A Level 1 AOA clarification

On Sun, 26 Dec 2004 at 21:58:05 in message
, Peter Duniho
wrote:
Thrust does contribute, yes. But the primary reason for requiring
additional power is that, while the wing is capable of generating the
necessary thrust at a lower airspeed, higher angle of attack (all the way up
to the stalling AOA of course), the higher angle of attack results in higher
drag, requiring higher thrust.

I think Peter that an aircraft will climb if trimmed to the same angle
of attack that it was using in level flight. It does this as long as
the lift is slightly less and the speed drops to produce _less_ drag
and lift, leaving more engine power and thrust to climb.

When climbing extra work must be done against gravity. That extra work
can come from increasing power or from reducing speed and therefore
drag.

Nitpicking point: wings do not create thrust! :-) You meant lift of
course.
--
David CL Francis

Greg Esres wrote:

The relative wind will be "coming from above", since that is the
direction in which the aircraft is traveling.

The relative wind doesn't ever "come from above" while the aircraft
has a positive angle of attack..by definition. ;-)

The relative wind always comes from the direction in which the aircraft is
actually traveling. If the aircraft is climbing, the relative wind comes from
above the horizon; ie. it is not horizontal.

Nor will the
aircraft stall with the relative wind "essentially horizontal."

It certainly will if the aircraft is neither climbing nor descending, is not
banked, and the pitch angle exceeds the stall angle of attack.

Sounds like you think there is a zero angle of attack in that
situation?

No, I don't.

George Patterson
The desire for safety stands against every great and noble enterprise.

CV wrote:

"From above"
is similarly meaningless, unless we specify whether we mean it
in relation to the wing/aircraft or the horizon.

Yes. I meant above the horizon and failed to say so.

George Patterson
The desire for safety stands against every great and noble enterprise.

"David CL Francis" wrote in message
...
I think Peter that an aircraft will climb if trimmed to the same angle of
attack that it was using in level flight.

Well, ignoring for a moment that I never meant to suggest anything about
what happens if you simply increase power without changing anything else
when just above stall speed... (my comments were simply about what
additional power *allows*...not what it *causes*)

You can't make that generalization. Changes in power affect elevator
authority (affecting trim), as well as necessary rudder input (changing
drag). It is entirely possible that when just above stall speed, an
increase in power will result in an increase in angle of attack, an increase
in drag, or both.

What you can say is that if the pilot maintains the same angle of attack,
but increases power, then the airplane will climb (I don't believe that
added drag from rudder will ever be MORE than the added thrust, but I could
be wrong about that). But that's not really what I was talking about.

It does this as long as the lift is slightly less and the speed drops to
produce _less_ drag and lift, leaving more engine power and thrust to
climb.

At an airspeed just above stall, a reduction in speed results in MORE drag.
There is a reduction in parasitic drag, but there is a greater increase in
induced drag, with a net increase in total drag (and that's ignoring drag
caused by the rudder and any other control surfaces that require a change in
position).

When climbing extra work must be done against gravity. That extra work can
come from increasing power or from reducing speed and therefore drag.

The extra work comes ONLY from a net surplus of power. A reduction in speed
is only guaranteed to produce a net increase in power available if the new
airspeed is higher than Vbg. It can sometimes also produce a net increase,
if the old airspeed was sufficiently higher than Vbg, and the new airspeed
is close enough to Vbg, even if less than, but you need to know more about
the old and new airspeeds in that case to say for sure what happens. More
importantly, a reduction in speed is guaranteed to produce a net decrease of
power available if the OLD airspeed is lower than Vbg (as it is when just
above stall speed).

Nitpicking point: wings do not create thrust! :-) You meant lift of
course.

Yes, of course. Thank you.

Pete

A reduction in speed is only guaranteed to produce a net increase
in power available if the new airspeed is higher than Vbg.

I think you mean higher than the airspeed for minimum power, which is
lower than Vbg.

Even that's not really true, since the power available curve isn't
flat. Vy is maybe closer to the truth.

