SITING AND COVERAGE OF GROUND RADARS 12) 
Precision is not required for most of this kind of 
work, and it will suffice to compute values for equa- 
tion (99) at each integral value of n and to consider 
the values for odd n’s (with the plus sign) as the 
average of the lobe. The lobe shape will be taken 
as sinusoidal and the range at the nulls obtained by 
using even values of n and the minus sign; f(y) and 
S(y— 26) are obtained from Figure 63, by using 
values of y and y — 20 from Example 11 corres- 
ponding to integral values of x. The values of z are 
obtained from Example 15. The computations are 
shown in Table 13. Had cliff edge diffraction been 
involved f(y) and f(y — 26) would be read from 
curves a8 in Example 18 with marked effects on 
the pattern. 
The lobes are plotted in Figure 46 using equation 
(74) and the value of L for odd numbered n’s. For 
intermediate values of n the factors are: 
Fractional value of n sin (90° n) 
0.33 0.500 
0.50 0.707 
0.70 0.891 
Using these three points above and below the lobe 
line and the maximum and minimum values from 
Table 13 the lobes may be plotted quickly as 
explained in Example 14. 
TABLE 13. Lobes for a medium-height radar. (Example 20.) 
= HOP 20) iG?) 2 
PMG 28) 20) DT f(Y — 26)p2D 
0 0.999 0.999 1.036 0.577 —0.597 0.402 32.2 
1 1.000 0.998 1.083 0.580 -+0.627 1.627 130.2 
2 0.999 0.997 0.980 0.735 —0.718 0.281 22.5 
3 0.999 0.994 0.884 0.823 +0.723 1.722 137.8 
4 0.997 0.992 0.938 0.890 —0.828 0.169 13.5 
5 0.992 0.989 1.082 0.912 -+0.976 1.968 157.4 
6 0.989 0.987 1.170 0.933 —1.077 0:088 7.0 
7 0.985 0.981 1.156 0.942 +1.068 2.053 164.3 
8 0.980 0.978 1.073 0.959 —1.006 0.026 2.1 
9 0.975 0.972 0.953 0.963 -+0.892 1.867 149.4 
10 0.970 0.967 0.825 0.968 —0.772 0.198 15.8 
11 0.963 0.961 0.696 0.973 -+0.651 1.614 129.1 
12 0.958 0.952 0.582 0.979 —0.542 0.416 33.3 
13 0.950 0.947 0.459 0.981 0.426 1.376 110.0 
14 0.941 0.939 0.377 0.984 —0.348 0.593 A474 
15 0.932 0.929 0.308 0.987 -++0.282 1.214 97.2 
16 0.923 0.920 0.261 0.989 —0.237 0.686 54.9 
17 0.913 0.910 0.223 0.991 +0.201 1.114 89.1 
18 0.903 0.900 0.192 0.992 —0.171 0.732 58.6 
19 0.893 0.890 0.170 0.992 -+0.150 1.043 83.5 
20 0.881 0.879 0.150 0.992 —0.131 0.750 60.0 
21 0.871 0.869 0.135 0.992 -+0.116 0.987 79.0 
22 0.857 0.853 0.121 0.992 —0.102 0.755 60.4 
23 0.844 0.841 0.111 0.992 -+0.093 0.937 75.0 
The General Lobe Formula 
The assumption of a sinusoidal lobe shape and the 
neglect of the phase of reflection and diffraction in 
the preceding section may in some cases lead to 
considerable error, especially when the direct and 
reflected waves are very different in strength. In 
general a more accurate method is required for sites 
over 1,000 ft in height, where vertical polarization 
is used or where it is desired to know the lobe shape 
in detail. The method given in this section provides 
a general solution of the coverage problem in the 
optical region (except along the bottom of the 
first lobe). 
The development of the lobe formula will be 
reviewed, and equation (99) will be given in a some- 
what different form. The expression for the electric 
vector due to the direct wave is 
Ey = = s(x) exp(— 2%). (200) 
Td 
For the reflected wave 
E, = FY icy — 26) Kexp (- jl z} , (101) 
where JH, = electric field intensity at the target 
due to the direct wave, microvolts 
per meter: 
E, = electric field intensity at the target 
due to the reflected wave, microvolts 
per meter; 
E, = electric field intensity at 1 mile in 
the equatorial plane of the antenna, 
microvolts per meter; 
f(y) = modified antenna factor for the direct 
wave (page 114); 
f(y — 20) = modified antenna factor for the 
reflected wave (page 118); 
R = a complex factor for the reflected 
wave given by 
R = Dpz {exp[—j(¢ + O]} ; (102) 
where D = divergence factor (page 
119); 
p exp (—7¢) = complex reflection factor (page 
118); 
z exp (—jf) = complex diffraction factor (pages 
111-114). 
The net field at the target is 
E,=EHi+ E,, 
Al Ey 
[Bin | 3 ae AAG) se hae = 20) 
Doz{exnt=ie+s+9)}|, (109 
considering only the absolute value of H7 and taking 
r = rg = d except where the path difference is 
involved. The path difference phase shift is 
5S =e G@= me - (104) 
Equation (103) may for convenience be written 
(Blo Ba. (105) 
The target is assumed to have a complicated form 
and to be changing its aspect constantly. The 
