wind Engineering Series deserve a special mention. The first ones were issued in 1971 [114, 115] and dealt with bluff-body aerodynamics. They were followed by an issue on the characteristics of atmospheric turbulence near the ground in 1974 [116] and by another issue about the response of flexible structures to atmospheric turbulence in 1976 [117]. They opened the way to an impressive series of high-level documents that strongly influenced wind engineering practice and research. In parallel, taking a cue from the Journal of Industrial Aerodynamics, published from 1975, the Japanese Journal of Wind Engineering was issued from 1976; Wind Engineering was published from 1977 to deal with wind energy technology; Engineering Structures, the journal of earthquake, wind and ocean engineering, was published from 1978. Other journals were increasingly populated by papers on wind engineering, e.g. the Proceedings of the Institution of Civil Engineers and the Journals of Engineering Mechanics and Structural Engineering, issued by the American Society of Civil Engineers (ASCE), causing a progressive transition from conference proceedings, as the main venue of these contributions, to international journals. New journals about atmospheric sciences, e.g. Monthly Weather Review, Atmospheric Environment, Boundary-Layer Meteorology, and the Journal of Applied Meteorology, strengthened this new trend. 1 The use of POD in fluid dynamics and turbulent flows originated from Lumley [105], who proposed

an attractive definition of organized or coherent structures, the characteristic eddies, and a method to extract them from a stochastic turbulent field through a linear combination of the eigenfunctions of its two-point covariance tensor. In 1970, he published his fundamental contribution to POD [99]; even if partly masked by complex mathematical developments and notations, it contained most of the future advances made on POD in any context [106, 107].

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Fig. 11.23 Contour of equal amplification factors over various escarpment slopes [130]

Choosing some of the papers that most contributed to the development of knowledge in this field and that would become in the future highly cited ones, Blackadar [118], Counihan [119] and Garratt [120] provided vivid pictures of the ABL. Csanady [121], Tennekes [122] and Simiu [123] contributed to establish the use of the logarithmic velocity profile. Paulson [124], Webb [125] and Businger et al. [126] discussed the properties of the ABL in neutral and non-neutral conditions. Panofsky and Townsend [127] and Antonia and Luxton [128, 129] investigated the effects of roughness changes. Taylor and Gent [69], Jackson and Hunt [70] and Bowen and Lindley (Fig. 11.23) [130] studied topography effects. Orography effects were investigated by Klemp and Lilly [131] and Clark and Peltier [132]. Research on atmospheric turbulence and its spectral properties was reported by Busch and Panofsky [133], Fichtl and McVehil [134], Pielke and Panofsky [135], Kaimal et al. (Fig. 11.24) [136], Wyngaard and Coté [137], Kaimal [138] and Kaimal et al. [139]. Gomes and Vickery [140] and Takle and Brown [141] made key contributions to wind speed statistics; Gomes and Vickery (Fig. 11.25) [142] pioneered the novel conception of extreme statistics in mixed climates. Tropical cyclones were studied by Smith [143], Russell [144] and Tryggvason et al. [145]. Tornadoes were investigated by Hoecker [146], Thom [147], Fujita [148] and Wen and Chu [149]; laboratory simulations of tornadoes were provided by Ying and Chang [37], Wan and Chang [150] and Ward [151]. Pioneering studies about thunderstorm downbursts were conducted by Ogura [152] and Mitchell and Hovermale [153] numerically, by Charba [154] by means of laboratory tests, and by Goff [155] through field measurements. The sector of bluff-body aerodynamics populated itself with contributions related to single cylinders—Vickery (Fig. 11.26) [156], Lee 2 [157]—and interfering 2 Armitt [108] pioneered the use of POD in bluff-body

aerodynamics by investigating the full-scale pressure measurements of a cooling tower. Without any reference to Armitt, Lee [157] represented

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Fig. 11.24 Logarithmic spectra (a) and cospectra (b) of the three turbulence components (u, v, w) and potential temperature (θ) [136]

Fig. 11.25 Extreme gust speeds for Onslow (a) and Brisbane (b) [142]

ones—Bearman and Wadcock [158], Zdravkovich [159], Zdravkovich and Pridden [160]—as well as with papers about the wind loading of buildings. The latter included studies about boundary-layer wind tunnels and those modified to achieve the formation of the boundary layer—Armitt and Counihan [161], Counihan [162], Cermak [163], Cook [164]—low-rise buildings—Eaton and Mayne [65], Surry and Stathopoulos [165], Morgan and Beck [166], where the effects of repeated wind loading were examined—high-rise buildings and cladding—Dalgliesh [64, 167], the covariance matrix of the circumferential pressure derived from wind tunnel tests on a twodimensional square cylinder in uniform and turbulent flows in terms of POD modes.

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Fig. 11.26 Spectrum (a) and span-wise correlation (b) of the lift fluctuations on a square-section cylinder [156]

Fig. 11.27 Probability density of pressure fluctuations in correspondence of a mean pressure coefficient: a greater than −0.1; b smaller than −0.25 [168]

Paterka and Cermak (Fig. 11.27) [168], Eaton [169]—interference between adjacent buildings—Paterka and Cermak [170], Reinhold et al. [171]. Sarpkaya [172, 173] investigated transient aerodynamics. Following the pioneering research conducted by Davenport [1] in the early 1960s (Sect. 9.6), Davenport himself [77, 78], Vellozzi and Cohen [79] and Simiu [80, 81, 174] gave new contributions to the dynamic alongwind response of structures. ESDU [117] and ECCS [175] introduced the tendency to evaluate wind loading effects (e.g. displacements, bending moments and shear forces) by means of the influence function technique. Shinozuka [41] and Shinozuka and Jan [176] introduced the use of Monte Carlo method to simulate multi-variate and multi-dimensional random processes; Shinozuka [177] applied this method to calculate the dynamic response of struc-

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Fig. 11.28 a Motion simulator; b threshold of perception of vibration [185]

tures. Following the line drawn by Davenport [77], Crandall [178] and Vanmarcke [179] studied the threshold crossing and formulated new models of the distribution of the maximum value. Vaicaitis and Simiu [180] and Soize [181] first studied the role of the quadratic term of turbulence in the dynamic response of structures. Vickery [182] inspected the elasto-plastic behaviour of structures under wind actions. Davenport [183] and Vaicaitis et al. [184] studied the alongwind, crosswind and torsional response of suspension bridges and tall buildings, respectively. Chang [43], Chen and Robertson (Fig. 11.28) [185] and Hansen et al. [186] opened one of the most classic and prolific sectors of wind engineering, the human response to the wind-induced motion of buildings (Sect. 9.2). Fundamental studies about vortex shedding were carried out by Gerrard [187] and Berger and Wille [188]. Vortex-induced vibrations (VIV) of cylinders were examined by Marris [189], Hartlen and Currie (Fig. 11.29a) [190], Skop and Griffin [191] and Iwan and Blevins [192]. Following Scruton (Sect. 9.7), new studies on the crosswind response of structures to vortex shedding were carried out by Wootton (Fig. 11.29b) [193], Walshe and Wootton [194] and Vickery and Clark (Fig. 11.30) [195]. As reported in Sect. 9.8, fundamental contributions to galloping were made by Parkinson and Brooks [196], Parkinson and Smith [197], and Novak [50, 198]. After the pioneering articles by Sabzevary and Scanlan [55, 56], the celebrated paper by Scanlan and Tomko [199] was a milestone for bridge aeroelasticity and flutter; followed by other contributions of the first author and his co-workers [200, 201], it was a turning point in wind engineering. The first modern papers about the vulnerability of buildings and cladding were provided by Minor et al. [202, 203]. Sugg [204] and Galway [205] illustrated the risk due to hurricanes and tornadoes, respectively. Davenport [206] published another pioneering contribution to structural safety and reliability under wind actions. In the wake of the research conducted by Melbourne and Joubert [35], the growing interest of scientific community towards pedestrian wind environment (Sect. 8.6) was stressed by Hunt et al. [207], Melbourne himself (Fig. 11.31) [208], Gandemer [209] and Penwarden et al. [210].

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Fig. 11.29 Crosswind response by: a Hartlen and Currie [190]; b Wootton [193]

Fig. 11.30 Normalised spectrum (a) and cospectrum (b) of crosswind pressure fluctuations [195]

Fig. 11.31 Comparison of various criteria for environmental wind conditions [208]

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Finally, it is worth noticing the debut of the first key contributions to Computational Fluid Dynamics (CFD). Deardoff [211] proposed a three-dimensional numerical model of turbulence at large Reynolds numbers, pioneering the use of Large Eddy Simulation (LES) based on the standard Smagorinsky model. Lauder and Spalding [212] applied Reynolds Averaged Navier–Stokes (RANS) equations.

11.2 The Birth of Wind Engineering The Fifth International Conference of the series of the meetings begun in Teddington, UK, 1963 (Sect. 11.1), was held in Fort Collins, Colorado, 1979, under the chairmanship of Jack Cermak [213]. It was also the first International Conference on Wind Engineering (ICWE). The conference included ten sections. Besides traditional contributions about wind structure and climate, bluff-body aerodynamics, dynamic and aeroelastic effects on structures, four innovatory sections were organised, just in the spirit of the new course: the first was addressed to the “Social and economic impact of wind storms”, in consideration of the ever-increasing economic losses due to the wind (Chap. 10); the second, “Local wind environment”, dealt with wind erosion (Sect. 8.3), natural ventilation and pedestrian comfort (Sect. 8.6); the third, “Physical and mathematical modeling”, included papers about stack gas dispersion (Sect. 8.2) and snowdrift (Sect. 8.4), stressing the use of wind tunnels for modelling the flow over complex terrain; the fourth, about “Wind engineering applications”, joined traditional studies on structural design with analyses about the dispersion of chemical vapours and natural gas, the siting of wind turbines (Sect. 8.1), and train aerodynamics (Sect. 7.7). As in the past, the organising committee selected some 100 papers out of 250 complete proposals submitted for presentation. This choice was originated to keep the average quality of the presentations high and to avoid parallel sessions as in previous meetings. Due to such choice, the Organising Committee decided to not include a technical session on “Wind-power generation” (Sect. 8.1). It is possible that this choice has contributed to definitively separate the two worlds of wind engineering and wind energy. Following the index of the proceedings, Session I “Social and economic impact of wind storms” reflected three major trends: the basic information as to the nature and extent of losses in property and life as a result of windstorms; the variety of measures taken to cope with their effects; the modes in analysing the decision as to what types of action should be taken by both individual and public managers of vulnerable property. Session II “Wind—characteristics and descriptions” contained two quite distinct parts. The first part dealt with intense wind phenomena, examining their properties for different wind types; taking inspiration from the paper by Gomes and Vickery about mixed climatology [142], Golden and Abbey [214] provided a state-of-theart of hurricanes, downslope mountain windstorms, tornadoes, thunderstorm wind gusts and downbursts; other papers dealt separately with different winds, especially

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Fig. 11.32 Aerodynamic admittance function [221] for: a various prisms; b surface points

tornadoes and tropical cyclones. The second part concerned the classical themes of the measurement and representation of the turbulent ABL. Session III “Local wind environment” gathered papers about a varied and complex area of research. In the wake of the pioneering studies by Melbourne and Joubert [35] and Gandemer [74], the pedestrian wind comfort around tall buildings remained the core of this session; this was enriched by new wind tunnel measurement techniques, by the analyses of the damage suffered from low-rise buildings close to high-rise buildings, by Aynsley’s study [215] about the wind generated natural ventilation of housing for thermal comfort, by the wind tunnel investigations conducted by Paciuk and Poreh [216] to inspect the ground-level environment in an open stadium, by an outdoor observation of over 2000 persons, carried out by Murakami et al. [217] in order to define suitable acceptance criteria for pedestrians, and by several basic studies on the wakes behind bluff-building. Sessions IV and V “Wind loading” provided an extensive sample of studies on bluff-body aerodynamics. Among these, Kim and Mehta [218] presented experiments, data acquisition, and roof uplift load measurements at the experimental building station in Lubbock, Texas; Blessmann and Riera [219] studied the interaction effects in neighbouring tall buildings; Holmes [220] conducted a novel research on mean and fluctuating internal pressures; Kawai et al. [221] investigated pressure fluctuations on the windward wall of a tall building, examining aerodynamic admittance (Fig. 11.32). Sessions VI and VII “Dynamic response” counted on many papers destined to be reference points. Kareem et al. [222] (Fig. 11.33), Reinhold and Sparks [223] (Fig. 11.34), and Sidarous and Vanderbilt [224] investigated the 3D response of tall buildings, Wawzonek and Parkinson [225] studied galloping and vortex resonance interaction, Kwok and Melbourne [226] elucidated the transition from random to deterministic response in lock-in conditions (Fig. 11.35), Shiraishi and Ogawa [227] used 2D sectional models to analyse 3D long-span bridges, Davenport [228] examined the gust factor for transmission lines. Sessions VIII and IX, “Physical and mathematical modelling” and “Wind engineering applications”, included a variety of papers that took up classic themes of wind science, temporarily shelved during the conference cycle limited to wind actions and effects on structures (Sect. 11.1); they dealt with stack gas and chemical vapour dispersion, snowdrifting, smoke movement within and around buildings, airport pol-

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Fig. 11.33 Spectral density matrix of crosswind forces at five levels of a tall building model [222]

Fig. 11.34 a Alongwind force, and b crosswind force modal spectra [223]

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Fig. 11.35 Crosswind response of a circular tower model [226]

lution, solar power plants, train aerodynamics, and other miscellaneous topics. Session X, “Wind-engineering practice” provided an extensive overview of wind loading codes and on methods finalised to this field. Further to these scientific and technical aspects, the 5th ICWE was fundamental for some key decisions taken by the IAWE Steering Committee Meeting. It was established that: (a) an effort had to be made at next conferences in order to include “Wind power”; (b) the IAWE Chairman compiled a draft of IAWE by-laws for consideration at the next ICWE; (c) the Editor of the Journal of Industrial Aerodynamics was to be approached by the ICWE Chairman, with a view towards the addition of a masthead statement representing it as the official IAWE journal; and, (d) an initiative aiming to establish an up-to-date document on worldwide wind codes was to be endorsed by the IAWE. Following these decisions, since 1980, the Journal of Industrial Aerodynamics became the Journal of Wind Engineering and Industrial Aerodynamics (JWEIA) and the official IAWE Journal. In 1982, a new compilation of Wind Resistant Design Regulations [229] was published under Ito’s chairmanship; it included the revision of some national codes, based on the wind engineering progress, and a few wind codes that were missed in the first edition [61]. The new IAWE Chairman, William (Bill) Melbourne, compiled and circulated a draft of the IAWE by-laws, to be subsequently submitted to the IAWE Steering Committee Meeting at the 6th ICWE, to be held in Gold Coast and Auckland (Australia and New Zealand, 1983). The document, made up of six articles, was quite short, simple and informal. Summarising its relevant aspects: (1) IAWE has two principal aims: the organisation

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of international meetings and the liaison with national and international organisations working in similar fields; (2) IAWE is governed by a Steering Committee which meets every four years at the ICWE venue. The IAWE Chairman is the ICWE Chairman. The Steering committee consists of one member from each country, plus an additional member for countries with a large number of representatives, and five additional representatives co-opted by Chairman; (3) IAWE is administered by the Chairman through Regional or National Secretaries; (4) IAWE uses the JWEIA as its official organ; (5) there is no formal IAWE membership, and membership is granted to ICWE registered participants; (6) the Steering Committee is vested with the responsibility to accept the proposal from a country to host the next ICWE. The ICWE venues are to rotate in sequence through the Europe-Africa, North and South America, and Asia-Australasia regions [230]. The Steering Committee Meeting at the 6th ICWE resolved to adopt these bylaws until the next meeting at the 7th ICWE and that such by-laws were circulated for discussion, with the aim of formal ratification at the next Steering Committee Meeting. In addition, it was resolved that IAWE endorsed the International Aylesbury Project and encouraged as many wind tunnel laboratories as possible to participate in it; with this goal, the first IAWE Committee was appointed composed by Davenport, Holmes and Cook. It was also resolved that IAWE endorsed the use of the term “Scruton Number” for the mass-damping parameter (Eq. 9.66), as a recognition of the contribution of Kit Scruton to wind engineering; this decision sounds as the first IAWE award to an eminent scientist. Dealing with the scientific and technical contents of the 6th ICWE, its layout was similar to the previous one. The major block of sessions dealt with wind, bluff-body aerodynamics, wind-excited response and structural aeroelasticity; some sessions on environmental wind engineering—natural ventilation, heat losses, dispersion of gaseous pollutants and shelters—were organised. Following a suggestion raised at the 5th ICWE, three specific sessions on wind power systems were held at the end of the conference. This decision was not sufficient to establish a sound and renewed cooperation between the wind engineering and wind energy communities. Despite common topics and joint objectives, these sectors will follow, till now, fairly independent ways, strategies and plans. Among the most significant and original contributions presented at the 6th ICWE, Isyumov and Poole [231] elucidated the wind-induced torque on square and rectangular building shapes. Kawai [232] investigated the applicability of strip and quasisteady theory for determining pressure fluctuations on square prisms. Tschanz and Davenport [233] introduced the high-frequency force-balance technique to evaluate dynamic wind loads through wind tunnel tests. Schuëller et al. [234] investigated the propagation of uncertainties in the reliability assessment of structures. Ruscheweyh [235] studied the aeroelastic interference between slender structures (Fig. 11.36). Vickery and Basu [236] spread their novel model of the crosswind response of chimneys [237, 238]. Kwok [239] described the effectiveness of tuned mass dampers by full-scale measurements at the Sydney Tower. Shiraishi and Matsumoto [240] classified the vortex-induced oscillations of bridges. Tachigawa [241] made pioneering studies on the trajectories of typhoon-generated missiles. Solari [242] illustrated and

