SITING AND COVERAGE OF GROUND RADARS 119 
a i es 
N 3000 MC 
120 
80 
9 DEGREES (LAG) 
40 
O12 NIE 
W ANGLE OF REFLECTION IN RADIANS 
ae HP — 3000 MC als 
SEA WATER 
€-= 81 
O = 1 MHO/METER 
VP—I00 MG \ 
DRY SOIL 
a as 0.24 0.36 
Ficure 70. Phase of reflection coefficient curves. Note: Solid curve represents seawater. Dotted curve represents dry soil. 
and angle of reflection for sea water and more 
gradually for dry land. The minimum point of the 
curves in Figure 69 is known as the pseudo-Brewster 
angle corresponding to a similar angle in optics. 
TasieE 12. Terrain reflection characteristics. 
Type of terrain €, co, mhos 
per meter 
Fresh water 81 10-3 
Sea water 81 1 
Rich soil 20 3 xX 10° 
Heavy clay 13 4 xX 107 
Rocky soil 14 2 < 1053 
Sandy dry soil 10 20m 
City—industrial area 5 NOY 
Cases not covered by Figures 69 and 70 may be 
computed from the following equations. 
Vertical Polarization: 
e-sinW — +/e, — cos? 
exp (—jo) = ——————— , (95 
meres Je) e,sinW + +/e, — cos? Vv 2) 
Horizontal Polarization: 
f Ve. — cos? ¥ — sin¥ 
ex = a 96 
pexp (—j¢) Rema eR (96) 
where Y = the angle of reflection measured from the 
horizontal ; 
€. = €, — J600d; 
€, = dielectric constant of the reflector rela- 
tive to air; 
o« = conductivity of the reflector, mhos per 
meter; 
r 
o = phase angle, lagging. 
ll 
wavelength, in meters; 
Some typical ground constants are given in 
Table 12. 
Divergence 
The reflected wave is scattered somewhat by being 
reflected from the spherical surface of the earth 
instead of a plane surface, and this reduction of field 
strength is taken into account by the divergence 
factor. This is dependent on geometrical considera- 
tions and may be expressed as follows (for y’ < 3°): 
D= ! (97) 
mr 
Ni ceca 
where 7 is the lobe number, 
is the wavelength, in feet, 
7’ is the reflection angle, in radians, obtained 
from equation 60. 
A convenient chart for obtaining D is given in 
Figure 71. The parameters are y’ in radians and nd, 
with \ expressed in feet. 
As y' approaches zero, n also approaches zero, and 
the equation is indeterminate. At the point of tan- 
gency of the line of sight and the earth, D is 0.5773. 
At low angles the field is modified by diffraction 
around the curved earth. The lower limit of the angle 
y’ for which the optical treatment is valid is usually 
given by 
3 
y' > am Tq 7 0.00382 Vr, (98) 
