PROPAGATION ASPECTS OF EQUIPMENT OPERATION 457 
distances d less than 10')'/*, \, and d in meters, and 
both antennas low, or antenna and target low (/u,ho< 
30°’*), the form of A is simplified so that a simple 
relation can be given for dmax. Otherwise, the 
methods of Chapter 5 must be employed. 
Ducts and Set Performance 
It has been found from field tests that atmospheric 
ducts are likely to be found close to the surface of the 
sea. The consequent increase in range may mask 
subnormal set performance. If the antenna is 
tilted upward so that no radiation reaches the earth, 
then the free-space discussion of thisChapter applies 
to the field determination or check of the per- 
formance figure. Otherwise field testing, when condi- 
tions are normal, can be accomplished by the use of 
permanent echoes or the use of a ship of known 
target cross section. 
Low Heights and Plane Earth Ranges 
For these conditions, the following relations must 
5 /, } 
hold: (Aye < 30078, d < 10*"’), 
where h, d and ) are in meters, 
In the dielectric case (see Chapter 5 ), generally 
applicable to radar, the value of A [equation (172) 
in Chapter 5] for F, = 1 andg = 1, becomes 
3 lik 
As ===, 9 
5 (9) 
Since A = AoA, and Ao = 3/87d, the preceding 
equation is equivalent to a path-gain factor value of 
Iihe 
A, = dp = 10 
Pp 7 dd (10) 
[See equation (55) in Chapter 5.] Instead of equa- 
tions (4) and (5), we now have [from equations (3) 
and (5) in Chapter 5] for a dielectric earth, 
Pee N ng see 7, ay38 
One-way, radio gain: = = Are F (11) 
mle ae os hythetc 
Two-way, radar gain: P, = 9rG? oan (12) 
Hence for maximum range, replacing P; by P,, 
and P,by Prin, 
yma et 
One-way,  dmex = \3 hehe? = ccs) es) 
Two-way, dma = pay nie) aus 
” P min 
The maximum range now depends on the antenna 
heights and on the target height. 
Radar Cross Section 
of Surface Craft 
Effective Height of Targets. Since the field varies 
considerably with height for a low target, the 
scattering by even simple geometrical objects 
requires integration. The formulas for radar in 
the last sectionapplyto a point target with radar 
cross section o at an effective height hog. 
In the case of a cylinder of radius a and length 
H, the radar cross section in a uniform field is 
o = 2raH?/. Under operating conditions the field 
is not uniform but a feasible approximation may be 
obtained by using the preceding value of o and a 
value of he equal to the average value of the target 
height. 
Maximum Range Vs Height Curves 
By the method reported in Chapter 5 and also in 
Chapter 6 , the maximum range versus height 
curves can be constructed for various values of A. 
These are of importance chiefly for low-angle aircraft 
coverage. If the performance figure, (Pp/Pmin)G?, 
is known, equation (5), in Chapter 5, defines the 
relation between o and A so that o can be taken as 
the curve parameter instead of A. Equation (5), 
Chapter 5, can be written 
Ip 
20log A = —5 log —? G?—5loga ~5log =. (15) 
A set of curves for a 10-cm radar is given in 
Figure 5 for a transmitter height of 30 meters. The 
curve corresponding to c = 31 square meters is indi- 
cated. The corresponding value of 20log A = —130 
was found from equation (15), using the value of 
5000; | | | | | 
2 
? 
2000) 
1000 = 5 
A RADAR WITH A 
PERFORMANCE Z 
FIGURE = 2184 
500 zm 
h,= 30m 
a |_| 
Ey 
i) 
= 
2 | 
=- 200 
3 
— 
3 
x 
100 
° 
2 
Z 
Ss 
oles 
50 Nv 
fs) 
iG Ar 
20 f ia |_| 
SG 
o£ 
5 K 
wu we 
Se 
10} |Last 
10 20 50 100 200 500 
Maximum Range in Kilometers 
Figure 5. Maximum range versus height curves for 
various targets. 
