The Minimum Drag of Thin Wings in Frictionless Flow

TLDR: The assumptions of thin airfoil theory are found to provide necessary conditions for the minimum drag of airfoils having a given total lift, a given maximum thickness, or a given volume as discussed by the authors.

Abstract: The assumptions of the thin airfoil theory are found to provide certain necessary conditions for the minimum drag of airfoils having a given total lift, a given maximum thickness, or a given volume. The conditions are applicable to steady or unsteady motions and to subsonic or supersonic speeds without restriction on the planform. The computation of drag and the statement of the conditions for minimum drag depend on the consideration of a combined flow field, which is obtained by superimposing the disturbance velocities in forward and reversed motions. If the planform of the airfoil and its total lift are given, it is found that, for minimum drag, the lift must be distributed in such a way that the downwash in the combined field is constant over the entire planform. If the planform is given and the thickness of the airfoil is required to contain a specified volume, then the thickness must be distributed over the planform in such a way that the pressure gradient of the combined field in the direction of flight is constant at all points of the wing.