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generalised his closed form solutions (Fig. 11.37) [243] to determine the alongwind response of structures. A dominant aspect of these papers was their publication on the JWEIA along with all those presented at the 6th ICWE. This initial custom, not exactly suited to the publication of papers on international journal, will be progressively modified by submitting the best contributions to a peer-review and selection process aiming to publish Special Issues about the main IAWE conferences. It is worth noting, however, that, unlike most other conferences, the papers submitted to the first ICWEs were subjected to a strict selection process based on the full version of the contributions. Besides the 6th ICWE, the first part of the 1980s was characterised by the publication of new books [244–257], by the appearance of new relevant journals for the wind engineering community—e.g. Probabilistic Engineering Mechanics (1986), the Journal of Fluids and Structures (1987) and Natural Hazards (1989)—and by other conferences—e.g. the Seminar on Wind Engineering in the Eighties (CIRIA, London, 1980), the Colloquium on Designing with the Wind (CSTB, Nantes, 1981), the Inter-

Fig. 11.36 Interference galloping oscillation of two elastic model stacks [235]

Fig. 11.37 Vertical (a), horizontal (b) and point-like (c) structural models [242]

11.2 The Birth of Wind Engineering

875

national Workshop on Wind Tunnel Modeling for Civil Engineering Applications (Gaithersburg, Maryland, 1982, chaired by Timothy Reinhold), and the International Conference on Design against Wind-Induced Failures (Bristol, UK, 1984). An event deserves a special mention. In 1985, the intermediate year between the 6th and 7th ICWEs, Prem Krishna organised and chaired the Asia-Pacific Symposium on Wind Engineering (APSOWE, Rorkee, India), with the aim of creating a forum for scholars and practitioners in the Asian and Australasian region [258]. It expressed the need to increase the frequency of regional scale meetings and was so successful as to be repeated, since then on every four years, as the Asia-Pacific Conference on Wind Engineering (APCWE, Table 11.3). Even more, it represented a reference model for the other Regional Conferences on Wind Engineering, held in EuropeAfrica since 1993 (EACWE) and in America since 2001 (ACWE). This new reality proved the pressing development of this discipline and offered multiple possibilities to present new studies; on the other, it made more difficult to follow the progress of this knowledge and shifted the most relevant papers from conference proceedings to international journals. The 7th ICWE, held in Aachen, in 1987 and chaired by Carl Kramer [259], did not modify the organisation of the previous 5th and 6th ICWEs and, conversely, was endowed with a partial return towards the dominant role of wind actions and effects on buildings and structures. The wind power sessions disappeared and limited space was given to environmental problems, often embedded in general contexts. This was quite strange since the organisers, Kramer and Gerhardt, had specific competences just in industrial aerodynamics. Perhaps this choice was due to the will of avoiding parallel sessions and of retaining distinct features for the 7th ICWE, held in Aachen in 1987, and the 6th and 7th Colloquia on Industrial Aerodynamics, held in the same city in 1985 and in 1989. These colloquia were also the last of these lucky and worldwide recognised meetings. Scrolling the index of the proceedings (again fully transferred into the JWEIA) to identify the most significant and original contributions, Cook and Pryor [260] studied

Table 11.3 Asian and Australasian Regional Conferences Number

Year

City

Country

Chair

1

1985

Rorkee

India

P. Krishna

2

1989

Beijing

China

T. F. Sun

3

1993

Hong Kong

Hong Kong

Y. K. Cheung

4

1997

Gold Coast

Australia

C. Letchford

5

2001

Kyoto

Japan

S. Murakami

6

2005

Seoul

South Korea

C. K. Choi

7

2009

Taipei

Taiwan, China

C. M. Cheng

8

2013

Chennai

India

N. R. Iyer

9

2017

Auckland

New Zealand

R. G. J. Flay

10

2021

Chengdu

China

M. S. Li

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the extreme wind speed in the UK-providing tools to take into account directionality and seasonality effects. Flay and Stevenson [261] discussed the spread of results when evaluating the integral length scale of turbulence through different methods. Lemelin et al. [262] proposed simple expressions for the wind speed-up over hills. Thoroddsen et al. [263] studied the cross-correlation of different loading components of tall buildings (Fig. 11.38). Shiraishi et al. [264] conducted pioneering investigations on the aerodynamic stability of bluff rectangular cylinders with corner-cuts. Hikami and Shiraishi [265] advanced the novelty of the rain-wind induced vibrations of cables in cable-stayed bridges (Fig. 11.39). Dionne and Davenport [266] stated a simple relationship between the gust response factor and the fatigue damage of steel structures. Modi and Welt [267] studied the dampening of wind-induced vibrations through liquid sloshing. Ruscheweyh and Sedlacek discussed the lack of suitable codes to assess the vortex-excited vibrations of slender structures and proposed a new method [268] destined to become, for many years, the major alternative to the Vickery’s and Basu’s one [236–238]. During the IAWE Steering Committee Meeting at the 7th ICWE, the by-laws presented at the 6th ICWE were approved with slight changes. The new tradition also began that Regional Secretaries and National Delegates provided written reports on the wind engineering activities carried out in the previous four years. As a recognition of the contribution of Martin Jensen, the IAWE endorsed the use of the term “Jensen Number” for the ratio provided by Eq. (7.1). After the 7th ICWE, in 1988 another turning point occurred when Manabu Ito organised and chaired the International Colloquium on Bluff Body Aerodynamics and its Applications (BBAA, Kyoto) [269]. Just like the APCWE expressed the need of meeting more frequently at regional scale, the BBAA showed the will of setting up a forum of experts in bluff-body aerodynamics. This pointed out the deep evolution of wind engineering: in the 1970s, scholars and practitioners involved in wind effects on buildings and structures felt the necessity to broaden their horizons through wider meetings on wind engineering; in the 1980s, wind engineering was a matter so wide to suggest the need for speciality forums besides the ICWEs. This

Fig. 11.38 Cross-correlation of the loading components for rectangular plan buildings [263]

11.2 The Birth of Wind Engineering

877

Fig. 11.39 Vibration amplitudes and weather conditions at Meikonishi Bridge [265]

Table 11.4 Colloquia on Bluff-Body Aerodynamics and its Applications Number

Year

City

Country

Chair

1

1988

Kyoto

Japan

M. Ito

2

1992

Melbourne

Australia

J. D. Holmes

3

1996

Blacksburg

Virginia

H. W. Tieleman

4

2000

Bochum

Germany

H. J. Niemann

5

2004

Ottawa

Canada

K. Cooper

6

2008

Milan

Italy

G. Diana

7

2012

Shanghai

China

Y. Ge

8

2016

Boston

United States

L. Caracoglia

9

2020

Birmingham

UK

H. Hemida

idea was so successful that, following the 1st BBAA, these colloquia were organised, since then, every four years (Table 11.4). The 8th ICWE, held in London, Ontario, in 1991, under the chairmanship of Alan Davenport [270], was characterised by an impressive growth of the number of papers selected (264) for the presentation in parallel sessions (48). This situation gave rise to a major departure from the previous practice: the papers were selected on the basis of two-page abstracts, instead of full-length papers, and distributed at the conference as preprints; the full papers were submitted prior to the conference and reviewed by attendees, before their publication as a special issue of the JWEIA. This matter was extensively discussed during the Steering Committee Meeting where different viewpoints were expressed on the opportunity that, during the next ICWEs, time for

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discussion had to be longer and more plenary sessions had to be organised including the best contributions. Independently of this, an aspect was apparent. Making recourse to parallel sessions, the titles of the conference sessions themselves provided the most relevant topics of wind engineering. Beside the traditional sessions about wind effects on buildings and structures—Wind (5), Bluff bodies (5), Wind-tunnel techniques (3), Tall buildings (2), Bridges (3), Low buildings (5), Roofs (2), Towers and chimneys (3), and Codes—some new sessions were organised on structures—Vibration and dampers (3)—as well as on other topics—Glass and cladding, Wind and waves, Ventilation, Shelter and other, Transportation, Atmospheric dispersion, Dispersion and drifting, Pedestrian winds (2), and CFD. Under this viewpoint, the 8th ICWE completed and made operative the wind engineering model depicted at the 4th ICWE, and partially implemented at the forthcoming conferences. In this renewed framework, the first sessions devoted to CFD at an ICWE deserve a special mention for the impressive growth that this matter would exhibit. It is also worth noticing that the 8th ICWE was the first held after the resolution passed at the United Nations General Assembly, establishing the 1990s as the International Decade for Natural Disaster Reduction (IDNDR), the project pursued by Frank Press to jointly reduce the impact of natural hazards [271]. Many innovative papers were presented at that time. Melbourne and Palmer [272] discussed the acceleration and comfort criteria for buildings undergoing complex motions. Wieringa [273] updated Davenport’s roughness classification, Lagomarsino et al. [274] investigated extreme wind speeds with high return period. Twisdale and Vickery [275] presented at an ICWE one of the first papers on thunderstorms. Marukawa et al. [276] studied the crosswind and torsional acceleration of high-rise buildings. Sarkar et al. [277] proposed a refined method to identify flutter derivatives. Kasperski and Niemann [278] developed the LRC method to identify unfavourable load distributions on structures. Tamura et al. [279] studied the wind loading of beams supporting flat roofs. Sun et al. [280] modelled tuned liquid dampers (Fig. 11.40). Yamazaki et al. [281] described the tuned active dampers on the Landmark Tower, Yokohama. Matsumoto et al. [282] made substantial advances in comparison with the previous study on rain-wind-induced vibrations [265]. Selvam and Holmes [283] and Murakami et al. [284] contributed two papers, based on CFD, for thunderstorm simulation and bluff-body aerodynamics (Fig. 11.41), respectively, destined to become reference points. Besides the 8th ICWE, the first years of the 1990s were endowed with the publication of new books [285–289], the appearance of the journal of Structural Design of Tall Buildings (1992), the organisation of many wind engineering conferences, e.g. the European Workshop on the Wind Effects and the Aerodynamics of Natural Smoke and Heat Ventilators (Luxembourg, 1992, chaired by Carl Kramer), the International Symposium on the Aerodynamics of Large Bridges (Copenhagen, 1992, chaired by Allan Larsen), the Inaugural Meeting of the International Wind Engineering Forum (IWEF) (Tokyo, 1994, chaired by Takeshi Ohkuma and Bogusz Bienkiewicz), the International Seminar on Wind, Rain and the Building Envelope (London, Ontario,

11.2 The Birth of Wind Engineering

Fig. 11.40 TLD-structure interaction: a model; b frequency response [280]

Fig. 11.41 Comparisons between CFD simulations and experiments [284]

879

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11 Advancements in Wind Science and Engineering

1994, chaired by Alan Dalgliesh). Three new conferences, however, deserve special emphasis. In 1992, Shuzo Murakami organised and chaired, close to the 2nd BBAA, the International Symposium on Computational Wind Engineering (CWE, Tokyo) [290]. It included two groups of sessions. The first, addressed to Fundamentals, dealt with Turbulence modelling and applications, Direct and Large Eddy Simulations and Numerical methods. The second, concerning Applications, covered a broad range of topics—Wind load, Wind-induced vibrations, Environmental problems, Pedestrian wind, Vehicle aerodynamics, Computer aided experiments and Computer graphics—in practice all the subjects of wind engineering. The CWE highlighted a new fundamental reality: the advent of CFD and the growth of computational tools as an alternative or an integration to analytical methods, wind tunnel tests, and full-scale measurements. It was so successful that, following the 1st CWE, these symposia were organised, close to the BBAA’s, also in 1996 and in 2000 (Table 11.5). In 1993, following the example of Prem Krishna, Nick Cook organised and chaired the European and African Regional Conference on Wind Engineering (EACWE, Guernsey, UK) [291]; like the APCWE, also the EACWE became, since then on, a traditional IAWE meeting, held in the intermediate year between two following ICWEs (Table 11.6). In 1994, the IAWE Polish Group organised the East European Conference on Wind Engineering (EECWE, Warsaw, chaired by R. Ciesielski, Janusz Kawecki and Jerzy Zuranski) [292], with the aim of creating liaisons between Western and Eastern European scholars and practitioners in wind engineering. Since it was difficult, for East European delegates to attend West European conferences, West European and overseas delegates were invited to join an East European wind engineering conference. This idea was so successful as to be repeated in 1998 and in 2002 (Table 11.7), giving rise to an impressive growth of international cooperation and knowledge exchanges.

Table 11.5 Symposia on Computational Wind Engineering Number

Year

City

Country

Chair

1

1992

Tokyo

Japan

S. Murakami

2

1996

Fort Collins

Colorado

R. N. Meroney and B. Bienkiewicz

3

2000

Birmingham

UK

C. J. Baker

4

2006

Yokohama

Japan

S. Murakami, M. Matsumoto, Y. Tamura

5

2010

Chapel Hill

North Carolina

A. Huber

6

2014

Hamburg

Germany

R. H. Schluenzen

7

2018

Seoul

South Korea

S. Lee

8

2022

London

Ontario, Canada

G. Bitsuamlak

11.2 The Birth of Wind Engineering

881

Table 11.6 European and African Conferences on Wind Engineering Number

Year

City

Country

Chair

1

1993

Guernsey

UK

N. J. Cook

2

1997

Genoa

Italy

G. Solari

3

2001

Eindhoven

The Netherlands

J. Wisse

4

2005

Prague

Czech Republic

J. Naprstek

5

2009

Florence

Italy

C. Borri

6

2013

Cambridge

UK

J. Owen and M. Sterling

7

2017

Liege

Belgium

V. Denoel and O. Flamand

8

2021

Bucharest

Romania

M. Iancovici

Table 11.7 East European Conferences on Wind Engineering Number

Year

City

Country

Chair

1

1994

Warsaw

Poland

R. Ciesielski, J. Kawecki and J. A. Zuranski

2

1998

Prague

Czech Republic

M. Pirner

3

2002

Kiev

Ukraine

M. Kazakevich and V. Grinchenko

The 9th ICWE, held in New Delhi, in 1995, under the chairmanship of Prem Krishna [293], was first characterised by a homage to Alan Davenport to commemorate his sixtieth birth anniversary. With such aim, Krishna invited some leading experts to contribute papers providing a state-of-the-art. These papers were brought together in a volume [294] that can be considered as the first IAWE publication. During the Steering Committee Meeting, the role of the EECWE was acknowledged and, following a proposal discussed there [293], a Working Group was created to pursue the World Wind Safety Initiative (WWSI), just in the intermediate year of the IDNDR. This group, composed by Davenport, Niemann, Walker and Krishna, was tasked with the development of guidelines for windstorms resistant constructions, in particular low- and non-engineered buildings. It had to advise and involve IDNDR secretariat and officials and to report results at the 10th ICWE. The 9th ICWE inaugurated a new tradition: as a post-conference exercise, selected papers out of the papers presented at that conference were published in a Special Issue of the JWEIA [295]. This novelty, often continued in the following years, only partially facilitated the identification of the most significant innovations. On the one hand, the selection procedure did not always focus on the best contributions; on the other, the proliferation of international conferences and journal papers made the enucleation of the most relevant news at ICWEs ever less strategic.

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11 Advancements in Wind Science and Engineering

Fig. 11.42 Full model of the Akashi Kaikyo Bridge [301]

Monomura et al. [296] , attempting to mention, even in this case, the most relevant papers,3 illustrated the full-scale measurements of the wind-induced vibrations of a transmission line in a mountain area. Sharma and Richards [297] described the computational and experimental modelling of the transient response of internal pressure to sudden openings. Murakami et al. [298] carried out CFD analyses on the windstructure interaction of an oscillating square prism. Choi [299] conducted numerical simulations of gust effects on the wind-driven rain around buildings. Matsumoto et al. [300] depicted various mechanisms of inclined cable aerodynamics. Miyata et al. [301] presented impressive wind tunnel tests for the Akashi Kaikyo Bridge (Fig. 11.42). Larsen [302] discussed the aeroelastic stability of suspension bridges under construction. Yamaguchi and Ito [303] investigated the modal damping of cable-stayed bridges. Richardson et al. [304] described the full-scale wind pressure measurements carried out at Silsoe Structures Building. Sharma and Richards [305] studied the effect of roof flexibility on internal pressure fluctuations. Jeary [306] described an analytic model and full-scale tests for damping. Pulipaka et al. [307] inaugurated a long series of contributions to the wind-induced effects on cantilevered traffic signal structures. Tamura et al. [308] elucidated the efficacy of POD in order to study wind-building pressure correlation (Fig. 11.43). Once again, the year of the 9th ICWE and those immediately following it were rich in events and initiatives. Several books [309–312] were published. In 1995, JeanLouis Lilien organised and chaired the International Symposium on Cable Dynamics (Liège, Belgium); it became a classic forum, repeated every two years since then up to 2009, where wind engineers working on cable aerodynamics and aeroelasticity could 3 The

list of the papers presented at 9th ICWE follows the index of the proceedings (1995). When the paper selected for the Special Issue (1997) is available, it replaces the one that appears in the proceedings. In some cases, the authors were not the same ones.

11.2 The Birth of Wind Engineering

883

Fig. 11.43 POD pressure modes for a low-rise building [308]

confront their knowledge with other viewpoints. Other conferences were held, e.g. the International Wind Engineering Forum (IWEF) Meeting on Structural Damping (Atsugi, 1995, chaired by Yukio Tamura and Alan Jeary), the IWEF Workshop on CFD for the Prediction of Wind Loading on Buildings and Structures (Tokyo, 1995, chaired by Tetsuro Tamura), the International Symposium on Advances in Bridge Aerodynamics (Lyngby, 1998, chaired by Davenport), the Jubileum Conference on Wind Effects on Buildings and Structures to honour Joaquim Blessmann (Gramado, Brazil, 1998, chaired by Jorge Riera), and the IWEF Workshop on CFD for Wind Climate in Cities (Hayama, Japan, 1998, chaired by Shuzo Murakami). Besides, three noteworthy journals were issued in this period: the International Journal of Climatology (1996), Wind and Structures (1998) and Wind Energy (1998). The most distinctive element of the 1979–1998 period, however, was the migration of the main contributions to wind engineering from conference proceedings to international journals. Even in this case, the following list represents an attempt to extract from a gigantic amount of papers the most relevant ones, or the most innovative, or the most cited in future. In the wind field, many researches on topography effects—Mason and Sykes [313], Bradley [314], Jackson [315], Taylor and Teunissen [316], Hunt et al.

