NBS

PB161596

ecknic&l tiote

^Boulder laboratories

92c. 95

CHARACTERISTICS OF POINT-TO-POINT

TROPOSPHERIC PROPAGATION

AND SITING CONSIDERATIONS

BY R. S. KIRBY, P. L. RICE, AND L. J. MALONEY

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the national standards of measurement and the provision of means and methods for making measurements consistent

with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials, devices, and structures; advisory services to government agencies on scientific and technical problems; invention and development of devices to serve special needs of the Government; and the development of standard practices, codes, and specifications. The work includes basic

and applied research, development, engineering, instrumentation, testing, evaluation, calibration services,

and various consultation and information services. Research projects are also performed for other government

agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's

unique competence is required. The scope of activities is suggested by the listing of divisions and sections on the inside of the back cover.

Publications

The results of the Bureau's research are published either in the Bureau's own series of publications or

in the journals of professional and scientific societies. The Bureau itself publishes three periodicals avail- able from the Government Printing Office: The Journal of Research, published in four separate sections,

presents complete scientific and technical papers; the Technical News Bulletin presents summary and pre- liminary reports on work in progress; and Basic Radio Propagation Predictions provides data for determining

the best frequencies to use for radio communications throughout the world. There are also five series of nonperiodical puolications: Monographs, Applied Mathematics Series, Handbooks, Miscellaneous Publications,

and Technical Notes. A complete listing of the Bureau's publications can be found in National Bureau of Standards Circular 460, Publications of the National Bureau of Standards, 1901 to June 1947 (SI. 25), and the Supplement to National Bureau of Standards Circular 460, July 1947 to June 1957 (SI. 50), and Miscellaneous Publication 240,

July 1957 to June 1960 (Includes Titles of Papers Published in Outside Journals 1950 to 1959) (S2. 25); av., il- able from the Superintendent of Documents, Government Printing Office, Washington 25, D. C.
NATIONAL BUREAU OF STANDARDS

No. 95

October 19, 1961

CHARACTERISTICS OF POINT-TO-POINT TROPOSPHERIC

PROPAGATION AND SITING CONSIDERATIONS

by

R. S. Kirby, P. L. Rice, and L. J. Maloney

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature. They are for sale by the Office of Technical Services, U. S. Department of Commerce, Washington 25, D. C.

DISTRIBUTED BY

UNITED STATES DEPARTMENT OF COMMERCE

OFFICE OF TECHNICAL SERVICES

WASHINGTON 25, D. C.

Price $2.50
TABLE OF CONTENTS

ABSTRACT

1. INTRODUCTION

BASIC TELECOMMUNICATION REQUIREMENTS

FUNDAMENTAL CONSIDERATIONS

2.

3.

4. THE SYSTEM LOSS AND TRANSMISSION LOSS

CONCEPTS

5. PROPAGATION MECHANISMS

6. METEOROLOGICAL CONDITIONS ASSOCIATED WITH

VARIOUS PROPAGATION MECHANISMS

7. LONG-TERM AND SHORT-TERM FADING

8. EVALUATING SYSTEM PERFORMANCE

9. BASIC SITING REQUIREMENTS

10. PRELIMINARY PLANNING AND MAP STUDIES

10. 1 Evaluation of the Parameters Affecting Site

Choice

a. Path Length

b. Antenna Height

c. Vegetation and Obstructions

d. Mutual Interference and Radiation Hazards

e. Site Area

f. Signal Takeoff Angle (Horizon Angle)

g. Distance to Radio Horizon

h. Terrain Clearance

i. Effect of Layers and Ducts

10. 2 Great-Circle and Rhumb-Line Computations

10. 3 Plotting Profiles

PAGE

1

2

5

11

13

22

26

38

53

58

59

59

60

60

60

61

61

63

65

67

67

73
PAGE

SPECIAL CONSIDERATIONS 77

11. 1 Site Availability 77

11.2 Site Development and Logistic Support 78

11.3 Vulnerability 78

11.4 Electromagnetic Wave Radiation Hazards 78

a. Biological Hazards 79

b. Physical Effects 85

c. Ionizing Radiation 87

THE SITE SELECTION TEAM 87

12. 1 Makeup of the Team 88

12. 2 Equipment 88

a. Essential Items 89

b. Desirable, But Less Essential Items 89

REFERENCES 90

APPENDIX 1 - Formulas for Fresnel Zone Calculations 1. 1 APPENDIX 2 - Earth Profiles 2. 1 APPENDIX 3 - Conversion Factors and Constants 3. 1
CHARACTERISTICS OF POINT-TO-POINT TROPOSPHERIC

PROPAGATION AND SITING CONSIDERATIONS

by

R. S. Kirby, P. L. Rice, and L. J. Maloney

1. INTRODUCTION

Since World War II there has been a tremendous developmen and expansion of telecommunication facilities in the frequency range above 100 Mc/ s. This has come about primarily because of the vast increase m the total amount of communications required and the need for high reliability. Particularly at these frequencies, the characteristics of the atmosphere and terrain affect the propagation of radio waves. The presence of the troposphere manifests itself in

many ways. One of its more important characteristics is the mech- anism which causes more efficient radio wave propagation than can be accounted for by diffraction alone. There have been several

different theories put forth to explain this phenomenon (all of which involve the troposphere, and in some instances the stratosphere as well) and the effect of the variations in atmospheric refractive index

upon the propagation of electromagnetic waves. Layers and ducts which are characterized by horizontally homogeneous discontinuities m the vertical gradient of refractive index, influence line-of-sight paths as well as non-line-of-sight paths. Regular fading as well as prolonged space-wave fadeouts are associated with these atmos- pheric conditions.

Interference to a communications system may occur as a result of favorable propagation from a remotely located transmitter operated on the same or on adjacent frequencies. Such long distance transmissions are associated with lower than average trans- mission loss for the propagation path between the undesired trans- mitting antenna and the desired receiving antenna. This is an important consideration when it is necessary to specify the service

of one facility in the presence of possible interference from another

tacility on the same or on closely adjacent channels.
-2-

2. BASIC TELECOMMUNICATION REQUIREMENTS

A typical radio communication circuit is required to perform

a function. Usually this function involves the transmission of informi ation from one location to another. The measurement of how well

! the circuit performs involves both the volume of information that can

' be transmitted during a given period of time as well as its accuracy

in faithfully reproducing at the output the same information that was

inserted at the input. The information can be of various forms,

either digital or analog.

Figure 1 shows a concept of a communication circuit with

one propagation path. The original message is inserted in the transmitter system where it becomes part of the modulation of an RF

electromagnetic wave radiated from the transmitting antenna. The

receiving antenna picks up only an infinitesimal amount of the power

radiated as well as unwanted radiations from many "f^"^

sources. The ratio of the power input to the terminals of the transmitting antenna to the resulting signal power available at the receiving antenna is known as system loss.

Transmission loss is less than system loss by the amount

of the antenna losses. Antenna losses are usually negligible for

antennas designed for use above 100 Mc/ s; an exception is the

uni-directional rhombic antenna. Basic transmission loss, sometimes called path loss, is the transmission loss that would exist

between isotropic antennas. The receiver itself contributes some

thermal noise. At the receiver output the signal carrying the

desired information must be of sufficient power relative to all of the

unwanted signals and noise combined to provide for a sufficiently

faithful reproduction of the original message. It can be seen that

there are many sources of RF interference and noise. Some are in

a sense controllable from the standpoint of adequate receiver design

and siting, and others are likely to be present in all cases. Alter

allowance for the transmission loss, sufficient transmitter power

must be used to overcome the combined effect of all of the sources

of unwanted RF power at the receiver. The fading characteristics

of transmission loss within short periods of time such as an hour

must be accounted for, and it is also necessary to estimate the

hourly median values of transmission loss likely to be exceeded for

a given percentage of the hours during the year.
r

TRANSMITTING SYSTEM

A

TRANSMITTER MODULATOR TRANSDUCER ^ MESSAGE

TO BE

/TRANSMITTED,

GE?

7

'"Keying Signal -MODULATED CARRIER OR

SIDE BANDS IN SSB SYSTEM

PROPAGATION CIRCUIT INCLUDING

& MULTIPLE TRANSMISSION PATHS

Atmosphi

Noise

TRANSMITTER

ANTENNA

RECEIVING

ANTENNA

RECEIVING SYSTEM

.A.

RECEIVED MESSAGEf

TRANSDUCER AND

DECOOING CIRCUIT ^

FREQUENCY SELECTIVE

CIRCUIT AND

DEMODULATOR

ffeceived Signal'- Original

Keying Signal* Noise and Distortions Thermal and

First Circuit Noise

FIGURE I
-4-

In planning and installing tropospheric communication

systems the engineer is faced with exacting problems in selecting

sites, choosing frequencies, and in determining what terminal

equipment is needed to accomplish the communication requirement

specified. It is important to realize the distinction between equipment performance and system performance. The latter includes

equipment performance, but it also includes the propagation

characteristics of the path. Transmission loss for nearly all

tropospheric paths is a variable. Good theoretical prediction

theories for transmission loss are of fundamental importance.

These theories should take into account the influence of irregular

terrain and of the troposphere while at the same time remaining

sufficiently tractable so as to lend themselves to engineering use. Formulas based on tropospheric propagation theories have been

developed which are useful for predicting tropospheric transmission

loss and its variability [Air Force Technical Order, 1961], Measurements of transmission loss can be used to improve such estimates

to some extent. However, there is no way to remove all of the

uncertainty concerning future levels of transmission loss that will

occur on a given transmission path. Actually in most cases the cost

of obtaining transmission loss measurements is seldom justified in

view of the period of time over which a measurement program would

have to extend in order to make a substantial improvement in the

estimate over that available from good predictions.

The concept of service probability has been found extremely

useful for formulating the various choices available to the engineer.

Section 8 explains service probability, which is the probability of

obtaining service of a given quality during a specified percentage of

the hours in a year. This concept provides an objective way to

balance the chances of success against the cost of installation and

operation. Basically, it involves taking all of the uncertainties into

account in a statistical sense and analyzing the probability of success

with various assumptions concerning the equipment and frequencies

to be used. For example, it is important to be able to consider how

much the chances of success would be improved if a higher powered

transmitter were to be used in one part of the circuit. This can be

measured directly in terms of the service probability.

Propagation factors other than transmission loss must be

considered. The improvement which can be realized with diversity
-5-

tr ans mission and reception depends on the degree of similarity in

fading occurring simultaneously on propagation paths separated by

space or frequency or with different polarizations. When wide

modulation bandwidths are used, selective fading can seriously

affect the quality of service.

3. FUNDAMENTAL CONSIDERATIONS

Before any useful prediction formula can be established,

the fundamental mechanisms of tropospheric propagation must be

thoroughly understood, and suitable propagation models must be

postulated. Even though there exists a vast amount of data showing

the attenuation experienced over almost any conceivable type of

propagation path, any attempt to develop a strictly empirical prediction method from these data alone without regard to causes and

effects of specific factors would be of little use. Quantitative predictions of scatter propagation are based largely upon theoretical

models which, on the one hand, describe the mechanism and, on the

other hand, lend themselves to mathematical treatment. Once the form of various factors is determined adequately the data become

useful in setting empirical constants.

One of the limitations that has beset various theorists in

constructing accurate models of the troposphere has been the relative difficulty of observing the atmosphere in sufficient detail at

extreme heights. Instruments in aircraft, balloons, and rockets

have provided some measurements, but the picture is far from

complete.

The amount of transmitted energy that actually arrives at

the receiver over a propagation path depends upon many factors.

One of the most important factors is the mode or combination of modes of propagation which is predominant over the path. In making

estimates of telecommunications system performance, it is impor/

tant to know what mechanism will be useful so that reliable estimates

of transmission loss and its variations can be made.

Broadly speaking, tropospheric waves are those which would not be present if there were no atmosphere, or which are

substantially modified by the presence of the atmosphere. Anomalies

in the refractive index of the atmosphere cause some radio frequency
-6-

energy to be scattered in the forward direction. Depending upon the

frequency and the path geometry, scattering can be the predominant

mode at distances in excess of the line-of-sight. Ducts and layers

! may also aid the propagation of radio energy to great distances.

I These same anomalies can also cause radio "holes" and fadeouts

| on line-of-sight paths due to the bending of the radio ray paths.

Figure 2 shows typical relationships between long-term

median basic transmission loss and distance for various frequencies.

It can be seen that at the shorter distances the ground-wave mode is

predominant, while at greater distances tropospheric scatter is the

stronger mode. Water vapor and oxygen absorption seriously limit

propagation in some bands above 10, 000 Mc/ s. Average variations

in hourly median transmission loss, V(p, 0), about the long-term

averages for tropospheric scatter are expressed in terms of time

distributions as a function of angular distance, 0. Similar long-term

hourly variations for line-of-sight tropospheric propagation are

expressed in terms of distance and the vertical angle through which

the propagation path travels from one terminal to the other. This

distribution function is termed V(p, d). The reader is referred to

another paper for a complete description of these empirical functions

and their application to prediction methods [Air Force Technical

Order, 1961 ]. The presence of ducts and layers accounts for some

of the variations observed in tropospheric scatter propagation.

These are least prevalent during winter afternoons in temperate

climates. Especially during these periods, propagation is in excellent agreement with forward scatter theory.

The weaker signals which are exceeded for large percentages

of time are important for service consideration, whereas the strong

fields which are exceeded for small percentages of time impose

interference limitations between services operating on the same or

adjacent frequencies. At present, predictions of service fields are

somewhat more accurate than those for interference fields.

For a given antenna size, higher gain and more directivity

can be realized at the higher frequencies. With parabolic antennas,

for example, the free-space gain varies approximately as 20 log f Since the gain is realized at each end, this factor offsets the increased basic transmission loss with increasing frequency. If free

space gains could be realized, the optimum frequency would always
o

00

MEDIAN BASIC TRANSMISSION LOSS FOR

THE GROUND WAVE AND TROPOSPHERIC SCATTER

MODES OF PROPAGATION OVER A SMOOTH SPHERICAL EARTH

Over Land o~ = 0.005 mhos/meter e - 15 Polarization: Horizontal

Transmitting and Receiving Antennas Both 30 Feet Above the Surface

100

i i i ii in=

Ground Wave

Tropospherlc Scatter

200 500 UOOO 2J0OO 5.000 IOjOOO 2O000

Frequency in Megacycles

SUM MM

FIGURE 2
-8-

be the highest which is in keeping with the limitations of accurate

positioning and for which antennas can be made.

The effective path antenna gain does not increase for a given antenna size as 40 log fmc in tropospheric scatter, and optimum frequencies for most scatter paths fall somewhere in the range

between 200 and 2000 Mc/s. Smaller antennas at shorter distances

usually optimize at the higher frequencies. The optimum frequency

is defined as that frequency at which a given grade of service can be

realized with minimum transmitter power. The tendency for receiver

noise figure and line losses to increase with increasing frequency

must also be taken into account in determining an optimum frequency.

As a general rule, a range of frequencies near the optimum will be

satisfactory. Figure 3 shows typical transmitter power requirements

as a function of frequency for paths over smooth earth at 150, 300,

and 500 miles. In these examples the tropospheric scatter mode is

assumed to be predominant, and the bandwidth and received signal

levels are sufficient for 24-voice channels. Parametric amplifiers

are assumed to operate at the receiver input terminals, providing

low noise figures. Figure 4 shows typical ranges of telecommunications using 10 kw transmitters for various types of information.

If the first circuit of the receiver is coupled to the actual

receiving antenna rather than to a lumped impedance of the same

resistance and reactance as that of the antenna, then the measured

value of the effective noise figure may be either larger or smaller

than the receiver noise figure as measured in the laboratory due to

the external noise picked up by the antenna. It should be noted that

a radiation resistance is not a real resistance and thus introduces

no noise into the receiver except to the extent that it absorbs noise

radiation from its surroundings. The effective noise figure of the

receiver antenna combination will be equal to the receiver noise

figure only when there are no transmission line losses and the

antenna happens to pick up the same amount of noise energy as would

be available from a resistance at room temperature.

With the exception of temperature noise, which is frequency

independent, all of the external noise decreases rapidly in intensity

with increasing radio frequency and becomes nearly negligible

above 300 Mc/ s. In an aircraft flying at high altitudes the external

noise energy from thunderstorms will be inversely proportional to

the fourth power of the radio frequency. For antennas nearer the
1

»

<=> <z> c

.. O

y

"' if—--

-j- s

3 -

3D

— 1 jIZZJ —1—1—

1

1

2)

CDcz

XJ

X)

CO

m

XIo

m

XI

Q.cr>

CDo

<m

1

<Z3 j_j | \'J

cn 1 s —

'"^K V

*, X

OJ ^

ro

Cn

(c

>3r

>v \ O CD

cm 5.*- V-j

.... sX

H

—H*11 3'

Ol

IV

~*

1

£ 1 llll

J

1

Oj

cn o?

^>

00—*l >sJ \ cn

cn ——H2 &

O O

cn

01o

—

K

T \n\1 s

3

a

T^C x]\

-N

« 1

1 1

i

3O

33

"n r\> XI -& o2 <

ro o

CD o

—i m

O o

ro 5 H

°c~n c H >o m Q

>

5

c

XJ i~ n£

2 "D H , TM £ =0 rj H m o JJ

rn T3 > XI o o 2

C XI CO CO

"0 S

m Si? i*3 3 3^

CO s< o zo m 3 o x

"0 3> "2

TJ XI H m

m > m 33 O CD 33 sH 33 o m H O ^; O X J> 33 cr o —

xi m

C 33

J> 2

m

2

i>2 o m

H CO

XI 2H

o

33 CO

J> CO 2 S Tl o

o "n H

m I XJ

CO m

>

33
, LU « > S °

(T CD -z. UJ fv < p CO

LU

U.

