The sonic flow about some symmetric half-bodies

Abstract

The approximate Tricomi equation relevant to sonic speed of two-dimensional small-distrubance flow is solved by separation of variables, where these are certain stipulated functions of the Cartesian velocity perturbations. The symmetric flow patterns obtained from this solution are shown to correspond to those about half-bodies, whose ordinates vary as xⁿ where 0·4 &\les n,<1, and x is the distance along the plane of symmetry. The surface pressures on such bodies are deduced.

In particular, the body whose ordinates vary as $x^{2|5}$ has a sonic surface velocity, except at the nose, where an edge-force which causes a drag force is shown to exist. On the assumption that a free-stream breakaway (at sonic velocity) occurs at the shoulder of a body, this solution thereby yields the flow about an aerofoil of the same shape having a flat base. This bluff-nosed section has only a little more than half the drag of a wedge on the same chord and base.