A Survey of Unsteady Hypersonic Flow Problems

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will no longer apply and a simple expansion from conditions downstream of the
nose would not exist. In this case, it will be necessary to apply Kennett's
small-perturbation analysis to a suitable bluff body flow solution to find the
nose conditions, and apply Halt's small perturbation analysis to a characteristics
solution of the steady flow downstream of the nose. Such analysis will apply,
of course, only for small amplitude motions of the body.
The results of small-disturbance theory will still apply for low aspect
ratio wings with sharp sections for which M oos A > 1, and for pointed slender
bodies for which Id6 < 1 at moderate incidence, and consequently, unsteady flows
around such bodies can be found from calculation of an equivalent series of
steady flows. But the only way of calculating the equivalent steady flows would
seem to be the characteristxs method - though some sunplification of the proce s
t.0
may be brought about by applying the linearized characteristics method of Ferri .
Newtonian impact theory provides a simple method for estimating the
aerodynamic forces on wings and bodies at incidenoes above those far shook
detachment, but the predictions made are necessarily unreliable. A satisfactory
method of dealing with these flows, for small amplitude motions of the bodies,
seems likely to involve the application of a small-perturbation analysis to a
satisfactory steady flow solution. Similar conclusions apply to the problems
of bluff bodies, and real vehicle shapes: In both cases analyses have been
made using Newtonian impact theory but these, obviously, have only limited value
and a small-perturbation analysis is required - if an adequate steady solution
exists.
In those oases where it has been suggested that a small-perturbation
analysis applied to a steady solution is likely to be the only way in which a
satisfactory unsteady flow analysis can be made, it has been made clear that the
method can only be applied for small-amplitude disturbances. There seems to be
no alternative to a quasi-steady analysis of the flow around a body is undergotig
large amplitude displacements. In practical oases this will certainly be
adequate for most oasewsince such motions are unlikely to involve large frequew
parameters.
APPENDIX III/