Calculation of the supersonic pressure distribution on a single-curved tapered wing in regions not influenced by the root or tip

Author / Creator

Vincenti, Walter G., author

Available as

Online

Summary

The shock-expansion method for the calculation of the pressure distribution on cylindrical wings in supersonic flow is here extended to tapered wings made up of single-curved (id est, developable) ...

The shock-expansion method for the calculation of the pressure distribution on cylindrical wings in supersonic flow is here extended to tapered wings made up of single-curved (id est, developable) surfaces. The method applies in regions of the wing where (a) the component of velocity normal to the surface rulings is supersonic and (b) the flow is not influenced by the presence of the root or tip. The calculation is carried out by regarding the single-curved surface as the limit of an inscribed polyhedron whose edges coincide with rulings of the actual surface. The changes of flow across an element consisting of an edge and subsequent face of the polyhedron are then found from elementary considerations of infinitesimal plane waves and simple geometry. The result, in the limit of the curved surface, is a pair of simultaneous, nonlinear ordinary differential equations for the components of Mach number normal aud tangential to the surface rulings. These equations are readily integated by standard numerical methods in any given case. Calculations are carried through in the present report for a biconvex triangular wing of aspect ratio 4 at two values of the free-stream Mach number.

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