VLF Radio Engineering. [14]

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Pergamon Press

international Series of Monographs in Electromagnetic Waves Volume 14 VLF Radio Engineering by A.D.Watt

INTERNATIONAL SERIES OF MONOGRAPHS IN ELECTROMAGNETIC WAVES Editors:

A.

L. Cullen,

V. A.

Fock and

J.

R. Wait

Volume 14

VLF RADIO ENGINEERING

VLF Radio Engineering BY

ARTHUR D. WATT Chief Scientist i DECO Electronics > Inc,, Boulder, Colorado, US, A.

PERGAMON PRESS OXFORD TORONTO

■

LONDON •

SYDNEY

■

EDINBURGH •

PARIS

•

•

NEW YORK.

BRAUNSCHWEIG

Perga mo n Press Ltd., Reading ton Hill Hall, Oxford 4 & 5 FiLzroy Square, London W.l Pergamon Press (Scotland) Ltd*, 2 & 3 Tevlot Place, Edinburgh I Pergamon Press Inc,, 44-01 21 si Street, Long Island City, New York 1J101 Pergamon of Canada, Ltd*, 6 Adelaide Street East, Toronto, Ontario Pergamon Press (Aust.) Pty. Lid., 20-22 Margaret Street, Sydney, N.S.W* Pergamon Press S.A.ECL*, 24 rue des Ecoles, Paris 5C Vieweg & Sohn GmbH, Burgplalz 1, Braunschweig

Copyright © 1967 Pergamon Press Inc.

First edition 1967

Library of Congress Catalog Card No* 67—1 S I 66

PRINTED IN GREAT BRITAIN BV BELL AND UAIN LTD., GLASGOW

3212/67

CONTENTS Preface

xiii

Chapter L Introduction

1

LI Background and Instructions

1

L2 Units

2

L3 Coordinate Systems

4

L3.1 L3.2 1.3.3 1.3.4

Vectors Fields Vector Multiplication Phasors

5 6 7 7

Chapter 2. Transmitting Antenna

11

2,0 List of Symbols

11

2.1 Basic Concepts

]5

Radiation Efficiency Calculation of Antenna Bandwidth Effects of Base or Feed Shunt Capacity Power Bandwidth Product 2.2 Vertical Supports

22 23 24 25 26

2.2.1 Wind and Wind. Loading Wind Loading Mechanical Oscillation of Condnctors 2.2.2 Tower and Mast Steel Requirements and Approximate Costs 2*3 Top Loading

26 29 31 31 37

2.3,1 Capaci ty 0 f Wire $e gmc uts Single Horizontal Wire Concentric Cable (Air Dielectric) Single Vertical Wire Parallel Horizontal Wires (Flat Top Antenna) Single Wire Inverted L Antenna Single Wire T Antenna Parallel Wires Equally Spaced in a Vertical Plane Capacity between Two Parallel Wires Remote from Ground Nonparallel Wires Top Loaded Vertical Antenna (Umbrella-type)

v

40 40 4i 41 4! 44 45 45 45 46 46

VI

CONTENTS

2.3.2 Physical Characteristics of Guys and Elevated Wires 2.33 Wires and Cables 23,4 Insulators Compression Cones Tubular Type Insulators in Series 2.4 Ground Systems H Field Loss Resistive Component E Field Loss Resistive Component Vertical Electric Fields Power Loss and Resistive Component for E Field Losses Wire Surface Interface Losses Calculation of H Field Ground Resistance Components when the Surface Impedance is Constant or has a Simple Radial Variation 2.5 Conductor and Tuning Coil Properties Skin Effect Proximity Effect Losses in Solenoid Coils 2.5J Inductance Single Straight Wire Two Long Straight Wires or Ground Return Single Layer Coil of Round Wire Coil Quality and Losses 2.6 Corona Corona Formation and Spark Breakdown Frequency Effects Electric Fields of Typical Geometrical Forms Corona Onset Voltage and Power Loss Calculations Effective Capacity Change Power Loss 2.7 Mode Excitation Factor Antenna Directivity 2.8 Characteristics of Actual VLF Antennas 2.8.1 Historical Review Prior to World War I Between World War I and World War II Following World War II 2.8.2 Electrical Parameters 2.8.3 Summary of Early VLF Antennas 2.8.4 Characteristics of Major Existing Antennas An n ap o 1 is. Mary I an d Balboa (Summit) Canal Zone Cutler, Maine

48 51 58 59 59 63 65 66 73 79 83 85

87 91 91 95 97 98 98 98 99 100 101 101 109 109 112 114 114 115 118 120 120 120 12J 122 122 129 129 129 136 139

CONTENTS

VII

Goliath, Germany Haiku, Oahu, Hawaii Jim Creek, Oso, Washington Lualualei, Oahu, Hawaii Rugby, England

144 148 149 157 163

2,9 Optimum Size and Multiple Unit Considerations

Chapter 3.

