152 



SITING AND COVERAGE OF GROUND RADARS 



u 20,000 



80 100 120 



DISTANCE IN MILES 



Figure 52. Lobe angles for Example 11. 



the origin rather than at the center of the antenna. 

 The error in the position of the center lines of the 

 lobes near the antenna is a limitation on this method ; 

 but this occurs in a region which, because of gap 

 filling, has no nulls and is therefore of little concern. 

 Another difficulty is that the lower lobes are actually 

 curved instead of straight; but as long as the site is 

 not too high, say under 100 ft (100 mc), the curva- 

 ture is small and unimportant. In general the method 

 of equation (62) gives reasonably correct lobe angles 

 for most high sites and with a moderate amount of 

 computation . This is the first step in the preparation 

 of the coverage diagram. Later sections will discuss 

 construction of lobes about these center lines. 



The General Lobe Angle Formula 



For very high sites (over 1,000 ft) and frequencies 

 over 200 mc, it is desirable to have a more accurate 

 expression for the locus of constant path difference 

 than is afforded by straight lines. This is of especial 

 interest in the first few lobes as these determine the 



low coverage which is of great tactical importance. 

 The method described here overcomes the limitations 

 of equation (62) and may be used for the highest sites. 

 In Figure 54 is shown the antenna above a curved 

 reflecting surface whose radius is taken as % of the 

 earth's radius to allow for atmospheric refraction. 

 The tangent plane CE makes an angle 6 with the 

 horizontal at the antenna, and d is given by — {di/ka) 

 as shown in Figure 49. 



hi = height of the center of the antenna above 



the earth's surface, in feet. 

 W = equivalent height of the antenna, in feet 



— equation (59). 

 r d = distance from the antenna to the target, in 



miles. 

 A = distance from the antenna to the reflection 



point, in miles. 

 B = distance from the reflection point to the 



target, in miles. 

 A = path difference, A + B — rd, in miles. 

 X = wavelength, in feet. 



