Bioengineering, Thermal Physiology and Comfort 044499761X, 9780444997616, 9780080874692

Table of contents :
Content:
Edited by
Page 1

Copyright page
Page 2

Symbols and Units
Pages 5-7

Preface
Pages 9-10
K. Cena, J.A. Clark

Chapter 1 the Physics of the Microclimate Original Research Article
Pages 13-27
J.A. Clark, A.J. Mcarthur, J.L. Monteith, A.E. Wheldon

Chapter 2 Measurement of Thermal Balance of Man Original Research Article
Pages 29-39
Y. Nishi

Chapter 3 Evaluating the Effects of Clothing on the Wearer Original Research Article
Pages 41-55
R.F. Goldman

Chapter 4 Human Skin Temperature and Convective Heat Loss Original Research Article
Pages 57-76
R.P. Clark

Chapter 5 Rational Temperature Indices of Thermal Comfort Original Research Article
Pages 79-98
A. Pharo Gagge

Chapter 6 Required Sweat Rate as an Index of Thermal Strain in Industry Original Research Article
Pages 99-110
J.J. Vogt, V. Candas, J.P. Libert, F. Daull

Chapter 7 Modelling of Heat Transfer in Man Original Research Article
Pages 111-120
Y. Houdas

Chapter 8 Exercise Physiology and Sensory Responses Original Research Article
Pages 123-144
R.R. Gonzalez

Chapter 9 Thermal Physiology of Man in the Aquatic Environment Original Research Article
Pages 145-156
I. Holmér, U. Bergh

Chapter 10 Climatic Change and Acclimatization Original Research Article
Pages 157-168
G.E. Folk Jr.

Chapter 11 Man in Extreme Environments, Problems of the Newborn and Elderly Original Research Article
Pages 169-179
D. Robertshaw

Chapter 12 Physiological Signals for Thermal Comfort Original Research Article
Pages 181-192
M. Cabanac

Chapter 13 Design Requirements for a Comfortable Environment Original Research Article
Pages 195-220
D.A. McIntyre

Chapter 14 Prediction of Local Discomfort for Man Original Research Article
Pages 221-227
P.O. Fanger

Chapter 15 the Dependence of Comfortable Temperatures upon Indoor and Outdoor Climates Original Research Article
Pages 229-250
M.A. Humphreys

Chapter 16 the Effects of Moderate Heat Stress on Mental Performance Original Research Article
Pages 251-267
D.P. Wyon, I. Andersen, G.R. Lundqvist

Chapter 17 Physics, Physiology and Psychology Original Research Article
Pages 271-283
K. Cena, J.A. Clark

Subject Index
Pages 285-289

Citation preview

BIOENGINEERING, THERMAL PHYSIOLOGY AND COMFORT

Studies in Environmental Science Volume 1 Atmospheric Pollution 1978 Proceedings ofthe 13th International Colloquium, held in Paris, April 25-28,1978 edited by M. M. Benarie Volume 2 Air Pollution Reference Measurement Methods and Systems

Proceedings of the International Workshop, held in Bilthoven, December 12-16, 1977 edited by T. Schneider, H. W. de Koning and L. J. Brasser Volume 3 Biogeochemical Cycling of Mineral-Forming Elements

edited by P. A. Trudinger and D.

1. Swaine

Volume 4 Potential Industrial Carcinogens and Mutagens by L. Fishbein Volume 5 Industrial Waste Water Management by S. E. jnrrgensen Volume 6 Trade and Environment: A Theoretical Enquiry by H. Siebert, 1. Eichberger, R. Gronych and R. Pethig Volume 7 Field Worker Exposure during Pesticide Application

Proceedings of the Fifth International Workshop of the Scientific Committeeon Pesticides of the International Association on Occu ational Health, held in The Hague, October 9-1( 1979 edited by W. F. Tordoir and E. A. H. van Heemstra-Leq uin Volume 8 Atmospheric Pollution 1980 Proceedings of the 14th International Colloquium, held in Paris, May 5-8, 1980 Volume 9 Energetics and Technology of Biological Eli m ination of Wastes Proceedings of the International Colloquium, held i n Rome, October 17-19, 1979 edited by G. Milazzo Volume 10 Bioengineering, Thermal Physiology and Comfort

edited by K. Cena and J. A. Clark

Studies in Environmental Science 10

BIOENGINEERING, THERMAL PHYSIOLOGY AND COMFORT edited by

K. Cena Environmental Physics, Institute of Building Science, Technical University of Wroclaw, Wybrzeze Wyspiahskiego 27, 50-370 Wroclaw, Poland and

J. A. Clark Environmental Physics, Department of Physiology and Environmental Studies, University of Nottingham School of Agriculture, Sutton Bonington, Loughborough, LEI2 5RD, Great Britain

ELSEVIER SCIENTIFIC PUBLISHING COMPANY Amsterdam - Oxford - New Y o r k 1981

Distribution of this book is being handled by the following publishers: For the U.S.A. and Canada ELSEVIER/NORTH-HOLLAND, INC. 52 Vanderbilt Avenue New York, New York 10017 For Albania, Bulgaria, Chinese People’s Republic, Cuba, Czechoslovakia, German Democratic Republic, Hungary, Korean People’s Democratic Republic, Mongolia, Poland, Romania, the U.S.S.R., Vietnam and Yugoslavia ARS POLONA Krakowskie Przedmieicie 7 00-068 Warszawa, Poland For all remaining areas ELSEVIER SCIENTIFIC PUBLISHING COMPANY 355 Jan van Galenstraat P.O. Box 211, 1000 AE Amsterdam, The Netherlands

Library of Congress Cataloging in Publication Data Main entry under title: Bioengineering, thermal physiology and comfort. (Studies in environmental science; 10) Papers presented at a conference held Sept. 4-7, 1978, at Karpacz, Poland, and sponsored by the Technical University of Wroclaw. Bibliography: p. Includes index. 1. Heat - Physiological effect - Congresses. 2. Man - Influence of climate - Congresses. 3. Clothing, protective Congresses. 4. Insulation (heat) Congresses. 5. Bioengineering - Congresses. I. Cena, Krzysztof. 11. Clark, Jeremy Austin, 1938111. Politechnika Wroclawska. IV. Series. [DNLM: 1. Biomedical engineering. 2. Adaptation, physiological. 3. Body temperature regulation. QT34 B6031 QP82.2.514BSG 612’.014462 80-1 6578

-

-

ISBN 0-444-99761-X (voI. 10) ISBN 0-444-41696-X (series)

Copyright @ Wroclaw Technical University Press, 1981

All rights rsservcd. No part of this publication may be reproduced, stored in retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in Poland

CONTENTS SYMBOLS AND UNITS

. . . . . . . . . . . . . . . . . . . . . . .

6

I. PHYSICAL PRINCIPLES AND MEASUREMENTS

. . . . . . MONTEITH andA. E. WHELDON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Measurement of thermal balance of man. Y . NISHI 3. Evaluating the effects of clothing on the wearer. R . F. GOLDMAN. . . . . . . . 4. Human skin temperature and convective heat loss. R . P. CLARK . . . . . . . . 1 The physics of the microclimate. J A CLARK. A. J MCARTHUR. J L

13 29 41 57

I1. MODELS AND INDICES OF HEAT EXCHANGE 5 . Rational temperature indices of thermal comfort. A . PHARO GAGGB . . . . . . 19 6. Required sweat rate as an index of thermal strain in industry. J J VOGT. V CANDAS. 99 J P LIBERTand F DAULL . . . . . . . . . . . . . . . . . . . . . . . .

.

. .

..

.

.

7 Modelling of heat transfer in man. Y. HOUDAS. . . . . . . . . . . . . . . . 111

I11. PHYSIOLOGY. WORK AND EXERCISE 8. 9. 10. 11. 12.

.

Exercise physiology and sensory responses. R . R GONZALEZ . . . . . . . . 123 Thermal physiology of man in the aquatic environment. I HOLMERand U BERGH 145 Climatic change and acclimatization. G E . FOLK Jr . . . . . . . . . . . . . . 157 1 69 Man in extreme environments. problems of the newborn and elderly. D ROBERTSHAW Physiological signals for thermal comfort. M CABANAC . . . . . . . . . . . 181

.

.

.

.

.

.

IV COMFORT. ITS SPECIFICATION AND CONSEQUENCES

.

.

13 Design requirements for a comfortable environment. D. A MCINTYRE . . . . . . . . . . . . . . . . . . 14. Prediction of local discomfort for man. P 0 FANGER 15. The dependence of comfortable temperatures upon indoor and outdoor climates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . M A HUMPHREYS 16. The effects of moderate heat stress on mental performance. D . P . WYON I ANDERSEN and G . R . LUNDQVIST. . . . . . . . . . . . . . . . . . . .

. .

. .

.

195 221 229 251

V . SUMMING-UP

.

17 Physics. physiology and psychology. K . CENAand J . A . CLARK . SUBJECT INDEX

. . . . . . . .

..............................

271 285

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SYMBOLS AND UNITS

The symbols used in the text, the quantities they represent and the appropriate S. I. units are listed below. Some local variants, which appear only briefly, are defined at the appropriate point in the text. Mean values of quantities are denoted by a bar over the symbol, in the conventional way. Most work in the field covered by this book now employs the units of the Systeme Internationale, which has considerably eased the task of the editors. However, there remain a few differences of practice. In particular, while many engineers continue to specify water vapour pressure in Torr (mm of Mercury), the majority of climatologists use the millibar; strictly, neither is an S. I. unit, though the latter sometimes disguise the millibar as the hecto-Pascal (lo2 Pa). On Professor Gagge's suggestion the S. I. unit of pressure, the Pascal, was adopted in this text. The multiple of the kilo-Pascal (kPa) is that used, as it is more convenient numerically. All vapour pressures in the text and f i g m have therefore been expressed in kPa, the form most likely to be met in future. The conversions between kPa and the Torr and millibar are relatively straightforward. When the water vapour pressure appears in the numerator of an equation, or alone, the conversion is 1 kPa

=

10 mbar = 7.5 Torr.

When the vapour pressure is in the denominator the ratios are I kPa-'

= 0.1

mbar-'

= 0.133

Torr-l.

Latin letters Units

surface area surface area estimated from DuBois formula specific heat convective heat exchange body characteristic dimension water vapour pressure water vapour pressure in ambient air saturation vapour pressure at skin temperature evaporative heat transfer insensible perspiration, or diffusive heat loss maximum evaporative heat loss respiratory evaporative heat loss sweating evaporative heat loss acceleration due to gravity = 9.81 (without subscript) body height heat transfer coefficient for convection, in water or air combined sensible heat transfer coefficient (her = h,i-h,) evaporative heat transfer coefficient mass transfer coefficient linear radiation heat transfer coefficient tissue (skin) conductance total heat transfer by sensible heat whole body dry heat transfer total evaporative heat transfer whole body evaporative heat transfer respiratory heat transfer clothing insulation clothing insulation in clo unit

m-2

m2 J kg-'

K-'

w m--2 m kPa kPa kPa

w m-2 w m--2 w m--2 w m-2 W m--2 in s-2 n~ W m--2 K-' W m-2 K-' W m-2 kPa-l m s-l W m-2 K-' W m--2 K-I W m-2 W

w W

W m2 K W-' cia

6

J

k K L M

Mn P

Q r Rn RS RL S sh

t

T

T-a Tb Tc T'l

To Tr

Ts TS" Tw V

v W

rate of heat storage thermal conductivity conductive heat exchange thermal irradiance metabolic rate net metabolic rate barometric pressure rate of heat production per unit volume of tissue resistance to heat or mass transfer net radiant heat transfer net shortwave radiation net thermal radiation rate of sweat production hourly rate of sweat production time temperature air temperature mean body temperature body core temperature dew point temperature operative temperature radiant temperature skin temperature surface temperature wet bulb temperalure air (wind) speed volumetric rates of blood flow, O2 consumption etc, as in text rate of production of external work

w m-2 W m-I K-l W m--2 W m--2 W W m--2 kPa W m--3 s m-1 W m--2

w m--2 W m--2 g m--2 s-* g m-2(hour)-' S

"C or K "C "C "C "C "C "C "C "C "C

m s-l m3 s-l W mW2

Greek letters Y R

e d

P

psychrometer constant latent heat of vaporization of water density Stefan-Boltzmann constant = 56.7 x lo-' ratio of transfer coefficientsfor sensible and latent heat (when not equal toy)

Dimensionless quantities im

F Gr

Le Nu Re RH Sh E

71 w

clothing permeability index for vapour transfer radiation form factor or clothing factor, according to subscript in text Grashof number Lewis number Nussel t number Reynolds number relative humidity Sherwood number emissivity for thermal radiation efficiency, sweating or mechanical work skin wettedness

kPa K-l J kg-l kg m--3 WmV2 K-4 kPa K-'

7

Clothing resistance to water vapour Ioss Water vapour transfer is modified by the presence of clothing, as is sensible heat transfer. The equation for sensible heat transfer has the form of Current

Potential Difference Resistance to Flow

=

'

The equivalent equation for evaporative heat transfer E i s a form of the psychrometer equation

where be is the vapour pressure difference between the skin surface and the environment, in kPa. For Zv to be expressedinunits of m2 K W-l , and therefore be identified with the clothing insulation, I, X must be a constant with dimensions K kPa-l. When sensible heat and water vapour transfer are both at rates well in excess of these possible by molecular diffusion, so that the transfer mechanisms are equivalent, Zv is equal to Z. Then it can be shown that at about 30"C, close to normal skin temperatures, E

=

16.5AejZ.

This gives the fortuitous benefit that when vapour pressures are expressed in kPa and insulation in clo (1') Ae E = 16.5 0.155 I' ' which may be conveniently rounded to give the equation used by GOLDMAN in chapter 3 E

==

100

-.Ae I'

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PREFACE Man is in many ways a unique animal and one of his most obvious differences from other species is his ability to “bioengineer” his environment, so that he is protected from the thermal extremes of ambient conditions. The physical principles of heat exchange are, however, common to all animals and even poikilotherms of mass greater than a few grams employ behavioural thermoregulation, which is essentially physical. Physiological thermoregulation enables homeothermic animals to tolerate a much wider range of environments than would be possible by behavioural thermoregulstion alone. The third strategy of thermoregulation, “bioengineering” the creation of a tolerable or comfortable environment where none previously existed is largely man’s. In nature the most obvious examples are the nests of small birds and mammals, but man’s control of fire and his building technology, which have become scientifically based in the present century, allow him to live in all terrestrial environments but the highest mountains. For many millenia man’s construction of shelters may have been primarily for protection from predation and from extremes of climate, but his increasing sophistication has long made comfort a prime requirement in buildings. In many parts of the world ‘native’ buildings were evolved, which were satisfactory for their particular conditions. However, the spread of a common technology has usually superseded traditional methods of construction, and only a scientific understanding of building will allow the design of comfortable environmen‘s with new materials and methods in any environment. The design of comfortable environments also presupposes a knowledge of what is comfortable. Hence there have been numerous studies of the thermal physiology of man and its relationships to his sensations of thermal comfort and discomfort, both at rest and during work. Despite man’s ability to engineer comfort over a wide range of ambient conditions, he is still, occasionally, faced with an environment in which his first priority is survival. In these circumstances it is his physiological competence in thermoregulation which is first tested, and secondly his ability to acclimatize to stress. For the very young and very old even a normal indoor environment may present a potentially lethal challenge, but even a healthy adult may experience tliermoregulatory stress during prolonged physical work or athletic endeavour. The thermal challenge presented by the aquatic environment may also provide useful information about man’s thermoregulatory ability. The purpose of this book is to review current knowledge of the physics and thermal physiology of man’s reactions to his thermal environment, outlined above, and how these affect his comfort, well-being and work performance. This is necessary information for the bioengineering of appropriate environmental Conditions for man’s various activities. Though the book was conceived as an independent entity, the Technical University of Wroclaw convened a school using the same title, “Bioengineering, Thermal Physiology and Comfort”, at which the authors came together to present and discuss their papers. This school was held at Karpacz, Poland, o n

10

4-7 September, 1978. Matters raised during the school have been incorporated in the concluding chapter. Neither publication of this book, nor the holding of the school at Karpacz, would have been possible without the generous support of the authorities of the Technical University of Wroclaw. In particular, the editors wish to acknowledge the personal patronage of the school by the President of the University, Professor T. P O ~ B S K I . The editors’ co-operation in preparation of the manuscripts for publication was also greatly facilitated by grants which enabled reciprocal visits to Poland and Great Britain in 1977-1978. Visiting fellowships were received from the Technical University o f Wroclaw (by J.A.C.) and the Science Research Council of Great Britain (by K.C.), and travel grants were awarded by the British Council and the University o f Nottingham (to J.A.C.) and by the Technical University of Wroclaw (to K.C.). On a more personal note the editors wish to thank all the authors, not least for their co-operation in agreeing to the editing changes inevitably required to produce a text of unified format from seventeen individual papers. In addition to some of the authors, J. Narqbski, P. Poczopko and J. A. J. Stolwijk acted as chairmen of sessions at the school. We also wish to acknowledge the help of A. J. McArthur in the initial stages of editing and of E. Sliwiliska, who assisted in the compilation of the index. We are also indebted to the special care and attention of those concerned with preparing the text for printing, in particular M. Gutterwil and E. Sobesto of the Wroclaw Technical University Press.

K. Cena, J. A . Clark

I. PHYSICAL PRINCIPLES EASUREMENTS

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Chapter 1

THE PHYSICS OF THE MICROCLIMATE J. A. CLARK, A. J. MCARTHLTR, J. L. MONTEITH Environmental Physics, Department of Physiology and Environmental Studies, University of Nottingham School of Agriculture, Sutton Bonington, Loughborough, LEl2 SRD, Great Britain.

A. E. WHELDON Department of Child Health, University of Nottingham Medical School, Queen’s Medical Centre,Nottingham, NG7 2UH. Great Britain.

CONTENTS Introduction Metabolic heat production Conduction Heat storage Radiation Thermal radiation Solar radiation Net radiation Convection Free convection Forced convection Mixed convection Evaporation Evaporation and convection Conclusions

INTRODUCTION

All animals, including man, respond to their surroundings and are particularly sensitive to the state of the thermal microclimate. Many cold-blooded animals attempt to keep body temperature within a preferred range by behavioural methods, moving into sunlight or shade. In contrast, homeotherms can maintain a constant body temperature by physiological responses to changes of microclimate, though these adjustments are often supplemented by ingenious stratagems of behaviour,

14

J. A. CLARKet al.

either by individuals or within groups. Man uses both physiological and behavioural methods of temperature regulation, but he has also developed the skill to control his own microclimate by heating and by air conditioning, or, less extravagantly, by selecting appropriate clothing. In this book, we review the processes by which man achieves thermal equilibrium with his environment. Some of these processes are physiological and involuntary, some are consciously controlled, and some depend on the subtle perception of “comfort”. Whatever process is involved, thermal equilibrium between a man and his environment depends on the physical mechanisms which govern heat transfer from the body core to the skin surface and from the skin through clothing to the environment. A review of the physics of microclimate is therefore an essential introduction to the physiological and psychological aspects of the subject which other authors will describe. The thermal comfort of man in an everyday environment, such as the home, factory or office, depends partly on the rate at which he exchanges heat with the environment and partly on his own level of work. In extreme thermal environments his tolerance of discomfort and, ultimately, his survival are decided by the competence of his thermoregulatory physiology. The heat balance equation, as employed in thermal physiology, therefore has both physical and physiological implications. Equation (1.1) is an application of the First Law of Thermodynamics - the law of energy conservation - and therefore satisfies the requirement that the sum of heat inputs, outputs and storage must be zero (MONTEITH, 1973; CAMPBELL, 1977). For practical purposes the components of the heat balance are usually expressed in power per unit area of the external surface of the body (e.g. W m-”. A convenient algebraic expression is M,,+R+H+G+J== 0. (1.1) When the energy conservation equation is expressed in this form, the balance is between terms which are heat gains by the body and those which involve heat dissipation. The usual sign convention is to ascribe a positive sign to the numerical values of the gains. Therefore metabolism is always positive and the other terms are usually negative. M, is the net flux density of metabolic heat, i.e. the total heat production of the body less the enthalpy transferred to the respiratory air stream per unit time, expressed per unit surface area. For a resting adult M, is about 60W m-’, and may increase by a factor of approximately 20 during exercise. R is the net radiative energy exchange between the surface and its surroundings and H is the total heat transfer by convection with the surrounding medium. Because the environment is usually specified in terms of temperature and humidity, H is usually divided into convection ( C )and evaporation (E),both carried by convective processes, so that

H = C+E. (1 -2) The error incurred by considering sensible and evaporative heat transfer separately is usually negligible. The circumstances in which this is not so are considered later. C is the heat transfer by conduction to solid substrates and J is the rate of change

The physics of rhe microclimate

15

of heat storage in the body. The numerical value of J will therefore be negative when the body temperature is rising, i.e. when storage is contributing to heat dissipation. Subsequent sections of this chapter outline, in turn, the factors which determine each of the components of the heat balance equation. METABOLIC HEAT PRODUCTION

A combination of physical and physiological mechanisms enables the adult human to maintain an almost constant core temperature (T,) in a wide range of environments. Metabolic responses to different thermal environments are best illustrated by considering a simplified energy balance, in which G = 0 and the body is in thermal equilibrium (i.e. J = 0). The remaining terms are M,, E , and the total sensible heat exchange, C + R . If we assume that sensible heat transfer obeys Fourier’s Law of heat exchange (STRUNK,1971) CS-R = h#,-TJ,

(1.3)

where hT is the overall conductance for sensible heat exchange, in W m-2 K-I, and T, is the ‘effective temperature’, i.e. that of the equivalent isothermal environment. Then M,+hT(T,-T,)+E

= 0.

