SITING AND COVERAGE OF GROUND RADARS 123 
Example 21. The General Lobe Formula. An inter- 
rogator equipment is used with the radar of Example 
20. It operates on 160 me; the height of the antenna 
above the sea is 500 ft; and thé distance.to the shore 
is 15,840 ft. The intervening land is too rough for 
coherent reflection. The antenna consists of two 
vertical radiating elements and parasitic reflectors. 
The radiators are approximately a half wavelength 
long and spaced a half wavelength apart. The maxi- 
mum distance.at which reliable interrogation may 
be obtained in the absence of a reflecting surface 
has been found to be 110 miles for this particular 
equipment. It is desired fo construct for this site 
the vertical coverage diagram of the interrogator 
system. 
The vertical pattern of a vertical half-wave dipole 
is given by K 
cos (5 sin v) 
fa = cos 7 
Since this factor is over 0.98 for angles up to 10 
degrees, f(y) and f(y — 26) will be taken as unity. 
The lobe angles are then computed neglecting ¢ and 
¢, as in Example 11. Diffraction and divergence are 
computed as in Example 15 and as on page 119. The 
results of these calculations are listed in Table 14. 
The values of p and $ depend on y’ and are read 
from Figures 69 and 70. Using equation (108), ¢’ 
is obtained and added to ¢. The sum ¢’ + ¢ is the 
net phase shift of the reflected wave from the values 
used in computing the lobe angles and is plotted 
against y in Figure 72. For purposes of comparison 
6 has also been plotted, but this curve is not required 
otherwise. The product Dpz is the relative strength 
of the reflected ray and is plotted in Figure 72. 
The points on the coverage diagram are obtained 
in polar form from equation (107). 
ALTITUDE IN FEET 
h 500 FEET 
SHORE LINE= 15640 FEET 
d=I10 MILES 
ANTENNA-VERTICAL HALF WAVE DIPOLE 
VERTICAL POLARIZATION 
The vector representing the reflected wave is shifted 
in the lagging direction by ¢’ + ¢ degrees when this 
sum is positive, and in the leading direction when 
the sum is negative. The effect of this phase shift 
on the point on the lobe being considered may be 
determined by inspection of Figure 72. 
Thus, to determine the first maximum point the 
following procedure may be used. At n = 1 the 
angle y is 0.0011 radian and ¢’ + ¢ is —14.8 degrees. 
This means that for the cosine term to be —1 the 
path difference must be increased until 6 is 194.8 
degrees. The angle ya at which this value of 6 occurs 
is found by interpolating between 0.00110 and 
0.00492 since 6 changes from 180° to 360° in this 
interval. This angle is then 0.00141 radian. Had the 
angle ¢’ + ¢ changed appreciably from 0.00110 to 
0.00141 the interpolation would be repeated using 
the new value of .’ + ¢. In most cases the new 
value of ¢’ + ¢ may be estimated from the curve, 
and the first approximation will be close enough. 
At 0.00141 radian Dpz is 0.501. Substituting this 
value: 
d 
1100/1 + (0.501)? — 2 X 0.501 X (—1) 
165.0 miles , 
which is laid off on the coverage diagram at an angle 
of 0.00141 radian. As many other points as required 
to sketch the diagram may be computed in a similar 
fashion. For an intermediate point it is convenient 
to use the net angle equal to 90° since the equation 
then reduces to 
d = 110V/1 + (Dpz)? . 
The angles of the lobes have been listed in Table 14 
under ya and the lobe lengths under d. 
Il ll 
RADIANS-> 0,08 0,07 0,06 0.05 0,04 
IWAN 
y 
= 
1 
= 
aaa 
i 
y 
[| 
(iN 
ANY 
A BIAY, 
Ficurt 73. Coverage diagram for Example 21. 
