NTIA REPORT 84-165

HANDBOOK OF RADIO WAVEPROPAGATION LOSS

.(100 - 10,000 MHz)WILLIAM E. FRAZIER

U.S. DEPARTMENT OF COMMERCEMalcolm Baldrige, Secretary

David J. Markey. Assistant Secretar\for Communications and Informat!on

DECEMBER 1984

HANDBOOKOF

RADIO WAVE PROPAGATION LOSS(100 - 10,000 MHz)

NTIA REPORT TR-84-165

~ILLIAM E. FRAZIER

DECEMBER 1984

TABLE OF CONTENTS

Subsection

FOREWORD •• 1_" ._ •••••••'•••'••-•••• e.' •• e.•.•••••••••••••••'•••••••••'••••••••••••

ACI<NOWLEDGEMENT .-'••••••••'••_•••••••••••'••-••••'•••••••••••••-•••••••••••••••

ABST'RACT•••••••••••••••••'•••••' '.-1-' ••••••••••••••••••••••••••••••••••••••

SECTION 1

INTRODUCTION

BACKGROUND ••••••••'.' ••.•• '•••••_.' ••••••••-.•••••••••••••••••••••••••••••••-•••

SCOPE•••.••,•.••-••••.••••'••-•.••••••.•.••••••••••.•••••••••••••••••'••••••••••-•••

BASIC MEDIAN TRANSMISSION LOSS CURVES ••"••••••••••••••••••••••••••••••••

EFFECTIVE ANTENNA HEIGHTS••••••••••••••••••••••••••••••••••••••••••••••

SECTION 2

APPLICATIONS

GENERA.L••••• -.- I: .'••' •••' I;' ••• '•• '•••' ••' ••• '•••-.- ••••••••••••••••••' ••••••• '•••••••

Example Problem'. 1-"-' •••'••'•.•. '•••••••••••-•••-••'••••••••••••.•••••••••••'•••••

PROPAGATION EQUATIONS AND CONVERSIONS ••••••••••••••••••••••••••••••••••

FREE-SPACE EqUATIONS•••••••••••••••••••••••••••••••••"••••••••.••••••••••

Power Density in Free Space ••••••••••••••••••••••••••••••••••••••••••••

Received Power in Free Space •••.••••••••••••••••••••••••••••••••••••••••

EQUATIONS USED WHEN THE ANTENNAS ARE NOT IN FREE SPACE •••••••••••••••••

A General Equation for Received Power ••••••••••••••••••••••••••••••••••

A General Equation for Power Density•••••••••••••••••••••••••••••••••••

COMPUTING THE ELECTRIC FIELD STRENGTH••••••••••••••••••••••••••••••••••

ii

iv

vi

vi

1

1

3

6

10

12

15

15

15

17

20

20

21

21

TABLE OF CONTENTS (Continued)

SECTION 3

TERMINOLOGY

SUPPLEMENTARY DEFINITIONS ••••••••••••••••••• ~.......................••• 23

MODIFICATIONS TO THE SMOOTH-EARTH MEDIAN TRANSMISSION LOSS............. 23

LIST OF ILLUSTRATIONS ,

Figure

1

2

3

4

Transmission loss and path geometry •• •.•••••••••••••••••,.•••••••

Sample format of transmission loss curves •••••.••.••••.•..••••.

Example of different effective antenna heights for the

same: structural antenna heights ••••••:••••••.• •.•.•'•••••.•. •••••••

Transmission loss for different effective antenna height.s ••••••

LIST OF TABLES

Page

4

5

7

8

'Table

1

2:

3

Page

PATH SURFACE ELECTRICAL PARAMETERS............................. 2

CONSTANTS FOR EqUATIONS ................... •.•••'• ••••••••••••.••••'.. 17

CONVERSION OF POWER DENSITY TO ELECTRIC FIELD STRENGTH......... 22

REFERENCES

APPENDIX A: CURVES OF BASIC MEDIAN TRANSMISSION LOSS

iii

26

A-I

FOkEWORD

The Integrated Propagation System (IPS) is a computerized propagation

prediction model that was used to calculate the propagation loss values in

this document. The methods in the IPS model predict the median value of radio

wave propagation loss at far field distances over a spherical earth for the

line-of-sight modes of surface wave, free space, and multipath; and for the

beyond-line-of-sight modes of smooth earth diffraction and tropospheric

scatter. The program includes routines that automatically select the

appropriate propagation mode, based on input parameters and path geometry.

The IPS model was developed using propagation methods described in CCIR Study

Group 5, Volume V entitled Propagation in a Non-Ionized Media. The

fundamental propagation methodologies used in the IPS and Ground Wave

Propagation (GRWAVE) (see CCIR Report 714) models are similar except the IPS

.model includes the tropospheric forward scatter mode. The following is a list

of reference CCIR Study Group V documents that describe the propagation

methods incorporated in the IPS model:

Recommendation 310 - Definitions of Terms Relating to Propagation in the

Troposphere

Recommendation 341 - The Gonceptof Transmission Loss for Radio Links

Recommendation 369 - Reference Atmosphere for Refraction

Recommendation 453 - The Formula for Radio Refractive Index

Recommendation 525 - Calculation of Free Space Attenuation

Recommendation 526 - Propagation by Diffraction

Recommendation 527 - Electri.ca1 Characteristics of the Surface of the

Earth

iv

Recommendation 530 - Propagation Data Required for Design of

Tropospheric-Scatter Trans-Horizon Radio Relay

Systems and Earth-Space Telecommunication Systems

Report 229 Electrical Characteristics of the Surface of the

Earth

Report 238 Propagation Data Required for Trans-Horizon Radio­

Relay Systems

Report 563 Radiometeorological Data

Report 7L4 Groundwave Propagation in an Exponential Atmosphere

Report 717 World Atlas of Ground Conductivities

Report 719 Attenuation by Atmospheric Gases

Report 878 Special Features of the Concept of Transmission

Loss in the Ground-Wave Propagation Case

v

ACKNOWLEDGMENT

Special appreciation is expressed for the efforts of Sharon Rugh and

Robert Wilson for applying the Integrated Propagation System (IPS) computer

model for calculating the transmission loss values, for applying graphics

programs for preparing the curves and graphs included in this report, and for

providing suggestions that were helpful in completing this task.

