SUPERSPHEROIDS - A NEW FAMILY OF RANDOM SHAPES

In the following we use the arc described by the two-dimensional super quadric equation (taking its exponent upsilon 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 supe rspheroids. For certain values of length and radius and assuming that 1 < upsilon < 2, we have determined new shapes that are appropriate fo r high speed missile radomes. We have found that the superspheroid wit h optimized exponent value upsilon = 1.381 can almost exactly reproduc e the traditional Von Karman radome geometry. Incidence angle maps and geometric properties have been determined for this superspheroidal fa mily. We have used a ray tracing analysis to obtain boresight error in duced by this family of shapes as a function of gimbal angle. The supe rspheroids are mathematically simple, can approximate most of the trad itional radome geometries quite well, and are exceptionally easy to ei ther program or use analytically.