CALCULATION OF RADIO GAIN 417 
h, is given by Figure 35, 
20 log gg’ is given by Figure 36, 
20 log Ao is given by Figure 3 in Chapter 2, 
F, is given by Figures 31, 32, and 33. 
2. Plane earth factor A,. This has been discussed in 
Section 5.7.1. A, is a function of p’d; p’ is given in 
Figure 44 and 20 log A; in Figure 45. The curve 
shift of A; with \ in the VHF band is less than 1 db. 
When p’d > 50, A: = 1/p’d, as in the dielectric 
case. 
3. The low height-gain Hy is a function of lh (see 
text onp.404). lis given by Figure 46, H,, or 20 log H, 
by Figure 47. H; depends on the curve parameter 
Q = «,/60cd which for sea water is 1/3) Since 
H,—lh for lh > 4, 20 log Hz can be found from 
Figure 34. 
4. hi, he > 4/landd > 50/p’. As in text onp.405 
{noting especially equations (151) and (153)], 
equation (184) reduces, when h > 4/landd > 50/p’, 
to 
3F 
A =~ (gg’h):(gg/h 185 
5 2 )i(99’h) 2 (185) 
Equation (185) may be used generally, provided 
(gg’h) is replaced by H;/l when h < 4/l, and the 
right-hand member is multiplied by Aip’d or, in 
decibels, 20 log Ai + 20 log p’d are added, when 
d <50/p’. In this formula d < 50/p’ is given in 
meters. 
5. Horizontal versus vertical polarization. It is of 
interest to compare the gain of vertically and hori- 
.04 
a 
JC ae ee 
p’ FOR USE WITH Ay 
SEA WATER VERTICAL POLARIZATION 
Rz1-10m 
WAVELENGTH ,} METERS 
FicurE 44. p’ versus) for sea water, vertical polariza- 
tion. 
Taste 8. Values of 4/1 and 50/p’ for various wavelengths. 
eR oN ty GS ee PS ill sek 
3 | 27 | 50 | 80 | 110] 148] 174 | 222] 267| 308] m 
2 | 17 | 17 | 30 | 50} 71) 100] 125/175) 200| km 
zontally polarized waves over sea water at VHF. 
(It has been pointed out earlier that there is no 
marked difference in attenuation between horizon- 
tally and vertically polarized waves for wavelengths 
less than one meter.) Equation (184) is valid for 
horizontally polarized waves also by using the 
appropriate F’, curve and putting g’ = 1 and can be 
made the basis of 8 comparison between vertical 
and horizontal polarization. See, for comparison, 
equation (160). 
For antennas at, or very close to, zero height, the 
gain-factor ratio depends on AF. While F, gives 
greater attenuation (lower gain) for horizontal than 
for vertical polarization, the difference between the 
two lies principally in the values of A:. For \ = 1 
meter, the ratio is 64,000 to 1 in favor of vertical 
polarization. For \ = 10 meters, the ratio is about 
8.6 X 10°. 
However, as the antennas are raised above the 
ground, the strength of a horizontally polarized 
field increases much more rapidly than does the 
corresponding vertically polarized field, for a given 
wavelength up to a certain height above which the 
field is substantially independent of polarization. 
For example, above a height of 3 meters for \ = 1 
meter, and above 77 meters for \ = 10 meters, the 
two fields are practically equal. 
6. Parameter A. As on pp- 413- 416 , curves can 
be drawn in terms of the parameter A where 
A 
— forh > 4/l, 
oO Ge 
A= (186) 
Al 
— forh < 4/1. 
ifs or jf 
tt 
PLANE EARTH GAIN FACTOR Aj, 
SEA- WATER 
VERTICAL POLARIZATION 
FOR P'd >140 USE FIG. 34 
PUTTING X= pid 
Figure 45. Plane earth factor A, for sea water, 
vertical polarization. Note: All db values are negative. 
