Chapter 8 
DIFFRACTION BY TERRAIN 
OUTLINE OF THEORY 
Introduction 
HE EFFECTS of diffraction around natural ob- 
T 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, however, rather certain from the 
observations that when the shape of the obstacle 
approaches one of the special shapes dealt with by 
the theory,. the latter gives a fair account of the 
facts. Such cases will not be found too frequently 
“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 (80 to 200 mc); 
for higher frequencies, the diffracted field is rela- 
tively unimportant. 
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 
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 
461 
accessory problems arise which will be dealt with 
in following sections. . The most important of these 
complications is caused by ground reflection. 
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Ficure 1. Diffraction around straight edge. 
In Figure 1, the area CAPBD forms an opaque 
screen bounded by a straight edge BPA. The width 
AB of the screen is assumed infinite in the mathe- 
matical theory, but is here shown finite for simplicity. 
The line connecting the transmitter 7’ to the re- 
ceiver & intersects the plane of the opaque screen 
in the point M whose distance from the edge is 
PM = hy. The shortest unobstructed path of the 
radiation is TPR. 
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 discussedin following 
text.The discussion here is limited to a qualitative 
visualization of the mechanics of diffraction in the 
text below; the final formulas used for computa- 
tions will then be written down at once. 
Mechanism of Diffraction 
The physical idea underlying the Fresnel-Kirch- 
hoff diffraction theory may be presented as follows. 
At points visible from T the field, to a first approx- 
imation, is equal to the free-space field Hy. This 
applies in particular to all points of the plane EHCDF 
containing the screen. The receiver R receives 
radiation from the open part HAPBF of the plane, 