(1.4)

Because man does not pant effectively, respiratory heat exchange does not change independently of metabolism in a given environment. Therefore, if we exclude behavioural thermoregulation, we need to consider only three strategies for the maintenance of thermal balance. These are most easily shown on a diagram showing how M,, C+R and E change with environmental temperature, as in fig. 1.1.

Fig. 1.1. Diagrammatic representation of relationships between heat production, evaporative and non-evaporative heat loss

Envir w e n t o l ternpemture

A zone of hypothermia: B temperature of summit metabolism and incipient hypothermia: C critical temperature; D temperature of marked increase in evaporative loss: E temperature of incipient hypenherma1 rise: F zone of hyperthtrmia; CD zone of least thermoregulatory effort: CE zone of minimal metabolism: BE thcrmoregulatory range. From MOUNT (1974)

The “metabolic diagram’’ (MOUNT, 1974) or “thermoneutral profile” (FOLK, 1974) is typical of a homeotherm with constant external insulation (i.e. a fixed insulation between the skin and the environment), The diagram may be divided into a number of zones, which correspond to the different strategies of physical and

16

J. A. CLARKet al.

physiologicsl control of the heat balance. At a fixed level of food intake and activity, the rate of mctrtbolism is minimal in the “thermoneutral zone”, between the lines C and E in fig. I . I . However, Mount defined a narrower zone, between lines C and D, as the “zone of least thermoregulatory effort”. This zone corresponds to the operation of the first and most economical strategy, that of regulating heat exchange by body conductance - brought about by v‘isoconstriction or vasodilation of capillnry b1oc.d vessels in the periphcral tissue. The more restricted zone of human comfort may be identified with the upper end of this zone. A second strategy is used at lower temperatures. Below the lower critical temperature (C in fig. 1.1.) evaporative heat loss and tissue conductance are minimal and ahnost constant, and h, is a minimum. Hence sensible heat loss from the body increases in proportion to the difference bctween T,and T, and, to maintain a steady core temperature, metabolic heat production must increase to compensate. The slope of the increase is proportional to the total thermal conductance of the body, and therefore depzids on both body insulation and clothing. According to BURTON and EDHOLM (1969), most adult mammals can increase their metabolic heat production by a factor of about three in response to cold stress alone, but much higher rates may be xhieved i n the short term by voluntary exercise. Because of his limited tissue insulation the lowest temperature a t which a naked adult may survive for long periods is about 2 “C, a value which, according to BURTONand EDHOLM (1969), is consistent with historical observations of the habitually naked natives of Tierra del Fuego. Most rc;rders of these p e e s are, however, much less hardy (FOLK, chapter lo). Shivering contributes to the involuntary response to cold. Non-shivering thermogenesis may also be found i n mammals. It is associated with brown fat deposits and has been observed in human babies (HEY,1974) though it is usually absent in adult humans. The zbility to increase metabolic rate in response to cold stress is reduced in the sick, the elderly and babies, in perticular. These groups are therefore more susceptible to hypothermia than the general population (ROBERTSHAW, chapter 11). The third strategy, that of regulating evaporative heat loss, is cmployed in hot conditions when sensible heat transfer is insuscknt to remove metabolic heat, above D in fig. 1.1. This is a strategy for which man is uniquely well equipped. His ability to secrete sweat in large quantities enables the body to control latent heat loss over a wide temperature range, so that the .thermoneutral zone extends well above that for comfort. In most environments the upper limit of this zone, known as the “upper critical temperature”, is determined largely by physical factors, which limit the rate of difliision of water vapour away from tlie skin. However, the ability to sweat may be rostrictcd in both the younz ar?d elderly, and may become “fatigued” even in athletes (CLARK, chapter 4). Above the upper critical temperature ( E i n fig. 1.1) latent heat loss is enhanced by active mechanisms, which themselves increase M and the risk of 3yperthermia. Many maminnls exhibit panting in this region, but, as noted earlier, this is not important for man. In practice, because the highest rates of work Ere rarely sustained for long periods, tlicrnizl storage in the body is often critical for the toleration by men of heat loads exceeding those w!iich may be dissipated by pssive evaporation of sweat.

The pliysics of’die microcliniiite

17

The metabolic diagram is complicated by other factors: real environments are rarely either constant or isothermal. Hence in order to evaluate the thermal environment it is necessary to know the separate transfer coefficients for convection, radiation and evaporation even when the objective is a single index of “environmental temperature” (GAGGE,chapter 5 ) ; the external clothing insulation may be varied at will, while metabolic heat production varies both between people and with time for one person. Generally, the higher is M,,, the wider is the thermoneutral zone and the lower are the lower and upper critical temperatures and the thermal limits of comfort (fig. 1.2). Thus GONZALEZ (chapter 8) observes that exercising subjects are

.-V

0

Fig. 1.2. Diagram of response of net metabolic heat production M , to environmental temperature T,

n

2

\

\

\

\

L-Jb

8

comfortable at lower temperatures than those preferred by resting subjects. Conversely, when the metabolic rate is depressed the thermoneutral zone is narrower and displaced to higher temperatures. Clothing, which is discussed in greater detail by GOLDMAN (chapter 3), controls the rates of transfer of sensible heat and water vapour as well as satisfyings social conventions. Its effect on sensible heat exchange is conveniently considered in terms of insulation. We may replace h, in equation (1.3) by an equivalent thermal resistance IT := lz;’, where IT has units of m2K W-I. If we take the simplest case of an isothermal environment in which the surroundings temperatures for convection and radiation are the same, the total insulation may be divided into three components acting in series: the body insulation, I b ; that of the clothing, I ; and the combined external resistance for convective and radiative transfer to the surrounding environment, I,. Hence

C+R

= (Tc-Te)/Vb+Z+Ie).

(1.5)

In p,ractice the combined external insulation ( l + I e ) is usaally considered as the clothing insulation, since the two are not easily separable and generally I $- I,. 2

- Bioengineering

18

J. A. CLARKet al.

The conversion between m2 K W-' and the clo unit (GAGGE, BURTON and BAZETT, 1941) is 0.155 m2 K W-' = 1 clo. CONDUCIION

Heat transfer by conduction occurs between the human body and solid surfaces such as chairs, beds and floors with which it is in contact. However, it is usually a small component of the total heat balance, for two reasons: first, the contact area is usually small; second, the thermal conductivity of the substrate is usually low. HEY, KATZand O'CONNELL (1970) measured the contact areas of supine babies, and found values of approximately 10% of the total skin surface area on firm substrates. This figure is likely to be representative for any normal posture of children or adults, but the fraction may increase by a few percent on compressible upholstery surfaces. Both wood and padded upholstery - the usual surfaces supporting a sitting or lying human - have low coefficientsof thermal conductivity, so that heat exchange through these is low .However, since conductive heat exchange is directly proportional to the local temperature gradient, contact with cold surfaces of high thermal capacity and conductivity, such as metal, solid plastics and stone, may cause high local rates of heat transfer and consequently local discomfort (FANGER, chapter 14). Most analyses of human heat balance therefore assume that conduction is negligible, though few measurements have been made. HEY, KATZ and O'CONNELL (1970) reported that 20 % of sensible heat loss from naked babies in a perspex metabolism chamber was by conduction through the floor, but this figure was reduced to about 3 % by a 1 cm thick foam mattress. These figures are consistent with measurements of heat loss from farm animals.

HEAT STORAGE

When the mean body temperature is constant the rate of heat storage ( J ) in the body tissues is zero, by definition, and in practice it is negligible over long time periods, in excess of a day for adult humans. However, over short periods J can be an important component of the heat balance, for example following the onset of exercise (GONZALEZ, chapter 8) and in circumstanceswhere J determines the tolerance time for work in severe environments (VOGTet al., chapter 6). The total capacity for heat storage in the body can be estimated as the product of its thermal capacity with the maximum tolerable change in mean body temperature. It therefore depends both on body mass and on the difference between the actual body temperature and the tolerable limits. For a man of mass 75 kg the heat storage changes by about 3Od kJ for each degree Kelvin change in mean body temperature (assuming that the specific heat of the tissues is close to that of water). A body temperature rise of 1 K in an hour therefore represents heat storage at a rate of about 85 watts. Expressed per unit area of surface, J m -45 W m-' in the sign convention used in equation (1.1). Heat storage is therefore likely to be important in man for

The physics of zhe microclimate

I9

periods of up to a few hours. In small animals it is important for periods of just a few minutes and only in the largest mammals is thermal storage a useful mechanism on a diurnal time scale. Children have a lower thermal storage potential than adults, associated with their small body mass and lower mass to surface area ratio. They are therefore at greater risk than adults in “severe” thermal environments, which include water at sea temperatures normal in summer in temperate climates (HOLM~R and BERGH, chapter 9). RADIATION

Both solar radiation and thermal radiation of terrestrial origin are important in the radiative energy exchange between the surface of the human skin or clothing and its environment. Their contribution to the heat balance has been reviewed by CENA(1974). In a terrestrial environment the two bands of electromagnetic radiation are effectively separate, solar or short wave radiation lying largely in a band of wavelengths from 0.3 to 3 pm, while longer wavelength thermal radiation from local sources lies mainly between 3 and 100 pm. THERMAL RADIATION

Thermal radiation transfer is the result of an exchange involving both emission and absorption. All surfaces emit thermal radiation at a rate depending on their surface temperature (T,)and emissivity (E). The emitted flux L(W m-’) is given by the Stefan-Boltzmann equation L =EUC,

(1.6)

where a is the Stefan-Roltzmann constant (a = 56.7 x lo-’ W m-’ K-4). The emissivity of skin and of almost all clothing materials is close to unity, as is their absorptivity for thermal radiation, so that the human surface can be treated as a “black body” for radiation in this band. The net exchange of thermal radiation, RL, is therefore given by the sum of the incident and emitted fluxes RL = L,-aT;,

(1.7)

where L, is the incident thermal radiation. Surfaces in typical human environments have temperatures in the range 270-300 K, so LL is usually between 300 and 450 W m-2. RLis usually negative, and this component of heat loss is similar in magnitude to the convective component from the outside of our skin and clothing. Indoors R, is often the largest pathway of heat dissipation. SOLAR RADIATION

The exchange of shortwave radiation (0.3-3 pm) is both more variable and more complex, since it depends both on surface colour and on the geometry of interception (CLARK and CENA,1976). Outdoors, intercepted solar radiation often exceeds meta-

20

J. A. CLARKe! al.

bolic heat production even in cold climates; indoors other high temperature sources of radiation, such as lamps, furnaces and electric fires, may also provide highly asymmetric sources of radiant energy. The net shortwave radiation flux, R,, is the product of the incident energy flux RSiand absorptivity a (1.8)

The spectral absorptivity and reflectivity of skin and clothing are strongly correlated with their colour. Typical values of a for skin are 0.85 for negroid subjects a n d 0.68 for Caucasians. Extreme values for clothing are M 1 for black and 0.3 for white fabrics for 6000 K (solar) radiation (ROLLERand GOLDMAN, 1967). Representative values of a for 250 K and 1200 K radiation are 0.65 and 0.85 for Caucasian skin, and 0.8 and 0.9 for medium grey clothing, respectively ( FANGER, 1970). NET RADIATION

The net radiant energy exchange obtained by combining equations (1.7) and (1.8) is

R = R,+ R,

=

aR,,-+L,-~T,".

(1.9)

Variations in the net radiation exchange over the body surface can affect comfort. Net radiant fluxes are usually quoted as averages for the whole of the body surface, as this is the quantity required for an evaluation of the overall heat balance, but some measurements of local radiative heat exchange have been made (CLARK, CENAand MONTEITH, 1973). The mean radiant exchange R is obtained by integration

R = - -1 [ R A .

dA

(1.10)

Though mathematically trivial, this equation reminds us that the radiation flux may vary greatly from point to point on the body. Moreover, the area ( A ) available for radiation exchange may be considerably different from the actual skin area, A,, assessed by the DuBois formula. Two factors may work in opposite senses: Because of shape and posture the area of the human body available for radiant exchange is reduced to less than the DuBois area. Considerable areas of skin or clothing are normally in contact with adjacent areas and so not available for radiant exchange. Further, some areas exchange radiation with other areas of the body, a t least in part. Posture enables a wide range of control of the ratio AIA,, from about 0.96 for a spreadeagled man to about 0.5 for the foetal position (GUIBERT and TAYLOR, 1953; MITCHELL,1974b). Contact with substrates such as chairs also reduces the area available for radiation. In contrast, the addition of clothing increases the external surface area. Measured values of the ratjo of the area of the clothed body to A, range from unity for minimal clothing to about 1.5 for the heaviest arctic assemblies. According to FANGER (1970) the ratio is typically about 1.2 for a suited male. Part of the insulative value of clothing is therefore lost by a concomitant increase in the surface area available for radiative and convective heat exchange.

77le physics of the mircoclimate

21

Changing the area for radiant exchange by posture is an effective form of behavioural thermoregulation. Posture also determines convective exchange, but to a lesser extent because convection is eliminated only by physical contact between adjacent body surfaces. In many circumstances, however, social pressures or occupational demands limit postural thermoregulation : it is more practical for an office worker to don an extra layer of clothing to reduce heat loss than to adopt a foetal position. However, the posture of babies nursed naked in incubators may play an important part in their thermoregulation. RUTTER(private communication) observes that full-term babies often adopt a spreadeagled position when the incubator temperature is high. Similar behavioural thermoregulation has been observed in other young mammals (e.g. MOUNT, 1967). It is often convenient to describe the radiation environment 8y its “mean radiant temperature”, TR(K). This is defined by

TR= [ ( L , + C Z R ~ ~ ) / G ] ~ * * ~ .

(1.11)

Provided that TRand the mean skin temperature, T,, do not differ by more than about 20 K, which is normally the case indoors, equation (1.9) may be simplified further, using a linear approximation, by substituting from equation (I .I I), whence R

= h,(TR-Ts),

(1.12)

where h, is a radiation transfer coefficient with a value of about 6 W ni-’ K-’ at temperatures close to 300 K.

CONVECTION

For a naked man, the thermal insulation (I, = l/hJ o f the boundary-layer of air around his body is an important component of his total resistance to sensible heat loss. A decrease in the insulation provided by this layer, due, for instance, to an increase in the rate of air movement, can cause a substantial increase in his sensible heat loss. In contrast, the insulation provided by the boundary-layer around a man immersed in water is small. The skin temperature of a naked man will therefore be almost identical to the temperature of the surrounding water and his sensible heat loss is determined largely by the insulation of his skin and body tissue. This depends on the control of internal convection (HOUDAS ct al., chapter 7). A decrease in the boundary-layer insulation due to an increase in the rate of water flow will in this case have little effect on heat loss. Provision of an insulating layer of clothing (e.g. wet suit) will reduce beat loss considerably and allow the temperature of the skin to rise above. that of the surrounding water. For a fully clothed man in air, a decrease in boundary-layer insulation alone will have little effect on his heat loss in the cold, but in hot conditions it helps to dissipate absorbed solar radiation. In contrast, a decrease in clothing insulation due to wind penetration will markedly increase sensible heat loss (NEWBURGH, 1970). Convective heat transfer from a clothed man is enhanced during exercise, both in air (R. P. CLARK, chapter 4) and in water (HOLMER and BERGH,chapter 9). Ventilation

22

J. A. CLARK et al.

of clothing due to movement also reduces the insulation provided (BELDING et al., 1947; CROCKFORD, 1970). It is difficult to quantify the effects of convection on the insulation of clothing, but there are well accepted theories which can be used to describe the heat exchange across the boundary-layer which separates a man from the bulk of the fluid in which he is immersed. Convection is the interchange of warm and cold fluid. The movements of fluid which carry heat away from the body surface may be driven by two mechanisms: “free c ~ n v e c t i o ndue ~ ~ to density differences in the fluid associated with temperature gradients; or “forced convection”, due to external forces such as wind. In each case the relationship between the rate of heat transfer, C, and the temperature difference between the surface and the air which drives the heat transfer

AT

= (Ts-Ta)

can be written as

C = NUkATfd,

(1.13)

where k (W m-’ K-I) is the thermal conductivity of the fluid, d is the characteristic dimension of the body and Nu is the Nusselt number. Nu is a dimensionless group which expresses the ratio of the actual heat transfer coefficient for convection, h, (W rn-’ K-’ ), to that expected for conductive heat transfer through thickness d of the fluid, i.e.

NU = h,d/k.

(1.14)

The calculation of a rate of beat loss by convection therefore requires the estimation of Nu, which depends on the size and shape of the body, the nature of its surface and the fluid properties (MCADAMS, 1954; MITCHELL, 1974a). Empirical relations are available in the engineering literature for simple shapes such as cylinders and spheres (e.g. KREITH,1958) and Nusselt numbers for human heat loss may be estimated with acceptable accuracy by treating the body as a smooth cylinder of appropriate characteristic dimension (MITCHELL,1974b). FREE CONVECTION

In free convection the fluid adjacent to a warm body becomes less dense than that remote from it and rises to be replaced by colder fluid. The consequent movement of warm air around the human body was first demonstrated by LEWISet al. (1969), using schlieren techniques (see R. P. CLARK, chapter 4). According to MONTEITH (1973), the Nusselt number appropriate for free convection from a human body is given by Nu = 0.63Gr0*25Pro‘Z5,

(1.15)

where Gr, the Grashof number, equals agd3AT/v3and Pr is the Prandtl number for the fluid. The quantities a and v are the coefficients of thermal expansion of the fluid

The physics of rhe riticroclirnafe

23

and its kinematic viscosity respectively, and g is the accerelation due to gravity. In air, for which Pr = 0.71, the above equation simplifies to Nu = 0.58Gr0*25. For values of AT between 1 and 20 K the corresponding values of 11, for a standing human, with d = 1.5 m, lie in the range from about 1.5 to 3 W m-z K - l . For a prone man, the boundary-layer is thinner (d assumed m 0.2 m) and values of h, are larger, in the range 2.5 to about 5.0 W m-’ K- .The respective heat flux densities would be 2.5 and 110 W m-’. In contrast, for a man lying in water the Prandtl number at 10 “C is 9.5, so that Nu = I . I G I - ~ .Calculation ~~. of Nu predicts that in water a AT of 1 K will give a heat flux of about 150 W m-2, a value consistent with the results discussed by HOLMBR and BERGH(chapter 9).

’

FORCED CONVECTION

In forced convection rates of heat transfer are determined by relative motions of the fluid driven by “external” forces, which includes the movement of limbs in swimming, and posture will be less important. The forced convection Nusselt number for a smooth cylinder is given by Nu = 0.26Re0.60Pro-33 for lo3

(1.16)

< Re < 5 x lo4 and Nu = 0.026Re0*81

(1.17)

for4x104 < R e < 4 x 1 0 5 , where the Reynolds number, Re, is the dimensionless group relating the fluid velocity, v, to its kinematic viscosity, Y , and to d (i.e. Re = Y ~ / Y ) .For air, substitution of the numerical value of Pr in equation (1.16) gives Nu = 0.23 For a man with d = 0.2 m this leads to values of h, of about 6 and 23 W m-’ K-’ at air speeds of 0.5 m s-’ and 5 m s-I, respectively. In water at 10 “C,a flow rate of only 0.5 m s-l gives a rate of heat transfer per unit temperature difference of about one-and-a-half kilowatts per m2. MIXED CONVECTION

Between free and forced convection there is a zone of mixed flow, in which both mechanisms contribute significantly to heat transfer. For Gr/Re* < 0.1 forced convection occurs, and free convection dominates when Gr/Re2 > 16 (KREITH, 1958). The upper limit corresponds to an airspeed of about 0.3 ms-’ for adults; so that in typical indoor conditions we lose heat by mixed convection. Unfortunately, estimation of the Nusselt number for this regime is difficult: according to FANGER (1970) the accepted procedure is to calculate Nu for both free and forced convection and use the larger. However, CAMPBELL (1977) suggests that in some circumstances the two processes may be additive. Perhaps the best procedure is to base estimates

24

J. A. CLARK et a).

of Nu for this range on published measurements of heat transfer from cylinders and spheres by mixed convection (e.g. YUGE,1960; OOSTHUIZEN and MADAN,1970). EVAPORATION

Man always loses some heat by evaporation of water through the skin. At low ambient temperatures this loss is almost constant and of the order of I0 yo of M,. In the heat and during exercise, however, the evaporation of sweat removes large quantities of excess heat from the body. Man has a tremendous capacity to produce sweat in response to heat stress: sweat rates can be as high as 0.5 g s-' (about 2 kg h-') for short periods and 0.25 gs-' (0.9 kgh-') over several hours. These correspond to heat losses of 1.2 and 0.6 kW, respectively. For comparison, the metabolic heat production of man increases from about 100W at rest to about 1 kW during strenuous activity. Evaporative heat loss depends, however, not only on the ability of the body to secrete sweat but also on the physical properties of the environment: if the maximum rate of evaporation is less than the rate of sweat secretion, heat dissipation will be impeded. Heat and water vapour transfer through the boundary-layer of the body take place by similar processes. The evaporation rate S', expressed as a mass flux per unit area of skin, can therefore be described by an equation similar to equation (1.13) S' = ShDAX/d, (1.18) where D is the molecular diffusivity for water vapour in air (mZ s-')and Ax the difference in water vapour concentration between the skin surface and the air. The absolute humidity has units of g m-' and is related to the quantity usually measured, the vapour pressure, e, by 3~ = 2170 e/T, (1.19) where c is i n kPa and Tin K . T h e Sherwood number Sh is the mass transfer analogue of the Nussclt number. Whereas the units for the sensible heat transfer coefficient in current literature are almost always those of the S.T. system, W m-' K-' , the presentation of mass transfer is less consistent. This is because three units of vapour pressure are used in conjunction with S.I. units: The Torr or nim of Mercury is used principally by engineers; the millibar (mbar) is employed by meteorologists and climatologists; the Pascal (usually kPa) is the recommended S.I. unit. The conversions are 1 kPa = 10 mbar

= 7.5 Torr.

