<DOC>
<DOCNO>
467
</DOCNO>
<TITLE>
thin airfoil theory based on approximate solution of the transonic flow
equation .
</TITLE>
<AUTHOR>
spreiter, j. r. and alksne, a. y.
</AUTHOR>
<BIBLIO>
naca tn 3970, may, 1957 .
</BIBLIO>
<TEXT>
the present paper describes a method for the approximate solution of the
 nonlinear equations of transonic small disturbance theory . although
the solutions are nonlinear, the analysis is sufficiently simple that
results are obtained in closed analytic form for a large and significant
 class of nonlifting airfoils . application to two-dimensional flows
with free-stream mach number near 1 leads, for instance, to general expressions
for the determination of the pressure distribution on an airfoil
of specified geometry and for the shape of an airfoil having a
prescribed pressure distribution and gives, furthermore, the correct
variation of pressure with mach number at mach number 1 . for flows that
 are subsonic everywhere, the method yields a pressure-correction formula
that is more accurate than the prandtl-glauert rule and compares
favorably with existing higher approximations . for flows that are
supersonic everywhere, the method yields the equivalent, in transonic
approximation, of simple wave theory . results obtained by application
of these general expressions are shown to correspond closely to existing
 solutions and to experimental data for a wide variety of airfoils .
</TEXT>
</DOC>