O CO

(/)

d z

jZ Q_ <

5^1

is

cu H—o

ro

11 o

CD <aco

o>c

eno

cu > i s Q w

,_ LU

O ^

CO UJU n Z 7 CO < — (T O Q_ X ^

ul LUX

Iu_O

Q.

>> \-Co

LZ -C o

CO •- ^w o

ro

11

-Z. o

ZJ • - c

°- "^ 2 ^ LU g Q o o < o cr => = -a 5 § Q. _ O o c en CO <o

'*_ Q>

x:

Ql

enoE< 3-

V

QOO

LU

CO

cr

LU

Q_

CO

LU

_lo><

LU

>-o

LUO

LU

cr

LO

LO

S31IIAI 31I11V1S Nl

39NVcd lAiniAllXVlAl

cro
-11-

ground the noise power will follow a slightly different frequency law

due to the frequency dependence of the propagation of the thunderstorm noise over the surface of the earth; this propagation factor

prevents all except local thunderstorms from being heard at high

frequencies and higher. Usually, cosmic noise will be of little

importance above 120 Mc/ s, and will form the lower limit to the

sensitivity of radio reception in the lower part of the very high

frequency band. The sources of this cosmic noise are not uniformly

distributed over the sky but tend to be concentrated in several regions

on the celestial sphere, the principal source being in the region

Scorpio-Sagittarius near the center of the galaxy. At frequencies

above 300 Mc/ s, black-body radiation temperature noise is usually

the principal source of noise external to the receiver. A directional

receiving antenna will absorb different amounts of temperature noise

energy as it is pointed in different directions. When receivers with

very low noise figures become available in the ultra-high frequency

band, it may turn out to be desirable to discriminate against groundreflected waves in order to reduce the received noise resulting from

the temperature of the ground. Discrimination against the groundreflected wave by means of highly directional receiving antennas has

already proved to be a valuable method on microwave relay circuits

for reducing and in some cases practically eliminating the adverse

effects of within line -of- sight fading due to the interference between

direct and ground-reflected components. Man-made noise decreases

rapidly with increasing frequency; the power in auto ignition noise

decreases with frequency at a rate somewhere between the inverse

square and the inverse cube of the frequency. By an appropriate

choice of receiving location, man-made noise may often be largely

avoided; thunderstorm and sun-spot noise are of importance only a small percentage of the time. Cosmic and temperature noise are

therefore the most important sources of external noise because they

are always present and set the ultimate limit to the sensitivity of

radio reception at very high frequencies and above [Crichlow, et al,

1955].

4. THE SYSTEM LOSS AND TRANSMISSION LOSS CONCEPTS

It has been found that the concepts of system loss and

transmission loss developed by Norton [ 1953, 1959 ] are convenient

for the analysis of system performance at all radio frequencies.

These are closely related terms differing only in that system loss
-12-

includes the effect of antenna circuit losses. For many applications,

particularly in the study of radio wave propagation, it is more convenient to have a definition which excludes antenna circuit losses

except those associated with antenna radiation resistances. This is

termed transmission loss.

The system loss of a radio circuit consisting of a transmitting antenna, receiving antenna, and the intervening propagation

medium is defined as the dimensionless ratio, P+/Pa

» where pt is

the radio frequency power input to the terminals of the transmitting

antenna and p' is the resultant radio frequency signal power available at the terminals of the receiving antenna. The system loss is

usually expressed in decibels:

l

s , 10 iog10(P;/ P;) = p; - p; db , m

This definition excludes any transmitting or receiving antenna

transmission line losses since it is considered that such losses are

readily measurable. It does include ground losses, dielectric

losses, antenna loading coil losses, terminating resistor losses in

rhombic antennas, etc. The inclusion of all of the antenna circuit

losses in the definition of system loss provides a quantity which can

always be accurately measured and which is directly applicable to

the solution of radio system design problems.

All that is required to express (1) in terms of transmission loss is to replace pl/pa with p / pa where pr

is the

radio frequency power radiated from the transmitting antenna, and

pa

is the resultant radio frequency signal power which would be

available from the receiving antenna if there were no circuit losses

other than those associated with its radiation resistance. In general,

at VHF and higher frequencies antenna circuit losses are negligible

with well designed antennas. When this is true, there is little

difference between the values of transmission and system loss.

In order to separate the effects of the transmitting and

receiving antenna gains and circuit losses from the effects of the

propagation, it is convenient to define the basic transmission loss,

L (sometimes called path loss), as the transmission loss expected
-13-

between fictitious loss -free isotropic transmitting and receiving

antennas at the same locations as the actual transmitting and receiving antennas. This serves also to define the path antenna gain, G , as the difference between L^ and the transmission loss, L,, expressed in decibels:

G = Ll - L (2)

P b

In some cases it may be quite difficult to measure the antenna circuit losses; thus it is convenient to define the path antenna

power gain, G , as pp

G = U - L (3)

pp b s

When antenna circuit losses are negligible the distinction between

G and G is not necessary, and in these cases the term is

p pp y simply called path antenna gain with the symbol G . P

5. PROPAGATION MECHANISMS

The following is a general description of various mechanisms

important to the propagation of a radio signal, such as free space

radiation, refraction, reflection from elevated layers, reflection of

radio waves by the ground and by obstacles on the ground, absorption

of energy by trees and buildings, diffraction over hills and over the

bulge of the earth, omnidirectional and forward scattering of radio

waves by the atmosphere, and the absorption of radio waves by the

atmosphere.

Terrain irregularities, climate, weather, and atmospheric

turbulence play principal roles in determining the strength and the

fading properties of a tropospheric signal. The troposphere is that

portion of the atmosphere responsible for the weather; properties

of the atmosphere from the surface well up into the stratosphere

affect the propagation of radio waves at all frequencies, but especially those frequencies above 40 Mc/ s. Estimates of transmission

loss and its long-term and short-term variability are essential to
-14-

the design and allocation of military and commercial communication

links and broadcasting and navigation facilities.

For all of the propagation mechanisms mentioned, the

effects of refraction, diffraction and absorption by trees, hills, and

man-made obstacles are often important, especially if a receiving

installation is low or is surrounded by obstacles. Absorption of

radio energy is probably the least important of these three factors

except in cases where the only path for radio energy is directly

through some building material or where a radio path extends for a long distance through trees. The following empirical relationship

for the rate of attenuation in woods has been offered by Saxton and

Lane [19 55].

A = d(0. 244 log^f - 0. 442) decibels, (f >100Mc/s) (4)

t 10 mc mc

where At is the absorption in decibels through d meters of trees

in full leaf at a frequency f megacycles per second.

mc

The situation with a high and a low antenna in which the low

antenna is located a small distance from and at a lower height than

a thick stand of trees is quite different from the situation in which

both antennas may be located in the woods. Recent studies at approximately 500 megacycles show the depression of signal strengths

below smooth earth values as a function of clearing depth, defined

as the distance from the lower antenna to the edge of the woods

[Head, I960 ]. Expressing this empirical relation in terms of a formula:

A^ = 52 - 12 log lrt d decibels, (5)

t 10 c

where A is the depression of the field strength level below smooth

earth values and d is the clearing depth in meters.

Studies made at 3000 Mc/s indicate that stone buildings and

groups of trees so dense that the sky cannot be seen through them

should be regarded as opaque objects around which diffraction takes
-15-

place. Semi-transparent obstacles causing a loss of signal of 10 db

or less include windows, tile or slate roofs, light wooden structures,

and thin screens of tree branches [McPetrie and Ford, 1946 ].

Field strengths obtained when a thick belt of leafless trees

is between transmitter and receiver are within about 6 db of those

computed assuming Fresnel diffraction over an obstacle slightly

lower than the trees. Loss through a thin screen of small trees will

rarely exceed 6 db if the transmitter can be seen through their

trunks. If sky can be seen through the trees, 15 db is the greatest

expected loss.

At 3000 Mc/ s the loss through a 23 centimeter thick dry

brick wall was 12 db and increased to 46 db when the wall was

thoroughly soaked with water. It follows that a brick building should

be treated as an opaque obstacle. 1. 5 db loss through a dry sash

window, and 3 db loss through a wet one were usual values. The

only objects encountered which showed a loss of less than 10 db at

3000 Mc/ s were thin screens of leafless branches, the trunk of a

single tree at a distance exceeding 100 feet, wood-framed windows,

tile or slate roofs, and the sides of light wooden huts. Horizontal

polarization provides a stronger signal than vertical polarization

just outside the shadow of a diffracting obstacle; the opposite is

true within the shadow. In general, for distances within optical

range, it is better to assume a plane earth rather than a curved

earth.

Studies at the National Bureau of Standards show that the

reflecting and diffracting effects of man-made structures predominate over actual absorption of energy in the materials. The interference effects of reflections from various parts of a wall will result

in large variations of field strength over short distances. Deviations

on the order of 20 db at 20 Gc/ s and 8 db at 5 to 10 Gc/ s are not

uncommon for antenna movements of a few inches and normal incidence of radio waves on a wall. Wall losses generally increase as

the angle of incidence increases; for example, at 60 degrees from

the normal the signal power loss may be from a few db to as much

as 10 to 15 db greater than the corresponding loss through a wall at

normal incidence, depending on frequency and the portion of the wall

which is directly in the path of the antennas.
-16-

To make clearer the interrelationships between various

propagation mechanisms and the conditions under which each is

dominant, let us consider the propagation paths illustrated in Fig. 5. Figure 5a shows a great circle path terrain profile under conditions

of normal refraction of radio waves in the troposphere. The height

of mountains and trees and the size of man-made features are considerably exaggerated for the amount of earth curvature illustrated

in the figure. The heavy dashed curves in Fig. 5a represent radio

horizon rays, curving downward because the average refractive

index of the troposphere normally decreases with height. The

horizon ray is drawn to clear the treetops rather than the mountain

top on the right-hand side of the figure, but with sparse tree coverage

or frequencies lower than 100 Mc/ s, the radio waves might not "see"

the trees.

The legend below Fig. 5a lists the propagation mechanisms

probably dominant over each of the transmission paths illustrated.

Between the ship at S and the plane at P1

, almost overhead, the

most important mechanism for propagation is radiation of energy

from the transmitting antenna into what may be considered "free

space" as if it were a vacuum containing only the transmitter and

receiver. The basic transmission loss, L ,, between isotropic

antennas in free space can be expressed as follows:

= 10 lo«lo(3r) = 36 - 581 + 2 ° lo«10fmc

+ 20 ^IC"

= 32.446 + 20 log, f + 20 1og,„d, decibels, (6) 10 mc 10 km

where d . and d, denote the distance between antennas expressed

in statute miles and kilometers, respectively, X. is the free space

radio wavelength, and f is the radio frequency in megacycles per

second.

The attenuation with distance of the free -space fields

results from the propagation of a fixed amount of energy through

spheres of larger and larger radius. The frequency dependence in

(6) reflects the decrease in the effective absorbing area of a receiving antenna as the frequency is increased.
PROPAGATION UNDER CONDITIONS OF NORMAL REFRACTION

Probably dominant mechanisms over each path ore : S-P. ; Free -space radiation.

P.-R,

S-P2 R-G

Vector addition of free-space and ground -reflected radio waves.

Knife-edge diffraction.

S-G ; Diffraction for distances less than 80 miles, forward scatter for greater distances.

PROPAGATION IN THE PRESENCE OF A GROUND-BASED DUCT AND AN ELEVATED LAYER

S-P, ; Free -space radiation S-P2 P-P I ' 2

P2-G

S-G

P-G

Leakage through the top of the duct, weak signals further atten- uated by reflection from the layer; somewhal affected by ground

reflection, especially S - Pz Vector addition of free-space and ground -reflected radio waves,

slighty affected by the presence of the layer.

Strong ducting signals.

FIGURE 5
-18-

When low gain antennas are used, as on aircraft, the frequency dependence indicates that the service range for UHF equipment

can be made equal to that in the VHF band only by using additional

power in direct proportion to the square of the frequency. Fixed

point-to-point communication links usually employ high-gain antennas at each terminal, and for a given antenna size, more gain

is realized at UHF than at VHF, thus more than compensating for

the additional loss at UHF indicated in (6). Where propagation is

not through free space, an additional advantage may sometimes be

gained for UHF by the use of diversity systems.

The effects of energy reflected from the ground sometimes

modify the above conclusions. Communication between terminals

located within radio line-of-sight of each other usually may be

considered to depend upon the reception of a signal composed of a

direct and a ground-reflected component added with the appropriate

phases. From the plane at P2 to the ground antenna at G in

Fig. 5a, the vector addition of free-space and ground-reflected

radio waves assumes a single ray reflected from a smooth plane or convex surface and obeying the laws of geometrical optics. The

path Pj - P2 , between the two airplanes, which might instead be

very high ground-based terminals, involves reflection from irregular

terrain. Supplements XIX and XXI of NBS Technical Note 26

[Herbstreit, 1959 ] discuss this problem and show results obtained

by adding a Rayleigh-distributed, ground-reflected wave to the

free space wave. A study of ground reflection coefficients by

McGavin and Maloney [ 1959 ] is also helpful in this connection.

Received signals in such a case will under most conditions vary

from 5 or 6 decibels above the free -space value to 20 decibels or more below that value.

The addition of direct and ground-reflected components

presupposes that the direct ray path clears obstacles between the

antennas enough so that any reflected ray path is at least a halfwavelength longer than the direct ray path. Although not illustrated

in Fig. 5, reflection from hillsides or obstacles off the great circle

path between the antennas often contributes a significant amount to

the received signal. For transmission just beyond the horizon, it may be desirable to discriminate against such off-path reflections

to reduce multipath fading problems. In other cases, antenna beams

may be directed away from the great circle path in order to increase

the signal level by taking advantage of off-path reflection or knifeedge diffraction.
-19-

Whenever we are not in free space, the basic transmission

loss L^ is the basic transmission loss in free space as given by (6)

plus an attenuation, A, in decibels relative to this free space value:

S = \t + A (7)

For instance, attenuation relative to free space for a signal composed of a direct wave component and a single ground-reflected

component is

A = -10 logB lrt 10

1 + (DR)

2

- 2 DR cos (9-c)

where D is a coefficient allowing for the divergence of energyreflected from a convex surface, R and c are the magnitude and

phase of the ground reflection coefficient, and is the geometric

path length difference between direct and ground-reflected rays,

expressed in fractions of a wavelength times 360 degrees or 2tt radians. The product DR is always less than or equal to unity.

Convenient formulas for as well as exact expressions can be

found in another paper [Air Force Technical Order, 1961 ]. Both

R and c are functions of the frequency f and the grazing angle

4< for the reflected ray.

Equation (8) is written so that A, the attenuation relative

to free space expressed in decibels, will be positive for transmission losses exceeding the free space value given by (6). When

the phase of the direct and ground-reflected waves is such that

cos (9 - c) is negative, A is negative, and the expected transmission loss is less than the free space loss.

As the height gradient of refractive index changes with

time, the horizon rays shown in Fig. 5a will bend less or more than

normal. With a gradient increase, for instance, ray bending will

increase. If a radio ray from Px to P2 passes near the large

mountain near G, the Fresnel-Kirchhoff knife-edge diffraction

theory, either beyond line-of-sight or just within line-of-sight, may

provide good estimates of the transmission loss between the airplanes
-20-

or any elevated terminals. Knife-edge diffraction is expected to be

dominant over the paths S-P2 and Pj -G in Fig. 5a. Over a smoother terrain profile the mechanism of propagation would still

be diffraction, with transmission loss increasing more rapidly with

distance than is the case for diffraction over a single knife-edge.

When antennas are just within line -of -sight of each other,

propagation is often troubled with a high percentage of "space -wave

fadeouts" originally defined to exist whenever a signal stays at

least 5 db below its monthly median value for more than a minute

[Bean, 1954].

Space -wave fadeouts may result from defocusing of radio

energy in some regions of space (radio holes), accompanied by a focusing effect and signal enhancement in other regions [ Doherty,

1952], or phase interference phenomena associated with slowly

varying refractive index profiles. In temperate continental climates,

space -wave fadeouts are likely to occur primarily at night and most

frequently during the summer months. These fadeouts are more

frequent at UHF than at VHF, and their occurrence can be correlated

with the occurrence of ground-modified refractive index profiles

[Bar sis and Johnson, 1961 ].

Prediction formulas are most useful for long surface-tosurface links such as the path S-G in Fig. 5a [Air Force Technical

Order, 1961; Barsis, Norton, Rice, and Elder [1961]. Usually,

diffraction or forward scatter are the dominant propagation mechanisms for more than half of any long period of time, so the associated theories are used to predict long term medians. Even where

well-developed stratification of the atmosphere results in a considerable amount of energy being propagated by means of reflection

from elevated layers more than half the time, a "forward scatter"

theory gives good predictions. A discussion of layer theory [Friis,

Crawford, and Hogg, 1957] includes one special case of great

interest for any comparison of tropospheric forward scatter and

reflection theories. For this case, attenuation relative to free space

is

A = K+ 10 log f^\ , (9)
-21-

where K depends upon the characteristics of the layer, d is the

path distance, ijj is the grazing angle (at the layer), and X. is the

free space radio wavelength. The distance dependence in (9)

arises from the fact that a layer of a given size subtends small

angles at the greater distances; the frequency dependence is significant as being the same as that confirmed by the work of Norton,

Rice, and Vogler [1955] comparing radio transmission loss data

with theories of tropospheric forward scatter.

