A Survey of Unsteady Hypersonic Flow Problems

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where W is the weight of the vehicle; S is the lifting area; R is the
radius of the flight path from the earth's centre. Thus when the speed is
high flight is possible at lower values of dynamic pressure than when the speed
is lcw.
The actual limits of the flight corridor depend on the design of the
vehicle, but Fig. 3 has been prepared to indicate the range of flight conditions
within which hypersonic vehicles may normally be expected to operate. The
minimum value of the parameter W/XI has been taken to be 15 lb/fta: only
vehicles involving light weight lifting structures are likely to give values .
of less than this; and the maximum value of dynamic pressure has been taken as
1000 lb/ft'. The lines in Fig. 3 representing the altitudes and speeds for
these constant parameters define a flight corridor in terms of minimum lift
and maximum dynamic pressure. Two bands are shown representing the speeds and
altitudes at which the-stagnation temperature will be 2000'R and 4CC9R. A
limit on stagnation temperature of 2OOO'R will permit flight in only a restricted
region; a limit of 4OCO"R permits a flight corridor extending to orbital speed.
Superimposed on the flight corridors defined by d.ynamiC pressure,
stagnation temperatures and lift in Fig. 3 are shown lines of constant Reynolds
number and constant values of the viscous interaction parameters, x. The
values of Reynolds number per foot that are likely to be met suggest that, at
the higher speeds and altitudes, laminar bcundarg layers will extend over much
of the vehicle surface, and flow separations will be more easily provoked than
at lower speeds, where much of the boundary layer is turbulent. The parameter
x indioates the importance cf interaotions between the boundary layer and the
external flow and is defined by the equation:
where o, is the constant in the tiscosity relation
CI T
-=ck
-T
m
. . . (1.2)
and is usually close to unity. The value of o,,, has been taken as unity in
Fig. 3. Values af x of O(O-5) and greater suggest that these interactions
will have significant effects on pressure distributions for sharp-nosed bodies
(Appendix II, Seotion 2.2).
Fig. 4 shows some possible trajectories for super-circular ballistic
re-entry (re-entn velocity is greater than circular orbital velocity), super
circular lifting re-entry, lifting exit, and expandable structure lifting
re-entry (W/SCL < 15): these are superimposed on the flight corridors defined
in Fig. 3. The ballistic trajectory shcws very high values of dynamic pressure
and stagnation temperature illustrating the severity of the conditions for this
form of re-entq which was mentioned before. The super circular lifting re-entzy
trajectory shows a condition of high dynamic pressure and stagnation temperature
in the early stages of re-entry, when the Mach number is very high, but the
Bfting exit trajectory shows a maximum dynamic pressure below the hypersonio
speed range.
APFEWDIxII/