TARGETS . 473 
with the wavelength. A ray which is reflected from 
all three surfaces is said to be triply reflected. 
Triply reflected rays always return to the radar and 
make the only large contribution to the radar cross 
section which ina corner reflector is 
4nrS* 
c= 
XG 
where S is the cross section of the triply reflected 
beam. Sis a function of the shape of the faces of the 
corner reflector and of the angle of incidence of the 
radiation. 
For a triangular corner reflector, o is given approx- 
imately by 
, (24) 
i a (1 — 0.00076 6), (25) 
where LZ = length of edge of reflector, 
@ = angle between direction of incidence and 
the axis of symmetry in degrees (6 < 26°). 
As a function of 6, o has a broad, flat maximum. 
Consequently, the return to the radar receiver from 
such a target is not sensitive to the precise orienta- 
tion of the axis of symmetry. 
AIRCRAFT 
Variation with Aspect 
Diagrams showing the dependence of c on orienta- 
tion indicate very large and irregular fluctuations. 
Radar cross section o« can change from values of 
nearly 1,000 square meters to a few square meters as 
a result of a change of aspect of a few degrees. These 
instantaneous values of the radar cross section are 
dependent on wavelength, polarization, details of 
plane design, areas of specular reflection, propeller 
rotation, etc. Reflection patterns have been meas- 
ured for a few simplified models by laboratory means 
(see Figure 1 as an example). It would be difficult 
to calculate instantaneous values of o by theoretical 
methods. 
In practice, however, an airplane is in motion and 
is affected by air currents. These factors cause the 
airplane, in a short interval of time, to present many 
widely different instantaneous values of o to the 
radar, so that the signal actually seen on the scope 
by the observer is in effect a time average, where the 
most violent fluctuations of instantaneous values 
of « have heen smoothed out. 
Measurement of o 
The radar equation for free space, equation (45), 
in Chapter 2, may be used for the computation of 
average values of o from observed instantaneous 
values, provided conditions are such that ground 
reflections are unimportant. The receivea power Ps 
is determined by matching the signal from the plane 
with the measured signal from a signal generator . 
The procedure followed in work at the Radiation 
Laboratory is to measure the maximum value of P2 
for each of a series of 3-second intervals. A plot is 
made of P2 against range d on log log coordinates. 
As might have been anticipated from equation (45), 
in Chapter 2, it is found that a line with a constant 
slope of —4 passes through the average of the 3- 
second interval maximum points, although the 
individual points fluctuate widely. The value of o 
corresponding to this line is calculated. 
The resulting value of o still cannot be called an 
average value because the maximum value of oc 
has been used for each point. Consequently these 
values of o, substituted into equation (45) in Chap- 
ter 2, cannot be expected to give the average value 
of Ps, or to give observed maximum ranges. How- 
ever, it is found that if the values of « thus computed 
are reduced 40 per cent, they give correct results. 
These empirical cross sections are relatively inde- 
pendent of wavelength. This result may be inter- 
preted to mean that a plane in motion behaves more 
or less like a collection of specularly reflecting sur- 
faces oriented at random, as equation (21) indicates. 
Attempts have been made to develop formulas 
giving operational cross sections as a function of 
some large feature of plane design, such as wing 
span or length of fuselage, but these attempts have 
not been successful. 
cc. 
& 
xs 
ro 
SS 
. 
Lp 
ce 
eo 
SX? 
ne 
eH 
ma 
[| 
ce 
Q 
ecaTvenge 
10 ARBITRARY UMTS. 
eS 
neces 
7 
Ficure 1. Aspect diagrams of B-17E, 5 degrees above 
horizon. 
