Simple Mathematical Models of Elastic and Flexible Wings in the Extreme Ground Effect

Abstract

The elasticity and flexibility of the lifting surface can play a particular role in ground-effect aerodynamics due to the expected increase of dimensions of wing-in-ground-effect vehicles, use of light materials and fabric, etc. Usually, to account for elastic properties and/or flexibility of the wing, we have to consider simultaneously the equations of aerodynamics and elasticity. In a more profound analysis, the formulations should also cover the equations of the dynamics of the vehicle. As a relationship, linking the deformations of a lifting surface with aerodynamic loading, we normally use equations of unsteady bending of an elastic plate accounting for forces, acting in its camber plane; see Bisplinghoff et al. [151].