<DOC>
<DOCNO>
917
</DOCNO>
<TITLE>
a method of calculating the short period longitudinal
stability derivatives of a wing in linearised unsteady
compressible flow .
</TITLE>
<AUTHOR>
mangler,k.w.
</AUTHOR>
<BIBLIO>
rae r. aero.2468.
</BIBLIO>
<TEXT>
  a method is developed for the
calculation of the pressure distribution
and the aerodynamic forces and
moments on a wing performing harmonic
pitching and heaving oscillations .
the calculation is based on the
assumption of inviscid potential flow
without shock waves and is restricted
to small incidence, so that the
linearized theory is valid .
  in contrast to other work in the
field the theory applies to all
mach numbers .  it is restricted to small
values of the reduced frequency
and should be valid for the usual range
of short periods occurring at
present in flight .  the formal solution
yields two integral equations for
the parts of the load, which are in phase
and go out of phase with the
oscillation,. these are of the same form
as the corresponding equation
in steady flow .
  the way is thus opened for solutions
over the whole mach number
range at small frequencies, if the
corresponding steady solutions can
be found .  the calculation is in fact
easiest for m = 1 and has been
done here for delta-wings to supplement
a previous supersonic calculation,
made on different frequency assumptions,
which broke down near m = 1 .
it appears from the two sets of results
that the short period oscillation
will be unstable near m = 1, if the apex
angle of the delta wing is
greater than about 60 .  this confirms a
now generally recognised trend .
  such results near m = 1 must of
course be invalidated to an
unknown extent by thickness viscosity and
shock waves at their maximum
effect .  nevertheless it is unlikely that
these factors will remove
the critical nature of the transonic damping
as calculated by this method .
with all its obvious limitations this method,
when extended to other
planforms, should provide a useful tool in
studying the effect of
geometrical parameters on the stability of
an aircraft at transonic
speeds .
</TEXT>
</DOC>
