SCATTERING AND ABSORPTION OF MICROWAVES 47 
fourth power is 
sin do 
At= of ss 35, (4 — cos in| ) (11) 
where _ 4ahiH 
ea ay 
h, = antenna height, 
H = height of ship above water 
including superstructure. 
The above result follows by integrating the received 
power over the height H, assuming perfect reflection 
from sea. 
Tt is seen in equation (11) that whether 5  < 7, 
the region called the “far zone,” or 69 > 7, the “near 
zone”’ (short ranges), materially affects the qualita- 
tive behavior of the factor A‘. In the latter region 
Aj=6. 
The radar cross section of a ship which does not 
exhibit marked specular reflection is given roughly by 
BH 
nN ? 
(12) 
where a = dimensionless constant dependent 
on ship design, 
B = the breadth of the aspect under 
observation, 
H = height of ship above water including 
superstructure. 
The approximate values of a to be used are indicated 
in Table 3. 
TaBLeE 3. Ship targets. 
Type of ship a Remarks 
Battleship 0.1 
Cruiser 0.1 
Aircraft carrier 0.05 Except at direct 
broadside aspect 
Submarine 0.01 t 
In Tables 4 to 7, values of co computed from 
equation (12) are called theoretical values. Experi- 
mental values are computed from observations made 
by the Naval Research Laboratory workers. with 
each quantity the mean of several observations. The 
200-me experimental result is unexpectedly low while 
the values at the higher frequencies are a little 
higher than would be anticipated. This points to the 
existence of some specular reflection for this ship, 
which would not be surprising in view of its great 
size. Considering the uncertainty in the experimental 
values, the agreement with the theoretical results is 
not unsatisfactory and bears out the assumed 
dependence on wavelength. 
The aircraft carrier shows pronounced specular 
reflection at the direct broadside aspect, particularly 
at the higher frequencies. These values of o are 
typical of the ship for aspects other than direct 
broadside. 
In Table 8, the same ship is analyzed at direct 
Tasve 4. Radar cross section of a battleship (BB-63), 
broadside aspect. a = 0.1, B = 270 m, H = 24m. 
J(me) a (exp), sqm __ a (theory), sqm 
200 0.12 x 10° 1.9 x 10° 
700 10.2 x 105 6.8 X 10° 
970 15. xX 105 9.4 X 10° 
3,060 110: =X 105 30. X 105 
TasLe 5. Radar cross section of a cruiser (CL-87), 
broadside aspect. a = 0.1, B = 180 m, H = 24m. 
(me) o (exp), sq m o(theory), sq m 
100 2.45 X 104 2.6 X 10¢ 
200 5.06 < 104 5.2 X 104 
700 7.79 X 104 18.1 < 104 
970 28.4 xX 104 25.1 < 104 
3,060 102.2 x 104 79.3 X 104 
TABLE 6. Radar cross section of submarine (SS-171), 
broadside aspect. a = 0.01, B = 83 m, H = 7.6 m. 
f(me) a(exp), sq m a(theory), sq m 
200 3.0 x 102 3.5 X 10? 
700 18.7 X 10? 12.2 < 10? 
3,060 71.4 X 102 53.4 x 102 
TasBLE 7. Radar cross section of aircraft carrier (CV-36), 
near broadside aspect. 2 = 0.05, B = 250 m, H = 46m. 
f(mc) o(exp), sq m o(theory), sq m 
200 0.22 « 10° 0.96 36 102 
700 2.6 x 105 3.4 xX 105 
970 6.3 xX 10° 46 x 105° 
3,060 11.3 x 105 14.4 x 10° 
TABLE 8. Radar cross section of aircraft carrier (CV-36), 
direct broadside aspect. 
f(me) a(exp), sq m 2 a(exp) 
200 0.055 x 107 1.2 X 10° 
700 10 xX 107 1.8 X 105 
970 5.0 x 107 4.8 X 10° 
3,060 71  X107 7.1 X 108 
broadside. No theoretical calculation of o has been 
attempted because of a lack of sufficient data from 
other ships of this type. The column 2c is near 
enough to a constant to indicate the existence of 
specular reflection. Since the hull at broadside can 
be considered as a flat surface, specular reflection is 
to be expected under normal incidence with a radar 
cross section proportional to 1/A? as indicated by 
equation (9). 
In view of the complicated reflecting properties of 
targets of operational interest, it may be said that 
the experimental results can be considered as being 
in fair agreement with theoretical predictions. 
ABSORPTION AND SCATTERING 
BY CLOUDS, FOG, RAIN, HAIL, AND SNOW 
The theory of the scattering and absorption of 
microwaves by a collection of spherical particles of 
known concentration, size, distribution, and given 
