Table Of ContentRADIO W A VE PROPAGATION
C O N S O L I D A T ED S U M M A RY T E C H N I C AL R E P O RT
OF THE
C O M M I T T EE ON P R O P A G A T I ON
OF THE
N A T I O N AL D E F E N SE R E S E A R CH C O M M I T T EE
CHAS. R. BURROWS, Chairman
STEPHEN S. ATTWOOD, Editor
1949
ACADEMIC PRESS INC., PUBLISHERS
NEW YORK, N. Y.
P U B L I S H E R S' N O TE
The consolidation of the three volumes of the Summary Technical Report
of the Committee on Propagation of the National Defense Research Com
mittee was undertaken because the limited edition of the Report published
by the Summary Reports Group of the Columbia University Division of War
Research and distributed by the War and Navy Departments restricted the
availability of this material after declassification. The manuscript and
illustrations for the three volumes Avere prepared for publication by the
Summary Reports Group of the Columbia Division of War Research.
This volume contains all the scientific information and report of exper
iments contained in the three separate volumes and omits only that part
relating to the administrative activities of the Committee, its origin and
organization, with a description of the needs of the armed forces which called
it into being.
THE PUBLISHERS
December 1948
F O R E W O RD
THE SUCCESS of the propagation program was the operation, and Lt. Comdr. Ralph A. Krause and Capt.
result of the wholehearted cooperation of many in Lloyd Berkner were similarly helpful in organizing
dividuals in the various organizations concerned, not Navy liaison and help.
only in this country but in England, Canada, New Officers and scientific workers of the U. S. Navy
Zealand, and Australia. The magnitude of the research Radio and Sound Laboratory at San Diego, California,
work accomplished was possible only because of the altered their program on propagation to fit in with the
willingness of the workers in many organizations to overall program of the Committee. Capt. David R.
undertake their parts of the overall program. In fact, Hull, Bureau of Ships, understanding the importance
the entire program of the Committee on Propagation of the technical problems, paved the way for effective
was carried out without the necessity of the Committee cooperation by this laboratory.
exercising directive authority over any project. Dr. Ralph Bown, Radio and Television Research
Dr. Hubert Hopkins of the National Physical Labo Director, Bell Telephone Laboratories, integrated the
ratory in England and Mr. Donald E. Kerr of the research programs undertaken by Bell Telephone
Kadiation Laboratory at the Massachusetts Institute Laboratories for the Committee on Propagation. This
of Technology, who were working on this phase of the joint research program included meteorological meas
war effort when the Propagation Committee was urements on Bell Telephone Laboratories property by
formed, were instrumental in giving a good start to meteorologists of the Army Air Forces working with
its activities. The largest single group working for the Col. D. N. Yates, Director, and Lt. Col. Harry Wexler
Committee was under Mr. Kerr. of the Weather Wing, Army Air Forces. The accom
The existence of a common program for the United plishments of the Committee on Propagation are a
Nations in radio-wave propagation resulted from the good example of the effectiveness of cooperation—all
splendid cooperation given the Propagation Mission parts were essential and none more than the rest.
to England by Sir Edward Appleton and his Ultra I want to thank Dr. Karl T. Compton, President of
Short Wave Panel. Later, through the cooperation of Massachusetts Institute of Technology, who was al
Canadian engineers and scientists, Dr. W. R. Mc ways willing to discuss problems of the Committee and
Kinley of the National Eesearch Council of Canada who helped me to solve many of the more difficult
and Dr. Andrew Thomson of the Air Services Meteor ones, and also. Prof. S. S. Attwood, University of
ological Division, Department of Transport, Toronto, Michigan, whose continual counsel throughout my
Canada, undertook to carry on a part of the program term of office was in no small way responsible for the
originally assigned to the United States. The program success of our activity.
