Re: but does the *earth* push up on the *wing*?

[William Beaty <billb@ESKIMO.COM>]

On Sat, 21 Aug 1999, Timothy Folkerts wrote:

> Let me jump into a field in which I know no more than has been discussed
> here and make two points.
>
> > Does the aircraft push down upon the earth and as a consequence the
> > earth lifts it up, or does the aircraft accelerate air downwards and
> > is lifted upwards as a consequence?
>
> 1.  An equivalent question might be "if I pull on one end of a rope or
> spring, does the person at the other end of the rope/spring feel the third
> law reaction force?  At a fundamental level the answer has to be NO, but at
> the practical level the answer is usually YES!

At the fundamental level the answer could also be "Yes, but after a delay
time caused by wave-propagation."


>  I apply a force to the end
> of the rope, and the END OF THE ROPE applies an equal and opposite force to
> me.  The end of the rope in turn applies a force to the next section and so
> on down the line to the other person.  Other than transmitting the force
> and introducing a negligible time delay, the rope can mostly be ignored and
> the force pair can be considered acting between the two people.  With a
> spring it is a bit more problematic, since the time delay can be much
> greater, but in equilibrium, it is clear that the two people feel equal and
> opposite forces.

Perfectly understandable so far.

> I would say the air is like a giant spring.

Here's an important detail.  If I stand upon the ground and throw a
baseball downwards, does the earth experience an enormous force BEFORE the
ball strikes it?  No.  As a result, we must agree that the air is not like
a giant spring as far as baseballs are concerned.

This idea has direct application to airplanes, because as I understand it,
airplanes essentially throw a "ball of air" downwards. (actually it is a
very long cylinder.)


>  The airplane produces the
> immediate lift by pushing against the spring, but eventually (since we have
> a closed system with the earth at the other end of the spring) the force
> must be transmitted to the earth.

The force certainly is transmitted to the earth, but the reason for this
is not because we have a closed system.  Instead it's because the earth
stops the downwards-moving air (it stops the air either by friction with
the atmosphere which rests upon the earth, or by having the
downwards-moving air collide with the earth's surface.) At this point in
the argument we don't need to involk a "closed system"  concept to explain
the force that is applied to the earth.

> So at a fundamental level the answer has to be NO - the earth and airplane
> don't form an action-reaction pair, but at the practical level my answer is
> that they effectively are such a pair.

If that is true, then how does the earth push upwards upon the airplane?
That is the issue I cannot get passed.  A force always has two ends.  If
the airplane pushes down on the earth, but the earth doesn't push upwards
upon the airplane, then there is no force between the earth and the
airplane.  Anything else would violate Newton's 3rd law.

Indeed, we don't even need to search for any airplane-lifting forces
produced by the Earth, since we have a good reason to expect a
lifting-force to appear upon the wing.  Whenever mass is accelerated
downwards by the wings, the wings immediately feel an upwards force as a
consequence.  Why do we have to wonder if the earth produces a second
lifting force?  Even in the long run, the earth's surface does not
participate in this near-instantaneous action/reaction event which occurs
between the wing and the nearby air it pushes upon.



> 2.  Now I'll go further out on a limb and take a shot at the machine
> gun/circulation debate.  Consider a large column of calm air.  An airplane,
> trimmed for level flight, is thrown into the column from a region which is
> a VACUUM.  What course will the plane take???
>
> I think (based mostly on intuition) that the plane will not immediately
> commence to level flight, but will sink for a moment until a "cushion of
> air" has built up under the wing.

In other words, you expect that the density of air under the wing (and the
static pressure of each air-parcel there) would rise significantly, and
drop significantly for the air above the wing.  (If the rise was
*IN*significant, we wouldn't have to include it in our thought picture!)

