Radar System Engineering

66 PROPERTIES OF RADAR TARGET,S [SEC.3.+
incident radar beam we thus obtain the cross section
47rA2
“=7” (7)
For general angles of incidence the cross section is a function of the
angle of incidence and it varies very rapidly when, as is assumed here,
the wavelength is small compared with the linear dimensions of the plate.
In a diagram of return power vs. angle of observation these variations
show up as the “Iobes.” The strong main lobe is normal to the plate and
the side lobes decrease rapidly with increasing angle. For small angles
O,but excluding the main lobe, the average cross section a (averaged over
several lobes) is given approximately by
4rrA’
@=— (8)
(27r19) ‘“
I’his result is independent of the size of the target, subject of course to
the limitation that the linear dimensions of the target are large compared
to the. wavelength.
For a cylinder of radius R and length 1, both large compared to X, we
obtain
R12
u=27r — A
(9)
for incidence perpendicular to the axis. For the same cylinder, if the
beam forms an angle O with the normal to the axis the average cross
section (averaged over several lobes) is approximated by
valid for small angles o excluding the main lobe.
For rur~ed surfaces, the formulas of geometrical optics can ordinarily
be used. 1 For a segment of spherical surface of radius R we find
(lo)
independently of the size of the segment and of the wavelength h. This
formula is valid as long as the diameter d of the segment (perpendicular
to the incident beam) is larger than v’2kR, and provided that the edge of
the segment deviates sufficiently ( > k/4) from a plane perpendicular to
the incident beam, since otherwise edge effects may become important.
If the surface is not spherical the formula is still valid if we take for R the
geometric mean of the two principal radii of curvature. The result is
the same whether the concave or convex side is turned toward the radar
transmitter.
I For more detaileddiscussionsee Vol. 13 of this series, (’hap. fi,