was further rounded out by the willingness of the New Credit is also due Bell Telephone Laboratories,
Zealand Government to undertake an experiment for which made my services available to the Government
which their situation was particularly favorable. Dr. and paid my salary from August 1943 to September
F. E. S. Alexander of New Zealand and Dr. Paul A. 1945, and to Cornell University, which has allowed
Anderson of the State College of Washington initiated me time off with pay to complete the work of the
this work. Needless to say, the labor of the Committee Committee on Propagation since September 1945.
on Propagation could hardly have been effective with
out the cooperation of the Army and Navy. Maj. Gen. CHAS. R. BURROWS
H. M. McClelland personally established Army co Chairman, Committee on Propagation
FOREWORD TO CONSOLIDATED EDITION
and engineers in the field of radio wave propagation are indebted
SCIENTISTS
^ to the Academic Press for making available to them this condensed volume
of the entire report of the Committee on Propagation of NDRC which other
wise would only be available in the two hundred and fifty copies of the three-
volume report printed for the government. This volume contains material
of great value to present and future studies of the problems encountered in the
propagation of radio waves not otherwise available to the public.
The results of the work of the Comimttee will eliminate repetitive steps
in many instances, and will serve as fundamental data in the approach to
future investigations. Furthermore, the text of Volume 3, complemented by
the contents of Volumes 1 and 2, may be easily adapted to classroom use.
The declassification of the Summary Technical Report makes it possible
to publish this consolidated edition of the three volumes. It will, in my
opinion, fill a need for the greater distribution of information essential to
further developments in the field of radio wave propagation.
CHAS. R. BURROWS, Director^
School of Electrical Engineering^
Cornell University ^ Itliaca, New York
October 15, 1948
PREFACE*
In this series of three volumes, which is part of absorption by the components of the atmosphere
the Summary Technical Report of NDRC, the Com becomes increasingly important while the problems
mittee on Propagation is presenting a record of its of absorption and scattering, as related to wavelength
activities and technical developments. The material and water droplet size, bear importantly on the abil
presented, concerning as it does the propagation of ity to track clouds and storms by radar.
radio waves through the troposphere, is of permanent [In a chapter] on echoes and targets, the reader
value both in war and in peace. will find an interesting treatment of some of the more
[In Volume 1, Part I] gives a critical overall view unusual problems concerning the radar behavior of
of the technical developments in the study of tropo targets. Volume 2 closes with a consideration of an
spheric propagation. Outlined is the general theory angle-of-arrival experiment.
of both standard and nonstandard propagation The material presented [inVolume 3] was prepared
together with descriptions and results of transmission by the Columbia University Wave Propagation
experiments carried out in widely separated parts of Group at the request of the Committee on Propaga
the earth and designed to test the theory. Included tion of the National Defense Research Committee.
also is a resume of the meteorological factors affect The International Radio Propagation Conference,
ing propagation of waves and their attenuation in meeting at Washington in May 1944, recommended
the atmosphere. that a book be prepared deajing with problems of
One of the important contributions of the NDRC radio wave propagation in the standard atmosphere
Committee on Propagation of permanent value is at frequencies above 30 megacycles. The importance
the publication of the technical papers presented at of these higher frequencies is apparent when it is
the several Conferences on Propagation. The first recalled that most radars operate in this range and
Conference was held at the Radiation Laboratory at that an increasing number of communication circuits
Massachusetts Institute of Technology in July 1943 are being equipped for operation above this fre
prior to the formation of the Committee on Propaga quency.
tion. Those sponsored by the Committee were the A certain amount of evidence from operational
second, third, and fourth Conferences held, respec theaters indicates that lack of familiarity with the
tively, in New York, February 194.4; in Washington, underlying theory of propagation and calculations
November 1944; and in Washington, May 1945. based thereon not infrequently has resulted in
The bulk of the material published is taken from ineffective installation and operation of radar and
the Columbia University reports and from the papers communication sets. This is ascribable, in part at
presented at the third and fourth Conferences; the least, to the lack of publications which give a clear
remainder comes from the second Conference. By picture of the problems of propagation or show how
careful selection it has been possible to avoid exces the important factors may be evaluated.
