124 



SITING AND COVERAGE OF GROUND RADARS 



TO DISTANT POINT P 



TT77T77 



Figure 14. Reflection from rough surface. 



The path difference 



A = 



H 



(1 - cos 2*) 



sin ^ 

 = 2H sin ^ . 



The corresponding difference in phase is 



2ttA 4ttH . 



* = 



sin SI^ 



(13) 



(14) 



Since the path difference increases as the grazing 

 angle increases, the diffusion is greatest when the 

 rays are perpendicular. When the angle is small, 

 near zero, regular reflection may be obtained. It was 

 suggested by Rayleigh to take as an upper limit for 

 the grazing angle, giving regular reflection, the value 

 corresponding to a phase difference of ir/4. By 

 equation (14) this angle is given by 



7T 



4 



4tt// 



sin "$> 



or 



sin * 



16// 



(15) 



For a given wavelength and lobe angle the terrain 

 at the reflection point may be examined to determine 

 the limiting height of the roughness for regular 

 reflections. Equation (15) may also be given in a 

 more convenient form using the approximation 

 sin ^ = \l> radians for small values of ^ : 



H = 



3,520 



(16) 



with H in feet, / in mc, and ^ in degrees. Thus for 

 100 mc regular reflection may be obtained over 

 ridges as high as 35 ft for a grazing angle of 1°, but 

 for 3,000 mc the roughness could not exceed 1 ft 

 in height at this angle. 



i5.4 .5 Diffraction at Obstacles 



The preceding considerations of Fresnel zones in 

 a wavefront will now be applied to the problem of 

 radio wave diffraction past hills, ridges, or nearby 

 objects. These obstacles will be treated as though 

 they were straight edges, narrow screens, or rec- 

 tangular slits. 



In Figure 15 is shown a distant source of radiation 



DISTANT 

 SOURCE I 



I 



Figure 15. Interference of waves at an edge. 



and a diffracting edge. The illuminated edge is 

 considered to send out secondary cylindrical wavelets 

 which interfere with the plane waves which are not 

 shielded by the edge. The dotted and solid lines are 

 spaced a half wavelength apart. In the unshaded 

 region the intersection of two dotted or two solid 

 lines indicates reinforcement and the intersection of 

 a dotted and a solid line indicates cancellation. 

 The loci of maxima and minima are parabolas 

 along which the relative intensities are practically 

 constant. In the shadow region, where only the 

 wavelets from the edge are propagated, the relative 

 intensity falls off continuously as the angle of 

 diffraction is increased, since the angle d (see Figure 

 10) approaches 90°. 



In Figure 16 is shown the zone system obtained 

 because of a diffracting edge with the source of 

 radiation at a distance behind the paper and with 

 the edge viewed from a screen on which diffraction 

 fringes are formed. The observer is within the 

 shadow region a distance be, and the zone system 

 is largely obscured as indicated by the dotted lines. 

 The radiation received at c comes from the exposed 

 zones, and its intensity is equal to a series of the 

 form nil — ?«2 +!»«••■ , etc., where mi is the 

 electric intensity due to the exposed portion of the 

 first uncovered zone, etc. The sum of this series is 

 a fraction of Wi since the outer zones tend to cancel. 

 As c is moved to the right, that is, further into the 

 shadow, my will decrease very rapidly without passing 

 through maxima and minima. 