ABSTRACT

This handbook is intended to assist in manual analysis techniques that

must be used when an automated analysis is not possible. It provides

estimates of radio wave propagation loss between transmitting and receiving

antennas above the assumed smooth-earth surface that were calculated using the

Integrated Propagation System (IPS) computer model. For many cases involving

electromagnetic compatibility analysis, the curves of predicted transmission

loss in this report may be used to estimate the transmission loss of the

desired and undesired signals. These loss values are given in dB as BASIC

MEDIAN TRANSMISSION LOSS for antennas with effective heights up to 5000

meters, operating in the 100 to 10,000 MHz frequency range, over land or sea,

at great circle earth surface distances up to 1000 kilometers. This handbook

is an initial document intended to be supplemented with additional curves that

will be provided on an ongoing basis.

KEY WORDS

Basic Median Transmission Loss

Electromagnetic Compatibility

Radio Wave Propagation

Transmission Loss

vi

SECTION 1

INTRODUCTION

BACKGROUND

The National Telecommunications and Information Administration (NTIA) is

responsible for managing the radio spectrum allocated to the U.S. Federal

Government. Part of NTIA's responsibility is to: ..... establish policies

concerning spectrum assignment, allocation and use, and provide the various

Departments and agencies with guidance to assure that their conduct of

telecommunications activities is consistent with these policies" (Department

of Commerce, 1983). In support of these requirements, NTIA periodically

develops aids to assist in spectrum engineering and analysis techniques. This

handbook provides estimates of radio wave far field propagation loss between

transmitting and receiving antennas above the assumed smooth surface of the

earth using the Integrated Propagation System (IPS) computer model. The

objective of this handbook is to assist in manual analysis techniques that

must be used when an automated analysis is not possible. This handbook is an

initial document intended to be supplemented with additional curves that will

be provided on an ongoing basis.

SCOPE

The curves in this handbook provide estimates of radio wave propagation

loss between transmitter and receiver terminals elevated above the assumed

smooth surface of the earth., The Integrated Propagation System (IPS) computer

model was used to calculate or predict all transmission loss values (NTIS,

1983) (Frazier, 1963). These IPS predictions were automatically plotted using

a graphics program and a computer-controlled plotter. The values are given in

dB, as BASIC MEDIAN TRANSMISSION LOSS. This terminology is used to specify

that the transmitting and receiving antennas are assumed to be isotropic and

that the predicted loss is the median value (50%) of a large distribution of

measured radio wave transmission losses, in dB. An isotropic antenna is a

theoretical point source that radiates equally in all directions.

The BASIC MEDIAN TRANSMISSION LOSS estimates are for antennas, up to 5000

meters in height, operating in the 100-10,000 MHz frequency range over

great-circle earth-surface distances up to 1000 kilometers. The antenna

heights are "effective antenna heights" above the smooth surface of the

earth. Effective antenna heights are discussed in detail later. All

estimates are based on vertically polarized transmissions over a homogeneous

earth surface, having electrical parameters of either sea water or average

land. Sea water is typical of ocean water, having a high salt content that

results in a good conducting surface along the transmission path. Average

land is assumed to have a moisture content that results in a conductivity

characteristic of soil that is neither too moist nor too dry. The

conductivity and relative permittivity (dielectric constant) of sea water and

average land in this report are given below in TABLE 1.

TABLE 1

PATH SURFACE ELECTRICAL PARAMETERS

SURFACE

Sea water

Average Land

CONDUCTIVITY

4.64 mhos/meter

0.005 mhos/meter

RELATIVE PERMITTIVITY

81

15

Transmission paths are assumed to be over a smooth spherical earth with

an effective earth radius to compensate for ray bending at low-to-medium

antenna elevations. An exponential reference atmospheric model was used to

compensate for ray bending at high antenna elevations.

The transmission loss curves are intended to be used in estimating the

signal level (field strength or power density) received at a given antenna.

The curves are based on propagation modes that provide a median (50 percent)

probability of occurrence. In an interference situation, there is at least

one undesired, or interference signal, that is present at the receiver

antenna along with the desired signal. The included transmiss·ion loss curves

may be used for estimating transmission loss for both the desired and

undesired signals.

-2-

Effects of terrain roughness, mixed path surfaces, vegetation, fading

relative to the median loss, and tropospheric ducting are not included in the

transmission loss curves. References are given for methods and data that may

be used to estimate ·these effects relative to the transmission loss in this

handbook.

Figure 1 illustrates the association between smooth-earth-path geometry

and the propagation modes represented by the transmission loss curves. The

lower part of Figure 1 shows the profile geometry of a smooth-earth path

between two antennas. The upper part of Figure 1 shows the transmission loss

relative to the path profile given in the lower part of the figure. On the

profile, the antennas are separated by a distance that is equal to the

smooth-earth radio 1ine-of-sight (LOS) distance. This is the maximum distance

at which the radio waves will be unobstructed by the curved surface of the

earth for the specified antenna heights. The radio LOS distance is greater

than the optical LOS distance on earth, in a normal atmosphere for the

specified antenna heights. Figure 1 shows that the maximum path distance

where the free-space loss is less than the smooth earth loss for specified

antenna heights is actually less than the radio LOS distance. The curve in

the upper part of Figure 1 shows that, at short distances, the transmission

loss is due to free space or mu1tipath, and at long distances, the

transmission loss is due to diffraction or tropospheric scatter. At path

lengths less than the maximum free-space-10ss distance, reflections from the

smooth earth may cause mu1tipath fading as indicated in Figure 1. The smooth

earth curves in this handbook follow the peak envelope of the mu1tipath lobes

and thus, the transmission loss at short distances is shown to be slightly

less than the free-space loss.

BASIC MEDIAN TR&~SMISSION LOSS CURVES

The basic transmission loss curves are plotted on standardized format

graphs as shown in Figure 2. All the curves are done on two-cycle semi10g

graph paper, with the ordinate giving basic median transmission loss, in dB,

and the abscissa giving the great-circle distance, in kilometers, along the

surface of the earth between the transmitter and receiver antenna sites.

There are two transmission loss curves on each graph. The straight line on

each graph is the Free-Space Transmission Loss. This is the loss determined

-3-

ANTENNA 2

PATH DISTANCE

4/3 EARI'H

MAXIMUM DISTANCE BEIWEEN ANTENNAS 1,2 FOR:-SPACE ross

I­:I:(!)

W:I:

l\NTENNA 1

I I lJ~ FREE-SPACE LOSS(J) MULTIPATH I I 'J:PP1?4c§ FADING : l 1'J'OJ{ ~ J SMOOTH-EARTH LOSS

~ I~ I I ,-,

I I I. ' ....I I =-i I

I i PATH I· DISTANCE

I I II I I

TX RADIO f' RX RADIO tHORIZON W. HORIZON

I , RADIO L1NE-OF-SIGHT.j::'-

I I I

Figure 1. Transmission loss and path geometry.

