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Waverider Should you wish to contact the
society or require general information please contact ASTRA
using the following Email address: Should you encounter any problems
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Page please
email: When anyone talks about "designing a
waverider", what would be usually understood is that a shape
of shock surface, and the shape of the wing leading-edge
that intersects it, are chosen. That's easy enough of
itself. The hard part is working out what the shape of the
under-surface of the wing that produces the shock. The
process can be given an extra twist if, as for instance in
Gordon Dick's flexwing waverider, the surface shape has to
satisfy additional constraints - imposed in Gordon's design
by its surface flexibility. Usually it is also necessary in this
process of design to assume a Mach number at which the wing
is flying, and something about the state of the air. Thus it
is usual to assume that the air behaves as what is called 'a
perfect gas', though that may be far from true if the Mach
number is high (say, 10 or more). Some of the recent US
designs have been made more accurate by including the
(generally small) effects of the air viscosity on the
airflow, and that implies that not merely speed but also the
altitude have to be chosen. All these assumptions, whatever
they are, are lumped together by talking about a design
condition. It may be that some particular types
of high-speed aircraft would fly for most of the time at one
particular Mach number. For example, this might be roughly
true in an aerogravity assisted fly-by of a planet. In such
an event, the choice of design condition could be quite
straightforward. However, that is not usually the situation.
The winged reentry vehicle, for instance, is an aircraft
that must operate at all Mach numbers from nigh on 30 down
to less than one. How can one choose a 'design condition'
for such an aircraft? Do we have to concede that, because no
single unique condition seems to be specially relevant, the
waverider design itself can have no relevance in such a
context? I believe not, but nonetheless for it to seem to be
relevant, one's view of the design process needs somehow to
be broadened. It was in the context of winged
reentry that I first proposed a waverider design (almost 40
years ago to the day). For that design I chose a plane shock
wave (just because it was the simplest shape to choose). In
combination with a delta platform, that produced the
so-called caret wing, still commemorated in ASTRA's logo.
This form of waverider has two special properties. Firstly,
it produces a constant pressure over the under-side of the
wing. Secondly, the shock remains plane over a range of
different design conditions. Moreover, it still has such a
range, even if the air does not behave as a perfect gas, or
even if it flies through a gas that isn't remotely like air.
So far as I know, the only waveriders that possess this
property are those designed with a plane shock. Put another way, given a particular
caret wing, then over a range of Mach number (M), there is
always some particular angle of attack (which changes with
M) at which the undersurface shock is plane. Indeed over at
least the lower part of this range, there are two angles for
which it is plane. As has been confirmed by wind tunnel
tests, this means that the flow is not very sensitive to
change of either angle of attack or speed. The air pressure
on the underside remains nearly constant and the shock
almost plane in an extended range of off-design conditions.
This simplifies the task of predicting what happens in such
conditions. I went through the exercise of
designing a reentry craft last year, and with the intention
of broadening the design condition, I started with a
(slightly modified) caret wing. Aircraft designers these
days, I'm told, are inclined to curl the lip at the mention
of a waverider, because they dislike the idea of the
spanwise droop of the wing - the technical term is the wing
anhedral. There is a basis for this, although I suspect that
prejudice sometimes clouds their judgment. I'll content
myself here by noting that the higher the design Mach
number, the flatter the wing underside. This is because the
shock wave 'stands off' from the wing surface by a very
small angle. So the wing anhedral doesn't necessarily have
to be large. For such a particular stand-off angle (of 2 and
a half degrees), the caret wing in my design had a design
range from reentry conditions down to M=16. In other words,
the entire flight range in which aerodynamic heating is most
intense. With a larger stand-off angle of 4 degrees, the
range even came down to M=11. However, there was a snag (there
usually is). At the lower Mach numbers of this range, the
angle of attack in the design condition was to small. The
top surface of the wing that accommodates the payload would
become forward-facing. Instead I wanted the craft to descend
at a sufficiently high angle that the upper wing surface was
in 'shadow' - in the vacuum left in the lee of the bottom
wing surface. This has the great advantage of reducing the
heat transfer to the payload (or occupants) of the craft.
Such limits imposed by aerodynamic heating must always take
precedence. One might be able to design a splendid aircraft
on paper, but it will be of no use if it is likely to burn
up. Consequently, I had to concede that
at lower Mach numbers the wing should operate at higher
angles of attack than in the design condition. Instead of
remaining plane, the shock wave had to become convex. Yet
though it was off design, it still remained a waverider.
That is, the shock wave (though curved) remained attached to
the leading edge. In the outcome, for one good reason or
another, I decided it was best to operate at a higher than
in the design condition at all Mach numbers, implying a
(slightly) bulging but attached shock wave. Nonetheless, I
still retained the caret shape, but only because this made
the calculation of the off-design condition simpler.
Otherwise, somewhat to my surprise, it seemed to have become
irrelevant. Page
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