# Spheroid RCS Computations

Spheroids with various axial ratios and material properties are modeled in FEKO to calculate the effect on RCS

Solving the scattered field from bodies of various shapes and material properties is a very common problem in electromagnetic theory. The radar cross section (RCS) of spheroids with various material properties and of different axial ratios are investigated in [1] and [2], respectively. Here perfectly electrical conducting (PEC) spheroids of different axial ratios are considered as well as spheres with different material properties.

Figure 1 shows two spheroid FEKO models. The oblate spheroid is formed by sweeping an ellipse around its short axis, and the prolate spheroid by sweeping an ellipse around its long axis. Using the definitions in Figure 1 of lengths a and c, the axial ratio is defined as c/a and oblate spheroids have an axial ratio smaller than 1 while prolate spheroids have an axial ratio larger than 1.

Figure 1: Spheroid FEKO models
(a) Oblate spheroid (b) Prolate spheroid

When computing the bistatic RCS an incident plane wave approaches the object along the z-axis. For all axial ratios the length a is kept at a constant value such that k0a = 3, where k0 is the wavenumber in free space. Figure 2 shows the RCS computed for PEC spheroids of different axial ratios.

Figure 2: RCS for PEC spheroids of different axial ratios
(a) Oblate spheroids (b) Prolate spheroids

With the axial ratio held constant at 1.0 (i.e. perfect spheres) the material properties are varied and the RCS shown in Figure 3. Notice that the RCS for each material is normalized to the area πa2 for direct comparison as the RCS at different frequencies are also compared in the case of fiberglass. As before a is chosen such that k0a = 3. The material properties used are shown in Table 1.

Figure 3: RCS for spheres with different material properties

Table 1: Material properties of spheroids
Material Relative permittivity Conductivity
Aluminium 1.0 3.538e7
Fiberglass (1MHz) 5.3 1.111e-9
Fiberglass (10MHz) 5.0 1.111e-9

### References

 [1] P.P. Lemos, A.N. magoulas, I.K. Hatzilau, "Electromagnetic Scattering from Real Scatterers: Impact of Material Electrical Characteristics to the Scattered Field", Hellenic Naval Academy, Greece. [2] P.P. Lemos, A.N. magoulas, I.K. Hatzilau, "Shape Dependence of the Scattered Electromagnetic Field of Spheroidal Real Scatterers", Hellenic Naval Academy, Greece.
Related content