The kilo-Pascal is employed in the remainder of this text. EVAPORATION AND CONVECTION

Because moist air is less dense than dry air, rates of free convection may be determined partly by gradients of water vapour concentration as well as by those of temperature. When heat and water vapour transfer occur together the temperature

The physics of’the niicrocliinore

25

difference in the Grashof number in equation (1.15) (and in the corresponding mass transfer equation, equation (1.18)) should therefore by replaced by the difference in “Virtual Temperature” T,, given by

(I .20)

T, = Ta(1+0.38e/p),

where p is the atmospheric pressure, in the same units as e. The effects of water vapour gradients on free convection, both in the free atmosphere and within insulating layers, have received little attention. However, MONTEITH (1973) showed that the Grashof number for a naked man could be underestimated by a factor of about three if the effects of vapour pressure gradients were ignored. The corresponding underestimation of heat and mass flux is about 30%. CENAand MONTEITH (1975) have shown that related effects may be significant for free convection within mammalian hair coats, and this factor warrants further examination in clothing. . The Sherwood and Nusselt numbers for free convection are related by Sh = NuL~’.~’,

(1.21)

where Le is the Lewis number. For water vapour in air Le = 0.90. Therefore if either Sh or Nu are known the other can be estimated. However, except in conditions of extremely high heat load, rates of evaporation are usually determined by the rate of sweat secretion rather than by the transfer processes directly, though sweat is secreted so as to maintain energy balance. In the human environment, the appropriate equation for forced convection, corresponding to equation (1.21) is

.

Sh

= Nu

(1.22)

Insertion of the value of Nu appropriate to the characteristic dimensions of an adult human and typical indoor air speeds, corresponding to Re = 7 . 4 lo4, ~ gives Sh = 200. This value is consistent with the measurements of Sh = 160 for man by CLIFFORD et al. (1959). According to RAPr (1970) the agreement between theory and measurements is good. CONCLUSIONS

The thermal environment affects man through the transfer processes between his body and its surroundings. The mechanisms of these processes have been outlined in the present chapter, and their evaluation is reviewed later by NISHI (chapter 2). Complete specification of a thermal environment is obviously a complex problem (MONTEITH, 1974), and in general it is necessary to describe not only the temperature gradient between a subject and the fluid (usually air) in which he is immersed, but also the respective transfer coefficients for evaporation, convected sensible heat and radiation, and the radiant field (MCTNTYRE, chapter 13). Because of the complexity of real environments, within buildings as well as is the open air, effective temperature indices have been developed. The aim of these indices, reviewed by GACCE (chapter 5), is to specify the environment by a single number in units of temperature, which is the most easily understood determinant of heat loss,

26

J.. A. CLARK et al.

Such indices may help to specify comfortable or tolerable environments with greater precision. However, man’s perception of the environment is complicated by his own psychological and physiological reactions (CABANAC, chapter 12): he may become bored with neutrality and be stimulated by a modest thermal stress (WYON et al., chapter 16). Because psychological factors are important, it is difficult to create environments which satisfy everyone (FANGER, 1970), though air conditioning engineers are engrossed in this task. Perhaps they should reassess their aims: HUMPHREYS (chapter 15) has collected results which suggest that habituation plays a targe part in our judgement of comfort, and that the rate of change of temperalure in particular, may be as important for comfort as the precision of control.

REFERENCES BELDING H. S., RUSSELL H. D., DARLINQ R. C., and FOLKG. E. (1947), Analysis offactors concerned in maintaining energy balance for dressed men in extreme cold Efects of activity on the protective value and comfort of arctic clothing, Am. J . Physiol. 149,223-239. BURTON A. C. and EDHOLM 0. G. (1969), Man in a Cold Environment. (Facsimile of 1955 edition), Hafner, New York, London. CAMPBELL G. S. (1977), An Introduction to Environmental Biophysics, Springer-Verlag, New York. CENAK. (1974), Radiative heat loss from animals and, man [In:] Heat Loss from AnimalsandMan, eds: J. L. MONTEITH and L. E. MOUNT.Buttenvorths, London. CENAK. and MONTEITH J. L. (1975), Transfer processes in animal coats. 111. Water vapour dirusion, Proc. R. SOC. Lond. B 188,413423. CLARKJ. A. and CENAK. (1976), Solar and thermal radiative loadr in the energy balance of man, Eng. Med. 5. 75-78. CLARK J. A., CENAK., and M o m m J. L. (1973), Measurements of the local he ntbulance of animal coats and human clothing, J. Appl. Physiol. 35. 751-754. CLIFFORD J., KERSLAKE D. McK, and WADDELL J. L. (1959), The efects of wind speed on maximum evaporative capacity in man, J . Physiol. 147, 253-259. CROCKFORD G. W . (1970), Protective clothing for fishing crews, Proc. R. Soc. Med. 63, 1007-1008. FANGER P. 0. (1970), Thermal Comfort, Danish Technical Press, Copenhagen. FOLK G. E. (1974), Adaptation and heat loss: The past thirty years, [In:] Heat Loss from Animals and Man, 4s.: J . L. MONTEITH and L. E. MOUNT,Buttenvorths, London. A. P., BURTON A. C., and BAZEITH. C., 1941, A practical system of units for the description GAGGE of the heat exchange of m a n with his environments, Science 94.428430. GUIBERT A. and TAYLOR C. L. (1952), Radiation area of the human body, J. Appl. Physiol. 5, 24-37. HEYE. N. (1974). Physiological control of body temperature, [In:] Heat Loss from Animals and Man, eds.: J. L. MONTEITH and L. E. MOUNT,Butterworths, London. HEYE. N., KATZ G., and O’CONNELL B. (1970), The total thermal insulation of the newborn baby, J. Physiol. Lond. 207, 683-698. KREITHF. (1958), Principles of Heat Transfer, Int. Text Book Co., Scranton Pa. USA. LEWISH. E., FOSTER A. R., MULLAN B. J., Cox R. N., and CLARK R. P. (1969), Aerodynamics of the human microenvironment, Lancet, 1273-1277. MCADAMS W . H . (1954), Heut Transmission, 3rd edition, McGraw-Hill, New York. MITCHELL D. (1974a), Convective heat transfer jkom man and other animals, [In:] Heat Loss from Butterworths, London. Auiinals and Man, eds.: J . L. MoNreim and L. E. MOUNT, D. (1974 b), Physical basis of thermoregulation, [In:] Environmental Physiology, ed. : MITCHELL D. ROBERTSHAW, Physiology Series One 7, Buttenvorths, London.

The physics of the microclimate

21

MONTEITH J. L. (1973), Principles of Environmental Physics, Arnold, London. MOUNT L. E. (1967), The CIimatic Physiology of the Pig, Arnold, London. MOUNTL. E. (1974). The concept of thermal neutrality, [In:] Heat Loss from Animals and Man, eds.: J. L. MONTEITH and L. E. MOUNT,Butterworths, London. NEWBURGH L. H. (1968), PhysioIogy of Heat Regulation and the Science of Clothing, (facsimile of 1949 edition), Hafner, New York, London. OOSTHUIZ~N P. H. and MADANS. (1970), Combined convective heat transfer from horizontal cylinders in air, Trans. ASME 92, Series C, 194-196. RAPP G. M . (1970). Convective mass transfer and the coejjfcient of evaporative hear loss from the human skin, [In:] Physiological and Behavioiiral Temperature Regulation, eds. : J . D. HARDY, A. P. GAGOE,and J. A. J. STOLWIJK, Thomas, Illinois. W. L.. and GODMAN R. F. (1967), Estimation of solar radiation environment,Int. J . Biometeor. ROLLER 11, 329-336. STRUNK T. H. (1971), Heat loss from a Newtonian animal, J. Theor. Biol. 33,3541. YVOET., 1960, Experiments on heat transjer from spheres including combined natural and forced convection, J. Heat Transfer, Trans. ASME 82, 214-220.

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Chapter 2

MEASUREMENT OF THERMAL BALANCE OF MAN Y.

"I1

Hokkaido Institute of Technology, Teine. Sapporo, Hokkaido 061-24, Japan.

CONTENTS The body heat balance Independent variables in the human thermal environment Ambient temperature Ambient vapour pressure Air movement . Mean radiant temperature or effective radiant field Clothing insulation Dependent physiological variables in the body heat balance equation Mean skin temperature Skin wettedness Metabolic energy production Sensible heat exchange by radiation and convection Operative temperature Clothing Radiation exchange Mean radiant temperature and effective radiant field Measurement of radiant exchange Convective heat exchange Evapora! ive heat exchange Conclusions THE BODY HEAT BALANCE

The thermal environment of man begins at the skin surface and extends outward to the surrounding media, which consist of the air we breathe; the clothing we wear; man-made sources of heat and cold necessary for our health and comfort; heat, cold and humidity caused by weather, and exposure to solar radiation. All these factors are characterized by temperature, or they in some way affect the heat transfer from the skin surface by radiation, convection, conduction, or evaporation.

Y. NSHI

30

The thermal exchange of man with his environment may be described by a heat balance equation relating independent environmental variables, dependent physiological factors and some properties of the boundary between the human body and the environment (GAGGE et al., 1971; GAGGE and NISHI, 1977; NISHI and GAGGE, 1971). The heat balance equation describing the thermal exchange between the body and its environment takes the classic form

M+ W*+R*+C*+E*+J*

= 0,

where M is the rate of metabolic energy production, W*the rate of work, J* is the rate of storage of body heat, E* the rate of evaporative heat transfer, R* the rate of radiant heat exchange and C* the rate of convective heat transfer. In equation (2.1) all terms have the units of work, J s-' or watts. For the present analysis the outer skin surface will be considered as the boundary separating the human body and its thermal environment. Alternatively all the terms in equation (2.1) can be expressed in watts per square metre (W m-z) as in equation (2.3) below. The outer skin area may be evaluated by the classic DuBois formula A - 0.202m0.425h0.725 (2.2) D -

9

in which the total skin surface area of the human body (A,) is in square metres, body mass (m) in kilograms, and height (h) in metres. At the skin surface, equation (2.1) takes the form given as equation (1.1) in chapter 1 of these proceedings. M,,+R+C+E+J=

0,

(2.3)

where M , is the net rate of metabolic heat loss from the skin surface, and conductive heat loss is neglected. In applications of equation (2.3) we will assume that the evaporative heat exchange ( E ) always occurs at the skin surface, and that the sensible exchange (i.e., R + C ) from the clothed body surface is the same as the dry heat flow from the skin surface to the clothing surface. The usefulness of the heat balance equation in any application of partitional calorimetry lies in the ability to calculate accurately (withinf5 % of M ) any four of its five terms. The fifth term, containing an unknown factor to be measured, may be found by difference. INDEPENDENT VARIABLES IN THE HUMAN THERMAL ENVIRONMENT

There are seven variables that must be measured to describe any thermal environment experienced by a human subject. AMBIENT TEMPERATURE

The ambient temperature (To,"C) of a gaseous environment surrounding the body, usually a mixture of air and water vapour, is defined as that measured at a point outside the thermal boundary-layer.

Measurement of tliermal balance of tnan

31

AMBIENT VAPOUR PRESSURE

The dew-point temperature (Td)is a fundamental measure of humidity in a moist environment. The ambient vapour pressure (e,) is an alternate fundamental measure of humidity. To a close approximation the water vapour pressure is equal to the at temperature Td,the “dew point”. There are many saturation vapour pressure eScTd, meteorological tables and psychometric charts available in engineering handbooks which relate saturated water vapour pressure (e,) to temperature (e.g. ASHRAE, 1977). A useful empirical relationship between e, and T is e,

= exp [16.6536-4030.183/(T+235)],

(2.4)

where e, is in kiloPascals (kPa). Other measures of humidity, but dependent on the ambient air temperature are relative humidity (RH),which is the dimensionless ratio e,/e, and wet bulb temperature (T,,,). If any two of the five variables, T,, e,, T,, R H , and Td are known, the other three may be found by use of a psychrometric chart or by use of the equation (2.4.1)

and the psychro,meter equation. For sea level e = escrw,-O.O66(T,-T,),

(2.4.2)

where e is in kPa. For e in millibars the psychrometric constant in (2.4.2) becomes 0.66 mb K-’, and for Torr 0.5 Torr K-

’.

AIR MOVEMENT

The movement ( v ) of the ambient air results from a) free buoyant motion caused by warm body in cool air medium; b) forced ventilation of the environment itself; and c) bodily motion caused by activity. Air motion is difficult to measure consistently; anemometers usually measure air movement caused by forced ventilation. Air motion over the body surface is a fundamental consideration, necessary for a complete understanding of both convective and evaporative heat exchange. MEAN RADIANT TEMPERATURE OR EFE‘ECTIVE RADIANT FIELD

The basic environmental variables that govern the exchange of heat by radiation are the mean radiant temperature ( T J , or in the energy mode, effective radiant field, RE which is defined as the radiant energy, in W m-’, exchanged by a human being with the imaginary black enclosure at temperature T,. CLOTHING INSULATION

The practical unit of clothing insulation is d o , which represents the effective insulation provided by a normal business suit worn by a sedentary worker in a comfortable indoor surrounding. The value of one unit d o is arbitrarily set at 0.155 m2 K W-I.

Y.NISHI

32

DEPENDENT PHYSIOLOGICAL VARIABLES IN THE BODY HEAT BALANCE EQUATION MEAN SKIN TEMPERATURE

Skin temperature (T,) may be measured by the use of appropriate sensors. Mean skin temperature, T,, may be defined as the average of a t least eight local values of T,, each weighted by the fraction of the total body surface represented. A useful weighting scale is head (7 oh), chest (17.5 yo),back (17.5 yo), upper arms (7 %), forearms (7 ?"), hands (5 yo),thighs (19 ?&), and legs (20 "/). Accurate measurements of skin temperature make it possible to determine the temperature and vapour pressure gradient that affect both the sensible and insensible heat exchange from the body surface. Skin temperature serves as significant index of the mode of regulation of body temperature. It may also serve as an index of our sensory judgments of heat and cold, including thermal comfort. SKIN WETTEDNESS

Skin wettedness (0)is defined as the ratio of the equivalent skin area covered with water (A,,,) to the total skin surface area ( A D ) ;or in practical terms as the ratio of the actual rate of evaporative heat loss to the maximum possible in the environment. BODY HEAT STORAGE

The rate of storage of body heat ( J , W m-2) is directly related to the rate of change in mean body temperature d TJdr (in K s-') by

in which cb is the specific heat of the body and m is the body mass in kg. Measured values of the specific heat of the body tissues are approximately3.5kJ kg-' K-'. In a state of physiological thermal neutrality, which occurs during rest and when there is no regulation of body temperature by sweating, the preferred mean skin temperature range is 33-34 "Cand rectal temperature is 36.9-37.1 "C.The corresponding range of mean body temperature would be 36.3-36.5 "C. METABOLIC ENERGY P R O D U U I O N

Metabolic energy production, M , in the basic heat balance (equation (2.1)) may be measured by the rate of oxygen consumption using the following equation for the relation between oxygen consumption and heat production, expressed in W m-2

M

= 352(0.23 R+0.77)(

Vo2/AD),

(2.6)

in which R is the respiratory quotient, which varies from 0.83 during rest to 1.0 during moderately heavy exercise. Voz is the rate of oxygen consumption in litres per minute at standard temperature and pressure.

Measurement of' thermal balance of m a n

33

The metabolic energy M may be expended in four ways: as metabolic heat which passes through the skin surface, M,,; as heat of vapourization of respired water vapour, E R ; as heat convected by respiration, C,; and as external work W. Thus the net rhetabolic heat in W m-2, passing through the skin surface is

M, = (M+ER+cR+ V I A , .

(2.7)

Because the ventilation of the respiratory tract is closely linked to the oxygen requirements of the body, both respiratory heat losses are almost proportional to metabolic rate. FANGER (1970) suggested that to a good aproximation ER and C, (for air at sea level) could be described by equations (2.8) and (2.9), respectively.

ER = 1 7 . 3 10-3M(5.87-e) ~

(2.8)

CR = 1 . 4 10-3M(34-TJ, ~

(2.9)

and

where both are expressedin W m-' ,e is in kPa and Tain degrees Celsius. In a typical environment (25 "C, e = 1.6 kPa, 50 % RH)ER accounts for about 1 % of M and is often ignored. Work (W) can be measured accurately on a bicycle ergometer or treadmill. The ratio, W / M , represents the mechanical efficiency (q) of the body doing work. In human beings the maximum mechanical efficiency, measured while pedalling on a bicycle ergometer, is approximately 18-22 % for an average person. Treadmill exercise is about 8-10 % efficient. For level walking and during most stationary activities, the mechanical efficiency is-zero and external work may be ignored. SENSIBLE HEAT EXCHANGE BY RADIATION AND CONVECTION

The exchange of sensible heat from the skin surface is usually accomplished first by conduction through clothing, and next by radiation and convection from the outer clothing or skin surface to the surrounding environment. OPERATIVE TEMPERATURE

The operative temperature (To) of human thermal environment is defined by GAGGE in chapter 5 as the temperature of an isothermal "black" enclosure in which man would exchange the same heat by radiation and convection from his body surface as he would in the actual non-uniform environment. By this definition, the dry heat exchange (HD= RSC) from the body surface, at temperature T,, is given by (2.10)

where hc, is the combined coefficient for heat transfer by radiation and convection in W m-2 K-', or by using ambient air temperature T, and mean radiant temperature, T, HD = h,(T,-Ta)+hr(T,,-Tr), (2.11) 3

- Bioengineering

34

Y . NISHI

in which h, is the convective heat transfer coefficient in W m-' K-' and h, the linear radiation exchange coefficient, also in W m-' K-'. Comparing equations (2.10) and (2.1 l), it follows that operative temperature is defined by

.

To = (hrTr+hcTa)/(hr+hc)

(2.12)

and that

hCr= h,+hc.

(2.13)

Thus by equation (2.12) operative temperature can also be defined as an average of T, and Tr, weighted by the respective heat transfer coefficients. CLOTHING

Sensible heat transfer through the clothing layer may be written as HD

= hd(~'-Tsu)Y

(2.14)

where h,, is the effective clothing conductance, in W m-' K-', and T, is now regarded as the mean temperature of the outer clothing surface. The reciprocal of h, is I , the effective insulation of the clothing worn, in m2 K W-'. The dry heat exchange from the clothing surface at temperature T,, is given by (2.15)

Hence, combining equations (2.14) and (2.1 5) to eliminate

TSu (2.16)

where F, is the dimensionless ratio (2.17) A thermal efficiency factor F,was first proposed by BURTONand EDHOLM(1 969). Thus the effective combined heat transfer coefficient from the skin surface is the product of Fc and her. By eliminating h, in equations (2.15) and (2.16) it may be seen that -

F, = (Eu-To)/(Ts-To).

(2.18)

et al., 1975). Thus, F, may be found by direct measurements of To,T,, and T,(NISHI RADIATION EXCHANGE MEAN RADIANT TEMPERATURE A N D EFFECTIVE RADIANT FIELD

The concept of effective radiant field RE was introduced by GAGGE et a]. (1967) as an aid to better understanding of high-temperature radiant sources. Mean radiant temperature (T,) is included in the definition for the effective radiant field as follows R E = h,(T,-T,),

(2.19)

Measurement of therriial balnnce of man

RE = hcr('o-'a),

35

(2.20)

where RE is in W m-'. The term (RSC)in the basic heat balance equation (2.3), may now be rewritten as (2.21) -

R

= F,[hr(Ts-Ta)-RE].

(2.22)

In establishing the general principles of sensible heat exchange above, the linear radiation exchange coefficient h, has been treated as a constant. For an unclothed = 34 "C at To = 29 "C, the ;,value of h, is subject at thermal neutrality, with 4.5 W m-' K-' for a lightly clothed subject (0.6 clo) with ? , = 31 "Cand To= 24 "C during thermal comfort, h, = 4.7 W m-' K-' ; for a well clothed subject (1.0 clo) = 27 "C and To= 20 "C, h, = 4.8 W rn-'K-'. These coefficients are with expressed per unit skin area, and are therefore lower then the radiative exchange coefficient obtained from the Stefan-Boltzmann relation.