Propagation

Foreword

171 171

3.0 List of Symbols

171

3.1 Basic Concepts

179

3.2 Ground Wave Propagation

180

3.2.1 Surface Impedance Concepts 3.2.2 Mixed Paths 3.3 Ray Theory and Sky wave Field Calculations

,

164

3.3.1 Ray Path Geometry 3.3.2 Effective Antenna Patterns and Ray Launching Factors 3.3.3 Ionospheric Reflection Coefficients Exponential Conductivity Profile Magnetic Field and Nonexponential Profile Effects Comparison of Experiment and Theory 3.3.4 Ionospheric Convergence Factor 3.3.5 Multiple Hop Considerations 3.3.6 Height Gain Factors 3.3.7 Calculation of Total Field Employing both Ground and Sky Waves 3.4 Waveguide Modes 3.4.1

Introductory FJat-earth Theory The Zero Order Mode 3.4.2 Theory of Higher Order Flat-earth Modes Phase Velocity Attenuation Rates Mode Excitation 3.4.3 Spherical-earth Theory (by J. R. Wait) 3.4.4 Approximate Approaches to Spherical-earth Modes Phase Velocity Approximations Attenuation Rate Approximations Eart h D etached M o de Appro x i m at i on s Mode Excitation Approximations Height Gain Function Approximations Mode Field Approximations Antipodal Fields 3.5 Mode Field Calculations and Comparison with Observed Fields

185 194 197 198 205 211 215 218 226 227 229 232 234 239 241 241 ' 244 246 248 250 260 270 276 280 281 284 287 290 291 297

Vili

CONTENTS

3.5*1 Mode Field Equations 3.5.2 Excitation Factors and Height Gain Antenna Foreground Cutback Factor Height Gain Factors 3.5.3 Attenuation Rates Experimental Procedures Combination of Attenuation Rates over Mixed Paths Earth’s Magnetic Field and Directional Effects Earth’s Surface Conductivity Influence Diurnal Variation Seasonal Variation Latitude Variation Solar Cycle Variation Average Day and Night Attenuation Rates 3.5.4 Phase Velocity Experimental Procedures Combination of Mixed Paths Earth’s Magnetic Field and Directional Effects Earth’s Surface Conductivity Influence Diurnal Variation Seasonal Variation Latitude Variation Solar Cycle Variation Sun’s Zenith Angle Variation Average Day and Night Phase Velocities 3.5.5 Short-term Amplitude and Phase Variations Solar Flare Effects 3.5.6 Field Strength and Phase Versus Distance 3*5.7 Group Velocity

299 303 317 319 319 320 321 322 325 326 327 331 332 333 339 340 346 351 354 357 361 362 364 365 365 369 373 374 382

3.6 Magneto-ionic Modes (Whistlers)

386

3.7 Effects of High Altitude Nuclear Explosions

390

Chapter 4. Receiving Antenna

397

4.0 List of Symbols

397

4.1

Basic Concepts

398

4.2 Inverse Launching or Coupling Efficiency

400

4.3 Characteristics of E Field Antennas

400

4,3*1

Vertical Whips Calibration Power Available 4.3.2 Grounded Horizontal Wire Antennas Power Available Beverage Antennas

400 404 405 408 410 411

CONTENTS

IX

4.4 Characteristics of H Field Antennas

413

4.4.1

Loops F ield Stren gth Voltage Relat ion ships Magnetic Cores Effective Height Shielding Calibration Power Output Available Loop Inductance

4.5 Thermal Noise Levels and Equivalent Noise Fields 4.5.1 Directly Coupled Antennas Equivalent Noise Fields Ferromagnetic Cores 4.5.2 Transformer Coupled Antennas Carrier Voltage Developed Across the Tuning Capacitor The Carrier to Thermal-Noise Ratio at the Tuning Capacitor Degradation in Carrier to Noise Ratio due to a Trans¬ former 4.5.3 Effective Noise Field with a Specified Receiver 4.6 The Loop Antenna in a Conducting Medium 4.7 Aircraft Antennas 4.7.1

Types Employed Flush Antennas 4.7.2 Calibration Techniques Airframe Influence on Antenna Effective Height or Area [n-flight Calibration 4.8 Aircraft Precipitation Static 4.8.1 Charge Generation Mechanism 4.5.2 Corona Discharge and Noise Fields Ca 1 culat io n of Eqn ivalen t No ise Field s 4.8.3 Aircraft Dischargers and Noise Suppression

Chapter

5,

Atmospheric Radio Noise Fields

426 427 427 429 429 430 430 431 434 436 438 438 439 439 439 442 443 443 444 445 446

449

5.0 List of Symbols

449

5.1 Basic Concepts

450

5.2 Noise Sources

451

5,2,1 Lightning Characteristics Return Stroke Current Moment Characteristics Lightning Discharge Statistical Data Electric and Magnetic Fields Produced by a Time Varying Vertical Current Frequency Spectra of Individual Return Strokes Frequency Spectra of Individual Predischarges A*

415 415 416 419 419 420 422 424

451 453 457 458 463 465

X

CONTENTS

Spectral and Polarity Differences for Cloud to Cloud and Cloud to Ground Discharges 5.2.2 Thunderstorm Distribution Magnitude of World-wide Thunderstorm Activity 5.2.3 Extraterrestrial Sources 5.3 Median Level

