470 ; PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
TaBLE 2. (y = 45°). 
|E/Eo| with  |E/Eo| without 
n v Zz ¢ diffraction diffraction 
(degrees) 
0 150 ne OF 6 0.10 0 
1 iboats 117 — 8 2.17 2 
2 0.83 1.03 —138 0.21 0 
3 0.50 0.82 —15 1.80 2 
4 0.17 059 -— 8 0.42 0 
5 -—0.17 0.42 11 1.42 1 
6 —0.50 0.31 42 0.80 iL 
7 —0.83 0.23 90 0.91 1 
8 -—117 0.18 157 0.88 1 
9 —1.50 0.14 240 0.99 1 
10 —1.838 0.12 338 1.12 1 
azimuth inclined by an angle 7 = 45° with respect 
to the coast line. Then, from equation (18), mo = 4.5. 
The results are given in Table 2. 
In the problem considered here, the angles of 
elevation are comparatively large (for n= 1, 
y = 1° 24’). If the effects of diffraction occur at 
lower angles, the divergence factor D must be taken 
into account (see Chapter 5). This is done by com- 
puting D for the angles desired and replacing z by 2D 
in equation (21). 
Cliff Site 
If the radar is sited on a cliff and if the land inter- 
vening between the radar and the reflecting plane 
(ocean) is rough, the equations given on page 46 9 
apply. We shall now consider the case where the 
radar is sited at some distance from the cliff edge 
and where the ground between the radar site and the 
cliff edge is reflecting. There are then two reflecting 
planes, the lower of which might be the ocean, or 
might be a reflecting land surface. In Figure 15, 
this surface has been designated as ocean. The upper 
coverage pattern corresponding to Table 1 is shown 
graphically in Figure 14. 
WITH DIFFRACTION 
XN —— — WITHOUT DIFFRACTION 
HEIGHT 
TITTIATTIA AAT ATTA TISLE, 
ZZ. TITIT7 777 
OISTANCE 
FE; IGURE 14. Coverage diagram (relative field strength). 
(Heights exaggerated 3.5 to 1.) 
It is seen from these data that the lobes near the 
critical ray (ray whose reflection point is at the coast 
line) undergo very considerable deformation. The 
Figure 15. Diffraction from a cliff site. 
plane is at a height H above the lower plane and the 
transmitter at a height hf; above the upper plane. 
Assume that the azimuth chosen is perpendicular 
to the direction of the cliff edge; the distance of the 
radar to the cliff edge is do. For any other azimuth 
(angle y in Figure 13), replace do by do/cos y in the 
following equations. 
Two images are shown in Figure 15 and two 
fictitious opaque screens, one corresponding to each 
image. The corresponding variables are distinguished 
by single and double primes. The lobe numbers are 
given by 
n= Aha 
r 
ME a Es) 
nN hy 
The critical angle, Yo = hi/do, is the same for both 
image transmitters. Thus 
0g See 
Ado’ 
Re 4(H + Iu)ky _ mo'’(H + In) 
Ado hy 
Further 
OP = Colic , 
V2n0! 
Ta Ul eM Al 
er 1 ie 
Again, the field is given by 
EVE (1) —alenia® gt izflemsan rats) s (23) 
The expression for the field strength [equation (23)] 
is in a form where all the quantities involved may be 
evaluated for any given height of transmitter, height 
of the cliff, and any wavelength by using graphs and 
tables given in earlier paragraphs. 