Sometimes no distinction can be made between "forward

scatter" from the turbulent atmosphere and the addition of "incoherent reflections" from patchy elevated layers. In either case,

what is desired is a statistical description corresponding to average

characteristics observed for a great many paths over long periods

of time; methods for predicting such averages derived from either

type of theory would be quite similar. It is natural to turn to a layer theory for the prediction of transmission loss if detailed information about expected layer heights and intensities is available.

See Smyth and Trolese [1947] or Josephson and Eklund [1958].

Tracing radio rays through the atmosphere is essential in

order to predict the transmission loss associated with most of the

propagation mechanisms mentioned so far. Refraction or bending

which exceeds the "normal" bending illustrated in Fig. 5a is

called super-refraction and in the limit becomes ducting. Within

a duct, which may be either elevated or ground-based, ray tracing

is generally pointless (and improper ) for angles of elevation above

the horizon which are less than a certain critical value, below which

the duct acts as a waveguide and traps energy associated with

frequencies above a certain critical frequency. Ducts are efficient

propagators at UHF and above, as commonly occurring duct heights

are large compared to the shorter wavelengths. Elevated layers,

on the other hand, are more efficient propagators at VHF than at

higher frequencies, because the layer thickness which represents

a sharp discontinuity of refractive index when wavelengths are large

is a relatively gradual change of refractive index with height for

propagation at the shorter wavelengths.

Ducts and elevated layers are not necessarily associated

with each other, but for convenience, Fig. 5b has been drawn to

illustrate propagation in the presence of a very thick ground-based
-22-

duct extending all the way up to an elevated layer. Propagation from

S to P1 is still mainly free -space radiation because the wave is

launched with a large angle of elevation above the horizon. Some

energy will leak through the duct from S to P2 and from P1 to P2 at any frequency; the path from Px to P2 may in some instances

correspond to the phenomenon of the "radio hole". The path P2 to G should be slightly affected by the presence of the layer,

especially at the lower tropospheric frequencies, but will probably

be unaffected by the presence of the duct, again because of the high

"take-off angle" of the radio energy. The paths S to G and Pj

to G illustrate the conditions for strong ducting signals at any

tropospheric frequency. Since the duct is shown to extend to an

unusually great height, the associated radio transmission loss will

be less than that in free space for these two paths.

6. METEOROLOGICAL CONDITIONS ASSOCIATED WITH

VARIOUS PROPAGATION MECHANISMS

Super -refraction sufficient to result in duct propagation is

produced (a) by a pronounced decrease of moisture with height

(moisture lapse), or (b) by a pronounced increase in temperature

with height (temperature inversion), and (c) particularly, by a combination of both of the above conditions. Of the meteorological

conditions conducive to guided propagation or trapping the most

outstanding are: (1) Over sea: flow of warm dry air over colder

water producing temperature inversions and evaporation into the

lowest layers; (2) Over land: nocturnal cooling of ground with clear

skies, calm air, or light winds (if moisture distribution is favorable);

(3) Over both sea and land: low level subsidence. Conditions in the

barometric high, including calm clear skies and especially low level

subsidence or sinking of an air mass, favor trapping (especially

during the night) but do not necessarily produce it. Conditions in the

barometric low, including strong winds, intense turbulence in the

lowest layers, and overcast skies are conducive to standard propagation.

As illustrated in Fig. 5b, when a transmitter is within a

duct, radar range is increased for surface targets such as ships

and aircraft flying in the duct. At the same time there is an increase in fixed echo strength of radar signals, and consequently in
-23-

ground clutter on radar scopes. This may be accompanied by a change in the range of detection for craft flying above the duct.

When the transmitter is outside the duct, the range may either be

increased or decreased from its standard value. Effects of nonstandard propagation are negligible when the angle of elevation of a target is over 1 . Guided propagation occurs almost exclusively

in the lowest 2, 000 feet above the ground and usually is confined

to the lowest few hundred feet, except in warm climates.

Standard propagation as illustrated in Fig. 5a results in a

slight downward bending of radio rays throughout the atmosphere,

so that the radio horizon is slightly farther than the geometrical

horizon. This is taken into account operationally by using coverage

diagrams with an earth's radius slightly greater than the true value;

on a diagram modified in this way radio rays appear as straight

lines. One of the objects of presenting this same terrain profile in

two different atmospheres in Fig. 5 was to show that the same propagation path can at different times represent line-of-sight, just

beyond the horizon, and far beyond the horizon propagation conditions,

and that the mechanisms important in these cases are different.

Interference between direct rays and rays reflected from

the ground gives rise to a lobe structure in the vertical cross section

of coverage, the position of which depends on the wavelength, the

height of antennas above the ground, and the refraction of the radio

waves. When a duct is present, the upper part of a diagram corresponding to reflection at high angles is unaffected by super-refraction.

Fig. 6 illustrates this phenomenon. It should be noted that space

wave fadeouts [Bean, 1954] weaken the signal normally corresponding to low angles of reflection by the ground but strengthen the signal

just beyond the radio horizon of an antenna.

Turbulence of the air has a distinct normalizing effect,

tending to smooth out the temperature and moisture variations

which are conducive to super-refraction and the formation of layers.

Moderate to strong winds produce a turbulent layer extending normally to a height of about 4, 000 feet. The air is well mixed within

this layer and consequently the standard type of refraction prevails.

Regions of a barometric low are characterized by strong to moderate

winds and pronounced turbulence in the lower layers. In addition,

low pressure areas usually have overcast skies; hence, a barometric
Q>o

Q.V

-O

C>O

10E 3 k. o 1 1 1 o

oc o

UJ t/> >-l— X 0) o

a.CO >o5

a>o o c 2 -o

a>

V) h- <v a>w < o Q.

0>

Q a> cr 'ttf .e < *- Q 1 o z c * < 3 a> 1— o 3

CO D1 "O VD zo C

a>o a> z o a>

k.3 o C7> < o u. z o

Q. 3

to z

</> x: ir Q>Q) UJ k. k. i- H— o

t- c < H—

o: o </> UJ c oc O o O* z +; '</) UJ

T3 UJ O o

u. k.

k. tr O "to U) ^— i- o>

_>» z "53

a> to x: 3C3

(AQ>U>Co
-25-

low will as a rule lead to propagation of the standard type illustrated

in Fig. 5a. It should be mentioned in passing that clouds and rain

storms will scatter and reflect radio energy in a different way than

the ordinary turbulence of the atmosphere scatters the radio energy.

Dutton [ 1961 ] discusses the synoptic climatology of duct

formations and shows how to trace rays through the atmosphere

under all sorts of super -refractive conditions which occur in

practice as well as under standard conditions. It appears that

elevated ducts would rarely trap energy from ground-based antennas

but that ground based ducts are of greatest importance to a study of

long distance tropospheric propagation.

The geometrical ray-optics theory is usually used to

estimate coverage by ray tracing techniques. This theory usually

assumes a relatively simple model for the decay of the radio refractive index with height above the earth, or possibly an airless

earth, and proceeds to the general solution of Maxwell's equations.

Just beyond the radio horizon of a transmitting antenna, the observed

radio fields result from diffraction over ridges, hills, or the bulge

of the earth. At one extreme is the case of diffraction over obstacles

so high and so isolated that a knife-edge diffraction theory gives

theoretical results which agree well with observations. At the other

extreme is diffraction over a smooth spherical earth. This condition

results in low field strengths which are soon exceeded, as one progresses beyond the horizon of an antenna, by radio fields produced

by reflection from elevated layers or by forward scatter radio waves.

Tropospheric forward scatter becomes a useful propagation mechanism for distances between roughly 100 and 1, 000 miles

and for frequencies between 40 and 10, 000 megacycles per second

when advantage is taken of recent developments of high power transmitters and high gain antennas suitable for use at these frequencies.

Our atmosphere even in its quietest state is turbulent, and

the refractive index of any small volume of air will fluctuate

measurably with time from its average value. If variations in time

are strongly correlated at points widely separated in space, the

"scale of turbulence" of the atmosphere is large, and "blobs" of

the medium behave as large obstacles in the path of the radio wave,

scattering energy primarily forward.
-26-

A small obstacle in the path of a radio wave scatters radio

energy equally in all directions. This is called Rayleigh scattering,

after Lord Rayleigh, who deduced that the amount of such scattered

energy is proportional to the fourth power of the frequency; with

this kind of scattering, blue light is scattered about 10 times as

efficiently as red light. Rayleigh scattering of radio waves results

from very small inhomogeneities in the refractive index structure

of the atmosphere as well as from such obstacles as raindrops.

7. LONG-TERM AND SHORT-TERM FADING

In temperate latitudes the seasonal variation of forward

scatter signals shows a minimum during the winter and the diurnal

trend has its minimum in the afternoon. These minima are on the

order of 10 decibels below the annual median value, except that

diurnal trends are less pronounced at great distances. Since the

signal level depends to some extent on atmospheric refraction, the

median signal level in low latitudes is usually higher. Long-term

variations are caused by slow variations in the propagation medium,

such as changes in the intensity of turbulence in the troposphere or stratosphere, varying stratification of the atmosphere, and changes

in average refraction conditions.

Short-term variability of radio signals is generally attributed

to phase interference among simultaneously occurring modes of

propagation; that is, to multipath effects. Recent work has indicated

that fading rates within radio line-of-sight are largely independent

of frequency but depend upon the number of atmospheric inhomogeneities or "blobs" that cross the propagation path each minute.

Beyond radio line-of-sight, fading rate tends to increase with frequency and depends, in a complex manner, on the relative importance

of various propagation mechanisms and on the state of the atmosphere.

Sometimes it is convenient to consider received VHF and

UHF fields as consisting essentially of two components; one has a slowly varying amplitude and results from some mechanism such

as ground wave propagation within the horizon, or diffraction

accompanied by ducting, or reflection from elevated layers in propagation beyond the horizon. Another component has a rapidly

fluctuating amplitude and results from atmospheric scattering.
-27-

Typical observed long-term and short-term fading characteristics can be seen from the results of a 17-day recording over an

803-km (509-mile) propagation path in the Pacific. Continuous propagation measurements were made using 409. 9 Mc/ s and 8. 6-meter

(28-foot) parabolic dishes during the period April 2-18, 1959. Fig. 7

shows a profile of this propagation path. The primary characteristics of this profile are the high elevation of one terminal and the

mountain obstruction at the horizon of the other terminal. Fig. 8

shows a two and one -half minute sample of the recorded transmission

loss on a slow-speed graphic recorder, together with a 9 -second

sample on a high-speed recorder. The fine detail in the latter

sample does not appear in the other recording because of its onesecond time constant. The time constant for the high-speed recorder

is on the order of 0. 01 seconds.

This example demonstrates the large range of values of

transmission loss which occur during short periods of time on

tropospheric scatter paths. Diversity reception is useful in overcoming much of this fading because the short-term fading at each

of the diversity antennas is relatively independent of the others, and

the received intelligence benefits from the receiver's ability to

select the highest signal.

In order to evaluate long-term time variations it is convenient to consider the hourly median transmission loss. This level of

transmission loss is exceeded for a total of one half of a given hour,

and the instantaneous values of transmission loss are less than the

hourly median for one half of the hour. A distribution of the hourly

medians gives a measure of the long-term time variations. In

Fig. 9 the hourly medians are shown by time of day for all 17 days

of measurement. Also shown are hourly variations in atmospheric

refractivity observed near the surface at the receiver site. It has

been found that long-term variations in transmission loss expressed

in terms of monthly or even weekly medians are well correlated with

similar medians of surface refractivity. Medians for periods less

than a week do not correlate well.

In predicting the performance of a tropospheric-scatter

communication circuit, we are primarily concerned with determining

the maximum hourly median values of basic transmission loss that

are likely to occur during a year or more of operation. The minimum values of transmission loss are not particularly important for
SU3131AI Nl N0I1VA3~I3

UJQ< , ^ 1-

UJ

-z. UJ Ul no UJ 00 GO —

CO UJ <

aaivM V3S

UJ <X om<

or 2 CO <

h- CL 1- ^ rr or

<r

UJ

u

hiii '> Ul S

lh <0 _i 3 on <. CO o < CO<

Q_ Ul O ^ ^

or< <

Ll CO O Ul

O

h- ^

hi <1 > 0>

nS U. \- o O co <d- or Ul n

>-

T o o UJ T =) ^

CJ

UJ

CL or

U. o o

c>OCD

co

Z>Q<

cr r^

CO UJ X

hcr

crO < u. UJ

UJ>

Sd313IAI Nl N0I1VA313
BASIC TRANSMISSION LOSS, db

CDC

jom

Mi

F—

^

M

L-_

BASIC TRANSMISSION LOSS, db

-— no ro ro

m

o

> o

T> :o

Z) o

I- m

o 00 O O H

CD 33

<£> OJ > en z <X> ^" 00

**

=< <:

f\5 T) CO > CO

->j

-fc ^o_ -z. T3d -fc. 1- o o 1 CD CO o CO CO n

> £ <

i- ° >

-i aj m

>

-Io

CO
DIURNAL VARIATIONS OF MEASURED DATA

APRIL 2-18, 1959

366 HOURS

d =806.3 km; = 89mr ; 8.6m PARABOLIC ANTENNAS

140

co 150 CO

O

o

CO

CO

CO

<

GC

160

170

190

330

• • H

•

i

1 Durly Me dians of Transmi ssion Lo 5S

•

•

•

•

•

•

•

•

•

•

• •

• •

* •

• . * • •

•• •

• •

•

•

. r-^U-

• •

• •

• :. r

• •

• i

:

'

:

• •

• •

•

•

•

•

"1—5

! ' : ":

1

i

!

'

i >

: • **

• • •

• * •

• •

• • •

:• • :

• i •

• 1" J J

:

:

• • • . .

• v :

!

i- r • •

• • : •

i [ :

* • ••

• • •

• . •

• •

• •

m

Hourly Surface Refractivity

3 6 AM

9 NOON 3

HOUR OF THE DAY

6 9 12 PM

FIGURE 9
-31-

service considerations, but they are important in evaluating interference characteristics.

Prior to making the measurements shown in Figs. 8 and 9,

an estimate of the distribution of hourly median basic transmission

loss was made using a prediction method developed by Rice, Longley,

and Norton, [ 1959 ]. Fig. 10 shows this predicted distribution together with the limits of probable error and the 90% confidence

bands. These bands can be interpreted in terms of the probability

that for a given number of similar predictions the indicated percentage of observed distributions will fall within these limits. For

example, only one out of ten observations would be expected to fall

outside of the 90% range between the 5% and 95% bands. Approximately 50% would fall within the probable error bands. It can be

seen that the measurements during the 17 -day period were in

excellent agreement with the prediction at levels of transmission

loss exceeding the median.

It is quite probable that the low values of transmission loss

associated with high fields are influenced by modes of propagation

other than scatter. Even though the path is extremely long, ducts

of this extent occur in the tropical maritime areas quite frequently.

The example chosen for Fig. 10 illustrates the fact that at present

it is possible to predict service fields with greater accuracy than

interference fields.

Over line -of-sight and knife-edge diffraction paths an

entirely different fading characteristic has been found to occur.

During periods of layering and ducting in the atmosphere these

propagation paths show a tendency to go into relatively deep fades

with long durations extending from periods of less than a minute to

an hour or more. During periods of uniform refractive -index lapse

rates these fades are much less intense or do not exist, or sometimes those that do exist are caused by multipath reflections which

arrive in such a phase and amplitude relationship that a slight change

in the lapse rate will cause a large change in the resultant field.

The latter type can be overcome in most instances by either relocating the terminal antennas or by the use of space diversity. The

fading characteristics associated with atmospheric discontinuities

such as ducts and layers have been termed space-wave fadeouts.

Ordinary space diversity does not appear to be helpful in overcoming
MEASURED AND EXPECTED DISTRIBUTION

OF HOURLY MEDIAN TRANSMISSION LOSS

All Hourly Medians

d = 806.3km; = 89 mil liradians

8.6m parabolic antennas

co

o

UJo

CO

COO

CO

CO

CO<

a:

130

140

150

160

170

180

190

200

210

> X

^Arfeasuretf/VOnsmissicin lo 55

J^nvfsofp

x^

S^-v.^

^^-. ~^1

95%I //>77//

5>A —

-

— . ._ =5=^ ^=;; rr— -- -— __

---. -^^

—~-—--^__

0.1 10 20 30 40 50 60 70 8( PERCENT OF HOURS

90 95 99 99.9

FIGURE 10
-33-

this type of fading, although there are indications that extremely

wide spacing, particularly with different heights, may be effective.

For convenience in analysis procedures a space -wave fadeout is

defined for line-of-sight and knife-edge diffraction paths to be any

fade in which the signal level drops more than 5 db below the monthly

median for a period in excess of one minute.

Space -wave fadeouts are more predominant in the UHF

band than in the VHF band. They are also much more predominant

in geographic areas where layers and ducts occur frequently. The

atmosphere along the southwest coast of the United States exhibits

persistent layering, and line-of-sight paths in this area are characterized by a large incidence of fadeouts even in the 100 Mc/s range.

