262 
The complex dielectric constant ¢, is 
where ¢, is the real part of the dielectric constant and 
« = 60ed is its imaginary part. o is the conductivity 
of the dielectric medium in mhos per m, and 4 is the 
wavelength, in vacuum, of the incident radiation. 
The generalized Fresnel formulas, for horizontally 
and vertically polarized waves, respectively, are 
Bie c wal ak 2) 
es SUR rN Se ee v — (6 — cos’) (horizontal) 
sin VW + (e, — cos? y)} 
_j%, S ie wu 2 $ , 
pe it _ €c8in W — (e,— cos? y) Grentical)? 
€, sin W + (€,—cos? y i 
where p denotes the magnitude of the complex reflec- 
tion coefficient and y is the angle of lag of the 
reflected component behind the incident component 
of the electric field. 
The results at 10 cm and for dry sand are given 
in Figure 4. The theoretical curves given on the 
graph do not necessarily represent the best fit. These 
curves were computed for e, = 4 and o = 0 (perfect 
dielectric). The experimental Brewster angle turns 
out to be around 23° (grazing angle). 
The experimental results for clay-sand soil are 
given in Figure 5. The theoretical curves are the 
same as those given in the preceding case, that is, 
for « = 4 and o = 0. It will be noted that the fit 
with the experimental values is less satisfactory in 
this case. The author attributes the discrepancy be- 
tween the observed and computed values of the re- 
flection coefficient, in part, to the quality of the soil 
which consisted of lumps of about a half wavelength 
diameter. In general the roughness of the ground con- 
tributes considerably to scattering. It is rather to be 
expected that a theoretical curve representing specular 
reflection coefficients from a smooth surface should 
not fit well the experimental data referring to such 
a rough ground. 
Saturated Ground. Table 2 represents the results 
obtained at 9 cm for the reflection coefficient of sat- 
urated ground. 
The most suitable values of «, and o or ¢ to fit both 
reflection and absorption measurements are e, = 24, 
o = 0.66 mhos per meter, and ¢ = 3.56, 
Tests carried out at 10 cm on ground of somewhat 
similar type (tidal flat and moist sand) are given in 
RADIO WAVE PROPAGATION EXPERIMENTS 
PLACE-NY STATE AG INSTITUTE 
EARTH- HARROWED FIELD, CLAY SAND 
SOIL-LUMPS 1"-2" DIAMETER 
- 08 
a 
b 
z 
w 
° 
= 06 
rs 
Ww 
° 
o 
3 
2 04 
3 g74 
z x HORIZONTAL POLARIZATION 
e © VERTICAL POLARIZATION 
9° 
nD 
H-APPROXIMATE THEORETICAL p} 
V-APPROXIMATE THEORETICAL p} 
fo} 4 8 12 46 20 24 28 
GRAZING ANGLE IN DEGREES y 
Ticur 5. Reflection coefficient p’ versus y. A\=10 cm. 
d=100, 300 ft. 
Figures 6 and 7. The theoretical curves in Figure 6 
correspond to a perfect dielectric (c = 0) with « = 
10. Since the conductivity of the soil is not zero, the 
true value of the reflection coefficient for vertical 
polarization cannot be zero at the Brewster angle. 
The data seem to confirm this point. 
The data of Figure 7 refer to moist and very smooth 
beach sand. It is thought that these observations are 
the most reliable so far as self-consistency is con- 
cerned. Again the computed curves refer to a perfect 
dielectric with «, = 15. 
An important difference between the measurements 
at 9 cm at a fixed location and those made at 10 em 
with the portable setup consists of the fact that at 9 
em direct absorption measurements could be per- 
formed in addition to measurements of the reflection 
coefficient ‘The electrical constants could thus be deter- 
mined at 9 cm without ambiguity. 
1.0 
_ 0.8 
a 
= 
2 
ws 
o 
Soe 
wu 
Ww 
8 
SHORT BEACH 
S 0.4 TIDAL FLAT AT LOW TIDE 
z SOME ORGANIC MATERIAL 
8 PRESENT 
im «#10 720 oO 
& 0.21 © VERTICAL POLARIZATION 
X HORIZONTAL POLARIZATION 
H-APPROXIMATE THEORETICAL Pp}, 
V-APPROXIMATE THEORETICAL p! 
{o) 
(9) 4 8 12 16 20 24 28 
GRAZING ANGLE IN DEGREES 
Ficure 6. Reflection coefficient p’ versus y. A\=10 cm. 
d=90 ft. 
TaBLE 2. Reflection coefficients of saturated ground. \ = 9 em.1,2 
Vertical polarization 
Grazing Calculated Observed 
angle €r = 24 €r = 25 Heavy Watered 
degrees o = 0.66 o¢=0 rain by hose 
22 0.31 0.31 0.28 0.32 
36.5 0.50 0.50 0.50 0.50 
46.5 0.57 0.57 0.58 0.58 
Horizontal polarization _ 
Calculated Observed 
€, = 24 €, =,25 Heavy Watered 
o = 0.66 ¢=0 rain by hose 
0.85 0.86 0.90 0.86 
0.78 0.79 eee 0.78 
0.74 0.75 0.72 0.74 
