"David CL Francis" wrote in message
...
[...] So under some conditions if you just raise the nose a little you can
find a new steady state where speed is slightly reduced but with the same
thrust you can climb at the same AoA..

Your theory sounds wonderful, but I doubt it holds water in practice.

Thrust does not reduce the required lift by much, especially not in the
light planes we tend to fly. Steady-state pitch angles in climbs tend to be
modest, meaning a tiny fraction of the thrust vector is the downward
component. Just 17% of the total thrust, for a 10 degree pitch angle.
Given how little thrust a light plane has in the first place (only a
relatively small fraction of the total weight of the airplane in the first
place, less than 10% in at least some cases, perhaps most cases), even
taking 20% (or even 34%) of that and applying it to lift just isn't going to
help that much.

Even assuming an airplane with a thrust-to-weight ratio of 1.0 (a rare
occurrance, but they do exist...some F-16s, for example), I'm not sure your
theory holds up very well. You might think that you could simply increase
thrust as you slow the airplane in order to allow a smaller AOA to suffice
to provide the remaining necessary lift. But there's a problem with that
idea.

If the AOA is kept small, then the increased thrust will prevent the
airplane from decellerating. To have a vertical component high enough to
support the airplane will require a horizontal component so high that the
airplane won't slow. If the AOA is allowed to increase, then what the
increased thrust is actually allowing is for the wing to stall without the
airplane being pulled downward by gravity (the wing WILL stall at the
appropriate AOA, regardless of airspeed). It's not demonstrating anything
about some "new steady state".

The above thought experiment should also illustrate another problem with
your theory: it ignores the change in the portion of lift actually
contributing to counteracting gravity that occurs due to pitch changes. See
below for more commentary on that.

Of course, to me the biggest problem intuitively with your theory is that I
am sure that aerodynamics involves only continuous functions. Given that,
if you assume more than one steady state, you are claiming that there are
multiple local minima/maxima between which are apparently "lower efficiency"
areas. And of course, if there's more than one, I see no reason to believe
that there are only two. This would then imply that the flight envelope has
numerous of these local minima/maxima points.

Given that in more than 100 years of study, this concept has never shown up
as a noted element of the relationship between speed, drag, and lift, I'm
inclined to believe that it's just not true (just as the idea of "cruising
on the step" is not true).

I admit that I have not brought out the equations and proved my point
irrefutably. Someone like Julian Scarfe or Todd Pattist would probably do a
better job discussing this, since they seem to be more "math oriented" (that
is, they don't mind crunching some equations now and then ). But I still
feel reasonably confident that there's no secondary "new steady state" one
can achieve by increasing AOA and taking advantage of thrust.

The extra work comes ONLY from a net surplus of power.

I agree with that. However that net surplus can come from either more
engine power or reduced drag. Because even in a modest climb the engine
thrust vector plus the lift vector combine to match the weight.

I assume by "the engine thrust vector" you really mean "the vertical
component of the engine thrust vector". Assuming that, I agree with your
statement, but I don't find it informative. The engine thrust vector has a
non-zero vertical component even during level cruise flight, and yes it does
contribute to counteracting gravity, reducing the lift required.

But when you ask the question about HOW MUCH it does this, the answer is
"not enough to change the fundamentals". Not for the airplanes we fly, and
I think probably not for any airplane.

Put another way if you are flying below the maximum lift drag ratio and
you increase the AoA to the optimum whilst keeping the same power the
aircraft should climb. This is self evident if you are flying level at
high speed and at a climbing power setting. Bring the nose up increasing
the AoA and your aircraft will definitely climb. Agreed?

I never said anything to the contrary. If you are at an angle of attack
lower than the best L/D AOA (and thus at an airspeed higher than the L/Dmax
airspeed), increasing pitch angle without a change in power will result in a
climb, yes.

But that has nothing to do with what happens at an airpseed near stall,
which occurs below the L/Dmax airspeed, and well above the best L/D AOA.

I think that is another way of saying what I have just said?

Well, since I seem to disagree with what you said, I sure hope not.

I cannot remember if we started off with an assumption that the aircraft
was only just above stall speed? If so then you are correct of course.

Yes, this part of the discussion was entirely about the regime of flight
near the stalling speed and AOA. Reducing drag by pitching up while above
L/Dmax airspeed is uninteresting, since that's a direct consequence of
slowing to an airspeed closer to L/Dmax airspeed.

Even in a steady glide the required lift is less than that needed in level
flight! That is easier to see because the drag vector helps the lift match
the gravity vector.

This seems like a good point at which to mention something else you've left
out and which I alluded to earlier...

Lift is always generated perpendicular to the wing's chord. Some people
like to call just the vertical component of this force "lift", but the
amount of force acting through the wing is the force perpendicular to the
chord.

However you label things, you cannot avoid the fact that when you change the
angle of the lift vector, the portion of the force created by the wing used
to counteract gravity is also changed. In particular, in the low-airspeed,
power-on example, even as thrust is helping support the airplane, you are
using your lift less efficiently, which means that the wing needs to
generate more total lift just to provide the necessary vertical component.

This is similar to the required increase in lift while in a turn, but due to
redirecting the lift vector in a different way.

Since the lift vector points slightly aft in level flight, even at high
airspeeds when the angle of attack is low, it's easier to see how this
negates at least some of whatever contribution thrust might make as the
angle of attack is increased. However, in gliding flight, the vector is
pointed forward, helping counteract the contribution drag makes to lift.

I wrote "at least some" up there, but it should be apparent from the
disparate magnitudes of the lift and thrust vectors that you get a much more
significant change in lift than you do in thrust.

The bottom line he even though thrust does contribute at least a little
to counteracting gravity, it does not do so in a way significant enough to
change the fact that, as you slow the airplane from any airspeed at or below
L/Dmax airspeed, you experience increased drag.

Pete