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11 Advancements in Wind Science and Engineering

Fig. 11.44 Coherence functions of the three turbulence components [328]

[317]—developed the method by Jackson and Hunt [70], or reported extensive campaigns of field measurements, firstly the one conducted on Askervein Hill. Smith studied orographic effects [318] and downslope winds [319]. Studies on turbulence benefitted from POD—Sirovich [320], Berkooz et al. [321]—and CFD—Ghosal [322], Moin and Mahesh [323]; experimental and theoretical research proliferated—Teunissen [324, 325], Høistrup [326], Olesen et al. [327], Mann [328] (Fig. 11.44), Tieleman [329]—leading to turbulence models still in use. Taking inspiration from Shinozuka [40, 41, 176, 177], there was a huge growth of the numerical simulations of stationary Gaussian [330], non-Gaussian [331] and non-stationary [332] wind fields; they greatly benefitted from fast Fourier transform (FFT) [333], discrete Fourier transform (DFT) [334] and POD [335, 336]. The velocity peak evaluation was linked to the gust duration and the structural size [337, 338]. Cook made contributions to extreme wind speeds [339] and their directional analysis [340]. New models of the probability of occurrence of tropical cyclones [341] and tornadoes [342] were developed. Wakimoto [343] and Hjelmfelt (Fig. 11.45) [344] investigated the structure and life-cycle of downbursts; Ivan [345] and Vicroy [346] depicted pioneering models of this phenomenon; Selvam and Holmes [283] used for the first CFD to simulate a downdraft current. Bluff-body aerodynamics was enriched with new papers [347], including those on vortex shedding [348, 349] (Fig. 11.46) and interference [350]. New reference contributions to boundary-layer wind tunnels (Fig. 11.47) [351] were published, as well as on similarity criteria [352, 353], high-frequency force-balance tests [233]

11.2 The Birth of Wind Engineering

885

Fig. 11.45 Structure of a thunderstorm outflow at the maximum intensity [344]

Fig. 11.46 Aerodynamic and hydrodynamic means for interfering with vortex shedding [348]

and methods to correct estimates related to linear mode shapes [354, 355]. Cook and Mayne [356] evaluated wind loading taking into account the distribution of extreme wind speeds and the uncertainties in the aerodynamic coefficients. Several papers on low-rise buildings [357–359], the transient effects of internal pressure due to sudden openings [360–362], tall buildings [363, 364] (Fig. 11.48) and building interference [365, 366] were published. A new series of papers appeared in which bluff-body aerodynamics took advantage of POD [367–370] and CFD [371, 372] (Fig. 11.49). The first paper about aerodynamic databases was also published [373]. In the 1980s, Solari developed the first closed form solution of the alongwind response of structures [243] and the equivalent wind spectrum technique, a method through which a multi-variate wind field could be approximated by an equivalent mono-variate wind field [374] (Fig. 11.50). From here, he derived the response spec-

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11 Advancements in Wind Science and Engineering

Fig. 11.47 a Spires and roughness in a wind tunnel; b triangular spire with splitter plate [351]

Fig. 11.48 PSD of the crosswind force (a) and torsional moment (b) for a square plan building [364]

trum technique [375] and a more efficient closed form solution [376]. In the same period, Kasperski [377], Holmes [378] and Davenport (Fig. 11.51) [379] observed that previous solutions were appropriate for displacements but not necessarily for other structural effects such as bending moments and shear forces; hence, they applied the influence function technique to determine any load effect associated with the alongwind vibrations. Piccardo and Solari [380] generalised the equivalent wind spectrum technique from the alongwind direction to the alongwind, crosswind and torsional components of the response developing, for each one, closed form solutions for slender structures [381]. The crosswind response of buildings was dealt with by Kwok and Melbourne [382], Kwok [383], Kareem [384], Kawai [385], and Vickery and Stackeley [386]. Contributions to the alongwind, crosswind and torsional response of buildings were provided by Kareem [387] and Tamura et al. [388].

11.2 The Birth of Wind Engineering

887

Fig. 11.49 Pressure coefficients on a low-rise building roof [372]: a k-ε-φ model; b standard LES

Fig. 11.50 Equivalent spectrum technique [374]: a frequency filtering; b actual and c equivalent time history

Kareem and Zhao [389] studied the non-Gaussian response of offshore platforms. Morisako et al. [390] analysed the elastic-plastic behaviour of buildings. Kwok et al. [391], Dutton and Isyumov [392], and Hayashida and Iwasa [393] studied aerodynamic devices to mitigate building vibrations. Tamura [394] published a stateof-the-art on damping devices to suppress the wind-induced response of buildings. Kareem [395], Kareem and Gurley [396], and Solari [397] addressed the propagation of uncertainties. Rojani and Wen [398], Davenport (Fig. 11.52) [399] and Kareem [400] published key papers on the reliability of structures under wind actions. Sarpkaya [401], Bearman [402] and Zdravkovich [403] made fundamental contributions to the physics of VIV. Vickery and Basu [237, 238] formulated the first VIV model for chimneys and slender structures, whereas Ehsan and Scanlan [404] proposed a VIV model for flexible bridges. In the wake of the pioneering Scruton’s work [19], Paidoussis et al. [405] and Laneville and Mazouzi [406] studied the ovalling of cylindrical shells. Parkinson and Wawzonek [407] and Bearman et al. [408] provided insights into the vortex shedding and galloping coupling. Jones [409] gave impulse to

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11 Advancements in Wind Science and Engineering

Fig. 11.51 Influence lines and mode shapes of a building [379] Fig. 11.52 Statistical factors of wind loading [399]

study the coupled crosswind and alongwind galloping. Martin et al. [410] and Currie and Turnbull [411] published pioneering papers on a form of alongwind instability of cylinders today known as Reynolds crisis. The aeroelastic oscillation of cables broke out in its importance and literature was filled with contributions on this matter. Drawing inspiration from the papers by Hikami [412], Hikami and Shiraishi [265] and Matsumoto et al. [282] on rain-wind-induced vibrations, this crucial topic for cable-stayed bridges was elucidated by Yamaguchi [413], Flamand [414], Matsumoto et al. [415], and Bosdogianni and Olivari [416]. At the same time, there was a proliferation of papers on bridge aerodynamics and aeroelasticity. Larose and Mann [417] published one of the first studies on the aerodynamic admittance of bridges. Booyapinyo et al. [418] elucidated torsional divergence. Novel research on flutter derivatives were carried out by Falco et al. [419] and Sarkar et al. [420]. Lin and Yang [421], Scanlan and Jones [422] and Jain et al. [423] studied multi-mode flutter. Many contributions to wind vulnerability and risk also appeared. In a sector traditionally aimed at publishing extensive reports, the papers by Minor and Mehta (Fig. 11.53) [424], Kareem [425, 426], Riesbame et al. [427] , Minor [428], Obasi [429] are worth noting.

11.3 Towards Wind Science and Engineering

889

Fig. 11.53 Wind damage to buildings [424]: a components; b surfaces due to openings

11.3 Towards Wind Science and Engineering Faced by a development so much pronounced as to result almost not controllable, during the 10th ICWE, held in Copenhagen, in 1999, under the chairmanship of Aage Damsgaard [430], the three Regional Secretaries, Ahsan Kareem, Shuzo Murakami and Giovanni Solari, submitted the Steering Committee Meeting an analysis on the growth of wind engineering from 1979, when the first draft of the IAWE by-laws was compiled, to 1999, when this document was still in force with marginal changes. Three aspects were apparent. The first was the growth in the number of scholars and practitioners. In the last 20 years, this number, as well as the interest towards this discipline, dramatically increased. This remark was strengthened by the proliferation of wind engineering books and by the growing number of papers in journals related to wind engineering. Moreover, more and more papers on this matter were hosted in an increasingly large number of journals, for instance, those published by ASCE. The second aspect involved wind engineering conferences. Besides the ICWEs few national, regional and international meetings were held up to 1979. This situation changed from 1985, when Prem Krishna conceived the first regional conference. The advent of the BBAA from 1988, of the CWE from 1992, and of the EACWE from 1993, contributed to the new panorama. Also the growing spread of national wind engineering conferences made such events, more and more frequently, focal points in the development of the wind engineering practice and of its knowledge. The third aspect concerned the participation and the contributions to wind engineering from different countries. Considering, as a reference, the participation at the international conferences, in the past it was circumscribed to few countries. At the end of the second millennium, the wind effects on built-up and environment represented one of the most relevant and pressing lines of research because of its importance and

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variety of scientific and technical issues. As a consequence, the number of scholars and practitioners involved in this field rapidly grew and their contributions to wind engineering and its conferences increasingly came from every part of the world. Based on these considerations, it was apparent that the IAWE organisation was conceived in a period in which the ICWEs were the only scientific and technical forum for a small number of delegates, coming from few countries, to discuss a narrow band of topics. This situation justified the article of the by-laws according to which the IAWE “will be governed by a Steering Committee which will meet every four years at the venue of an International Conference”. Over the years, this situation changed. At the end of the 1990s, the wind engineering calendar was full of initiatives that suggested creating a permanent coordinating authority and specific guides. The scientific, technical and social impact of wind engineering expanded so much that many IAWE fields interacted with those of other associations, e.g. the World Meteorological Organisation (WMO), the World Wind Energy Association (WWEA), the Council on Tall Buildings and Urban Habitat (CTBUH), the International Association for Bridge and Structural Engineering (IABSE), the International Association for Structural Control and Monitoring (IASCM), the International Association for Earthquake Engineering (IAEE) and the International Association for Structural Safety and Reliability (IASSAR); thus, liaisons with other communities had become desirable. Moreover, a better coordination was needed between the IAWE chairman, regional secretaries and national delegates, in order to agree on decisions and spread information. Since wind engineering research was appearing in many journals, it was also time to reflect on the role and aims of the official IAWE journal, the JWEIA. The IAWE Steering Committee Meeting at the 10th ICWE acknowledged this framework and decided the following actions [430]: (a) to introduce few specific amendments into the by-laws, to give IAWE the possibility of operating more efficiently in the four years between two subsequent ICWEs; (b) to appoint an international committee (Damsgaard, Holmes, Kareem, Mehta, Murakami and Solari as the Chair) aiming to open a wide debate on the organisation of the association. Other actions were undertaken by the IAWE at the 10th ICWE. Confirming the need of coordinated activities, four networks were established or consolidated to develop joint projects, stimulate advances and spread wind culture. The working group on Storm Shelter, appointed at the 9th ICWE, gave rise to the Workshop on Wind disaster reduction related to housing (with a steering committee including Davenport, Niemann and Krishna). A working group was appointed on International codification (chaired by Holmes, Kasperski and Cook), to encourage standardization and make various codes homogeneous through the organisation of workshops. Two informal working groups were constituted on Bridge aerodynamics (with a steering committee made up of Scanlan, Jones, Diana, Larsen, Matsumoto, Baker and Miyata) and on Cable Aerodynamics (chaired by Jones and Matsumoto). Once again, the year of the 10th ICWE and the following ones were rich in new initiatives, comprehending the publication of books [431, 432], the issue of journals (e.g. The International Journal of Ventilation in 2002), the International Advanced School on Wind-excited and aeroelastic vibration of structures (Genoa, Italy, 2000,

11.3 Towards Wind Science and Engineering

891

Table 11.8 Americas Conferences on Wind Engineering Number

Year

City

Country

Chair

1

2001

Clemson

North Caroline

T. A. Reinhold

2

2005

Baton Rouge

Louisiana

M. Levitan

3

2009

San Juan

Puerto Rico

H. J. Cruzado

4

2013

Seattle

Washington

D. Reed and A. Jain

5

2017

Gainesville

Florida

F. Masters

6

2021

Lubbock

Texas

Daan Liang

chaired by Solari) and many conferences, e.g. the first International Symposium on Wind and Structures for the twenty first Century (Chejudo, South Korea, 2000, chaired by Choi, Kanda, Kareem and Solari), later called Symposium on Advances in Wind and Structures, the Engineering Symposium to honour Alan Davenport for his 40 years of contributions (London, Ontario, 2002) and the first International Conference on Footbridges (Paris, 2002), a structural type dominated by lightness and elegance, putting wind actions and effects in a prominent role. In 1999, after 25 years of leadership, Ian Harris handed over to Nick Jones the charge of Editor of the JWEIA. In the same year, during the 3rd International Conference on Engineering AeroHydroelasticity (EAHE), held in Prague under the chairmanship of Balda, it was pointed out the existence of three parallel series of events on similar topics—the International Conferences on Flow-induced vibrations (FIV), from 1973, the International Symposia on Flow-structure interaction, aeroelasticity, flow-induced vibration and noise (FSI, AE and FIV+N, from 1984), and the International Conferences on (Engineering) AeroHydroelasticity (from 1993)—and the advisability of harmonising and coordinating these activities. This led to the limited advance of holding the first two events in alternate years [3]. Following the resolution at the 10th ICWE, the 1st International Codification Workshop for Wind Loads was held in 2000 at the venue of the 4th BBAA (Bochum, chaired by Niemann and Holmes), with the aim of encouraging and facilitating more commonality in national, regional and international wind loading codes and standards. Resuming the tradition begun in 1975 [61, 229] and then interrupted, an informal volume of the current codes and standards of several countries was distributed, providing a state-of-the-art in this field. This workshop was repeated in Kyoto, in 2001, under the chairmanship of John Holmes and Yukio Tamura. In the same year, replacing the previous US National Conferences on Wind Engineering, the 1st Americas Conference on Wind Engineering (ACWE) was held in Clemson, North Caroline, under the chairmanship of Reinhold [433]. Like the APCWE and the EACWE, also the ACWE became, since then on, a traditional meeting of the IAWE calendar, to be held every four years (Table 11.8). It completed the current layout of the three Regional Conferences. Few months after the 1st ACWE, during the 3rd EACWE (Table 11.6), it was resolved that, after the 1st and 2nd EECWE, the 3rd EECWE, to be held in Kiev

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in 2002, had to be the last of this series. Born for improving liaisons between East and West Europe, the EECWEs attained their goal so thoroughly that no reasons still existed to keep the EECWEs separated from the EACWEs. On the impetus of this success, it was agreed to open an analogous series of African Conferences, aiming to develop cooperation between Africa and Europe; accordingly, a committee was tasked (Goliger as the chair, Borri, Mulenga, Niemann, Solari, Stigter and Wisse) with the formulation of a proposal. This committee, later coordinated by Wisse, Baker and Hoffer, stressed the difficulty of obtaining European supports to develop advanced strategies in the African continent. In the meantime, the committee appointed to promote the IAWE development (with Larsen and Matsumoto on behalf of Damsgaard and Murakami, and Jones as an invited guest) carried out a widespread open discussion and established contacts with other associations in order to understand their different frameworks. At the end of this work, this committee issued a novel draft of the IAWE by-laws4 and a new scheme for its organisation. Compared with the past tradition, it contained many innovatory aspects, two of which deserve special consideration. First, IAWE members, in the past individuals, became member organisations, i.e. associations or societies for wind engineering representing one or more nearby countries accepted into membership. Individual members of affiliated organisations were IAWE individual members; individuals, private firms and other organisations might become IAWE supporting members. It was expected that such a scheme might provide a strong impulse towards the birth and growth of several organisations, increasing the number of individuals involved in IAWE activities. Second, the Steering Committee was replaced by a General Assembly supported by an Executive Board that manages the IAWE between two subsequent ICWEs. This Board is composed by the IAWE President, the former President, the Chair of the next ICWE, the three Regional Coordinators, three Regional Representatives, the Secretary General, and Consultative Members co-opted by the President. Separating the roles of the IAWE President and of the ICWE Chairman, previously held by the same individual, aimed at allowing the first to dedicate himself to IAWE affairs and development, and the second to organise an event, the ICWE, so much complex and burdensome to require a full involvement. The Secretary General, who is responsible for the IAWE Secretariat, manages IAWE activities and is the IAWE reference point. This proposal was unanimously approved by the Steering Committee at the 11th ICWE, held in Lubbock, Texas, 2003, under the chairmanship of Kishor Mehta [434]; after less than 30 years from IAWE constitution, this resolution opened a new era for wind engineering and its association. In this way, following elections, the first Executive Board of the IAWE included Solari (as the first president of the new IAWE course), Mehta (past-president), Cheung (12th ICWE chairman), Kareem and Holmes (former American and Asia-Pacific coordinators), Stathopou4 The

new IAWE By-Laws were made up of 19 articles: (1) Name; (2) Aim; (3) Language; (4) Membership; (5) Finances; (6) Regions; (7) Conferences and Conference Chairs; (8) President; (9) Regional Coordinators; (10) Regional Representatives; (11) Secretary General and Secretariat; (12) Executive Board; (13) General Assembly; (14) Regional Assemblies; (15) Committees; (16) Official Journal; (17) Official Web Site; (18) Amendments to the By-Laws; (19) Dissolution.