One example of the frequency dependence of space -wave

fadeouts over knife-edge diffraction paths can be seen in a comparison of the results of two different circuits in Alaska. Dickson, et

al [ 1953] analyzed a 30-day period of measurements from Yakutat

to Gustavus, Alaska, over Mt. Fairweather and found that the transmission loss during this entire period varied from its mean value

by less than ± 2 db. These measurements were made at 38 Mc/ s. Later one of the White Alice tropospheric circuits was installed over

almost the identical path. This circuit used 900 Mc/ s. Recordings

of transmission loss obtained at this frequency show a high incidence

of deep fading, many fades exceeding 20 db below the median level.

An example of this type of fading on a 223-km path over a knife-edge type obstacle in Colorado is shown in Fig. 11. In this

test a 751 Mc/s signal was transmitted directly over Pike's Peak,

which was visible from either terminal. Insofar as the peak acts as

a knife edge, Fresnel-Kirchhoff diffraction formulas can be used to

estimate the transmission loss. An estimate of basic transmission

loss based on a simple, one-ray solution gives a value of L^ = 179 db.

Actually, there are probably some ground-reflected rays involved

which modify the single-ray analysis. The ground is extremely

rough, making a rigorous analysis of its effect very difficult. The

median value of basic transmission loss for the period of the example was found to be 189. 4 db for an antenna at an elevation of

17. 4 meters (57 feet) above ground and 198. 7 db for an antenna at

8. 2 meters (27 feet) above ground. Some of the additional loss may

be attributed to the fact that the top of the peak is not a true knife
PROPAGATION BY KNIFE EDGE DIFFRACTION

AT 751 Mc/s

TRANSMITTER POWER 500 WATTS

TRANSMITTING ANTENNA 4.3 m. DISH Gt=26.7db, Ht =7m.

RECEIVING ANTENNAS (I) CORNER REFLECTOR Gr =l3.9db, H r = 17.4m.

(2) 3.3m. DISH Gr =23.6db, H r =8.2m.

RECORDINGS MADE 0000-0200 JUNE 23,1960

CORNER REFLECTOR

o

3.3 METER DISH

0145 0130 0115 0100 0045 MOUNTAIN STANDARD TIME

0030 0015

Figure II
-35-

edge, but is actually curved both along and normal to the path of

propagation.

A point of interest in the data shown on Fig. 11 is the

relatively frequent occurrence of deep and prolonged fadeouts.

These are believed to be similar to the space-wave fadeouts on

line-of-sight paths which are associated with the occurrence of

non-linear refractive index profiles in the atmosphere [Bean, 1954;

Bar sis and Johnson, 1961]. A radiosonde observation, Fig. 12,

obtained from Stapleton Field in Denver, Colorado, during the

period 0430 - 0500 MST on 23 June shows the presence of a weak

layer. This sounding was obtained considerably off the propagation

path and there may have been more pronounced layering nearer the

mountains. The data obtained from this sounding are plotted in

refractivity units versus altitude in Fig. 12.

Figure 13 illustrates an analysis of six hours of recording

for the 223-kilometer path which passes over Pike's Peak. The

figure shows distributions of fade duration for various depths of

fading, as well as distributions of signal duration for various levels

above the median. It should be emphasized that this period is

characterized by moderately severe fading. Other periods of

recording show little or no fading and there are some periods during

which the fading was even more severe. It can be seen from Fig. 13

that fades of fairly long duration occur frequently. The deeper fades

occur less frequently and with shorter durations than the shallow

fades. For a small percentage of the time the signal faded in excess

of 20 db below the median.

Periods of high signal level are analyzed in the same

manner as the fades. The duration and the percentage of the

recording period that signal levels exceeded the median are shown

on the right hand side of Fig. 13. The range of levels for high

fields goes only on the order of 6 db above the median compared

to 2 1 db below for the fades. The experiment from which these

data were obtained is currently underway. It is hoped to obtain

a complete year of recordings at frequencies ranging from 100 Mc/s

to 10 Gc/ s over this path using sample recording runs of one week

per month.
RADIOSONDE DATA OBTAINED AT STAPLETON FIELD, DENVER

0430-0500 MST JUNE 23, I960

aiuu

8700

8300

7900

7500

7100

6700

6300

5900

5500

5100

4700

4300 — PIK re pr n is /locI0 7m . to rLHrXj-tcJci in

3900

3500

3100

2700

2300

1900 — BELII AW qn^m — TABLE MESA, 1666m

1500 1

i

)0 1 o i;SO 1, )0 1"fO 1!)0 2 Zi10 2!J0

2"'0 2i)0 3 33 REFRACTIVITY, N

FIGURE 12
CUMULATIVE DISTRIBUTIONS OF BASIC TRANSMISSION LOSS

FADE AND SIGNAL DURATIONS FOR

KNIFE EDGE DIFFRACTION AT 751 Mc/s

DATA OBTAINED 0000-0600 MST JUNE 23, I960

DURING MODERATELY SEVERE FADING CONDITIONS

co

co

CO

O

co<

m

185

190

195

200

205

210

215

220

225

230

1

x>? > ^c^^

sV s%

0.01 0.1 I 5 10 30 50 70 90 95 99 999 9999 PERCENT OF TIME ORDINATE IS NOT EXCEEDED

CO

Id

<

o

COo

LUQ

<

trO

0.7

0.5

0.3

0.2

0.1

0.07 0.05

0.03

0.02

0.007

0.005

«fej is.

^,<?^

5.3 Tn uisr &

%

#

c^

b ~?i 5/1

h i

3 / w

% •JjL <<« / <°/ \

X «6/

b K

\%

\

\

-

__

.

f / \9?>^t>

-*% \ I

/ 1 / ^ i

\"D

ra

1 4•

\

\

1

1

1

i

i

i

1

Ml '

0.01 0.05 0.1 05 5 10 20 30 40 50 40 30 20 K) 5 0.5 0.1 Q05 001 PERCENTAGE OF TIME

TRANSMISSION LOSS EXCEEDED THE

VALUE INDICATED WITH A DURATION

EXCEEDING THE ORDINATE

PERCENTAGE OF TIME

TRANSMISSION LOSS WAS LESS

THAN THE VALUE INDICATED WITH A

DURATION EXCEEDING THE ORDINATE

FIGURE 13
-38-

8. EVALUATING SYSTEM PERFORMANCE

In order to specify what equipment is needed to carry out

the communication function and how well it is likely to perform over

a given communication circuit, (or, in the case of a system in operation, to measure its performance) it is necessary to make an analysis including all of the pertinent factors involved. We are interested

in the effects of coding, modulation, transmitter and antenna performance, propagation and noise, and receiver and terminal equipment performance. The following equation relates the power

required at the output terminals of a transmitter with the propagation

and equipment performance factors associated with a communication

circuit [Norton, 1956]:

P = U - G +L +F+B + R- 204 dbw ( 10a)

t b p t

or

R=P -U+G - L - F - B + 204 db (10b)

t b p t

In equation (10):

P is the transmitter power in decibels above one watt.

L

b

is the basic transmission loss.

G is the effective path antenna gain.

L includes transmitting antenna, transmission line

and associated losses.

F is the effective noise figure of the receiver including

transmission line and matching network losses, L , as well as the effects of receiver, cosmic, and

man-made noise.

B is 10 log 10 b, where b is the total RF or IF bandwidth in cycles per second (including the effect of
-39-

drift between transmitter and receiver oscillators).

R is the pre -detection RMS-carrier -to-RMS-noise

ratio for the bandwidth, type of modulation, and

order of diversity used, and is usually expressed

as an hourly median value.

204 is a constant equal to -10 log 10 kT, where k is

Boltzmann's constant and the reference temperature,

T, is taken to be 288 Kelvin or 60 Fahrenheit.

It is the noise power in a one -cycle bandwidth

expressed in db below one watt.

The capability of a communication circuit is usually specified in terms of the errors that occur during a given time period.

Errors can be defined in terms of the percentage of words that are

missed and teletype errors in terms of character or bit errors.

Because of their digital character, teletype errors are easier to

analyze quantitatively than analog information such as voice or facsimile. It has been found that the ratio of voice errors to teletype character errors on a typical multiplex circuit operating by

the tropospheric scatter mode is on the order of 100:1, in some cases.

One of the most difficult parameters to predict or even to

measure is the transmission loss. This includes both terms L,

and G . The Air Force Technical Order [1961] presents methods

for estimating transmission loss for all modes of propagation involved in transmitting signals through the troposphere. Over most

paths the transmission loss varies with time, and it is necessary to

estimate the maximum values that are likely to occur. This is

usually expressed in terms of hourly median values of transmission

loss likely to be exceeded for various percentages of the hours of

the year. The primary difficulty with measuring transmission loss

in order to predict performance lies in the fact that measurements

are usually made over short periods of time, and little information

can be resolved from such measurements regarding the long-term

variability. In most cases predicted rather than measured values

provide the more reliable estimates of long-term median transmission loss. Line-of-sight and knife-edge diffraction measurements can be misleading when the measurements are made under

stable atmospheric conditions. Even in areas where ducts and
-40-

layers are rare, it is important to consider the possibility of radio

holes [ Doherty, 1952] and space-wave fadeouts in estimating meximum values of transmission loss if the circuit is to be highly reliable. Estimates of the reliability of the prediction methods outlined

in the Air Force Technical Order [ 1961] are given by Barsis,

Norton, Rice, and Elder [1961].

Probably the easiest factor to determine in (10) is the line

loss, L . It can be seen, however, that it is important, particularly

in high-power transmitter installations, to use transmission line with

low loss and to carefully match impedances.

No simple tabulation of values of R, F, and B can be made;

Florman and Tary [ 1961 ] deal with this subject in great detail.

Typical values are given for these factors by Barsis, et al [ 1961 ],

but these should be considered as only state-of-the-art guide lines

and subject to change and improvement. B, F, and kT together

determine the noise power against which the signal must compete.

The pre -detection signal-to-noise ratio, R, is related to the receiver

output signal-to-noise ratio which in turn is related to the error

rate. For any telecommunication system there is a relationship

between the error rate and R which depends on many factors, including the type and manner of modulation, the characteristics of

fading, the order of diversity, and the method of combining diversity

signals.

Because there are uncertainties in the prediction of all the

values on the right hand side of (10a), particularly in predicting

L, - G , performance estimates are made in terms of statistical

probability. For this purpose the service probability concept is

defined. It is important to understand the service probability concept thoroughly. Service probability, designated F(t), is a number

between zero and unity which expresses the probability of obtaining

service of a given quality; i. e. , a certain percentage of errors or

less, during a specified percentage of the hour in a year. For

example, a service probability, F(t) = 0.95 would be interpreted

to mean that on the average 95 paths out of 100 randomly chosen

paths with the same nominal parameters would be expected to provide the specified quality of service for at least the percentage of

hours in the year indicated by p.
-41-

In order to illustrate the application of service probability

and also to demonstrate the use of a simple, approximate formula

for use in estimating transmission loss with tropospheric scatter,

the following example is used.

Let us assume that it is desired to use the Haswell to

Table Mesa, Colorado, path for a tropospheric scatter communication link. An approximate estimate of the transmission loss expected

is obtained using the prediction methods described in a recent Air

Force Technical Order [1961]. Basic transmission loss, L, , equal

to the winter afternoon tropospheric scatter component, l^mc*

can be expressed approximately as a free space loss, Ln-xf* plus a

scatter loss, A, such that L = L,

f + A, where

A = 48 + d, / 16 = 48 + d .. / 10 (11) km miles

at 100 Mc/ s with L, r given by (6). Additional loss at higher frequencies should be allowed for by adding 1 db at 600 Mc/ s, 8 db at

1000 Mc/ s, and 17 db at 5000 Mc/ s.

The use of this empirical approximation neglects effects of

terrain, meteorology, antenna height, and many other factors that

are taken into account in the refined prediction methods of Rice,

Longley, and Norton [ 1959 ], and of the Air Force Technical Order

[ 1961 ]. Fig. 21 (discussed later) shows a gross terrain effect

presented as a function of the sum of horizon elevation angles

(take-off angles, 9 ., 9 cr ) expressed in degrees, or as a function

of the angular distance 9 = 2tt(9 , + 9„_)/ 0. 360 + d/a expressed mr ct cr

in milliradians, where a is an effective earth's radius. An analysis

of the relative accuracy of the empirical estimates and the refined

estimates has been made using data from propagation paths for

which a large number of measurements are available. The variance

of observed values relative to the estimates using (11) was found to

be on the order of o- rc= 47 db whereas for the precise predictions

the variance was more on the order of cr2 = 17 db2. The effect of

rc

the variance of observed relative to predicted values is taken care of

in the process of determining the service probability, as will be

shown in this example.
-42-

It is necessary to determine first the optimum frequencyrange for this path. This can be determined on the basis of antenna

performance and equipment factors, such as line loss and noise

figure, all of which are frequency-sensitive parameters. For the

purpose of illustration we can assume an FM system with 120-voice

channels, 60-foot parabolic antennas operating with dual diversity,

and receivers with conventional RF amplifiers. Table 1 gives

values used in this analysis for application in (10a) together with an

indication of the source of the values.

Fig. 14 shows the results of this analysis plotted to show

the frequency dependence of the required power expected to provide

an acceptable grade of service for fifty per cent of the winter afternoon hours. The purpose in plotting this curve is to determine an

optimum frequency range and to estimate additional losses resulting

from the use of frequencies which may not be optimum. The optimum

frequency range using the empirical estimate of transmission loss

can be taken as 275 to 550 Mc/ s. For comparison a similar curve

is shown which is based on refined estimates of transmission loss.

The empirical estimate is somewhat more optimistic than the refined estimate in terms of transmitter power requirements. Also,

the optimum frequency range using the empirical estimates comes

out somewhat higher. A limited number of measurements over this

path at 409. 9 Mc/ s and at 1040. 1 Mc/ s indicates that both estimates

may be too optimistic.

In order to allow for prediction uncertainty it is convenient

to determine the probable error range for the estimates. This

error range has been determined from a large number of measurements made over tropospheric scatter paths. Differences between

measured and predicted values of transmission loss expressed in

decibels are approximately normally distributed with a mean of zero.

The total dispersion for this type of distribution can be expressed in

terms of a variance, <r , which is the mean of squared deviations

between estimated and observed values. This analysis shows that

the variances depend on the particular part of the distribution of

hourly median values of transmission loss for which the estimate

applies. Values of transmission loss near the median or somewhat

greater can be predicted more successfully than values at the

extremes. Since we are interested in high reliability, we are most

concerned with the variance associated with transmission loss not
-43-

Table 1

*

w >

p n H

a *1

CO o

*• H

n 2 CD o H

r+ CDn

3" * O

!* o

H> n »-•

CD o

•i P a. a CD & H d i—

N* c sO

TO o 0- H-l

CD • 4

o

c*

t o a

o

ao

b

JT>

a

o

£ ° *

£ 0- P

CO CD JT. h. Ro

•O ^

&* * ir s<s

^ p.

rt- CD <» g p N

3 &

era £ p p S a

5' 5 o

. ~^ CD o

o (exp for afte h r O > H O *1 > J- CT 3 p o •i o" 3

CD n TO i>r i a H* U

3 s S

1 ft CD i *?

K° <" 3 CD M» 3 if ft

l-H

CD h)

o. o. a G- a a

<r c 57 a* c cr

>

erec

p>4

4

I

CD

CDm

*0P

n

CD

(reP

en

Io

c

cm

M

CJ

a

H^ *— C*

1P

c

p

r+

P

D.0)o

e

cm

ts> >-• o^

h- oo a^ oo >-< >-•

oo ooo

0^0^ t\> tsJ 00o 0^ H- OO it 4^ <j o o v£> o Ul •— oo 00 o r

I— 0> H*

oo o^ oo

c^a

o

X)

ft

CD Q

C

CDn ° 2
DETERMINATION OF OPTIMUM FREQUENCY RANGE FOR

TROPOSPHERIC SCATTER COMMUNICATIONS

BETWEEN HASWELL AND TABLE MESA, COLORADO

FOR 120 VOICE CHANNELS USING DUAL DIVERSITY

60 FT DISHES AND CONVENTIONAL RF AMPLIFIERS

TRANSMITTER POWER IS VALUE EXPECTED TO PROVIDE

SERVICE FOR 50% OF THE WINTER AFTERNOON HOURS, F(t) = 0.5

2,000

o

>-o

2

LUoUJ

or

.000

700

500

300

200

USING RE ESTIMATEFINED 0F L bmsv

USING EMPIRICAL ESTIMATE (DF Lbms

20 25 30 35

TRANSMITTER POWER IN db ABOVE I WATT

40 45

FIGURE 14
-45-

exceeded for 99% or 99. 9% of the hours of the year. Barsis, Norton,

Rice, and Elder [ 1961 ] give the values of a standard deviation cr appropriate when the refined estimating procedure is used. When

the empirical estimates of transmission loss are used, the variance

cr 2 can be expected to be higher, re An analysis was made to determine how much higher the

variance should be when the empirical estimate is used. In this

analysis, a number of scatter paths for which long series of measurements were available were studied. Estimates of the distribution of

transmission loss were made using both methods. The variance for

the empirical estimates was found to be on the order of 30 db higher

than the variance using the refined estimates.

Figure 15 is a plot of the standard deviations, cr

' , associated with the percentage of hours in a year for which the estimate

applies. The values on this chart are appropriate only for estimates

made using the empirical formula and are consequently considerably

larger than the values of cr given by Barsis, Norton, Rice, and

Elder [ 1961 ]. The graph was constructed by assuming

cr 12 = <r * +30.

re reHaving selected an optimum frequency range and determined

the amount of required power expected to provide a specified grade

of service for fifty percent of the winter afternoon hours, it is now

necessary to determine the power required to provide this same

grade of service as a function of the number of hours in the entire

year. Since these will be expected power levels, the service probability remains F(t) = 0.5. In order to do this it is necessary to

know how the hourly median transmission loss is expected to vary

throughout the year relative to the winter afternoon hourly median.

