SITINS AND COVERAGE OF GROUND RADARS 113 
the height and wavelength to obtain the range of 
any zone of any lobe. 
In order to read the relative intensity and phase 
lag of the reflected wave from the diffraction graphs, 
Figure 27 and Figure 28 respectively, it is necessary 
to have m expressed in terms of v. In Figure 19 the 
path difference is by definition of m 
nN 
ms 
[N= 5° (84) 
Equation (23), with A = d — 8, yields 
dv? 
A=—, 
hence 
vy 
It is also desirable to have an expression for v in 
‘terms of x and 7. This is obtained by substituting 
v?/2 for m in equation (82) and solving 
Ln? 2 
The width of the zones, that is, along a chord at 
‘d; parallel to the minor axis of the elliptical rings, 
Ficure 60. Width of Fresnel zones. 
may be obtained from Figure 60. Zone m is shown ° 
with a chord length b. The distance from the image 
antenna to the intersection of the chord and ring m 
is 1 + md/2. From this may be written 
(i a my =P+ 6) (87) 
- Neglecting m?\2/4 since it is small compared to the 
other terms, 
P+ ml =P + (2) , 
b= V4mn, 
= dy Ly cs ahs 
~ cos¥W > mdr’ 
from equation (78), since W is small. 
Where earth curvature effects are appreciable the 
effective height, from equation (59), should be used. 
b = 4h,’ e (88) 
To apply this method the distance of the shore- 
line, d;, is substituted in equation (81), and the 
equation is solved for 71, the terrain factor. This 
quantity is a constant for a particular azimuth and 
is substituted in equation (86) along with the values 
of m desired and solved for v. The values of m corre- 
sponding to these values of v are the numbers of the 
zones which intersect the shoreline for each value 
of n. These values of v are entered in Figures 27 and 
28 to obtain the intensity and phase lag relative to 
that which would be obtained if the rough land were 
replaced by the sea. 
Example 15. Shoreline Diffraction. A radar station 
is assumed to have the same height and frequency 
as in Example 11. The shoreline distance is 3 miles, 
and the intervening land is occupied by a large 
city. hi = 500 ft; f = 200 me; di = 15,840 ft. At 
this distance the effect of earth curvature is less than 
1 per cent and may be neglected. The greatest angle 
at which waves are reflected from the sea is given by 
500 5 
75,840 S< Gi} = isch 
In equation (16) the maximum height of roughness 
for regular reflection is 
3,520 
H = 300 x 181 
= 9.7 ft. 
The land is evidently a diffuse reflector. From 
equation (83) 
_ dd _ 15,840 x 4.92 
~ (i)? (600 — 4.5)? 
Substituting in equation (86) for n = 2 
_ | PSU Dine 
v= pax Dap ee = BN, 
y2 
m == 
2 
T; = 0.317. 
= 2.23 . 
That is, somewhat more than two zones are com- 
pletely formed on the sea. In order to determine 
which sign to use in reading Figure 27 it is only 
necessary to know whether the main reflection point 
d, for this lobe falls on the land or the sea corre- 
sponding to shadow or illuminated regions. A more 
general procedure is to solve equation (63) using the 
shoreline distance for d; : 
4 X (500 — 4.5)? 
~ 15,840 X 4.92 TaD. 
For all values of 7 less than 12.6, d, will be on the 
sea and equation (84) applies to the near edge, and 
the minus sign is used in equation (82) corresponding 
to +v in Figure 27. For n greater than 12.6 the 
