Classical Theories
Summary
Here are some important statements regarding slender bodies, to which actual aircraft
and missiles are associated at transonic and supersonic speeds.
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 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
Equivalent Body of Revolution
The Transonic Area Rule