476

5.3.1 Level Variation vs. Frequency 5.3.2 Level Variation vs. Geographic Location and Time Long-term Variations Random Variations of the Average Noise Field 5.4 Short-term Statistics

Modulation,

Frequency Spectra,

476 4B0 505 506 509

5.4.1 Amplitude Probability Distributions 5.4.2 Pulse Spacing Statistics

Chapter 6,

465 466 469 473

509 513

and Receiving System

Performance

523

6,0 List of Symbols

523

6. L Basic Concepts

525

6.2 Communication Theory and Modulation Considerations 6.2.1 Information Transmission Theory 6.2.2 Modulation Methods and Theory Amplitude Modulation Phase Modulation Frequency Modulation 6.3 Freq uency Spectra an d Ban dwi dth Requ i reme n Is 6.3.1 Periodic Functions and the Fourier Series 6.3.2 Nonperiodic Functions and the Fourier Integral 6.3.3 Impulse and Step Function Response of Linear Low Pass Filters 6 3 A Spectra of On-Oif Keyed Transmitters 6.3.5 Frequency Spectra of FSK Transmitters 6.4 Carrier to Noise and Error Calculations Statistics of a Carrier plus Thermal and VLF Atmospheric Noise instantaneous Amplitude Distributions Instantaneous Frequency Distributions for Thermal Noise Calculation of FM Noise Output for Thermal Noise, CjN > 1 Instantaneous Frequency Distributions for Atmospheric Noise 6.4.2 Carrier to Noise Requirements for Precise Frequency Measurement

525 526 529 530 530 530 531 531 534 534 538 540 544

6.4.1

545 549 551 554 556 558

CONTENTS

6.4.3 Comparison of Calculated and Measured Errors 6,5 Typical Communication Systems 6.5.1 Data Rates, Keying Rates, and Band widths AM Systems FSK. Systems 6.5.2 System Performance Factors idealized Performance and Gaussian Noise System Performance in the Presence or VLF Atmospheric Noise Effects of Noise Distribution on Performance Factor Chapter 7. Complete Systems Considerations

7.0 List of Symbols 7.1

Basic Concepts

7.2 Calculation of Power Requirements and Performance Reliability 7.2.1 Power Requirements for a Specified Path 7.2.2 Performance Reliability for a Specified Power Calculation of Median Carrier Fields Carrier to Noise and Communication Reliability 7.2.3 Prediction Reliability 7.3 Calculation of Bandwidth Requirements Transmitting Antenna Bandwidth Degradation of System Performance Dne to Limited Transmitter System Bandwidth 7.4 Economic Factors m Design 7.4.1 Transmitting System Cost Factors Transmitter Costs Tuning Equipment Radiation System Ground System 7.4.2 Selection of Optimum Efficiency Resistance Efficiency Relationships Investment Costs vs. Efficiency Determination of Yearly Operating Costs vs. Antenna System Efficiency Total Transmitting System Yearly Costs

XI

563 568 568 569 569 570 572 574 577 581

581 583 586 587 590 591 599 606 608 608 610 611 612 612 613 613 613 618 621 623 623 624

Appendices

A.

Abbreviations

629

B.

Conversion Coefficients

633

C.

Electric and Magnetic Fields Produced by a Time Varying Vertical Current

637

Antenna Current Voltage Relationship and Power Radiating Capabilities near Self-resonance

641

D.

Xli

CONTENTS

E.

Voltage and Current Distribution {Constant Impedance) Voltage and Current Distribution {Varying Impedance)

645 647

Electrical Properties of the Ionosphere

651

EA E+2 E3 E.4

Effective Permittivity of an Ionized Medium (without a magnetic held or collisions) Effects of Collisions (no magnetic field) Effects of Energy Dependence of the Collision Frequency Effect of a Magnetic Field Electron Density and Collisional Frequencies Lunar Effects

651 653 654 654 658 665

F.

Solar Radiation and Sunspot Cycles Long-term Periodic Fluctuations of Solar Activity Nonperiodic and Short-term Variations in Solar Radiation Cosmic Ray Intensity Variations

669 669 671 673

G.