100 1000GREAT CIRCLE DISTANCE (km)

f= 1OOMHz,h 1= 1m,h2 = 1OOm,V.P.,Land and Sea Water

Space Loss

80

m 100-0.......---

(f) 120(f)

0-l

z 1400enIJ) 1602:(/)Z~ 180r~

IlJlI Z .

~ 200 I0I. I •

~ 220 rv)'23 240

26010

FIGURE A-l.

Figure 2. Sample format of transmission loss curves.

by the given frequency and distance in free space, which does not include the

ef fects of the earth or of antenna heights. The other curve gives the

Smooth-Earth Transmission Loss. This loss includes the effects of a smooth

spherical earth and is the value that should be used for the frequency,

distance, and effective antenna heights given. All the figures in this

handbook have a standardized and abbreviated summary of the parameters under

the figure. These standardized abbreviations· of the parameters include the

transmission frequency, in MHz; one antenna height (hi)' in meters; the other

antenna height (h2), in meters; V.P. for vertical polarization; and the path

surface type (sea water and or land). Note that the path transmission loss

will be the same regardless of which antenna is identified as the transmitter

or receiver.

For the actual transmission loss curves (see Figures A-I through A-132 in

APPENDIX A), there are two smooth earth transmission loss curves, one for land

and one for sea water. There are a number of figures where the land and sea

water curves are identical and thus, appear as a single curve for both.

To obtain values of transmission loss from the curves in A.PPENDIX A for

frequency, antenna heights, and path surface that are different from those on

the curves, but within the range of parameter values on the curves, an

interpolation procedure should be used to estimate an intermediate value

between the curves.

EFFECTIVE ANTENNA HEIGHTS

An effective antenna height is the structural antenna height that is

increased to take into account the average terrain elevation along the

transmission path. The effective antenna height is never less than the

structural antenna height. The input antenna heights to the IPS model must be

the effective antenna heights. Therefore, in order to utilize transmission

loss values from the curves, the antenna heights on the curves must be

representativ'e of the effective antenna heights for the user's transmission

path.

Figures 3 and 4 are illustrated examples of effective antenna heights and

the transmission loss prediction errors that could result from using incorrect

effective heights. Figure 3 shows two different transmission path geometries

-6-

I.......I

2km

.'

Effective height

",~j-,10 kIn

PATH A

50m

50'" Effective hei~~ '1 !!fec~~ heigh~ ,50fJ\ Ai

500 IIi

PATH B

Figure 3. Example of different effective antenna heights for the same structuralantenna heights.

Smooth Earth Lossf= 1OOMHz.Ved.Pol..Land

Fre~ SPPCE:} l-oss

490m~530m

100GREAT CIRCLE DISTANCE (km)

Transmission loss for different effective antenna heights.

1000

Cf..)

(Y)

CD

although both have structural antenna heights of 50 meters at each end of the

path. Path A has the 50-meter structural antennas located on local terrain

elevations of 500 meters, while the average terrain elevation along the path

for the left antenna site is 60 meters, and for the right antenna, the average

elevation is 20 meters. For this example, these average terrain elevations of

60 km and 20 km are determined for the teJ:rain along the path from 2 km to

from each antenna. For the left antenna, the center of radiation is 550

meter;s above sea level and 490 meters above the average terrain. at that end of

the path. Similarly, the right antenna height is. 550 meters above sea level

,. and 530 meters above the average terrain elevation at that end of the path.

The effective antenna heights for the upper path are· thus, 490 meters and 530

meters.

Figure has transmission loss curves that correspond to Path A and

Path B shown in Figure 3. The Path A curve is for effective antenna heights

of 490 meters and 530 meters, and the Path B curve is for effective heights of

SO meters and SO meters. The loss differences between the two curves on

F-igure- 4 are solely due to the differences in the effective antenna heights

IPS smooth earth model., As shown in Figure 4, for a transmi~sion

of SO km, the transmission loss difference between the curves is

22.A dB. At a distance of ISO km, the loss difference is 45.5 dB. The

22.4 dB and 45.5 dB differences represent the prediction error that would

result for the paths in Figure 3 if the effective antenna heights used in the

IPS computer model do not represent the path geometry.

Path B has the same SO-meter structural antennas' located> on a smooth

earth surface (plateau) that is 500 meters above sea level. For this path,. no

terrain. adjustments are necessary, since the structural antenna' heights are

the effective antenna heights. This is because the average terrain elevation

along the path ·is equal to each site elevation. Thus, for Path B, the

transmission loss will be the same as if the 50-meter antennas were placed at

level (assuming atmospheric refractivity changes. are negligible).

-9-

SECTION 2

APPLICATIONS

GENERAL

Transmission loss is only one parameter in the equation to determine

received signal level in, and system perfo.rmance of, a telecommunication

link. It is important to know the relationship of transmission loss to other

parameters such as, t.ransmitter power, antenna gains, and interference

criteria. To demonstrate this relationship, a summary of the system coupling

equation and. the important parameters are given in the following section for

simple system models.. A sample problem is given to illustrate the application

of the transmission loss curves in the solution of an interference problem.

The simplest system. moliel for evaluating electromagnetic compatibility

(EMC) is one that. represents standard deterministic prediction equations for

the desired and undesired signals at the receiver input (CCIR, 1983). The

desired signal at the receiver input is determined by Equation 1.

SIN(dBm) ST(dBm) + GT(dBi) + GR(dBi) - L(dB) (1)

signal at the receiver input

signal from· the transmitter

transmitter antenna gain (typically mainbeamdesired

gain)

GR =. receiver antenna gain

L = basic transmission loss for desired signal path

(the median loss (50%) should be used here).

where:

A simple evaluation would be to compute SIN and compare this value with a

performance threshold. If the level of SIN exceeds the threshold, then a

level of acceptable desired signal performance is available. The signal could

also be readily converted to a signal-to-noise ratio (SiN) since, in Equation

2:

-10-

where:

=

=

=

signal-to-noise ratio at the receiver input

equivalent input noise. power

( 2)

and all other terms are previously defined. An identical analysis can also be

performed for the interfering signal in terms of the input power or the input

interference-to-noise ratio (liN). The evaluation of liN is often employed in

EMC analyses.

