Not an average software engineer--beautiful page (imperfect spelling)! Why does detection scale as the 4th root of the RCS? Nice problem for the radiation theory part of a graduate electrodynamics class.
Not an average software engineer--beautiful page (imperfect spelling)! Why does detection scale as the 4th root of the RCS? Nice problem for the radiation theory part of a graduate electrodynamics class.
It shouldn't, under the assumptions they are opening up with. Inverse square law twice is appropriate for an approximation that the reflection is entirely diffuse because you assume that the diffuse reflection is uniform in all directions away from the illuminated surface. A single inverse square law is appropriate (with both distances added to each other before squaring) under the approximation that the reflection is specular.
> Why does detection scale as the 4th root of the RCS?
Because the power returned to the antenna scales as the -4th power of the distance to the target, and detection depends on that power being greater than some threshold. If the fourth power (rather than the square) is surprising, think of the reflection as re-transmitting the power that arrived at the target. The incident power on the target goes as RCS/r^2, and the power that makes it back to the original antenna gets another factor of 1/r^2, so the return scales as RCS/r^4.
It's a 4th power because you're doing the inverse square law twice, once for the outbound pulse and once for the reflection.