<DOC>
<DOCNO>
404
</DOCNO>
<TITLE>
two dimensional transonic flow past airfoils .
</TITLE>
<AUTHOR>
kuo,y.a.
</AUTHOR>
<BIBLIO>
naca tn.2356.
</BIBLIO>
<TEXT>
  this report concerns the problem of constructing solutions for
transonic flows over symmetric airfoils .  the aspect of the problem
emphasized is, of necessity, not how to form a solution for compressible
flow but how to simplify the initial phase of the problem, namely, the
mapping of the incompressible flow .  in the case of the symmetric
joukowski airfoil without circulation, the mapping is relatively simple,
but the coefficients in the power series are difficult to evaluate .  as
a result, the problem requires simplification .  instead of the exact
incompressible flow past the airfoil, an approximate flow is used, which
is derived from a combination of source and sink .  this flow differs
only slightly from the exact one when the thickness is small .  by the
same method, the flow with circulation is also considered .
  after the incompressible-flow functions are approximated in this
fashion, the numerical calculation of the corresponding compressible
flow, by the hodograph theory, does not present any
essential difficulty .
</TEXT>
</DOC>
