Chapter 8 

 DIFFRACTION BY TERRAIN 



8 1 OUTLINE OF THEORY 



*ii Introduction 



THE EFFECTS of diffraction around natural ob- 

 stacles of complicated shape are difficult to 

 analyze. Theory offers two lines of approach to 

 diffraction problems, both based on the substitution 

 of contours of simple shape in place of the natural 

 obstacle. 



The first and oldest method, known as the Fresnel- 

 Kirchhoff method, is an approximate procedure for 

 calculating the diffraction by a flat screen. It yields 

 comparatively simple formulas for the diffracted 

 field; the present chapter is concerned with a 

 presentation of this method. 



The second method is based on the fact that the 

 wave equation can be solved for obstacles of very 

 simple geometrical shape, especially cylinders and 

 spheres. If the curvature of a hill is fairly constant, 

 so that its shape can be approximated by a cylinder 

 or sphere, the field behind the hill can be obtained 

 by the use of this method. 



Observations on diffraction by obstacles in the 

 short wave and microwave region are very sparse. 

 It is, therefore, not possible to present a consistent 

 body of results that could be utilized in radio prac- 

 tice. It seems, howe^'er, rather certain from the 

 observations that when the shape of the obstacle 

 approaches one of the special shapes dealt with bj^ 

 the theory, the latter gives a fair account of the 

 facts. Such cases will not be found too frecjuently 

 in practice. The hope is nevertheless justified that 

 the right order of magnitude is obtained by a judi- 

 cious application of the theory. The main applica- 

 tion is in the lower frequency band (30 to 200 mc) ; 

 for higher frequencies, the diffracted field is rela- 

 tively unimportant. 



8.1.2 



The Fresnel Diffraction Theory 



The Fresnel-Kirchhoff approximate theory was 

 originally developed to account for the diffraction of 

 beams of light when cut off by diaphragms, slits, and 

 similar optical devices. In applying this theory to 



170 



the propagation of radio waves over the earth, only 

 one basic problem is usually encountered, namely 

 that of diffraction around a straight edge. In the 

 present section, the general method of handling this 

 problem and obtaining numerical results is given. 

 On applying the method to actual cases certain 

 accessory problems arise which will be dealt with 

 in Sections 8.3 and 8.4. The most important of these 

 complications is caused by ground reflection. 



FiGUHE 1. Diffraction around straight edge. 



In Figure 1, the area CAPBD forms an opaque 

 screen bounded by a straight edge BPA. The width 

 AB oi the screen is assumed infinite in the mathe- 

 matical theor}', but is here shown finite for simplicity. 

 The line connecting the transmitter T to the re- 

 ceiver if? intersects the plane of the opaque screen 

 in the point M whose distance from the edge is 

 PM = ho. The shortest unobstructed path of the 

 radiation is TPP. 



In a purely geometrical theory, the point R would 

 be in the shadow of the screen and would receive no 

 radiation. If the wave nature of radiation is taken 

 into account, it is found that an electromagnetic 

 field is generated in the shadow of the screen; the 

 waves are bent around the obstacle. 



The mathematical derivation of the diffraction 

 formulas will not be given here as it is rather intri- 

 cate; however, the problem is discussed in Section 

 8.2. The discussion here is limited to a qualitative 

 visualization of the mechanics of diffraction (Sec- 

 tion 8.1.3); the final formulas used for computa- 