Sun’s Zenith Angle and Sunrise-Sunset Times

677

PL

Geomagnetic Field

685

Answers to Problems

689

Author Index

693

Subject Index

697

Other Titles in the Series

703

PREFACE The increasing demand for very reliable long-range communication and navigation systems and the realizations of the capabilities of VLF (very low frequency) radio in meeting these demands, has done much to arouse a keen interest in this area of the radio frequency spectrum* The main objectives of this book are to provide: a detailed coverage of the fields involved in VLF radio engineering, a compendium of basic antenna, propagation, and system engineering information, and a guide for applying the information in the solution of practical problems* Although much of the interest in VLF stems from the communication aspects, there are many other areas of application for the material presented here. These areas include: navigation, basic ionospheric research, meteorology and thunderstorm study and tracking, standard frequency and time distribu¬ tion, geological studies and minerals exploration. A book of this type is only made possible by information gathered from a large number of individuals. Since the material presented is based upon the efforts of many research workers, it is hoped that “our book” will be of assistance to those who have aided in its preparation as well as to those who follow in our footsteps, I am particularly indebted to my good friend J. R, Wait whose help, advice, and generously furnished reprints and other source material have made this book possible. Another associate, W. W. Brown, has cheerfully encouraged me during this work. His vast store of information on the properties and design of VLF transmitting antennas has contributed greatly to this particular chapter R. D. Croghan, who willingly served as coauthor of Chapter 3, has also assisted in preparing material for Appendices E and G, Helpful advice and information has been obtained from many other individuals, including: J* A. Pierce, W. E* Gustafson, F, M. Malone, H* A. Wheeler, W, S* Alberts, G, F. Lcydorf, F. S* Mathews, E. L. Maxwell, R* W. Plush, A. N. Smith, R. F. Linfield, T. E. Devancy, L* K* MacMillan, M. DishaL, A, G. Jean, C. J. Chilton, K. A* Norton, F. Horner, W. Q. Crichlow, L. Ball, D* D* Crombie, and W* E. Garner. Most of the drafting was done by my son, D* R. Watt* R* L* Hill, Sr., provided help with the editing and illustrations. Some illustrations were also done by G. Uridll, E* Obcrteuffer, and N. Kline* ■ Also of great help has been the encouragement in this work of Mr* L. H* Carr and J, A. Krcek, the patience of my wife Ann, and the careful and capable preparation of the manuscript by Mrs, Winifred M. Werth. xiii

MV

PREFACE

Thanks are also due the publisher, Robert Maxwell, for his interest and encouragement and to the members of his staff for the careful attention they gave the book during its production and printing. Finally, the importance of doing rather than just reading or observing cannot be stressed too heavily. To assist in this process, representative problems are included at the end of each chapter. It is important that those interested in becoming proficient, gain first-hand experience both in making physical observations and in performing some of the calculations. In this regard, the advice found in James, Chapter I :22, “But be ye doers of the word, and not hearers only, deceiving your own selves”, cannot be emphasized too strongly. Boulder^ Colorado

A. D. Watt

June, 1966

It is with considerable sadness that I must advise that my friend, Mr* L. K* MacMillan, passed away June 30, 1966* Mac gave me much encouragement in the preparation of this material and was looking forward to seeing its completion. Those of us who knew him will long remember his friendly and congenial manner. Me is survived by his wife and son* A. D* Watt

CHAPTER 1

INTRODUCTION 1.1. BACKGROUND AND INSTRUCTIONS

The material in this book is presented around the communications aspect following the flow of information bearing energy from the transmitting to receiving locations followed by a section on complete systems which considers the interrelationship of the various factors. An attempt has been made to indicate these interrelationships and yet to make the treatment in each section as independent as possible. Since this is a dynamic fleld where material is constantly being added, provision has been made for the reader to add material such as: data on new transmitting stations, additional references, recent values of propagation attenuation coefficients, etc., at the end of each chapter* The rationalized MKS system of units is used in the electrical derivations and, unless otherwise indicated, the factors employed will be in the basic units such as: meters, cycles per second, volts, amperes, etc. Cost factors are in United States dollars (1959). Mechanical forces, weights, etc,, arc in some cases given in English or United States terms. The term “ton” equals 2000 U.S. pounds, and term “kip” equals 1000 U.S. pounds. The main chapters are numbered consecutively and each chapter is sub¬ divided into sections numbered, c.g. IT, 1.2, etc., with subsections numbered 1.1.1, 1.1.2, etc* Additional subdivisions are by italic headings. Equations and figures are numbered consecutively within each section of a given chapter. References employed within a given section are presented at the end of each section along with, in some cases, general reference material* Symbolism in a work involving many different fields becomes rather complex and, although an attempt is made to use uniform symbols throughout this book, it is necessary in some cases to employ the same symbol for different physical quantities. In view of this* a list of symbols employed is presented preceding each chapter. In general, when equations employ a basic MKS unit, there will be no specifying of units. Frequently, in engineering usage, it is desirable to use units other than the basic MKS values, in which case they will be indicated in a bracket following the symbol as follows:

X [km] = 30/"1 [fcc/sj*

(LIT)

It should be pointed out that in the bracketed unit designator, we will riot attempt to include the power to which the symbol is raised* f 1

2

VLF RADIO ENGINEERING

Regarding tbe use of logarithms, ]n is used for the natural log, and Log is for the log to the base 10. When employing equations in which the logarithm of a given factor is employed, this may at times be designated in decibel terms as follows; 10 Log (100QP) = P [db, kw], (1.1.2) where the bracket indicates that the P factor employed is in decibels relative to 1 kilowatt In some areas, precise values of physical quantities are not available at the time of this writing. This is particularly true in tbe areas of: ionospheric characteristics and their time varying properties, the effective earth’s surface conductivity over the globe, and atmospheric radio noise levels* To permit a consistent over all analysis, it has been necessary to employ provisional values in many cases such as the solar cycle variations in attenuation rates, etc. As knowledge increases, it is hoped that these provisional values can be replaced with more accurate ones*