This relationship has been established empirically and is expressed

in terms of a function V(p, 9), presented by Rice, Longley, and

Norton [ 1959 ], and in the Air Force Technical Order [ 1961 ]. The

expected hourly median level of basic transmission loss exceeded

for (100 - p) percent of the hours of the year is next obtained from

the V(p, 0) values appropriate for all hours in the year for the

angular distance, 9 = 34 milliradians, applicable to the HaswellTable Mesa path. See Table 2. The values from Table 2 are plotted

in Fig. 16.
o

Q.

b

II Q.

b~

o or

o-> UJ>

o<x> UJI

U.

r

o

en C3CO cc m 3

o O UJ 10 I cc _J

_l<

0)

u. or-o U.O

OC>J z

UJo

cc g> UJ

a.

S139I03Q Nl °f-0 N0I1VIA3Q QdVQNVlS
-47-

TABLE 2

Expected Long-Term Variation, V(p, 9), and Transmitter

Power Expected to Provide the Desired Grade of Service

for the Indicated Percentage of Hours Per Year

at 500 Mc/ s over the Table Mesa-Haswell Path.

Expected Power, P(0. 5, p)

= 21.7 - V(p, 9) dbw

from (10a) with P = P(0.5,p), L=:U(p)

-2.5

3.0

7.8

10. 1 13.

18. 3

22.4

24. 5

26.2

29.0

32.2

The final step in the procedure is to determine the probability of service for specific terminal equipment. Up to this point,

all the equipment characteristics except actual transmitter power

have been specified. We may wish to determine, for example, the

probability that a one -kilowatt transmitter will provide the specified

grade of service, or alternatively what the probabilities are of

obtaining other grades of service. It is now necessary to determine

a standard normal deviate, t, such that the probability of exceeding

a value, t, in a normal distribution of mean zero and standard

deviation cr = 1 will be the service probability, F(t). The values

of t associated with the time availability, p, can be found using

the following relationship for any fixed value of transmitter power,

P

t = Po

: P - P(0. 5,p) t=— (12)

<r' (P) re

Percent of Hours

During the

P

Year

V(p,9)db

0. 1 24.2

1.0 18.7

5.0

10.0

13.9

11.6

20.0 8.7

50.0 3.4

80.0 -0.7

90.0

95.0

-2.8

-4. 5

99.0 -7.3

99.9 -10. 5
o

Q

<

O_JO

o

<

UJ

_l

GO<

OCU. >=« °5

<U.

coO

CO

"*UJ

<

X

i°

XQo z

UJ«

yen O UJ > 1

ss

H

(TU.

"- CD

UJ

11VM I 3A08V qp Nl (d 'Q0)d d3M0d U3±JLIlAISNVdl Q3±03dX3
-49-

It is important to note that the only difference between this estimate

of t and the estimate of t for the refined estimates of L. is in bm

the use of or

rather than cr which allows for the additional

re re error range introduced in the empirical estimate of transmission

loss. In this example, setting PQ

= 30 dbw (1 kw), the values of

F(t) are determined from Fig. 17 as a function of t, as given by (12)

and listed in Table 3. A similar computation showing the service probability for

10 kw of transmitter power instead of 1 kw can be simply made by

adding 10 db to the values in column (3). The new set of values of

F(t) is determined in the same manner. Fig. 18 shows the final

relationship between service probability and percentage of the hours

of the year the specified grade of service or better is expected to be

available. The service probability should be interpreted to mean

that if a large number of paths of similar configuration were considered, the percentage of hours during the year, p, for which the

specified grade of service is available will vary from path to path.

The percentage of paths for which p will be greater than the value

on the ordinate of Fig. 18 is on the average 100 F(t). Another way

of stating this is that when F(t) = 0. 95 then 9 5 percent of the paths

are expected to provide the specified grade of service more than

p percent of the hours.

Figure 18 shows different methods for estimating the transmission loss expected over the path. The solid lines are based on

empirical estimates and the dashed lines are based on refined estimates of transmission loss. The solid lines are steeper because the

prediction uncertainty is greater. For significantly large values of

service probability such as F(t) = 0.95, the refined estimate indicates

greater time availability than the empirical estimate. On the average,

refined estimates for predicting service probability will provide more

certainty of service than the empirical estimates and the result will

normally be a reduction of transmitter power requirements in the

terminal equipment. Therefore, it is recommended that when it is

important to specify equipment requirements as accurately as possible, the refined estimating procedure should always be used. Empirical formulas such as (11) are most useful in making preliminary

estimates of the feasibility of propagation paths. To insure a high

probability of service from a given transmitter, F(t) may be arbitrarily chosen as 0.9 or 0.95, and sufficiently high values of P
CO <

Ll. O tO

CO

I- UJ

CD<

CDO

QCCL

LUI

\

V T

V

__j_-j__|-4—,- --- ._ ^ -. 4'r~i~f~ ~i 1 r

- y^T

\ \\

i.

1 !

i

;

; \ '

i ! L - ,

1 !

'

i i

Sj \

I \\ | jl

' \ !

,

:

, 1 -pr^ i-^- !,

'

: ~-f^~ 1

1 l

:

' ^—

i

r^:-—~ ii^-~^r~^- rr1 rh~- : i 1

' ttti H-(-

j_l—

.

1 1—

|

~- - — 1 1

; ;

I — i - -— — V - -J 1 -—

'

; 1-

. ^_ _ ___ __ __j ^_i —- — —J - .

^L\\

|\

\

i

i 'ii!

\

iN ~r \|V \

i i\

-

> [ [ 1——j

1

i >-- -,— — - — j ; , +—-—' • ; — ' I'M f-** ^ ' ' ' '

1 lJ t

1 \l

en

en

OS

en

en

en

en

lo <- UJ

[I

LOd
-51-

O

UiO

OO

m oo s i—•

ooo o Ul nO

I— I— tv OO 00 IV

IV cv

Ul tv

on s o^

Ul 00

CV o

OO

CV

00

sO

sO

OO

Ul

CV Ul

-o 1—-^J Ul OO 1—

CV Ul o ^1 o Ul 00 o CV m

vD

O rf*- i— s h- tv

CV t— I—

OOO 1o io

CV -J

—•

00 Ul

—«

cv o ^ 1—" t—•

tV oo OO o o

ooO oo 1—

Ul !—• cv OO

-X) vO 00 ~J ^J Ol OJ tv

00 Ul o vO o Ul vO ^J

~J ~J ^J *s oo 1— -0 O0 Ul

tJ^ I—I. oc4

en 3 3

0) >T3CDH > O < (D p 3 I-1 ' rt- 1—

fu

U cr

•"- H-1 ^r*

*1 !-••

H

fU 0Q 3 *o

cr • -* U- o u' • CD i—• » Ul

tV P >d Pa 3

^TM"

u

3'

t) o

II OOoa

cr 4 H+> TO o o & ° CT .Ul

-3q o1 H ^ n

*—

O

>a •Ul

>o

CTQ o .3

^3 S

CD<O

CDo

cr

crOo >

tdM

oo
co X» o«5 iQ Al ° a: o

ui ~ O

° o Q. £c?o' zt -

LTJ ui -

<-> uj 2

k q_ < UJyl Q-Lh

co ^ CO >^ H OT

UJ UJ

>- K -J h£iu

-j < 03 - W „

OQ >" j2 ^CD

UJ ^ =f Q O i= Ul

0. O O

Ul — °- o 9= x — 3 UJ > Q

CC Ul ui or co <

1

i f 1

/

t /

• s^

/ r

*

o

>

/

/'

TJ / /

/

1 /

/ /

7^~

/

< r

f // / ,

j A/1 o A 2

yy o + 2 // 1— ,— <x

o -

i b Q2

i o / >»^i '/

r /

-J cvj " < O o o >

• °<NJ-. 1- < w u" '

-1 .. D < in 2 .. b

M s O £ >

cx J^ 2 -9

>-2 — r- _1 —

UJ

a: en

«r

. v\ —r

,—

'

XI 3» tO UJ 7" °2 jj >" 1- "O "S - ED N

LO UNC §3 j

X" r 3 o -*

ro 2

ifloz (i)OZ

nO < 00 Q <l/)0

MATES

1

RANSMI5 PREDIC1 UJ CO Q 1- 2 UJ 5 or a. H

1" Q P'-Q to u_ 2 (flli- z

uj o < UJ O <

1

1

1

1

83

S3

CD<

CDo

CE

CL

UJO

>

ITUJ

00

UJ

05

OS

05

I/O 03

yV3A 3H1 JO SanOH TV 30 lN30H3d Nl 30IAU3S 30 3QVd9 Q3l3l03dS 3H1 30 ' d

l A±l~ll8\niVAV 31AII1
-53-

required to insure that the time availability, p, exceeds some high

value such as 99 or 99.9 percent.

Figure 18 shows only one method of displaying the service

probability concept. This method is most useful in comparing the

effectiveness of various proposed types of terminal equipment. For

example, the use of different transmitter power levels, antenna

sizes, diversity configurations, receiver r-f amplifiers, etc. , can

be readily compared. This type of display does not specifically

require the use of the relation between grade of service (error rate)

and input RMS-carrier -to-RMS-noise ratio, R. This relation may

just as well be defined by the user. Other useful displays can be

shown, some of which require defining the above relation and some

of which do not. For example, a slight variation in the formulation

of the solution would make it possible to show the service probability

and corresponding percentage of hours in the year for various values

of R. The estimated relationship between R and error rate given

by Barsis, Norton, Rice, and Elder [ 1961 ] can be used to show

the distribution of the expected error rate for all hours of the year

as a function of service probability. This would provide much more

detailed information regarding the performance of a single, specific

terminal configuration than would the Fig. 18 type display.

9. BASIC SITING REQUIREMENTS

Proper consideration of siting is perhaps one of the most

important factors in determining the ultimate success of the communication circuit as well as its cost. Tropospheric propagation

involves many types of mechanisms, but in this section we are primarily concerned with three basic types. These are tropospheric

scatter, line-of-sight, and obstacle gain. The latter two are similar

in that both involve relatively short paths for which the terminals,

or each terminal and obstacle, are visible to each other. This

condition is described as being intervisible. The terminals for

tropospheric scatter propagation paths are not intervisible. Site

selection requires a proper balance between choosing good sites

which fulfill technical requirements (taking advantage of natural

terrain features, avoiding sources of interference) and other considerations such as accessibility and availability of sites and logistic

support.
-54-

In most instances the concept of a tropospheric scatter

communication system begins with a requirement for multichannel

voice, teleprinters, and other types of transmission between several

specific locations. Usually the first attempt at selecting sites for

the terminal facilities is to consider as potential sites those locations

which can be seen by microwave relay or can be reached by short

runs of cable from the communication relay centers. This approach

almost invariably limits the selection of sites so severly that little or no advantage can be taken of natural terrain features, and many

high-powered terminal and relay facilities are required. When

intersiting is accomplished by short scatter circuits or, in some

instances, by obstacle diffraction paths, this siting restriction is

largely removed. The problems of site hardening and vulnerability

are also considerably alleviated in those locations where such considerations are important.

There are many disadvantages to selecting sites in remote

locations. These result almost entirely from consideration of

logistics and site development, including access. High mountain

tops make the most ideal sites for tropospheric scatter terminals

when they are available, insofar as efficient propagation is concerned.

They are usually sufficiently remote so that man-made noise and

radiation hazards to nearby facilities need not be considered. However, the cost of site development in such locations is often prohibitive. Local thunderstorms are frequently associated with

mountain tops and can be somewhat troublesome.

Quite often other military activities, such as aircraft communication and warning facilities, require mountain top locations.

In many cases collocation can be tolerated by both facilities, resulting in a considerable reduction in the cost of site development and

logistical support.

It is important for those engaged in the selection of sites to

keep open minds about various possibilities for setting up communication paths. Advantage can often be taken of factors which are not

apparent in planning the circuits until the site survey work is underway. For example, it may not occur to a site selector who is

attempting to select terminal locations for a line-of-sight relay that a somewhat beyond line-of-sight path will accomplish the communication requirement just as well and will quite likely eliminate some of
-55-

the requirements for remote relay facilities. The site selection team

will rarely have all the factors at hand in order to make a completely

objective, final selection of sites. In almost every case a number

of possibilities should be evaluated by the site selectors leaving the

final selection until all of the factors, technical and otherwise, can

be assembled and weighed.

The primary use for line-of-sight paths in the Air Force is

in inter siting between communication relay centers and long-distance

communication terminal facilities and in some cases where shorthaul communication is required, such as between nearby military

facilities. In mountainous terrain, predominant peaks or ranges

are frequently located on or near the great circle path between

proposed sites, and in such cases advantage can be taken of obstacle

gain propagation for reasonably long distances. When such a path

is feasible, tremendous economies are effected, and the possibility

of using an obstacle -gain path should not be overlooked.

Because of the difficulty with maintenance and operation of a large number of line-of-sight relays the use of multi-hop paths for

long distance communication has not been emphasized greatly. In

the future it is possible that few frequency bands in the UHF and

lower SHF regions of the spectrum will be available, and more

reliance will necessarily have to be placed on higher frequencies,

perhaps as high as 40 Gc/ s. Fixed point-to-point allocations of

certain bands up to this frequency have already been made internationally at the Administrative Radio Conference - Geneva, 1959,

and have been incorporated into the U. S. national table of frequency

allocations. Frequencies of this order will be useful primarily in

line-of-sight applications.

The primary consideration in selecting sites for line-of-sight

paths is not only to insure that the terminals selected are line-ofsight, but also to insure that the entire first Fresnel zone is clear of

obstructions. Obstructions within the first Fresnel zone may usually

cause increased fading and a decrease in reliability; however, in

some cases it may be desirable to tolerate this to some extent by

increasing the power rather than using two systems in tandem. A

profile showing the concept of first Fresnel zone clearance and the

effect of obstructions within the first Fresnel zone is shown in Fig.

19. Height is shown in meters and distance in kilometers. Often
ILLUSTRATION OF FIRST FRESNEL ZONE

CLEARANCE FOR LINE OF SIGHT PATHS

HALF WIDTH OF FIRST FRESNEL ZONE, y,' AT ANY DISTANCE d' FOR A PATH WITH TOTAL DISTANCE d

X U. 4(2d'-d)2 -" l/2 4/L1 (2d + X)2

EXAMPLE OF TRANSMISSION LOSS VARIATIONS

AT 800 Mc/s WHEN LESS THAN FIRST

FRESNEL ZONE CLEARANCE EXISTS

DISTANCE FROM GEOMETRIC LINE OF SIGHT TO TOP OF OBSTACLE IN METERS

FIGURE 19
-57-

a map study will indicate that such clearance exists when in fact

vegetation or other obstructions are present which interfere with

the clearance. The first Fresnel zone consists of the locus of all

points in space which are associated with paths exactly one -half

wavelength longer than the straight-line distance between the two

terminals. It is an ellipsoid of revolution with its foci at each of

the two antennas.

Having more than first Fresnel zone clearance will not

necessarily be helpful. This is because reflections from surfaces

located anywhere on the first Fresnel zone will arrive in phase with

the direct wave. If path length differences are integral multiples of

wavelengths, the energy will arrive out of phase and degrade the

signal to an extent dependent upon the smoothness of the reflecting

surface.

Sometimes terrain clearance is considerably in excess of

first Fresnel zone clearance. If the terrain in the area of reflection

is relatively uniform, in particular if it is over water, a large number of lobes are likely to occur with deep minima. Variations in

refractive index will cause fading associated with vertical motion

of these lobes at the receiving location. Vertical diversity and

antenna tilting can be used to overcome this type of fading. Normally

the vertical diversity antennas are separated in height by half the

vertical distance between lobes. This distance will depend upon the

geometry and the radio frequency contemplated for the path. In

cases where lobing is a possibility, the site selector should compute

the expected vertical separation using the geometric ray optics so

that an estimate of the height of tower required for vertical diversity

antennas can be made. The Air Force Technical Order [ 1961 ] describes this procedure in detail.

In many cases the requirements for communication involve

paths which are short but are not intervisible. In these cases the

decision will have to be made whether to meet the requirement with

a multihop line -of -sight circuit using relays or by a short not-lineof-sight circuit. Technically there is nothing wrong with the multihop circuit, but the practical problems of operating remote relays

limit their effectiveness considerably. When the site survey party

is confronted with the problem on non-intervisible terminals, they

will not have all the facts at hand to make an intelligent decision as
-58-

to which type of path to settle on. In this case it is usually best to

make the survey with both possibilities in mind.

10. PRELIMINARY PLANNING AND MAP STUDIES

Good topographic maps are essential for planning propagation paths for tropospheric propagation. Scales of 1:250, 000 or

1:500, 000 can be used for overall planning and for preliminary

selection of sites, but these usually do not have enough detail for

extensive studies of the terminal areas and important parts of the

propagation path. They do indicate where these areas are and in

what locations more detailed maps are essential.

Maps of the continental areas of the United States may be

obtained from the U. S. Geological Survey and from the U. S. Coast

and Geodetic Survey. Other areas of the world are covered by the

Army Map Service series. Very excellent maps can also be purchased locally in many foreign countries. U. S. Embassies and the

U. S. Army Corps of Engineers can frequently be of great assistance

in obtaining them.

