Line-Vortex Theory for Calculation of Supersonic Downwash

摘要

The perturbation field induced by a line vortex in a supersonic stream and the downwash behind a supersonic lifting surface are examined for the purpose of establishing approximate methods for determining the downwash behind supersonic wings. Lifting-line methods are presented for calculating supersonic downwash. An unbent lifting line (horseshoe-vortex system) is used to compute the downwash behind rectangular and triangular wings and the results are compared with the exact linearized solutions. The chordwise position of the lifting line giving the best average agreement with the exact solution is noted for each wing. A bent lifting line is used to approximate the triangular wing, and the results are in good agreement with the exact solution except for points within 1/2 chord of the wing trailing edge. The use of a bent lifting line seems promising for obtaining accurate estimates of the downwash behind swept wings.