1.2. UNITS

In the early stages of physics and engineering, it readily became apparent that standards of measurement must be adopted whereby consistent units could be employed by workers in a given field* Several systems soon grew up in the various areas of interest, and it was only after great efforts towards unification that we now have available an absolute system of units which can be employed throughout all phases of engineering and physics* The MKS or GIORG1 system is an “absolute” system of the units since every quantity may be measured or expressed in terms of (hopefully) three basic fundamental units: the meter for lengthy the kilogram for mass, and the second for time. Length, mass, and time are all fundamental factors* each of which can be referred to a given standard that is assumed to be invariant. Table L2*l shows the three basic quantities and their symbols which will be used throughout this book. Following the basic relations, we have the various derived mechanical quantities such as velocity, acceleration, etc. Here each of the derived quantities is indicated by a specific symbol, and in addition, the equivalent dimensions in terms of the three basic standards are given* When electrical terms are considered, it is found necessary to define one other fundamental factor (such as charge, current or magnetic perme¬ ability). Various choices can be made as to which factor is considered fundamental. The ampere can be defined as the current which transports 1 coulomb of charge in one second* Since the ampere is related through mag¬ netic permeability to mechanical forces by well-known relations, we can * These three factors or units arc only fundamental by definition and, as we shall see it has been necessary to add a fourth factor, to account for electrical circuit or field behavior.

3

INTRODUCTION

[§1.2

Tadle 1.2.1. Rationalized MKS System

Quantity basic Length Mass Time mechanical Velocity Acceleration Force Weight Energy (work) Power

Defining relation and dimensions

Symbol

Unit

/ m t

fundamental fundamental fundamental

meter, m kilogram, kg second, sec

V

= = = —

meter/second meter/second2 newton — 1 kg/m sec2 newton (g cl 9*8 meter/ sec1) jonle = 1 newton meter watt = joule/second

a

F W U P

/r1 vr1, ft~2 ma} rnlt~2 mg, mlt~ 2

— N, ml2t~2 1 = UimPt~3

electric circuits Charge Current Potential Resistance Conductance Capacity Reactance Power

q I V R G C X P

fundamental = qr1 = Uq~\ m/5r V1 = VI-1, mCt-'q-2 --= R^1i nz~1i~ 2t2q2 — qV~l, m~Jl~2t2q2 = -iVI-\mFi-'(r2 = HR, ml2r3

coulomb ampere volt ohm mho (siemens) farad — coulomb/volt ohm watt

Magnetic circuits Magnetic flux Inductance

4 L

= -j Vdt, mPr'r1 = iRa~2, 2’nniPq~2

weber = volt sec henry, ohm second

EM fields Charge density

P* or po

= ql-2,gl-3

I E * D

= ir2, r2r‘q = Vl~ *, mlt~ 2q~1 = Q, = Pin 1.11 x W'13h*f4C.

(2.1.13m)

REFERENCES (2.1) Jordan, E* C*, Electromagnetic Waves in Radiating Systems, Prentice-Ha 11, New York, 1950. Wait* J* R*, Electromagnetic Radiation from Cylindrical Structures, Perga mon Press, New York, Appendix, p* 189, 1959a.

26

VLF RADIO ENGINEERING 2.2-

§2.2]

VERTICAL SUPPORTS

To obtain the effective vertical electric moment for VLF transmitting antenna, self-supporting towers or guyed masts are used for antennas over flat terrain; while in rough terrain, the mountains on either side of a canyon have been employed for a number of installations. Mountain supported antennas are in general each a unique structure and they will be considered later under specific installations in section 2.8. The details of support structure design are complex, and we will only attempt to summarize some of the factors of support design and cost estima¬ tion. The factors considered are those of interest in preliminary planning of VLF transmitting installations, and in optimizing the design of transmitting antenna structures or overall systems. The support structures must be designed to withstand wind loading and, in some cases, ice loading. In addition, at VLF, most support structures are required to withstand a rather heavy horizontal pull-off at the top of the support from the top hat structure. Top loading is generally employed in order to raise the capacitance of the radiating structure as well as to obtain an increase in effective height. Top loading is essential if appreciable power is to be radiated at VLF from antennas whose physical height is in the 200-300 m region typical of many existing VLF antenna structures. 2.2.1. Wind and Wind Loading

The wind encountered in nature can be considered as having both long and short term variations in velocity. Jn practice, the wind is frequently charac¬ terized as having a mean velocity which is usually specified in terms of a fiveminute mean wind velocity, u [5 min], or in some cases, onc-hour mean values, v [1 hr]. The actual mean wind velocity encountered at various geographical locations can be quite different as is shown by the wind velocity maps* in Fig, 2.2.1. The long-term variations in the mean wind velocities arc accounted for by changes in the contours of such maps from month to month as can be seen from looking at the various maps contained in the sources quoted. In addition to this, there is a statistical variation throughout each month and the values shown are for the five-minute mean wind velocities which are exceeded 1 % of the time in each month. It should be emphasized that detailed structures in high wind areas, etc., arc not included in this map. For locations other than those shown on this map, estimated values of wind velocities can be made once knowledge is obtained relative to the typical characteristics of the location. For example, proximity to hurricane belts, tornado zones, or mountain type winds all can have a great influence. * Numerous maps are given in the Handbook of Geophysics [1961], Visher [1954] presents average wind maps for the U.S. and also presents maps showing relative distribu¬ tion of tornados, hurricanes or special winds.

