AIRCRAFT 



185 



The results for a rectangular plate are practically 

 the same as for a disk. If the dimensions of the 

 plate are b and c, ira^ is replaced by be in equation 

 (20) and equation (21); equation (19) is replaced by 



AttVc- 



sm 



cos 8- 



I -— - sm d • cos (f) 1 



2Trb 

 X 



• {' 

 smi 



sin^ • coscj) 

 2-irc 



sin 9 • sm (/) 



) 



2xc 



sin 6 • cos (f) 



(22) 



where the sides b and c are parallel to the x and y 

 axes, and sin d cos cj), sin d sin (j), and cos 9 are the 

 direction cosines of the direction of incidence rela- 

 tive to the plate normal. 



These results hold when the linear dimensions 

 of the target are large compared with the wave- 

 length. If the linear dimensions are small compared 

 with the wavelength, a plate of area S, oriented so 

 that the normal to the plate is in the direction of 

 incidence, has a radar cross section given by 



_d2T-S^ 



(23) 



9.2.4 



Corner Reflectors 



The corner formed by three mutually perpen- 

 dicular conducting planes forms what is called a 

 corner reflector. The faces may be triangular or 

 square or have other shapes, depending on how the 

 planes are bounded. A line drawm to the corner 

 making equal angles with the three edges is called the 

 axis of symmetry. 



Reflection from a corner reflector may be analyzed 

 by the methods of geometrical optics, provided the 

 linear dimensions of the reflector are large compared 

 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. The radar cross section of a corner reflector 



47rS= 



(24) 



\\'here S is the cross section of the triply reflected 

 beam. S is a function of the shape of the faces of the 

 corner reflector and of the angle of incidence of the 

 radiation. 



(1 -0.00076 02), 



(25) 



For a triangular corner reflector, e is given approx- 

 imately by 



3\- 



where L = length of edge of reflector, 



6 = angle between direction of incidence and 

 the axis of sjonmetrj^ in degrees {6 < 26°). 

 As a function of 6, a 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. 



9^ AIRCRAFT 



9.3.1 Variation with Aspect 



Diagrams showing the dependence of a on orienta- 

 tion indicate very large and irregular fluctuations. 

 Radar cross section c 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 <r 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 

 \\idely different instantaneous values of c 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 o- have been smoothed out. 



9.3.2 



Measurement of a- 



The radar equation for free space, equation (45), 

 in Chapter 2, may be used for the computation of 

 average values of (t from observed instantaneous 

 values, provided conditions are such that ground 

 reflections are unimportant. The received power Po 

 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 Pi 



