122 



SITING AND COVERAGE OF GROUND RADARS 



Figure 11. Fresnel zones. 



a point P to the left. It is desired to know the effect 

 at P of the secondary wavelets emanating from the 

 wavefront. A straight line is drawn from the distant 

 source to point P cutting the wavefront at C. In the 

 wavefront with C as a center are drawn circles such 

 that the first is a half wavelength further from P than 

 C is, the second is 2 half wavelengths, etc., so that 

 the secondary disturbance from any circle will reach 

 P half a wavelength ahead of those from the circle 

 enclosing it. 



If PC = b, the radius n of the first zone may be 

 obtained from 



b + 



V- = n 2 



Neglecting A 2 /4, the radius n = \/o\ and the 



radii, r 2 = \/'2i\, r 3 = y/3b\, etc., and in general 



r m = V^b\ . (11) 



The corresponding areas are approximately -irbX, 

 2wb\, 3irbX, and mirbX. The area of the central zone 



is irb\, and each succeeding ring or zone is slightly 

 greater. 



The effect which one of the zones produces at P 

 is proportional to its area and inversely proportional 

 to its distance from P. These factors compensate as 

 the radius increases, so that the successive zones 

 may be regarded as producing equal and opposite 

 effects at the point P. The zones become less effective 

 further from the center owing to the increased 

 obliquity, since the effect at P is proportional to 

 1 + cos 6 (see Figure 10). The resultant effect may 

 be represented by a series of terms of alternate sign 

 which decrease slowly at first and then more rapidly, 

 eventually becoming zero, thus: 



S = mi — m-i + ra 3 , etc., 



1 , 

 = ^ + 



1 



xnii 



m 2 + 2 m 3 



I 1 i 1 



! { g Wl8 — ?»4 + 2 W! i 



+ 



^m„ 



