Re: Airfoil lift, new article

[William Beaty <billb@ESKIMO.COM>]

Some bait to temp the unwary.   :)

See the message below.  Can you see the flaw in Mr. Scarfe's diagram and
arguments?  It is two-dimensional!  In 2D, a wing can push on the distant
ground instantly, since the air cannot escape in a direction out of (or
into) the plane of the diagram.  Wing pushes down on air, air pushes down
on Earth, Earth doesn't move.  Earth pushes up on air, air pushes up on
wing, wing levitates without having to eject any KG of air downwards.
Flight by "ground effect," with the altitude made irrelevant

In my opinion, this is the central flaw in conventional aerodynamics'
explanation of flight.  2D wings fly, it is true, but they employ a
fundamentally different machanism than 3D aircraft.  3D aircraft fly by
conservation of momentum, while 2D aircraft fly by contact forces like a
hovercraft.  A 3D aircraft ejects KGs of air downwards like a rocket (or
helicopter!), while an aircraft in a 2D world interacts with the surface
of the Earth.  In a 2D world, it doesn't matter how high the airplane
flys, it is still essentially riding across the earth's surface, and hence
there is no need for it to permanently deflect the streamlines of oncoming
air.  In a 3D world, an aircraft must permanently deflect the streamlines,
otherwise there would be no net change in the momentum of the air, and no
F=MA force.

"Circulation theory"  is flawed.  It works great for predicting the
lifting force.  But if we use it to explain flight, then we are ACTUALLY
explaining how wings might function in a vertical version of "flatland."
3D aircraft function by profoundly different principles.

If anyone on PHYS-L enjoys "lifting force" debates, please feel free to
wade on into the rec.aviation.piloting discussion.

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William J. Beaty                             SCIENCE HOBBYIST website
billb@eskimo.com                             http://www.amasci.com
EE/programmer/sci-exhibits          science projects, tesla, weird science
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Author: Julian Scarfe
Email:jas1@scigen.co.uk
Date:1999/01/12
Forums:rec.aviation.piloting,rec.aviation.student

J Kahn (jkahn@planeteer.com) wrote in response to JSD's critique:
> : With all due respect:
>
> I have a problem with your discounting the upwash bit John... if the
upwash
> : was beneficial to the generation of lift, the upwash would have to be
> : produced by a source *external* to the wing.  When you throw the ball
> : up to me I benefit from the upward energy because *you* imparted the
> : energy, not me.  The upwash the wing has to deal with is produced by
> : the same wing, not an external source... It's accelerating a mass
> : upward, the mass wasn't accelerated by an external source.

Mark Mallory wrote:
> This is correct; Denker is in error here.  Unlike the situation in the
> baseball analogy, the airflow in front of the wing *initially* has ZERO
> upward momentum.  The upwash represents a *change* (increase) in the
upward
> momentum of the airflow, which must be accompanied by a *downward*
reaction
> force on the wing.  Similarly, a *downward* change in airflow momentum
> must be accompanied by an *upward* reaction force on the wing.  The
total
> lift of the wing will be equal to the NET downward momentum change of
the
> air as it passes the wing.
>
> However, it's possible to show that there is ZERO net downward momentum
> imparted to the air by the passing of a lift-generating airfoil;

You're *all* right: you're just talking about different chunks of air!

A'                       A                 B
B'
|                        |                 |                             |
|                        |                 |                             |
|                      ^ |                 |                             |
|      --->            | |    ---------    | |                           |
|     AIRFLOW            |      WING       | V                           |
|                        |                 |                             |
|                        |                 |                             |
|                        |                 |                             |
X'-----------------------X-----------------Y-----------------------------Y'

Consider a situation where air flows from a plane (in the geometrical
sense)  A'X' at "forward infinity" through a plane AX just ahead of the
leading edge of an aerofoil (loosely a "wing" for consistency), through BY
just behind its trailing edge, to B'Y' at "aft infinity".  Consider X'XYY'
to be the surface of the earth a long way below the wing.

Let's look at the vertical component of the momentum flux p of the airflow
as it passes each vertical plane, the force f on the wing and the force on
the horizontal plane in each region.

Conservation of momentum in each zone ("control volume") requires:

pA'X' - pAX = fXX'             (1)

pAX - pBY = f_Wing + fXY       (2)

pBY - pB'Y' = fYY'             (3)

Adding 1+2+3 gives

fXX' + fXY + fYY' + f_Wing = pA'X' - pB'Y' which tends to zero as the '
planes move away towards forward and aft infinity.  So the total force on
the imparted on the air by the wing is equal opposite to the total force
imparted on the air by the ground; or lift is equal opposite to the total
force imparted on the air by the ground, which is what Mallory said.

Provided the length (area in 2D) XY  is much smaller than X'Y', (2) can be
approximated by

pAX - pBY = f_Wing

which is the momentum argument that Denker puts in point 1 of his
critique.  The upwash (- pAX) in front of the wing contributes additively
to the downwash behind (pBY). Anderson and Eberhardt have "slipped a
sign"!

I don't like the momentum argument very much on the basis that there's a
term like fXY in any control surface that you pick.  In the case of the
choice XABY, it is vanishingly small and the momentum change pAX - pBY is
a way to calculate the lift. But in the case of any surface X'A'B'Y' that
fills space, the term is of the same order of magnitude as f_Wing (1/2 in
the 2D case and 1/3 if I remember rightly for the 3D case, though it's a
somewhat academic point).

That's why I think you have to be very careful about using macroscopic
conservation of momentum arguments around wings. The only thing that you
can be sure of is that the sum of the force on your control volume and the
momentum flux into it is equal and opposite to the lift.  But if you know
the velocity field everywhere anyway, why not just apply Bernoulli at the
surface of the wing and calculate the pressure directly, like
aerodynamicists have been doing for a century?



Bill Beaty made the interesting (but, IMHO, mistaken) point:

> Yes, a 2D simulation is equivalent to an infinite wing, and for an
> infinite wing, if there is any net change in the air motion after the
> wing has passed, then an infinite amount of momentum had to be created,
> because all of the air far above and below the wing had to be deflected
> as well.

Yes, but the "wing" has infinite span: the lift per unit span is finite.

> In 2D space, if one streamline is permanently deflected, they ALL must
> be permanently deflected.  Hence a 2D situation is fundamentally
> different than a 3D situation, there are fewer degrees of freedom for
> each parcel of air, and the air behind an infinite wing had better NOT
> move downwards.

To an extent, this is true. Some of the downwash can be attributed to the
trailing vortices.  Nevertheless, if the 3D to 2D transition so
fundamentally changes the physics, how come calculated and measured 2D
lift coefficients are equal to the limit of 3D lift coefficients at large
span?

> Even a "thin slice" 2D simulation is bizarre, because if there is any
> net deflection of the air, then ALL the air out to infinite distances
> above and below the wing must be deflected too.  This represents an
> infinite mass and an infinite momentum change.  Hence, 2D aircraft can
> fly without deflecting any air, but 3D aircraft operate by significantly
> different rules.

The 2D aircraft "deflect air" just like the 3D ones.  At plane BY as seen
above, there's a large momentum change over a small area.  At plane B'Y',
the momentum change is infinitesimal over an infinite area. One highly
misleading aspect of the Anderson and Eberhardt paper is the implication
that the deflection angle as "permanent", i.e. the same at BY as B'Y'.
It's not, in either 2D or 3D.

--

Julian Scarfe