An expression is derived which relates the pressure on a wing in a supersonic free stream to the pressure on a thin wing with the same surface shape. The expression is used to find the pressure distribution for caret wings and flat delta wings with attached flow at their leading edges. The compression surface pressure distributions found are in good agreement with existing experimental and theoretical results, except when large pressure changes occur in the pressure behind the attached shock wave. Some expansion surface results are also obtained for wings with an isentropic expansion at the leading edge. The effects of flow and geometry changes on the pressure distribution are investigated. It is found that a small improvement in the lift/drag ratio of a caret wing can be obtained by halving the anhedral required for the plane shock wave condition.
The inviscid supersonic flow in corners with swept leading edges and attached shock waves is investigated. Supersonic linear theory is applied to the flow behind the leading edge shock wave to reduce the non-linear errors normally associated with linear theory. These non-linear errors in the flow are further reduced by equating an expression based on the exact conditions near the leading edge and that behind the shock wave to its linear theory equivalent. The resulting analytical expression describes the flow between the leading edge shock wave and the body. A number of examples of pressure distributions on the wing surface are given which demonstate the surprising accuracy of the method even at high Mach numbers. Further examples of its application are given in:-
Theoretical Pressure Distributions on Four Simple Wing Shapes for a Range of Supersonic Flow Conditions.
by J. Pike. Aeronautical Research Council, Current Paper No. 1178, HMSO, London, March 1971.
The equations for the exact inviscid conditions near swept leading edges used in the paper are given in:-
Attached flow conditions on sharp supersonic leading edges.
by J. Pike, R.A.E. Technical report No. 72078, Aug. 1972.
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Last amended: July 2014.