RADAR CROSS SECTION OF SIMPLE FORMS 



183 



9.1.5 



Scattering Coefficient 

 or Characteristic Length 



This parameter has also been called the radar 

 length of the target. The definition is 



L = d 





(10) 



\\ here E,. = field strength at the receiver, 



Ei = field strength incident on target. 



It is evident that 



(11) 



connects L with radar cross section. The radar gain 

 becomes 



1 \ 3X / 



A' 



(12) 



9.2.1 



RADAR CROSS SECTION 

 OF SIMPLE FORMS 



Spheres 



The radar cross section of any large curved con- 

 ducting surface having principal radii of curvature 

 Pi and p2 at the reflection point is given by 



(7 = TTplp-z. (13) 



This formula applies if the surface is sufficiently 

 large and sufficiently curved to contain many 

 Fresnel zones. For a sphere of i-adius a, where 

 a >> \, 



(T = Tva-. (14) 



Thus, in the case of a large conducting sphere, the 

 radar cross section is equal to the geometrical cross 

 section and is independent of wavelength. 

 The result for small spheres (a < < X) is 



0- = 1447r" 



(15) 



There is no simple formula for the radar cross 

 section in the region a r-^\. 



'''^'^ Cylinders 



The radar cross section of a cylinder \A-hose length 

 is large compared with the wavelength is 



2Tralr 



(16) 



where 



a = radius, 



L = length (L >>X). 



This formula assumes that the direction of inci- 

 dence is normal to the cyHndrical surface. If the 

 cylinder is tilted so that there is a small angle 6 

 between the normal to the cyhnder and the direction 

 of incidence, the result is 



2TaU- 



sin 



2TrLd 



2irLd 



(17) 



This result holds for small angles of tilt 6 such that 



9.2.3 



sm y = I 



Plates 



A flat plate of area .S with all dimensions large 

 compared with X and oriented so that the normal 

 to the plate is in the direction of incidence, has a 

 radar cross section given by 



S'- 



= 4:r" 



X- 



(18) 



regardless of shape. 



For a circular plate (a disk) of radius a, whose 

 normal is at an angle 9 with the direction of incidence, 



<r = Tra- 



cote 



<T'-')l 



where Ji is the first-order Bessel function, 

 maximum value is at ^ = 0, where 



47r5rt4 



(19) 

 The 



(20) 



This agrees with equation (18), since at normal 

 incidence S = ira". 



The peculiar feature of equation (19) is that the 

 maximum at 5 = is very sharp. For example, if 

 \/a = 1/10, (T is only 1/10 of its maximum value 

 when e = 1.25°. 



The average value of a- over all orientations is 



cr = — 7ra\ (21) 



2 



This result is independent of wa\-elength and sug- 

 gests that a large number of flat plates oriented at 

 random will have a cross section independent of X, 

 or that a few surfaces of rapidly changing orienta- 

 tion may have this property. 



