Progress In Electromagnetics Research Symposium Proceedings, Xi’an, China, March 22–26, 2010
619
Radar Cross Section of a Cavity in a Finite Elliptic Cylinder
N. Altın1 and E. Yazgan2
1
2
Turkish Aerospace Industries, Inc., Ankara, Turkey
Electrical & Electronics Engineering Department, Hacettepe University, Turkey
Abstract— In this paper, the part of the cockpit of the air vehicle in a far field with a plane wave
of warning, scattering fields from cockpit part is assumed to be radiate in free space. Fuselage of
the air vehicle is modeled finite elliptical cylinder and a large cavity is mounted in the sidewall
of a finite elliptical cylinder. The part of the cockpit of the air vehicle is modeled close to the
real model. A Radar Cross Section (RCS) analysis of cockpit part is calculated using together
Shooting and Bouncing Ray (SBR) and Geometrical Optics (GO) methods and RCS analysis of
elliptical cylinder is calculated Uniform Geometrical Theory of Diffraction (UTD) and Physical
Optics (PO) method. Shooting and Bouncing Ray (SBR) using for analyses does not limit the
form of model. By using of proposed method, outputs for cockpit part and fuselage RKA analyses
were provided.
1. INTRODUCTION
In computational electromagnetic, the scattering of EM waves of very large objects from wavelength
to examine the geometrical and physical optics-based techniques are known for a long time. However, in practice, widespread use of geometrical optics-based approach is by means of the shooting
and bouncing rays (SBR) technique. SBR method is developed recently by the authors [7–9].
Two very different approaches have been proposed thus far for obtaining the RCS due to the
interior irradiation of open cavities in the high frequency regime. First of these approaches is the
waveguide modal method. Typically, the cavity under consideration is assumed to be elongated in
a preferred direction and have a uniform cross section along that direction. The field inside the
cavity is then expressed in terms of the known waveguide modes. The unknown modal coefficients
are found via application of the reciprocity relationship and Kirchoff’s approximation [2, 3].
Second of these approaches is the shooting and bouncing ray method. Scattering fields of large
and complex objects are calculated with ray tracing technique which is one of the high frequency
techniques. In this technique involves tracing a dense grid of geometrical optics rays originating
from the incident wave into the cavity through its opening. After multiple bounces from the interior
walls of the cavity, the rays eventually exit the cavity through the opening. The scattered field
associated with each exit ray is then determined by a physical optics scheme. The total scattered
field results from summing the scattered field due to individual rays. This approach has the feature
that a real physical problem can be modeled closely, taking into account the noncircular opening
of the cavity, the wall coating and the longitudinal bending or twisting of the cavity. It is so simple
in concept that there is virtually no restriction on the shape or material loading of the cavity [4].
In the literature, rectangular cavity was used to represent a structure such as a cockpit in an air
vehicle and has been flush mounted in the sidewall of a finite circular cylinder [2, 3]. In this study,
fuselage of the air vehicle is modeled finite elliptical cylinder and a large cavity is mounted in the
sidewall of a finite elliptical cylinder. The part of the cockpit of the air vehicle is modeled close
to the real model. Shooting and bouncing ray method was used for the cavity, and finite elliptical
cylinder effects were accounted for via the Uniform Geometrical Theory of Diffraction (UTD) and
Physical Optics (PO). To resolve discontinuity in the RCS analysis of elliptical cylinder PO method
is used. Many numerical methods have been developed for the purpose of solving complex structure
of an object from the effects of electromagnetic wave scattering problem.
2. DIFFRACTION MECHANISM AND MODEL
Fuselage of the air vehicle is modeled finite elliptical cylinder and a large cavity is mounted in the
sidewall of a finite elliptical cylinder as shown in Fig. 1.
2.1.
Analysis and Calculation
For RCS, there are four scattering sources as shown Fig. 1. They are mirror reflection field of
ellipse, diffraction field in the ellipse, cavity, creeping wave interactions of the cavity and ellipse.
This is shown in Figs. 2 and 3. The cavity contribution is found by using ray tracing method. In
PIERS Proceedings, Xi’an, China, March 22–26, 2010
620
Figure 1: Finite elliptical cylinder and cockpit illuminated by a plane wave.
Figure 2: Intuitive ray path tracing inside the cockpit.
the SBR method, a large number of parallel rays from the direction of the incident plane wave are
“shot” into the cavity. Each ray that enters the cavity bounces off the walls and eventually exits
the structure via the aperture opening. The exiting rays contribute to the backscattering field and
then calculate the RCS. Below the scattering mechanism of each source and computing method
will be analyzed.
2.2.
Incidence Field of Ellipse
At P (r, φ) position in the Fig. 1, a unit amplitude plane wave incident at angle φi is described as
follows.
E i (r, φ) = A · ejkr cos(φ−φi )
(1)
where A is the amplitude and value is one.
2.3.
Mirror Reflection Field of Ellipse
As shown in Fig. 1, the plane wave is incident on the elipse from a direction ϕ, the incident ray at
the point of reflection Qr is reflected. Reflected field formula is as follows.