[§2.2

TRANSMITTING ANTENNA

27

The actual wind velocities used in designing vertical supports must be modified by a factor which allows for higher wind velocities as height is increased above the surface, A typical example of the increase in velocity with height is shown in Fig. 2.2.2. This variation in velocity with height is caused by the frictional forces on the wind near the earth’s surface where a boundary layer is formed. The actual characteristics of this boundary layer will, of course, depend upon local terrain features. Short-term variations in wind velocity about a given mean value are usually accounted for in what is defined as a gust factor, where the gust factor is defined as the velocity which lasts for a given gust duration relative to the

Fig. 2.2.1. Calculated steady wind speeds (= 5 min median) in miles per hour at 10 ft height which is exceeded 1% of the lime in January- (from Handbook of Geophysics* 1961),

mean velocity for a five-minute period. An example of a typical gust factor is shown iu Fig, 2.2.2a. It is interesting to note that for periods of approxi¬ mately one second, the wind velocity can be approximately twice that of the five-minute mean value. It is expected that the exact structure of this gust factor curve may differ from one geographic location to another. Although the gust factor increases appreciably for periods less than 1 see, the large moment of inertia for most large physical structures, such as we are concerned with here, tends to average these forces over a period of several seconds.

10

10*

{Smin}

JO3

GUST DURATION, seconds

Fig. 2.2.2a.

Gust factor vs. fiust duration (data from Sherlock in Handbook of Geophysics, 1961),

0M

[§2.2

29

TRANSMITTING ANTENNA

Critchfield [1960] reports (p. 66) that measurements at ML Washington, Mew Hampshire, on 4 December, 1934 gave wind velocities in excess of 150 m.p.h. for several hours with a peak reading of 231 m.p.h, He also reports (p. 126) that tropical hurricanes can have five-minute mean velocities of 150 m.p.h. with gusts estimated at 250 rmp.h. He estimates that tornados have wind velocities in excess of 200-300 m.p.h. One additional factor which must be considered is the fact that atmospheric density decreases with altitude. This effect will reduce the horizontal wind forces as will be seen in the following discussion of wind loading and drag forces. The manner in which the density of the earth’s atmosphere decreases with height is shown in Fig. 2.2.3.

0.3

REUTIVE density( 04 0.5 OS 1-

0.7

O.s

-1

0,9

n

V\

n

l -]—I

-

Winte

■

!\ \\ s,

S^rnrrr.T^1 K\

Bs =Winricj'SurloceOwicI iy

!

V\

1_1

Q

0.2

0.4

0.6 Q.B 1.0 ATMOSPHERIC DENSITY^ ,ko/m3 □

f.E

\ 1.4

Fto. 2.2.3. Variation of atmospheric density with height above sea-level (data From Humphreys in Handbook of Chemistry ami Physics, 28th edition, p. 2516, 1944).

Wind Loading The actual force exerted on an object exposed to the wind can be considered as composed of the sum oT the pressure drag and viscous drag. The pressure drag which is in essence caused by the impinging air particles producing a higher pressure on the windward side of the object as compared to the leeward side, produces a drag which is proportional to the velocity squared times the density times the size squared. The viscous drag which in air is only important for very slow speeds and small objects is proportional to the speed times the viscosity times the size. The manner in which the transition from these two regions occurs was determined in a now classical paper by Reynolds [1883] in which he found a dimensionless factor which is now called the Reynolds

30

VLF RADIO ENGINEERING

§2-2]

number* which is equal to the velocity times the length times the density divided by the viscosity. At low Reynolds number, the flow is essentially laminar while at high Reynolds number* it becomes turbulent. The transition zone depends a great deal upon the exact shape of the objects being considered but in general is in the order of several thousand. The wind pressure component produced per unit area of exposed surface perpendicular to the wind is given by the relationship

(2,11) wherep is the pressure per unit area, g is the acceleration due to gravity, Sa is air density, and v is wind velocity. If we use g = 9.8 m/sec2 and 5a = 1,2 kg/m3 at sea level, we obtain p = 0.061^,

(2.2.2)

where p is in kilograms per square meter and v is in meters per second. Velocity pressure can also be expressed as p|lb/ft2] = 0.024n2[m,p.hd.

