472 ; PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
becomes 
2 
=? = GG (e) As, (12) 
RADAR CROSS SECTION 
OF SIMPLE FORMS 
Spheres 
The radar cross section of any large curved con- 
ducting surface having principal radii of curvature 
p, and pe at the reflection point is given by 
o = Tipe. (13) 
This formula applies if the surface is sufficiently 
large and sufficiently curved to contain many 
Fresnel zones. For a sphere of radius a, where 
a>>, 
o = 7a’. (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 < < }) is 
- of 
o = 1447° Ti (15) 
There is no simple formula for the radar cross 
section in the region a ~ X. 
Cylinders 
The radar cross section of a cylinder whose length 
is large compared with the wavelength is 
oat, (16) 
This formula assumes that the direction of inci- 
dence is normal to the cylindrical surface. If the 
cylinder is tilted so that there is a small angle 6 
between the normal to the cylinder and the direction 
of incidence, the result is 
(17) 
This result holds for small angles of tilt 6 such that 
sin 6 = 0. ; 
a = radius, 
L = length (L>>n). 
Plates 
where 
A flat plate of area S with all dimensions large 
compared with \ and oriented so that the normal 
to the plate is in the direction of incidence, has a 
radar cross section given by 
o=4r—, (18) 
regardless of shape. 
For a circular plate (a disk) of radius a, whose 
normal is at an angle 6 with the direction of incidence, 
2 
c= 7a? [cote de (24sin a) | ; (19) 
where J; is the first-order Bessel function. The 
maximum value is at @ = 0, where 
_ 4nat 
2 
This agrees with equation (18), since at normal 
incidence S = za?. 
The peculiar feature of equation (19) is that the 
maximum at @ = 0 is very sharp. For example, if 
d/a = 1/10, co is only 1/10 of its maximum value 
when 6 = 1.25°. 
The average value of o over all orientations is 
ees 
o 5 7a. (21) 
This result is independent of wavelength and sug- 
gests that a large number of flat plates oriented at 
random will have a cross section independent of 2. 
or that a few surfaces of rapidly changing orienta- 
tion may have this property. 
The results for a rectangular plate are practically 
the same as for a disk. If the dimensions of the 
plate are b and c, za? is replaced by bc in equation 
(20) and equation (21); equation (19) is replaced by 
sin (27 sin 6 - cos ) 
8 nN 
a sin @- cos@ 
(20) 
o 
4rb?c? 
oc = — 5 cos 
2 
sin = sin 6 - sin ) 
Sa (22) 
= sin 6- cos@ 
where the sides 6 and ¢ are parallel to the 2 and y 
axes, and sin 0 cos ¢, sin @ sin g, and cos @ 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 
_ 32° $8 
o Z 
3 
(23) 
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 drawn to the corner 
making equal angles with the three edges is called the 
axis of symmetry. 
Reflection from a comer reflector may be analyzed 
by the methods of geometrical optics, provided the 
linear dimensions of the reflector are large compared 
