Copyright © A. Filippone (1999-2003). All Rights Reserved.

High Speed Aerodynamics

Classical Theories


Here are some important statements regarding slender bodies, to which actual aircraft and missiles are associated at transonic and supersonic speeds.

Equivalent Body of Revolution

For wing-body combinations one of the most important conclusion of a linearized transonic flow is the possibility of reducing the system to an equivalent body of revolution. Away from a slender body, the flow is axial-symmetric, and equivalent to the flow around a body of revolution. On the body itself the flow is equal to that past the equivalent body of revolution plus a two-dimensional incompressible cross-flow (Oswatisch- Keune, 1955).

The Transonic Area Rule

The pressure drag of a generic slender body differs from that of the equivalent body of revolution, from which the drag is minimal. This difference is identically zero if the slender body has an axi-symmetric or cylindrical rear end. Both conditions can in fact be satisfied by missiles and fast aircraft.

The equivalent body of revolution theory implies that the drag is also at a minimum when the slender body has a smooth cross-area distribution (Whitcomb, 1956). This idea was tested in the 1950s at NASA with various configurations having smooth and indented bodies.

Figure 1: Crosswise area distribution of transonic aircraft

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Copyright © A. Filippone (1999-2003). All Rights Reserved.