Er (s, φi ) = Ei (Qr )
r
p
e−jks
ao (γr )/2Rs,h (ξp , Xp ) √ r
s
(2)
where Ei (Qr ) is incident field to reflection point on the ellipse surface, Rs,h (ξp , Xp ) is the uniform
theory of diffraction reflection coefficient [1, 8, 13], a0 (γr ) is the radius of curvature at any point γ
on the elliptical surface [1,8,13]. s and h are respectively soft and hard boundary condition.
2.4. Diffraction Field on the Ellipse
The surface diffracted field at any observation point is given by
d
³
´
¡ ¢
ejks1
E1d sd1 , φi = E i Q01 Ts,h (ξd1 , Xd1 , t1 ) q
sd1
(3)
where Ei (Q01 ) is an incident field at attachment point Q01 , Ts,h (ξd , Xd , t) is the uniform theory of
diffraction surface diffraction coefficient [1, 8, 13].
2.5. Cavity RCS
The cavity contribution is found by using ray tracing method. In the SBR method, a large number
of parallel rays from the direction of the incident plane wave are “shot” into the cavity. Each
ray that enters the cavity bounces off the walls and eventually exits the structure via the aperture
opening. Exit rays involve calculating the ray tube divergence factors and the reflection coefficients.
The exiting rays contribute to the backscattering field and then calculate the RCS [4].
By summing over each ray tube, expressions for Aθ and Aφ due to each exit ray tube are obtained
as follows.
¸
·
·
¸
jk0 X
Ex (xi , yi ) cos φi + Ey (x¢ i , yi ) sin φi
Aθ
¡
· ejk0 (sx xi +sy yi ) (∆xi ∆yi ) Ii
(4)
=
Aφ
−Ex sin φi + Ey cos φi cos θi
2π
i all rays
Progress In Electromagnetics Research Symposium Proceedings, Xi’an, China, March 22–26, 2010
where
1
Ii =
(∆xi ∆yi )
Z
621
Z
dxdyejk0 [(u−sx )x+(v−sy )y]
(5)
ith exit ray tube
And (∆xi ∆yi ) = area of the exit ray tube, Ex (xi , yi ) and Ey (xi , yi ) are respectively x and y
components of the outgoing field on the exit ray tube [4].
2.6.
Total RCS
Fuselage of the air vehicle is modeled finite elliptical cylinder and a large cavity is mounted in the
sidewall of a finite elliptical cylinder as shown in Fig. 1. Total radar cross section of fuselage and
cockpit is given as below.
RCS of elliptical surface is obtained as follows.
"¯
¯ #
¯E r (s, φi ) + E d (s, φi )¯2
RCSellipticalsurf ace = lim 2π s
(6)
s→∞
|E i (s, φi )|2
RCS of cockpit is given as below.
RCSφφ = 4π |Aφ |2
(7)
2
(8)
RCSθθ = 4π |Aθ |
Field arises from cockpit is calculated only when incidence angle φ is at the range of 0◦ –55◦ by
formula (7 or 8)
To eliminate discontinuity in the RCS analysis of elliptical surface, physical optic (PO) method
is used [12]. When PO method added to UTD, provide an improvement to discontinuity near the
θ = 90◦ direction.
Consequently, RCS analysis of Fig. 1, combination of UTD, PO and SBR method are used. In
the following, RCS value is examined for hard and soft polarization.
3. NUMERICAL RESULT
The UTD/SBR methods were used to compute monostatic RCS in θ = 0◦ plane. The cockpit
depth is d = 1.2983 m and length is L = 3.4457 m. Operating frequency is 5 GHz. The elliptical
cylinder is a = 4.5 m and b = 1.55 m as shown in Fig. 1. RCS value is examined for hard and soft
polarization.
In Fig. 3, It is shown RCS of finite elliptical cylinder for soft and hard polarization at 5 GHz.
RCS of finite elliptical cylinder is calculated UTD method but it was observed discontinuity in the
φ = 90◦ . To remove the discontinuity, Physical Optics method is used. The RCS pattern with an
∆φ = 0.8◦ aspect increment is sketched in Fig. 3.
As shown in Fig. 4, RCS of cockpit is calculated SBR method for soft and hard polarization at
5 GHz. The result is shown in Fig. 4 between 0◦ ≤ φ ≤55◦ .
The RCS of air vehicle fuselage and cockpit is sketched in Fig. 5 for hard and soft polarization
at 5 GHz.
φ
Figure 3: Only RCS of finite elliptical cylinder at 5 GHz.
PIERS Proceedings, Xi’an, China, March 22–26, 2010
622
θθ
φφ
φ
Figure 4: Only RCS of cockpit at 5 GHz.
4.
φ
Figure 5: RCS for cockpit in a finite elliptical cylinder at 5 GHz.
CONCLUSIONS
The RCS of a cockpit of the air vehicle was calculated by using SBR method, and the RCS of the
finite elliptical cylinder was calculated by using UTD/PO method. In this paper, the calculated
result is at 5 GHz for hard and soft polarization. It was found that exterior scattering and cockpit
effects dominate the RCS.
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