DIFFRACTION BY HILLS 



177 



top of the ridge forms the diffracting edge (P in 

 Figure 8). If the profile of the ridge is somewhat 

 more compUcated, the effective diffracting edge might 

 be a purely mathematical line, as shown in the lower 

 part of the figure. The height ho is conveniently 

 determmed from a profile of the transmission path 

 obtained from a topographic map. If the heights 

 hi, hi, and h of transmitter, receiver, and obstacle, 

 respectively, above a given reference level such as 

 sea level are given, we have 



, dihi + d'yhi , 



ho = — n, 



di + d. 



(12) 



where the signs have been chosen so that ho is nega- 

 tive when the receiver is in the shadow of the ridge 

 and positive when it is in the illuminated region. 

 Now, by equation (3), 



V = ho 





\ 



2h 



(ai + a,). (13) 



In these equations, give the angles ai and ^2 the same 

 sign as ho and give v the same sign that ho has in 

 equation (12). 



The ratio of the field to the free-space field at the 

 receiver is now given by | E/Eo | = siv), defined Ijy 

 equation (7) and plotted in Figure 4. In Figure 9, 

 this ratio is given in decibels as a function of the 

 quantity x = —ho/^\d (all lengths in meters). 

 The successive curves in Figure 9 correspond to 

 different values of the ratio di/do or d^/di (choose 

 whichever one is the smaller). Only the field below 

 the line of sight is shown. 



8.3.4 



Field Near the Line of Sight 



The fact that just above the line of sight the field 

 increases above its free-space value may sometimes 

 be used to obtain a favorable site (Figure 10). The 

 maximum value of the field is about 1.17 times the 

 free-space value (Figure 4), equivalent to 1.36 db. 

 On the other hand, there are advantages in avoiding 

 a Une TR that is too close to grazing the top of 

 an intervening obstacle, as this will substantially 

 reduce the signal. At the line of sight, the signal is 

 6 db below free space. In order to get approximately 

 the free-space value of the field, the crest of the 

 obstacle should be sufficiently below the line TR 

 so that V > 0.8 where v is given by equation (13), 

 ho being the clearance between the line TR and the 

 obstacle. In cases where the heights and distances 



are not quite certain, it is therefore preferable to- 

 select a higher and definitely unobstructed site 

 rather than to try to utilize the small gain that might 

 possibly be had from the diffraction field. 



30 



0.15 0.2 0.3 0.4 0.6 0.8 1 



2 3 4 6- 



Figure 9. Field in shadow behind a diffracting ridge. 



Figure 10. Diffraction field above the diffracting edge. 



8.3.5 Diffraction with Reflecting Grovmd 



When the ground near the transmitter or receiver- 

 is smooth and reflecting, the diffraction problenx 

 becomes very complicated. It can be solved by the- 



