A Relationship Between Wave Drag and Induced Drag

A formulation for the induced drag of a wing in subsonic or transonic flow is derived from entropy considerations. This approach shows how wave drag and induced drag are related. The new formulation is cast in a form similar to that used in the classic induced drag derivation thus allowing a theoretical comparison of the two approaches. If there are no shock waves in the flow the two formulations agree theoretically only in the case of an elliptic wing loading, although calculations indicate that the quantitative difference may be relatively small. If shock waves are present they can increase or decrease the induced drag leading to the idea of a reduction in the sum of induced and wave drag by a judicious tailoring of the flow over the wing.