46 TECHNICAL SURVEY 
It can be shown’ that the ratio of the received 
power Pz, to the output power P, is given by 
2 
Bat a LS 
ih OP Cea ia) fee (6) 
The gains G;, G, and path factor A, are defined in 
Volume 3, Chapter 2, and ) is the wavelength of the 
radiation used. (See also Volume 3, Chapter 9.) This 
formula can be used for the determination of o. Or 
if o is known, it may serve to calculate the possible 
range. (It may be noted here that sometimes oA; 
is called radar cross section.) Also, a characteristic 
length L, sometimes called the scattering coefficient, 
is occasionally defined in relation to « by 
o = 4rL’. (7) 
For simple targets « may be calculated. Table 1 
contains a few calculated radar cross sections. 
AIRCRAFT TARGETS 
Diagrams showing the dependence of o on the 
orientation of the aircraft indicate very large and 
irregular fluctuations. The radar cross section can 
change by 100 to 1 with a change of aspect of only 
a few degrees. These varying values of the radar 
cross section are dependent on wavelength, polari- 
zation, details of plane design, etc. Reflection pat- 
terns such as shown in Figure 1 have been measured 
in the laboratory for a few simplified models. Actually 
an observer would see only the time average of the 
LS 
wes 
f=100 MC POLARIZATION 
HORIZONTAL 
Er=SCATTERED FIELD STRENGTH 
IN ARBITRARY UNITS 
&=GORRESPONDING RADAR 
GROSS SECTION IN SQUARE 
ETER 
Ficure 1. Aspect diagram of a B-17E at 5 degrees 
above horizon. 
8See Volume 3. 
radar cross section of a plane, and it is only this 
average value which is of operational importance. 
Table 2 gives measured values of o for various 
aircraft. These are the values to be used in equation 
(6). As far as is known, these empirical cross sections 
. 
TasLE 2. Airplane radar cross sections. 
Airplane o, sqm o, sq ft 
SNC 3.9 42 
SNJ . 5.0 54 
OS-2U 9.5 100. 
Taylorcraft 9.5 100 
CESSNA 9.5 100 
O-47 10 110 
AT-11 11 120 
SWB 13 140 
15-D (Curtiss Wright) 23 250 
J2F 25 260 
JRE 30 320 
PBY 31 340 
B-18 36 380 
B-17 45 480 
B-29 67 710 
are independent of wavelength. This result may be 
interpreted to mean that a plane in motion behaves 
more or less like a collection of good reflecting 
surfaces oriented at random. It is worth noting in 
this connection that the radar cross section of a 
cireular plate. of radius a, whose normal is at an 
angle @ with the direction of incidence, is 
2 
= 7a? [cot 6X Jt (= sin a) | F (8) 
where J; is the first order Bessel function of the first 
kind. The maximum of o occurs for @ = 0, when 
equation (8) reduces to 
4ra4 
ee arn @) 
This sharp maximum of o at 6 = 0 is the phenom- 
enon of specular reflection. The average value of 
o over all values of @ turns out to be 
Wn 
Cavg = guna . (10) 
This result is independent of wavelength and suggests 
that a large number of specularly reflecting surfaces 
oriented at random will have a cross section inde- 
pendent of ), or that a few surfaces of rapidly chang- 
ing orientation may have this property. The lack 
of dependence of wavelength of aircraft radar cross 
sections might be understood on the basis of these 
results. 
SHIP TARGETS 
A ship being a collection of both complicated and 
flat surfaces, a rigorous computation of the radar 
cross section of any given ship of known design is 
not feasible. Nevertheless, the Naval Research 
Laboratory workers have been able to give a good 
account of these problems.374376388392,417.421 
The path factor in the formula (6) raised to the 
