Supersonic airfoils

A supersonic airfoil is a cross-section geometry designed to generate lift efficiently at supersonic speeds. The need for such a design arises when an aircraft is required to operate consistently in the supersonic flight regime.

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. The sharp edges prevent the formation of a detached bow shock in front of the airfoil as it moves through the air. This shape is in contrast to subsonic airfoils, which often have rounded leading edges to reduce flow separation over a wide range of angle of attack. A rounded edge would behave as a blunt body in supersonic flight and thus would form a bow shock, which greatly increases wave drag. The airfoils' thickness, camber, and angle of attack are varied to achieve a design that will cause a slight deviation in the direction of the surrounding airflow.

Drag

At supersonic conditions, aircraft drag is originated due to:

Skin-friction drag due to shearing.

The wave drag due to the thickness (or volume) or zero-lift wave drag

Drag due to lift

Therefore, the Drag coefficient on a supersonic airfoil is described by the following expression:

CD= CD,friction+ CD,thickness+ CD,lift

Experimental data allow us to reduce this expression to:

CD= CD,O + KCL2

Where CDO is the sum of C(D,friction) and C D,thickness, and k for supersonic flow is a function of the Mach number. The skin-friction component is derived from the presence of a viscous boundary layer which is infinitely close to the surface of the aircraft body.