164 



SITING AND COVERAGE OF GROUND RADARS 



Table 10. Antenna pattern factors. 



Array with screen 



Vertical pattern /a 



Two radiators spaced 

 Four radiators spaced 



Two sets of four radiators each 



(Vertical spacing between 

 centers of sets is 3X.) 



cos | - sin 7 ) sin ( - cos 7 



cos ( - sin y 1 cos (it sin 7) sin I - cos 7 



cos ( - sin 7 ) cos (w sin 7) X 



cos (37r sin 7) sin I -j cos 7 ) 



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. 



f A = 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 



I 23456769 



VERTICAL ANGLE IN DEGREES 



Figure 63. 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 59X/Z) 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 68.8X/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. 



15.6.14 



Local Terrain Effects 



The vertical pattern of the antenna may be 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 

 effects of particular terrain features will suggest 

 methods of combining them to analyze a particular 

 site. 



A large, flat land area will in general produce lobes 

 and nulls at angles given by equation (57) with an 

 envelope twice as large as the free space pattern. 

 If the land area is not level, the lobe pattern will be 

 tilted by the angle of the land. However, the problem 

 is essentially a matter of diffraction since the land is 

 of limited extent. Equation (16) should be used to 

 determine whether the area is sufficiently flat to act 

 as a regular reflector. 



If the land is flat from the antenna out to a 

 distance d\ the relative intensity of the reflected ray 

 is Yi when di = hi X cot y. This assumes the land 

 beyond di to be nonreflecting and that the distant 



