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The Quarterly Journal of Mechanics and Applied Mathematics 1954 7(2):203-221; doi:10.1093/qjmam/7.2.203
© 1954 by Oxford University Press
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A SECOND-ORDER THEORY FOR THREE-DIMENSIONAL WINGS IN SUPERSONIC FLOW

M. H. CLARKSON

( Department of Mathematics, The University Manchester )

A method is developed for determining the pressure distribution to second order for a certain class of wings which require the use of three independent variables to describe the flow.

The flow investigated is that of an inviscid perfect gas which is everywhere supersonic.

The method is used to obtain the pressure distribution to second order for a trapezoidal wing which has the ends raked outside the Mach cones from the tips and which is rolling at constant angular velocity. The rolling moment coefficient is also found. The method also yields the position of the shock surface, to the first order in the disterbance velocity, in the case of compressive flow and the boundary of the region of expansion in the case of expansive flow.

The mathematical complexities encountered in applying the method to more complicated wings are exhibited by a discussion of a rectangular wing.


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