The undesired signal at the receiver input is given similarly by

Equation 3.

undesired transmitter signal power

undesired transmitter antenna gain (mainbeam or

where:

lIN = undesired receiver input power

ITGTl =

(3)

sidelobes)

GRl = receiver antenna gain in direction of interference

LI - basic transmission loss for undesired signal path,

(a 10% to 50% loss should be used here)

The next logical step in increasing the complexity of the calculations

would be to compute (S/I)IN and compare this to a performance threshold to

determine if the level of performance is acceptable or not acceptable. The

(S/I)IN is given by Equation 4.

-11-

and the criteria are:

(S/I)IN (dB) > (S/I)TH (dB)

(S/I)IN (dB) < (S/I)TH (dB)

where:

(4)

acceptable performance

unacceptable performance

(S/I)TH = desired-to-undesired performance threshold criteria

(see CCIR Report 526 for typical performance

criteria)

and all other terms are previously defined.

Example Problem

To demonstrate application of the transmission loss curves in this

handbook, the curves are used in the solution of an example telecommunications

problem. This example problem involves a mobile station receiving two

cochanne1 virtually polarized EM signals simultaneously; one desired signal

and one undesired signal. The objective is to determine whether the

interference to the mobile station receiver is acceptable. The following

parameters are known for the telecommunications systems.

-12-

Parameter

ST = 100 watts

hT = 10 meters

Gr = 8 dBi

hR = 1 meter

GR = 0 dBi

NIN = -128 dBm

(S/N)IN = 15 dB

(S/I)TH = 7 dB

IT = 15 watts

hI = 50 meters

GT1 = 7 dB!

Base Station

(desired signal transmitter)

Base station transmitter output power

Base station effective antenna height

Base station antenna gain

Mobile Station

(desired signal receiver)

Mobile station effective antenna height

Mobile station antenna gain

Mobile station input noise level

Mobile station input signa1-to-noise ratio

Mobile station criteria for FM to FM marginal performance

Interfering Station

(undesired signal transmitter)

Interfering station's transmitter output power

Interfering station's effective antenna height

Interfering station's antenna gain

The distance between the base station and a specific location of the

mobile station is known to be 60 km over a land path. Since the terrain is

smooth along the path, the smooth-earth transmission loss curves in APPENDIX A

may be- used to estimate the propagation loss. The basic median transmission

loss between the base station and the mobile station is determined, using the

-13-

curve for land in Figure A-127, to be L(b) = 171 dB for hR = hI = 1 m,

hT = h2 = 10 m, and f = 100 MHz at a distance of 60 km. The level of desired

signal at the input to the mobile station can now be determined using

Equation 1.

+ GT(dBi) + ~(dBi) - L(dB)

+ 8 + 0 - 171

= ST(dBm)

50

= -113

SIN(dBm)

SIN(dBm) =SIN(dBm)

The (S!N)IN at the mobile receiver is determined using Equation 2.

(S!N)IN(dB) = SIN(dBm) - NIN(dBm)

= -113 - (-128)

(S!N)IN(dB) = 15

The distance between an interfering station and the specific location of

the mobile station is known to be 53 km over a smooth land path. The

propagation loss between the interfering station and the mobile station is

thus determined, using the curve for land in Figure A-128, to be

LI(dB) = 153 dB for hR = hI = 1 m, hI = h2 = 50 m, and f = 100 MHz at a

distance of 53 km.

The level of the undesired signal at the input to the mobile station is

determined using Equation 3.

IIN(dBm) = IT(dBm) + GTl (dBi) + ~1(dBi) - LI(~B)

= 42 + 7 + a 153

IIN(dBm) = -104

The desired-signal-to-interference-signal ratio at the mobile receiver

input is determined using Equation 4.

(S!I)IN(dB) = SIN(dBm) - IIN(dBm)

= -113 (-104)

(S!I)IN(dB) = -9

-14-

The calculated value of (S/I)IN(dB) = -9 is compared

desired-to-undesired performance threshold criteria (S/I)TH = +7.

(S/I)IN(dB) = -9 < + 7 = (S/I)TH(dB)

to the

Since the calculated value of (S/I)IN is less than the threshold value of

(S/I)TH' an unacceptable interference situation exists between the interfering

station and the mobile station.

PROPAGATION EQUATIONS AND CONVERSIONS

Equations are given to compute the power density and field strength

produced by a transmitter in free space (i.e., a region in which there are no

substances to reflect, absorb, refract, or otherwise affect the radio

waves). Then the equation is given for computing the power available at the

terminals of a receiving antenna that is illuminated by the transmitting

antenna. The parameter "basic free-space transmission loss" (Lbfs ) is

introduced to allow this received power to be computed with a compact formula

(CCIR, 1982b).

These equations are followed by expressions that can be used when the

path between the transmitter and receiver (or observation point) is not in

:':free space. The parameter "basic transmission loss" (Lb) is introduced to

allow convenient calculations for these genera1-environment problems.

FREE SPACE EQUATIONS

Power Density in Free Space

Assume that p(watts) is input to an antenna that is 100 percent efficient

and radiates isotropical1y. Consider observation points at a distance of

r(meters) from the transmitter. The power density at these points is now the

power per unit area flowing through a spherical shell of radius r with a

center at the transmitting antenna. At any point on this sphere, the power

density Pd (W/m2), is determined by Equation 5.

-15-

where:

Pt(W)

241Tr (m)( 5)

Pd = power density

Pt = the power delivered to the transmitting antenna

r = distance

and, where r is in statute miles (there are 1609 meters in one statute mile):

(Sa)

If the problem input parameters remain as now stated, but the desired

output is in dB above 1 mW/m2 (i.e., dBm/m2), then:

= 10 log[Pd(:W/m

2

y]."r (ill)

~

( 5b)

or, for statute miles:

- 10 log[P~ (W) x 30.73 x 10-g x 10 3]r (mi)

= 10 log Pt(W) - 20 log r(mi) + 10 log (30.73 x 10-6)

= 10 log Pt(W) - 20 log r(mi) - 45.12

and, the transmitted power is expressed in dBm (i.e., dB above 1 mW):

Pt(dBm) = 10 log Pt(mW) = 10 log Pt(W) + 30 (Sc)

-16-

so that:

but generally:

where:

K = a constant dependent on the unit of measurement used to

express r (see TABLE 2) and all other terms are

previously defined.

