The aerodynamic derivatives with respect to a rate of yaw for a delta wing with dihedral and at incidence at supersonic speeds

Abstract

Expressions are developed on the basis of an unsteady flow analysis for the yawing derivatives for a delta wing with small dihedral at small incidence flying at supersonic speeds. The assumptions of the linearised theory of flow are made throughout; only first-order terms in the rate of turn are considered. The terms dependent on the dihedral alone are continuous and decrease numerically with rising Mach number. The remaining terms are discontinuous at a Mach number at which a leading edge becomes supersonic; in particular the rolling-moment component due to incidence changes sign; the other derivatives may do likewise in certain circumstances. The approximate theory developed in the paper breaks down as a leading edge nears the Mach wave from the vertex of the wing. The yawing amplitude for which the results quoted present reasonable approximations decreases rapidly as this condition is approached; in particular the contributions of the leading-edge suction become undefined. Earlier results based on strip theory are greater numerically than those derived in the present paper by significant amounts that increase with Mach number and aspect ratio. The two theories agree for vanishingly small aspect ratios.