sive repetition; and yet on continuing projects, such A considerable volume of basic material on
as transmission studies, it is possible to follow their propagation had appeared in technical journals
development over a considerable period of time. before World War II, and during the war a great
Some of the material has been published in quantity of classified material has come from
Volume 1 of this series — that dealing with the laboratories and operational theaters, illustrating
theoretical aspects of propagation, both standard and new applications of old principles, giving valuable
nonstandard. In [Part I of Volume 2] the subject information on propagation problems as well as on
considered is meteorology: first theory,-then equip characteristics of radar and communication sets,
ment, and finally the development of forecasting antennas, targets, siting problems, etc. But this
techniques in which the ultimate goal is the ability information has not been coordinated under one
to predict radio performance from meteorological cover for practical use by signal personnel in the
measurements made considerably earlier. field. The Columbia University Wave Propagation
[In Part II of Volume 2 a chapter] on reflection Group was asked to undertake this task, and it is
coefficients presents a certain amount of new material hoped that this book will, in some measure, answer
which, however, tends to confirm previous views and the need.
further substantiates formulas already available. Our effort, then, has been to provide a hook
[In a chapter] on dielectric constant, absorption, and designed for men with college training in radio,
scattering, the reader will find a considerable volume physics, or electrical engineering, which states the
of new material. With decreasing wavelength the basic laws of propagation, that is, shows how the
characteristics of the earth and the atmosphere
•The Editor's Prefaces to the three volumes of the Sum
mary Technical Report of the Committee on Propagation control the propagation of radio waves; gives the
have been consolidated and abridged for reprinting as the
fundamental properties of the basic types of antenna
Preface to the present volume.
VI PREFACE
systems, particularly their directivity and gain; One of the main functions of the NDRC Com
gives the reflecting properties of targets such as mittee on Propagation was to bring about a rapid
airplanes for use in detection by radar; teaches the exchange of information between the laboratories
reader how to calculate field strength or obtain the and Service units working on the subject, and make
coverage diagrams given a particular set, power, and the results available to all workers technically con
site; gives the fundamental information required in cerned with the military application of radar and
the above calculations for application to the radar other short wave radio equipment. To fulfill this
and communication sets used in operational theaters; function the Columbia University Propagation
and provides illustrative material and sample calcu Group operating under contract with the Committee
lations which show how the laws of propagation periodically published a comprehensive bibliography
may advantageously be used in the location and on propagation, beginning in the spring of 1944.
operation of radar systems, communication sets, and Its fifth and last edition, issued in August 1945, is
countermeasure equipment designed to deceive the included [in the General Bibliography]. [This]
enemy and to prevent jamming of equipment by General Bibliography lists reports *on tropospheric
enemy action or by mutual interaction of our own sets. propagation issued by numerous Service and civilian
The reader [will find in the Appendix] a summariz organizations and is a rather exhaustive accumula
ing review of six transmission experiments carried tion of the efforts made during the war in this field by
out in widely separated geographical locations; Great Britain, Canada, New Zealand, Australia, and
namely, Massachusetts Bay, San Diego, Arizona, the United States. With a few exceptions, original
Antigua, West Indies, and Great Britain. The basic reports listed in the Bibliography have been micro
objectives here have been to learn the facts concern filmed. A few, such as summary reports issued by
ing transmission, and, as far as possible, to correlate the Columbia University Wave Propagation Group
them with the transmission theory given in Volume 1 and the compiled Propagation Reports, are included
in the present series.
and with the meteorological factors presented in
Volume 2. STEPHEN S. ATTWOOD
EDIIOR
PARTI
SUMMARY
Chapter 1
STANDARD PROPAGATION
INTRODUCTION is achieved when the two doublets are parallel to
each other and perpendicular to the line connecting
BY STANDARD PROPAGATION IS meant radio wave their centers. If their distance apart, d, is large com
propagation through an atmosphere free from pared to the wavelength, the ratio of power trans
irregular stratifications, particularly of vertical dis mitted to maximum useful power received is found
tributions of water vapor and temperature. With from electromagnetic theory to be
irregular stratification the propagation is said to be
nonstandard and will be treated extensively in the P2 _ ( ^\
(1)
later chapters. V"S irdJ '
P i"
In this chapter the fundamental general relations
between transmitted and received power is first re where λ and d are measured in the same units. Here
viewed; then the main factors influencing the trans P2 is the power delivered to a matched load at the
mission of electromagnetic waves such as refraction, output terminal of the receiver and Pi the power fed
diffraction, and dielectric properties of the ground to the transmitting antenna.