TABLE 2

CONSTANTS FOR EQUATIONS

Units of r K1 K2

Statute miles 75.12 36.58

Nautical miles 76.34 37.80

Kilometers 70.99 32.45

Feet 0.67 -37.87

Meters 10.99 -27.55

Received Power in Free Space

The effective aperture (Ae ) of an antenna is defined by:

where:

P (W)r

A (m) =~-~e 2

Pd(W/m )( 6)

Pr =the power delivered to a matched load at the terminals

of the receiving antenna

-17-

This aperture is computed by:

where:

A (m)e

= g (numeric)A(m)24'11' ( 6a)

g == the power gain of the antenna expressed as a ratio relative

to the gain of an isotropic antenna that is 100 percent

efficient

A= the wavelength of the radiation

For an isotropic antenna that is 100 percent efficient, g == 1 and:

A (m)e

( 6b)

and all terms are previously defined. A formula for the power received by

such an antenna in free space can be obtained by adding Equations 5 and 6b to

Equation 6. The result is:

2 2 [A(m) ]2Pr(W) == Pd{W/m) Ae(m) == Pt (W)[4'11'r(m)J (7)

Here, A and r have the same units, and Pr and Pt have the same nonlogarithmic

units (e.g., watts, milliwatts, etc.). If the problem is specified in terms

of frequency (f) rather than wavelength, then one can substitute:

A(meters) 300== ~f7":(MH-=-z~) (7)

into the preceding equation and obtain:

569.9Pt

P == ---------......,..r (f(MHz) x r(meters»2

where Pr and Pt are in the same nonlogarithmic units.

( 8)

If the transmitted power and received power are expressed in the same

logarithmic units (e.g., dBm or dBW), then the proper equation can be obtained

-18-

by taking the logarithm (base 10) of each side of this equation and

multiplying the results by 10. Thus:

Pr = Pt - 20 log f(MHz) - 20 log r(meters) + 27.55 (8a)

This can be adapted to other units (e.g. t when r is in statute miles):

P'r = Pt - 20 log f(MHz) - 20 log r(miles) - 36.58

Equation 8b is frequently written as:

where the basic free space transmission loss (Lbfs) is given by:

Lbfs = 20 log r(units) + 20 log f(MHz) + K2t

(8b)

( 9)

(10)

where values for K2 appear in TABLE 2 for different units of r t the slant

.. range (CCIRet 1982c) •.

The preceding equations for received power are for' lossless (1.e., 100

percent efficient) isotropic antennas at both ends of the link. If the

transmitting antenna is not like this t then the power density (Pd ) in front of

receiving antenna changes to:

(11)

where Gtand Gr are the transmitter and receiver antenna gains, respectively,

relative to a loss less isotropic antenna (dimensionless units). If the

receiving antenna is not lossless or isotropic t its effective aperture is

given by Equation 6a. Inserting Equations 11 and 6a into Equation 6 yields:

P = P G G r--.J2r t t r tLmrJ

-19-

(12)

In logarithmic units (and allowing use of f instead of X):

P/dBW) = Pt(dBW) + Gt(dBi) + Gr(dBi) - 20 log r(miles)

- 20 log f(MHz) - 36.58 (13)

In this case, add

.the gain of lossless (100 percent efficient)

isotropic antenna.

= Pt(dBw) + Gt(dBi} + Gr(dBi} - ~fs(dB) (14)

manufacturers' values before using them in Equation 13.

Some manufacturers specify gain relative to a loss less 1/2 X

Gt(dBi) = 10 log GtGr(dBi) = 10 log Gr

dBi = de·cibels above

rather than relative to an isotropic antenna.

Equations 10 and 13 yields the equation for power available at

terminals of the receiving antenna when the transmission medium is free

2accounts for the 1l(41Tr ) spreading loss in free space, a

region free from reflecting, absorbing or refracting materials. The terms Grand Gt are receiver and transmitter antenna gains, respectively, in dBi.

These terms also account for losses within the antennas due to the lack of 100

percent radiation efficiency.

There may be other losses between the outputs of the transmitter and the

transmitting antenna. These can be ohmic losses (e.g., in transmission lines,

wave guides or antenna couplers). Mismatch losses can also occur. Similar

losses may exist between the receiving antenna and the input to the

receiver. Also, there may be differences in the polarization of transmitting

-20-

and receiving antennas. To account for these losses when calculating the

power at the input terminals of the reciever (Pr)' Equation 14 should be

modified to read:

Pr = Pt + Gt + Gr - ~fs - (OTHER LOSSES)

where Pt is the power available at the output of the transmitter.

(15)

In many cases, the space between the two antennas will contain

atmospheric effects (e.g., rain) or irregular earth obstructions (e.g., hills

and mountains). Thus, the basic free space transmission loss (Lbfs ) will

frequently not be appropriate. Instead, the more general, basic transmission

loss (Lb ) is needed. The received power equation becomes:

(16)

A General Equation for Power Density

An equation for predicting power density in a non-free space environment

can be obtained by entering Equations 16 and 6a into Equation 6 and solving

for Pd. The result is:

2\Pd,(dBm!m ) = Pt,(dBm)' + G~ - ~. +20 log (f (MHz»

-38.54 - (Losses between the transmitter (17)

output and the transmitting antenna)..

COMPUTING THE ELECTRIC FIELD STRENGTH

If the engineer/analyst needs to know the electric field strength at a

point in space, it may be computed from the power density., In the far field

of the transmitting antenna, these quantities are related by:

E2

(V/m, rms)Pd(W/m2, avg) = -~-n~-~

-21-

( 18)

where:

E = electric field strength

n = the impedance of free space = 1201TU or =377r1.

rms = root mean square.

TABLE 3 is a set of conversion equations for a variety of units.

TABLE 3

CONVERSION OF POWER DENSITY TO ELECTRIC FIELD STRENGTH.

Erms = 19.42

E = .61 xrms

(p ) 1/2avgP . 20

10 avg/

Erms in VIm, Pavg in W/m 2

Erms in VIm, Pavg in dBm/m2

Erms in dBll VIm, Pavg in dBm/m2

... Pa.vg = Erms - 115.8

Pavg

Pavg

CErms

)2

= -==--=-=-376 •. 99

= 20 log Erms +

in W/m2 , Erms in VIm

Pavg in dBm!m2 , Brms in VIm

Pavg in dBm/m2 , Erms in dBll VIm

:E rms = rIDS electric field. strength,

Pavg = average power density.

NOTES: 1) Transmitter duty cycle effects must be taken into accountindependently, as must all nonsinusoidal waveforms.

2) All relations apply only in the far field.

-22-

SECTION 3

TERMINOLOGY

SUPPLEMENTARY DEFINITIONS

In using some references, analysts come across other terms that are used

in the calculation of received power. To aid in correlating these with the

terms used in this section, some of the more common terms are defined below.

