180 



DIFFRACTION BY TERRAIN 



to the path difference between the reflected and 

 direct rays. 



The absolute value of the field is 



— = V(l -3)= + 43sini^(7rn+ 0- (21) 



Figure 12 in Chapter 5 may be used for the numer- 

 ical evaluation of this ecjuation. 



The formula can readily be generalized to the 

 case where the reflected ray is weakened by (1) a 

 reflection coefficient, R, different from unity, and 

 (2) the effect of the earth's curvature expressed by 

 the divergence factor, D, (Chapter 5). If, moreover, 

 the phase lag at reflection is not tt but ir + 0', the 

 equation becomes 



p I 



= V(l - zRD)-+izRD sin^ H (t'i + 4)' + i). 



E, 



8.4.4 



(22) 



Example 



Assume the following conditions. A radar set of 

 200mc(X = 1.5 meters) is sited at a height /ii = 15.3 

 meters (aliout 50 feet) and at a distance to a straight 

 shore line of ck = 195 meters (about 0.12 mile). 

 The ground between the radar and the seashore 

 is level but can be considered as rough for prac- 

 tically any angle of elevation, on applying the 

 criterion of Section 8.3.2. The coverage diagram 

 will first be determined in the azinuith perpendicular 

 to the coast line, where di = do, or cos 7 = 1. 

 Then by ecjuation (18), ?io = 3.20. With this value 

 of 7io the variable v is determined by equation (19). 

 We shall confine ourselves to integral values of n, 

 that is, to those angles which, in the presence of 

 simple reflecting ground, correspond to lobe minima 

 and maxima. Having obtained v, one then deter- 

 mines z and j' from Figures 4 and 5. The field in 

 terras of the free-space field is then obtained from 

 equation (21), either by direct computation or by 

 means of Figure 12 in Chapter 5. The numerical 

 data for the first five lobes are summarized in 

 Table 1. The last column of this table contains the 

 values of E/Eo which would be obtained if the magni- 

 tude of the reflection coefficient were assumed to be 

 zero over land and unity over the sea and if diffrac- 

 tions were neglected. 



The same calculations are carried out for an 

 azimuth inclined by an angle y = 45° with respect 

 to the coast line. Then, from equation (18), «o = 4.5. 

 The results are given in Table 2. 



It is seen from these data that the lobes near the 

 critical ray (raj^ whose reflection point is at the coast 

 line) undergo very considerable deformation. The 



coverage pattern corresponding to Table 1 is shown 

 graphically in Figure 14. 



WITH DIFFRACTION 

 WITHOUT DIFFRACTION 



Figure 14. Coverage diagram (relative field strength). 

 (Heights e.xaggerated 3.5 to 1.) 



In the problem considered here, the angles of 

 elevation are comparatively large (for n = 1, 

 i/- = r 24'). If the effects of diffraction occur at 