are surveyed; and finally the computation of the The gain G of any directive antenna is the ratio of
field at the receiver for various heights of transmitter the power transmitted by a doublet to the power
and receiver above a homogeneous smooth earth of transmitted by the antenna in question, to produce
given electromagnetic properties is very briefly dis the same response in a distant receiver, when, both
cussed. The last subject divides naturally into the transmitting antennas are adjusted for maximum
determination of the field above the line of sight and transfer of power. The gain of a receiving antenna is
the determination of the field below the line of sight similarly the ratio of the power delivered to the
m the earth's shadow. transmitting antenna when a doublet receiving an
The text of the present chapter largely follows the tenna is used to the power delivered to the transmit
book, issued by the Columbia University Wave ting antenna to produce the same response when the
Propagation Group [CUDWR WPG] under the title antenna in question is used at the receiver.
Propagation of Radio Waves through the Standard Two methods of expressing antenna gain are in
Atmosphere conunon use: the one just indicated where the gain
is measured as the ratio of the power in the optimum
direction relative to that of a doublet, and the other
POWER TRANSMISSION where the gain is that relative to a hypothetical iso
tropic radiator which is one assumed to radiate the
Certain relations occur so frequently in wave same power density in all directions. Simple geomet
propagation problems that it is convenient to rical considerations show that the gain of a doublet
summarize them here before entering into a descrip over that of an isotropic radiator is 3/2 so that the
tion of the characteristic features of short wave gains expressed in the former system are converted
propagation. Some of these are mere definitions; into the latter system by multiplying them by 3/2.
some are consequences of electromagnetic theory. In the equations below, the gain is expressed relative
It is convenient to use, as a standard antenna, one to the doublet.
which has a length which is small compared to the If transmission takes place, not in free space, but
wavelength, designated as "doublet." Such doublets over a conducting ground, in a refracting atmosphere,
may be used for both the transmitting and receiving etc., the power ratio will be expressed as
antennas. In the latter case it is assumed that the
load resistance is matched to the output resistance
(2)
of the antenna. In free space, optimum transmission
TECHNICAL SURVEY
ίο a matched load is
-Ii ΙΟΙ
-βο E^ 3X2
- 12θ7Γ 87Γ ^'^' ^"^^
The combination pf equations (3) and (4) gives again
-32 -70 5r- the general transmission formula (2).
The lower limit of possible receiver sensitivity is
4 i-
set by the thermal noise in the receiving system. At
ordinary temperatures the thermal noise power in
-βοΕ-
watts is very approximately
2 Β Pnolse = 4 . IQr^^Af, (5)
where Δ/ is the radio-frequency bandwidth of the
-9θΡ-
receiver in megacycles.
The minimum power P^,„ required for intelligible
reception being usually in excess of the thermal noise
-looF power, it is customary to use the ratio PmiJPnoise
8
expressed in decibels as a measure of the receiver
sensitivity Ten times the logarithm of this ratio
(to the base 10) is the sensitivity of the receiver in
-not- 0.5 r-
decibels above thermaf noise.
a4|.