Antenna Factor. This is 10 log of the square of the ratio of the

electric field intensity (Vim) at the antenn.ato the terminal voltage (V).

Antenna gain can be computed from the antenna factor using Equation 19.

G = 20 log f - Af - 30 (19)

where G is the gain in dB, and Af is the antenna' factor in dB.

Transmission Loss. This is 10 10g10 of the ratio of the power input to

the transmitt.ing antenna to the power available from the receiving antenna.

If it is designated as loss (L) in dB, it can be related to Lb through:

L =1- -G.-G-b t r (20)

MODIFICATIONS TO THE SMOOTH-EARTH MEDIAN TRANSMISSION LOSS

Modifications of the smooth-earth transmission loss from terrain

roughness, mixed path surface, foliage, rain, and long-term time-dependent

power fading must be determined from other sources and added to the

smooth-earth transmission loss predictions obtained using the methods in this

handbook. Comments on the effects of these phenomena, relative to the

smooth-earth transmission loss, are given below along with appropriate

references.

Terrain roughness along the transmission path can produce transmission

loss variations above and below the median loss. Generally, the loss will

increase over rough terrain for beyond-the-horizon paths relative to the same

distance over a smooth earth. Line-of-sight transmission over rough terrain

can produce short term multiple reflections that are referred to as multipath

-23-

or fast fading. Multipath is characterized by rapid variations about the

median loss from a 3 dB improvement to a deep fade of 30 dB or more of the

signal. References for the effects of multipath and rough-earth effects are

(Rice, 1966), (Powell, 1983), (NTIS, 1983), (CCIR, 1982d), and (Weissberger,

1982).

Mixed path surface transmission can be significantly different than

transmission over a path having uniform electrical characteristics. A typical

mixed path would be from a ship at sea to an inland station. Propagation

characteristics could change abruptly at the land-sea boundary. This

phenomenon is important for low antennas at frequencies below about 160 MHz.

References for the effects of mixed path propagation are (Millington, 1949),

and (Weissberger, 1982).

Foliage attenuation must be considered when either antenna is very near,

or emersed in, trees or other foliage. Determining the effects of foliage on

the propagating signal requires detailed knowledge of the environment.

Although in some cases, foliage may improve the signal propagation, the usual

effect is increased attenuation relative to the median. References for

foliage attenuation are (Saxton, 1955), (Kinase, 1969), (J & B, 1966),

(Weissberger ,.. 1982), and (CCIR, 1982d).

Rain attenuation becomes important for transmissions at frequencies in

the 10-30 GHz range. This phenomenon produces the largest variations in

signal phase and amplitude on earth-space line-of-sight paths. References for

the effects of rain attenuation are (Crane, 1979), (CCIR, 1982e),and

(Welssberger, 1982).

Tille-dependent power fading (long term) must be considered for

propagation over beyond-the-horizon paths. This phenomenon causes variations

relative to the median loss due to large-scale slow changes in the

atmosphere. It is a function of time of day, time of year, and geographic

location. The transmission loss curves in this handbook provide estimates of

the median loss (50%) of log normal distribution of transmission losses. The

variation about this median for any other percentile (10%, 90% ,etc.) can be

estimated using an emperical model for long-term time-dependent power fading

given in the references below. As an example, for a given propagation path,

the transmission loss for a 10% pro~abi1ity may be 10 to 15 dB less than the

median loss (50%). Also, for a 90% probability, the loss may be 30 dB more

-24-

than the median loss. The method and data to estimate long-term

time-dependent power fading are well documented in (Rice, 1966), (Weissberger,

1982),. (NTIS, 1983), and (Powell, 1983).

Tropospheric ducting is a significant anomalous propagation mode for

frequencies above 100 MHz. The probability of occurrence of tropospheric

ducting typically is less than about ten percent of the time. The ducting

mode usually is not a reliable or continuous mode of propagation. Ducting

occurs as the result of atmospheric stratification that is found typically in

coastal regions. Tropospheric ducting can produce unusually high signal

levels relative to the median value. Estimates of the worldwide probability

of occurence of tropospheric ducting and the resultant signal enhancement from

ducting may be determined using (CCIR, 1982a) and (Ortenburger, 1978).

-25-

REFERENCES

CCIR (1982a), Report 718-1, Effects of Large-Scale Tropospheric Refraction

on Radiowave Propagation, Volume V, Propagation in Non-Ionized Media,

XV Plenary Assembly, Geneva, Switzerland, 1982.

CCIR (1982b), Recommendation 525-1, Calculation of Free Space Attenuation,

Volume V, Propagation in Non-Ionized Media, XV Plenary Assembly, Geneva,

Switzerland, 1982.

CCIR (1982c), Recommendation 341-1, The Concept of Transmission Loss for Radio

Links, Volume V, Propagation in Non-Ionized Media, XV Plenary Assembly,

Geneva, Switzerland, 1982.

CCIR (1982d), Report 236-5, Influence of Terrain, Irregularities and

Vegetation on Tropospheric Propagation, Volume V, Propagation in

Non-Ionized Media, XV Plenary Assembly, Geneva, Switzerland, 1982.

CCIR (l982e), Report 721-1, Attenuation by Hydrometeors, In Particular

Precipitation, and Other Atmospheric Particles, Volumes V, Propagation

in a Non-Ionized Media, XV Plenary Assembly, Geneva, Switzerland, 1982.

CCIR (1983), Handbook, Spectrum Management and Computer-Aided Techniques,

Geneva, Switzerland, 1983.

Crane (1979), Crane, R.K., Prediction of Attenuation by Rain, Environmental

Research and Technology Incorporated, Concord, Massachusetts, August

1979.

Frazier (l963),Frazier, W.E., Anderson, D.S., A Propagation ~lodel for

Electromagnetic Compatibility, Ninth Tri Services conference on

Electromagnetic Compatibility, Unclassified Proceedings, lIT Research

Institute, Chicago, Illinois, October 1963.

-26-

REFERENCES (cont.)

J & B (1966), Jansky and Bailey Engineering Department, Tropical Propagation

Research, Final Report, Volume I, Atlantic Research Corporation,

Alexandria, Virginia, 1966.

Kinase, A. (1969), Influences of Terrain Irregularities and Environmental

Clutter Surroundings on the Propagation of Broadcasting Waves in the

VHF and UHF Bands, NHK Technical Monograph No. 14, Japan Broadcasting

Corporation, Tokyo, Japan, March 1969.

Millington (1949), Millington, G., Groundwave Propagation Across a Land/Sea

Boundary, Nature, January 22, 1949.

