SITING AND COVERAGE OF GROUND RADARS 
Since the earth’s radius ka is perpendicular to GH and 
CDE, the tangent angle is 6. It is always negative; 
a ta | 
a akha. haeO? et) 
, A ae 
y=7+0= di 5,280 ° (62) 
4(m — 
n is an add integer for lobe maxima and an even 
integer for lobe minima, -hi in feet, d; in miles. 
The value of d; to substitute in equation (62) 
must also satisfy equation (58). A convenient method 
of solving these equations is to plot a curve of 
equation (59) and also of equation (58) in the form 
ee ACE 
~ -5,280did * 
Corresponding values of hi’ and d, for the desired 
value of m are then substituted in equation (62). 
While equation (62) is subject to the same sort 
of limitation as equation (57), it will be noted that, 
in the region of greatest interest, that is, small 
angles, hy’ is itself small, and this tends to compen- 
sate the error. The modifications introduced permit 
the use of the simple plane earth formulas, since for 
a particular angle the tangent plane is taken as the 
reflection surface. 
The angle y given by equation (62) is the trans- 
formed angle to be used in constructing the vertical 
coverage diagram based on a modified earth radius 
of ka = 5,280 miles. If the true angle is desired, the 
true earth radius a = 3,960 miles must be used in 
equation (62) instead of 5,280 miles. 
n (63) 
4 
3 
EQUIVALENT HEIGHT hyIN FEET 
00 
50 
100 
EXAMPLE 
hy FEET 
f MG 
500 
MULTIPLY 
ORDINATE BY I0 
30 40 
DISTANGE dq IN MILES 
Fieure 50. Equivalent height graph. 
Examples 11 and 12. Lobe Angles Corrected for 
Earth Curvature. Lobe angles will be computed by 
this method for two radar sites. 
Example 11 
In 
= 500 ft 
f = 200 mc 
From equation (59) 
hy! 
dy 
= 500 — 
2 
TaBLE 6. Lobe angles for radar. (Example 11.) 
Example 12 
hy = 3,000 ft 
f = 100 me 
2 
hy’ = 3,000 — Gig 
2 
Equation (60) Equation (61) Equation (57) 
¥rom Figures ; A dh Equation (62) m 
50 and 51. Y 1.23 hy’ ) 5,280 yY=7 +0 Y ane 
n hy’ d; radians radians radians degrees radians 
0 0 31.6 0 — .005983 —.005983 —0°20'22”” 0 
I 341.5 17.8 -003602 — .003372 +.000230 +0° 0/47” .00246 
2 414.0 13.1 005943 —.002481 .003462 0°11/54”” .00492 
3 448.0 10.2 .008238 —.001932 -006306 0°21/39”” 00739 
4 464.6 8.4 .010592 —.001591 009001 0°30'56’’ 00985 
5 475.5 7.0 .01294 — .001326 01161 0°39/54"" .0123 
6 481.4 6.1 .01532 —.001155 .01417 0°48/43”” .0148 
7 486.0 5.3 01772 —.001004 01672 0°67/29/" 0172 
8 489.0 4.7 -02011 —.000890 .01922 1° 6’ 4” .0197 
9 491.6 4.1 .02252 —.000776 .02174 1°14’45/” 0221 
10 493.2 3.7 .02493 — .000701 02423 1°23/19/” 0246 
ll 494.6 3.3 02734 —.000625 02672 1°31/55”” 0271 
12 495.5 3.0 02978 —.000568 02921 1°40/26’” 0295 
13 496.1 2.8 .03222 — .000530 03169 1°48/58” .0320 
14 496.6 2.6 .03468 —.000492 .03419 1°57'33”” 0345 
15 497.1 2.4 .03720 —.000454 03675 2° 6/23” .0369 
16 497.4 2.3 -03955 —.000436 03911 2°14'30” 0394 
Wee 497.6 2.2 -0420 —.000417 0416 2°23! 2!’ 0418 
18 497.8 21 0445 — .000398 0441 2°31/44”” 0444 
19 498.0 2.0 0469 —.000379 0465 2°39/54”" 0468 
20 498.2 1.9 .0494 —.000360 .0490 2°48/30"" 0492 
21 498.4 1.8 .0518 —.000341 .0515 2°57’ 8” 0517 
22 498.6 1.7 .0542 —.000322 .0539 3° 5/22/" 0541 
23 498.8 1.6 .0567 —.000303 .0564 3°14’ 0” 0567 