(2.2,3)

The actual drag which is experienced by an object exposed to the wind is given by the relationship Drag = CDApp,

(2.2.3a)

where CD is the drag coefficient which can be defined as the ratio of effective area to projected area, AJf is the projected area of the object, and p is the pressure per unit area as defined previously. Streeter [195S] gives various values of CD for typical geometrical forms. As might be expected, the drag coefficient is found to be a function of Reynolds number where the Reynolds number is given as NRc=S-^,

(2.2.3b)

where v is the viscosity in kilograms per meter per second. A nominal value for the viscosity of the air is 1.8 x 10“ 4 Poises which is equal to 1.8x10“ 5 kgjm sec. An example of the magnitude of the Reynolds number encountered in practice for wires can be obtained by assuming d = 0.2 , v = 10 m/sec, which yields a Reynolds number of 1.3 x 104. For the normal range of wire sizes and wind velocities, the Reynolds number is expected to range from 103 to 103, Within this range, the behavior is quite predictable in general and CD for smooth cylindrical objects is very close to 1.2. At a Reynolds number of about 3 x 103, an abrupt shift in the flow pattern can occur and the drag coefficient can drop to about 0.3. Typical drag coefficients for variously shaped cylindrical structures are shown in Table 2.2.1 where the material is

[§2,2

31

TRANSMITTING ANTENNA

obtained from Lindsey [1938]. An application of wind loading in the design of guy towers is discussed by Cohen and Perrin [1957]. Mechanical Oscillation of Conductors

It is well known that cables subject to even moderate winds can, at times, undergo rather severe mechanical oscillations which will, if not corrected, result in destruction of the cable spans. Davis, Richards, and Scriven [1963] have described the manner in which oscillations can build up in supported cables. In the discussion which follows, it is pointed out that the mechanical Table 2.2.1,

Typical Drag Coefficients for Various Cylinders in Two-dimensional Flow* Body shape Circular cylinder

-^

Elliptical cylinder

-

0 2:1

-i4:1 8:1

Square cylinder

——Q o

Triangular cylinders

— „ - —^ 120* p --

i 120C

—*-

90^

2

■-- 60»[> — ^ lj4, and kn is an appropriate constant given in Table 2*3.4.

[§2.3

43

TRANSMITTING ANTliN NA

It is interesting to note that for long wires the capacity goes up almost directly with n if the spacing D is large compared to the height above ground. For closer spacing it is readily apparent that the proximity effect appreciably reduces the capacity contributed by each wire. Figure 2.3.3 shows the manner in which capacity builds up with n for a typical configuration. The results are Table 2,3.4. Value nfkn for use in eq. (2.3JO) for Parallel Wire Formula n

tin

n

AJn

//

kn

n

Ar,

2 3 4 5 6 7

0 0.067 ,135 .197 .252 .302

8 9 10 II 12 13

0.347 ,388 .425 .460 .492 .522

14 J5 16 17 18 19

0.550 .576 .601 .625 .647 .668

20 30 40 50 100

0.688 .847 .970 1.063 1.357

Number of Wiris m Fla*fop. n Fig. 2.3.3,

Capacity of parallel wines to an Enfinite ground screen.

normalized so that the manner in which the capacity approaches that of a solid sheet of the same overall dimensions can readily be seen. For two wires, kfl = 0 and C//Oif/ro] =

48.32 Log (4/i/rf) — 2/c H- Log (2A/D)*

(2.3.11)

The effective loss in capacity due to proximity effects is shown in Fig. 2,3.4 where it can be seen that if the spacing between wires is about equal to or

44

§2,3]

VLF RADIO engineering

greater than the height, each wire contributes almost all of its individual capacity. For closer spadngs, appreciable reduction in capacity is noted, particularly for large diameter wires.

■ Hefgfal lo Sputmg Ratio. h/D

Fig. 2,3.4, Effective capacity to ground of two spaced wires relative to twice the capacity of a single isolated wire to ground. (Calculated for ijh do, somew hat simitar results occtEf for small if ft ratio,) Table 2.3.5. Values of the Constant X for Wires at Right Angles [eq. (2.3.12)]

Kir I'll

0

0.2

0.4

0.6

0.8

TO

5.0

0 0,1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 5.0 10

0 0.055 ,099 *135 ,164 .186 .204 .218 .229 .237 .243 .189 .130

0 0.064 J16 .157 .189 .214 .233 .247 .258 ,265 .271 .200 .137

0 0.072 .129 .173 .207 .233 .253 .267 .27S .285 ,290 ,207 .141

0 0.078 .137 .184 ,222 .248 ,267 .282 ,292 .298 ,303 .213 .144

0 0.083 .146 .195 .233 .260 .278 .293 .302 .308 .313 .216 .146

0 0.088 .155 .206 .243 .269 .286 .302 .311 .317 ,321 .218 .147

0 0.J25 .207 ,262 .296 ,323 .340 ,352 .358 .362 ,365 .232 .155

Single Wire Inverted L Antenna

The capacity of such a configuration can be approximated by adding the contributions of the horizontal and vertical sections. This value will,

[ §2-3

45

TRANSMITTING ANTENNA

however, be high due to the proximity effect reduction. The capacity can be closely calculated for an antenna with a top section of length / at a height d above ground, a vertical length /' and height above ground at the base of h* by the relation C[«tf] =

_24.16(F+D_ {III' + 0[Log (4 hfd) - k] + {I'll+2'}[Log (21'Id) - k'l + X

(2.3.12) The X term takes into account the mutual effects of the two portions of the antenna, and its value is given in Table 2.3.5.