Fs

TSu

MEASUREMENT OF RADIATION EXCHANGE

A simple direct measure of oured Bedford globe

human beings is obtained by using a skin-col15)m, diameter) and by using the formula (2.23)

where v is the ambient air movement in m s-' and Tg is the globe temperature. The first term in the bracket is the value of h, for a sphere at temperature 27 "C. The second term is Bedford's formula for the convective heat transfer coefficient for a 6 inch globe. The factor 0.76 converts the radiation field that the globe "sees" to that appropriate for a sitting human being with 0.6 clo insulation, as, because of its shape much of the body "sees" other parts of itself and in consequence, its radiative area is considerably less than A,. CONVECTIVE HEAT EXCHANGE

Measurements of h, in the laboratory for various standard activities are presented in tables 2.1 and 2.2. The theoretical value proposed by RAPP(1973) in table 2.1 is baeed on a sphere with 75 cm diameter; those by MISSENARD (1971) in table 2.2 are based on a long 17 cm diameter cylinder. Values by the naphthalene method, reported by NISHIand GACCE(1970), represent the first direct measurements of h, during exercise, treadmill walking, and free walking without the use of calorimetry. The values presented have an experimental basis up to speeds of 1.8 m s-'. For greater air velocities they are still useful as first-order estimates. Finally, values of h, vary widely over the surface of the body. Table 2.3 illustrates local h, values observed and GAGGE (1970) during rest and various types of exercises. by NISHI

Y. NISHI

36

T a b l e 2.1 Convective heat transfer coefficient (hJ in normally ventilated environment Condition Seated Seated Standing Seated on bicycle Pedalling bicycle Pedalling bicycle at 60 rpm

h,

Investigator

4.1 2.9&0.9 4.5f0.3 3.4 4.8&0.8 6.0

Remarks

RAPP(1973) WINSLOWet al. (1936) WINSLOWet al. (1936) WINSLOW et al. (1936) WINSLOWet al. (1936) NISHI and GAGGE (1970)

Theoretical Partitional Partitional Partitional Partitional

Calorimetry Calorimetry Calorimetry Calorimetry

Naphthalene method

T a b l e 2.2

Formulae relating the convective heat transfer coefficient (h,) to air velocity Formula

Activity

h, = 11.6 h, = 3.42+5.93~ h, = 0.53 h, = 8.6vfW

Investigator

Seated Seated Treadmill Free walking

Remarks

Y, room air movement (1971) Y, room air movement Nisai and GAGGE(1970) vfw, speed of t~-eadmill NISHI and GAGGE,(1970) Y/W, speed of walking

WINSLOWet al. (1936)

MISSENARD

T a b l e 2.3 Local convective heat transfer coefficient (Ac), in W m-’ K-I, during rest and exercises in normal air movement (0.154.2m s-’)

Body Region Resting

Free walking Bicycle

Sitting

10.9 m s-’ (1.8 ms-’ 60 rpm

Head Chest Back UpwrForearms arms Hands Thighs

3.2 4.2 5.4 7.2 9.5 4.4

2.5 3.6 4.5 4.8 6.7 3.3

4.0 3.2 6.4 4.3 8.3 4.7 6.0 6.7 ‘17.0 3.2 5.3

2.4

3.9 6.6 10.8 11.2 16.3 5.2

4.6 7.2 15.4 11.6 17.2 4.7

2.8 5.0 7.7 8.7 12.5 6.7

Legs

Mean (hc)

3.7 3.1 10.5 5.8 14.4 8.4 11.8 8.4 17.0 12.0 11.1 6.0

The relation of room air movement to the coefficient h, has limited significance. When a subject is active, such as when pedalling a bicycle ergometer, the measured value of v for the ambient air has even less significance. In evaluating the effect of both air movement and activity, it is more practical to consider the resulting value of h, as an index of “relative air movement” rather than use the actual value of the air movement itself.

Measuremelit of thermal balance 01. man

37

EVAPORATIVE HEAT EXCHANGE

The heat loss by the evaporation of sweat is man’s most effective means of survival in the heat. The evaporative heat loss ( E ) itself is the best single physiological index of his environmental stress. Since the beginning of human calorimetry, observed changes in E have been the quantitative basis for measurements of the combined transfer coefficient and the individual transfer coefficients for radiation and convection for the particular experimental arrangement used (WINSLOW et al., 1936; COLIN and HOUDAS,1967). In partitional calorimetryE may be found from the rate of change in body mass A, as measured by a sensitive balance. The most successful balance used for this purpose has been the Potter Bed, described in US Patent 3,224,518 and 3,360,002. This balance is designed without any wearing knife edges and has proven useful for continuous measurement of body weight during both rest and heavy exercise (SALTIN et al., 1970). In such studies E is determined by the following relation

E = 60m A/AD,

(2.24)

where h is the rate change of body mass in grams per minute and 1 is the latent heat of vapourization of water (A = 2450 J g-I). To evaluate E,, the total evaporative heat loss from the body (E)must now be corrected for respired vapour (ER)using equation (2.8). The validity of equation (2.24), as a direct measure of evaporative heat loss, depends on the ability of the sweat produced at a rate to evaporate completely on the skin surface. Without active sweating the average sized person would lose weight by respiratory and skin diffusion at a rate of approximately 0.5 g min-’. When working at 50 % of maximum oxygen capacity in 30 “C To and 50% RH, the value of h would be about 10-12 g min-’. The maximum evaporative heat loss (En,)from a totally wet skin surface is proportional to the water vapour pressure difference from the skin surface to the ambient air. The maximum evaporative capacity per unit area of wet skin may be written as

Em = 16.5hcF,,(es-e),

(2.25)

where e, is the saturation vapour pressure at skin temperature, in kPa. The factor of 16.5 is the reciprocal of the psychrometer constant at sea level, which may be derived from the Lewis relation. The term FeCin equation (2.25), known as Permeation Efficiency Factor (NISHI and GAGGE,1970b), has been added to take account of clothing worn. The factor F,, is analogous to Fc for dry heat exchange. For normal porous clothing, such as worn every day by an average person, it has been shown experimentally (NISHIand GAGGE, 1970b) that :

Fee = (1 +0.92hCI)-’, where I is the clothing insulation for sensible heat transfer.

(2.26)

Y. NISHI

3b

Skin wettedness is an expression of the efficiency of evaporative regulaton. The wetted area of the skin (A,,,)may be defined as that area of the skin which if covered with sweat, would provide the observed rate of skin evaporation under the prevailing condition. Thus by this definition

E

= AwEm/AD = WE,,,,

(2.27)

where w is a dimensionless number between 0 and 1. w -. A J A , = EIE,,,.

(2.28)

When E can be evaluated experimentally, since E,,, is obtained from the basic observations of Ts, To,T,, h, and I , it is possible to evaluate skin wettedness a t any time by equation (2.28). Skin wettedness ( 0 )ranges from a certain minimum value, which occurs when there is no evaporative heat loss by regulatory sweating, to a maximum theoretical value of unity. At the minimum the evaporative heat loss from the skin surface (Ed)is entirely due to the diffusion of water vapour through the outer layers of the skin. When regulatory sweating begins, evaporative heat loss may occur by diffusion as well as by the evaporation of sweat (E,). When the skin surface is completely wet (Le. o = l), E is attributed entirely to regulatory sweating (E,). The ratio EJE,,, describes the skin wettedness due to sweating (ors), the ratio E,/E, is the skin wettedness due to diffusion (cod), and the total wettedness w at any time is given by GAMEet a!. (1971) as 0

= mdf(l-Od)w,.

(2.29)

From data reported by BREBNERet al. (1955), the minimum value of w may be 0.06. The significance of the maximum possible evaporative capacity (EJ for clothed and unclothed humans was first emphasized by BELDINGand HATCH(1956) when they proposed their Heat Stress Index.

CONCLUSIONS

Heat balance equations, describing human heat exchange by radiation, convection, evaporation and conduction from the skin surface with the thermal environment have been outlined in this chapter. The environmental variables in the basic heat balance equation that must be measured are the ambient air temperature, the mean radiant temperature or effective radiant field, the ambient water vapour pressure or humidity, air movement as it affects the convective and evaporativc heat loss, and clothing insulation. The physiological variables in the heat balance equation are skin temperature, skin wettedness, mean body temperature, metabolic energy consumption and the ra?e of external work. A more complete description of the heat balance equation, with more details applicable to special and aquatic environments is given in a previous review by GAGGE and the present author (GACGE and NISHI, 1977).

Measwetirent of thermal bolnnce of

mala

39

REFERENCES American Society of Heating, Refrigerating and Air-conditioning Engineers (ASHRAE) (1977), Handbook of Fundamentals, ed.: Carl W . MACPHEE.,New York. BELDING H. S. and HATCH T. F. (1956), Index for evaluating heatstress in terms of resultingphysiological strain, ASHRAE Trans. 62, 213-236. BREBNER F. F. KERSLAKE D. McK, and WADDEL J. L. (1956). The diffusion of’ water vapour through human skin, J. Physiol. (London) 132, 225-231. BURTON A. C. and EDHOLM 0. G. (1969), Man in a Cold Environment (Facsimile of 1955 edition), Hafner Publishing Co., New York. COLIN J. and HOUDASY. (1967), Experimental determination of coefficient of heat exchange by convection ofthe human body, J . Appl. Physiol. 22, 31-38. FANGER P. O., Thermal Comfort (2nd ed.; facsimile of 1970 edition), McGraw-Hill, New York. GAGGE A. P., RAPPG. M., and HARDY J. D. (1967), The effective radiant field and operative temperature necessary for comfort with radiant heating, ASHRAE Trans.73, 1-9. GAGGE A. P., STOLWIJK J. A. J., and NISHI Y.(1971), An effective temperature s a l e based on a simple model of human physiological regulatory response, ASHRAE Trans. 77, 247-262. GAGGE A. P. and NISHI Y. (1977), Heat exchange between human skin surface and thermalenvironnaent [In:] Handbook of Physiology. Reactions to Environmental Agents, ed.: D. H. K. LEE,Bethesda, Md. Am. Physiol. SOC.,sect. 9, chapt. 5, 69-72. MISSENARDA. (1971), Exchange thermiques du corps humain avec /‘ambiance, Rev. GBn. Therm. 117, 765-770. NISHI Y. and GAGGE A. P. (1970a), Direct evaluation of convective heat tramfer coefficient by naphthalene sublimation, J . Appl. Physiol. 29, 830-838. NISHIY. and GAGGEA. P. (1970b), Moisturepermeation of clothing - a factor governing ihermul equilibrium and comfort, ASHRAE Trans. 76, 137-145. NISHI Y. and GAGGEA. P. (1971), Humid operative temperature. A biophysical index of thermal sensation and discomfort. J . Physiol. (Paris) 63, 365-368. NISHI Y. GONZALEZ R. R., and GAGCEA. P. (1975), Direct measurement of clothing heat transfer properties during sensible and insensible heat exchange with thermal environment, AS H U E Trans. 81, 183-199. RAPPG. M. (1973). Convecfiveherit transferjor nude man, cylinders and spheres at low air velocities, ASHRAE Trans. 79, 75-87. SALTINB., GAGGEA. P., and STOLWIJK J. A. J. (1970). Body temperatures andsweatingduring thermal transients caused by exercise, J . Appl. Physiol. 28, 318-327. WINSLOWC.-E. A., HERRINOKIN L. P., and GAGGEA. P. (1936), Tl7e determination of radiption and convection exchanges by partitional calorimetry, Am. J . Physiol. 116,669-684.

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Chapter 3

EVALUATING THE EFFECTS OF CLOTHING ON THE WEARER R. F. GOLDMAN U.S.A. Research Institute of Environmental Medicine, Natick, Massachusetts 01760, U.S.A.

CONTENTS Introduction The five levels of analysis Units The permeability index i, Determination of I and im The copper man Physiological chamber trials Conclusions from specific studies Problems in the cold Problems in the heat Impermeable materials Effects of different materials or treatment Effect of drape or venting Summary

INTRODUCTION

Clothing has been designed to a much greater extent by fashion and by iechnological developments in indus’ry than by any scientific analysis of the heat exchange allowed by clothing between the wearer and his environment. However, requirements to maximize survival time, extend performance time and improve the general comfort of soldiers exposed to extremes of Arctic, de:ert or tropic environments have required the development of a multi-disciplinary, multi-level program at this laboratory. These scientific analyses, essential to deal with environmental extremes, can also be applied to suggest clothing design; for less extreme environments and to evaluate the relative contributions of various factors to thermal aspects of clothing comfort.

42

R. F. GOLDMAN THE FIVE LEVELS OF ANALYSIS

A multidisciplinary approach has been evolved at the USA Research Institute of Environmental Medicine in Natick, Massachusetts to assess the thermal interactions between the environment, the uniform worn, the man and his job. Studies are conducted at five different levels of analysis, with each level providing information which can be related to the others, as follows: I ) the physical heat transfer characteristics of the uniform materials are measured using classical heated flat plate theory, and also a unique “sweating” flat plate; 2) complete clothing a: semblies, with and without such additional items as gloves, headgear or back packs etc., are evaluated on a “sweating” copper manikin fo,. the heat transfer characteristics of the clothing assembly; the values obtained are used in calculations in a programmed computer model to predict the wearer’s tolerance limits ; 3) carefully controlled physiological trials are carried out in climatic chambers with volunteer subjects dressed in these clothing systems, to validate or refine the computer predicted limits; 4) controlled small scale studies are conducted in the field or at the work site. Groups of men wear specified clothing systems and carry out specified tasks under conditions of environment, terrain and work rate where physiological problems are anticipated, based upon experience in climatic chamber trials; 5) studies with these clothing systems are carried out, collaboratively, during actual field opera.ions scheduled by Army elements or other groups. Specific details of the methodology for the laboratory studies (i.e. physical plate material studies, biophysical copper man evaluations and tolerance predictions and physiological chamber validation experiments) are presented below. The methods used in field studies are adapted for each problem, are therefore difficult to generalize and will be included when discussing the results. UNITS

Some years ago, physiologists working in the field of clothing and the associated heat transfer from a man developed a technique to determine how much heat would pass through a garment by thermal radiation and convection from the skin (GAGGE et al., 1941). The difference between a man’s skin temperature and the ambient tcrnperature was taken as a gradient across which, to avoid a change in body temperature, he had to eliminate the difference between his metabolic heat production and the heat he could lose by evaporation of sweat from his skin or of water from his lungs. The non-evaporative component was assumed to pass through the clothing by radiation and convection heat transfer. They then defined the insulation I of a clothing system, plus the overlying still air layer. In terms of SI units their “clo” unit is equal to 0.155 m2K W-’. The dry heat transfer (HD)to the surroundings (i.e. convective plus radiative), in units of W m-’, is given by

HD = AT/?

(3.1 a)

Effects of’clorhing

43

or, when insulation is expressed in clo (Z‘)

HD = AT/O.l55Z’,

(3.1 b)

where AT is the temperature difference between the skin and ambient air, in Kelvin. This equation states that heat flow equals the driving force, in this case a temperature difference, divided by a resistance. This basic approach for radiation-convection heat loss yields a quantitative assessment of how good a given uniform is for a resting man in cold weather, since radiation and convection are major avenues of heat loss in the cold. However, for a working man in the cold evaporation of sweat becomes an important avenue of heat loss. Furthermore, radiation and convection heat loss decrease with increasing ambient temperature while evaporative cooling rises. Thus, the insulation value alone is insufficient in the heat. THE PERMEABILITY INDEX, f,

A similar form of equation can be used to predict evaporative heat transfer HE HE = 16.5(eS-eJ1, to allow the use of the same units for I in equation (3.2) as in in equation (3.la) the constant must have the dimensions of K kPa-’, i.e. the inverse of those of the “psychrometer constant”. The derivation of equation (3.2) is given in the introductory chapter. The gradient for evaporative transfer is the difference between the vapour pressure at the skin surface (e,) and the ambient vapour pressure (eJ in kiloPascals (kPa). Using the slope of the wet bulb lines on a psychrometric chart a vapour pressure difference can be converted to an equivalent temperature gradient. One can then determine the evaporative heat loss from a square metre of surface with a given water vapour pressure; e.g. at 35°C (the skin temperature of a sweating man) there would be a vapour pressure of 5.6 kPa at the skin, and the gradient will thus be 5.6 kPa minus of this laboratory the ambient air vapour pressure e,. The late Dr Alan WOODCOCK proposed that the evaporativeheat transfer for a nude man, or for any clothing system, could be expressed as the ratio of the actual evaporative heat loss, as hindered by the clothing, to that of a wet bulb with equivalent insulation (WOODCOCK, 1962). He suggested expanding equation (3.2) to include a dimensionless permeability index (i,) so that: HE = 16.5i,n(es-ea)/I. (3.3a) The index ,i could range from 0, for a system with no evaporative transfer, to 1 for a system which had no more impedance to evaporative heat transfer than the usual wet bulb thermometer. The conventional wet bulb, of course, is ventilated, and the still air layer is greatly reduced. Since a soldier is surrounded by a relatively undisturbed air layer, i, seldom approaches 1.0 for a man, but is limited in still air to about 0.5. When 1 is expressed in clo units (1’)and e in kPa equation (3.3a) may be approximated to HE= 100i,,,(es-ea)/Z‘. (3.3b)

44

R. F. GOLDMAN DETERMINATION OF I AND i,,,

Figure 3.1 a shows the flat plate apparatus used in measurement of the insulation value. The apparatus consists of a test section (A), surrounded on all four sides by a guard section (B) with another guard section ( C ) beneath the entire upper plate. All three sections are instrumented with plate temperature sensors, heating elements and thermostats. The sample to be tested (0) is placed on the surface and the entire assembly is placed in a constant temperature cabinet. In operation, power to the guard sections is controlled so that their surface temperature is identical to that of the test section. Thus there is no gradient for heat loss from the bottom or edges of the test section. After equilibrium is established the power required by the test section equals the heat lost through the insulation, and can be expressed as a flux density per degree of temperature gradient from the plate surface to ambient air. This can be converted to the corresponding insulation for the sample plus the adhering air layer, using equation (3.1). If a thin cotton “skin” is placed on the plate surface and a water level is maintained at the surface of some small holes drilled in it then the “skin” wicks out enough water to maintain a constant, saturated, vapour pressure under the fabric sample. A constant ambient vapour pressure is maintained in the measuring chamber and power requirements measured, just as for the dry plate. The value of i,,, can be determined for a given sample plus its adhering air layer by means of equation (3.3). Figure 3.la shows the “sweating” flat plate and its water supply in the constant temperature and humidity chamber with its control and recorder panel. The flat plate determinations of I and i, are primarily of use in selection of the fabrics to be used in a clothing system. The effects on heat transfer of different weaves, perforations, different finishes or treatments, the effects and best arrangement of multiple layers, etc. can all be established using the sweating flat plate (FONSECA, 1967). Heated, dry and “sweating” cylinders have been developed to mimic the cylindrical shape of the body. These are useful for studying wind penetration through clothing, and effects of spacer materials, but factors of drape, fit, and shape are difficult to simulate even on a cylinder. Also, a complete uniform is made up of a number of different components, protecting various parts of the body, so that evaluation of a complete clothing system requires a more sophisticated model 1965). than a cylinder (FONSECA and BRECKENRIDGE, THE COPPER MAN

The solution has been the development of life sized, heated copper manikins. Figure 3.1 b shows a manikin with his “sweating” cotton skin. The heat provided to the manikin to maintain a constant skin temperature can be measured and the ambient temperature and vapour pressure of the test chamber can be controlled; skin and air temperature and vapour pressure are measured. Thus, the sensible and evaporative heat losses caused by a given gradient of temperature and vapour pressure can be calculated for any clothing system worn. This technique has been in use for the last 15 years. Using the insulation and evaporative transfer indices, with some physiological knowledge, tolerance times can be predicted, for a given

Effects of clothing

45

C

Fig. 3.1. Laboratory Test Methodology a) The "sweating" flat plate apparatus for assessing material characteristics; the diagram inset shows the test section A, upper B and lower C guard sections and the position of the materlal to be evaluated D b) The sweating copper manihin used to assess non-evaporative (I) and evaporative (im) heat transfer characteristics of a complete uniform assembly c) Volunteer subjects, each with a different clothing assembly, seated in the climatic chamber during a rest break. The cables leading overhead from each subject carry rectal and skin tcmpcratuce information

tack, for men in the chambers and in the field. The heat stored by the body must be the difference between the heat produced at work and that lost by evaporation and by radiation and/or convection through the clothing system. Since the average man has 1.8 m2 of surface area, by estimating his skin temperature @"), total dry

R. F. GOLDMAN

46

heat transfer (El,*), in watts, can be calculated for any given ambient dry bulb temperature To as

H i = 1.8HD = 1.8(Fs-Ta)/1

(3.4a)

(3.4b) Similarly one can calculate the maximum evaporative heat transfer from a body, through clothing, for any given ambient vapour pressure

HZ

=

1.8HE= 29.7(5.9-eJ1,

(3.5)

where a 36 "C skin temperature has been assumed for the clothed sweating man, giving e, = 5.9 kPa. If heat production, respiratory heat loss and solar heat load gain are known, one can calculate whether the man can eliminate all the heat he is producing or whether some of it will be stored in his body. The specific heat of human tissue is 3.47 kJ kg-' K-', therefore the body temperature of a 70 kg man will be increased by 1 "Cfor each 240 kJ stored. This allows prediction of tolerance as the time to reach a given body temperature. A computer program has been devised (GIVONIand GOLDMAN,1971, 1972, 1973a, 1973b; PANDOLF et al., 1976) which incorporates many of the significant physiological, physical and environmental factors involved in human heat transfer. If the appropriate values for clothing, environment and metabolic heat production are supplied, the .model will predict the body temperature (rectal and skin) and heart rate response of a n individual under the chosen conditions. However, the predicted responses are frequently checked by actual environmental chamber exposures of men. PHYSIOLOGICAL CHAMBER TRIALS

Standard protocols have been developed for these trials; for example, one requires two fifty-minute walks, separated by a ten-minute break, followed by a one hour rest (see table 3.1). Figure 3.1 c shows subjects in an environmental chamber, during a rest period. The men are seated on benches placed on one of the large four man treadmills. Each subject is wearing a different garment since, as usual, choice of the garments and subjects was randomized on each day. Each subject is wearing a rectal catheter, to measure deep body temperature, and a three point skin temperature harness. Two connecting cables from each man are led outside the chamber to the instrumentation shown in figure 3.1 c. Each subject's rectal temperature is indicated continuously on one of the eight meters at the base of the master timer. Skin temperatures are recorded sequentially on the recorder, along with the rectal and chamber temperatures. Each point printed is simultaneously encoded and punched on the digital punch tape system shown at the right. This tape is used as a permanent record and is also fed into a programmable calculator system (HP 9825) for prompt data reduction and analysis. The results are plotted, frequently superimposed on a preliminary plot o f the predicted responses, so that the agreement can be checked.

