162 



SITING AND COVERAGE OF GROUND RADARS 



effective height, from equation (59), should be used. 



b = 4V J- . (88) 



\ n 



To apply this method the distance of the shore- 

 line, di, is substituted in equation (81), and the 

 equation is solved for 7\, the terrain factor. This 

 quantity is a constant for a particular azimuth and 

 is substituted in equation (86) along with the values 

 of n desired and solved for v. The values of m corre- 

 sponding to these values of v are the numbers of the 

 zones which intersect the shoreline for each value 

 of n. These values of v are entered in Figures 27 and 

 28 to obtain the intensity and phase lag relative to 

 that which would be obtained if the rough land were 

 replaced by the sea. 



Example 15. Shoreline Diffraction. A radar station 

 is assumed to have the same height and frequency 

 as in Example 11. The shoreline distance is 3 miles, 

 and the intervening land is occupied by a large 

 city, h = 500 ft; / = 200 mc; di = 15,840 ft. At 

 this distance the effect of earth curvature is less than 

 1 per cent and may be neglected. The greatest angle 

 at which waves are reflected from the sea is given by 



500 

 15,840 



In equation (16) the maximum height of roughness 

 for regular reflection is 



X 57.3 = 1.81° 



H = 



3,520 



= 9.7 ft 



200 X 1.81 



The land is evidently a diffuse reflector. From 

 equation (83) 



diX 15,840 X 4.92 



T 1 



(V) 2 (500 - 4.5) 2 

 Substituting in equation (86) for n = 2 



0.317 . 



-f 



317 X 4 



- 2 + 



0.317 



= 2.11 



m = - = 2.23 . 



That is, somewhat more than two zones are com- 

 pletely formed on the sea. In order to determine 

 which sign to use in reading Figure 27 it is only 

 necessary to know whether the main reflection point 

 d\ for this lobe falls on the land or the sea corre- 

 sponding to shadow or illuminated regions. A more 

 general procedure is to solve equation (63) using the 

 shoreline distance for d\ : 



4 X (500 - 4.5) 2 

 15,840 X 4.92 



= 12.6 



For all values of n less than 12.6, d x will be on the 

 sea and equation (84) applies to the near edge, and 

 the minus sign is used in equation (82) corresponding 

 to +y in Figure 27. For n greater than 12.6 the 

 plus sign is used in equation (82) and — v in Figure 

 27. Thus, for n = 2 and v = +2.11, is read in 

 Figure 27 the relative intensity z = 0.980 and in 

 Figure 28 the phase lag, f = —0.103 radians. Other 

 values are listed in Table 9. 



The width of the second zone may be computed 

 from equation (88). The effective height for n = 2 

 is obtained from Figures 50 and 51 and is 414 ft. 



/2 



b = 4 X 414 



4 



= 1,656 ft 



15.6.12 The Modified Antenna Pattern 



The vertical directivity of the antenna is modified 

 by the local terrain. Unless the ground under the 

 antenna is an extension of the reflection plane the 

 modification of the free space directivity character- 

 istics should be taken into consideration in the 

 calculation of radar coverage. 



The vertical pattern of the antenna in the absence 

 of a reflecting surface is referred to as the free space 

 pattern, f A . This is usually given in the instruction 

 manual for the set. If this pattern is not available 

 or if the antenna has been modified, the vertical 

 directivity may be computed by methods given in 

 the next section. Local terrain effects are treated in 

 some detail as they are in many cases a controlling 

 factor. The resultant effect of the local terrain and 

 free space pattern is called the modified antenna 

 pattern, f(y). It does not include the effect of the 

 main reflecting surface. 



