Superspheroids: a new family of radome shapes

We use the arc described by the two-dimensional superquadric equation (taking its exponent ν to be any positive real number) in the first quadrant only and revolve it about its major axis to obtain a body of revolution family of geometric shapes called superspheroids. For certain values of length and radius and assuming that 1<ν<2, we have determined new shapes that are appropriate for high speed missile radomes. We have found that the superspheroid with optimized exponent value ν=1.381 can almost exactly reproduce the traditional Von Karman radome geometry. Incidence angle maps and geometric properties have been determined for this superspheroidal family. We have used a ray tracing analysis to obtain boresight error induced by this family of shapes as a function of gimbal angle. The superspheroids are mathematically simple, can approximate most of the traditional radome geometries quite well, and are exceptionally easy to either program or use analytically