On the application of subsonic linearised wing theory to second-order forces and moments Part 1 General principles and mathematical models Part 2 Edge forces and roll-rate derivatives

Abstract

The report comprises two contrasting and complementary approaches to the evaluation of the second-order aerodynamic side force and yawing moment on lifting wings when leading-edge and side-edge forces play an important ro1e. In Part I the usual lifting-surface model, in which the vorticity is placed on a planar surface, is shown to lead to inconsistent results ; consistent results are obtained when the vorticity is placed on the camber surface while the standard lifting-surface integral equation takes its usual form. In a further supplementary momentum analysis involving the Trefftz plane, the side force and yawing moment are derived from approximate expressions which avoid calculation of any edge forces. In Part II the analysis of linearised subsonic lifting-surface theory is extended to provide expressions for the leading-edge and side-edge forces. The side force and yawing moment under conditions of asymmetric spanwise loading are obtained as the sum of three contributions, from normal pressures, leading-edge suction and tip suction. These quantities are used to treat lifting wings in roll, and from a few numerical examples some general trends in the theoretical derivatives are observed. The related evidence from experiment and from semi-empirical methods is discussed, and one such method is transcribed for use in conjunction with the theoretical computations. Much of the non-linear experimental behaviour of the side force and yawing moment due to rate of roll can be accounted for by the removal of an increasing proportion of the theoretical edge forces as the lift increases.