T a b l e 3.1 Standard protocols for clothing studies

Cumulative time 0

115 120 170

Schedule: Protocol I Approx. 0800 Report to tropic chamber dressing room. Weigh canteens and urine containers. Subjects strip nude, void, defecate. Weigh nude. Put on catheter, skin harness, uniform, pack. Weigh clothed, with helmet liner and pack. Obtain initial pulse rate, rectal temp., skin temp. Approx. Procedure Cumu- Approx. hour lative hour 0900 Enter tropic wind tunnel maintained at “approtime0 0900 priate”c0ndition. Rest,sittingfor 115 minutes ,without pack. Continuous rectal and skin temp. recording throughout test period. Water ad lib. Pulse rates at 6@ and 115 minutes. 1055 Weigh clothed, with helmet liner and pack; weigh 50 0950 and refill canteens. 1100 Subjects walk for 50 minutes at 5.6 km hr-I 60 lo00 Pulse rates at 25 and 50 minutes. 1150 Rest, sitting, for 60 minutes. Pulse rates at 30 110 1050 and 60 minutes 120 1 loo 180

230

1250

1200

Leave tropic wind tunnel. Weigh clothed, with helmet liner and pack. Strip and dry thoroughly. Weigh nude. Weigh canteens. Tabulate all water intake and output and calculate 2-hour evaporative water loss at rest, total evaporative water loss and total sweat production.

Schedule: Protocol I1 __-

-

Procedure Enter tropic wind tunnel maintained at “appropriate ”condition. Walk for 50 minutes at 5.6 km hr-l. Continuous rectal and skin temp. recording throughout test period. Water ad lib. Pulse rates at 25 and 50 minutes. Rest, sitting for 10 minutes. Pulse rates at 10 minutes. Walk for 50 minutes at 5.6 km hr-l. Pulse rates at 25 and 50 minutes. Weigh clothed, with helmet liner and pack; weigh and refill canteens. Rest, sitting for 60 minutes without pack. Pulse rates at 30 and 60 minutes. Walk for 50 minutes with pack at 5.6 km hr-I. Pulse rates at 25 and 50 minutes.

48

R. F. GOLDMAN CONCLUSIONS FROM SPECIFIC STUDIS

Having established the scientific approaches on which our program is based, we will emphasize some specific studies directed to clothing for extremes of cold and heat. A clothing system to minimize heat loss for an inactive man under Arctic conditions must cause a severe heat stress problem as the man increases his heat production by activity, if he does not remove most of his Arctic protective clothing.

PROBLEMS IN THE COLD

Man’s thermal problems in extreme cold have two possible solutions: increasing heat supply or decreasing heat loss. Inefficient clothing design can increase heat production during activity; for example, “friction” in multiple layer clothing increases heat production by about 16%, and footwear weighing 1 kg increases the energy cost of locomotion as much as 5 kg carried on the torso. However, this approach is not really desirable since such solutions are useless at rest, and during physical work men wearing Arctic clothing usually produce too much heat. Techniques for increasing physiological heat production other than by shivering (e.g. increased dietary protein, non-shivering thermogenesis with cold acclimatization) are generally ineffective, so if extra heat is to be provided it must be by auxiliary heat. For inactive subjects dressed in full Arctic clothing, a i little as 3 watts to each hand and 5 watts to each‘foot has proven adequate for comfort at -57 “C with a 4.5 m s-’ wind for more than six hours (GOLDMAN, 1964). Decreases in heat loss can be accomplished only by reducing convective, radiative or evaporative heat exchange. Sensible heat loss is largely a function of the thickness of insulation. Using the relationship of 0.243 mz K W-’ (1.57 clo) per cm of thickness, much has been accomplished. However, the problems of clothing weight per se, clothing bulk and hindered mobility, and the dramatic increases in the surface area available for heat loss as one increases the radius of insulation around the body’s cylindrical sections- particularly such thin human cylindricalsections as the fingerslimit further improvement. Lightweight, non-wove nbatts of material are increasingly bcing substituted for conventional insulat’ng materials in parka liners, gloves and sleeping bags. lmproved outer wind-proof materials and closures are also desired to reduce the loss in insulation of clothing as wind and/or subject movement rate increases (HOLLIES and GOLDMAN, 1977). The specification of insulation for the combined heat loss by radiant and convective heat transfer, obscures consideration of radiant heat loss per se. Reflective insulation is in disrepute, since a highly publicized reflective lining system for outercoats was a failure in really reducing rdaiant heat loss from the body. However, new techniques deposit reflective materials on tough, light, thin plastic materials which dramatically increase the insulation of non-woven, lightweight batt materials, with little increase in weight or thickness. Unfortunately, most of the measured increase simply represents a return to the 0.24 mzK W-’per cm standard found with conventional materials; the free path length in the non-woven, batt, materia%

Effecls of’clothing

49

reduces the insulation per unit thickness because of increased radiant heat losses through the materials. The use of reflective materials simply reduces these losses. A “sandwich” of several layers of batt insulation between two thin windbreak surface layers, which has an insulating value of 0.54 m2 K W” (3.5 clo), could be improved to 0.84 m2 K W-’ (5.4 clo) merely by adding three reflective layers of about 1 mm thickness each, but 0.74 m2K W-’ (5 clo) would be expected for a conventional material of this same thickness without any reflective materials. At present it is difficult to maintain the critical spacing required to demonstrate these benefits of reflective layers in non-woven materials. During fabrication into clothing the insulating batt is compressed below the critical spacing dimension required; i.e. compression produces reduced thickness and returns free path length toward that of conventional materials. Work is currently underway to develop practical clothing items which achieve the improvements in insulation and reductions in weight that we feel are possible with multilayer batts incorporating such reflective materials. Most of these materials, so far, are impermeable to water vapour. Since for a man at rest about 25% of total heat loss is by evaporation (half from the respiratory tract, half from the skin) vapour bamer materials might be useful; moisture released by the body when absorbed into the clothing substitutes water - a good heat conductor - for trapped air, and thus reduces insulation. Vapour barrier boots have proven highly successful at slowing foot cooling rates; but problems arise when feet are not dried regularly and dry socks donned. The potential for use of reflective materials within such vapour barrier items seems quite promising. Newer reflective materials appear highly vapour permeable, but tend to be so heavy that the benefit of reduction in weight of using the non-woven batts disappears. A number of devices have been proposed over the years for reducing the respiratory heat loss; generally these do not seem to be worth their problems, at least in healthy young individuals. Similarly, face masks to reduce the exposed skin surface have been tested, but again are generally not worth the trouble; a good parka hood with a controllable apkrture adequately shields the face and minimizes exposed surface area. For the few individuals exposed to conditions sufficiently extreme to require such items, modern technology can provide portable life support systems which provide a comfortable microclimate within a completely encapsulating clothing system. In summary, auxiliary heating,’ substitution of lightweight batt insulation, incorporation of reflective insulation where practical and, ultimately, climate controlled clothing systems are the promising new approaches being developed for cold weather clothing. PROBLEMS IN THE HEAT

During heavy exercise in extreme heat, man becomes almost totally dependent on evaporation of sweat for the cooling required to dissipate his heat production (MJ, at rest or at work. M,, ranges from about 58 W m-? (I met) at rest to a peak production of perhaps 580 W m-’ (10 met) for short periods. A value of 175 W m-*(3 met) can be used for an average man’s heat production during light industrial work. We 4

- Bioengineering

50

R. F. GOLDMAN

have shown that our average subject, when allowed to unconsciously adjust his speed while “working hard”, tends to select an average heat production of 290 W m-2 (5 met) (HUGHES and GOLDMAN, 1970). The equivalent evaporative cooling, required when ambient air temperature approaches skin surface temperature, is 520 watts. This in turn requires evaporation of some 750 grams of sweat per hour if the evaporation occurs at the skin surface: the sweat rate required to produce the same cooling can double if evaporation occurs from the clothing surface rather than from fh e skin, as a result of the increase in the insulation between the point where evaporative cooling takes place and the skin surface. In contrast, the maximum sustainable sweat production is 1000 grams per hour for a well heat acclimatized man; the importance of removing heavy clothing during activity is obvious. The problem becomes still more obvious if one considers the difficulty of avoiding dehydration; by getting the litre of water required to replace this body water loss each hour. When the man stops exercising the sweat trapped in his clothing will eventually evaporate and provide undesirable additional cooling. The copper manikin I values reflect both material thickness and the air insulation trapped between the skin and clothing, a function of material stiffness, i.e. drape. Because the skin to air temperature gradient for non-evaporative heat loss is small in the heat, the important value is iJZ; this indicates the fraction of the maximum evaporative cooling possible in a given environment without wind, since these manikin values are “still air” determinationc. Thus, a man wearing just a fatigue uniform (inL N 0.5; I’ rn 1.35 clo) can obtain about 37 % of the maximum cooling possible (iJZ’ = 37 W m-’ kPa-’), while with a heavier clothing system (im- 0.5; I’ w 2.5 clo) only 20 yois available. In chamber studies of the physiology of unclothed 1965) body et al., 1965; IAMPIETROand GOLDMAN, men in the heat (GOLDMAN heat storage of about 330 kJ was enough to make a number of the volunteers stop working; a heat storage of about 660 kJ resulted in heat exhaustion in 50 yo of those who had continued, while almost no one could tolerate 920 kJ. Note the correspondence of these critical levels of heat storage with the heat debt levels of 330 kJ waking a sleeping subject, and the 630 kJ inducing marked shivering. Hard work in a 35 “C, 50 :h relative humidity (RH) environment is so severe a combination that the predicted tolerance time is less than l+ hours; even wearing just the usual fatigue uniform; in reality the fatigue uniform would rapidly become sweat soaked and this, in combination with any natural ambient air motion, would result in a considerably longer tolerance time than this predicted value. Arctic protective uniforms, however, cannot readily wet out with sweat and heat exhaustion can occur as easily in the Arctic, if a high work level is sustained without appropriate reduction in clothing. While the copper man based predictions are useful in ranking clothing systems, they obviously should be supplemented by physiological chamber trials to assess the effects of body motion, wind and the efficiency of sweating, a s shown by HOLLIES and GOLDMAN (1977). Men walking on treadmills under controlled conditions cannot indicate all the problems that will occur in troops attempting to perform their military missions in the field. While thermal effects resulting from the addition of packs, body armour, helmets, weapons, etc. have been measured both on copper

51

Efecis of clothing

manikins and in physiological cha.mber studies (GOLDMAN, 1969; JOY and GOLDMAN, 1968), the problems associated with military tasks other than marching, and with solar heat load, terrain and wind variation are impossible to reproduce indoors. IMPERMEABLE MATERIALS

In the study presented in fig. 3.2, a commercial vinyl raincoat was worn either full length or cut down by 1/4, 1/2 or 3/4 of the total length. It is notable that both the Z and the i,,, /Zvalues determined on the sweating copper man reflect this linearity. During the rest period there is no body heat storage, but by the end of the walk the mean heat storage values rank in the exact order predicted. However, the difference observed between the 1 /4 and 1 /2 length garments is smaller than one would anticipate from the physical values, and reflects a physiological compensation that occurred. The extra sweat a man will produce as his body temperature rises can be evaporated to provide additional cooling if sufficient unimpeded body surface area is available.

-

7

Rest

Rest

.z r

200

Y

y \

aJ

\

-

CJ' 150

\ \

P 0

\

tn

g

\

\

\

4 -.

100

1

x

I\

U

0 m

50

\

0

0 0

X

- 50 I 0

30

90

60

120

150

180

210

Time

(mtn)

Fig. 3.2. Mean body heat storage for eight subjects, at rest and during a 5.6 km hr-' treadmill walk. The sweating copper manikin measurements of I' suggest that the permeability index values are a linear function of the percentage of the surface covered with imMrmeable materials. While the subjects can eliminate all of their resting heat production regardless of raincoat system, the effects of increased impermeable area are clearly evident during the walk. Conditions: air temperature 29.4 "C, wet bulb temperature 22 "C 0 --full length, 1.7 clo (0.26 m 2 K W - I ) ; U-

r: 0

.-.-

3/4 length, 1.6 d o (0.25 m2 K W-'); 1/2 length, 1.5 clo (0.23 rnz K W - ' ) ;

..-..-

114 length, 1.4 clo (0.22 m 2 K W-')

R. F. GOLDMAN

52

The average sweat production did increase as a function of increased impermeable coverage, and in the case of the 1/2 length garment enough of this extra sweat was able to be evaporated to compensate for the increased body area covered by and impermeable layer. The still greater sweat production of men wearing the 3/4 and full !cngth garments could be not evaporated in sufficient quantities to compensate. EFFECT3 OF DIFFERENT MATERIALS OR TREATMENTS

In the study presented in fig. 3.3, fire resistant uniforms made up of either one or two layers of a new “Nomex” synthetic fibre were evaluated in comparsion with a standard cotton “fatigue” and a standard cotton tropical combat uniform. All sets of these four uniform types had been laundered but not starched and, as a substudy, an additional group (8 se’s) of the fatigue uniforms was laundered and then a0 7

Y

al cn

2 0

300

c

vr

c

Q

(Ir

200 1 ,

U 0

0 100

0

I

1

I

1

I

I I ,

I

I

Effects of clothing

53

heavily starched. Results from the copper manikin gave a value of im/Z = 34 W m-* kPa-’ and essentially similar values of insulation for all but the two-layer Nomex uniform. The physiological measurements obtained on subjects during the chamber experiment confirm these physical results. The average heat storage values for subjects wearing the four garments with the same i,/I values ranged between 260 and 290 kJ at the end of the fifty-minute walk, while the corresponding value for the two-layer Nomex garment, which had i,/Z = 31 W rn-’ kPa-’, was 365 kJ. Thus, variation in wicking and wetting characteristics, associated with differences in fibres or finish, which might have produced a difference between results obtained under static laboratory test conditions and those obtained on actual humans in chamber studies, did not; the relative results predicted from the static copper man tests were confirmed by the chamber evaluation.

-

Rest

Walk

200

7

Y

c o,

150

0,

P

2 Ln 4-

100

0

a

r

2 0

50

m

0

* I I

I

-50 30

0

60

90

I 120

I

180

1%

210

Time (min) Fig. 3.4. The physiological effects of shoulder yoke vents: these are more difficult to asscss from the values given in the figure legend, since they are obtained from a stationary, sweating copper manikin. Putting a vent into an impermeable coated fabric raincoat siguificantly increases the wearer’s heat loss while walking; a loose fitting poncho with hood, in theory the worst of the garments because. of the greater area covered, has a very similar physiological effect to a vented impermeable raincoat, because of the flapping and billowing associated with walking in a poncho pumping air. Adding a vent to an already air permeable raincoat (“standard”) produces little or no add itional heat loss. Conditions as for fig. 3.2. coated raincoat, 1.7 clo (0.26 m* K W-’);

0a-.-

A..-. .0 X

poncho, 1.8 clo (0.28 rn2KW-l); coated rainco % with vent, 1.7 clo (0.26

.- . . standard raincoat, 1.7 clo (0.26 I

---

m2

K W-’);

W-’); standard raincoat with vent, 1.7 clo (0.26 m 2 K W-’) 1112 K

54

R. F. GOLDMAN EFFECTS OF DRAPE OR VENTING

The results of another study of raincoats is presented in fig. 3.4; impermeable coated fabric raincoats, both with and without a vent inserted under a flap across the shoulder area, were compared with water repellent but vapour permeable raincoats cut to the same fashion and again both with and without the vent. The standard Army poncho, which is an impermeable loose cape with hood, was also included in the study. The copper man I values were essentially the same for all garments, while the permeabilities showed little or no difference associated with venting, i, was 0.26 for the permeable coats, 0.16 for the impermeable coated fabric coats and 0.11 for the poncho. However, the results of the physiological evaluation showed a significant advantage for the vent in the impermeable coated fabric raincoat, but no advantage for the vent in the permeable coat. In addition, the average heat storage of men wearing the poncho was nearly as low as that of men wearing the vented impermeable garment. Thus, the ability offered by an impermeable garment wi!h a vent, or by a billowing impermeable garment was of significant advantage to subjects walking in such garments; on the other hand, a vent in an already permeable garment seemed to offer little or no additional air exchange. Thus, with respect to factors of fit and drape or cut which provide ventilation features, the static physical test values require careful interpretation. Additional studies, involving flapping the garments during the copper manikin measurements, have been encouraging, but the technique requires additional refinement (HOLLIESand GOLDMAN, 1977). SUMMARY

In summary, the combined measurement of I and i, on heated sweating copper manikins is a valuable tool for predicting a rank order of thermal stress effects for clothing assemblies worn in the cold or heat. Care must be taken if air permeabilities differ widely or if clothing design allows unusual air exchange during subject motion; HOLLIES and GOLDMAN (1977) have recently described modifications to the static manikin measurement to allow for air motion and for subject generated air motion. This allows precise prediction of the rectal temperature (GIVONIand GOLDMAN, 1972) and heart rate (GIVONIand GOLDMAN, 1973a), responses of a man as a function of his clothing, his heat production (GIVONI and GOLDMAN, 1971), his state of acclimatization (GIVONIand GOLDMAN, 1973b) and the ambient environment. Thus assessment of the insulation and evaporative conductance of a clothing system can provide an accurate estimate of the thermal advantages of one garment or fabric relative to another. There are effects of cut, drape and fit which must receive special consideration (HOLLIESand GOLDMAN,1977). The techniques presented are valuabIe tools in clothing design and such evaluations are desirable in studies of the man-clothing-job-environment system for ordinary clothing, as well as for advanced clothing systcins with artificial environmental conditioning. The advantages of carrying out in the laboratory and climatic chamber the detailed evaluations of the thermal protection, and problems, associated with protective clothing systems should be obvious; precision measurement allows assessment of small differences, and prediction is possible for any combination of clothing,

Effects of clothitig

55

work level, wind and temperature. Similar precise techniques are being developed for measurement of the protection afforded to the extremities (hands, feet, face) by gloves, boots, face masks, hoods, etc. Thus, field evaluations of the thermal protective aspects of Arctic gear should never be carried out until the ‘%homework”in the laboratory has been completed, and then only as a validation of the laboratory findings under field conditions. On the other hand, the laboratory cannot provide the wear testing, the blowing snow and the realism of the field environment. Personnel involved in planning, carrying out or evaluating the results of such field evaluations should insist on having the results of the laboratory and/or climatic chamber evaluations of the specific items to be tested, before planning the details of the field evaluation. REFERENCES

FONSECA G. F. (1967), Moisture transjkr through perforated impermeable foam insulations, Textile Res. J. 37, 1072-1078. FONSECA G. F. and BRECKENRIDGE J. R. (1965), Windpenetration through fabric systems, Textile R a . J. 35, 95-103. A. C., and BAZETTH. C . (1941), A practical system of units for the description GAGCEA. P., BURTON of lieat excharge of man with his environment, Science 94,428430. GIVONIB. and GOLDMAN R. F. (1971), Predicting metabolic energy cost, J . Appl. Physiol. 30,429433. GIVONIB. and GOLDMAN R. F. (1972), Predicting rectal temperature response to work, environment and clothing, J. Appl. Physiol. 32, 812-822. GIVONI B. and GOLDMAN R. F. (1973a), Predicting heart rate response to work, environment and clothing, J. Appl. Physiol. 34, 201-204. GIVONI B. and GOLDMAN R. F. (1973 b), Predicting efects of heat acclimatization on heart rate and rectal temperature, J. Appl. Physiol. 35, 875-879. GOLDMAN R. F., GREEN E., and IAMPIETROP. F. (1965), Tolerance of hot wet environments by resting men, J. Appl. Physiol. 20, 271-277. GOLDMAN R.F. (1969), Physiological costs ofbody armor, Mil. Med. 134,204-209. GOLDMAN R. F. (1964), The Arctic soldier: possible research solutions for his protection, Proc. 15th Alaskan Science Conf. 15, 114-135. HOLLIES N. R. S. and GOLDMAN R.F. (1977), Clothing Comfort: Interaction of Thermal, Ventilation, Construction and Assessment Factors, Ann Arbor Science, Michigan. HUGHES A. L. and GOLDMAN R. F. (1970), Energy cost of “hard work”, J . Appl. Physiol. 29,570-572. IAMPIETRO P. F. and GOLDMAN R. F. (1965), Tolerance of men working in hot, hirmid environments, J. Appl. Physiol. 20, 73-76 JOY R. J . T. and GOLDMAN R. F. (1968), A method of relating physiology and military performance, Mil. Med. 33, 458-470. PANDOLF K. B., HAISMANM. F., and GOLDMAN R. F. (1976), Metabolicenergy expenditure and terrain coejficientsfor walking on snow, Ergonomics 19,683-690. WOODCOCK A. H . (1962), Moisture transfer in textile system, Textile Res. J. 32,628-723.

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Chapter 4

HUMAN SE IN TEMPERATURE AP D CO TVECTIT E HEAT LOSS R. P. CLARK Laboratory for Aerobiology, Medical Research Council, Clinical Research Centre, Hnrrow. Middlescx, HA1 3UJ .Great Britain.

CONTENTS

Introduction Skin temperature measurement Skin temperature distribution at different environmental temperatures The effect of solar radiation on skin temperature Exercise and temperature distribution Temperature distribution over infants nursed in incubators The evaluation of mean skin temperature Convective heat loss from the body Natural convection Heat transfer to the boundary-layer The effect of posture on convective heat loss Forced convection The 'pendulum effect' Heat loss in highly turbulent flows Heat loss in air-conditioned buildings Conclusions

1NTRODUCI'ION

Much has been written about the thermal interaction between man and the environment. Classic works by authors such as WNSLOWand HEBRINGTON (1949) and BURTONand EDHOLM(1955) have long ago described the basic physical and physiological principles which have formed the basis of much further research. Recently new techniques have become available which enable investigations of the human micro-environment to be made in fresh ways. Some of these techniques and their results are discussed in this paper.

