A Combination of the Quasi-Cylinder and Slender Body Theories

The Quasi-Cylinder and slender body theories for the supersonic flow past bodies of revolution have been much used in recent years because, for reasonably simple body profiles, these theories permit a simple and rapid calculation of the first-order pressure distributions and aerodynamic forces. It is assumed in both theories that the body profile slope is small; in the quasi-cylinder theory it is also assumed that the body radius is nearly constant, whereas in the slender body theory it is assumed that the thickness ratio of the body (maximum diameter/length) is small.In the present note these two theories are combined completely. From a strictly mathematical point of view nothing is gained by this combination, and, furthermore,application of the combined theory to a particular case is in general a little more laborious than application of either of the original theories.