As may be seen from this brief outline, the problem
of transmission in free space is a very simple one from
0.3
.l2o|-^ the engineering viewpoint. There are certain ques
tions regarding noise limit, receiver sensitivity, and
-J
-Í50 matching of the load which constitute refinemerts of
the above procedure. They are of interest primarily
for those concerned with receiver design; apart from
- ζ these the problem of power transmission may be con
- -<
2 0.1 r sidered solved by these formulas. The most impor
.I40b-• < tant and difficult part of ultra short wave propagation
then becomes the quantitative determination of the
path factor A ρ as a function of the geometry of the
transmission path, electromagnetic properties of the
-ΐ200 -I50E- 0.05|
ground, refractive properties of the atmosphere, etc
0.04
300
-I60F- 0.03
400 OPTICAL PROPERTIES OF THE
EARTH'S SURFACE AND ATMOSPHERE
1500
0.02|
-170b- REFLECTION COEFFICIENTS
In dealing with standard propagation it is usually
assumed that the ground has electromagnetic prop
i 1000 0.01^
-160«-- erties which are constant over the length oif the
transmission path. Deviations from this idealized
FIGURE 1. Nomogram for free space transmission between behavior are treated below as diffraction phenomena.
parallel doublets. The electromagnetic properties of the ground
are completely described by its complex dielectric
constant,
where G^ift are the antenna gains of the transmitting €c = 6r — J€t = €r — ^60σλ, (6)
and receiving systems, respectively, and A ρ is the
*'path factor." The nomogram, Figure 1, gives this where Cr is the relative dielectric constant, σ the con
ductivity in mhos per meter, and λ the wavelength
relation for (ri = (r2 = Ap= 1. Often the electric field
in meters. In general, and especially in the micro
at the position of the receiver is desired. It is given by
wave region, €r and €< are themselves functions of
the frequency. Figure 2 shows the variation of the
(3)
real and imaginary parts of the complex dielectric
constant of sea water at 17 C for ultra-high fre
where Ε is in volts per meter, Pi in watts. If Ε is quencies according to the best available experi
known, the power delivered by the receiving antenna mental data.
STANDARD PROPAGATION
140f f—
120\
100
Í 80
O
ü
o ) \
S 60i
)—V
40|
20
) σ\ FO R σ-: OS PEI Í METE
1 1 1 1 1 1 jt ti h- -i
Λ
FIGURE 2. Dielectric constant of sea water at 17 C.
The reflection coefficient is given by Ffesners
R = .^ = tiÉi^±=-y^^^^¿á, (8)
formulas. Let ψ indicate the angle between the
€e sin φ + V — cos^ φ
incident ray and the horizontal reflecting surface.
Then, for horizontal polarization where μ designates the magnitude of the reflection
coefficient, and φ the phase lag of the reflected ray
at reflection. Figure 3 illustrates the amplitude of the
sin ψ + V€c — cos^ φ reflection coefficient for sea water as a function of
the angle ψ for several frequencies. Figure 4 shows
and for vertical polarization the corresponding phase lag at reflection.
1
1 I
HORIZK 3NTALPO LA—RI\Z ATIO 1 ΙΙΘΘΟΟ VERTICAL Ρ η>ηΐ2 ΑΤΙΟΝ
\ noMc
\\ \ ΙΙΛΛδδ \ \ Ν
V \\ \ \ \
\ \\ V
111122220000 \ \ Ν
\\ \ \, \ \
\\ \.
\, \
\ Λ. IIIIDDDDOOOO**** \
\ \^\ \ \VE\R TICAL POLARIZATION ^ OOÓÓ \ Ν Ν,ΛΝ Ο ΟΜΟ Ν Ν
\ .\
6600
33..00**
00 ^ 1 Vi 1?—4• 4 5.5 ·
FIGURE 3. Amplitude, ρ, of the reflection coefficient FIGURE 4. Phase lag, φ, of the reflection coefficient
versus reflection angle, φ, from ψ = 0 to ^ = 5.5° for versus reflection angle, ψ, from ^ = Q to ψ = 5.5° for
sea water. sea water.
4
TECHNICAL SURVEY
From the practical viewpoint the following sum e = partial pressure of water vapor in milli
mary may give an overall picture of the more out bars,
standing features of ground and sea reflection. Τ = absolute temperature.
