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I am trying to design a hyper sonic aircraft in line with X-15 for my Aircraft design project. This requires me to figure out the preferred airfoil shape for the wing.

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    $\begingroup$ If there was one optimal shape for all situations, this would be easy to answer, as it's written it's impossible to answer. $\endgroup$
    – Ron Beyer
    Sep 17 '16 at 18:09
  • $\begingroup$ I'm not sure this question has to be on hold, Wikipedia article provides a seemingly valid answer to this broad question: "Supersonic airfoils generally have a thin section formed of either angled planes or opposed arcs (called "double wedge airfoils" and "biconvex airfoils" respectively), with very sharp leading and trailing edges". $\endgroup$
    – mins
    Sep 18 '16 at 12:42
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At hypersonic speed the local drag grows with the inclination of the local surface against the free stream. Thus, the best shape is a thin wedge. Drag will scale with the cube of the thickness ratio of the wedge.

Depending on the maximum tolerable heat load, you should choose a pointed leading edge (highest heat load, smallest drag) or a blunt leading edge, where the separated shock will reduce local heat loads, albeit at the price of much higher drag.

Ideally, past its maximum thickness the airfoil tapers down towards a thin trailing edge, and again a wedge shape will cause the least amount of drag.

In the picture below (source) you can barely see the tip airfoil of the X-15:

North American X-15

It used a simple, blunt wedge at the vertical tails because the vacuum at the rear face provided additional directional stability. However, for lowest drag, a double wedge of the smallest thickness possible should be used.

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