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los, Matsumoto and Baker (American, Asia-Pacific and Europe-African representatives, respectively). The position of European-African regional coordinator remained initially vacant due to Solari’s appointment as IAWE president. Thanks to this renewed framework, Giuseppe Piccardo was appointed Secretary General and the IAWE Secretariat was established at the University of Genoa. Levitan, Choi, Naprstek and Jones were invited to join the Executive Board as consultative members. The election of the European-African Regional Coordinator was delayed to the 4th EACWE, in 2005, and, before that date, Baker made its function. On 17 September 2003, during the 5th International Symposium on Cable Dynamics (Santa Margherita, Italy), the IAWE was formally established through a deed; accordingly, formal steps were carried out to make IAWE a legal entity in Italy. As a consequence of these steps, many member organisations were accepted into membership and formal relationships were established with the representatives of different countries. Thanks to this action, between 2004 and 2005, the IAWE recognised 18 member organisations and promoted the foundation of similar associations in countries that until then were mostly informally involved in wind engineering (Table 11.9). The official IAWE website5 (www.iawe.org) was opened on 22 September 2005, and a new strategy was applied with regard to the forthcoming CWE 2006. From 1992 to 2000, CWE Symposia and BBAA Colloquia were held in close cities or countries, with a temporal gap not exceeding one week. It was apparent, however, that their joint organisation was difficult and individuals involved in both fields rarely had the opportunity of attending both. For this reason, in 2002, the BBAA Colloquium was held, while the CWE Symposium was delayed. This led Masaru Matsumoto, Shuzo Murakami and Yukio Tamura to offer themselves for organising the next CWE, in 2006, under the auspices of the Centre Of Excellence (COE) on Wind effects on buildings and urban areas, Tokyo Polytechnic University (TPU), directed by Tamura. Following this proposal, the next CWE had to be held in Yokohama (Table 11.5), creating a perfect sequence of the most important wind engineering conferences (Table 11.10). Meanwhile, Ted Stathopoulos (2005) was appointed as the new Editor of the JWEIA. The three Regional Conferences in 2005, were excellent test beds to put into practice the new procedures and to discuss IAWE programmes and prospects. During two meetings of the Executive Board [3], it was decided: (1) to accomplish renewed liaisons with international organisations working in wind engineering and similar 5 The

first issue of the IAWE website included nine points: (1) “About IAWE” provided the aims and a history of the association, the by-laws subsequently in force, the constitution deed, IAWE officers, the references of the Secretariat, the application forms for IAWE membership, a list of wind engineering conferences and chairmen; (2) “Members and Contacts” provided the references of member organisations, supporting members, and other contacts; (3) “Official Journal” provided a link to JWEIA; (4) “Committees” listed the initiatives under the IAWE umbrella; (5) “Next Conferences” reported the calendar, references and links to next meetings; (6) “Newsletters” was in progress; (7) “News & Information” contained announcements and reports; (8) “Links” listed journals, books, associations, projects, laboratories and research groups; (9) “Archives” gathered the superseded information.

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Table 11.9 IAWE member organisations Number

Member organisation

Acceptance

1

Czech Society for Mechanics, Wind Engineering Group

2004

2

Taiwan Association for Wind Engineering

2004

3

Japanese Association for Wind Engineering

2004

4

Indian Society for Wind Engineering

2004

5

Wind Engineering Institute of Korea

2004

6

Asociacion Nacional de Ingenieria del Viento, Spain

2004

7

Associazione Nazionale per l’Ingegneria del Vento, Italy

2004

8

UK Wind Engineering Society

2004

9

American Association for Wind Engineering

2004

10

Australasian Wind Engineering Society

2005

11

China Civil Engineering Society, Wind Engineering Group

2005

12

Comité Nacional de Cálculo de Estructura de Hormigón, Cuba, Subcomité de Viento

2005

13

Norwegian Society for Wind Engineering

2005

14

Royal Institution of Engineers, KIVI NIRIA, The Netherlands, Stuurgroep Windtechnologie

2005

15

Hellenic Scientific Society of Wind Engineering, Greece

2005

16

Open Joint-Stock Company V. Shimanovsky Ukrain Research and Design Institute of Steel Construction, Wind Engineering Group

2005

17

Windtechnologische Gesellschaft, Germany, Austria and Switzerland

2005

18

Association de l’Ingénierie du Vent, Belgique, France and Suisse

2005

19

Polish Association for Wind Engineering

2009

20

Hong Kong Wind Engineering Society

2011

21

Brazilian Association for Wind Engineering

2011

22

The Danish Wind Engineering Society

2013

23

Mexican Association of Wind Engineering

2015

24

Romanian Association for Wind Engineering

2017

Table 11.10 Sequence of the IAWE Conferences (K = 2003, 2007, 2011,…) Year

Conference

K

International Conference on Wind Engineering (ICWE)

K +1

International Colloquium on Bluff-Body Aerodynamics and its Applications (BBAA)

K +2

Regional Conferences on Wind Engineering (ACWE, APCWE, EACWE)

K +3

International Symposia on Computational Wind Engineering (CWE)

K +4

International Conference on Wind Engineering (ICWE)

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fields and to perfect the contacts with the World Wind Energy Association (WWEA); (2) to create Senior and Junior IAWE Awards (up to four for each category), to be awarded every four years at the ICWEs; (3) to manage CWE Symposia under IAWE umbrella. Following these decisions, a memorandum of agreement between IAWE and WWEA was signed in 2006, in New Delhi, at the World Wind Energy Conference, and a call for candidatures to IAWE Awards was distributed in summer 2006. Accordingly, the first IAWE Awards Committee was nominated (Baker as the chair, Diana, Letchford, Meroney and Y. Tamura), which in March 2007, communicated the Executive Board the first winners of the Senior Awards—Cook, Kareem and Murakami—and of the Junior Awards—Carassale, Gurley Gurley, K. and Kitagawa (Table 11.11). While this procedure was being developed, an evident truth came out. Many of those who were currently considered fathers of wind engineering were recognised by various institutions in different ways. Kit Scruton and Martin Jensen were linked with the homonymous numbers through two resolutions assumed by IAWE in 1987 and 1991 respectively. The ASCE set up medals entitled to Jack Cermak6 (in 2002) and

Table 11.11 IAWE Awards Year

Senior Award—Davenport Medal

Junior Award

2007

Nick Cook (UK)

Luigi Carassale (Italy)

Ahsan Kareem (USA)

Kurtis Gurley Gurley, K. (USA)

2011

Shuzo Murakami (Japan)

Tetsuya Kitagawa (Japan)

John Holmes (Australia)

Tracy Kijewski-Correa (USA)

Masaru Matsumoto (Japan)

Claudio Mannini (Italy)

Giovanni Solari (Italy)

Maria Pia Repetto (Italy)

Barry Vickery (Canada)

Atsushi Yamaguchi (Japan)

2012

Ted Stathopoulos (Canada)

John Schroeder (USA)

2013

Haifan Xiang (China)

Bert Blocken (The Netherlands)

2014

Giorgio Diana (Italy)

Forrest Masters (USA)

2015

Peter Irwin (Canada)

Vincent Denoel (Belgium)

2016

Yukio Tamura (Japan)

Tim Tse (Hong Kong)

2017

Bill Melbourne (Australia)

Teng Wu (USA)

2018

You-Lin Xu (Hong Kong)

Kazuyoshi Nishijima (Japan)

2019

Kenny Kwok (Hong Kong)

Frank Lombardo (USA)

6 The

Jack E. Cermak medal, established by the Engineering Mechanics Institute (EMI) and the Structural Engineering Institute of the ASCE, has been awarded to: A. Kareem, 2002; A. G. Davenport, 2003; Y. Tamura, 2004; G. Solari, 2006; P. Irwin, 2007; T. Stathopoulos, 2009; J. Paterka, 2010; N. Isyumov, 2012; W. H. Melbourne, 2013; K. C. Mehta, 2014; J. Hunt, 2015; Q. S. Li, 2016; X. Chen, 2017; H. J. Niemann, 2018.

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to Robert Scanlan7 (in 2003). The Windtechnologische Gesellschaft (WTG) set up a medal to honour Otto Flachsbart.8 It was evident this gallery of illustrious scholars missed the person who more than any other was acknowledged as the pioneer and the symbol of wind engineering: Alan Garnett Davenport. The idea was therefore born that the IAWE Senior Award had to be the Davenport Medal. This issue gave rise to reactions of extraordinary enthusiasm and approval, bearing witness to the enormous esteem and affection that the wind engineering community tribute to Alan Davenport, a master of humanity, science and engineering [435]. Meanwhile new conferences were held (e.g. the International Conference on Impact of wind and storms on city life and built environment, COST-14, Brussels, Belgium, 2004, chaired by Borri and van Beeck). New books were published [436, 437] and new journals appeared (e.g. the Journal of Wind and Engineering). The 12th ICWE, held in Cairns, Australia, in 2007, under the chairmanship of John Cheung [438], was attended by 347 registered participants coming from 28 different countries. During the General Assembly, the IAWE recognised the definition of Wind Engineering provided by Cermak in 1975 [163]—“Wind engineering is best defined as the rational treatment of interactions between wind in the atmospheric boundary layer and man and his works on the surface of Earth”—and endorsed the use of the term “Tachikawa Number”, i.e. the ratio of aerodynamic to gravity forces, as the main non-dimensional parameter determining debris trajectories [439]. It also resolved that the BBAA had to be held under the IAWE umbrella (conditional to approval at the BBAA in 2008), completing the framework of the wind engineering international conferences (Table 11.10). Finally, Yukio Tamura was elected as the new IAWE President. Also thanks to the great support of Shuyang Cao, the new Secretary General, the era of Tamura’s presidency (2007–2015) was characterised by great initiatives, starting with the creation of the IAWE logo, many of which carried out in cooperation with the Global Centre Of Excellence Programme (GCOE-TPU, 2008–2013) on New frontier of education and research in wind engineering, directed by Tamura himself with the cooperation of Ahsan Kareem, which followed the COE-TPU Programme (2003–2008). Its articulation according to three research lines—wind hazard mitigation, natural/cross-ventilation, pollution and wind environment—testified its broad objectives and prospects. Tamura promoted and chaired six International Symposia on Wind effects on buildings and urban environment (ISWE, 2004–2013), seven Workshops on the Regional harmonisation of wind loading and wind environmental specifications in Asia-Pacific economies (APEC-WW, 2004–2012), the yearly Korea–Japan Joint Workshop on Wind Engineering (JaWEiK, 2005–2011), later the China–Japan–Korea Joint Workshop on Wind Engineering (CJK, from 2012), a successful series of 7 The

Robert H. Scanlan medal, established by the EMI of the ASCE, has been awarded to: E. Simiu, 2003; J. E. Cermak, 2004; A. Kareem, 2005; M. Shinozuka, 2006; M. Matsumoto, 2007; N. P. Jones, 2008; G. Diana, 2009; H. F. Xiang, 2010; Y. Fujino, 2011; Y. L. Xu, 2012; Y. Tamura, 2016; G. Solari, 2017. 8 The Otto Flachsbart medal, established by the WTG, has been awarded to: A. G. Davenport, 2000; J. E. Cermak, 2007; G. Solari, 2013.

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Advanced Schools—initially under the COE umbrella (2006–2007), then labelled as International (IAS, from 2007)—and VORTEX-Winds, a Virtual Organisation for Reducing the Toll of EXtreme Winds, co-chaired with Kareem in order to create a cyber-based data-enabled virtual organisation for wind load effects on civil infrastructures (since 2007) [440]. In the framework of these activities, the ISWE4 held in Tokyo in 2009 aimed at creating Cooperative Actions for Disaster Risk Reduction (CADRR) based on the recognition that, while wind-related organisations like IAWE had been effectively working to develop technologies, codes and standards for wind hazard mitigation, there had been a dearth of coordinated activities with other international bodies, like United Nations (UN) and Non-Governmental Organisations (NGO), to bring these technologies to work for less fortunate communities in low-lying areas, which were often struck by devastating wind storms with attendant escalating loss of life and associated perils. From here, the International Group for Wind-Related Disaster Risk Reduction (IG-WRDRR) [441] was born (chaired by Kareem with the participation of Stathopoulos, Letchford and Borri); it was launched in Geneva, Switzerland in 2009, at the Global Platform for Disaster Risk Reduction, organised by UN and other NGO. In turn, it generated a series of events such as the International Forum on Tornado disaster risk reduction for Bangladesh (Dhaka, Bangladesh, 2009, 2013), the Workshop on Wind-related disaster risk reduction activities and interorganisational collaborations and the Pre-Conference Event on Climate change and wind-related disaster risk reduction activities in Asia-Pacific Region (Incheon, Korea, 2010), the 5th International Disaster and Risk Conference (IDRC, Davos, Switzerland, 2014), the IAWE Public Forum at the 3rd UN World Conference on Disaster Risk Reduction (Sendai, Japan, 2015). In the middle of this unrepeatable period, the 13rd ICWE was held in Amsterdam, in 2011, under the chairmanship of Chris Geurts [442]. During the IAWE General Assembly, the terminology of “Alan G. Davenport Wind Loading Chain” was approved to identify the procedure introduced by Davenport [1] in order to link wind climatology and micrometeorology, bluff-body aerodynamics and structural dynamics within a homogeneous framework.9 It was decided to grant IAWE awards annually (Table 11.11). In addition to the IG-WRDRR (2009), many new Working Groups (WG) were established—the WG for International High-Frequency ForceBalance (HFFB) comparison project, chaired by Holmes from 2007, the WG for a Benchmark on the aerodynamics of a rectangular 5:1 cylinder (BARC), coordinated by Bruno, Salvetti and Ricciardelli from 2008, the WG on the International Enhanced Fujita (EF) scale, chaired by Kopp from 2013. During this period, new books were published [443–450] and a number of cooperative projects were carried out, e.g. “Wind and Ports” (2009–2012) [451] and “Wind, Ports and Sea” (2013–2015) [452], under Solari’s leadership, and the ‘111’ Project for “Innovation on mitigating wind-induced disaster of infrastructures sensitive to

9 Four years later, the General Assembly held at the 14th ICWE in Porto Alegre resolved to simplify

this terminology as “Davenport Chain”.

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wind”, from 2013, chaired by Qingshan Yang at the Beijing Jiaotong University, China. The 14th ICWE held in Porto Alegre, Brazil, in 2015, under the chairmanship of Acir Loredo Souza [453] was first characterised by the end of Tamura’s presidency and by the election of Ahsan Kareem as the new IAWE President. On this occasion, two new symbols were inaugurated, the IAWE Key and the Davenport Chain, which would be handed down from the past-president to the new one. A replica of these two symbols was presented to Solari as the past-president. Awards were awarded to Piccardo and Cao, the two Secretary Generals who made the regular and profitable development of the new IAWE course possible in the 2003–2015 period. Parallel to these events, with the advent of the third millennium, the culture of wind and its effects on territory and environment has been experiencing deep developments concerning the appearance of increasingly specialised or large-scale laboratories, the proliferation of the study of non-synoptic wind phenomena and the joint critical review of the fundamentals of the discipline, the renewed role of CFD, the exponential growth of the structures inspired by the aerodynamic control of the shape, the growing attention towards climate changes, the development of courses aimed at the education in wind science and/or engineering, the widespread presence of skilled wind professionals in the work world, and an almost uncontrolled evolution of the journal papers. Enumerating the new laboratories that have been coming to light in this period is impossible. Some of these, however, deserve a special quotation. In 2001, the University of Miyazaki in Japan, implemented an active multi-fan wind tunnel [454] thanks to which it is possible to realise unsteady flow conditions and to control the turbulence scale. In 2005, at the University of Western Ontario, the Three Little Pigs was inaugurated, a laboratory that simulates in full-scale the wind-induced pressure on building roofs and facades. Between 2005 and 2011, the Florida International University built the Wall of the Wind (Fig. 11.54a), a laboratory where large-scale models or small full-scale buildings can be collapsed. In 2010, the Institute for Business and Home Safety’s Research Center in Chester set up a laboratory with a huge test chamber of 44.2 × 44.2 × 18.2 m. In 2013, under the leadership of Horia Hangan, the Western opened the Wind Engineering, Energy and Environment (WindEEE) Dome (Fig. 11.54b), the first facility that replicates large-scale synoptic (atmospheric boundary-layer flows) and non-synoptic (tornadoes, downbursts and gusts) winds as well as their combinations [455]. Research and literature on non-synoptic phenomena—tropical cyclones [456] and above all tornadoes [457], thunderstorm downbursts [458, 459] and downslope winds [460]—have been growing out of all proportion, generating a renewed interest towards revisiting the fundamentals of wind engineering. When Davenport published his 1961 paper [1], the design wind, identified with an extra-tropical cyclone, produced stationary Gaussian actions on structures usually modelled as linear systems. These hypotheses are now being rediscussed, giving rise to treatments where wind, aerodynamic loading and structural response take on non-stationary, non-Gaussian and nonlinear features [461]. They call for using advanced formulations as well as measurements and simulations oriented to the new framework.

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Fig. 11.54 a Wall of the Wind, b WindEEE Dome [455]

Fig. 11.55 CFD study of pedestrian-level wind conditions in urban areas [462]: a grid (2.8 million cells); b wind speed ratio contours based on steady RANS

CFD [462], which had long been treated as a promising but also potentially dangerous tool, has been making a leap in quality and is fully entering into the category of the operational tools. This has become a common practice in environmental problems (Fig. 11.55) [463–466], mainly governed by the mean wind flow, and also, progressively, in structural engineering [467], where CFD is more and more frequently used in the predesign phase as an appropriate instrument to compare the efficiency of various solutions, for example, the shape of bridge decks [468], before subjecting to wind tunnel tests the ones selected as more suitable. At the same time, the role of aerodynamic design and shape control has been taking off. The effectiveness of replacing structures with predefined shape, designed to withstand wind actions with adequate safety and comfort, with structures where the shape is selected to minimise aerodynamic wind actions and structural response first emerged in the field of long-span bridges (Fig. 11.56) [468, 469], then it spread throughout the design of high-rise buildings (Fig. 11.57) [470, 471], finally, it is pervading the entire construction sector, which is not always culturally and technically prepared with regard to an evolution of this magnitude. Coming from the climatology sector, the first studies on climate changes have also been spreading in wind engineering [472, 473]. All show the conviction and

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Fig. 11.56 Messina Strait Bridge: a rendering; b wind tunnel tests at the Politecnico di Milano

Fig. 11.57 PSD of the crosswind loading of buildings with different shapes [470]

evidence of the increase in the Earth’s temperature. Judgments on the consequences of this phenomenon are instead varied and controversial. The warming of Earth’s surface increases the convective potential energy creating more moisture. On the other hand, disproportionate warming in Arctic leads to less wind shear in midlatitude areas prone to windstorms. While the study of the balance between these conflicting trends still is in a pioneering phase, nature more and more often provides situations different from those matured over the centuries, in respect of which a robust culture and shared ideas in a necessarily interdisciplinary-sectorial vision are still missing.

