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Much of the basic understanding of aerodynamics is a result of research conducted in the early part of the twentieth century. A prominent example is the understanding of the cause of the drag due to lift, or induced drag. In this explanation the drag due to lift is connected with the trailing vortices that can be seen behind a wing. In this paper an explanation is derived for the existence of all wing drag, including drag due to lift. The drag formulation arises from the relationship of surface pressure to entropy generated predominantly by vorticity in the flow field. This new formulation allows the total drag to be split into the contributions made by different flow features. It also leads to suggestions on how to reduce drag

In the future, it will be possible to manufacture very small, robust machines, which may be attached to the surface of a wing allowing the classic boundary condition of “no-slip” to be altered at will. It is also possible that the heat transfer through the wing surface can be controlled. This paper reports an investigation into the possible benefits to aerodynamics that will occur if such machines become available. It is found that imposing an isothermal wing surface can increase the lift drag ratio of wing at transonic cruise and allowing slip at the surface can have the same effect. Both these effects are additive. It is found that control of heat transfer on a wing at hypersonic wing can act as a control device, comparable to that due a moderate flap deflection.

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.