<DOC>
<DOCNO>
1373
</DOCNO>
<TITLE>
nose drag in free-molecule flow and its minimization .
</TITLE>
<AUTHOR>
tan,h.s.
</AUTHOR>
<BIBLIO>
j.ae.scs. 1959, 360.
</BIBLIO>
<TEXT>
  the superaerodynamic nose drag of a body in a free-molecule
flow involves two parameters ..  the speed ratio s between
ordered and random molecular motions (modified mach number),
and the temperature ratio between the solid surface
and undisturbed gas .  simplifications of the drag formula are
obtained at hypersonic as well as low-subsonic extremes .  to
minimize the drag on a nose of specified length and base radius,
the ordinary method of calculus of variation was found inadequate
.  a generalized approach has, accordingly, been developed,
and the specification of end conditions is discussed at length .
  results of the present investigation indicate that in all cases
an optimum nose requires a flat tip .  the optimum nose curve
for the hypersonic extreme does not depend on the temperature
ratio, but that for the low-subsonic extreme varies in the following
manner ..  for a hot body the curve is convex,. for a cold body,
concave .  an optimum solution exists in a restricted range of
specification only .  with prescribed tip and base radii the admissible
nose length is bounded below for the cases of hypersonic
and low-subsonic hot body and bounded above for the case of
low-subsonic cold body .  a vanishing tip radius leads to an infinitely
long nose in the former and a vanishing nose in the latter
case .
  optimum nose curves for several temperature ratios at the lowsubsonic
extreme, as well as the one for hypersonic extreme, are
presented .  it is observed that at the low-subsonic extreme, with,
the hot-body solution asymptotically approaches
the hypersonic solution--i.e., a slender conventional warhead
with a flat tip,. whereas with, the cold-body solution
asymptotically approaches the minimal-surface solution--i.e.,
tip radius, a flat disc .
</TEXT>
</DOC>