11.3 Towards Wind Science and Engineering

901

Far beyond the International Advanced Schools on Wind Engineering, mentioned above, the teaching of this matter has become more and more classic in many universities all over the world, giving life to a new generation of professionals and scientists with a robust background in wind engineering. They have been finding many work opportunities in the academic sector as well as in the industrial one, also thanks to the birth of several wind engineering consulting companies such as RWDI, CPP and BMT; the latter inherited the sumptuous legacy of NPL. Other companies have created specialised offices in wind engineering. Others are favouring the recruitment of professionals skilled in this field. Collaborations about the wind between the academic and industrial world have been developing everywhere, likewise the alternation of job positions between the two fields. Just in the spirit of the new trend, in 2006 the Texas Tech University opened the first doctoral programme in Wind Science and Engineering [474]. In 2018, the University of Genoa inaugurated a doctoral curriculum with the same title. A now delicate issue that deserves reflection remains to be treated: the publication of papers in international journals, fundamental means of dissemination. It exhibits an exponential growth, partly due to the evolution of knowledge, partly caused by the role assumed by bibliometric parameters as an academic tool to evaluate scientific production. This has been stimulating researchers and scholars to entrust their main results to an international arena; on the other hand, it has been producing an uncontrollable explosion of papers, not always fully original, to which the proliferation of open-access journals has been contributing not always in favour of quality. Bearing in mind that this paragraph refers to an almost contemporary activity, and as such not easy to evaluate, a picture emerges within which it is difficult to identify the most significant and innovative papers of this period. Attempting to make a choice despite this remark, the study of the wind has been enriched by contributions about the changes of terrain roughness [475], topographic effects [476] and the use of sodars [475] and lidars [477]. Turbulence analysis has been increasingly using POD [478, 479] and CFD [480]. New contributions to represent atmospheric turbulence [481] and efficient methods for its simulation [482, 483] have been appearing. The statistical analysis of the wind speed has seen the emergence of new models for the parent population [484] and extreme values [485, 486]. Research has been continuing on tropical cyclones and the various strands of their analysis [456, 487–490]. A parallel situation has been occurring for tornadoes [457, 491]. A new generation of papers aiming to represent the downburst velocity field has been appearing [492–496], as Davenport prophetically predicted [22]. The THUNDERR project carried out by Solari [497] through an Advanced Grant 2016 of the European Research Council (ERC) is providing a significant boost to these studies. In the field of bluff-body aerodynamics, new states of the art have been appearing [498]. New contributions to interference have been publishing [499]. CFD [500, 501] has become an essential tool for examining the pressure field. The studies about the pressure peaks on cladding and roofs have become increasingly important [502]. The use of electronic databases [503–505] has proven to be more and more useful. The application of CFD has been established to optimise the building shape [506, 507].

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More and more papers describe the laboratory tests and CFD simulations aiming to inspect the tornado and downburst wind loading of structures [508–510]. The research on the wind-excited response of structures has also shown many advances. Studies aimed at assessing wind-loading effects have been continued [511–513]. New closed form solutions of the dynamic alongwind, crosswind and torsional response of slender structures [514, 515] have been developed. New models to determine the dynamic response of buildings with 3D coupled modes [516] have appeared. POD has been becoming an essential tool for assessing the dynamic response of structures [517, 518]. Studies have been carried out on the damping of buildings [519], human perception to building vibrations [520, 521], aerodynamic devices to mitigate building motion [470, 471], the control of vibrations [522]. Research on wind-induced fatigue [523–525] has burst. The interest towards performance-based design [526, 527] is growing. The literature has been filling up with papers that deal with the dynamic response of structures to transient events, first of all downbursts [528–532]. Even the developments and innovations on aeroelasticity are irrepressible. New states of the art [533] and calculation models [534, 535] on vortex-induced vibrations have appeared. Research has been carried out on the galloping of slender structures [536] and of coupled systems [537]; CFD has become a calculation tool even for galloping [538, 539]. New studies on rain-galloping [540, 541] have been flanked by early research on the dry galloping of yawed cables [542–544]. Papers on the coupling of galloping with VIV [545] have appeared. The study of bridge aerodynamics and aeroelasticity has been enriched by new contributions on buffeting [546], torsional divergence [547], flutter derivatives [548, 549], multimode flutter [550–552] and nonlinear analyses [553, 554]. Finally, a series of papers is quoted that do not belong, as the previous ones, to the classical rings of the Davenport chain, but are joined by the interest created and the remarkable number of citations received, in their own sector, despite their relatively recent publication. They concern the aerodynamics of sailing [555, 556], vehicle and train aerodynamics [557–560], wind turbines and wind farms [561, 562], the atmospheric diffusion of pollutants [563], snow drift [564], windbreaks [565] and pedestrian environment [566, 567]. Starting from them and the state-of-the-arts they provide, the readers interested to these topics may rebuild an extensive literature. Only the passage of time can tell us how many and which of the above-mentioned papers will really play an important role and, above all, how many and which papers the author has not been able to put in evidence or, simply, he did not know, will have provided a relevant contribution to the progress of wind science and engineering.

References 1. Davenport AG (1961) The application of statistical concepts to the wind loading of structures. Proc Inst Civ Eng 19:449–472

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Author Index

A Abbe, C., 191, 327, 358 Abbey, R.F.Jr., 869 Abelard, P., 19 Abe, M., 366, 367 Abercromby, R., 189, 192 Ackeret, J., 283, 665 Ackermann, W., 499 Adachi, J., 725 Adams, F.U., 540 Ader, C., 483 Adie, A., 105 Adrain, R., 117, 118 Agricola, G., 64 Agrippa, 55, 66 Aiken, H.H., 315, 317 Albenga, G., 691 Albert, 28 Alberti, L.B., 60, 61, 77, 78, 99, 330 Albertus Magnus, 19, 26 Alen, W.van, 683 Alexander the Great, 38, 68 Alexander VII, 63 Alfani, G., 677, 690 Algue, J., 806 Ali, B., 405 Amenophis IV, 51 Ames, J.S., 495, 501 Amin, M., 853 Ammanato, B., 68 Ammann, O., 658 Amontons, G., 99 Amundsen, R.E.G., 617 Anaxagoras, 14 Anaximandros, 12, 14

Anaximenes, 12, 14 Anco Marzio, 66 Andreau, J., 572 Andrée, A., 225 Andrews, E.S., 711 Andronikos Kyrrhestes, 30 Ang, A.H.S., 853, 861 Antonelli, A., 687, 689, 690 Antonia, R.A., 864 Antonio da Ponte, 68 Apollodorus, 67 Appleton, E.V., 336 Arai, H., 619, 620, 849 Arakawa, H., 363 Aratus, 29, 30 Archer, 756 Archibald, E.D., 332, 370, 371, 401 Archimedes, 23, 109, 222 Archytas, 39 Aristarchus, 13 Aristotle, 15, 16, 19, 22, 54, 90, 91, 95, 174 Aristoxenus, 22 Arita, Y., 845 Armitt, J., 865 Arnoldus, 47 Arnstein, K., 711 Arouet, F.M., see Voltaire Arrhenius, S.A., 592 Arroll, A., 522 Ashley, H., 508 Aspdin, J., 243 Assmann, W., 333 Atanasoff, J.V., 315 Atlas, D., 337 Augustus, 55, 66

© Springer Nature Switzerland AG 2019 G. Solari, Wind Science and Engineering, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-18815-3

925

926 Aulus Gellius, 39 Autonne, L., 305 Averroes, 19 Avicenna, 19 Avogadro, A., 224, 225 Aynsley, R.M., 863, 870 B Babbage, C., 111–113, 313 Babington-Smith, B., 312 Backus, J.W., 318 Bacon, F., 89–91, 103, 172, 192 Bacon, R., 19, 26, 40, 79, 222 Baden-Powell, B. F. S., 481, 484 Baes, L., 720, 721 Bagnold, R.A., 595, 596, 598, 602, 617 Bailey, A., 471–474, 639, 685, 710, 714 Baird, R.C., 744 Bairstow, L., 497 Baker, B., 264–266, 451, 452 Baker, C.J., 862, 880 Bakke, P., 299 Balda, 891 Baldwin, F.W., 487, 488 Baliani, G.B., 123 Baltard, V., 238 Barczys, D.A., 337 Barlow, P., 255 Barratt, P., 337 Barrow, I., 110 Barstein, M.F., 707, 728–730 Bartholomew of Parma, 31 Bartoli, G., 862 Bartolomè de Las Casas, 69 Basu, R., 873, 876, 887 Batchelor, G.K., 368, 399, 400, 510, 590 Bates, C., 622–624 Bayes, T., 116 Bazin, H.E., 293, 294 Bearman, P.W., 865, 887 Beaufort, F., 208, 210, 364 Beauvois, W., 522 Becher, J.J., 136 Bechi, S., 217 Becker, A., 761 Becker, C., 761 Becker, R., 413 Beck, V.R., 865 Bede, 18, 19 Beeckman, I., 153, 244 Bekker, M.G., 618 Belanger, F.J., 238 Bel Geddes, N.M., 532, 533, 545, 547 Belgrado, J., 157

Author Index Belidor, B.F. de, 157, 231 Bell, A.G., 160, 314, 315, 487, 488, 547 Bellamy, E., 630 Beltrami, E., 305 Bénard, H., 285, 361 Bender, C.B., 256, 806 Benedetti, G.B., 98, 120 Benezet, 67 Bennett, H.H., 594, 595, 623 Bennett, R., 46 Benvenuto, E., 25, 152 Berger, E., 867 Bergeron, T.H.P., 345, 815, 816 Berkooz, G., 884 Bernbeck, O.E.G., 623 Bernoulli, D., 116, 125–127, 150, 156, 162–164 Bernoulli, Jakob, 111, 115, 116, 153, 155, 244, 248 Bernoulli, Johann, 111, 125, 126, 162 Bernoulli, N., 125 Bernstein, S.N., 300, 301 Berry, C., 315 Berti, G., 97, 98 Besancon, G., 333 Bessemer, H., 239 Bessler, J.E.E., 570 Besson, J., 230 Best, A.C., 413, 414 Betz, A., 283, 293, 492, 493, 565, 720, 723, 724 Biancani, G., 97 Bienkiewicz, B., 878, 880 Biggs, J.M., 697, 725 Bilau, K., 569, 570 Biot, J.B., 224, 225 Biram, B., 105, 106, 332, 370 Biringuccio, V., 64 Birkhoff, G.D., 297 Birnbaum, W., 498–500 Bisplinghoff, R., 508 Bitsuamlak, G., 880 Bixby, W.H., 203, 442, 658, 692 Bjerknes, C.A., 340 Bjerknes, J.A.B., 341 Bjerknes, W.F.K., 341 Bjorkdal, E., 426 Blackadar, A.K., 864 Black, J., 142 Blackman, R.B., 415 Blair, W.R., 335 Blake, T.E., 522 Blanchard, J.P., 224 Blanjean, L., 696

Author Index Blasius, P.R.H., 283, 289, 290, 299 Bleich, H.F., 667, 780–782, 784, 785, 789, 790 Bleriot, L., 488, 489 Blessmann, J., 883 Blevins, R.D., 863, 867 Blocken, B., 895 Blomberg, M.P.F., 546 Bodrov, V.A., 625 Boerhaave, H., 137 Bogardus, J., 242, 243 Bogolyubov, N.N., 771 Boileau, L.A., 238 Bolin, B.R.J., 352 Boltzmann, L., 152 Bonnetot, J.F.B., 226 Boole, G., 112 Boot, H., 337 Booyapinyo, V., 888 Borda, J.C. de, 177, 201, 202, 204, 443 Bordillon, T.J., 249 Borel, E., 300 Borgia, C., 76 Borrelli, G.A., 226 Borri, A., 892, 896, 897 Bortkiewicz, L., 119 Bort, L.T. de, 178, 333 Borum, F.S., 824 Bosanquet, C.H., 583 Boscovich, R.G., 157 Bosdogianni, A., 888 Bossut, C., 201, 202 Bouch, T., 261–264 Bouguer, P., 105, 201, 204, 215 Boulton, M., 237 Bounkin, K., 709 Bourry, E., 740 Boussinesq, J.V., 134, 135, 293, 376 Bowen, A.J., 864 Boyle, R., 100, 102, 136, 137, 146, 148 Bradbury, R., 354 Bradley, E.F., 883 Braham, Jr. R.R., 361 Brahe, T., 32, 92, 93, 122 Branca, G., 137 Brancusi, C., 686–688 Brandes, H.W., 178 Brantley, J.Q., 337, 831 Breer, C., 534 Breguet, L.C., 493 Breit, G., 336 Brewer, G., 485, 497 Briggs, H., 109 Brightmore, A.W., 711 Brocklesby, J., 179

927 Brooks, C.E.P., 624 Brooks, C.F., 359, 426, 427 Brooks, N.P.H., 867 Brown, D., 219 Browne, I.C., 337 Brown, J.M., 864 Brown, R., 338, 831 Brown, S., 245–247, 250 Brunel, I.K., 247, 252, 253, 260 Brunet, F., 238 Bruno, G., 89, 90 Bruno, L., 897 Brunt, D., 363 Brush, C.F., 564 Bryan, J.G., 354 Buchan, A., 191 Buckingham, E., 286 Budd, R., 545 Budyko, M.I., 707 Buffon, G.L.L., 116, 311 Bumstead, H.A., 495 Bunyakovskii, V.Y., 119 Burattini, T.L., 226 Burdon, R., 236 Bureau, R., 335 Burges, J.M., 331 Burgess, W.S., 513, 533 Bürgi, J., 109 Buridan, J., 27, 28 Burney, W., 207 Burr, E., 658 Burr, T., 259 Busch, N.E., 864 Bush, V., 313 Businger, J.A., 864 Butler, H.C., 603 Buys-Ballot, C.H., 183 Byers, H.R., 359, 361, 362 Byrd, R.E., 566 Byron, A.L., 112 C Caborn, J.M., 628, 629 Cabot, J., 211 Caesar, 18 Cailletet, L.P., 444, 445 Calder, K.L., 415 Caligula, 217 Cambise II (the second), 602 Camichel, C., 744 Campanella, T., 89, 90 Canovetti, C., 444, 447 Capen, F., 191 Capper, J., 174

928 Caracoglia, L., 877 Carassale, L., 895 Cardano, G., 32, 89, 99, 108, 113, 120 Carnot, N.L.S., 145–147, 494 Carpenter, F., 329 Carruthers, N.B., 426, 427, 863 Cartwright, D.E., 310, 311 Carus-Wilson, C.A., 540 Cassini, G.D., 194 Cassini, J., 198 Cassius Dio, 67 Castelli, B., 98, 124, 125 Castigliano, C.A., 260 Catchpole, 234 Cauchy, A.L. de, 129–131, 159 Cavalieri, B., 109 Cavallo, T., 223 Cave, C.J.P., 334 Cavendish, H., 142 Cayley, G., 82, 226–228, 456, 481 Cecco d’Ascoli, 27 Cederblom, J.E., 484 Celebi, E., 226 Celebi, H.A., 226 Celsius, A., 99 Cermak, E.J., 3, 480, 586, 847, 852, 862, 865, 866, 869, 895, 896 Cervantes Saavedra, M. de, 230 Chaldini, E., 165 Chaley, J., 249 Chang, C.C., 852, 855, 864 Chanute, O., 481, 484, 485 Chapman, E.H., 215, 401 Charba, J., 864 Charlemagne, 19, 67, 72 Charles d’Amboise, 77 Charles II Stuart, 217 Charles, J.A.C., 524 Charles the Bald, 67 Charney, J.G., 349–354, 368 Charnock, H., 411 Chasseloup-Laubat, G. de, 524, 525 Chatellier, H.L., 148 Chauvenet, W., 302 Chebyshev, P.L., 119, 120, 299, 300 Cheers, F., 761–765, 767, 768 Chefren, 70 Cheng, C.M., 875 Chen, P.W., 867 Chen, X., 870 Cheops, 50 Chepil, W.S., 596–600, 624 Cheung, J., 847, 896 Chevalier de Méré, 114

Author Index Chiodi, C., 682, 683 Choi, C.K., 875, 882, 891, 893 Choi, E.C.C., 882 Church, P.E., 583 Chu, S.L., 864 Ciarnait, 46 Cicala, P., 503 Cicero, 17, 29 Cicogna, P., 93 Ciermans, J., 111 Ciesielski, R., 880, 881 Clapeyron, B.P.E., 146 Clark, E., 263, 359, 659 Clark, T.L., 864 Clark, W., 867 Clauser, F.H., 772 Clausius, R.J., 147 Clement III, 31 Clements, F.E., 594 Cleopatra, 217–219 Cobb, J.R., 530 Cochran, L.S., 862 Coffin, J., 182, 184 Cohen, E., 722, 728, 866 Colardeau, E., 444, 445, 447 Colechurch, P., 67 Collar, A.R., 507, 508 Collinson, P., 221 Colmar, C.X.T. de, 111 Colonnetti, G., 690 Columbus, C., 170, 171, 211, 212, 234 Condorcet, A. de, 202 Consolazio, W.V., 639 Constantin, A., 565 Cook, J., 170, 215, 873, 875 Cook, N.J., 862, 881, 884, 885, 895 Cooley, J., 415 Cooper, K.R., 877 Cooper, T., 266, 267, 724 Cooper, W., 220 Corby, G.A., 366, 410 Coriolis, G.G., 175, 186, 187, 348, 351, 356, 363, 366, 367, 375–377, 380, 381, 404, 674 Cornelisz, C., 229 Cornish, V., 609, 610, 612 Corriez, M., 335 Cosimo II dè Medici, 96 Costanzi, G., 711 Coté, O.R., 864 Cottacin, P., 240 Cotte, M.L., 177 Cottier, J., 203 Coulomb, C.A., 156, 164, 202, 205

