Lift-Deficiency Functions of Elliptical Wings in Incompressible Potential Flow: Jones' Theory Revisited

Jones' work on the lift-deficiency functions of an elliptical flat wing in incompressible flow has been reviewed by generalizing the expression of the wing downwash for any aspect ratio and employing better approximations for both the latter and the lift-deficiency functions of a flat airfoil in incompressible potential flow. Better approximations for the wing's lift-deficiency functions was obtained as series of exponential terms using constrained nonlinear optimization; these may effectively be used as semi-analytical reduced-order models. Simpler parametric forms of the lift deficiency functions have also been derived and excellent agreement found with Jones' original results. It is thus shown that Jones formulated a sound theory for calculating the unsteady loads of elliptical flat wings but employed crude approximations for its elements.