120 TECHNICAL SURVEY 
1000 Py -7-1h 
es LoS SSSI 
HASSSRSESE NOES \ 
Sa 
CN 
a Nee 
NG 
eae NN | 
Figure 71. Divergence factor graph. 
where k is % and 2 is in feet. 
For angles below this limit the theory for diffrac- 
tion of radio waves around the earth is required for 
a rigorous solution. However, in practice it is found 
that angles as low as the first maximum (n = 1) may 
be treated by the ray theory with little error. 
Applying equation (98) to Example 11 
y’ > 0.00382 /4.92 = 0.0065 radian. 
In Table 6 this corresponds to n = 2.25. However 
using n = 1 and 7’ = 0.0036 the divergence factor 
D is found from Figure 71 to be 0.58. For angles 
below y’ = 0.0086 it is necessary to estimate D. 
Experience indicates that a fair minimum value to 
select for D is 0.5773. For angles much below the 
first maximum, the optical treatment gives values 
of field strength which are too low because it neglects 
diffraction. This may be compensated in part by 
using values of D between 0.5773 and 1.0. 
Lobe Lengths 
The contributions of the direct and reflected waves 
may now be added to obtain the length of the lobes. 
= [f(y) + fly — 28) zpD]do (99) 
where L is the distance to the end of the lobes or 
the nulls, in miles. do is the maximum range (in 
miles) at which a given response (usually the mini- 
mum detectable signal) would be obtained if the 
antenna were in free space. If the lobe diagram were 
plotted for some signal level above the minimum 
detectable, d) and ZL would be correspondingly 
smaller. 
Example 20. Lobes for a Medium Height Radar. A 
200-me radar using horizontal polarization has an 
antenna composed of two groups of dipoles spaced 
three wavelengths between centers, each group 
having four dipoles spaced \/2, as in Example 16. 
The antenna is 500 ft high and 3 miles inland as in 
Examples 11 and 15. It is desired to compute the 
vertical coverage pattern. 
From previous tests on this type of equipment it 
‘is known that the maximum range that would be 
obtained in free space do is 80 miles. Since the 
polarization is horizontal, p will be taken as unity. 