58

R. P. CLARK SKIN TEMPERATURE MEASUREMENT

In any study of man's thermal interaction with the surroundings, it is first necessary to measure the physical variables that control heat exchange with the environment. Temperature is one of the most important of these variables, because it is the difference between the skin surface temperature and that of the surroundings that enables the body surface to exchange heat with the environment. In most environments the skin is warmer than the surroundings and thus the heat transfer is away from the body to the ambient air. In some situations, for instance in hot climates, this may be reversed, and the body may gain heat from the environment where the air temperature is greater than the skin temperature. In these circumstances the body will still be able to lose heat by sweating and can achieve thermal balance, but at a higher body temperature (and therefore at a higher skin temperature) than in environments which are cooler than the skin surface. The classical idea of skin surface temperature distribution comes from the concept of a central hot core from which heat emanates to the surrounding tissues. This concept leads to a skin surface distribution where the temperature decreases as the distance from the 'core' increases. As we shall see in the following sections, this gives an accurate description only for a person at rest in moderate and warm environments. In warmer conditions and during exercise, where there are local areas of heat production, or in situations where there is considerable sweating, this classical pattern is greatly modified. Skin temperatures have generally been measured with thermocouple or thermistor surface contact probes. Temperatures read from a number of probes indicate the distribution over an area. However, even if a large number of measurements are taken it is difficult to obtain a detailed pattern of skin temperature distribution. In contrast, the relatively new technique of infra-red thermography enables detailed mapping of temperature distribution. The thermal radiation from the body surface, which is determined by the skin surface temperature, is received by a camera containing an infra-red detector. The signal from this detector is processed electronically to present a television-like picture, where various tones of grey represent particular temperatures. A refinement is to present the thermogram as a coloured display, where specific colours are assigned to particular temperatures. The technique enables temperetures over the whole body to be visualized without contact with the surface. Thus a further advantage is that a subject is not restricted in his activities. Infra-red thermography has recently been used in a number of investigations described in the following sections. SKIN TEMPERATURE DISTRIBUTION AT DIFFERENT ENVIRONMENTAL TEMPERATURES

Figure 4.1 is the thermogram of a young male subject (mean skinfold thickness of 4.2 mm) and shows the steady state skin temperatures at an environmental temperature of 11 "C with minimal air movement. One immediate and obvious feature of this thermogram is the large range of temperature between different regions.

8

Fig. 4.1. The steady state temperature distribution over a subject in a climatic chamber at a dry bulb temperature of 11 "C. Black and white reproduction of infra-red colour thermograms. Adjacent grey arms differ in teinpcratrire by 1 "C

60

R. P. CLARK

The temperature distribution of the skin surface may be related to that of the whole body by regarding the body as having a hot central 'core' away from which temperatures diminish. If the central 'core' is the abdominal cavity, the thorax, the brain, and the spinal cord. The skin over these areas will be warm because of its proximity to the 'core'. For example, the skin of the axilla is normally 1-2 cm from the 'core', whereas that of the buttocks may be as much as 6-7 cm away. At cool and moderate environmental temperatures the infra-red thermogram largely confirms the concept of a warm 'core' and cool periphery. Additional features reflect either the metabolism or the conductivity of the structures underlying the skin surface. For instance, there is a warm area under the axilla and another on the skin over the spine and shoulders. Areas of skin over bony tissue, for instance at the elbows and the knees, and over fat areas, such as the buttocks, are cooler. Although skin temperature is affected by environmental temperature, thermograms taken at 11 "C and 20 "C show many similar features. The main difference is that in the warmer conditions the underlying body structures are less evident, probably due to the greater thermal gradient through the skin in cooler environments and higher rates of local heat loss with less lateral diffusion of heat. At environmental temperatures above 27 "C the features due to the underlying body structures become less distinct. Figure 4.2 shows the skin temperature distribution at an air temperature of 31 "Cout of doors, in shade, with air movement of about 1 m s-I. Large areas of the skin surface are at the same temperature and the features such as the warm spine and the cold buttocks are no longer visible. At these higher air temperatures the gradient between the skin and the surroundings is small and there is consequently little convective cooling. Evaporative heat loss due to sweating is, however, considerableand these changesin the modes of heat loss combine to produce a more uniform temperature over the body. Whereas the skin temperature range at environmental temperatures between 10" and 20 "C is 10-12 "C at 31 "C this range is reduced to about 4-5 "C. THE EFFECT OF SOLAR RADIATION O N SKIN TEMPERATURE

The effect of solar radiation on skin temperatures has been investigated thermographically. The subject was exposed to sunlight at a dry bulb temperature of 31 "C.Areas of the body receiving direct radiation increased in temperature, surfaces such as the hair and swimming trunks reaching 48-50 "C. However skin temperatures increased by 5-6 "C only, to 38-40 "C.These results show differences between 'passive' surfaces such as the hair and clothing and a surface such as skin, which can thermoregulate actively by changes in blood supply and convective and evaporative heat losses. Temperatures over shaded areas actually decreased slightly during exposure to the sun, because of increased sweating. EXERCISE A N D TEMPERATURE DISTRIBUTION

Skin temperature distributions can be affected markedly by other factors. Exercise, in particular, (an greatly modify them. A recent study using infra-red thermography has demonstrated the temperature changes that may occur during running (CLARK,

Skin temperature and convection

61

Fig. 4.2. Steady state temperatures over a subject out of doors in shade at a dry bulb temperature of 31 "C. Air velocity about 1 m s-l. Black and white reproduction of infra-red colour thermograms. Adjacent grey areas differ in temperature by 1 "C

MULLANand PUGH, 1977). The temperature distribution over an Olympic class athlete was observed with the runner stationary, running on a treadmill at 4.5 m s-' in 'still air' and on a treadmill at 4.5 m s-l in the presence of wind at an equal velocity, to simulate outdoor running. These experiments were conducted at an air temperature of 11 "C in a climatic chamber. They were subsequently repeated out of doors on a running track, at 21 "C, when the Olympic class athlete was compared with a good club standard athlete during a one hour run. Measurements showed that the temperature distribution was changed completely during the exercise, reaching steady values after about twenty minutes. The changes were produced by changes in skin blood supply, sweat rate and evaporative cooling. Changes also occur because of convective cooling due to the motion of the limbs through the air, and in the metabolism in underlying structures, e.g. the increased

62

R. P. CLARK

heat output of the active muscles. This resulted in raised temperatures over the muscles, the arms and legs and cooling of the areas not overlying structures of high heat production. Measurements with the runner on a treadmill, both in the presence of wind and in 'still air' enabled an assessment of which temperature changes were caused by changes in blood flow and metabolism, and which were due to environmental cooling. In 'still air' the skin over the abdomen for instance, cooled as the exercise progressed while the temperatures over the active muscles of the thighs increased. Initially the hands and arms were cool; but later in the run there was a large increase in skin blood flow, just before the onset of sweating, which caused the hands and arms to rise by several degrees and become visible on the thermogram, as shown in fig. 4.3. When this experiment was repeated in the presence of wind, the temperature changes were larger and more rapid. The whole body was cooled more but the patterns of increased temperature due to active muscle were still dominant. When the Olympic class athlete was compared with the club standard man out of doors on a running track, the initial temperature distribution and its change during exercise was similar. However the different abilities of the two athletes to thermoregulate were strikingly demonstrated when the club standard man stopped sweating and had to retire with anhydrotic heat exhaustion (PUGH,1972). The thermogram showed that the cessation of sweating was followed by an immediate rise in skin temperature of more than 10 "C. This observation substantiated previous findings that cooling by increased airflow alone is not sufficient to account for the observed fall in skin temperatures during running. There must be sweating as well. Perhaps the most significant finding in this study of athletes was the re-distribution of skin temperature during exercise when the highest temperatures were found to coincide with the surfaces over active muscles. This elevation of skin temperature is evidence of direct heat transfer from the muscles to the skin surface, and is obvious despite other fictors such as local variations in air flow or sweating. Thermography is also sufficiently sensitive to show skin temperature changes associated with transient thermal stimuli. For example fig. 4.4 shows a series of thermograms which display the skin temperature distributions before and after taking a hot drink (CLARKet al., 1977b). TEMPERATURE DISTRIBUTIONS OVER INFANTS NURSED IN INCUBATORS

Measurements of the temperature distributions over infants nursed in a conventional incubator have been made recently (CLARKet al., 1978) at temperatures between 28-33 "C. The results showed a temperature distribution reminiscent of that found over the adult in moderate and warm environments (fig. 4.5); the 'hot core' with temperatures diminishing towards the extremities was clearly demonstrated. Very few features reflected the metabolism or conductance of underlying structures, except at the lower end of the temperature range where some structures were just beginning to appear. Of particular interest is the temperature distribution over the head, which in the infant accounts for some 20% of the total body area. The metabolism in the brain

Fig. 4.3. The temperature distribution over a subject on a treadmill in a climatic chamber at 11 "C.a - before running, b - five minutes after starting to run and c - after twenty minutes running and just before the onset of visible sweating. Black and white reproduction of infra-red colour thermograms. Adjacent grey areas differ in temperature by 1 "C

Skin temperature and convection

65

Fig. 4.5. Steady state temperature distribution over a baby nursed in an incubator. Air temperature 32 "C. Black and white reproduction of infra-red colour thennogram. Adjacent grey areas differ in temperature by 0.6"C

is also a large proportion of the total heat production in the neonate. Temperatures over the head were similar to those found over the warm central part of the body: in this sense the head may be regarded as part of the 'hot core' of the body. THE EVALUATION OF MEAN SKIN TEMPERATURE

A comparison was made of the mean skin temperatures obtained by analysis of infra-red thermograms and those obtained from thermocouple probe readings for the athletes and the neonates. The mean skin temperatures for the whole body agreed to uiithin 1.5 "C However, for particular body regions in the athletes, the mean values obtained by the two methods differed by up to 4 "C.Where large variations of temperature exist over small distances, the positions of probes are critical for their reading to be representative of the area considered. For instance, during exercise the skin temperature of the knee was more than 10 "C lower t?an that over the calf muscle, the distance between these areas was about 10 cm only. For the whole body a number of probe measurements (11-13 here) averaged out such positional inequalities between the two methods. For calculations of heat loss from the body it is essential to have a measure of mean surface temperature for each area. The complex skin temperature distributions shown therefore present a difficulty for models designed to simulate heat transfer from the body surface. Much simpler distributions are found in inanimate objects, which have led to the mathematical forms used to model heat transfer from the body. 5

- Bioengineering

66

R. P. CLARK CONVECTIVE HEAT LOSS FROM THE BODY

The temperature difference between the skin and the surroundings enables the body to exchange heat by conduction, convection, evaporation and radiation, and to achieve thermal equilibrium. Convective heat transfer varies due to the environment and activity and this is described in the following sections. NATURAL CONVECTION

For a subject with a mean skin temperature lower than air temperature, the air adjacent to the skin surface will become heated by conduction and will rise due to buoyancy. This results in an envelope of air moving upwards which surrounds the body (fig. 4.6). This natural convection boundary-layer flow forms an imporiant part of the humm micro-environment. It is the mechanism by which heat is lost from the body by convection, and is also important in the transport of desquamated skin particles which often carry micro-organisms and produce an airborne infection hazard. This air flow has been visualised and filmed using a schlieren optical system (CLARK and Cox, 1974; LEWISet al.. 1969). The system essentially consists of a parallel beam of light focussed to a particular point. If any of the light rays in the parallel beam are bent by passing through air with a different refractive index, the focus of the beam is displaced from its original position. By arrang'ng for the undeviated beam to be focussed through a coloured filter and for the displaced beam to be focussed through a different colour it is possible to visualise heated air streams as one colour against a background of another. Figure 4.7 shows a diagram of the schlieren optical system used to visualise the boundary layer flow over the whole body. These studies revealed a convective upflow of air which is thin and slow moving at the ankles and lower legs, but which

Fig. 4.6. A diagram of the natural convective air streams over a stand-

ing subject

quickly increases in velocity and thickness and is vigorous over higher parts of the body. At face height, for a standing naked subject, the maximum air velocity is between 0.4 and 0.5 m s-' .The corresponding boundary-layer thickness is 0.15-0.20 m. The plume of hot air above the head extends for at least 1.5 m before dispersing into the general room air, The total volume of air entrained is around 600 litres per minute at an air temperature of 25°C.

Skin temperature arid convection 'B'

'A

L i ght

67

mrabollc mirror

source

2nd Mirror

. Y

, 1 '

outer strips

Fig. 4.7. Diagram of the schlieren optical system

The natural convective boundary-layer flow may be characterised as being either laminar or turbulent. The parameter that describes the state of the flow is the Grashof number (Gr). This non-dimensional group is the ratio of viscous forces to buoyancy forces in the flow and is given by

where g is the acceleration due to gravity, v is the kinematic viscosity of the air, T, and T,are the mean air and skin temperatures, respectively, in degrees Kelvin, and h is the vertical height on the body. Figure 4.8 shows the relationship between the Grashof number and the vertical height on the human body, indicating regions of laminar, transitional and turbulent flow. When the Grashof number is less than lo9 the flow is laminar; when it exceeds 1Olothe flow is fully turbulent. For a standing naked subject with an 8-10 "Ctemperature difference between his skin and the air, the flow is laminar up to a height of 1 m, and becomes fully turbulent at 1.5 m; the region between the navel and the head is subject to transitional flow. Clothing modifies this pattern by reducing the external temperature gradient, but this is not as important in defining the flow as the vertical height, which appears as h3 in the equation. However, for a clothed man, when the temperature difference between the clothing and the air is small, it is possible to have a laminar boundary layer over the whole body. The velocity and temperature profiles have been evaluated for convective boundary-layers, around cylinders and flat plates. Measurements have been made in the flows around the human body, using thermocouple probes and constant temperature hot wire anemometers (CLARK,1973), but the complex shape of the body makes analysis difficult. Typical temperature and velocity profiles found in the convective

R. P. CLARK

65

r

Turbulent f l o w

Ir;

I

j;

Grashof number

Fig. 4.8. The variation of Grashof number with vertical height over the body surface, for a skin temperature of 33 "C and an ambient temperature of 25 O C

\U15 11

0

01

03

05

07

13

15

09

Dlstance f r o m heated surface ( c m )

Fig. 4.9. Typical velocity and temperature profiles in the natural convective boundary-layer flow

over a standing man

flow are seen in fig. 4.9. The velocity must be zero at the skin surface, increasing to reach a maximum value at about one third of the boundary-layer thickness. Subsequently, the velocity falls to ambient air velocity at the outside of the layer. The temperature profile is a smooth curve from the skin temperature at the body surface to the temperature of the surrounding air at the outer margin of the boundary layer. HEAT TRANSFER TO THE BOUNDARY-LAYER

Heat transfer from the body surface to the surroundings equals k dT/dy, (where k is the thermal conductivity of the air, and dT/dy is the slope of the temperature profile at the skin surface). The convective heat loss is therefore directly proportional

Skin temperature and convection

69

to the slope of the temperature gradient at the body surface. Thus, the thickness of the boundary-layer flow at any point will determine the local heat transfer from the body surface. Where the boundary-layer is thick, e.g. over the face and the upper parts of the body, heat transfer rates will be low. In contrast, over the ankle and lower legs the boundary-layer is thin and the rate of heat transfer will be high. The thick flow over the upper parts of the body such as the face and head afford a degree of thermal protection to the body by reducing the heat loss. THE EFFECT OF POSTURE ON CONVECTIVE HEAT LOSS

From the above description of the relationship between convective heat loss and boundary-layer thickness, it can easily be appreciated that posture will have an effect on convective heat loss because of the dependence of the convective flow pattern on vertical height. For example, the boundary-layer flow over the head and face of a standing man has developed over the full height of the body; the flow is thick the temperature gradient is shallow and consequently local convective heat loss is low. In contrast, when the subject is lying down the flow over the head and face is quite different, as illustrated in fig. 4.10. In this case the flow over the face

Fig. 4.10. The natural convective flow patterns over the head, for two postures

5tcnt!nq

and head has developed over the head only. The maximum air velocity over the face in a supine position is about 0.05 m s-' only, compared to 0.5 m s-' when standing. The insulating properties of the boundary-layer flow are effectively lost lying down. Recent experiments to measure convective heat output in these two postures have shown that the heat loss from the head in the lying position is about 30% higher than in the standing posture (CLARKand TOY, 1975a). These experiments used small surface calorimeters which measured the local heat loss from several areas of the face directly (CLARKet al., 1972). The relationship between convective boundary-layer flow and heat loss was clear; when the boundary-layer was thin higher heat transfer rates were recorded than from the areas where the boundary layer was thicker.

70

R. P. CLARK

When sitting, the boundary-layer flow is more complicated than in either the lying or standing positions. The flow over the horizontal knees and thighs interacts with the flow developed over the upper part-of the body so that the boundary-layer flow and heat loss over the head and face is little different from that in the standing posture. FORCED CONVECTION

When the body is exposed to a wind or is moving through the air, the natural convective boundary-layer flow is displaced and the body loses heat by forced convection. The variables that influence forced convection are the mean air velocity and the nature of the flow (i.e. whether it is laminar or turbulent), and the flow direction. The degree of turbulence and its scale can have a profound effect upon the heat loss. Many studies of heat loss from man in forced convection have been carried out, both indoors in climatic chambers and out of doors. The results of such studies are generally expressed in terms of the relationship between the heat transfer coefficient, h, (W m” K-’), and the mean air velocity to which the subject is exposed. However, most measurements have been made with unidirectional airflows. KERSLAKE (1972) has reviewed the results of such experiments, and gives the expression h, = = 8 . 3 ) 4 , where v is the air velocity in m s-I. Measurements of the heat loss distribution round the human head have demonstrated the dependence of forced convection on air flow direction in a unidirectional air stream (CLARKand TOY, 1975b). In practice the body is rarely subjected to truly linear forced convective flows; out of doors the wind is invariably turbulent. During movement the trunk and head only, of a person walking or running, perform a motion approaching straight line translation through the air. The moving limbs perform swinging motions ; the thighs and upper arms behave as pendulums and the lower legs and forearms have whiplash movements. These swinging movements modify the boundary-layer flow. THE ‘PENDULUM EFFECT

Studies using the schlieren optical system have shown the air-flow patterns around moving limbs (CLARKet al., 1974); complementary measurements of the local convective heat loss were also made. Visualization of the air flows around the legs of a runner have shown that the ‘pendulum effect’ produces completely different flow patterns to those found in linear flows. The flow around a swinging thigh forms a bow wave and a trailing wake and these are alternately established and reversed by each change in direction of the swinging leg. The flows around the lower legs and forearms, which perform a whiplash movement, are similar in nature, although more complex. Classical fluid dynamics and heat transfer theories are inappropriate for these conditions, as the movements of the body during walking and running are far more complicated than those associated with man-made structures on which the theory is based. Translation of the body through the air produces additional complications; a unidirectional airflow is superimposed on the alternating flows produced by the

Skin temperature and convection

71

'pendulum effect'. Schlieren visualisation shows similar flows around swinging and translating heated cylinders, used to simulate the action of the limbs during movement. Measurements of local convective heat loss around the thigh of a runner on a treadmill were made in a climatic chamber. The results show that, both in still air and in the presence of wind, the distribution of convective heat loss around the circumference of the thigh is different from that in a unidirectional airflow. Graphical integration was used to obtain a value for the overall heat transfer coefficient around the thigh. The coefficient was about twice as high as expected in a unidirectional wind equal to the mean velocity of the oscillating leg. A linear wind, representing the effect of translation of the body, further increased the convective heat loss. On the basis of these results it is estimated, that the heat loss from the whole body (assuming the trunk, head and face to have uniform translation) will be about twice that expected by considering the whole body to be in a uniform wind and applying the formula h, = 8.3 h. HEAT LOSS IN HIGHLY TURBULENT FLOWS

Heat losses may also be amplified when a subject is stationary in the presence of a turbulent or 'buffeting' wind. In this case, if the scale of turbulence is large in relation to the size of the man, the air will be continually changing direction. Such conditions have recently been studied in the harsh environment found beneath a hovering helicopter(CLAR(Ket al., 1976a; CLARKet al., 1976b; CLARKet al., 1977a). This work formed part of the evaluation of clothing for personnel who work on the landing decks of ships a t sea in the arctic. Measurements made beneath hovering helicopters confirm that the highly turbulent nature of the flow produced, for a given mean wind speed, much higher cooling coefficients than expected for the mean velocity. For instance, coefficients of up to 80 W m-* K-l were found at mean wind speeds of 20 m s-' ;the convective cooling predicted by the 'traditional' formula at this windspeed is about 30 W m-' K-' . One consequence of such high rates of heat loss is that people exposed to air movements of this kind at low temperatures require clothing with better thermal insulation than has hitherto been thought necessary. A particularly vulnerable area is the face, which is often left unprotected. In such environments subjects wearing highly insulating clothing may lose up to 40 % of their total body heat loss from the exposed face. The effects described in the preceding section have been discussed by CLARK(1976), and are summarised in fig. 4.11. HEAT LOSS IN AIR-CONDITIONED BUILDMGS

Thermal comfort in the environment where people live and work has received 1977). One problem much attention in recent years (HUMPHREYS, 1975; FANGER, has been to investigate comfort during exposure to air streams from different directions and at different levels of turbulence (OSTERGAARD et al., 1974). Such air streams will modify the convective boundary-layer flow around the body, and these modi-

R. P. CLARK

72

fications may be sensed by the bodyss the effeccomfort or discomfort. Recently studies have been carried out to asesses the effects of unidirectional downflowing air streams on patients and staff in a hospital ward (CLARKand MULLAN,1977). Fwc&

ccmectiw situatlons

Subject in a

Hwt loss in the highly turbu1eP.t flow)

inifa-m

b?fwoth a MicC$W h :%D L?/m-2K-i ct .%.in3s:Wds

SubJect runrmg wind h,- 303 \Nm-2K-’ h , ~ 8 3 ~ ‘ T W r n - ~ K - ’ at L.5 m s - ’

cf

and 9.w

ms-l

Fig. 4.1 1. Forced convective cooling for three kinds of air movement, h, denotes the convective heat loss coefficients

This work was carried out at Mount Vernon Hospital, Northwood, England during a three year clinical trial to assess the use of special air systems in the treatment of major burn injuries. This trial involved the construction of a new burns unit equipped with sophisticated air conditioning systems. The unit was designed to provide an acceptable thermal environment both for the badly injured patients and the staff who attended them. At the same time the air conditioning was required to produce bacteriologically clean conditions to reduce the chance of airborne cross infection, which is a major problem in treating large burns. The unit had four special care rooms where patients were nursed during the initial period of their treatment. These rooms had canopies suspended from the ceiling which produced a linear downflow of ultra-clean air beneath which the patients were nursed. It was possible to study convective cooling at two different velocities of the downflowing air (either 0.65 m s-’ or 0.30 m s-I). The results were compared to those obtained in the same room when the air conditioning was turned off. In the experiments a heated model was used to determine overall convective cooling coefficients. This model was an elliptical cylinder with a total surface area of 1.2 mz and thus represented the average bodysurface area. It was fitted with electrical heaters, the power was supplied from a control console where the voltage and current were measured. Thermocouple thermometers were used to measure the temperatures of the model surface and of the surrounding air. Experiments were carried out to determine convective cooling coefficients with the model freely suspended in air both vertically and horizontally. In addition, the tests were repeated with the cylinder resting horizontally on a hospital bed. The coefficients were determined with the cylinder completely uncovered and also when it was covered with a sheet; this represented the degree of bedding that was used within the burns unit. The relationship between posture and the convective boundary-layer flow has been discussed carlier, where it was shown that the convective flow over a standing

Skin temperature and convection

73

subject was quite different from that found oter a prone subject. The modification to the boundary-layer flow by the linear downflowing air streams is illustrated diagrammatically in fig. 4.12. Table 4.1 shows the relationship between cooling coefficients, posture and the speed of the linear downflowing air. For the vertical cylinder the downflowing air streams were too slow to produce forced convection.

n n n

Fig. 4.12. Diagram of the modification of the convective upflow by downflow in different postures

T a b l e 4.1 Convective cooling coeficients for a cylindrical model horizontal and vertical in 'still air'and when exposed to linear downflowing airstreams at two different velocities Convective cooling coefficient h, (W m-z K-') Downflow Downflow 'still air' 0.30 m s - I 0.65 m s-' Vertical cylinder Horizontal cylinder

6.7 6.6

5.9 5.7

4.5 10.8

However, the convective cooling coefficient decreased as the velocity of the downflowing air increased; the downflow competed with the vigorous convective upflow generated over the whole height of the cylinder. The interaction of the two air streams slowed down and thickened the boundary-layer flow, decreasing the temperature gradients; smaller gradients lowered convective heat loss. The effects for the horizontal cylinder were different. When the downflow w a s 0.30 m s-l the cooling coefficient was lower than in 'still' air. Conditions of forced convection were produced when the downflowing air speed was increased to 0.65 m s-l, and this was reflected in a large increase in the convective cooling coefficient.

