398 PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
For n = 1, corresponding to the first maximum, 
p is approximately 1/r, since R = nr > 2. Accord- 
ingly, we begin with p = 0.1. 
2. dp = 22.5 km (from Figure 2), and 
3. From equation (112), 
R = 9.58. 
4, From equation (121), 
“u= ae = 62.028 
hy 
_ and hence 
he = 1,861 meters. 
5. At d = 100 km, the free-space attenuation 
(Figure 3 in Chapter 2) is 
20 log Ay = — 115. 
I 
1 
! 
i 
T 
1 
1 
1 
\ e 
4 2 
i 
Fixed’ Distence 100 Km I 
bh. = | 30m | i ; 
in 1 0° 
X= 15m || 
k = 4 Hl 
73 Jt ‘ L 
G,, = | 24 (13-5 0B) H ) 
G, 2 0 ( 0 pp) 1 \ 
f = 200MC { \ 
laa F 
1 
AI 
1 
14 
Free Spoce 
Radio Gain 
Line of Sight 
Bz 
Orang gONON Lon 
PEEEELEEEEEEEH 
30 125 =6 =100 =30° 
tO tog Pe/P, 
Figure 25. Radio gain in decibels versus height hz. 
Horizontal polarization. 
6. Compute the factor 
“| (1 — D)?+.4D sin’ 
From equation (117) 
D = 0.980, 
== = 1.010, 
r 
& 
Q = nm = (1.019) - (8.1416) = 3.19 radians, 
we 1.60 radians, 
2) 
sin? : = 0.9992. 
From Figure 12, 
20 log Va — D)?+4D sin? = 6 db. 
Hence 
20log A = 
10 log = = — 109 db + 10 log GiG2 = — 95.5 db. 
1 
7. The foregoing values, together with results 
obtained with other values of p, are listed in Table 1. 
The value of P2/P; [equation (8)] is represented 
graphically in Figure 25. 
— 115 db + 6db = — 109 db, and 
Rapar Gain: Two-Way TRANSMISSION 
Knowing the values of 20 log A, the corresponding 
values of P:/P; are given by equation (5). Taking 
G, = G2 = 18.5 db, 1677/9 = 5.58, \ = 1.5, 
Ps 
10log = = =274+7.5+17 + 40log A — 20log 1.5, 
= + 40logA + 48. 
Type Ill. Radio Gain Versus 
Distance for Given Antenna Heights 
A radar used over the sea has a wavelength of 
1.5 meters. The transmitter is 30 meters above 
sea level and the target is at an altitude of 1,000 
meters above the sea. The power gain of the trans- 
mitting antenna is 13.5 db, the polarization hori- 
zontal. The one-way radio gain is to be found as a 
function of distance. Also, the radar gain at the 
TABLE 1* 
Radio Gain Radar Gain 
R h 3 D 101 = 10 | zn 
Pp s 2 wD t °8 Py 6 Py 
0.15 6.16 0.0337 1,396 0.655 1.03 0.96 5 —96.5 —172 
0.1 9.58 0.0225 1,861 1.019 1.60 0.98 6 —95.5 —170 
0.05 19:68 0.0112 3,216 2.09 3.29 0.995 —11 —112.5 —204 
0.04 24.70 0.00898 3,885 2.63 4.13 0.997 4 —97.5 —174 
0.03 33.05 0.0067 5,005 3.51 5.52 0.998 3 —98.5 —176 
0.02 49.74 0.0045 7,235 5.29 8.31 0.999 5 —96.5 —172 
0.01 99.76 0.0022 13,917 10.61 16.67 1.000 4 —97.5 —174 
* See also Table 5. 
t 20 logy (1—D)? + 4D sin? (@/2). 
Se eee 
