The Application of Subsonic Theoretical Aerodynamics to Active Controls

Abstract : Analytical and numerical studies are made of aerodynamic forces for wing and control-surface motion with general time-dependence in linearized subsonic flow. Alternative formulations are discussed, with particular attention to one in the time domain where quasi-steady displacement and rate terms are combined with a residual history term. An accurate calculation procedure is devised, and results are illustrated for a high-aspect-ratio wing at Mach number 0.8 with trailing-edge, leading-edge and all-moving tip controls. Emphasis is placed on asymptotic behaviour at small and large times. Individual control characteristics are compared over a wide range of control rate. The usefulness of the quasi-steady approximation is established for hinge moments and is analysed for lift, where the rate and history terms become important together. The rapid lift response to the leading-edge control and the sluggish lift response to the trailing-edge control are explained. These forces in the time domain are confirmed by Fourier transform calculations in the frequency domain, which show the extent to which the range of frequency can be truncated. The control-surface motion to produce a known time-dependent force is determined. It is remarkable how rapidly the controls can neutralize the growth of lift as the wing enters a step gust.