P. R. CLARK

74

The convective heat loss coefficients for the heated cylinder, freely suspended in air, on a mattress uncovered, and covered by a sheet are shown in fig. 4.13. The arrows in the top part of the figure indicate the direction and thickness of the convective air-streams generated around the cylinder. The lower part of the diagram shows the convective heat loss 'envelope' where the radial distance from the cylinder circumference to the edge of the dotted area is proportional to ,the local convective heat loss from the cylinder surface.

Cylinder treely suspended

Cylinder on a mattress

Cylinder on a mottress and covered with a sheet

Mat tress h,= 1 2 8 Wrn-'K-'

h, = 9 L W m-'z K -

h,= 6 1 W rn'2K-'

Fig. 4.13. Diagrams of air flows and convective cooling coefficient 'envelopes' for a horizontal cylinder in three configurations, h, denotes the overall heat loss coefficient

The effect of the mattress is to eliminate part of the convective envelope and the sheet further modifies part of the envelope, indicated by the larger dots. The overall cooling coefficients determined are shown beneath eacb diagram, but, because of the difficulty in separating heat loss due to convection, radiation and conduction, the coefficients are presented here as total heat loss coefficients (he, Wm-2 K-'). Table 4.2 summarizes the coefficients measured in these experiments. The results showed that if the air speed was too high, the patient, who was horizontal, was at a thermal disadvantage compared with attendant nursing staff who were upright; this was an important factor in determining the correct air temperature for the treatment of the patients. It was shown that comfort for patients and staff could be prejudiced by high ventilation rates, even though they were considered desirable from a microbiological point of view. Nevertheless, when the air flows in the burns unit were permanently reduced to 0.30 m s-' , it was found that over a period of many months, the bacterial cleanliness was substantially the same as previously at the higher air flow rate of 0.65 m s-'. Experience in this unit and in other air conditioned hospital areas suggests that air velocities greater than 0.30 m s-l are not necessary from either a thermal comfort or microbiological standpoint;

Skin temperature and convection

75 Table 4.2

Overall cooling coefficients for a horizontal cylindrical model freely suspended and when placed on a bed in ’still air’, exposed to linear downflows at two different velocities Overall cooling coefficient h, (W rn-I K-I) Downflow Downflow ‘still air’ 0.30 m s-l 0.65 m s-I ~~

Horizontal cylinder freely suspended in air Horizontal cylinder on a bed, uncovered Horizontal cylinder on a bed, covered with a sheet

~~

12.8

11.0

17.4

9.4

13.3

12.5

6.1

9.1

5.8

higher air speeds produce nursing management problems and patients may be exposed to excessive heat loss, especially in areas where they may be nursed for long periods. CONCLUSIONS

Thermography produces a very detailed pattern of skin temperature, which is seen to be much more complex than has been revealed by thermocouple and other techniques. However, it is perhaps comforting to those who have used thermocouple techniques that the mean skin temperatures measured by the two methods agree reasonably well. Nevertheless, regional skin temperatures measured by thermocouples and thermography may be very different. The pattern of temperature change in different activities or in different environments, as shown by thermography, would also be very difficult to predict or demonstrate without this technique. This is particularly true in studies of the changing temperature distribution during exercise, where rapid changes occur over the whole body due to the effects of environmental cooling, extra heat production in the muscles and changed skin blood flow. The results obtained by thermographic and schlieren methods have modified a number of ideas on temperature distribution and convective heat loss. The complex nature of skin temperature distribution, and its variation with different environments and with exercise, can be demonstrated over the whole body with a detail which would be difficult to achieve with probe techniques. The description of the convective boundary-layer flow given by visualization of the moving air streams presents information which is largely different to that previously found in physiological textbooks. In the past great emphasis has been placed on the study of man in extremes of heat or cold. In contrast many of the current problems in environmental physiology are concerned with more normal environments, where the body’s response is often more difficult to measure. .The techniques described here are sensitive enough to provide visual demonstration of many of the thermal effects to which the body responds, and which otherwise are difficult to describe adequately.

76

R. P. CLARK REFERENCES

BURTON A. C. and EDHOLM 0. G. (1955), Man in a Cold Environment, Edward Arnold, London. CLARK R. P. (1976), Convective heat loss from the human body, Eng. Med. 5, 67-68. CLARK R. P. (1977). Environmental physiology and thermography, Proceedings of the Society of Photo-Optical Instrumentation Engineers, Vol. 110. CLARKR. P. (1973), The roIe of the human micro-environment in heat transfer andparticle transporl, PhD thesis, The City University, London. CLARKR. P. and Cox R. N. (1974). An applicationof aeronautical techniques to physiology, 1 - me human micro-environment and convective heat transfer, Med. Biol. Eng. 12, 270-274. CLARKR. P., Cox R. N., and TOYN. (1972). A surface plate calorimeter for measuring local heat transfer in fiee and forced convection within the human micro-environment,J. Physiol. 223,10-12. CLARK R. P., CROSSK. W., GOFFM. R., MULLAN B. J. STOTHERS J. K. and WARNER R. M. (1978), Neonatal whole body thermography, J . Physiol. 280, 2P-3P. B. J. (1977a). Heat loss studies beneath hovering helicopters, CLARKR. P., GOFFM. R., and MULLAN J. Physiol. 267, 6P-8P. B. J. (1977b), Skin temperaturesduringsunbathing and some CLARK R. P., GOFFM. R., and MULLAN observations on the effect of hot arid cold drinks on these temperatures, J. Physiol. 267, 8P-9P. R. P. and MULLAN B. J., (1977), Convectivebody cooling in air conditioned buildings, J. Physiol. CLARK 267, 9P-llP. B. J., and GOFFM. R., (1976a), A study using infra-red thermography of CLARKR. P., MULLAN cIothing assemblies for use by personnel working beneath operating helicopters, Royal Naval Personnel Committee Report ES 4/76. CLARK R. P., MULLAN B. J., and GOFFM. R. (1976b). Air velocity and convective cooling coeficient measurements beneath a Sea King helicopter, Royal Naval Personnel Research Committee Report ES 1/76. CLARK R. P., MULLAN B. J., and PuGH L. G. C. E. (1977), Skin temperatures during running - a study using infra-red colour thermgraphy, J. Physiol. 267, 53-62. B. J., PUGHL. G. C. E., and TOYN. (1974), Heat Iosses from the moving limbs CLARKR. P., MULLAN in running: the ‘pendulum’ effect, J. Physiol. 240, 8P-9P. CLARK R. P. and TOYN. (1975b), Forced convectionaround the human head, J . Physiol. 244,295-302. CLARKR. P. and TOYN. (1975a), Natural convectionaroundthe human head, J . Physiol. 244,283-293. FANGER P. 0. (1977), Thermal comfort in indoor environments, F:]Thermal Analysis - Human Comjort- ZndoorEnvironments,SymposiumProceedings, Nat. Bur. Stand. Specialpublicat ion 491, and J. E. HILL. Washington, eds.: B. W. MANGUM M. A. (1975), Field studies of thermal comfort compared and applied, Proceedings of the HUMPHREYS Symposium on Physiological Requirements of the Microclimate in Industry, Building Research Establishment England, Current papers, CB 76/75. D. McK. (1972), The Stress of Hot Environments, Cambridge University Press. KERSLAKE LEWISH. E., MULLAN B. J., FOSTER A. R., Cox R. N., andCLARK R. P. (1969), Aerodynamics of the human micro-environment, Lancet (i), 1273-1277. G. W. and ROSENBAUM J. C. (1963), Surface temperature measurement with thermocouples, MOLNAR [In :] Temperature, Its Measurement and Control in Science and Industry, Vol. 3, Part 3, Biology Chapman and Hall, London. and Medicine, ed.: J. D. HARDY, J., FANGER P. O., OLESENS..and MADSENTh. L. (1974). The efecr on man’s comforr OSTERGAARD of a uniform airjlow from diferent directions, ASHRAE Trans. 80, 142-157. PUGHG. (1972), The gooseflesh syndrome - acute anhydrotic heat exhaustion in long distance runners, Br. J. Physical Educ. 3, 50-56. L. P. (1949), Temperature and Human Lve, Princeton University WINSLOW C. E. A. and HERRINGTON Press.

.

11. MODELS AND INDICES OF HEAT EXCHANGE

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Chapter 5

RATIONAL TEMPERATURE INDICES OF THERMAL COMFORT A. PHAROGAGGE John B. Pierce Foundation Laboratory end Department of Epidemiology and:Public Health, Yale University. New Haven Connecticut 06519, U.S.A.

CONTENTS Introduction Thermal comfort Thermal indices Operative Temperature The role of clothing in sensible heat exchange Temperature indices of insensible heat exchange Humid Operative Temperature The New Effective Temperature (ETC) Standard indices Standard Operative Temperature Standard Operative Vapour Pressure Development of a psychrometric chart for estimating Standard Effective Temperature (SET*) Sweating SET*, clothing and environmental acceptability The relation between ET* and SET* and warm discomfort during exercise Indices of cold discomfort Discussion Conclusions INTRODUCTION

The search for a simple physical index-of human response to the thermal environment has been vigorously pursued for the past half century. Engineers, psychologists and physicians, have each had an objective unique to their own professional interests. Ventilating engineers, who started in the 1920'~~ sought methods to predict the response of occupants to temperature and humidity in homes and buildings with

80

A. PHARo GAGGE

the newly developed central heating and air conditioning. Psychologists were interestcd in how human sensations of warmth and cold relate to the temperature of the environment. Physiologists were interested in how the thermal living environment affects the regulation of the human body temperature and how the effector processes necessary for this regulation (i.e. sweating, vascular changes, shivering and behavioural changes) affect human judgments of heat and cold (HALDANE,1905). Finally, the physician was interested in the health of persons exposed to extremes of cold, heat and humidity. All of these professional groups have at one time or another generated physical and physiological indices, which have served as predictive indices of thermal comfort, of thermal sensation, of heat and cold tolerance and of performance. The present chapter will describe physical or physiological indices of the thermal environment which have already been proven useful or which may prove valuable in future. There will be no attempt to present a complete review and evaluation of past work. Basic principles will be established by which indices, for thermal comfort in particular, may be developed and their usefulness judged.

THERMAL COMFORT

A definition of thermal comfort is necessary, if it must be related to any “index”. In the past such a definition has never proven to be simple. Cold and warmth were not recognized as separate human sensations until the latter part of the 19th century. Thermal comfort, as a measurable entity, was first recognized by the heating and ventilating engineers (HOUGHTEN and YAGLOU, 1923). They defined a “comfortable” environment as one sensed by the occupant as neither warm nor cold. Until the 196O’s, engineers have continued to measure comfort quantitatively by the use of category scales involving the following word sequence: cold -cool - slightly cool -comfortable - slightly warm -warm hot For purposes of statistical analyses each category is assigned a number either in a sequence from 1 through to 7 or on a positive, and negative scale (+3 to -3). to distinguish warmth or cold, with zero for neutral or comfortable, The above pragmatic approach to thermal comfort proved acceptable at first to engineers and perhaps to the early psychologists. However, it has never proven fully acceptable to physiologists, who recognized early that a state of thermal discomfort was not associated always with positive thermal sensation but with the nature of the tbermoregulatory response (by sweating, vascular changes, and shivering) to the physical environment itself. WINSLOW, HERRINGTON and GAGGE(1937) thus introduced the sensory categories scale of L6plea~nt’7-‘gunplea~ant.)-L’VeTYUnPleasant7’, which sensations were considered distinct and different from those with a temperature basis. In a later study GAGGE,STOLWIJK and HARDY(1967), used categories of “comfortable”-“slightly uncomforta ble’7-“~eryuncomfortable”:it was demonstrated that sensations of “slightly cool” or “slightly warm” could also be associated with

-

Indices of thermal confort

81

pleasantness or comfort. The studies by CHATONNET and CABANAC (1965), and later by CABANAC (1971) and STEVENS, MARKSand SIMONSON (1974) have revolutionized our understanding of the latter sensations. These show that local temperature sensations on the skin surfaces, whether warm or cold, may be either pleasant or unpleasant, depending on the mean body temperature and/or skin temperature. Currently, the clearest definition of “comfort” is the one used by the American Society of Heating, Refrigerating and Air-conditioning Engineers in their Standard for Thermal Environmental Conditions for Thermal Occupancy. This defines comfort as “that state of mind which expresses satisfaction with the thermal environment”. By such a definition comfort is given both a physiological and sensory basis. Thermal discomfort in either warmth or cold can be treated as a single variable which has been shown to follow a power law (STEVENS, MARKSand GAGGE, 1969). Alternatively, where we are concerned with a population rather than individuals, a state of “thermal comfort” is reflected by the percentage of those persons exposed to a given environment who indicate that it is “acceptable”. There never will be a perfect environment; there will always be a small percentage who will be dissatisfied. On statistical grounds, FANGER (1970) has set the ideal figure at 95 yo satisfied. For engineering applications the ASHRAE Standard has set the percentage satisfied at 80 for a comfortable environment. THERMAL INDICES

Because of the complexity of man’s thermal environment, even in indoor conditions, there have been many attempts to produce a satisfactory index to specify his environment by a single number. The usual dimension of such indices is temperature, which must be based on the heat balance equation, discussed by J. A. CLARKet al. and NISHIin chapters 1 and 2 of this book. The following sections of this review outline the derivation of some of the rational indices and discuss their application for the prediction of comfort and safety in work. OPERATIVE TEMPERATURE

In addition to the basic temperatures, ambient (To),and mean radiant (F,),the simplest derived environmental temperature index for sensible heat exchange is Operative Temperature (To); which is defined as the temperature of a uniform black (4n) enclosure in which a human occupant would exchange the same amount of heat by radiation (R) and convection (C) as i n the actual non-uniform environment. By this definition, RSC = h c r ( ~ s , , - ~ o ) , (5.1)

R+ C = h, (Tsu -Tr)+h, (Fsu-T>.

(54

where C and R are in units of W m-2 and T,,, is the mean temperature, in “C,of the outer surface of the occupant, whether it be skin or clothing, h, is the linear radiation 6

- Bioengineering

82

A. PHARO GAGGE

exchange coefficient given by

h, = (0.72)(5.67X 10-8)4[0.5(T,+Ta)+27313, when T, > T,,

> To,

or by

h, = (0.72)(5.67 x lo-') 4 [0.25 (Tr+T,+2 TSJ+273l3, when T,,> (T,+TJ/2, where in each case the factor 0.72 is the fraction of the total human body surface contributing to radiation exchange and the term in the second bracket is the Stefan-Boltzmann constant, in W m-2K-4. h, is the convective heat transfer coefficient, a function of air velocity Y , and pressure. From equations (5.1) and (5.2)

T, = (h,T,+~,TJ/h,Y (5.3) where the combined coefficient h,, = h,+h,. Operative Temperature is thus an average of T, and To,weighted by the respective linear radiative and convective heat transfer coefficients observed at the body exterior surface. Equation (5.3) may be rewritten as or

where 2ZB, Effective Radiant Field, represents the radiant heat received by the human occupant only from those radiative surfaces in the surrounding enclosure whose temperatures direr from To. When the various temperatures contributing to T, differ widely (e.g. solar heat against cold walls of a room) the relative absorptance of the various body surfaces must be considered. Skin and clothing surfaces may be considered black for thermal radiation. Operative Temperature, as derived and defined here, has appeared in the literature in many forms. Perhaps the earliest was the Tempdrature Resultante of Missenard ; other descriptions are Equivalent Temperature and Corrected or Adjusted Dry Bulb Temperature, used by the English and American engineers. Operative Temperature is a direct measure of the environmental heat stress on a human subject due to sensible heat exchangealone, and is not to be confused with the Effective Temperature and YAGLOU (I923), which is an empirical index of stress (ET), used by HOUGHTEN caused by both sensible and insensible heat exchange. THE ROLE OF CLOTHING

IN SENSIBLE HEAT EXCHANGE

Clothing adds a resistance to the flow of heat from the body surface to the outside. We may assume that the sensible heat transfer from the outer clothing surface (at mean temperature, T,J to the environment at Tois the same as the heat transferred

Indices of thermal comfort

83

through clothing, it can be shown that

R S C = hcr(T,--T0)7

(5.6)

R S C = h,F,(~,-T,) or hb(T,-To),

(5.6')

where the thermal efficiency factor, F,, equals l/(l+hJ) and I is the clothing insulation in units of m2 K W-l . Any form of sensible heat transfer which approximately obeys Newton's Law of Cooling may be described by a product hLr(T,--T2, where h:, is the effective sensible heat transfer coefficient involved (in W m-z K-l)' in our case equal to (hcrFc).For any environment, hir is primarily a function of Y, I and atmospheric pressure (in gases), as well as of the density and conductivity of the medium, which may be water, another fluid or various gas mixtures. A rigorous treatment of all these variables is being presented in other chapters in the present book, and has been reported elsewhere (GAGGE and NISHI,1977) for normal living environments. TEMPERATURE INDICES OF INSENSIBLE! HEAT EXCHANGE

Insensible heat loss by the evaporation of water and sweat from the skin surface must involve the gradient of vapour pressure from the skin surface to the ambient air. The evaporative heat transfer from an area of completely wet skin surface in air, as for sensible heat exchange, is a function of air movement, clothing insulation worn ( I ) and barometric pressure ( p ) in air. The permeability of clothing to water vapour is also a significant factor. A well established theorem of mass and heat transfer is that both convective and evaporative heat transfer from a wet surface are affected in the same way by air movement and air density (LEWIS,1922). This general analogy between convection and evaporation has been extended to normal everyday clothing. Thus the maximum evaporative heat loss (Em, W m-2) from a wet skin surface may be described by an equation analogous to equation (5.6) for sensible heat, as follows: E,,, = 16.5h,Fe,(e,-e,), (5.7) where 16.5 is the reciprocal of the psychrometric constant (K kPa-') at sea level and varies inversely with p . This may be derived from the Lewis relation. h,, the convective transfer coefficieEt, varies as the product ( V ~ ) O . FeC ~ ~ .is the permeation efficiency of water vapour through clothing, which for normal clothing is equal to the ratio l/(l+0.92hCZ).e, and e, are the saturation vapourpressures at Tsand Td,respectively, where Tdis the dew point temperature. The effectiveinsensible heat transfer coefficient hi (later in equation (5.9)) is described by the term hi = 16.5h,Fec. For a normally clothed subject ( I = 0.09 mz K W-' or 0.6 clo) in still air, F, would be 0.8 and the effective insensible heat transfer coefficient 43 W m-2 kPa-' . An accurate algorithm (Antoine equation) relating temperature and saturation vapour pressure is es = [16.6536-4030.183/(T+235)], where T is in "C and e, in kPa.

A. PHAROGAGGE

84

Em,as described in equation (5.7), represents the maximum heat loss by evaporation from a completely wet surface. Under these conditions the skin has a “wettedness” ( 0 )of unity. Generally, only a fraction of the skin surface is wet with moisture and it is never completely dry. When there is no sweating (E, = 0 ) , evaporation on th: skin surface is caused by diffusion of vapour through the outer layers of the skin (Ed). For normal comfortable but slightly cool conditions, this is equivalent to a wettedness ( w ) of approximately 0.06 (BREBNERet al., 1956). Skin wettedness therefore ranges from a minimum of 0.06 to unity during the course of body temperature regulation by sweating. The total evaporative loss ( E ) can be described by the equations: E = EdI-E,, (5.8) 0.94E,+0.06Em,

(5.8‘)

WE,.

