Line-vortex theory for calculation of supersonic downwash

Mirels, Harold Haefeli, Rudolph C

The perturbation field induced by a line vortex in a supersonic stream and the downwash behind a supersonic lifting surface are examined to establish approximate methods for determining the downwash behind supersonic wings. Lifting-lines methods are presented for calculating supersonic downwash. A bent lifting-line method is proposed for computing the downwash field behind swept wings. When applied to triangular wings with subsonic leading edges, this method gives results that, in general, are in good agreement with the exact linearized solution. An unbent lifting-line method (horseshoe-vortex system) is proposed for unswept wings. This method is applied to determine downwash behind rectangular wings with aspect ratios of 2 and 4. Excellent agreement with exact linearized theory is obtained for both aspect ratios by placing the lifting line at the 1/2-chord point. The use of lifting-lines therefore appears promising for obtaining estimates of the downwash behind supersonic wings.

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