Munk の定理と亜音速揚力面理論について

概要

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It is known that the induced drag associated with a given lift distribution of a wing of any planform in incompressible flow can be calculated by using the Prandtl lifting-line theory. This face is based on Munk's stagger theorem. From the standpoint of the lifting-surface theory, on the other hand, the induced drag is equal to the rearward component of the resultant normal force minus the leading-edge thrust. In this paper, the expression for the induced drag in terms of lifting-line theory is derived directly from that due to the lifting-surface theory for subsonic compressible flow. The two expressions for the induced drag are thus shown to be equivalent. The derivation of the lifting-line expression from the lifting-surface one brings us also a proof of Munk's three theorems from the lifting-surface point of view. Further, the isoperimetric problem in the calculus of variations for finding the lift distribution which makes the induced drag minimum is formulated from the standpoint of the lifting-surface theory.