In article ,
Martin Gregorie wrote:

Sure, Cl is dependent entirely on AoA, but is not a linear
relationship throughout the range:

- It is linear at small angles.
- When the AoA is high enough for the upper surface flow
to start to separate the Cl tends to a constant value with
increasing AoA.
- If the AoA continues to increase even further you reach
a point at which the Cl starts to decline, reaching zero
at an AoA of 90 degrees.

I'm with you on all that.


However, my understanding is that a stall occurs when the lift
generated by the wing drops below the load the wing is required to
support.

No, a stall is when increasing AoA decreases lift. There might well
still be more lift that the weight of the aircraft, especially at high
speed. The only reasons to avoid such stalled flight a

- high drag and thus inefficient
- the aircraft is unstable in roll, making it difficult or
impossible to control.

Presumably you've seen aircraft such as the F/A-18 demonstrate a slow
pass at very high and stalled angle of attack? They are getting some of
their support from the downward component of the engine thrust, of
course, but with an AoA of, say, around 30 degrees it would need a
thrust:weight ratio of around 2 in order for thrust to be enough to
support the entire aircraft weight. It would also require *huge* drag
in order to avoid accelerating at such a thrust level. The F/A-18 has
nowhere near that amount of thrust, so the majority of the support is
clearly still coming from the stalled wings. In that situation the
aircraft is unstable, and would probably be improssible to fly like that
without the computer reacting very quickly to unwanted rolls.

So the F/A-18 can be happily flown in steady-state stalled straight and
level flight primarily because of the computer control and also because
the extra drag is less than the engine thrust available.


For a given wing the generated lift is proportional to the Cl and to
the square of the speed, so at a fixed AoA you can reduce the speed
until the lift is no longer sufficient for flight, at which point the
wing stalls.

Well, ... no :-)

If you maintain a fixed AoA, and the speed is such that the lift is less
than the weight of the aircraft then the aircraft will start to follow a
downwards parabolic path (not as sharply downwards as in a zero-G
pushover, but similar).

What happens next depends on what else (if anything) you are holding
constant.

Suppose, for the sake of concreteness, that you are initially flying
straight and level at 60 knots and you then fix the AoA such that the
wings are producing only half the lift required to support the glider.

Normally a glider will accelerate, increasing the lift (and drag, but
not by much). The extra lift will cause the path to become less sharply
curved downward and things will come to equilibrium (or oscillate
around) the point where the combined lift and drag are equal and
opposite to gravity. For a typical glider polar curve this will happen
at an airspeed of around 1/sqrt(0.5) times 60 knots, or 85 knots, plus
or minus a little due to drag.

So all you've acheived is to change the trimmed speed from 60 to 85
knots.

Or, look at it the other way around. Maybe you were flying straight and
level at 85 knots, and then you somehow instantly decrease the airspeed
to 60 knots (maybe a gust up the tail). The lift is no longer
sufficient to maintain level flight. But the glider doesn't stall. It
just drops the nose and accelerates until it has returned to the trimmed
speed of 85 knots.

In no way are the wings ever stalled.


If you stipulate constant speed as well as constant AoA (presumably via
some large and adjustable drag, magical or otherwise) then the flight
path will become steeper until the combined lift and drag vectors are
again exactly equal to and opposite the gravity vector. This will
result in a much steeper flight path, but still stable.

Let's suppose again that you are at 60 knots and reduce the AoA to
produce only half the lift required for flight and then continue to
maintain exactly 60 knots somehow. Alternatively, suppose you're flying
trimmed for level flight at 85 knots and then apply airbrakes to reduce
and maintain 60 knots, while keeping the same trim (AoA).

What happens?

The AoA/speed are insufficient for flight at 60 knots and so the nose
drops. If you draw up the force vectors then you will find that the
glider will stablize in a 60 degree descent at your desired constant 60
knots. Lift (from the wings) is still 0.5 of the weight just as it was
initially (but it's in a funny direction, tilted 60 degrees forward from
vertical). Drag (from the airbrakes) is 0.866 of the weight, tilted 30
degrees from vertical. The horizontal components of lift and drag are
equal and opposite and cancel out. The vertical force to oppose gravity
comes 25% from the wings and 75% from the airbrakes.

In no way are the wings ever stalled.


No matter what you do, if you start with the wings not stalled then
there is nothing you can do that will stall them while all the time
keeping the AoA constant.

If you see the nose drop and don't like it and pull back on the stick to
try to prevent it then that is an entirely different matter -- you're
increasing the AoA which certainly *can* stall the wings.

-- Bruce