(5.8“)

= =

Thus whenever E, = 0, E = E d ; when E, = Em,Ed is always zero. The total heat loss from the skin surface (H,) is thus the sum of the sensible and insensible terms given, in W m-2, by H, = hr,(T,-T,)+wh:(e,-e,).

(5.9)

When rearranged this becomes (eu-4

=

(-do)[ ~ o - ( ~ s - ~ s / ~ ; ) l ,

(5.9’)

where y = hf,/h: is the ratio of the transfer coefficients for sensible and insensible heat, and has units of kPaK-’. The significance of equation (5.9) may be realized by representing it on a psychrometric chart with Toon the abscissa and e on ordinate (see fig. 5.1). Equation (5.9‘)

Fig. 5.1. A psychrometric chart showing the effects of vapour pressure (el, temperature and skin wettedness (w) on the heat balance. Other symbols as defined in text

Indices of thermal comfort

85

describes a straight line between two points; point OP, whose coordinates are the Operative Temperature and vapour pressure actually observed at the location of the subject, and an imaginary point CP, whose coordinates are TS--Hs/h:,, and e,. The slope of the locus CP-OP is -y/w. The ratio y = hb/h: is a unique transfer characteristic of the total environmental heat exchange for a human subject. It is a function of air movement, clothing worn and barometric pressure. The CP-OP locus represents the combinations of Toand e that would result in the same total heat loss (H,) from the skin surface. When o = 1, the' resulting locus would represent the upper theoretical limit of the zone of evaporative cooling. When o w 0.06, there is no regulatory sweating, and the resulting locus will represent the lower threshold for sweating. y has a value of 0.11 kPa K-' for a normally clothed sedentary subject in still air and decreases with clothing insulation, as well as with increasing air movement and barometric pressure. Since thermal comfort is associated with T, M 33" to 34 "C and with o = 0.06, clothing insulation has a major effect on the T, necessary for comfort but has a less significant effect on the upper limit of evaporation. Increasing air movement raises both the T, for comfort and the upper limit of evaporative regulation. Increasing barometric pressure, over the range 1-4 atmospheres, has little effect on the T, for comfort, but significantly narrows the zone of evaporative regulation. y is inversely related to the permeability index, ,i described in GOLDMAN'S review (chapter 3). According to his definition i,,, = (l6.5y)-I, and i, is dimensionless. HUMID OPERATIVE TEMPERATURE

The Humid Operative Temperature (To&is defined as the uniform temperature of an imaginary black enclosure at 100% relative humidity (RH) in which a moist object or human subject would have the same total heat exchange by radiation, convection and evaporation as he (or it) would in the actual environment. By this definition equation (5.9) becomes (5.10)

By equating (5.9) and (5.10), Humid Operative Temperature is obtained by solution of the equation: (-.-eS(Toh,)

= -(Y/d@o-To/J,

(5.1 1)

which may be solved by iteration. Graphically, Tohis the abscissa at the intersection of the CP-OP locus in fig. 5.1 with the 100% RH (saturation) curve. As the skin surface dries (i.e. o +O), Tohapproaches To in value. For the case of a normally clothed subject (y = 0.11) the value for To,is 23" when o = 0.06, and 33", when o = 1. The values so derived are numerically similar to those given by the old 6Lclassical"EffectiveTemperature (ET) scale of HOUGHTEN and YAGLOU (1923).

86

A. PHmo GAWE THE NEW EFFECTIVE TEMPERATURE (@T*)

The new Effective Temperature (ET+)index, as now used by the American Society of Heating, Refrigerating and Air-conditioning Engineers (ASHRAE) is defined as the temperature of an imaginary uniform black enclosure at 50% RH in which a human subject would have the same total heat exchange by radiation, convection and evaporation as he would in the actual environment. By this definition, and by analogy with equations (5.10) and (5.11) above, ET* is obtained by solution of the following equation (5.12) = - ( Y / 4 Vo-TET’) eo-0.5 %*),,( or (5.12‘) 0.5%(,,*)+(Y/4 TET’ = e,+(dw) To * Thus in fig. 5.1, ET* is the abscissa at the intersection of the CO-OP locus with the 50% RH curve. Again, for our clothed sedentary subject the range of ET+ for o = 0.06 to w = 1 is from 24” to 42” C. The virtue of an ET+ type scale is that the values 24” for ‘%omfort”and 42 “C for “hot-very uncomfortable” match the “temperature” experience of an average North American or North European far better than the corresponding index range of 23.5” to 33 “C for To,,; saturated environments are relatively unknown to an average person. When rewritten as equation (5.12‘), ET+ can be solved by iteration with a pocket calculator (NISHI, 1977). For both To, and ET+ the same environmental characteristic, ly, applies to both the imaginary enclosure and test environment. The indices, calculated from (5.11) and (5.12), may be used to represent any values of Toand e in terms of the standard environment with a fixed relative humidity, such as 100% or 50%. STANDARD INDICES

The value of a “standard” index is its ability to describe the total heat exchange in any environment in terms of the heat exchange that would occur in a known familiar environment. Alternatively, if the human response to a well tested environmental condition is known, it should be possible to predict human response to any test condition in terms of that to a known condition. Our ability to predict the equivalence of different environments by the use of rationally derived indices will save the thermal physiologist or heating and ventilating engineer a great deal of experimental effort in the revalidation of known laboratory results. To apply successfully any such equivalencytest, it is necessary to know the effectivesensibleheat transfer coefficients, including the clothing insulation concerned, in both the test and standard environments. This is now a distinct reality. There are basically two types of Standard Indices - Standard Operative Temperature, for sensible heat transfer and Standard Operative Vapour Pressure for the insensible heat transfer. STANDARD OPERATIVE TEMPERATURE

Standard Operative Temperature (T’Jis defined as the temperature of a uniform enclosure (i.e. with T,= To)in which an occupant in still air at sea level, while wearing 0.6 clo as standard, would lose the same Eensible heat as he would in the test environment.

Indices of thermal comfort

87

By this definition for the test environment R+C

= h:,(Ts-To)

(5.13)

and for the standard environment

R+C

=h ~ s ( ~ s - ~ s o ) ,

(5.13')

where his is the effective sensible heat transfer coefficient for the standard eiiviron nient. Thus Tso = ( h ~ ~ / ~ ~ ~ ~ ) T , + ( l - Tj* h~,/h;j) (5.14) Equation (5.14) provides a method for predicting combinations of clothing insulation, air movement and barometric pressure that would have the Same sensible heat exchange as in the standard environment. STANDARD OPERATIVE VAPOUR PRESSURE

Standard Operative Vapour Pressure (e,,) is defined as the vapour pressure oa uniform enclosure in which an occupant, while wearing 0.09 mzK w-' (0.6 clo) standard, would lose the same insensible heat from his skin surface as he would in the test environment. If the insensible heat transfer coefficients are hi for the test and hi, for the standard environments, respectively, by definition E = wh:(e,-e,) = wh:(~&-eso)

(5.15) (5.159

thus

eso = ( ~ i / h ~ s ) e ~ - ( l - ~ ~ / h ~ ~ ) e s .

(5.16)

By use of equations (5.14) and (5.16), it is now possible to plot any beat transfer equation, such as equation (5.97, in terms of T, and e,, on a psychrometric chart analogous to fig. 5.1. The slopes of the various loci fot constant wettedness would now be h;,/(oh:,) or - y / w . The definitions of (a) Standard Humid Operative Temperature (TJoh)and (b) Standard Effective Temperature (SET") now follow logically: (a) Tsohis defined as the temperature of an imaginary enclosure at 100% RH in which a sedentary human occupatlt, dressed in standard clothing (I = 0.09 mz K W-' or 0.6 clo) in stillair, would lose the same totalheat by sensibleand insensible heat transfer as he would in the actual environment. TJohis given by the solution of an equation (similar to equation (5.11) : eSO-eS(Tsoh)

= -(vs/W)(Tso-Tsoh)

(5.17)

Graphically Tsohis the abscissa at the intersection of a locus with slope (-vJ/o) through the point (Tso,eso)on a psychrometric chart, with the 100% RH saturation curve. (b) SET* has a similar definition to Tsohexcept that the enclosure would have 50% RH. It is obtained by solution of the following equation, similar to equation (5.121, es0-0.5 es(sET*)= -(~Jm)(Tso-T&p*) (5.18)

88

A. PHARO GAGGE

or 0.5 es(SET*)+(Y’s/‘”))

TSET* = eso+(ys/o)

(5.18‘)

Tso9

or the intersection of the line with the 50 % R H curve. How equations (5.17) and (5.18) can be used to convert a psychroinetric chart for the test condition to the equivalent under the standard condition will be illustrated later, in fig. 5.6. DEVELOPMENT OF A PSYCHROMETRIC CHART FOR ESTIMATING STANDARD EFFECTIVE TEMPERATURE (SET*)

The standard environment chosen for a SET*-comfort chart is one describing typical heat transfer factors in a North American or European home or office building for a sedentary subject. The probable metabolic rate is between 55 and 65 W m-2 and the average total heat loss from the skin surface between 50 and 58 W m-” during thermal equilibrium. The applicable heat transfer coefficients, to be chosen as standard, arc listed in table 5.1. The values for the combined coefficients h,, It,, h:, and y Table 5.1 Standard heat transfer coefficients in air Heat transfer coefficients Activity

Sedentary M,, = 55 to 65 W rn-z (still air)

sensible (W rn-I K-’ ) hC = 3.0 h, = 4.4 h,, = 7.4 hLr = 4.4 tp

Moderate activity M,, = 165 to 180W rn-2 v = 0.8 ms-‘

=

=: =

h, = 50

1 = 0.09 m 2K W-I

11: = 40

(0.6 do) F = 0.6 I;; = 0.8

he

12.1 7.8

tp

I and F

0.11 kPaK-I

h, = 7.6 A, = 4.4 h,,

insensible (W rn+ kPa-’)

= 0.083

=

125

11; = 95

1 = 0.05 rn2K W-l (0.3 do) F = 0.6

r;, = 0.75

kPa K-I

Symbols as in text.

will increase slightly with Operative Temperature, due to the 4th power radiation law. Those here apply during “comfort”, when T, = 33 to 34 “C and Fsuis about 30 “C and To = 25 “C. The standard environment, defined in table 5.1, is very familiar to our daily experience and one for which there exists much experimental evidence (obtained at the Pierce Laboratory, Kansas State University, the Technical University of Denmark, and elsewhere) especially over the Operative Temperature range 15 to 40 “Cand relative humidity range from 20 % to 70 %. The chart in fig. 5.2 represents a series of loci for constant SET, any point of which will satisfy equation (5.9), the basic surface heat balance equation, as well a s

Indices of tltertnal cornfort

15

20

x 30 35 Operahe ternperdure ( T o r)r Ts0)

LO

L5

OC

Fig. 5.2. Psychrometric chart for evaluating Effective Temperature (ET*) from Operative Temperature (To) and humidity (eJ. The relative humidity lines apply when To = T, = T,. The category scales indicated are those observed in many studies in the field of heating and ventilating engineering. Since the standard coefficients for sedentary subjects (Table 5.1) are used here, the present chart can be used for SET* determinations in terms of Tsoand e,

equation (5.12) which defines ET* or SET,since the standard coefficients from table 5.1 are used in the calculations. In practice, during the regulation of body temperature the values of Fs, and E, (due to regulatory sweating) both increase with increasing environmental heat stress. In the cold E, is zero and 2", drops, in part due to vasoconstriction. In deriving fig. 5.2, a two-node model of body temperature regulation (GAGGE et al., 1971;NISHI and GACCE, 1977) has been used to develop the necessary realistic values for both Tsand o. The SET values represent those expected after one hours exposure to the conditions concerned. A category scale for thermal sensation, comfort and acceptability has also been marked in fig. 5.2, which summarizes our experience for the standard environment. Studies of the physiological background of fig. 5.2 show that, below 22" SET is essentially a linear function of Ts, temperature sensation and cold discomfort (see fig. 5.7); both psand internal body temperature are functions of the time of exposure. Below 15 "C,the body compensates by shivering. In heat stress, once skin wettedness has reached a maximum (w l), body heating sets in. Loci of constant SET above 41.5" all have the same slope, v j s , and each degree above 41.5" would represent a rise, after one hours exposure, of approximately 0.25"C in mean body temperature for an average size person (70 kg). For SET values above 41.5", the principal problem for the engineer and physiologist is tolerance time, discussed by VOGTet al. in chapter 6. If a total rise in body temperature of 1 "C is set as the limit of tolerance for health and performance, then on our chart this tolerance limit would be reached in the 45-46" SET range after 1 hour of exposure.


1 prolonged exposure is unsafe because E, cannot be realized. Safe exposure times must then be computed from the difference @,-Em), which is a heat storage rate, by fixing the maximal heat quantity whose storage will not increase the body temperature by more than an accepted amount. If w < 1 the Required Sweat Rate, S,, can be computed by dividing E, by the product of the efficiency of sweating and A . S, = E,/?lA

(6.5)

S, (g m-’s-’) represents the sweat rate needed to achieve thermal balance. It allows both for the evaporation and dripping of sweat, and may be compared to S,, the possible sweat rate that an individual can produce according to his acclimatization status. If S, < Sp no special problem arises. If S, > S,, it is necessaiy to compute safe exposure times from their difference, (S,-S,,). Clothing reduces radiative and convective heat transfer as well as the removal of heat by evaporation. It must therefore be taken into account in the calculation of Required Sweat Rate. The thermal efficiency factor and permeation efficiency factor given by NISHI (1965) were used. The required sweat secretion rate (Shr) in grams per hour for a subject of area A = 1.8 m2 is S,,, = 3600 S,A, where S, comes from equation (6.5). Therefore

For industrial application, we neglected E, and Ei in equation (6.1), since they are usually small compared to the other terms of the heat balance equation. Heat transfer coefficients and clothing factors used in our calculations were based on the work of MISSENARD (1973) and NISHIand GAGGE (1969), respectively. VALIDATION OF THE REQUIRED SWEAT RATE

In order to validate the use of the Required Sweat Rate, for assessing physiological strain in actual work and heat stress situations, the Required Sweat Rate was compared to sweat rate measurements on miners working in hot dry conditions. Calculation of the Required Sweat Rate necessitated measurement of six variables in each work place. Oxygen consumption iiieasurements were made with a Douglas bag method. Each measurement took at least five minutes. All typical work operations were sampled. From these results mean values of energy expenditure for each work period and for each work shift were computed. For the different work phases measured energy expenditures were between 105 W and 490 W. The mean values over whole work shifts ranged between 140 W and 325 W. Clothing insulation was estimated from tables (FANGER, 1970). Values were between 0.0155 and 0.062 m2 K W-’ (0.1 and 0.4 clo, respectively). Air temperatures

J. J. VOGTet al.

104

were measured by mercury thermometers, the range was 24 to 46 "C.Mean radiant temperatures, calculated from globe temperature measurements, were between 26 and 48 "C.Wet bulb temperature, read on an aspirated psychometer, was between 19 and 31 "C.Air velocity was measured near the miners body with a vane anemometer, measured values were between 0.1 and 4.2 m s-I . Sweat rates were computed from time changes of body weight. At the beginning of the work shift the miner was weighed and his clothing was noted. During the work shift an observer noted every ingestion of water or food and the volume of urine excreted. Body weight was measured as often as possible in order to determine the time course of sweat loss. Figures 6.2 and 6.3 show the relationships between the observed sweating rate and the Required Sweat Rate, computed for the whole work shift either by taking the mean values of the Required Sweat Rates computed for each work period (fig. 6.2) or taking the sweat rate calculated from mean values of energy expenditures, clothing and environment for the whole duration of the working shift (fig. 6.3). Correlations are highly significant (p < 0.001). The standard error of estimates is less than 100g h- and corresponds to the lack of precision of the estimated coefficientsin the heat exchange equation as well as to the possible inaccuracy of the different measurements. The two regression equations do not differ significantly. The rates of sweat loss observed ranged from 100 g h-' to 1400 g h-', and the total sweat loss by individuak was between 900 g and 3400 g for a complete shift. /

lOWr

q I

L

y=11079x

1133) 1002 r=O88L

+

n.58 I 0

I

I

m

I

I

LOO

I

I

I

Eo3

I

800

I

1

1wo

Required Sweat Rate lgh-')

Fig. 6.2. Observed sweat rate plotted against Required Sweat Rate. Required Sweat Rates are mean values computed for each work period

Sweut rate and thermal sweat

y : l12L2x

n.59 1

0

I

?a,

I

,

601 ? 9 3 2 r.0892

,

I

MD

LCC

Required Sweat

+

,

105

1

BW

I

I

1OW

Rate (ch-’)

Fig. 6.3. Observed sweat rate plotted against Required Sweat Rate. Required Sweat Rates computed from mean values of metabolic heat production, clothing and environmental conditions for the whole duration of the working shift

DISCUSSION

This study shows that the two procedures give almost identical values of Required Sweat Rates (see figs. 6.2 and 6.3). However, the Required Sweat Rate assumes steady sweating only. Our study shows that, despite this simplification, the actual sweat rate can be predicted with sufficient accuracy, at least in the observed working conditions. S,,, underestimated the sweat rate actually observed by about 100 g h-‘ (figs. 6.2 and 6.3). For comparison the P4SR index is plotted in fig. 6.4. For all conditions P4SR underestimates observed sweat rate by approximately 100 g h-’ . The two indices (Required Sweat Rate and P4SR) are significantly correlated. When both are expressed in g h-’, for nude men, (P4SR) = (1.013 S,,-40) with an error of f 6 8 g h-’ (r = 0.95 and n = 58). For clothed men (P4SR) = (1.120 Sh,-50) with an error of &SO g h-’ (r = 0.94 and n = 58). The increased barometric pressure in mines explains this underestimation. Figure 6.5 shows the relationship between the observed sweat rate and the index currently used in French mines, the “Temperature RCsultante Minitre”. In this case correlation is poor. As the observed sweat rate is representative of physiological strain imposed by working conditions, we can conclude that Required Sweat Rate is a good index.

J. J. VOGTet al.

106

f

.

y = (0905 x

n.58

OL

, 0

3

I

I

I

I

LW

200

predicted Four Hour

151 89) t 8L.S

+

r.0921

,

.

I

I

1

1

I

1WG

Bm

6M)

Sweat Rate i g h - ’ )

Fig. 6.4. Observed sweat rate plotted against Predicted Four Hour Sweat Rate (PIISR) values

g

c

@lJ-

B ml0

200 -

,il 20

y = i38L6 x

-

n.70

,

56LL)

1553

I

1

15

?

r -0689

30

Temphture R k l t a n t e Minibre

35 (OC!

Fig. 6.5. Observed sweat rate plotted against “Tempkrature R6sultante M mi6xe”

”

Sweat rate and therniol strain

107

REQUIRED SWEAT RATE AS AN INDEX OF HEAT STRAlN IN INDUSTRY

As shown above, the Required Sweat Rate correlates very well with observed sweat rates. Can it be usedforassessing heat strain in industry? In order to answer to this question the different conditions which such an index has to satisfy must be examined. These are: that the index shall take into account the six influencing factors : metabolic heat expenditure, clothing, air and mean radiant temperature, humidity and air velocity; that the index shall allow an evaluation of the degree of discomfort as well as of safe exposure times; and that the measurements and calculations required shall be simple and rapid. How far does Required Sweat Rate satisfy these conditions? Being derived from the heat balance equation, S, is directly related to the physiological strain; the larger the Required Sweat Rate, the larger the physiological strain. The Required Sweat Rate corresponds to the sweat rate which must be realized in order to match the heat stress. Its value depends very little on heat acclimatization, which increases only the maximal sweating capacity making tolerable an otherwise intolerable heat stress. The ratio of Required Sweat Rate to maximal possible sweat rate indicates the strain in a given situation. Estimations of discomfort and of tolerance times require different limits of sweat rate. FANGER, (1970) proposed a comfort value of sweat rate depending on metabolic energy expenditure according to the empirical equation So = (0.6 Mn-35), where So is the optimal sweat rate (g m-' h '). If Required Sweat Rate lies between zero and So, we can consider that man is in his comfort range. Upper tolerable values can also be proposed for two cases: for maximal sweat rate and for maximal sweat loss. The maximal sweat rate depends on the acclimatization of the individual. Non-acclimatized people cannot sweat more than 600 to 700 g h-l, while acclimatized people may sweat much more. Values near 2500 g h-' have been observed, but for industrial applications we consider that 1000 to 1300 g h-' is the likely maximum, Conditions in which Required Sweat Rate is lower than this threshold are tolerable. Figure 6.6 shows on the psychrometric chart maximal conditions for Required Sweat Rate in a range between 1000 and 1300 g h-'. These values can be compared with limits proposed by MULLERand WENZEL (1961) for young acclimatized men. For Required Sweat Rates from 400 to 700 g h-' comparison can be made with limits proposed in the U S A . by National Institute of Occupational Safety and Health (KAMON,1975). The upper tolerable limits of total sweat loss must also be set. Dehydration will occur when the conditions are such that drinking during the exposure cannot compensate for the amount of water lost (LEITHEAD and LIND, 1964). We consider that a sweat loss of 4 to 5 litres is the tolerable maximum for a workshift. In 1966 the World Health Organization proposed a total sweat loss of 4 litres per shift as an upper limit of sweat loss, even if the sweat rate itself is tolerable. From this limit we can calculate a Recommended Working Time (RWT), in hours, as (RWT)

= 4000/S,,,.

(6.7)

J. J. Vocr et al.

108

Ambient wpour pressure [(POI

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(OCI

(ms-’)

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(wI

37

09 01-09

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3L

05

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