Remarks on Low-Aspect-Ratio Configurations in Supersonic Flow

Abstract

Simple low-aspect-ratio configurations are examined to oblin a qualitative understanding of wing-fuselage interference nd effect of a missile. Slender-body theory gives :>r a wing-body combination a value of lift which does not deend upon afterbody length. This value of lift is compared with hat given by the more exact linearized three-dimensional theory. sTonlinear and viscous effects are not considered. A theorem is proved concerning the lift of certain wings (or ving-fuselage combinations) with a long afterbody of span qual to the maximum span of the wing. I t states that at any upersonic Mach Number the value of lift according to linear heory tends to that predicted by slender-body theory as the ength of the afterbody tends to infinity. The effect of a finite ifterbody can also be determined by linear theory, and a comDarison can be made with slender-body theory for certain planar systems. These results may be applied qualitatively to wing-body combinations. They indicate that , for no afterbody, slender-body theory overestimates the lift of the combination and that , for a short afterbody, it may equal or even underestimate the lift. For an infinitely long afterbody, it agrees exactly with linear theory if the afterbody span equals the maximum wing span; if the afterbody is narrower, it overestimates the lift.