104 
TECHNICAL SURVEY 
TasBLe 7. Lobe angles for radar. (Example 12.) 
Equation (60) Equation (61) Equation (57) 
From Figures : i dh Equation (62) i 
50 and 51 Y' = 2.46 hi 5,280 Y=7 +80 cy, ah, 
n hy’ dy radians radians radians degrees radians 
0 0 77.4 0 —.01466 —.01466 —0°50/24” 0 
1 930 64.3 .002645 —.01218 — .00954 —0°32’49’". .00082 
2, 1245 59.2 .003952 —.01121 —.00726 —0°25’ 0” -00164 
3 1458 55.5 005063 —.01051 —.00545 —0°18/44” 00246 
4 1638 52.2 .006007 —.00989 —.00388 —0°13'20” 00328 
5 1788 49.2 .006880 — .00932 —.00244 —0° 8/22” .00410 
6 1910 46.7 .007730 —.00885 —.00112 —0° 3/52” .00492 
7 2013 44.4 .008550 —.00841 +.00014 +0° 0/29” .00574 
8 2108 42.4 009335 —.00803 -00130 0° 4/28” 00656 
9 2195 40.6 -01018 —.00769 -00249 0° 8/33” 00738 
10 2246 38.8 .01095 —.00735 .00360 0°12'22” .00820 
11 2308 37.2 01173 —.00705 .00468 0° 16’ 6” 00902 
12 2359 35.8 01251 —.00678 .00573 0° 19’41” .00984 
13 2408 34.4 01328 —.00651 .00677 0° 23/16” .01066 
14 2452 33.1 .01404 —.00627 .00777 0°26/44”” 01148 
15 2488 32.0 01484 —.00606 .00878 0°30'10”” 01230 
16 2525 30.8 .01558 —.00583 .00975 0°33/31”” 01312 
17 2559 29.7 .01635 — .00562 01073 0°36’50’” 01394 
18 2588 28.7 .01712 —.00544 .01168 0°40’ 8” .01476 
19 2623 27.8 .01782 —.00526 .01256 0°43’10” 01558 
20 2638 26.9 .01866 —.00509 .01357 0°46/40” .01640 
21 2662 26.0 .01940 —.00492 01448 0°49/48”” .01722 
22 2685 25.1 02030 —.00475 .01555 0°53/26’” 01804 
23 2702 24.4 .02093 — .00462 .01631 0°56’ 4” .01860 
Reading values of h;’ and d; from Figure 50 and sub- 
stituting in the above equations, curves of n and d 
are plotted in Figure 51. From these two curves 
may be read the values of hy’ and d; corresponding 
to integral values of n. The calculation of y’ and @ 
from equations (60) aud (61) are conveniently per- 
formed by arranging columns as shown in Tables 
6 and 7. 
For purposes of comparison with equation (62) 
the last column gives values of y computed by means 
of equation (57). In Table 6 the error in the figures 
computed from equation (57) is seen to be consider- 
it} 
500 
aN = aw 
ee re 0  C | ea Re EN 
SS SS 
== 
Fu [a ae) 
10) 30 40 
50 60 70 
DISTANCE d, IN MILES 
(0) iio} 2 
Ficure 51. Reflection area graph. 
ably below n = 10; for higher values of n the two 
formulas tend to show fair agreement. In Table 7 
the disagreement is marked even at n = 23 indicat- 
ing that equation (57) is unsuitable for high sites. 
The lobe angles are shown in Figures 52 and 53. 
The lines of constant altitude over the modified 
earth are plotted from equation (49). The lobe 
angles are constructed by drawing radial lines from 
the center of the antenna, while the height in feet 
at a given distance is obtained by multiplying y 
(in radians) by 5,280 times this distance in miles. 
The lines have not been drawn close in because of 
the crowding and because they actually start near 
the origin rather than at the center of the antenna. 
The error in the position of the center lines of the 
lobes near theantenna is a limitation on this method; 
but this occurs in a region which, because of gap 
filling, has no nulls and is therefore of little concern. 
Another difficulty is that the lower lobes dre actually 
curved instead of straight; but as long as the site is 
not too high, say under 100 ft (100 mc), thé curva- 
ture is small and unimportant. In general the method 
of equation (62) gives reasonably correct lobe angles 
for most high sites and with a moderate amount of 
computation. This is the first step in the preparation 
of the coverage diagram. Later sections will discuss 
construction of lobes about these center lines. 
These equations are plotted in Figure 50. From 
equation (63): 
12 , 
ey) n = 0.000077 22" | 
"= 5,280 X 4.92 X dy’ dy 