Author Index Counihan, J., 865 Coupard, C., 709 Courant, R., 350 Court, A., 703 Cox, H.R., 501 Coxwell, H., 225 Coyle, D.C., 679, 680, 683 Crain, C.M., 416 Cramer, H.E., 422 Crandall, S.H., 728 Cremona, L., 260 Cret, P.P., 546 Crocco, G.A., 455, 462 Crocé-Spinelli, J., 225 Crosby, 443 Crozier, W.D., 592 Cruzado, H.J., 891 Csanady, G.T., 864 Ctesibius, 24 Cubitt, J., 260 Cubitt, W., 234 Cugnot, N.J., 139 Culmann, K., 260 Currie, I.G., 867, 888 Curry, M., 515, 516 Curtiss, G.H., 487, 488, 532 Cusano, N., 99 D Da Costa, V.V., 636 D’Alembert, J. le Rond, 92, 117, 125–127, 157, 176, 202, 215, 218, 232, 275, 276, 282, 296 Dalgliesh, W.A., 849, 880 D’Alibard, T.F., 221 Dalrymple, A., 207 Dalton, J., 144, 176 Dampier, W., 170, 174, 175 Damsgaard, A., 847, 889 Danti, G.B., 40 Danusso, A., 689–691 Darby, A. I, 236 Darby, A. III, 236 Darcy, H.P.G., 293 D’Arlandes, F., 223 Darrieus, G.J.M., 571 Darwin, C., 210 Dashiell, 443 Da Silva Leme, R.A., 303 Dassié, S., 215 Davenport, A.G., 3, 412, 728, 732, 735, 736, 738, 739, 847–850, 858, 867, 870, 873, 876 Daverio, A., 690

929 Davidson, K.S.M., 516–521 Davis Jr., W.J., 541 Davison, A.E., 756, 757 Davis, W.M., 359 Davy, H., 144, 150 Deacon, E.L., 408–410, 420, 423, 425 Dean, A.G., 546 Deardorff, J.W., 869 Deaves, D.M., 858 Defant, F., 363, 364 Defoe, D., 206 Deharme, E., 538 Delagrange, L., 489 Della Porta, G., 89, 90, 96, 137 Delle Colonne, L., 94 Democritus, 14, 17, 21, 23, 109 Den Hartog, J.P., 693, 697, 741, 742, 744, 757, 759–761, 768, 769, 771 Denoel, V., 881, 895 Den Uyl, D., 623 Depperman, C.E., 358 Derham, W., 162 Descartes, R., 28, 90, 95, 96, 99, 109, 110 Desdouits, M., 445, 447 Devik, O.M., 341 Diana, G., 877, 890, 895 Diaz, B., 210 Dickey, W.L., 747 Dick, J.B., 639–641, 716 Diderot, D., 117, 215, 218, 232 Didion, I., 203 Dietlein, J.F.W., 252 Dimaschqi, al, 44 Dines, W.H., 329, 330, 333, 347, 443, 446–449, 452, 465, 705 Dingle, W.R.J., 620 Dionne, M., 876 Diou, de, 240 Dobson, G.M.B., 377, 378, 381, 386, 576, 580 Dockstader, E.A., 746 Dodd, E.L., 302 Doppler, C.J., 337, 338, 831 Dorothée C.F., 139 Douglas Baines, W., 843 Dove, H.W., 178 Dreyfuss, H., 547, 548 Dronia, H., 574 Dryden, H.L., 289, 297, 331, 684, 685, 709, 712 Du Bois, A.J., 657 Du Buat, P.L.G., 202, 204, 205, 446, 459, 694, 709, 711 Duchemin, N.V., 203, 204 Duchène-Marullaz, P., 859

930 Duckert, P., 335 Duckworth, J., 813 Du Hamel, H.L., 157 Duhem, P.M.M., 354 Dumas, R.J., 423 Duncan, W.J., 500, 501, 505 Dunn, G.E., 358 Dunn, L., 665 Durand, W.F., 494, 495, 497 Durst, C.S., 405, 425–427 Du Temple de la Croix, F., 487 Dutert, C.L.F., 240 Dutton, R., 887 Dyrenforth, R.S.G., 813 Dyunin, A.K., 619 E Eads, J.B., 260 Eaton, K.J., 847, 858, 866 Eckart, C.H., 305 Eckert, J.A.P., 316, 317 Eckert, W., 318 Edge, S.F., 525 Edgeworth, R.L., 204 Edward, I., 55 Edwards, A.T., 765, 844 Ehsan, F., 887 Eiffel, A.G., 203, 238, 260, 261, 286, 329, 371–374, 442, 444, 447, 449, 455, 464, 470, 525, 565, 674, 692, 710, 712, 720 Eilmer of Malmesbury, 40 Einstein, A., 316, 512, 569 Ekman, V.W., 375–377, 380–382, 401 Elcano, J.S. de, 212 Elder, J.W., 478 Eldridge, C., 659 Eliassen, A., 351 Elizabeth I, 55 Ellet, C.jr, 252, 254 Ellicott, 200 Elliott, W.P., 589 Ellis, D.L, 505 Elmacinus, G., 40 El Mansur, 51 Elton, J., 46 Empedocles, 14, 21 Enami, Y., 854 Epicurus, 17 Erskine, R., 637, 638 Esbjerg, N., 622, 623 Escande, L., 744 Espy, J.P., 180–182, 185, 186, 189, 221 Essenwanger, O.M., 427 Estoque, M.A., 364

Author Index Etkes, P.W., 583 Euclid, 22, 23 Euler, L., 116, 125, 127, 128, 130, 132, 149, 150, 156, 162, 163 Evans, O., 140 Evelin, J., 592 F Faccioli, M., 489 Fage, A., 297, 388, 391, 497, 694, 718 Fahreneit, D.G.D., 99 Fairbairn, W., 232, 237, 258 Falconer, W., 206, 207, 218 Fangui, 68 Farman, H., 489 Farquharson, F.B., 662–665, 670, 698 Faventinus, Marcus Cetius, 61 Favre, A.J., 423 Fawbush, E.J., 823, 824 Feller, W., 300 Felt, D., 113 Ferdinand II dè Medici, 96 Ferdinand II the Catholic, 211 Ferdinand III, 100 Fermat, P. de, 110, 111, 114, 115 Fermi, E., 316, 317 Ferrari, L., 109 Ferrel, W., 182, 184–189, 342, 349, 375 Feynman, R., 317 Fhakya-Khan, 241, 242 Fichtl, G.H., 864 Fick, A.E., 577, 578 Ficker, H. von, 405 Fidler, T.C., 451, 691, 692, 722, 726 Fiedler, F., 535 Field, J.H., 367 Findeisen, T.R.W., 816 Fingado, H., 503 Finley, J., 244 Finley, J.P., 191, 359, 818 Finney, E.A., 611, 613–617 Finzi, G., 443, 447 Firmino da Bellavalle, 31 Fisher, E.L., 364 Fisher, G., 221 Fisher, R.A., 302 Fitch, J., 139 Fitzroy, R., 190, 208, 210 Fjörtoft, R., 351, 352 Flachat, E., 238 Flachsbart, O., 283, 471, 693, 712, 713, 716, 718, 720, 721, 723, 896 Flagg, E., 679 Flamand, O., 881, 888

Author Index Flammarion, C., 189 Flay, R.G.J., 875, 876 Fleming, R., 680, 681, 692, 711, 828 Flettner, A., 569 Fleury, C.R. de, 238 Flora, S.D., 827–829 Floris V, 47 Follet, K., 75 Fontaine, P.F.L., 238 Fontana, N., 109, 114, 120 Förchtgott, J., 366 Forlanini, E., 228 Fourier, J.B.J., 144, 158, 592 Fowler, J., 264, 265 Fraenkel, K., 226 Frahm, H., 693 Francis I, 77 Franck, A., 449 Franck, N., 475 Franklin, B., 176, 221, 222, 236, 658 Frazer, R.A., 500, 501, 505, 670 Fréchet, M.R., 302, 304 Frederick II, 116, 176 Frederick, J., 231 Fredholm, E.I., 309 Free, E.E., 594 Freeman, J., 352 Freitag, J.K., 680 Friedrichs, K., 350 Frizzola, J.A., 849 Froude, W., 220 Fujino, T., 845 Fujino, Y., 896 Fujita, T.T., 210, 362, 363, 368, 821, 831, 864 Fulke, W., 20 Fulks, J., 823 Fuller, R.B., 532–534, 545, 631–634, 638 Fung, Y.C., 508, 697 Fuss, N., 248 G Galien, J., 223 Galilei, G., 20, 28, 77, 87, 91, 93–98, 100, 109, 114, 117, 120–124, 136, 137, 153, 154, 159, 160, 173, 194, 244, 280, 444 Galsworthy, J., 862 Galton, F., 189–191 Galway, J.G., 867 Garratt, J.R., 864 Garrick, I.E., 503–505 Gassendi, P., 137 Gaudard, J., 446 Gauss, C.F., 117, 118, 708 Gaviglio, J.J., 423

931 Gay Lussac, L.J., 146, 224, 225 Gengis Khan, 46 Gent, P.R., 864 Georgescu Gorjan, S., 686 Gerber, H., 264 Gerdel, R.W., 621 Gerhardt, J.R., 416, 863, 875 Germain, M.S., 165 Gerrard, J.H., 867 Geurts, C., 847, 897 Gevorkiantz, S.R., 625 Ge, Y., 847, 862, 877 Ghiocel, D., 863 Ghiotti, E., 691 Ghosal, S., 884 Gibbs, J.W., 152 Giblett, M.A., 330, 413, 414, 420, 425, 426 Gifford, F.A., 589, 590 Gilbert, C., 679 Gim Yu-Sin, 41 Giovanni da San Gemignano, 47 Giovannozzi, R., 695, 711, 716, 719 Girard, A., 109 Girard, P.S., 157 Girschick, M.A., 306 Givoni, B., 638 Glaisher, J., 189, 193, 225 Glauert, H., 493, 565 Glauert, M.B., 298 Gnedenko, B.V., 303, 304 Goad, J., 192 Goff, R.G., 864 Goldberger, P., 675 Gold, E., 643 Golden, J.H., 41, 530, 869 Goldie, A.H.R., 413 Goldstein, S., 280, 296, 388 Goliger, A., 892 Gomes, L., 864, 869 Gongwer, C.A., 297 Gonzaga, F., 174 Gordon, A.H., 863 Gordon, C.H., 354, 358 Gordon, L.D.B., 260 Gorgias, 14 Gorjan, S.G., 686 Gorshenin, N.M., 625 Görtler, H., 296 Goss, W.F.M., 539, 540 Gramme, Z.T., 563 Gravesande, W.J., 197 Gregory, P.H., 593 Gresley, H.N., 543 Griffin, O.M., 867

932 Grinchenko, V., 881 Groot, J. de, 120, 232 Grossatesta, R., 31 Guericke, O. von, 100–102, 137 Guggenheim, D., 497, 549, 566, 665, 748 Guido da Vigevano, 47, 48 Guidotti, P., 226 Guido Ubaldo del Monte, 120 Guldberg, C.M., 189, 381 Gumbel, E.J., 303, 304, 429 Gunn, R., 363 Gurley, K., 887 Gusmao, B.L. de, 223 Gutenberg, J., 60 Gutsche, F., 297 H Hadamard, J.S., 354 Hadley, G., 175, 176, 180, 182, 184, 186, 187, 342, 349, 375 Hadrian, 55 Hagen, G.H.L., 278, 443, 447 Halitsky, J., 586 Halladay, D., 560–562 Hallberg, S., 618 Halley, E., 122, 123, 172, 173, 175, 176, 179, 180 Hammel, A., 539 Hammurabi, 42 Hangan, H., 898 Han Hsin, 40 Hann, J.F. von, 147, 364, 365 Hansen, M., 289, 292, 534 Hansen, R.J., 867 Harbeson, J.F., 546 Hargrave, L., 333, 481–484, 487 Harris, A.J., 862 Harris, C.L., 472, 713 Harris, R.I., 857, 891 Hartlen, R.T., 867, 868 Hartree, D.R., 296 Hasley, W.F., 812 Hatshepsut, 33 Haupt, H., 259 Haurwitz, E., 363 Hayashida, H., 887 Hay, J.S., 587 Hazen, H.A., 443, 447, 821 Heald, R.H., 297 Hedley, W., 140 Hegel, G.W.F., 252 Heilmann, J.J., 538 Heisenberg, W.K., 399 Hellmann, G., 401, 421, 422

Author Index Helmholtz, H.L.F. von, 132, 146, 148, 281, 340, 491 Hemida, H., 877 Hendrik, F., 215 Hennebique, F., 244 Henne, E.J., 536, 537 Henry, J., 189 Henry, T.J.G., 427 Henson, W.S., 228 Heraclitus, 14, 17 Herapath, J., 149, 150 Herath, F., 335 Herbert, D., 46 Herbulot, J.J., 521 Hergessell, H., 334 Hermann, J., 149 Hermite, G., 333 Hermogenes, 55 Herodotus, 34, 602 Heron, 24, 25, 44, 137 Herreshoff, N.G., 512 Herring, A.M., 484 Herschel, W., 193 Hertz, H., 340 Hesiod, 34, 54 Hesselberg, T., 341, 426 Hiddessen, F. von, 334 Hiemenz, K., 284 Hikami, Y., 876, 888 Hilbert, D., 316 Hildebrandsson, H., 178 Hill, G., 684, 709 Hilst, G.R., 587 Hinze, J.O., 400 Hipparchus, 23–25 Hirai, A., 667, 673, 775, 847, 850, 852 Hjalmar, E., 304 Hjelmfelt, M.R., 884 Hoadley, D., 830 Hobbes, T., 89, 91 Hodge, J.M., 255 Hoecker, W.H.Jr., 829, 864 Hoffer, R., 862, 892 Hogg, A.D., 844 Høistrup, J., 884 Hollerith, H., 113 Holmes, D., 337, 831 Holmes, J.D., 862, 877 Holton, J.R., 863 Homer, 17, 34 Honnef, H., 571, 572 Hooke, R., 100, 102–104, 122, 123, 136, 137, 148, 153–155, 161, 172, 173, 175, 206, 236, 330

Author Index Hooper, S., 234, 235 Hopf, L., 290 Hopkins, H.G., 335 Hopper, G.M., 318 Horeau, H., 238 Horsburgh, J., 174 Hoste, P., 215 Hotelling, H., 306 Houghton, E.L., 863 Hovermale, J.B., 864 Howard, E., 630 Howard, L., 178, 574 Howe, W., 259 Huang Ti, 51 Huber, A., 880 Huddart, J., 174 Huet, P.D., 105, 106 Hugh, 19, 26, 289, 331, 594, 623, 684, 709 Hülsmeyer, C., 336 Humboldt, A. von, 178, 179 Hunsaker, J.C., 455, 466, 494, 495 Hunt, G., 350 Hunt, J.C.R., 864, 867, 884 Hütter, U., 572, 573 Hutton, C., 203–205 Huygens, C., 99, 114, 115, 121–123, 137, 194, 244 Hyatt, T., 244 Hypocrites, 54 I Iancovici, M., 881 Ide, J.J., 495 Idrac, P., 335 Imai,T., 549 Ireland, E., 550, 746 Irminger, J.O.V., 455–458, 467–470, 474, 565, 625, 639, 709, 713, 716, 717, 828 Irwin, P., 895 Isabel, 211, 632 Isidore, 18, 19, 31 Islitzer, N.F., 587 Isyumov, N., 849, 858, 873, 887, 895 Ito, M., 855, 862, 872, 876, 877, 882 Ivan, M., 884 Iwan, W.D., 867 Iwasa, Y., 887 Iyer, N.R., 875 Izakson, A.A., 296 Izumi, Y., 864 J Jackson, P.S., 884 Jacobi, K.G., 143

933 Jacobs, M., 566 Jacobs, W., 407 Jain, A., 891 James II, 217 Jan, J.M., 866 Jaray, P., 527–529 Jarrait, N., 522 Jatho, K., 487 Jeanneret, C.E., see Le Corbusier Jeantaud, C., 524, 525 Jeary, A., 883 Jeffreys, H., 355–357, 363, 368 Jeffries, J., 224 Jenatzy, C., 525 Jenkinson, A.F., 303 Jensen, M., 474–478, 586, 619, 625, 627–629, 646, 714, 715, 847, 876, 895 Jensen, R., 830 Jensen, R.A., 585 Jevons, W.S., 113 Jing Dong, 68 Jinman, G., 183, 184, 341 João II, 210, 211 Joessel, 448, 449 Johansen, F.C., 297 John Duns Scotus, 19 John I, 47 John of Alexandria, 27 John of Eschenden, 31 Johnson, E.F., 681 Johnson, G.D.B., 609 Johnson, L.B., 817 Johnson, L.G., 303 Jones, B.M., 493, 494 Jones, H., 827 Jones, K.F., 888 Jones, N.P., 888, 890, 896 Jones, R.T., 506 Jones, W.P., 506 Jordan, M.C.E., 305 Joubert, P.N., 852, 867, 870 Jouffroy d’Abbans, C.F.D., 139 Joukovsky, N.Y., 456, 489 Joule, J.P., 146, 147, 150 Jousse, M., 231, 232 Juleff, G., 64 Junkers, H., 455, 466, 505, 515 Jurin, J., 175–177 Juul, J., 572 K Kac, M., 309 Kahanamoku, D.P.K.M.H., 522 Kai Kawus, 38

