The different paper doesn't agree on the actual circular trihedral corner reflector RCS's formula.
Is it 15.6*pi*(radius)4 /(wavelength)2 or 15.6*(radius)4 /(wavelength)2 .
In another term, is there the pi number in the formula or not?
15.50314 r^4/wavelength^2 is the RCS of one quadrant seen at 45 deg to 2 faces and parallel with the third face. The RCS will increase as the projected area increases (as the square of the projected area), but I don't expect the projected area will increase as much as root pi which is what is needed for the first formula. It only increases by root 2 when rotated 45 degrees from normal to one face.
I expect the second formula is correct (but approximate).
One quadrant (ignoring all the others because they will not contribute when 3 faces of one quadrant are visible) has area pi r^2/4, so rcs normal to one face is 4 pi (pi r^2/4)^2/wavelength^2. Rotate 45 deg and all reflections still hit another face, and width of reflector increases by root 2, so RCS of quadrant is 8 pi (pi r^2/4)^2/wavelength^2 which is 15.50314 r^4/wavelength^2.
Rotation so the third face can be seen will not result in the whole visible area having the required reflections, so the projected area will not increase by even as much as root 2. It probably drops and then rises to something like 15.6 r^4/wavelength^2. Try the geometry!
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