Indicial response functions in weak ground effect

This analytical study concerns unsteady aerodynamic loads acting on a wing section in the presence of a flat ground. Assuming that the amplitude of the transversal motion of the wing is sufficiently small, and the distance between the wing and the ground exceeds half a chord, closed-form analytical expressions are obtained for the lift and the pitching moment. They involve two (and only two) standard indicial response functions that convolve with the records of the wing's motion and the gust through which the wing has passed in the course of its motion. Both standard functions are obtained as asymptotic series in the ratio of the wing's quarter chord to its average distance from the ground, and approximated by elementary functions. Out of ground effect, they recover the comparable functions of Wagner and Küssner; in ground effect they exhibit shorter settling times, inferring shorter “memory” of the aerodynamic forces. Also obtained are the added mass and moment of inertia of the wing, and the location of its aerodynamic center. Ground effect increases the added mass and moves the aerodynamic center of the wing backwards.