For horizontal polarization over the sea the reflec The mixing ratio, s, which is practically equal to
tion coefficient may be taken as unity and the phase specific humidity, is connected with e by the relation
shift as ISO degrees for frequencies up to and includ
ing the centimeter range, for practically all angles of e = O.OOieips . (10)
reflection. Over land there is a slight decrease of the
A recent analysis^^* has shown, moreover, that this
amplitude of the reflection coefficient with increasing
expression for refractive index must, on theoretical
angle; for instance, for a frequency of 200 mc, at
grounds, be substantially independent of frequency
an angle of 15 degrees the reflection coefficient has
down to the shortest waves employed in microwave
decreased to 0.9 or slightly more for moist soil and
engineering.
to 0.8 or slightly more for dry soil. These statements
In an average atmosphere temperature, pressure,
apply whea the ground or sea surface is reasonably
and water vapor density decrease with height, and,
smooth. In order to decide whether'a surface is
in the lowest few kilometers where most of the short
smooth or rough, Rayleigh's criterion, explained
and microwave propagation takes place, it may be
below, is usually applied. When the surface is rough
assumed to a good approximation that the decrease
or wavy, irregular scattering predominates and re
of refractive index with height is linear though the
duces the intensity to a small part of the value
rate of decrease is somewhat dependent on the cli
attained with a smooth surface.
mate. In middle latitudes it is given by
For vertical polarization the curve of the magnitude
of the reflection coefficient versus the angle goes ^ = -0.039 · 10-« per meter . (11)
through a minimum (see Figure 2). When the imagi
nary term of the complex dielectric constant is Refraction at the boundary of two media is fa
negligible so that the ground behaves like a pure miliar from optics and is expressed by SnelFs law:
dielectric material, the reflection coefficient goes to
Wi cos «1 = 712 cos «2 , (12)
zero at a certain angle (Brewster angle). Ordinary-
soil nearly fulfills this condition. For instance, at a where Wi and 712 are the refractive indices of the two
frequency of 200 mc the Brewster angle occurs at media and ai and «2 the angle between the boundary
about 12 degrees with moist soil and at about 21 and the direction of the ray in the first and second
degrees with dry soil. media respectively. In the atmosphere the refrac
For the ocean surface, and vertical polarization, tive index is a continuous function of height, and the
the imaginary part of the dielectric constant cannot sudden change of direction at a boundary is then
be neglected, and the reflection coefficient as a func replaced by a curvature of the rays. Equation (12)
tion of the angle does not vanish at any angle but can be written
goes through a minimum, the pseudo-Brewster angle. η cos α = no cos ao (13)
The actual variation of amplitude and phase lag is
represented in Figures 2 and 3 for the smdl angles of where η and a are now continuous functions of the
reflection which are most important in practice. height and the subscript 0 designates a reference level.
The above formulas refer to a plane earth. If the
When the ground is rough the reflection coeffi
earth's curvature is taken into account so that the
cient for both types of polarization is feduced to a
planes relative to which the angle a is measured-are
very small value. For 10-cm waves and still more for
replaced by spheres about the earth's center, for
shorter ones, most types of land are rough. A reflec
mula (13) must be modified; and the mathematical
tion coefficient of 0.2 may be taken as representative
analysis shows^^^ that it is replaced by
for an average ground covered with vegetation. A
slightly ruffled sea is a fairly good reflector for 10-cm
nr cos a = ηοΓο cos ao (14)
waves but appears somewhat rough at shorter wave
where r is the distance from the center of the earth
lengths.
to the level considered.
If now we set r = ro (1 -|- h/ro) where Λ = r — ro
STANDARD REFRACTION
and h/ro is a small quantity and, furthermore, if we
Numerous experiments have resulted in the fol note that with a linear gradient of η
lowing formula for the refractive index of moist air:
(15)
IN ine 79 / L 4,800e\
η - 1) · 10« = - e + - γ ")
we obtain on substituting into (14) and neglecting
small quantities of the second order
where η = the index of refraction,
ρ = the barometric pressure in millibars
1 + cos α = cos «0 (16)
(1 mm mercury = 1.3332 mb),
