Summary.
The two-dimensional surface giving minimum pressure drag for given lift coefficient in supersonic flow is considered. The method adopted is a small perturbation of a plane surface; the pressure is expressed as a power series in the perturbed slope and third order terms are neglected. The shape of the optimum surface is found to be a double wedge surface, with a single discontinuity in the surface slope. The compression surface is concave at the discontinuity for Mach numbers below about 1.4 and above 3, and between these it can be slightly convex. The performance (for a ratio of specific heats of 1.4) is compared with that of the plane wedge, and the improvement is found to be very small, except at hypersonic speeds when improvements of greater than 1% are obtained. Similar results hold for waveriders (three dimensional wing shapes) based on two-dimensional flow fields.

Comment.
This report shows that the lift to drag ratio of any waverider compression surface which deflects the flow directly downwards cannot be significantly greater than the lift to drag ratio of a two-dimensional wedge. That is, if significant performance improvement is to be achieved, it must involve some form of interference effect, where the pressures introduced by the surface inclination at some point favourably influence the pressure at other points on the surface.

Availability.
Aeronautical Research Council Reports are available as R&M 3543
or email J A C K @ J A C K P I K E . C O . U K

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Last amended: Dec 2013.