Single Wire T Antenna

This antenna consists of a single horizontal wire oflcngth / at a height h above ground. A vertical wire of length V is attached at the center and reaches to within h' of ground. The capacity can be calculated from the relation. c[wif] _24.16(/ + Q_

= (///+ 0[Log (4/i/d)-fe]+ (!'// + /')[Log ill'Id)-fc'] +(/ + 2/'//+ V)-X ‘ (2.3.13) where X is again obtained from Table 2.3.5, and k and k1 from Tables 2.3.2 and 2.3.3 respectively. It can be noted that the reduction in capacity due to mutual effects is greater for the T than the inverted L since both sides of the top section are in close proximity with the vertical.

Parallel Wires Equally Spaced in a Vertical Plane

Employing the same nomenclature used under the sections on single vertical wire and the parallel wires of parallel horizontal wires (flat top antenna), we can write the capacity to ground as 24.16/'rc C ---* Log (2/7d) +— Log (/'/£>)-n(k'+fc„)

(2.3.14)

n

where the constants k' and k„ can be found in Tables 2.3.3 and 2.3.4. Capacity between Two Parallel Wires Remote from Ground

In many instances it is desirable to find the capacity between wires in an antenna system. Basically the capacity per unit length between two wires of diameter d separated by a distance D is -V that of one wire to a plane

46

VLF RADIO ENGINEERING

§2.3]

intersecting the wires so from (23.4) and (2.3*6), we can write 12.08 C/I-' Log

'D-h(D2-f/2)n

L

d

(2.3.15)

\

12.08 Log (2 Did)

when djD is small*

(2.3.16)

Nonporollel Wires

Grover [1926] gives rather precise relations for a number of nonparallel conditions; however, in general, capacities between themselves or to ground for wires at various angles can be closely approximated by breaking the wires in short sections and rotating them to parallel positions so that eqs* (2.3*6) or (2*3.16) can be employed for each section and the individual contributions summed to obtain the total effective capacity. To assure reasonable accuracy, the wire segments should be chosen such that the ratio hid or Dfd docs not vary by more than 10-20% between segments that are considered as being rotated about their mid-point* Top Loaded Vertical Antenna {Umbrella-type)

It is well known that the effective height hL. of an electrically short vertical antenna is essentially equal to one-half its physical height and that top loading will increase both the effective height and the capacity to ground of such an antenna, Bel rose and Thain [1954] and Smith and Johnson [1947] have experimentally shown the effects of simple top loading on vertical radiators. Data from Belrose and Thain [1954] is shown in Fig. 2*3.5 where it is apparent that for this particular configuration, where $ = ha for the eight guys, the maximum effective height occurs when the height at which the insulators are placed is such that kfjha ^0,35* It must be emphasized that this is not necessarily the optimum point since the capacity continues to increase with /?'/V The curves shown in Fig* 2,3.5 may vary slightly with top hat wire size and mast diameter. In general, this variation is expected to be small if typical mast and wire sizes are employed. It is informative to consider the effects of these variations in he and C upon the maximum power which can be radiated as well as antenna bandwidth. From (2*L11), it is apparent that for a constant limiting voltage, the maximum radiated power possible will increase with C2 and and the relative power capability can be obtained as shown. A top loading ratio h!jha of 0.7 is seen to produce and increase in power capability of 8 and based on eq* (2.1.13c) a bandwidth increase of 3. Increasing the horizontal span s is shown by Belrose and Thain [1954] to

[§2-3

TRANSMITTING ANTENNA

47

fleloHve Rawer ond Bandwidth'

further increase the effective height and capacity; however, physical and economic factors arc likely to prevent s from becoming large compared to ha. Since the small scale model employed had very little sag in the guys, it is likely that to obtain the same relative results for large full scale antennas may require that s/h# be 1,2 or 1,3. Detailed measurements have been carried out by Alberts [1961] on a top loaded monopole with 15 guy levels. The geometry is shown in Fig, 2.3,5a

where it is indicated that the top 4 levels with 8 guys per level, i.e. 32 guys are active. The effective capacity over a non-loaded monopole is seen in Fig, 2,3.5b to increase by a factor of 7 when h*jh& is 0.8 as compared to the capacity increase of about 3 for the 8 guy case in Fig. 2,3,5, The variation of effective height with number of active guys and guy length is shown in Fig, 2.3.5c. It should be pointed out that the active guys were “sagged” to simulate the catenary sag of full size cables and insulators.

Il

[§2.3

49

transmitting antenna

which some of the following data was obtained is the Wire Rope Engineering The parabolic form for the general case of an inclined span is shown in Fig. 2.3.6. All the dimensions in this section can be in meters and kilograms* or, if preferred, in feet and pounds where t is the cable Handbook [1946].

rc

9

a

7

>■

5 CL