3.2 Radar Cross Section of Radar Targets
27
From which, using (3.13) formula, we will receive (3.15) expression. Thus, RCS of
smooth convex body of doubled curvature does not rely upon wavelength. Calculation
results by (3.15) formula represent a fact with an error nor more than 20% at condition
of ρ 1 ρ 2 > 2λ.
As an example, find RCS of a ball with ρ radius. Surface equation can be represented as D(x, y) = ρ +
ρ 2 −
x 2 + y 2
. Here, the point of stationary phase
also will be a point x 0 = y 0 = 0, and the second differential coefficients of D will
be equal D
x 2 (0, 0) = D
y 2 (0, 0) =
1
ρ
, D
xy (0, 0) = 0.
Substitution of these equations in (3.12) formula will determine the ball RCS:
A = πρ
2
.
(3.17)
which equals to just an area of its cross section.
Clarify a physical sense of stationary phase points.
As a condition D
x = D
y = 0 is executed for them, then this means that in
these points, a tangent plane to body surface will be parallel to datum plane MM,
i.e., perpendicular to direction of wave propagation. Consequently, these segments
of researched body give the main contribution into a field, scattered into direction to
receiving antenna.
It is possible to easily calculate within an examined RCS method of flat target
located perpendicularly to direction of wave propagation. In this case, D = const
and the whole target surface used to be a “glare.” For this reason, it is more reasonable
to directly use (3.4) formula from where another formula arises:
A =
4π S
2
λ 2 .
(3.18)
A (3.18) formula testifies on possibility of some another approach to target RCS
calculation. At examining of a target location, i.e., perpendicular to Poynting vectorFlux density of electromagnetic energy, on its surface besides narrow area of a size
about λ near a border, the in-phase currents of equal amplitude are excited. This
means that a target can be examined as antenna with in-phase uniform amplitude
field distribution (the abovementioned narrow area near a border does not play a
serious role as it is admitted that targets are extremely larger than λ), directional gain
G of which can be calculated according to the known formula:
G =
4π S
λ 2 .
(3.19)
Field power, scattered by perfectly conducting target, will be equal to power of
wave incident on it (with regard to the fact that current irregularity at target edges
can be neglected), which obviously will be written as P = rad S; accordingly,
the power flow density of antenna scattered wave with regard to target directional
properties will be as follows:
27
From which, using (3.13) formula, we will receive (3.15) expression. Thus, RCS of
smooth convex body of doubled curvature does not rely upon wavelength. Calculation
results by (3.15) formula represent a fact with an error nor more than 20% at condition
of ρ 1 ρ 2 > 2λ.
As an example, find RCS of a ball with ρ radius. Surface equation can be represented as D(x, y) = ρ +
ρ 2 −
x 2 + y 2
. Here, the point of stationary phase
also will be a point x 0 = y 0 = 0, and the second differential coefficients of D will
be equal D
x 2 (0, 0) = D
y 2 (0, 0) =
1
ρ
, D
xy (0, 0) = 0.
Substitution of these equations in (3.12) formula will determine the ball RCS:
A = πρ
2
.
(3.17)
which equals to just an area of its cross section.
Clarify a physical sense of stationary phase points.
As a condition D
x = D
y = 0 is executed for them, then this means that in
these points, a tangent plane to body surface will be parallel to datum plane MM,
i.e., perpendicular to direction of wave propagation. Consequently, these segments
of researched body give the main contribution into a field, scattered into direction to
receiving antenna.
It is possible to easily calculate within an examined RCS method of flat target
located perpendicularly to direction of wave propagation. In this case, D = const
and the whole target surface used to be a “glare.” For this reason, it is more reasonable
to directly use (3.4) formula from where another formula arises:
A =
4π S
2
λ 2 .
(3.18)
A (3.18) formula testifies on possibility of some another approach to target RCS
calculation. At examining of a target location, i.e., perpendicular to Poynting vectorFlux density of electromagnetic energy, on its surface besides narrow area of a size
about λ near a border, the in-phase currents of equal amplitude are excited. This
means that a target can be examined as antenna with in-phase uniform amplitude
field distribution (the abovementioned narrow area near a border does not play a
serious role as it is admitted that targets are extremely larger than λ), directional gain
G of which can be calculated according to the known formula:
G =
4π S
λ 2 .
(3.19)
Field power, scattered by perfectly conducting target, will be equal to power of
wave incident on it (with regard to the fact that current irregularity at target edges
can be neglected), which obviously will be written as P = rad S; accordingly,
the power flow density of antenna scattered wave with regard to target directional
properties will be as follows: