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The Quarterly Journal of Mechanics and Applied Mathematics 1949 2(2):136-152; doi:10.1093/qjmam/2.2.136
© 1949 by Oxford University Press
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SUPERSONIC FLOW PAST THIN WINGS I. GENERAL THEORY

G. N. WARD

( Department of Mathematics, The University Manchester )

The linearized potential problem of supersonic flow is solved for nearly plane wings of arbitrary shape of planform and section. The velocity field is divided into its symmetrical and antisymmetrical parts, which are treated separately. The results for the symmetrical part have been given before, by A. E. Puckett, and are only considered briefly. The results for the antisymmetrical part are determined by extending an integral equation method used previously by J. C. Evvard in a more restricted problem. The Kutta-Joukowski condition is applied to the velocity at the trailing edge in order to make the solution determinate. Expressions are given for the potential on the wing, from which the velocities can be obtained. For the smaller aspect ratios, the analysis becomes complicated and only an indication of how the results can be obtained is given. The velocity is singular at the subsonic leading edges and the forces on the wing have to be determined by a limiting process which is illustrated by obtaining expressions for the lift and drag forces. All the results are completely general and no special cases are considered.


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