The first step in planning tropospheric propagation paths is

to obtain the small-scale coverage, say 1:250, 000, of the entire

area under consideration. Index maps of all the areas likely to

come under more intensive scrutiny can be obtained from appropriate sources at the same time. From these maps a tentative selection

of terminal locations is made bearing in mind that the satisfaction of

the technical requirements is only part of all of the considerations

that must eventually be taken into account. After a number of possible paths have been tentatively selected, path profiles are plotted

from large scale maps. These profiles will not show important

obstructions and vegetation. These can only be determined by

visiting the proposed sites.

The primary technical considerations required for choosing

a site can be listed in the following categories, some of which apply

to tropospheric scatter and line-of-sight paths, while others are

more important for one or the other type of path. Those which are

common to scatter, line-of-sight, and obstacle-gain paths are:

1. Path length
-59-

2. Antenna height

3. Vegetation and obstructions

4. Mutual interference and radiation hazard

5. Site area

Those factors primarily of concern for tropospheric scatter paths

are:

6. Signal takeoff angle (horizon angle)

7. Distance to radio horizon

Those factors primarily of concern to line -of- sight and obstacle -gain

paths are:

8. Terrain clearance

9. Effect of layers and ducts

All of these technical factors, together with site availability

and support, affect the choice of the site in varying degrees for

different conditions. Consequently, several sites should be investigated and evaluated.

10. 1 Evaluation of the Parameters Affecting Site Choice

a. Path Length

The effect of such slight variations in path length as may be

encountered in selecting a site will be negligible. For a given

tropospheric scatter path a change of one mile in path length introduces a change in transmission loss of approximately 0. 1 db;

consequently, decreasing the total path length by 10 miles decreases

the transmission loss by only 1 db on the average.

For line -of- sight and obstacle gain applications, the transmission loss is frequently estimated in terms of the loss below free

space. The free -space loss is proportional to the square of the total

distance. Doubling the distance, for example, will cause the freespace transmission loss to increase by 6 db. The remaining part

of the total transmission loss will depend on many factors, but it is usually greater for long paths than for short ones. In addition,

time variations are dependent upon distance. Long-term variations

are estimated empirically in a recent Air Force Technical Order

[1961].
-60-

b. Antenna Height

In tropospheric scatter propagation the main effect of

increasing antenna height is to decrease the takeoff angle. Raising

the antenna above the surrounding terrain may reduce the transmission loss caused by interference between direct and groundreflected waves.

In line-of-sight and obstacle -gain applications the effect

of antenna height is best evaluated in terms of terrain clearance

which is discussed in subsection h.

c. Vegetation and Obstructions

Merely plotting a profile of terrain heights does not give an

accurate display of the actual propagation path in every case.

Obstacles, particularly vegetation, are frequently present. The

degree to which vegetation affects propagation is relatively uncertain;

sparse growth is more penetrable than heavy growth, and lower frequencies penetrate more than higher frequencies. The safest procedure is to consider that vegetation such as trees, vines, and high

grass or weeds is impenetrable to radio frequency energy. The top

of the vegetation is thus used in determining the terrain clearance

and the takeoff angle.

d. Mutual Interference and Radiation Hazards

Collocation of terminal facilities with other activities is

often desirable for economical installation and operation. Often,

terminals are collocated with aircraft communication and warning

services. In such cases particular consideration will have to be

given to the possibility of mutual interference. All frequencies

generated by the equipment, including those from frequency multipliers and local oscillators must be considered as possible sources

of interference to sensitive receivers. High-energy RF fields can

overload receiver input circuits at frequencies other than those to

which the receivers are tuned.

The problems associated with collocation cannot be treated

adequately in a general manner. Each installation presents its own

set of problems which must be studied separately. For example,
-61-

collocation with major air bases is sometimes necessary, but there

is a danger that high levels of man-made noise may occur during

some periods of time due to the many and varied activities that may

be carried out on these bases. High-speed electronic computers

often cause trouble. Radiation of strong RF fields in areas where

aircraft operate, particularly in approach zones, should be avoided.

The radiation hazard to personnel and equipment within the

immediate vicinity and within the beam of a high-power transmitter

should be considered in siting. It is known that very high-power

radio frequency energy can be injurious to humans and animals, can

burn out crystals in electronic equipment, and can cause detonation

of some types of explosives. While the radiation hazard is not

alarming in most cases, the site selector should avoid a site necessitating transmission directly across an airfield runway, highway or

a residential or otherwise populated area within approximately onehalf mile. Further information on the radiation hazards can be found

in Section 11.4.

e. Site Area

The type of terminal that is planned for line-of-sight communications will largely dictate the requirements for the site. Some

of the important considerations are: accessibility, security, availability of power, and the relative difficulty of developing the area.

In most cases there will be a requirement for a building and a tower;

however, in some microwave installations, all of the operating and

maintenance facilities are completely contained in the tower.

Additional area may have to be provided for large antennas, such as two 120-foot paraboloids with a 200-wavelength separation.

f. Signal Takeoff Angle (Horizon Angle)

The takeoff angle is one of the controllable technical factors

in tropospheric scatter propagation. The takeoff angle as defined in

Fig. 2 is the angle between the horizontal at the radiation center

of the antenna and a ray extending from the radiation center of the

antenna to the radio horizon. It is recommended that the takeoff

angle be computed from accurate topographic maps because of the

difficulty of positioning a transit at the intended center of radiation,

which may be at a considerable height above ground. Transit observations cannot be corrected for this height effect in most cases,
SITE CHOICE CONSIDERING TAKE-OFF ANGLE

RAY TO RADIO HORIZON

HORIZONTAL RAY

DEFINITION OF TAKE-OFF ANGLE

HORIZONTAL RAY

RAY TO RADIO HORIZON

BEST SITE

RAY TO RADIO HORIZON

WORST SITE

FIGURE 20

HORIZONTAL RAY
-63-

because horizons are often different for the different heights. When

the antenna is to be sited at a height where transit observations cannot be made and no satisfactory maps are available, it will be necessary to obtain the profile information by other methods. Stereo

aerial photographs can be used effectively for this. Sometimes

arrangements can be made for special photographic flights, if

photographs are not available.

Accurate altimeters are sometimes used to measure relative

heights along the path azimuth. The leapfrog method uses two altimeters. In this method progressive height differences are measured

along a line, and the profile is plotted from these. Profile informaation may be obtained relatively rapidly in this manner and is sufficiently accurate for this purpose. For a description of the leapfrog

method see Breed and Hosmer [ 1953].

Except in those rare cases where the consideration of one or more of the other geometrical parameters outweighs the effect of

the takeoff angle, the site with the most negative angle should be the

first choice with a zero angle the second, and the smallest positive

angle the last choice.

As the takeoff angle is increased, transmission loss increases, resulting in a weaker received signal. The effect of the

takeoff angle on the transmission loss is very significant; this added

loss is approximately 12 db per degree. Consequently, in choosing

a site, every effort should be made to take advantage of the effect

of the takeoff angle of transmission loss. A rough approximation of

the effect will have to be made on the spot by the site selection team

before more elaborate transmission loss calculations can be undertaken. For this purpose Fig. 21 has been prepared showing this

relationship. Figure 21, together with the empirical method for

prediction of transmission loss discussed in Section 8, will enable

the site survey team to make quick comparisons of the relative

merits of various paths under consideration.

g. Distance to Radio Horizon

The major effect of distance to the horizon is to change the

takeoff angle in beyond the horizon propagation. Maintaining a constant takeoff angle, the distance to the horizon can vary widely
EFFECT OF TAKEOFF ANGLE AT ONE SITE ON

TRANSMISSION LOSS FOR COMMUNICATIONS

USING TROPOSPHERIC SCATTER PROPAGATION

LUINIUI 1 IUIN5 NtbtbSAKY l"UK USt Uh bKAKH

ANTENNA AT 20 FEET OR HIGHER ABOVE TERRAIN

ANY FREQUENCY BETWEEN 100 MC AND 10,000 MC

ANY PATH DISTANCE GREATER THAN 200 MILES

EXAMPLE: AN INCREASE OF TAKEOFF ANGLE

FROM +1° TO +2° INCREASES THE —

TRANSMISSION LOSS BY 12 db.

THE RECEIVED SIGNAL WILL THUS

BE 12 db WEAKER.

+ 2° +3° +4° +5° + 6° TAKEOFF ANGLE 9r IN DEGREES

SUM OF TAKE OFF ANGLES= O.7(0mr -^)OR 0.7{9mr ^)

FIGURE 21
-65-

with a relatively minor effect on the transmission loss. In general,

for a constant takeoff angle, the greater the distance to the horizon

the smaller the transmission loss. Fig. 22 is an illustration of

varying distances to the radio horizon with the same takeoff angle.

h. Terrain Clearance

Although the maintenance of first Fresnel zone clearance

in line-of-sight propagation is a somewhat arbitrary requirement,

it is a good one since it will usually assure minimum transmission

loss. The same concept can be applied to obstacle-gain paths by

considering these to be made up of two paths, as if the obstruction

were a relay terminal. Sometimes paths will be chosen which have

much more than first Fresnel zone clearances. In such cases a large number of fine lobes may be formed, due to interference

between direct and ground reflected rays. Changes in the height

gradient of refractive index will shift the position of these lobes and

cause fading, particularly when the reflection point is over water.

In many cases, vertical space diversity may be used to compensate

for this type of fading.

The reflection coefficient of the ground is expressed in

terms of the ratio of the reflected to the incident field strength.

Vertically polarized waves are reflected with less efficiency than

horizontally polarized waves. Both the dielectric constant and the

conductivity are important in determining the reflection coefficient,

but at VHF and above the dielectric constant plays the predominant

role. If the terrain is rough and covered with vegetation, a large

part of the incident energy will be scattered and some will be

absorbed. Rayleigh's criterion of roughness can be applied as a guide in determining whether or not the reflected wave will be

specular or will be scattered to some extent. Sometimes, the first

Fresnel zone associated with the reflected ray path intersects the

reflecting surface . If the terrain roughness is small enough so that

Ah < \/(l6 sin i|i), (13)

then the reflected energy will be specular. In (13) Ah represents

the standard deviation of terrain heights and ijj is the angle the
ILLUSTRATION OF VARYING DISTANCES TO

RADIO HORIZON WITH SAME TAKE-OFF ANGLE

RAY TO RADIO HORIZON

HORIZONTAL RAY

RAY TO RADIO HORIZON

HORIZONTAL RAY

(b

RAY TO RADIO HORIZON

HORIZONTAL RAY

FIGURE 22
-67-

incident and reflected rays make with the reflecting surface. Formulas for computing the extent of the Fresnel zone are given in

Appendix 1

.

i. Effect of Layers and Ducts

The major effect of layers and ducts is to bend and deflect

radio waves. In some line-of-sight cases, when transmitting through

a discontinuity in refractive index, the transmission loss is increased

by as much as 30 db. The effect is more pronounced on long paths

and when the ray path is nearly tangent to the duct. Obstacle -gain

paths using relatively steep takeoff angles are not as likely to be

affected. Overwater paths are most likely to be affected because

of the persistence of low-level ducts and layers.

10.2 Great-Circle and Rhumb-Line Computations

Before a final selection of sites can be made it is necessary

to plot accurate path profiles. These should whenever practicable

be plotted during the site survey so that any discrepancies can be

checked and vegetation or other obstructions can be included on the

profile. Geographic coordinates of the two ends of the path are

normally expressed in units of longitude and latitude.

In most cases line-of-sight paths are not long, and it is not

always necessary to make great-circle computations in order to

determine the location of the path with sufficient accuracy. Either

the line can be drawn directly on the map, or a rhumb line (which

is much easier to compute than a great circle) can be used. It is

recommended that this procedure be limited to those cases in which

the difference in longitude is not much more than one -half degree.

The rhumb line will more nearly approximate a great circle near the

equator than at greater latitudes. A rhumb line is defined as a line

which intersects all meridians at the same angle. Except in special

cases, it is not a great circle and is therefore not the shortest

distance between two points on a sphere.

The computation of rhumb lines, given the terminal coordinates, involves only very simple trigonometric formulas. We can

designate the two terminals as A and B, their latitudes $ and
-68-

$„, and their longitudes A. and A . Since the rhumb line inter

B -A. B

sects meridians at the same angle, the bearing angles X and Y

are supplements of each other. Figure 23 is an example of a rhumbline path between two points. To minimize the distortion resulting

from the mercator projection in which the meridians are shown

parallel to each other, it is convenient first to determine the middle

latitude, 3> ,. M

*M = ( *A + *B)/2 (U>

Then:

(A - A ) cos $ A B M . , _. tanX= j- —- (15)

( *A " V

Y = 180° + X (16)

In the above equations it is usually more convenient to subtract the

smaller from the larger number in each case and adjust the angles

into the proper quadrants to obtain azimuth later. Some obvious

adjustments must necessarily be made when the terminals are in

different hemispheres.

To compute the distance A to B it is convenient to convert

the differences in latitude and longitude into minutes with decimals

for the fractional parts, since a minute of latitude is equal to one

nautical mile. Then the approximate rhumb-line distance d, from

A to B can be expressed as follows:

d = ($ - $ ) / cos X nautical miles . (17) A B
EXAMPLE OFAMERCATOR PROJECTION WITH

A RHUMB LINE APPROXIMATION TO THE

GREAT CIRCLE PATH FROM A TO B

(SCALE ON ORIGINAL 1:100,000)

ACTUAL DISTANCE 84.530 km

SCALE SIZE 0.84530 m

41° N

45' $ B =40°39'I5"N

A B = 104° 14' 30" W

30'

A

15' A A

= 104° 46 45 W

40° I

F

j^

CO

LU E

U oo

?" zz < ; \-U) UJ Q rs; CO _< UJ

Z> _i

h- <r O t; < CO

45' 30' 15

<£ m

= 40° 28' 22.5" , cos $m

= 0.76071

( NOTE: 1 1 1. 12 km x Q7607I = 84.530km)

X = 48° 26' 28" , Y -228° 26' 28"

DISTANCE FROM A TO B = 60.720km

FIGURE 23
-70-

To convert from nautical miles to other units use the following:

d(nautical miles) X 1. 8520 = kilometers

d( nautical miles) X 1. 508 - statute miles

More accurate conversion factors are listed in Appendix 3.

In those cases in which it is necessary to compute the

actual great circle path, the initial bearings and the distance and

the location of intermediate points can be computed by reference to

the spherical triangle shown in Fig. 24. A good table of trigonometric functions is necessary, and should be included among the items

the survey team carries with it. In Fig. 24 the spherical triangle

is shown as PAB, where A and B are the terminals, (B having

the higher latitude) and P is the pole in the same hemisphere as

B (north or south). B' is any point along the great circle path from

A to B and is solved by reference to the spherical triangle PAB'.

<&», «3?Tg and $ are the latitudes of A, B, and B', respectively;

C and C are the differences in longitude between A and B and

between A and B'; while Z and Z' are path lengths from A to

B and from A to B', respectively. The following are convenient

for the solution of this triangle, both by manual means and by automatic digital computation using trigonometric subroutines.

To compute initial bearings X and Y:

Y - X C

tan —- = cot —

a _ $

sin /

$b + 4

cos (18)

Y + X C

tan - = cot — cos sin

B A

(19)
(POLE CORRESPONDING TO HEMISPHERE OF B)

SPHERICAL TRIANGLE FOR

GREAT CIRCLE PATH COMPUTATIONS

FIGURE 24
-72-

Y+XY-X -— „ J Y + X Y-X v + —r = Y and — - = X (20)

To compute great circle distance, first compute the angle Z,

expressed in degrees:

tan — = tan

r B A"1

J L sin **)/(-

Y - X \ -] (21)

To compute latitude, $„,» given the longitude difference, C

cos Y' = sin X sin C sin 3? . - cos X cos C (22) A

cos <£ = sin X cos $ / sin Y' (23)

To compute longitude difference, C, given latitude, <3?

t

sin Y' = sin X cos <£ . / cos <i>

,

A B'

C 1 Y' - X

cot — = tan - cos

3> , + $ A B 1 A

/

(24)

sin

B A

(25)
-73-

Equations (18) through (21) have been published by the International

Telephone and Telegraph Corporation [ 1956 ]. To convert Z in

degrees to other useful units of length use the following constants:

ZX 111.120 = kilometers

Z X 69. 047 = statute miles

Z X 60.000 = nautical miles.

Since the radius of the earth varies somewhat from place to place,

the precise conversion of the arc, Z, in angular units to distance

will require different constants. The above constants strictly apply

for an earth radius of 6366.7 km; however, the error introduced by

this approximation is extremely small and can be ignored in this

application. With this radius one minute of great-circle arc is

exactly equal to one nautical mile.

10. 3 Plotting Profiles

In most cases the great-circle path will traverse more than

one of the large-scale topographic maps from which the profile will

be constructed. A very convenient and accurate way to draw the

great-circle path on these maps is as follows:

(1) Construct a mercator grid chart large enough so that

both terminals can be plotted on the grid. A mercator

grid is a projection of the spherical meridians and

parallels of latitude upon a cylinder tangent to the

earth at the equator. It is not useful at latitudes near

the poles, and the scale is not constant. However, at

most latitudes encountered and for distances of a few

hundred miles, the distortion can be tolerated.

