SITING AND COVERAGE OF GROUND RADARS 115 
as in Figure 62. In practice the spacing may be 
DIPOLE 
Figure 62. The reflecting screen. 
more nearly \/8 but for y less than 30° the method 
given here is satisfactory and avoids a complicated 
analysis. The path difference QR is (A/2) cos y, and 
- the phase difference is 7 cos y. Then 
fa = cos wt — cos (wt — m cos y) . (92) 
From the relation 
cos A — cos B = —2sin3(A + B) sin} (A — B), 
it follows that equation (92) may be written in the 
form 
. v 5 Tv 
fa = — 2s (« — 9 008 7) sin (5 cos 7) : 
Dealing only with the rms value, 
fa = sin (5 cos ) (93) 
For small angles this factor is usually unimportant. 
Factors are given in Table 10 for some typical arrays 
with horizontal radiators in a vertical column and 
a reflector screen. 
Example 16. Vertical Pattern of an Antenna. Using 
the eight element array in Table 10, the relative 
intensity at angle of 5° from the horizontal is com- 
puted as follows. 
fa = cos (90 sin 5°) cos (180 sin 5°) 
cos (540 sin 5°) sin (90 cos 5°), 
cos 7°51’ X cos 15°41’ 
X cos 47°4’ X sin 89°39’, 
= 0.9906 X 0.9628 X 0.6809 X 0.9999, 
= 0.65. 
The main vertical lobe is plotted in Figure 63. The 
first null is at 9°36’ and the half-power beam width 
2 
2 
RELATIVE INTENSITY 
° 
VERTICAL ANGLE IN DEGREES 
Ficur® 68. Vertical pattern of a typical antenna. (Ex- 
ample 16.) 
is 4.53°. It will be noted that the effect of the 
reflector screen may be neglected for small angles. 
The pattern from a parabola is closely dependent 
on the feed system which controls the uniformity 
of illumination. To reduce side lobes it is common 
practice to taper the illumination toward the edge 
of the dish. This is accompanied by a broadening of 
the beam and a loss of gain. The half-power beam 
width for uniform illumination is 59\/D degrees, 
where D is the diameter of the aperture. The first 
side lobe is then about 2 per cent of the maximum. 
A typical dish with a tapered feed would have a 
half-power band width of 68.8\/D degrees. This 
reduces the first’ side lobe to 0.5 per cent. Some 
designs are further modified by deforming the dish, 
off-center feeds, etc., so that: the patterns may not 
be easily computed. Such patterns are best obtained 
experimentally and are usually given in the manual 
for the equipment. 
Local Terrain Effects 
The vertical pattern of the antenna maybe modi- 
fied by reflection from local flat areas or by diffraction 
over hills or other obstacles. To take these effects 
into account, factors are computed from the diffrac- 
tion equations which are used to modify the direct 
and reflected ray patterns. 
A detailed method of calculating f(y) cannot be 
given because of the great variety of sites encoun- 
tered. However, the following discussion of the 
TasE 10. Antenna pattern factors. 
Array with screen 
Vertical pattern f4 
» 
Two radiators spaced 3 
a A 
Four radiators spaced 3 
Two sets of four radiators each 
(Vertical spacing between 
centers of sets is 32.) 
7 ain (Ve 
cos 3 sin Y } sin 2 cos Y 
rae EB 2 a 
cos ( sin 7) cos (7 sin Y) sin ( cos 7) 
7. E 
cos ( sin ) cos (x sin Y) X 
cos (37 sin Y) sin ( cos v) 