934 Kaimal, J.C., 864 Kalinske, A.A., 585 Kamm, W., 530–532, 534, 535 Kampé de Fériet, M.J., 368, 582 Kämtz, L., 179 Kanda, J., 891 Kang Tai, 37 Kanishka, 71 Kantola, C., 547 Kao Yang, 41 Kareem, A., 862, 886–892, 895–898 Karhunen, K., 309 Karman, T. von, 124, 126, 133, 283–288, 293, 295–298, 378, 383, 387, 392, 395, 396, 399–402, 404, 408, 490, 492, 497, 503, 509, 566, 598, 620, 665–667, 694, 696, 697, 711, 739, 741, 742, 744, 748, 757 Kasperski, M., 878, 886, 890 Kassner, R., 503 Katzmayr, R., 721 Kawai, H., 870, 873, 886 Kawecki, J., 880, 881 Kazakevich, M., 881 Keefer, S., 254, 255 Kelvin (Lord), 99, 146, 147, 340, 366, 456 Kendall, M.G., 311 Kepler, J., 32, 92, 93, 109, 122, 123 Kernot, W.C., 454–456, 709 Ketchum, M., 711 Khan, F.R., 853 Khinchin, A.Y., 301, 307, 308 Kidder, F.E., 680 Kijewski-Correa, T., 895 Kim, S.I., 870 Kimura, K., 621 Kind, R.J., 861 King, F.H., 594 King, L.V., 331 Kircher, A., 11, 12 Kirchoff, G.R., 133, 165 Kitagawa, T., 895 Klemperer, W.B., 528, 534, 535, 711 Klemp, J.B., 864 Knight, W., 495 Knoller, R., 455, 466 Knox, S., 495 Kobayasi, T., 363 Koenig-Fachsenfeld, R. von, 531 Kolmogorov, A.N., 301, 397, 398 Komarov, A.A., 619 Konishi, I., 860 Kopernik, N., 92–94, 122 Kopp, G., 897 Kosambi, D.D., 309

Author Index Kosco, G., 812 Koten, H. van, 862 Kovasznay, L.S.G., 297 Kozak, J.J., 697, 698, 728 Kramer, C., 847, 863, 875, 878 Krantz, J.B., 240 Krassovsky, V.I., 565 Kratzer, A., 574 Krebs von Cues, N., 61 Kreil, C., 189 Kremser, V., 377 Kreutz, W., 619, 625 Krishna, P., 847, 862, 875, 880, 881, 889, 890 Krönig, A.K., 150, 151 Kruckenberg, F.F., 542, 543 Krylov, N.M., 771 Kublai Khan, 170 Kuethe, A., 331 Kuhler, O., 548 Kumme, R., 569, 570 Kungshu Phan, 40 Küssner, H.G., 499, 506 Kutta, M.W., 490 Kutzbach, J.E., 412 Kwok, K., 862, 873 Kyeser, K., 42 L Labrouste, H., 237 La Cour, P., 455, 458, 564, 565, 622, 623 Lagomarsino, S., 878 Lagrange, J.L., 128, 129, 143, 144, 158, 162, 164, 165, 299, 782 Laing Moo, 40 Lambert, J.H., 162 Lamb, H., 277, 355, 366, 388 Lamb, W.F., 683 Lamson, C., 484 Lamy, F., 173 Lana Terzi, F., 222 Lanchester, F.W., 491–493, 497, 759 Landsberg, H.E., 635, 636 Landweber, L., 297 Laneville, A., 853, 887 Lange, A., 529, 530 Langford, 174 Langley, S.P., 372–374, 443, 446, 447, 456, 457, 459, 481, 485, 487, 494, 497, 524 Langmuir, I., 362, 813, 816, 817 Lansdowne, Z., 833 La Peltrie, D. de, 564 Lapham, I., 191

Author Index Laplace, P.S. de, 118, 128, 129, 143, 144, 157, 177, 299, 300 Larose, G.L., 888 Larsen, A., 878, 882 Lauder, B.E., 869 Lautenschlager, C.F., 525 Lavender, T., 498 Lavoisier, A.L., 142, 143, 177 Lay, W.E., 530, 531 Le Baron Jenney, W., 674, 680 Lebesgue, H., 308 Leblanc, 250 Le Bris, J.M., 481 Le Brun, N.E.C.H., 676 Le Corbusier, 634–636 Le Dantec, M., 444, 447 Lee, B.E., 864 Lee, E., 233 Leeghwater, J.A., 229 Lee, S., 880 Lehmer, D.H., 312 Leibniz, G.W. von, 104, 110–112, 114, 115, 126, 153, 155, 231, 244 Lemelin, D.R., 876 Lenin, V., 490 Lennox, C., 218 Leonardo da Vinci, 8, 27, 40, 76, 77, 87, 99, 111, 112, 124, 137, 194, 221, 226, 330 Leopoldo I dè Medici, 99 Lesage, 243 Letchford, C., 875, 895 Lettau, H.H., 298, 407 Letzmann, J.P., 359, 822–824 Leucippus, 14, 17 Leurechon, J., 97 Leutmann, J.G., 104 Leverrier, U.J.J., 190, 332 Levitan, M., 891 Lévy, M., 445, 657 Lewis, H.M., 335 Lewy, H., 350 Ley, W.C., 192 Lhermitte, R.M., 337 L’Hopital, Guillame-Françoise-Antoine de Sainte-Mesme, 111 Li Beng, 68 Li Ch’üan, 38 Liddell, C., 260 Lienhard, F., 659 Liepmann, H.W., 416, 417, 419, 509, 510, 728, 732 Lilien, J.L., 882 Lilienthal, K.W.O., 443, 444, 449, 451, 481, 482, 484–486, 490, 515, 523

935 Lilly, D.K., 864 Lincoln, A., 191, 548 Lindeberg, J.W., 300 Lindenthal, G., 657, 658 Lind, J., 105, 106, 329 Lindley, D., 864 Linpergh, P., 232 Lin, Y.K., 863, 888 Lipton, T.J., 513 Li, Q.S., 895 Lloyd, J., 823 Locke, J., 104 Lodge, J., 522 Loève, M., 309 Loewe, F., 620 Loewy, R., 545, 548 Long, R.R., 367 Long, S., 259 Longuet-Higgins, M.S., 310, 311 Loomis, E., 181, 182 Lopez, J.L.S., 636 Loredo Souza, A., 847, 898 Lorenz, E.N., 353, 354 Lossen, 251 Lössl, F. von, 443, 447, 449 Loudon, J.C., 194 Louis the Pious, 67 Louis, V., 238 Louis XIV, 104 Louis XVI, 223 Lucan, 35 Lucius Annaeus Seneca, 18 Ludlam, F.H., 362 Lumley, J.L., 310, 863 Lungu D., 863 Luxton, R.E., 864 Lyapunov, A.M., 299, 300 M Mabrey, J.F.M., 754 MacCready, P.D., 416 Mach, E., 459 Mach, L., 455, 456 Maclaurin, C., 162, 197 Madaras, J., 569, 570 Madeyski, A., 765 Magellano, F., 170, 211 Magiotti, R., 97, 98 Magnus, H.G., 134, 135, 199, 489, 569, 756 Mahesh, K., 884 Mairan, J.J. D’ortous de, 162 Mallock, H.R.A., 285 Maney, G.A., 681 Manly, C.M., 485

936 Mannesmann, O., 443, 447 Mannini, C., 895 Mann, J., 888 Man Singh I, 60 Manuel I, 211 Marat, J.P., 143 Marconi, G., 192, 334, 335, 511, 513, 516 Marcus Aemilius Lepido, 66 Marcus Aurelius, 17 Marcus Cetius Faventinus, 61 Marey, É.J., 455, 459, 460, 485 Margoulis, W., 495 Mariotte, E., 102, 121, 154, 155, 194, 195, 204 Markov, A.A., 299, 300 Mark, W.D., 863 Marrett, P., 219 Marris, A.W., 867 Marsenne, M., 160, 161 Martin, B., 105 Martin, W.W., 888 Martuccelli, J.R., 766 Marukawa, H., 878 Mason, P.J., 883 Masters, F., 891, 895 Mas’udi, 44 Mas’udi, al, 44 Matsumoto, M., 873, 880, 882, 888, 892, 893 Mattice, W.A., 425 Mauboussin, P., 529 Mauchly, J.W., 316 Maury, M.F., 182, 184 Maxim, H.S., 444, 455, 458, 459, 463, 483 Maximov, N.A., 623 Maxwell, J.C., 151, 152, 260, 378 Mayer, A., 635 Mayer, J.R. von, 146 May, H.I., 853 Mayne, J.R., 858, 865, 885 Mazouzi, A., 887 Mc Lure, N.R., 266 McCormick, R.A., 416, 417, 422, 424 McCurdy, J.A.D., 487, 488 McLean, 366 McVehil, G., 864 Medici, G. dé, 77 Mehta, K.C., 847 Meier-Windhorst, A., 744 Meikle, A., 234 Melan, J., 657, 658 Melbourne, W.H., 847, 850, 852, 860, 862, 867, 870, 872, 878, 886 Mellor, M., 620 Menabrea, L.F., 260 Merle, W., 32

Author Index Meroney, R.N., 880 Michele da Cuneo, 171 Mickl, J., 530 Mildner, P., 405 Milemete, W. de, 42 Miljutin, N.A., 631 Miller, P., 139 Miller, R.C., 824 Millikan, C.B., 296 Mills, R., 674 Minor, J.E., 867, 888 Mises, R.E. von, 288, 301 Mitchell, K.E., 864 Miyata, T., 882, 890 Mobius, A.F., 260 Modi, V.J., 876 Mohammed, 31 Mohn, H., 189, 381 Mohr, O., 260 Moin, P., 884 Moisseiff, S.L., 658–660 Moivre, A. de, 118 Molchanov, P.A., 335 Molitor, D.A., 678 Möller, E., 536 Möller, M., 359 Monet, J.P.A. de, 177 Monge, G., 158 Monier, J., 243 Monin, A.S., 411, 590 Monomura, Y., 882 Montanari, G., 173, 174 Montgolfier, J.E., 26, 223 Montgolfier, J.M., 26, 223 Montgomery, J.J., 481 Montgomery, R.B., 403, 404, 409, 411 Montmort, P.R. de, 115 Moore, F., 193 Moore, T., 89 Morgan, J.W., 865 Morin, A., 203 Morisako, K., 887 Morland, S., 111 Morris, C.T., 681 Morrison, R.J., 193 Mo Tzu, 40 Mouillard, L.P., 483 Mozhayskiy, A.F., 487 Müldner, W., 362 Mulenga, 892 Müller Breslau, H.F.B., 260 Muller, F.P., 858 Müller, J., 108 Müller, J.H. von, 111

Author Index Munk, M.M., 493, 513, 528 Murakami, S., 862, 870, 875, 878, 880, 883, 889, 892, 893, 895 Murphy, P., 194 Musschenbroeck, P. van, 157, 158, 221 Muthesius, H., 631 Muys, C.D., 229 Mycerin, 70 N Nagel, F., 717 Nägeli, W., 625 Nakagawa, K., 845 Namyet, S., 725 Nansen, F.W.J., 375, 377 Napier, J., 109, 111 Napier Shaw, W., 333, 356, 639 Napoleon III, 190 Napoleone Bonaparte, 158 Naprstek, J., 881, 893 Narita, N., 854 Narses, 67 Nash, J., 237 Natrus, L. van, 232 Navier, L., 123, 157–159, 226, 247 Necho, 34 Nekrasov, P.A., 300 Nelson, W.H., 831, 832 Nemorarius, J., 27 Neri di Fioravante, 67 Nero, 39 Neumann, J. von, 312, 316, 317, 349 Newberry, C.W., 843, 855, 862 Newcomen, T., 139 Newman, M., 318 Newstein, H., 368 Newton, C., 834 Newton, I., 77, 110, 122, 124, 149, 195 Nielsen, T., 467, 710 Niemann, H.J., 877, 878 Nieser, H., 858 Nikuradse, J., 283, 290, 291, 294, 295, 408 Nipher, F.E., 445, 449 Nishijima, K., 895 Nishitani, H., 855 Noble, W., 161, 217, 218 Noguchi, I., 533 Nøkkentved, C.D.N., 467–472, 474, 475, 625, 639 Nolan, T., 680 Norton, G., 357 Novak, M., 853, 867 Nowicki, M., 635 Noyes, Le Varne, 562

937 Nyberg, C.R., 483 Nyquist, H., 314 O Obasi, G.O.P., 888 Obukhov, A.M., 399 Ogawa, K., 870 Ogura, Y., 416 Ohkuma, T., 878 Okauchi, I., 850, 851 Okubo, T., 854 Olesen, H.R., 884 Olivari, D., 888 Omar I, 44 Omar T, 416 Omori, F., 740 Onsager, L., 399 Ooishi, W., 347, 349 Oresme, N., 28, 31 Orman, W.T. van, 426, 427 Orville, H.T., 445, 460, 485, 487 Osler, A.F., 107 Ostrogradskii, V., 119 Otis, E.G., 242 Owen, E., 478, 480 Owen, J., 881 Owen, P.R., 478 Ozker, M.S., 747 P Pachacutec, 69 Pacioli, L., 76 Paciuk, M., 870 Paeschke, W., 405, 407–409 Pagon, W.W., 405, 410, 415, 694, 695, 698–700, 703, 711, 725, 741, 742, 744, 746, 828 Paidoussis, M.P., 887 Paine, T., 236 Pajot, L.L., Comte D’Ons-en-Bray, 105 Palladio, A., 61, 62, 259, 629 Palladius Rutilius Taurus Aemilianus, 61 Palmén, E.H., 347 Palmer, T.R., 878 Panofsky, H.A., 424, 864 Papin, D., 137, 139 Papoulis, A., 863 Pappus, 24, 25 Pardies, I.G., 244 Parent, A., 155, 156 Parker, B., 630 Parker, J., 243 Parkinson, G.V., 768, 769, 771–774, 844, 853, 867, 870, 887

938 Parmalee, R.A., 853 Parmenides, 13 Parry, W.E., 221 Pascal, B., 100, 111, 114, 115 Pasquill, F., 587, 589, 592 Passel, C.F., 645 Paterka, J.A., 866 Patterson, J., 327 Paulson, C.A., 864 Paxton, J., 239 Pearce, J.A.jr, 194 Pearce, R.P., 364 Pearson, A., 821 Pearson, J.L., 583 Pearson, K., 306 Pecora, L.J., 639 Peirce, B., 302 Peltier, J.C.A., 358 Peltier, W.R., 864 Penaud, A., 228 Penwarden, A.D., 867 Perier, F., 100 Perlat, A., 335 Perrin, H., 722, 728 Perry, T.O.P., 443, 562 Peslin, H., 189 Peterson, E., 720 Peter the Great, 125 Pett, P., 217 Pfalz, K.T. von, 177 Phillips, H.F., 454, 455, 482 Phillips, N., 352, 353, 457 Philo, 24, 25 Philolaus, 13 Picard, J., 194 Picasso, P., 512 Piccardo, G., 886, 893 Piddington, H., 180, 186 Pielke, R.A., 864 Pierson, W.H. Jr., 363 Pietro d’Abano, 27 Pigot, T., 161 Pike, Z.M., 594 Pinney, E.J., 667, 778, 780, 781 Piobert, G., 203, 204 Pirner, M., 881 Pitot, H. de, 105, 329 Pizarro, F., 63 Planck, M., 146 Plato, 15, 16 Platzman, G., 352 Pliny the Elder, 17, 18, 30, 32, 35, 68 Plotinus, 18

Author Index Pohlhausen, K, 288 Poincaré, J.H., 300, 340, 354 Poisson, S.D., 118, 119, 123, 129–131, 144, 145, 157, 158 Poleni, G., 203 Polly, J., 232 Polo, M., 41 Poncelet, J.V., 202 Poole, M., 873 Pope, A., 31, 63, 90, 863 Poreh, M., 870 Porsenna, 66 Poschmann, von, 105 Post, G.B., 675, 679 Post, H.W., 347 Poyet, B., 248 Prandtl, L., 134, 280–284, 286, 288, 290–296, 298, 299, 364, 369–371, 377, 382, 383, 387–390, 392, 401–404, 455, 465–468, 471, 492–495, 499, 526, 529, 565, 586, 598, 693, 694, 712, 724 Pratap Singh, 60 Pratt, C., 259 Pratt, T.W., 259 Press, F., 878 Press, H., 419 Price, P., 748 Price, R., 116 Price, W.I.J., 618 Price, W.S., 766 Pridden, D.L., 865 Priestley, C.H.B., 416 Priestley, J., 142 Prior, M.J., 877 Proctor, D., 592 Prony, G. de, 158 Protagoras, 14 Ptolemy, C., 23–25, 31, 32, 92, 108, 192 Publius Ovidius Naso, 18 Publius Terentius Varro Atacinus, 29 Publius Vergilius Maro (Virgil), 17 Pugh, H.L.D., 618 Pulin, A., 538 Pulipaka, N., 882 Purdy, C.T., 675, 676, 679 Putnam, P.C., 429, 566 Pyrrho, 17 Pythagoras, 13, 20–22, 24, 159 Q Qazwini, al, 44 Queney, P., 366, 367, 410 Quervain, A.A. de, 334