NTIS (1983), National Technical Information Service, Master Propagation

Systems (MPS11) User's Manual, NTIS-PB83-178624, (Computer Tape

NTIS-PB83-173971), 1983.

Ortenburger (1978), Ortenburger, -L.N., et al., Radiosonde Data Analysis III,

Summary of Maps of Observed Data, GTE Sylvania Incorporated, Mountain

View, California, December 1978.

Powell (1983), Powell, J.R., The Terrain Integrated ,Rough Earth Model (TIREM),

ECAC-TN~83-002, DoD ECAC, Annapolis, Maryland, September 1983.

Rice (1966), Rice, P.L., et al., Transmission Loss Predictions for

Tropospheric Communications Circuits, Technical Note 101, Volumes I and

II, National Bureau of Standards, Washington. D.C., May 1966.

Saxton (1955), Saxton, J.A., VHF and UHF Reception, Effects of Trees and

Other Obstacles, Wireless World, May 1955.

-27-

REFERENCES (Cont.)

Weissberger (1982), Weissberger, M., et al., Radiowave Propagation: A

Handbook of Practical Techniques for Computing Basic Transmission Loss

and Field Strength, ECAC-HDBK-82-049, Dop ECAC, Annapolis, Maryland,

September 1982.

-28-

APPENDIX A

CURVES OF BASIC MEDIAN TRANSMISSION LOSS

This appendix contains curves of Basic Median Transmission Loss in dB for

frequencies of 100 MHz, 1,000 MHz, and 10,000 MHz. Est~mates of transmission

loss for frequencies between 100 MHz and 10,000 MHz may be determined by

interpolation between the curves. TABLE A-I is included to help locate the

transmission loss curve for a particular combination of frequency and antenna

heights.

A-I

;p­I

N

T~~LE A-I: CURVES OF BASIC MEDIAN TRANSMISSION LOSS

LIST OF TRANSMISSION LOSS FIGURES

f(MHz)

~1 10 50 100 200 500 lK 2K 5K

hI (m)

100 1 A-127 A-128 A-I A-2 A-3 A-4 A-5 A-610 A-129 A-130 A-13l A-7 A-8 A-9 A-lO A-ll50 A-12 A-13 A-14 A-IS A-16 A-17 A-18

100 A-19 A-20 A-2l A-22 A-23 A-24200 A-25 A-26 A-27 A-28 A-29500 A-30 A-3l A-32 A-33

lK A-34 A-35 A-362K A-37 A-385K A-39

1000 1 A-132 A-40 A-4l A-42 A-43 A-44 A-45 A-4610 A-47 A-48 A-49 A-50 A-51 A-52 A-53 A-5450 A-55 A-56 A-57 A-58 A-59 A-60 A-6l

100 A-62 A-63 A-64 A-65 A-66 A-67200 A-68 A-69 A-70 A-7l A-72500 A-73 A-74 A-75 A-76

lK A-77 A-78 A-792K A-80 A-8l5K A-82

10000 1 A-83 A-84 A-85 A-86 A-87 A-88 A-89 A-9010 A-91 A-92 A-93 A-94 A-95 A-96 A-97 A-9850 A-99 A-lOO A-lOl A-l02 A-l03 A-104 A-lOS

100 A-106 A-l07 A-l08 A-l09 A-110 A-Ill200 A-112 A-I 13 A-114 A-lIS A-116500 A-117 A-118 A-119 A-120

lK A-12l A-122 A-l232K A-124 A-125SK A-126

Example: f(~lz) = hl(m) = 200 meters, h2(m) lK meters, curves in Figure A-27.

80

co 100u'--"

Vi 120t/10 ,

Z ~40I ,0(/")Vi 160:2if;Z« 180er::

? f-I

W

~ 2000w:2 220uifj

«cO 240

260

I--

~~ -r-------

r--.

---------I~ - r--h-~ ~ - e-

~Sea Water

Ir-.Land

~'"t'--

"'" I I !i'-- """r,"'-

~ IIIf'..

"" II!

----~ I I

I

~ I

1'-"~

'"'" r"\.1'\

10 100 1000GREAT CIRCLE DISTANCE (km)

FIGURE A-1. f= 1OOMrlz,h 1 =--= 1m,h 2 = 1OOm,V.P.,Land and Sea Water

.I

i1r

III

ILanrr+i~ uTl I[ II I

~! iJitll1·.····.1· . ha~t_. fl •.

f=:-:::=----

r--_______ ti------l~ I I I ! I I I I

80

160

180f-

Vi 120t/j . .o-l I25 140 ~(f) IUi:2V)Z<{er::

co 100""0

'---"

:r+.-

uU)

ca 2401'\

26010 100 1000

GREAT CIRCLE DISTANCE (km)FIGURE A-2. f= 1OOMHz,h,= 1m)h 2 ::-..::200m,V.P.)Land and Sea Water

80

OJ 100u

"--"'

if) 120if)

0-i

z 1400V)l/) 160:2if)

Z<: 180n::::

;J> f-IVl Z

<: 2000LJ

~ 220uIf)

Ci5 240

260

~ I~-== ---...:::::::::------b---r----.r-------I-----~ r---- r-- t-I-

.......... t----1---- r--.. -F:::::t'-.. 't'"'-. SeaWater ------r--

I ~" I ""-.t-r-

I •r-......

I ...... t'--

~~1'--.I

I LandI

II

~\II

II

iI

I I ~ i

I ~!

I iI I II """""

I

I~I ~ !

r"., I

~

10 100 1000GREAT CIRCLE DISTANCE (krn)

FIGURE A-3. f= 1OOtv1Hz,h,= 1m,h 2 =500m,V.P.,Land and Sea Water

80

---..m 100u'--'"

v:(/) 1200--.-J

z°140VjVi~(/) 160z<:r>"----~

~ 180I zC\

<:-0

~ 200uIf)

« 220ill

240

...

~

~'---.

--- r.::::: r----I--h---.-~

I-------- r-~ Ir---....

I I ----~ ~.• ----.. t----,-.. II ;----..,~ 9~~ Water

r-- t---

r-- Lcmd I ""I'-, r--t--I--I--! I I

'" I I

!I, I~,\ I Ii

I I I.i \\I i I I

I i III II ~ II

I II- ~I

I I~cI

~

!f-

~I I !

"" "'" \

10 100 1000GREAT CI~CLE DISTANCE (km)

FiGURE A-4. f-l OOMHz)h, = 1rn)h 2 = 1km)V.P.,Lond and Sea Water

80

.---....co 100""0

"--'"'

if)(I) 1200-l

Z,-...140'---'

U1tn2(I) 160z<:0::::

:r r-180-..;j z

<:Qw

200:2

UIJ)« 220co

240

.' ,

..