"Greg Esres" wrote in message
...
A reduction in speed is only guaranteed to produce a net increase
in power available if the new airspeed is higher than Vbg.

I think you mean higher than the airspeed for minimum power, which is
lower than Vbg.

Yes...sorry, I use Vbg as a nice "landmark", since it's very close to the
actual speed in question. I guess I should be more explicit about that,
especially in this context.

Yes...sorry, I use Vbg as a nice "landmark", since it's very close
to the actual speed in question. I guess I should be more explicit
about that, especially in this context.


I thought so. You couldn't be right about so much and get that one
wrong. ;-)

On Tue, 28 Dec 2004 at 16:55:05 in message
, Peter Duniho
wrote:
It does this as long as the lift is slightly less and the speed drops to
produce _less_ drag and lift, leaving more engine power and thrust to
climb.

At an airspeed just above stall, a reduction in speed results in MORE drag.
There is a reduction in parasitic drag, but there is a greater increase in
induced drag, with a net increase in total drag (and that's ignoring drag
caused by the rudder and any other control surfaces that require a change in
position).

HI Peter. How easy it is to get slightly confused on Usenet! What I was
trying to say is that if you maintain the same AoA then the lift drag
ratio remains the same, but because the lift required when climbing is
less than when flying level you can climb at a reduced speed but with
less drag. 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..

There is a maximum lift drag ration at a modest angle of attack. Above
_and_ below that angle of attack that ratio worsens.

When climbing extra work must be done against gravity. That extra work can
come from increasing power or from reducing speed and therefore drag.

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. 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?

A reduction in speed
is only guaranteed to produce a net increase in power available if the new
airspeed is higher than Vbg. It can sometimes also produce a net increase,
if the old airspeed was sufficiently higher than Vbg, and the new airspeed
is close enough to Vbg, even if less than, but you need to know more about
the old and new airspeeds in that case to say for sure what happens. More
importantly, a reduction in speed is guaranteed to produce a net decrease of
power available if the OLD airspeed is lower than Vbg (as it is when just
above stall speed).

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

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.

--
David CL Francis

"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

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)

Lift in a 10 degree climb should be reduced about 1.5%.

I'm not sure your theory holds up very well.

"His" theory is mentioned in a number of aerodynamics books.

Although I agree that a small increase in AOA would not contribute
enough vertical component of lift to overcome the initial increase in
induced drag, there are ways to get into this regime of flight. If
you had enough unused AOA left to generate a load factor, you could
change the flight path then return the AOA to its original value. The
aircraft may be able to stay on a steeper flight path due to the
reduced parasite drag and reduced effective weight. Don't forget that
thrust will increase slightly with a lower airspeed.

To have a vertical component high enough to support the airplane
will require a horizontal component so high that the airplane won't
slow.

Not really clear on what you mean by that. The only component of
thrust that accelerates the airplane is that parallel to the flight
path. If the angle of climb remains the same, then increasing thrust
will obviously accelerate the airplane. However, as thrust increases,
the angle of climb increases up to the point that the component of
aircraft weight along the flight path is equal to the increase in
thrust.


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.

All of the above is very vague. What I hear you say is "I don't want
to believe you." ;-)

There are an infinite number of steady states; every time I move the
elevator, I create a new steady state.

Given that in more than 100 years of study, this concept has never
shown up

I doubt you're familiar with even 1% of the 100 years of aerodynamic
research and thought. I'm certainly not.

You should realize that "I've never heard of it so it must be false"
is a weak argument.

Lift is always generated perpendicular to the wing's chord.

No, for subsonic flight, it's perpendicular to the *local* relative
wind, the relative wind that is modified by wingtip vortices. If lift
were perpendicular to the chordline, you would have induced drag in a
wind tunnel, and you don't.

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.

This is based on your mistaken notion above.

Since the lift vector points slightly aft in level flight,

Only because of induced drag.

However, in gliding flight, the vector is pointed forward, helping
counteract the contribution drag makes to lift.

No, the lift vector is perpendicular to the local relative wind
causing it. There is a rearward component (called "induced drag"),
but there is no component forward along the flight path.