Author Index Quintus Horatius Flaccus, 55 R Radok, U., 620 Rado, L.L., 636 Rae, W.H., Jr., 863 Rameau, J.P., 164 Ramelli, A., 230 Rammler, E., 304 Randall, J., 337 Rankine, W.J.M., 147, 220, 255, 256, 260, 263, 358, 657, 658, 823 Ransome, E.L., 244 Rateau, A.C.E., 448, 463 Rathbun, J.C., 685 Rausch, E., 726–728 Rawson, H.E., 377 Rayleigh (Lord), 133, 134, 151, 287, 297, 310, 311, 361, 363, 393, 429, 489, 491, 509, 661, 694, 712, 848 Raymond, A., 636 Raymond, C.W., 658 Redfield, W., 180, 181, 186, 341 Redpath, J., 246 Reed, D., 891 Regiomontano, G., 40 Reichardt, H., 389, 586 Reichelderfer, F., 825 Reichel, M.W., 443, 447 Reid, W., 180, 186 Reissner, H.J., 499, 667, 775, 777 Relf, E.F., 297, 498, 742 Renard, C., 444, 449, 454, 455, 462 Renau, B., 215 Rendel, J.M., 252 Renou, E., 178, 574 Repetto, M.P., 895 Revkovskii, S., 119 Reye, T., 189 Reyher, S., 104 Reynolds, O., 11, 135, 198, 278–281, 284, 292–294, 373, 383, 390, 414, 415, 461 Riabouchinsky, D.P., 286, 331, 455, 463 Riccati, G., 164 Riccati, J., 157, 164 Ricciardelli, F., 897 Ricci, M., 98 Rice, S.O., 310, 510, 732, 734 Richards, D.J.W., 844 Richardson, A.S., 766–768, 844 Richardson, G.M., 882 Richardson, L.F., 345, 383, 384, 386, 578, 592 Richards, P.J., 882 Ricotti, M., 526

939 Ricour, F., 538 Ricour, M., 445, 447 Riebsame, W.E., 888 Riehl, H., 358 Riera, J.D., 870, 883 Ritter, A., 260, 657 Ritter, W., 657 Ritz, W., 661, 679, 782 Robert, C., 824 Robert, N., 223 Roberts, O.F.T., 577–580, 582, 632 Robertson, L.E., 867 Robertson, R.H., 679 Roberval, G.P. de, 77, 109, 114, 115, 121 Robins, B., 198–201, 443, 680, 692 Robinson, J.T.R., 107, 327 Robitzsch, M., 335 Rodgers, C.P., 489 Roebling, J.A., 252 Roebling, W.A., 256 Rogallo, F.M., 523 Rogallo, G., 524 Rojani, K., 887 Romain, P.A de, 224 Roosevelt, F.D., 566, 595 Roots, E.F., 621, 622 Rosemeyer, B., 534 Roshko, A., 297, 298 Rosin, P., 304 Rossby, C.G.A., 317, 347–351, 358, 359, 401–404, 409, 411 Rotch, A.L., 482 Rouse, 200, 201, 204, 206–208, 263, 443 Rouse, H., 368, 585 Rozier, J.F.P. de, 223, 224 Rudolf, P.O., 625 Ruedy, R., 297, 741, 761, 765 Rufius Festus Avienius, 29 Rufus, W., 67 Rumpler, E., 526, 527 Rumsey, J., 139 Runge, C., 490, 492 Ruscheweyh, H.P., 873, 876 Russell, J.S., 253 Russell, R.R., 864 Rykatcheff, M., 334 S Sabzevari, A., 855, 867 Sachs, P., 863 Sadeh, W.Z., 852 Saffir, H.S., 210, 359, 817, 855, 861 Sahure, 33, 34 Saint Augustine, 18, 19

940 Saint Dunstan, 11 Saint-Loup, 443 Saint Peter, 125, 189, 190, 299 Saint Thomas Aquinas, 19, 27 Saint-Venant, J.C.B. de, 129, 131 Sakata, H., 855 Salomon de Caus, 137 Salter, C., 388, 392–394, 397, 414 Salvetti, M.V., 897 Samson, 46 Sandström, J.W., 341 Santorio, S., 99 Santos-Dumont, A., 488 Sanuki, M., 329 Sanzio, R., 62 Sarkar, P.P., 878, 888 Sarpkaya, T., 866, 887 Sasaki, T., 363 Saulnier, J., 237 Saunderson, N., 116 Sauveur, J., 161 Savery, T., 137, 139 Savoi-Carignan, de, 630 Savonius, S.J., 569, 570 Scanlan, R.H., 503, 508, 789, 854, 855, 863, 867, 887, 888, 890, 896 Schadt, C.F., 585 Schaefer, V.J., 362, 813, 816, 817 Scheele, C.W., 142 Scherbius, A., 314 Scheutz, E., 112 Scheutz, G., 112 Schickard, W., 111 Schlör, K., 529, 530 Schluenzen, R.H., 880 Schmidt, E., 305 Schmidt, F.H., 363 Schmidt, W., 383, 386, 415, 574 Schmitt, F.E., 810 Schoemaker, R.L.A., 710 Schreiber, P., 332 Schriever, W.R., 846, 847, 855, 862 Schroeder, J., 895 Schubauer, G.B., 289, 331, 392 Schubert, E., 609 Schueller G.I., 874 Schuster, A., 306 Schwedler, J.W., 260 Scorer, R.S., 362, 367, 368, 410 Scoresby, W. jr, 208 Scott, R.F., 359, 617 Scott, R.H., 192, 193 Scrase, F.J., 359, 405, 413, 414, 577

Author Index Scruton, C., 505, 666, 670, 672, 698, 747–749, 751, 754, 768, 769, 842, 845, 847, 850, 867, 873, 887, 895 Sears, W.R., 503, 506, 507, 509, 861 Sébert, H., 445 Sedlacek, G.N., 876 Seely, B.K., 592 Seelye, C.J., 821 Segrave, H.O. de Hane, 530 Seguin, C., 249 Seguin, J., 249 Seguin, M., 249 Seguin, P., 249 Seitfert, R., 712, 713 Seitz, H., 721 Selberg, A., 667, 790, 791, 844 Seleucus IV, 217 Selfridge, T.E., 487, 488 Selvam, R.P., 878, 884 Senecio of Nuremberg, 40 Serrell, E.W., 254 Severance, C., 683 Sfintesco, D., 861, 862 Sforza, L.M., 76 Shannon, C.E., 313, 314 Sharma, R.N., 882 Shatswell, O., 513, 515 Shaw, W.N., 187, 210, 333, 356, 381, 638 Shellard, H.C., 705, 708, 843 Sheppard, P.A., 407–409, 416 Sherlock, R.H., 331, 410, 425, 429, 584, 697, 699–701, 705, 734 Sherwood, W., 536 Shima, K., 845 Shinozuka, M., 853, 866 Shiotani, M.S., 849 Shiraishi, N., 870, 873, 876, 888 Shiraki, K., 853 Shlichting, H., 283 Showalter, A., 823 Sidarous, J.F.Y., 870 Siegert, A.J.F., 309, 310 Sigsfeld, R.H.B. von, 333 Simiu, E., 860, 863, 864, 866, 867 Simmons, L.F.G., 297, 388, 393, 394, 397, 414, 742 Simon Magus, 39 Simpson, C.C., 833 Simpson, C.L., 587 Simpson, G.C., 359 Simpson, R.H., 817, 818 Simpson, T., 116 Singell, T.W., 698, 715

Author Index Singer, I.A., 849 Siple, P.A., 643–645 Sirovich, L., 884 Sivel, T., 225 Sizzi, F., 94 Skop, R.A., 867 Skramstad, H.K., 289 Slutsky, E.E., 307 Smagorinsky, J., 352, 353, 369 Smeaton, J., 139, 199–201, 204, 206–208, 233, 234, 236, 243, 263, 443, 562 Smith, A.C., 220 Smith, Albert, 681, 711 Smith, Alexander, 218 Smith, Alfred, 711 Smith, C.S., 723 Smith, D.R., 669 Smith, F.C., 664 Smith, H.W., 416 Smith, J.C., 747 Smith, J.D., 867 Smith, R.A., 592 Smith, R.B., 884 Smith, R.K., 864 Smith, R.L., 337, 831 Smith-Rose, R.L, 335 Smith, W., 246 Snefru, 33 Socrates, 14 Soize, C., 867 Solari, G., 862, 881, 889, 895 Solberg, H., 341, 342, 344 Soldati, N., 447 Somerset, E., 137 Sommerfeld, A., 278 Soreau, R., 446, 448, 449 Sorge, G.A., 165 Sosostris II, 50 Spalding, D.B., 869 Sparks, P.R., 870 Spearman, C., 306 Spinoza, B., 115 Spivak, H.M., 297 Spofford, C.M., 711 Spurr, H.V., 680, 681, 683 Stackeley, A., 886 Stahl, G.E., 136 Stalker, E.A., 584 Standen, N.M., 852 Stanton, T.E., 451, 452, 455, 461, 462, 709 Starrett, L.G., 824 Stathopoulos, T., 895 Steers, G., 219 Stein, C.S., 635

941 Steinman, D.B., 658, 776 Stepanov, K.M., 593 Stephens, O., 519, 521 Stephenson, G., 140, 141, 258 Stephenson, R., 258 Stephens, R., 521 Sterling, M., 881 Stevens, E.A., 219 Stevens, J. III, 218 Stevens, J.C., 219, 511 Stevenson, D.C., 876 Stevenson, T., 370 Stevens, R.L., 218 Stevin, 77, 120, 121, 229 Stibitz, G.R., 314, 315, 317 Stieltjes, T.J., 308 Stigter, 892 Stockbridge, G.H., 740 Stokes, G.G., 131 Stommel, H.M., 580 Stout, M.B., 331, 425, 700 Stout, W.B., 532, 545 Straaten, J.F. van, 643 Strauss, J.B., 659 Strindberg, N., 225 Stringfellow, J., 228 Strom, G.H., 586, 621 Strouhal, V., 277, 739 Strutt, J.W., see Rayleigh Sturm, R.G., 741 Stussi, F., 665 Styles, D.F., 850 Suckstorff, G., 359 Sugg, A.L., 867 Sun, L.M., 878 Sun, T.F., 862, 875 Surry, D., 865 Susruta, 51 Sutton, O.G., 369, 370, 405, 409, 580–582, 588, 592 Sverdrup, H.U., 350, 405 Swain, G.F., 711 Swiger, W.F., 746 Swithinbank, C.W.M., 621 Sykes, R.I., 883 Sylvester, Harold Mac Tavish, 710, 711 Sylvester, J.J., 305 Symington, W., 139 Szilard, L., 316 T Tachigawa, M., 873 Takle, E.S., 864 Tamura, T., 883

942 Tamura, Y., 878, 880, 882, 891, 893, 895, 896 Tanaka, H., 621, 878, 880 Tartini, G., 164 Tatin, V., 228 Taylor, B., 161 Taylor, C.E., 485 Taylor, G.I., 307, 309, 377, 378, 576 Taylor, P.A., 883 Tcheremoukhin, A., 709, 715 Teesdale, L.V., 831 Telesio, B., 89 Telford, T., 156, 236, 246 Teller, E, 316 Tennekes, H., 863, 864 Tepper, M., 368, 827 Tesla, N., 312 Teunissen, H.W., 883, 884 Thales, 12, 15, 20 Thang-stong rGyaf-po, 69 Thelwall, E., 193 Themistocles, 170 Theodorsen, T., 501, 774 Theophrastus, 16, 90 Thibault, 204, 446 Thiesen, 448 Thomas, P.H., 568 Thom, H.C.S., 705, 864 Thompson, B., 143 Thompson, P., 350 Thomson, W., see Kelvin Thornthwaite, C.W., 407 Thoroddsen, S.T., 876 Thullenar, C. van, 834 Tice, J.H., 359 Tieleman, H.W., 877, 884 Tippett, L.H.C., 302, 304, 311 Tissandier, G., 225 Titov, V.A., 609 Titus Lucretius Carus, 17 Toaldo, G., 205 Todeschini, M., 569 Tollmien, W., 283, 289, 549 Tomko, J.J., 867 Töpfler, C., 284 Tornquist, E.L., 761 Torricelli, E., 124 Totila, 67 Townend, H., 388, 391 Town, I., 259 Townsend, A.A., 400, 864 Trajan, 67 Trento, F., 62 Trevitick, R., 140 Triefenbach, J., 609

Author Index Truesdell, C., 244 Tryggvason, B.V., 864 Tschanz, T., 873 Tse, T., 895 Tsiolkovsky, K.E., 443, 455, 459, 718 Tukey, J.W., 415 Tulley, J., 173 Turing, A.M., 314 Turnbull, D.H., 888 Tuve, M.A., 336 Twain, M., 255 Twisdale, L.A., 878 U Ukeguchi, N., 855 Ulam, S.M., 312 Ulfada, C., 46 Umemura, S., 853 Unwin, R., 630, 709 Unwin, W.C., 454 Urbano VIII, 94 Utsugi, M., 363 Uyl, D.D., 623 V Vaicaitis, R., 867 Vanderbilt, H.S., 519 Vanderbilt, M.D., 870 Van der Hegge-Zijnen, 289 Van der Hoven, I., 421–423, 847 Vanderperre, L.J., 710, 720 Vanmarcke, E.H., 867 Varenius, B., 178 Varignon, P., 121 Varney, T., 741, 756 Vasco da Gama, 170, 211 Vellozzi, J., 866 Venturi, G.B., 203, 586, 641, 860 Verantius, F., 244 Verrocchio, 76 Vettin, 370, 371 Viannay, P., 521 Vicat, L.J., 243, 249 Vickery, B.J., 850 Vicroy, D.D., 884 Viète, F., 109 Vincent, G.S., 664 Vincent, N.D.G., 471, 639, 714, 716 Vince, S., 133, 134, 203 Viollet-le Duc, 74 Visher, S.S., 809 Viviani, V., 98 Vogt, H.C., 456 Voisin, G., 489

Author Index Voltaire, 122 Vonnegut, B., 362, 813, 816 Vuuren, C. van, 232 W Wadcock, A.J., 865 Waddell, J.A.L., 723 Wadsworth, G.P., 354 Wagner, A., 364 Wagner, H.A., 499, 504 Wakimoto, R.M., 884 Walcott, C.D., 494 Walker, G.R., 862 Wallis, J., 110, 121, 161 Walshe, D.E.J., 755, 844 Walter de Milemete, 42 Walter, W., 619 Wan, C.A., 864 Wan Chen, 37 Wannenburg, J.J., 643 Warden, R., 367 Wardlaw, R.L., 850, 853, 854 Ward, N., 864 Ward, N.B., 830 Warner, E.P., 495, 513 Warren, J., 259 Warr, G.F., 260 Warsap, J.H., 718 Waterston, J.J., 151 Watson, G.L., 513 Watson, J.C., 359 Watson, T.J., 315 Watson-Watt, R.A., 337 Watt, J., 139, 140, 237 Wawzonek, M.A., 870, 887 Wax, M.P., 420 Weaver, W., 755 Webb, E.K., 418, 864 Wegener, A.L., 359, 815, 822 Wehner, H., 298 Weibull, E.W., 304, 428, 848 Weick, F.E., 496 Weis-Fogh, T., 478 Weisskopf, G.A., 487 Weizsäcker, C.F.F. von, 399 Wellington, 445 Wells, A., 455, 458 Welsh, J., 225 Welt, F., 876 Weng-Cheng, 68 Wenham, F.H., 453, 455 Wen, Y.K., 864, 887 Wernwag, L., 252

943 Westgate, J.M., 594 Wexler, H., 350, 827 Weyl, H., 305 Whipple, S., 259 Whitbread, R.E., 844, 860 Whittingham, H.E., 849 Wichmann, H., 362 Wiener, N., 307, 308, 729 Wiener, P.L., 636, 637 Wieringa, J., 878 Wieselsberger, C., 283, 286, 712 Wigner, E., 316 Wilcke, J.C., 823 Wild, H. von, 107 Wilkins, J., 226 Wilkinson, J., 236 Wilkinson, M., 410 Wilks, S.S., 303 Wille, R., 867 Willett, H.C., 363 William of Ockham, 19, 27 Williams, F.C., 318 William the Conqueror, 67 Wilson, A.C., 681 Wilson, W.M., 681 Wing, S.P., 699 Winslow, C.E.A., 638 Winter, H., 723 Winthrop, J., 173 Wisse, J., 881 Wittlesey, J.H., 635 Woelfle, M., 625 Wold, H.O.A., 307 Wolff, C., 104 Woltmann, R., 104, 203, 205 Woodgate, L., 754 Woodruff, G.B., 697, 728, 747 Woodruff, N.P., 598 Woolf, A., 140 Wootton, L.R., 867 Wouters, I., 710 Wragge, C.L., 805 Wren, C., 121 Wright, F.L., 631, 632 Wright, O., 455, 486–488, 534 Wright, W., 288, 487, 492, 493 Wu, T., 895 Wyatt, T.A., 853, 861 Wyngaard, J.C., 864 X Xenofon, 54 Xenophanes, 13

944 Xerxes, 170 Xiang, H.F., 895 Xu, Y.L., 862, 895, 896 Y Yaglou, C.P., 639 Yamaguchi, A., 895 Yamaguchi, H., 882, 888 Yamaguchi, T., 853 Yamamoto, C., 416 Yamazaki, S., 878 Yang, J.N., 888 Yang, Q., 847, 898 Yehlu Chhu-Tshai, 46 Yoshisaka, T., 621 Young, G., 305 Young, T., 156 Yuan Huang-T’ou, 41

Author Index Yule, G.U., 307 Z Zahm, A.F., 455, 460, 466, 494 Zapf, N., 547 Zdravkovich, M.M., 865, 887 Zeno of Citium, 17, 29 Zeno of Elea, 13 Zeppelin, F.A.H.A.G. von, 549, 833 Zhao, J., 887 Zhukovsky, N.Y., 455, 456 Zienkiewicz, H.K., 478, 480 Zingg, A.W., 596 Zon, R., 623 Zoser, 70 Zuranski, J.A., 880, 881 Zuse, K., 313, 318 Zyl, J. van, 232