428 : PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
The factor 
F, = (22)? @? (207) 
eons 
»> 1 + 27,/6 
represents the effect of earth, curvature in increasing 
the attenuation over that of a plane earth at zero 
height [i.e., (0) = 1] and equation (205) is now of 
the form 
E eS 2EvAF, (208) 
If 6 is large (e.g., \ small), 27,,/5 in equation (207) 
may be neglected and r, replaced by 7,,,,80 that the 
shadow factor is practically independent of ground 
constants. The shadow factor is represented graphi- 
cally in Figures 32 and 58. Where the factor 27,/6 
cannot be neglected, as in the VHF range, vertical 
polarization over sea water, the dependence of 
F, on 6 is accommodated by changing the abscissa 
from ¢ = sd to 7 = s/d where s’ = sf(6), and by 
representing F', by a family of curves in Figure 58, 
whose parameter is given by dotted lines in Figure 
57. f(6) is represented also in Figure 57. For” < 0.4, 
F, is less than 1 db below unity. This corresponds 
to a distance over which the earth may be considered 
plane, i.e., d < 10*’7, as given in text onp.405. 
The greater the wavelength, the smaller the effect 
of the earth’s curvature. 
If the antennas are elevated, F, can still be used 
for the first mode for great distances where the first. 
mode gives most of the field. 
Sample Calculation 
for Very Dry Soil 
The general solution given in text onp.421is here 
illustrated for the case of doublet antennas, either 
horizontally or vertically polarized, placed at various 
heights over an earth assumed to be very dry soil 
for which the constants are «, = 4, and o = 0.001 
mho/meter. The following graphs cover, in decimal 
steps, the frequency range of 30,000 to 0.03 me or 
wavelengths \ = 0.01 to 10,000 meters. 
Figure 59 gives the free space radio gain A» and 
the radio gain A decibels over very dry soil, as a 
function of distance d for doublets at zero height. 
Figure 60 gives the first mode height-gain factors for 
transmitter and receiver heights, h; and he, respec- 
tively. 
To obtain the radio gain under different conditions 
it is merely necessary to add the decibel gains of the 
transmitter and receiver antennas, the radio gain for 
zero height (Figure 59), the height-gain factor 
(Figure 60) for the transmitter, and a similar figure 
aul 
eet 
~100 
SS SS ff Sreeeeoe See 
RADIO GAIN 
a 
fo] 
fe} 
-500 
100,000 1,000,000 
DISTANCE d IN METERS 
Figure 59. Free-space radio gain Ay (—- —).and radio gain A, in decibels, for propagation over very dry soil with 
doublet antennas on the ground ( 
for horizontal polarization and —— for vertical polarization). Numbers on the 
curves give the wavelength \. Note: Radio gain is independent of the radiated power. 