:)


>  (Much like a car "thrown" along a road
> with the wheels just barely touching the ground would settle until the
> shocks had compressed enough to carry the weight.)  The initial downward
> acceleration would be considerably less than g due to the collisions, but
> more than zero.  Once the cushion builds up, the acceleration falls to
> zero.  To get this cushion ahead of the wing (which is the only place it
> does any good) the air must be moving forward along the bottom.  This
> sounds like John Denker's "circulation" although I see it as an effect, not
> a cause, of lift.

I think your view is quite accurate, except that I suspect that the
pressure/density changes are incredibly small.

You've raised a very important point.  If we push upon the air, it is
unlike pushing upon the earth, in that a blob of air immediately moves
while the earth would not.  Because the wing deflects the air, the wing
feels a pressure, yet the pressure of each passing parcel of air need not
rise.  Impossible?  Not if we think in terms of energy.  When the wing
pushes/pulls upon the air, rather than the air pressure rising (and
storing potential energy in each parcel of air), the air changes its
velocity (and stores the same energy as KE.)

You know, I hadn't gone deeply enough into the "air deflection"
explanation to see this phenomenon before.  I knew that the wing does not
change the static pressure of the surrounding air by much.  Now I can see
why this is so.  It's because the air can exert a force upon an object
through two independant methods: by static air pressure, or by changes in
momentum of the air.  Cool!

But the air pressure *MUST* increase, since the only thing touching the
wing is the air.  Wrong.  If the wing deflects air, the wing itself will
feel static pressure within its substance, but the air does not,
instead the air experiences an immediate deflection.



> If my intuition about the initial dip in elevation is correct, this would
> suggest that the "machine gun" model is a bit simplistic.  While it
> explains much of the lift, it can't explain all of it.  The compression
> (i.e. increased pressure) of the air under the will also contribute a
> significant amount to the lift.


If the increased static pressure of each parcel of air is a millionth? or
billionth? of the pressure of the atmosphere, then it would be small
enough to ignore.  It will always be there, but then the bouyancy force of
the atmosphere also slightly lifts the plane, yet we ignore it.  (An
airplane resting inside a huge vacuum chamber weighs slightly more than
when it is outside the vacuum chamber.  The atmosphere acts like an
"ocean" which makes all objects immersed within it seem lighter.)


> Or put it another way.  If "Maxwell's demon" could catch and remove the
> deflected air molecules right after they hit the wing, there would still be
> considerable lift.  But if they are not caught, they will to some extent
> bounce back up from air molecules below them, hit the wing a second time,
> and provide extra lift.
>
> Well, I've wasted too much of my afternoon on this, so I better get ready
> for classes, which start on Monday.  I'll try to find time to defend my
> views if people find this though provoking.

Thanks much for your message, because while I was typing the above, my
"light bulb" went on and I suddenly understood an entirely different
aspect of all this stuff.

If the airplane throws air downwards, why don't we end up with extra air
on the ground?  If the airplane flys by picking "air baseballs" out of the
sky and flinging them downwards, then where does the downwards-moving air
finally end up?  THAT'S where the "closed system" argument crops up.  If
the airplane transports mass downwards, this eventually (in the very long
run) must build up a pile of mass which reaches up and applies a force to
the plane.  Yet there is no obvious force on the wings pushing upwards
from the earth.  What goes on here?

When a volume of air is suddenly accelerated downwards and remains moving
downwards, it parts the air in front of it, and the parted air closes up
again after the downwards-moving air has passed.  Air that had been in
front of the downwards-moving parcel has been moved to the rear of that
downwards-moving parcel.  The air that was moved to the rear was
momentarily accelerated, but then it was decellerated again so no momentum
was lost by the parcel that is moving.

In this way the downwards-moving parcel progressivly "exchanges places"
with each succeeding parcel in front of it.  As a result, no mass builds
up near the ground, even though a parcel of mass did move downwards to the
earth.  No mass builds up, so we need not look for "back pressure" which
reaches upwards from the earth and pushes upon the wing.

Sound sensible?


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