# RCS of a Sphere Confusion

1. Jun 16, 2015

### Xyius

Hello,

I am having an issue understanding something about the RCS of a sphere.

The radar cross section of a sphere in the back-scattered, mono-static direction is simply equal to the spheres cross sectional area, for wavelengths much less than the circumference.

http://www.remcom.com/examples/conducting-sphere-bistatic-scattering.html

They are looking at a sphere with a diameter of 0.254 meters, meaning it has a circumference of 0.7980 meters. They are illuminating it with a plane wave of frequency 10 GHz, meaning it has a wavelength of 0.03 meters. This makes the ratio of circumference to wavelength equal to roughly 27. According to the radar cross section handbook, this is well within the regime of having an RCS equal to its cross sectional area, which would be equal to $\pi R^2=\pi (0.254/2)^2=0.0507$.

In the link, Figure 3 shows that in the mono-static direction (the main lobe), the RCS has a value of roughly 15 dBsm. This corresponds to about 32 meters squared. What gives? How can this be equal to 32 meters squared? I must be misunderstanding something. :\

2. Jun 16, 2015

### Xyius

A ha! I got it! The number I was looking at corresponded to the opposite end of the sphere, if I look at the extreme values, and convert to linear, I get the cross sectional area.