(2) On this grid all of the available topographic maps can

be overlaid to scale in their relative positions as in

Fig. 2 5. A straight line drawn between the two terminals on this grid is a rhumb line, and indicates approximately where the great circle will cross the individual

maps.
-74-

(3) Latitudes or longitudes where the line crosses the edge

of each map are next selected, and the corresponding

longitude or latitude which lie on the great-circle as

well as the great-circle distance from either terminal

are computed using (18) - (25). Additional points

showing the position of the great-circle path within

the maps may be added to the maps and joined together

with lines to show the position of the great-circle path.

An example of this type of procedure for Fig. 2 5 is

shown in the following tabulation:

TABLE 4

Coordinates for Locations Along the Great-Circle Path

from Haswell to Table Mesa, Colorado, Shown in

Fig. 25. Underlined Coordinates were Given and

the Other Coordinates were Computed.

I *103°jongitude

09 ' 17.077"

103° 17 26.340"

103° 30 00"

103° 51 56.952"

104° 00 00"

104° 30 00"

104° 37 30"

104° 45 01.584"

104° 45 00"

104° 52 30"

104° 54 01.908"

105° 03 05.076"

105° 07 30"

105° 12 11.052"

**105° 13 52.3"

*Haswe'

**Table .

LIvlesa

Distance Distance in

Latitude in km Statute Miles

38°22 49. 5"N

38°30 00" 17. 803

45. 112

11.062

38°40 59.304" 28. 032

39°00 00" 92. 496

109.773

57. 474

39°06 54.864" 68. 210

39°32 23.964" 173.651 107.902

39°38 42.180" 189. 501 117.750

39°45 00" 205. 355

205. 301

127.602

39°44 58.704" 127. 568

39°51 13.644" 221. 054 137. 357

39°52 30" 224. 265

243.203

252. 418

139. 352

40°00 00" 151. 120

40°03 38.700" 156. 845

40°07 30" 262. 172

265.681

162.906

40°08 53.2" 165. 087
LAYOUT OF PROPAGATION PATH BETWEEN

HASWELL AND TABLE MESA COLORADO SHOWING

TOPOGRAPHIC COVERAGE AVAILABLE FOR DETERMINING PROFILE

TABLE MESA

RECEIVER SITE AZIMUTH 137° 03' 10.8" LONG. 105° 13' 52.3" W

LAT 40° 08' 53.2" N. W

HASWELL

TRANSMITTER SITE AZIMUTH 318° 22' 02.4"

LONG. 103° 09' 17.077" W. LAT 38° 22' 49.5" N.

38*

<S) 5000 K 4000

DISTANCE IN MILES

60 80 100 120

DISTANCE IN KILOMETERS

265.68 km

FIGURE 25
-76-

It is inevitable that in some cases adequate topographic maps

do not exist or those that do exist will be of doubtful accuracy. This

makes the process of constructing accurate profiles exceedingly

difficult. Celestial observations and other surveying techniques may

be needed in order to establish the great circle path terrain profile

between the antenna terminals. Often it is possible to determine

radio horizon elevation angles or take-off angles, 6 and 6 , in to °

et er

the field. The angular distance is

0=9 +9 +d/a radians, (26)

et er

where d is the path distance and a is an effective earth's radius

factor which allows for average radio ray bending in the atmosphere.

Commonly used values for a are 5280 miles or 9000 kilometers.

The best celestial method for determining true azimuths in

northern latitudes is that of Polaris observation. Polaris rotates

in a small circle (radius 55') about the axis of the earth in the celestial sphere. Its altitude is approximately equal to the latitude of

the observer. For azimuth determination Polaris is best observed

at elongation, either east or west. Observations at other times

require accurate timing of the sighting. At high northern latitudes

and in all southern latitudes azimuth determinations can be made by

forenoon and afternoon sun observations or by sights on circumpolar

stars. Latitudes and longitudes can be observed by similar methods.

The determination of longitude requires the access of very accurate

time. Instruments with high precision and equipment with filters

and reticle illumination for sun and star observations, such as

theodolites, are recommended for this work. Non-illuminated

instruments can be used for star observations by deflecting a small

amount of light from a flashlight through the objective lens of the

instrument. The reader is referred to standard surveying textbooks

such as Breed and Hosmer [ 1953 ] for a detailed description of the

procedures for celestial observations.

Frequently in site survey work it is necessary to obtain a reasonably accurate azimuth quickly without resorting to night-time

Polaris observations. In many cases a magnetic azimuth corrected

to true azimuth by applying magnetic declination is sufficient, but is

not particularly reliable. A method which is quite reliable, but
-77-

which does not appear in standard textbooks, is to observe the sun

to transit the meridian at local apparent noon when it is at its highest

altitude and is true north or south from the observer. For this

observation the sun can be observed for ten or twenty minutes before - and after transiting. Two or three pairs of observations at the same

altitude before and after transiting can be averaged to obtain an

azimuth accurate to about ten to twenty minutes of arc. Parallax

and semi-diameter corrections can be automatically compensated

for by taking altitude observations on the lower or upper limb and

setting the left limb of the sun on the vertical cross hair before

transit and the right limb after transit. This method will not work

when the sun transits near the zenith. At other times of the day a graph of the sun's azimuth versus time can be plotted in advance for

the period of planned observations. In this case correction will have

to be made for the sun's semi-diameter. Parallax errors will be

within two seconds of arc and can be ignored. The Nautical Almanac

[yearly] and Ageton's "Deal Reckoning Altitude and Azimuth Table, '

[ 1943 ], are recommended publications for the site survey party if celestial observations are contemplated.

11. SPECIAL CONSIDERATIONS

Many special considerations in addition to the technical

requirements enter into the selection of transmitting and receiving

sites. Some of these considerations can be anticipated; others will

be peculiar to each survey.

11.1 Site Availability

In populated areas the acquisition of valuable land is not

only expensive, but may lead to misunderstanding and hard feelings,

particularly in foreign countries. Fortunately, by virtue of the

tendency for hill-tops to be less valuable land in most areas, this

problem is not too serious for tropospheric communication terminals

and relays. The acquisition of cultivated land should be avoided

whenever possible. Many foreign countries are also sensitive about

the erection of structures in their park lands and scenic areas.
-78-

11.2 Site Development and Logistic Support

Many otherwise ideal sites will inevitably be eliminated

from serious consideration because of the lack of access and the

difficulties associated with logistic support. This is perhaps one

of the most difficult factors to evaluate in choosing terminal locations, and requires the utmost consideration. In some cases such

difficulties may be partially overcome by collocating with other

facilities which also require this kind of site. This is difficult to

accomplish in many cases because of the high radiated power levels

of the tropospheric transmitters. However, many examples of

collocation have been accomplished, particularly with aircraft warning installations.

11.3 Vulnerability

Adequate security is difficult to achieve over a large number

of remote line-of-sight relays and terminals. This is one reason

that line-of-sight propagation is not considered favorably for longdistance, military communication. There are two aspects to vulnerability c One involves actual damage or destruction of facilities, and

the other involves jamming. To some extent protection from damage

can be accomplished by site hardening. Intentional jamming is less

of a threat with line-of-sight communication because jammers must

be relatively close to the receivers, because of the highly directive

antennas used and the poor long-distance propagation of the frequencies normally used on line-of-sight paths.

In the event of hostilities the prospect of incidental destruction or large communication complexes resulting from attacks on

military facilities makes the isolation of strategic communication

trunk-line terminals from other military activities desirable. Long

intersite paths connecting military bases with these trunk-line

facilities will materially assist in accomplishing a desirable degree

of isolation.

11.4 Electromagnetic Wave Radiation Hazards

In the siting of communication terminals, careful consideration should be given to the possible effects of electromagnetic

energy on the human body and on physical objects such as radio

equipment, electrically detonated explosives, volatile gases, etc.
-79-

a. Biological Hazards

Since the early days of World War II, thought has been given

to the possible biological effects of electromagnetic radiation on the

human body. At that time a study was made of U. S. personnel

engaged in the operation and testing of relatively low-powered radars.

This study revealed no evidence of radar-induced injury to human

beings.

During the past ten years, with the development of more

powerful equipment, interest in this problem has increased and a number of experimental programs have been initiated. An air frame

manufacturer engaged in the installation, testing, and servicing of

powerful airborne transmitters instituted a comprehensive medical

program for its several hundred employees working with radar and

those who might be exposed to microwave energy. This program,

which has been operating since 1954, constitutes one of the longest

continuous surveys of radar-exposed personnel in the United States.

No acute transient or cumulative physiological or pathological

changes attributable to microwaves have been revealed by this study.

However, in view of the trend toward ever increasing power, >

it is possible that a serious biological hazard may be created.

Research on this problem is being coordinated by the Air Research

and Development Command. Damage may conceivably occur to those

body systems not equipped with adequate means of heat regulation.

In this category are included the lens of the eye, the testes, and

internally the liver, gall bladder, and gastrointestinal tract. The

vulnerability of the body is further affected by the ambient temperature, humidity, the heat loss factor of the particular organs and

their temperature sensitivity. The sensitivity of the lens and the

testes is due to a poor ability to dissipate heat and to their physical

locations relative to the body surface.

The undesirable effects of excessive temperature in the

whole body, the lens of the eye, and the testes are heat disablement,

lenticular opacities, and tubular injury, respectively. Although

cataract production has not been experimentally established as an

electromagnetic radiation effect in man, the formation of lens

opacities in animals subjected to such radiation suggests the need

for precautions in situations where the human eye is exposed.
-80-

Experimental investigations of the biological hazard of

electromagnetic radiation have been carried out, primarily on

animals, but to a very limited extent on humans in the frequency

range of 100 to 35, 000 Mc/ s. Based on these data, a hazardous

electromagnetic radiation level of 10 milliwatts per square centimeter, or greater, has been established by the Armed Forces and

most of the industrial laboratories in the country. It is believed at

the present time that the continuous exposure to power density levels

not exceeding 10 milliwatts per square centimeter of average power

does not constitute a hazard. Due to the lack of data on the effects of

chronic exposure, no time factor has been included.

It is highly probable that in the not too distant future, with

the anticipated increase of system power levels, it will be necessary

to provide personnel working in the vicinity of the transmitting facilities with protective clothing and to provide shielded passageways

through the potentially hazardous areas.

There are several sub-divisions within the transmitting

system where significantly different electromagnetic power levels

exist. First, we have a high power density in the transmission line,

which normally is closed and therefore not readily accessible. Next,

the power is conveyed by the transmission line to an antenna feed

which in turn feeds the energy to the antenna. The energy in transit

from the feed to the antenna is no longer enclosed and is therefore

more accessible than the inside of the transmission line. This area

normally has a larger cross -sectional area than the transmission

line and therefore a lower power density. Finally, the energy is

radiated into free space by the antenna. Here, when we radiate the

energy to the outside world, we face the biggest problem in the control of electromagnetic radiation hazards. The dependence upon

distance of the energy is indicated in Fig. 26. At distances close to

the antenna, in what is known as the near field, or Fresnel region,

the power is contained within a beam of about the same size as the

antenna aperture. This beam, however, is not uniform, but tapered

across the aperture in order to keep the power in the side lobes to a minimum. The power density in the beam decreases smoothly from

a maximum at the center of the aperture to a minimum at the aperture

edge, which is about 10 db below the maximum.
jom

ro

0)

Omom

33

-<

~n

"n o

3)

M os m > o

T)

m > H

31

m > jj CD ^ OI- 2> O HO > ^ ^:Hm o 2

II 2 "n > o^m

33om2

COH

^C
-82-

The near field may be described approximately by:

D

2

where

d is the distance from the antenna

D is the largest aperture dimension

\ is the wavelength

The power density in the field along the parabolic antenna axis can

be obtained as follows:

WJ = 8.48 w

a

.433 sin '

- vf)—{(!)-(t)-Wt)}]

(28)

/ 2 W , is the power density, w/ cm at distance d

w is the mean power density across the apefture, w/ cm2 , obtained by dividing the total power by the area in

cm2 of the dish.

^2

m = 2Xd

If we designate the limit of the near field, D

2 / (2. 5\), as

d , (28) can be written as

^=3. 664 [sin2

(_£)

^ird k ^-rrd

.1 L + . 270 ^-(ra)-" (**)!] U9)
-83-

This equation is plotted as a function of distance in terms of d in

Fig. 27. From the curve, d or the distance at which the maximum power density occurs is seen to be about 0. 58 d . Similarly,

the maximum power density is seen to be equal to about 4. 1 1 times

the mean power density across the antenna aperture.

As the distance from the antenna exceeds the value given in

(27), the beam begins to diverge until finally the power density is

decreasing in accordance with the inverse square law. This region

is known as the far field, or Fraunhofer region, and is described

approximately by (17).

d . > Fraunhofer

D

(30)

The power density at the center of the beam in the Fraunhofer region

is given as follows:

W = P

t g

t w/ m (31)

4tTd

Ranges for the 10 mw/ cm power density value are shown in Table 5

for various frequencies, antenna gains, and transmitter powers.

TABLE 5

Typical Ranges for Which the Power Density Exceeds 10 mw/ cm

t D

(kw) (ft)

75 120

75 60

50 60

50 28

10 60

Freq.

(Mc)

400

400

1000

1000

8000

d max max

mw/ cm2 (ft)

29. 34 1359

117. 35 340

78.23 849

359.23 185

15.65 6793

10

(ft)

3280

1447

2949

870

11712
RATIO OF POWER DENSITY ALONG THE AXIS OF A PARABOLIC ANTENNA

TO AVERAGE POWER ACROSS THE FACE OF THE ANTENNA

Somple Calculation

f = 800 Mc Pt = 30 kw

60ft Parabolic Dish

1.40 1.50
-85-

P is the transmitter power

t ^ D is the diameter of the parabolic reflector

Freq is the frequency of operation

Pjmax is the maximum power density

d is the distance from the antenna at which the maximum max

power density occurs

d.

n

is the distance from the antenna within which the power

density can be expected to exceed 10 mw/ cm2 where

p is the antenna input power, watts

g

is the antenna power gain

d is the distance from the antenna, meters

Equation (31) may be used to calculate the approximate distance

within which a given system will produce a radiation field with a power density equal to or greater than 10 milliwatts per square

centimeter.

P

t g

t d= 4^W mGterS ' (32)

with W in watts per square meter. This equation again is valid

only for d > D

2

Where calculations based on the above equations (or the

possible existence of reflections) indicate a hazardous area, final

conclusions and decisions should be based on field measurements.

b. Physical Effects

Photo flashbulbs may be ignited if brought in the direct

beam of some equipment at distances less than 300 to 350 feet.

Under certain circumstances dry steel wool may be ignited. Neon

gas tubes will light in the presence of low intensity microwave fields,
-86-

Care should be taken to avoid handling of volatile liquids in a high level RF field. Sparks are known to occur at various points

on metal structures when touched by portions of the body or by

metallic objects held in the hand. The possibility of igniting volatile

liquids, such as aviation gasoline, by these RF-induced sparks is a matter of concern. In order for gasoline to be ignited by a spark,

the following conditions must exist: (a) inflammable gasoline vaporair mixture must exist; (b) the spark must contain a sufficient amount

of energy; (c) the gap across which the spark occurs must be a certain minimum distance, which is termed the "quenching" distance.

Investigation has shown that inflammable mixtures are not

found at distances greater than six inches in any direction from

exposed puddles of gasoline. The DC voltage required to break down

an air gap of the minimum quenching distance for propane is approximately 2 500 volts. The RF voltage required is believed to be about

the same as that required for DC.

During recent years several accidents have occurred

involving electrically initiated explosive devices. These accidents

have been attributed to currents induced by radio frequency fields.

The devices known as electro-explosive devices are designed to

function by the passage of an electric current through them. Among

such devices are primers, detonators, squibs, blasting caps, rocket

ignitors, etc. Unfortunately, the problem of vulnerability of electroexplosive devices to RF radiation fields has only been superficially

examined. Because of this and of the serious nature of an accidental

explosion, they are presumed to present a dangerous hazard in the

presence of high level RF fields. It is recommended that they should

not be used or stored within 7000 feet of a transmitting antenna.

With the rapid increase in power levels used at radio frequencies, it is possible for previously unknown properties to be

demonstrated by certain materials at these higher power levels. An

example of this was a situation in which an inert gaseous fluorine

compound, selected on the basis of published data, was used in a pressurized wave guide. Arcing in the wave guide was found to

liberate large amounts of fluorine. Except for action by alert

personnel, the planned use of this gas might well have resulted in

injury and possible death.
-87-

The increase in transmitting power levels introduces the

question of possible interference with other communication systems.

Although this question has not been thoroughly explored, the potentially serious consequences of such interference makes mandatory

the consideration of such possibilities.

c. Ionizing Radiation

In addition to the biological hazard created by electromagnetic energy at microwave frequencies, there is also a potential

hazard from ionizing radiation produced by modern radio frequency

power tubes. These tubes include magnetrons, klystrons, thyratrons,-

and other types. Levels up to 200 roentgens per hour have been

measured from certain klystrons. This is quite disturbing in view

of the fact that the present maximum allowable exposure level has

recently been reduced from 300 to 100 milli-roentgens per week.

The large number of radioactive electron tubes which have

come into common use constitutes another potentially harmful

source of ionizing radiation. The Air Force inventories over 500

types of these tubes containing such radioactive materials as carbon

14, cobalt 60, and radium 226. While disposal of this type of tube

presents a problem, the high level of radiation resulting from

storage of such items is more important to personnel. Continuous

monitoring of radiation levels should be maintained. It should be

realized that radio frequency electromagnetic fields have a degrading

effect upon the measuring capabilities of many of the common types

of dosimeters. The film type dosimeter, however, accurately

records high levels of ionization even in strong radio frequency

fields.

