Rotary aerodynamic derivatives in the asymptotic theory of a high-aspect-ratio wing

The linear problem of inviscid incompressible flow around a high-aspect-ratio wing at an angle of attack and in the presence of steady pitching and rolling rotation is considered. The main integral equation of the problem is reduced to a sequence of one-dimensional integral equations without use of the matched asymptotic expansions method. The first few terms of the series for the circulation distribution over the wing surface are calculated. For an elliptic high-aspect-ratio wing the corresponding aerodynamic forces are calculated. The derivatives of the aerodynamic coefficients of the wing with respect to the angle of attack and the angular velocities are determined. The asymptotic expressions obtained are compared with the results of numerical calculations of the corresponding derivatives using the discrete vortex method.