<DOC>
<DOCNO>
1108
</DOCNO>
<TITLE>
a study of second-order supersonic flow theory .
</TITLE>
<AUTHOR>
vandyke,m.d.
</AUTHOR>
<BIBLIO>
naca r.1071, 1952.
</BIBLIO>
<TEXT>
  an attempt is made to develop a second approximation to the
solution of problems of supersonic flow which can be solved by
existing first-order theory .  the method of attack adopted is an
iteration process using the linearized solution as the first step .
  for plane flow it is found that a particular integral of the
iteration equation can be written down at once in terms of the
first-order solution .  the second-order problem is thereby
reduced to an equivalent first-order problem and can be readily
solved .  at the surface of an isolated body, the solution reduces
to the well-known result of busemann .  the plane case is
considered in some detail insofar as it gives insight into the
nature of the iteration process .
  again, for axially symmetric flow the problem is reduced to a
first-order problem by the discovery of a particular integral .
for smooth bodies, the second-order solution can then be calculated
by the method of von karman and moore .  bodies
with corners are also treated by a slight modification of the
method .  the second-order solution for cones represents a
considerable improvement over the linearized result .  secondorder
theory also agrees well with several solutions for other
bodies of revolution calculated by the numerical method of
characteristics .
  for full three-dimensional flow, only a partial particular
integral has been found .  as an example of a more general
problem, the solution is derived for an inclined cone .  the
possibility of treating other inclined bodies of revolution and
three-dimensional wings is discussed briefly .
</TEXT>
</DOC>