~=:::~ ......' .. --- ,

'.

~...;~

.~=--

~

------:::::.:: ,.,...

~~........ r-.'. .........1'----.

~ -~I

.........

"t------~ Sea Water

---..Land

r---I

k= ~ \' i

!

I \S II I

Ii

~II .

~,

""'"~ \,\

10 100 1000GREAT CIRCLE DISTANCE (km) ,

FIGURE A-5. f= 1OOMHz,h 1 1rn,h 2 . 2km,V.P.,Land ond Sea Water

80

...--,.en 100'D...........,

if)

Vi 1200---l

Z0 140if)V)

2en 160z<{rv'-'-.>--:P

180I

zco<t:0

~ 200.e::::.

u

S2 220en

240

- : .....

:--". ~--....... ---~ ~

~~~~:::=: ::::::~~

~--.::~::::~

"~:~ --~~~ "'.. r---_.......'\ -r-~

1')\ II I..[iud· \ ~ea Watel:" II I I I

I i

...... \ I I 11! i I~ I i

. """ I'"I ~ '\.

I ~·1 I

10 100 1000GREAT CIRCLE DISTANCE km)

FIGURE A-5. f .1 OOMHz.h t :;::;: 1rn,h 2 --5krn,V.P.• Land and Sea Water

00 L0 Q)..-- +-"

0$:

0Q)

(/)

""0Ca

-0,-...c

EE.::t. .:-.'--/ Q...

w. >u ~

z E<{a1-0tf)N

° 0 11° N'-··w ~~ ~u ­(l:0- ..--U II1-£<{ ~

W N(l:I

0 2oo

I..._--- _.......-_...- ---- -;7

I /I ./

l /I // /I IIif /

f /.

1I//

I /I /t J

I II . II I

:; I,11/II

.

I

'j0 0 0 0 0 0 0 ° 0CD 0 N .q- 1O CD 0 N .q-

.,.... .-- ,.....~ ..-- ..- N ('\J ('\J

(8P) SSOl NOISSI ~I\JSNVt.J.l. NVICJ3V\) JISV8

A-9

o

I'.1'I-

.KI

<{

w(l:

::Jou..

80

.............OJ 100u''''-

If)

tn 1200--..!

Z0 140<./)if)

2:If) 160z<r::

:t> CLI f---~

1800 z<r::0

sg 200u

~ 220IT)

240

--.I II. I

-

r~

I-

.~~

II

f

! I...........I"f",

-. !0,

I II

~ I

. :

I I~

,,!

I~

1:

II~

~;

"-

J

1"-

i

~

-

1'\

,.

1\

i

!r--:-

~ .i

II !L10 100 1000

GREAT CIRCLE DISTANCE (km)FIGURE A-8. f-'-l OOMHz,h,-l Om,h 2 =500m,V.P.,Land and Sea Water

80

,--.....en 100""0

"'--".VIL0 1200-J

Z0 140ViVI:2'Jl 160z<

;J> er::II-' 180I-' z

<{

0

~ 200u-VI<{ 220m

240

II II

--t::--

~r--..r-----

I'.

I......... f"..

I~ -

I '\I

\

I~r

I~

I

I~ I

r

'"I~I'"

I

. "'-r\

--10 100 1000

GREAT CIRCLE DISTANCE (km)FIGURE A-g. f= 1OOMHzth J = 1Om,h 2 = 1km,V.P.tLond and Sea Water

I

~-

80

120

140,. I 1- -u u_ "1\ 1 'ii II I I \ I j -l J

I i I \ I160 r . I I "'-- I

I ! i f"-.... i LJI ! " I

180 I I I "'I"" III! I++-,,-I I I I H- I~

I I

200

240

220

....----.. ---~ 100~Ul!J)

0----l

Z0!J)!J)

2iJ)

Z«0:::::r ~

f-'ZI\)

«0L:.J:2

UVi«OJ

10 100 1000GREAT CIRCLE DISTANCE (km)

FIGURE A-10. f= 100MHz,h,-1 Om,h 2 =2km,V.P.,Lond and Sea vVoter

80

----.ill

100D'-..-/

(J)v')

0120......J

z0VJ

140Vi2:UJZ«

160CL~ f--If--'

Zw«0 180u2:

u-(f) 200«co

22.0

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"',,,,,,:- I .I Ni\-

r- I l' I i"bJI I _J I I II I II

10 100 1000GREAT CIRCLE DISTANCE (km)

FIGURE A-11. f= 1OOMHz,h t = 1Om,h 2 =5km,V.P.,Lond and Sea Water

80

~

m 100u.-----(f)(f) 1200

I--'

Z0 140if)Vi-:2(f) 160z<

;J;- et:::I f-I-' 180+:- Z

<t:0

~ 200uVi<t: 220Q)

240

-I

Ir

~~-

i~

~ <:

If"-..-.r- r-

I~I~

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I

I

I

I~ I

""'" - '--"-

~ II

I'"I-

'\

1\I I I JI

10 100 1000GREAT CIRCLE DISTANCE (km)

FIGURE A--12. f= 100MHz,h 1=50m,h2 =50m,V.P.,Lond and Sea Water

80

,--...[1J 100u"'-/

IJ)(/) 1200.....J

Z0 140c.nVi2V) 160Z<

:t:-o:::

If-

I-' 180Vl z

<[.

0

~ 200uif)

<[. 220m

240

~ I I~ - r--

~~ - .-.........,

r-- ---'" I-~

~ '"I 111

f"...

[~! I I-------~ 1 I

t'-... !

'" I

I ~f'.-...." I

f"-,I~

I'\.

[\

10 .100 1000GREAT CIRCLE DISTANCE (km)

FIGURE f.,-13. f= 1OOMHzJ"1=50m,h 2 = 1OOmtV.P.,Land and Sea Water

80

....-....OJ 100""0

'----'"

tf)(J) 1200~

z0 140V)V>2if) 160z«

~ 0:::I i--I-'

1800'.Z«0w:2 200

UV)« 220CD

240

I I

I I I I I I II I I I I I

L 'I

I

I--

r ~

."--..~

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I

I I~

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I

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- I

''''

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I

I I I III

r-

I I I I J IIII

10 100 1000GREAT CIRCLE DISTANCE (km)

FiGURE A-14. f-100MHz,h,==50m,h 2 =200m,V.P.,Land and Sea Water

80

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