THE CALCULATION <)i' VKKTICAI, COVKHAGE 



165 



boundary acts as a diffracting edge. As di increases 

 further, the relative intensity increases to about 1.18 

 and then decreases again ami oscillates about unity 

 in gradually decreasing swings. This is accompanied 

 by a variation of phase. 



Several typical terrain problems will be solved in 

 detail to illustrate the methods. 



Example 17. Limited Reflecting Area. A 200-mc 

 radar, Figure 64, with an antenna as described in 



h,«50 FEET t= 200 MC 



LAND REFLECTING FROM 600T0 3000 FEET 



U), \A* 



IMAGERS. REFLECTING ROUGH LAND' 



SURFACE DIFFUSE REFLECTOR 



4000 6000 I2P00 



DISTANCE^ IN FEET 



Figure 64. Lobes from a limited reflecting area. 



Example 16, is 50 ft above a smooth reflecting surface 

 (a lake) which extends from 600 to 3,000 ft. From 

 to 600 ft and from 3,000 ft on is rough land. The 

 shore line diffraction method will be used to deter- 

 mine the effect of the reflection from the limited 

 area upon the antenna pattern f A . The vertical 

 pattern is plotted from Figure 63 and shown dotted. 

 To obtain the pattern for the reflected wave the 

 shore at 600 ft is taken as a diffracting edge, and the 

 relative intensity computed as a function of y as 

 though the surface from 600 ft on were a perfect 

 reflector. This is then repeated using the shore at 

 3,000 ft. The difference between these two functions 

 is then the effect of the area between 600 and 3,000 

 ft. From equation (83) for n = 1 



From Figure 27, using the plus sign for r, wi and the 



minus sign for w 3i oooj ' s obtained the relative intensity 



2 6 oo = 1.073; 2 :! . = 0.375. 



The reflection factor for n = 1 is given by 



z = i.()73 - 0.375 = 0.698. 

 From equation (57) 

 1 X 4.92 



T 



= 0.0246 radian = 1.41° . 



4 X 50 

 Other values are given in Table 1 1 . 



Table 11. Limited reflecting area. (Example 17.) 



^3, ooo 



^600 23_000 



fr /(7) 





 0.1 





 0.14 



0.4 0.56 



0.5 0.70 



0.6 0.85 



1.0 1.41 



1.5 2.11 



2.0 2.82 



3.0 4.23 



4.0 5.64 



5.0 7.05 



+ 1.30 



+ 1.26 



+ 1.15 



+ 1.11 



+ 1.071 



+0.918 



+0.727 



+0.535 



+0.155 



-0.237 



-0.619 



+0.583 

 +0.498 

 +0.241 

 +0.155 

 +0.077 

 -0.279 

 -0.707 

 -1.136 

 -1.995 

 -2.853 

 -3.710 



1.177 

 1.181 

 1.164 

 1.153 

 1.142 

 1.073 

 0.960 

 0.838 

 0.592 

 0.393 

 0.277 



0.870 

 0.810 

 0.645 

 0.592 

 0.544 

 0.375 

 0.257 

 0.186 

 0.116 

 0.082 

 0.067 



0.307 

 0.371 

 0.519 

 0.561 

 0.598 

 0.698 

 0.703 

 0.652 

 0.476 

 0.311 

 0.210 



0.693 

 0.658 

 0.973 

 1.147 

 1.314 

 1.700 

 1.223 

 0.349 

 1.475 

 0.689 

 1.210 



0.693 

 0.658 

 0.973 

 1.147 

 1.314 

 1.650 

 1.137 

 0.314 

 1.090 

 0.386 

 0.436 



The values of z multiplied by f A from Figure 63 

 are plotted in Figure 65 as the reflected pattern . The 



DIRECT PATTERN - f A 

 N 



Y DIRECT PAT 



/ 



/ 



) 



REFLECTING 



PLANE 



IMAGE 



^ 



EFLECTED PATTERN - z f. 



_i_ 



0.2 0.4 0.6 0.8 



RELATIVE INTENSITY 



1.0 



Figuke 65. Components of the modified antenna for a 

 limited reflecting area. 



resultant of the two vectors, f A and zf A , in terms of 

 n is given by the cosine law: 



f T = Vl + 2 2 - 22 cos (nir) . (94) 



Thus for n = 0.1 



f T = Vl + (0.371) 2 - 2 X 0.371 cos (O.br) = 0.658 



