<DOC>
<DOCNO>
561
</DOCNO>
<TITLE>
a geometric problem related to the optimum distribution
of lift on a planar wing in supersonic flow .
</TITLE>
<AUTHOR>
graham,e.w.
</AUTHOR>
<BIBLIO>
j. ae. scs. 1958, 771.
</BIBLIO>
<TEXT>
  the problem studied may be regarded as a problem of geometry
.  its simplest form (loosely stated) is then as follows ..  a
mountain rises up from the x-y plane .  determine the exact
shape of the mountain knowing only the cross-sectional area of
every possible cut which can be made through the mountain with
a vertical plane .  in a more complicated version of the problem,
the given information might be restricted to the cross-sectional
area of every cut which can be made by a vertical plane inclined
less than 45 to the y-axis .
  this latter case has direct applications to certain minimum
drag problems in supersonic flow .  the shape of the mountain
corresponds to the (unknown) shape of the optimum lift distribution
on a planar wing .  the cross-sectional area of a cut is
the integrated value of the lift along a straight line crossing the
wing plan form .  for a restricted range of line inclinations, these
optimum integrated lift values can sometimes be determined
directly .  here it is assumed that they are given .
  the problem in its simplest form was originally solved by
radon, who found solutions for a large class of such problems .
the derivation presented here may perhaps be more readily
understood .
</TEXT>
</DOC>