12. THE SITE SELECTION TEAM

Upon the thoroughness of the work of the Site Selection Team

will depend the ultimate success of the entire circuit. The intelligent

selection of sites for line-of-sight facilities is important. At the

conclusion of an assignment the team will prepare a report which

will describe all the tentative sites and serve as the basis for the

ultimate selection of sites. The development of information to make

up this report is the concern of the team throughout all of its work.
-88-

12. 1 Makeup of the Team

Depending on the extent of the survey two to five individuals

are recommended for this work. At least two of these should be

competent in survey techniques. It is not recommended that a single

individual be sent on such a mission alone, because no matter how

competent he may be, there are so many details to be looked into

that he will be overwhelmed. There is also a psychological advantage in having more than one individual because the many decisions

that must be made can be talked over, and decisions are likely to be

made more rationally as a result. The Site Selection Team must

always bear in mind that it is not necessarily making the final site

selection. More often than not it is selecting a number of possible

locations and developing as much information as possible so that

an intelligent selection can be made later when all of the facts are

assembled.

Lack of a proper understanding of this principle is responsible for the reluctance on the part of some local commands, particularly those in populated foreign countries, to permit the team to

investigate sites which may cause some difficulties in their own

areas of administration. The sites that are left frequently leave

much to be desired and may fail in some cases even to meet the

minimum technical requirements. When doubts like these arise, it

is always better for the team to investigate additional sites even

though tact must be exercised.

12.2 Equipment

The equipment that the team carries will consist primarily

of surveying instruments and drafting instruments. The amount of

equipment will depend upon the type and extent of the survey and the

mode of transportation. Transportation is one of the most difficult

problems. In populated areas where roads are relatively abundant,

a car exclusively assigned to the team is of inestimable assistance.

In any case, because of transportation problems, it will always be

necessary to limit the equipment to bare essentials. The following

list divides items of equipment into the essential items and the

desirable items:
-89-

a. Essential Items

Theodolite or transit with tripod

Altimeters (2)

Tables of Trigonometric Functions, logarithms, and

celestial ephemeris

Tape (100' minimum, 300' invar preferred)

Camera and film

Protractor

Straight edge

Slide rule

Notebook and pencils

Maps

Map scale or variable scale

Parallel ruler

Red bunting

Binoculars

Flashlight

Hatchet

Plumb -bob

Water purifying pills

b. Desirable But Less Essential Items

Small computer (hand operated)

Range poles

Stadia rod

Portable dark room

Many other items will be found useful in special circumstances. A great deal of thought will necessarily be devoted to the

special problems of particular areas. Items for personnel safety

and comfort head this list. In some cases it may even be desirable

to send an individual to the area in advance of the survey to determine the needs more thoroughly.
-90-

REFERENCES

Ageton, A. A. , Dead reckoning altitude and azimuth table, H. O. 211,

third ed. (Superintendent of Documents, Government Printing

Office, Washington, D. C. , 1943).

Air Force Technical Order, Ground telecommunications performance

standards, Part 5 of 6, Tropospheric systems, prepared by the

Central Radio Propagation Laboratory of the National Bureau of

Standards under sponsorship of the Ground Electronics Engineering and Installation Agency (Directorate of Engineering, ROZM)

United States Air Force; T. O. 31Z-10-1, published under

authority of the Secretary of the Air Force, June 15, 1961.

Barsis, A. P., K. A. Norton, P. L. Rice, and P. H. Elder, Performance predictions for single tropospheric communication

links and for several links in tandem, to be published as an

NBS Technical Note, 1961.

Barsis, A. P. , and M. E. Johnson, Prolonged space -wave fadeouts

in tropospheric propagation, NBS Technical Note No. 88,

(February 8, 1961), PB 161589, $2.00.*

Bean, B. R. , Prolonged space-wave fadeouts at 1, 046 Mc observed

in Cheyenne Mountain propagation program, Proc. IRE, 42,

No. 5, (May 1954).

Breed, C. B. , and G. L. Hosmer, The principles and practice of

surveying, Vol. II - Higher surveying, seventh ed. (John Wiley

and Sons, Inc., New York, N. Y. , 1953).

Crichlow, W. Q. , D. F. Smith, R. N. Morton, and W. R. Corliss,

Worldwide radio noise levels expected in the frequency band 10

kilocycles to 100 megacycles, National Bureau of Standards

Circular 557, (August 25, 1955); the derivation in this report

for f is correct only in the case where t and t are equal

c t to t . o

Order by PB number from the Office of Technical Services, U.S.

Department of Commerce, Washington 25, D. C. Foreign remittances

must be in U.S. exchange and must include one -fourth of the publication price to cover mailing costs.
-91-

Dickson, F. H. , J. J. Egli, J. W. Herbstreit, and G. S. Wickizer, | Large reductions of VHF transmission loss and fading by the

presence of a mountain obstacle in beyond-line-of-sight paths,

Proc. IRE, 41, 967-969, (August 1953). See also the discussion

of the paper "by J. H. Crysdale, Proc. IRE, 43, 627, (May, 1955

Doherty, L. H. Geometrical optics and the field at a caustic with

application to radio wave propagation between aircraft, Cornell

University School of Electrical Engineering Research Report

EE 138, (Sept. 1952).

Dutton, E. J. , On the climatology of ground based radio ducts and

associated fading regions; to be published as an NBS Technical

Note, (1961).

Florman, E. F. , and J. J. Tary, Signal-to-noise ratio, power,

and bandwidth requirements for tropospheric communication

systems; to be published as an NBS Technical Note, (1961).

Friis, H. T. , A. B. Crawford, and D. C. Hogg, A reflection theory

for propagation behind the horizon; Bell Telephone System

Technical Journal 36, 627-644, (1957), Monograph No. 2823.

Head, H. T. , The influence of trees on television field strengths at

ultra-high frequencies, Proc. IRE 48, 1016, (June I960).

Herbstreit, J. W. , and P. L. Rice, Survey of Central Radio Propagation Laboratory research in tropospheric propagation 1948-

1956; NBS Technical Note No. 26, (September 1959), PB 151385,

$4. 00.

*

International Telephone and Telegraph Corporation, Reference data

for radio engineers; Fourth edition, p. 732 (published by the

International Telephone and Telegraph Corporation, New York

N. Y. , 1956).

Order by PB number from the Office of Technical Services, U.S.

Department of Commerce, Washington 25, D. C. Foreign remittances

must be in U. S. exchange and must include one -fourth of the publication price to cover mailing costs.
-92-

Josephson, B. , and F. Eklund, Some microwave propagation experiences from a just-below-horizon path, IRE Trans. Antenn.

Prop. AP-6, 176-178, (1958).

McGavin, R. E. , and L. J. Maloney, Study at 1,046 megacycles per

second of the reflection coefficient of irregular terrain at grazing

angles, J. Research NBS, 63D , No. 2, (Sept. -Oct. , 1959).

McPetrie, J. S. , and L. H. Ford, Some experiments on the propagation oyer land of radiation of 9.2-CM wavelengths, especially

on the effects of obstacles, Proc. IEE 9 3, Part 3-A, Nos. 1-4,

531-538, (1946).

Norton, K. A. , Transmission loss in radio propagation, Proc. IRE

41, 146-152, (1953).

Norton, K. A. , Point-to-point radio relaying via the scatter mode

of tropospheric propagation, IRE Trans. Commun. Syst.

CS-4(1) , 39-49, (1956).

Norton, K. A. , Transmission loss in radio propagation - II. NBS

Technical Note No. 12, (June 1959), PB 151371, $3.00. See

also K. A. Norton, System loss in radio wave propagation,

J. Research NBS 63D, 53, (1959).

Norton, K. A. , and A. C. Omberg, The maximum range of a radar

set, Proc. IRE 35_, No. 1, 4-24, (January 1947).

Norton, K. A. , P. L. Rice, and L. E. Vogler, The use of angular

distance in estimating transmission loss and fading range for

propagation through a turbulent atmosphere over irregular terrain,

Proc. IRE 43, 1488-1526, (October 1955).

The Nautical Almanac (also the American Ephemeris and Nautical

Almanac). Issued each year by the Nautical Almanac Office,

United States Naval Observatory, U. S. Government Printing

Office, Washington, D. C.

* Order by PB number from the Office of Technical Services, U.S.

Department of Commerce, Washington 25, D. C. Foreign remittances

must be in U. S. exchange and must include one-fourth of the publication price to cover mailing costs.
-93-

Rice, P. L. , A. G. Longley, and A. P. Barsis, Transmission loss

calculations for tropospheric communication circuits, to be

offered for publication as an NBS Technical Note in 1961 or

1962.

Rice, P. L. , A. G. Longley, and K. A. Norton, Prediction of the

cumulative distribution with time of ground wave and tropospheric

wave transmission loss: part I - the prediction formula, NBS

Technical Note No. 15, (July 1959), PB 151374, $1.50.*

Saxton, J. A. , and J. A. Lane, VHF and UHF reception - effects of

trees and other obstacles, Wireless World, 61, 229-232,

(May 1955).

Smyth, J. B. , and L. G. Trolese, Propagation of radio waves in

the lower atmosphere, Proc. IRE 35, 1198, (1947).

Order by PB number from the Office of Technical Services, U.S.

Department of Commerce, Washington 25, D. C. Foreign remittances

must be in U.S. exchange and must include one-fourth of the publication price to cover mailing costs.
1.

I APPENDIX 1

Formulas for Fresnel Zone Calculations

In ray tracing the reflection of a ray is usually shown for

simplicity to occur at a point. Actually the entire surface is illuminated

nd r eradiates, but the resulting field at the receiver arrives with such a

hase and amplitude relationship that the contributions very nearly

cancel each other except for a small elliptical zone in the center. This

is called a Fresnel Zone, since it is closely related to the Fresnel

Zones of diffraction theory. The length of the ray path at the edge of

the first Fresnel Zone is one-half wavelength longer than the geometrical ray path. More generally the length of the reflected ray path at the

outer edge of the n Fresnel Zone is n half -wavelengths greater than

the geometrical path. Norton and Omberg [ 1947] have derived formulas

for the intersection of the Fresnel Zone with a plane surface which are

useful in evaluating terrain roughness and other factors involving

reflections. Figure 28 shows the geometry of Fresnel Zones on a

plane earth. With one terminal (usually the lower one) at the origin

the position of the center of the ellipse, the semi-major and the semiminor axes can be computed by means of the following formulas:

x = d

o 1

(h - h

)

i + £_

2h

x

[ 1 + (h

x + h

2

) 2

/n7,(R + n?,/4)]

(1-D
CDC

3)

CD o

rnom

-i

3)<

3Jm

ISI Om>r->mm>

33
- 1.3 -

x

l =

1 + 2R)(*) abn\

sin 6

n\

1 + (»¥)

(\ + h

2

)'

a + b + n\ 1 + nVH+^

4h

l h

2

d-2)

and

v^s abnX.

a + b + —

4

(1-3)

Under the conditions that one terminal is much higher than the other

and also is many wavelengths high, these formulas may be replaced by

approximate formulas with very good results:

c ^ d

o 1

i + 2h sin \\j (1-4)

V sin i|i L1 + 4h sin ijj (1-5)

y = x sin v|j (1-6)

In (1-4) through (1-6), ^ » ~\

, h

2

» h
2.1

APPENDIX 2

Earth Profiles

In plotting profiles of propagation paths it is convenient to use

a standard profile paper with an exaggerated vertical scale. This type

of grid allows for ray bending to a first approximation by increasing

the actual earth1 s radius, a , to an effective value, a. When the

o distance involved on the profile is much smaller than the effective

earth's radius the spherical surface can be approximated by a parabolic

surface by the following simple formula:

Ah=£- (2-1)

where Ah is the height of a plane at distance d from its point of tangency

on a sphere of radius a.

The actual radius of the earth is 3960 miles or 6370 km. It has

been common practice in the past to assume a/a = 4/3 which gives an

effective earth's radius of 5280 miles. A better value and one which

more nearly approximates the CRPL reference atmosphere with

N ~ 316 is a/a = 1.41. The effective earth's radius then is 9000 km.

s o This gives a convenient relationship which can easily be remembered.

If Ah is expressed in meters and d in km, (2-1) becomes Ah = d /18

(or conversely d= 3 */~2Ah).
2.2

It is relatively easy to construct a profile grid using any conrenient scale for distance and for height. Referring to Figure 29,

;onvenient height and distance scales are first arbitrarily selected.

To construct the grid it is best to start in the center and let d increase

both directions. Later the distance scale can be shifted so as to

start from either end or any other location. The same grid can be

used for a number of height and distance scales. If the distance scale

Ls changed by a constant, C, the height scale is changed by the square

2

iof this constant, C . For example, to increase the distance scale

by a factor of 2, it is necessary to use a height scale increased by a

Ifactor of 4.

h
CONSTRUCTION OF PROFILE GRIDS USING ARBITRARY EARTH RADIUS, a ACTUAL EARTH RADIUS, a

Q

= 6,370 km, 3,960 MILES

GENERAL FORMULA

Ah =

RECOMMENDED VALUE OFa/o„=l.4l

Ah -

d 0«m) An(METERS) " 18

"7"

i32.000j

j 28.000

1

124000]

Imooo!

1 16.0001

1 12.0001

! 8.000!

! 4.0001

8,000

7.000

6.000

soooj

4.000

3.000

2.000

2.000 i

1.750 !

1.500!

1,250 !

I.OOO!

750|

500 a

Ui

H

50

no M0

120 m

10

J40 so mH

100

J0O

400 JUL

440

_I20_

_240_

48)

I30_

260

520

J40_ _2»_

560

B0_

300

600

SO

640

340 _»_ _80_38) »

X aoc

FIGURE 29
3.1

APPENDIX 3

Conversion Factors and Constants

The international meter is the universal standard of length

throughout the world. Its actual length is known with an accuracy

lof about one part in ten million. Under the guidance of the

I International Committee of Weights and Measures work is in

progress toward the establishment of an atomic standard for

length measurement. The inch, originally the width of a man's

thumb, has been different in length as has been the foot, the

yard, the mile, etc. , in different countries owing to the use of

different conversion constants from the meter.

In October 1958 the International Committee adopted the

international yard as exactly 0. 9144 meters. Listed below are

many of the constants to be used to convert various units of length

into other units in keeping with the new definition.
3.2

8 8

c = 2. 9 97925 x 10 m/sec = 9. 8357 11942 x 10 ft/sec

5 = 1.8628 24231 x 10 mi/sec

X(100 Mc/s) = 2. 9 97925 meters = 9. 8357 11942 feet

_3

= 1.8628 24231x10 miles

1 meter = 39. 370 07874 inches = 3. 2808 39895 feet

= 6. 2137 11922 x 10

-4

miles

1 foot = 0. 3048 meters 1 inch = 2. 54 cm

1 statute mile = 1. 6093 44000 km = 0. 8 6897 62419 nautical miles

1 nautical mile = 1. 852 km = 1. 1507 79448 statute miles

1 radian = 57. 295 77951 degrees

1 degree = 17.453 29252 milliradians

tt = 3. 1415 92654

e = 2. 7182 81828

Radius of the earth for which 1* = 1 nautical mile is 3437. 74677 nautical:

= 3956.08833 statute miles

= 6366. 70702 km
3. 3

The National Bureau of Standards follows the

recommendations of the International Committee on Weights and

Measures to use new prefixes for denoting multiples and submultiples of units. In addition to the 8 numerical prefixes in common

use, which are given in the table below, the Committee expanded the

list by adding the 4 prefixes marked with an asterisk. Thus, for

-12

example, 10 farad is called 1 picofarad, and is abbreviated 1 pf.

Multiples and Sub -multiples

i ooo ooo ooo ooo = io

12

1 000 000 000 = 10

9

1 000 000 = 10

1 000 = io

3

100 = 10^

10 = 10

0. 1 -1

= 10

0.01 = io"

2

0.001 = io3

0.000 001 = io"

6

)0 000 001 - 10

" 9

o.ooo ooo ooo ooi = io

12

Prefixes Symbols Pronounciation

tera* T ter a

giga* G ji'ga

mega M

kilo k

hecto h

deka dk

deci d

centi c milli m

micro M- nano* n na/ no pico* P pi CO

S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

HONAL BUREAU OK STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, L).C, and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineering in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the

front cover.

WASHINGTON, D.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology.

Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standard Refer- ence Materials. Applied Analytical Research.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer Structure. Plastics. Dental Research.

Metallurgy. Thermal Metallurgy. Chemical Metallurgy. Mechanical Metallurgy. Corrosion. Metal Physics. Electrolysis and Metal Deposition.

Mineral Products. Engineering Ceramics. Class. Refractories. Enameled Metals. Crystal Growth. Physical

Properties. Constitution and Microstructure. Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. "Inorganic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. Operations Research. Data Processing Systems. Components and Techniques. Digital Circuitry. Digital Systems. Analog Systems.

Applications Engineering.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Solid State Physics. Electron Physics. Atomic Physics.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. Molecular Kinetics. Mass Spectrometry.

Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Cryogenic Technical Services. Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research.

Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services.

Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Standards. High Frequency Electrical Standards. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency ana Time Interval Standards. Electronic Calibration Center. Millimeter-Wave Research.

Microwave Circuit Standards. Radio Systems. High Frequency and Very High Frequency Research. Modulation Research. Antenna Research.

Navigation Systems.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exosphere

Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.
NBS