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National Advisory Committee for Aeronautics, Report - On the Application of Transonic Similarity Rules to Wings of Finite Span

The transonic aerodynamic characteristics of wings of finite
span are discussed from the point of view of a unified small
disturbance theory for subsonic, transonic, and supersonic
flows about thin wings. Critical mmination is made of the
merits of the various statements of the equations for transonic
flow that have been proposed in the recent literature. It is
found that one of the less widely used of these possesses con-
siderable advantages, not only from the point of view of a prior
theoretical considerations but also of actual comparison of
theoretical and experimental results. The similarity rules and
known solutions of transonic-flow theory are reviewed, and
the asymptotic behavior of the lift, drag, and pitching-moment
characteristics of wings of large and small aspect ratio is
discussed. It is shown that certain methods of data presentation
are superior for the efl'ective display of these characteristics.

The small perturbation potential theory of transonic flow
proposed apparently independently by Oswatitsch and
Wieghardt, Busemann and Guderley, von Karman (refs. 1
through 6), and others is now supplying a fund of information
regarding transonic flow about aerodynamic shapes. Solu—
tions have been given for two-dimensional flow around
airfoils at both subsonic and supersonic speeds in papers
by Guderley and Yoshihara, V‘mcenti and Wagoner", Cole,
Trilling, Oswatitsch, Gullstrand (refs. 7 through 16), and
others.

In the application of these results to specific examples,
two items of theoretical interest have been noted
(see, in particular, refs. 8, 17, and 18). (a) The theoretical
results appear to be applicable at Mach numbers far removed
from 1 even though, in most cases, the results have been
obtained from equations valid only in the immediate neigh-
borhood of sonic speed. (b) In the application of theoretical
results to specific examples at Mach numbers other than 1,
it has been noted that certain ambiguities exist in the
theoretical determination of aerodynamic quantities. It is
one of the purposes of this report to investigate these two
points.