Rebuttal to John Denker's Critique
of Eberhard/???'s

"How Airplanes Fly"
Mr. Denker says:
>   1) The paper contains the statements ?This upwash actually contributes
>   to negative lift and more air must be diverted down to compensate for
>   it.? and ?upwash is accelerating air in the wrong direction for lift.?
>   It is easy to see that these statements are wrong. Suppose you are
>   standing on a coffee table above a hard concrete floor. You throw a
>   baseball downward, rather hard. During the throwing motion, the recoil
>   forces you upward a little. Now suppose the baseball hits the floor,
>   bounces back up, and is caught by you. Interestingly, when you catch
>   the ball you and your glove are forced upward again. The analogy to
>   airplanes is clear: both the incoming upwash and the outgoing downwash
>   make positive contributions to the lift.

Obviously it is NOT easy to see that their statements are wrong, otherwise
we wouldn't be arguing about it!  :)

Let's repair your baseball analogy.  Suppose I throw a very light baseball
at the air below a wing.  The baseball bounces off the air.  As a result,
the air is driven downwards, and the baseball bounces upwards.  Because
the air doesn't remain still, the baseball now moves more slowly.  The
baseball hits the bottom of the wing and bounces again.  The wing is
driven upwards, and the baseball is driven downwards more slowly.  The
baseball bounces off the air again, so the air goes downwards and the ball
goes upwards.  When everything is complete, the baseball has forced the
air downwards and forced the wing upwards, and the baseball has lost
energy as it performed work upon the wing and upon the air. 

The original baseball analogy is incorrect because it models the air as a
solid surface of very high mass: a surface which will not move when
struck.  Air is not like this.  When something pushes on the air, the air
moves.  The wing is also not like this: when something pushes on the wing,
the wing moves.

>   To be sure, when you first throw the baseball, you must expend energy.
>   On the other hand, each bounce off the bottom of the coffee table
>   transfers upward momentum to you, without further expenditure of
>   energy.

The above statement is wrong because each bounce of the baseball off of
the coffee table transfers upward momentum to you, which slows the
baseball.  Each bounce off of the "floor" (the air layer) flings air
downwards and slows the baseball.  The baseball will rapidly be slowed,
while the coffee table will move upwards, and the air layer below it will
move downwards.  The baseball has done work upon these masses.  These
masses didn't just accelerate apart without any energy being expended.

>   The analogy to airplanes is this: Obviously, the airplane must expend
>   some energy to create the circulatory motion that is responsible for
>   the upwash and downwash. However, after the circulation is
>   established, it tends to perpetuate itself with only rather minor
>   additional energy inputs.

The above issue is very interesting.  To me it appears that it is correct
for any wing which flies in a two-dimensional world.  If the wing cannot
deflect any air downwards, then it loses no energy to the air.  Therefor,
if the wing initially creates a circulation around itself, this
circulation will persist until it is damped by viscous forces.  As long as
the 2D wing can inject a bit of energy to fight the slowing of the
circulation, the circulation will persist, and will produce continuing
lifting force. 

In a 3D world things are very different, because the circulation "leaks"
from the wingtip, and a long wake of circulating air is produced.  The
wing must continuously inject a large amount of energy into its

>  The energy of the downwashing air bounces
>  off the lower air and returns in the upwash. (You should not imagine
>  that any typical air molecule makes a round trip. The energy
>  nevertheless returns, after being passed from molecule to molecule.)
>  The contributions are summarized in the following table
>  energy contribution   momentum contribution
>     upwash                input upward
>    downwash              output upward

Because the "bouncing" ignores the motion of the "floor", the arguement is
wrong, and the table above is wrong.  I believe that simple physics can
apply here: if there is an inwards-directed force between the wing and the
air, then the wing will be forced towards the air, and the air will be
forced towards the wing.  Therefor, if the wing causes air to accelerate
upwards, the wing will be accelerated downwards, hence upwash creates
negative lift.
>   Since the paper does not correctly account for the energy of the
>   upwash, its calculation of induced drag is wrong. It is not merely
>   wrong in principle, it is wrong in ways that lead you astray, as will
>   be discussed below.

Since the paper correctly points out that an upwards acceleration of air
must create a downwards acceleration of the wing, the above assertion is
incorrect.  Momentum is conserved:

  M(air parcel) * Accel(air parcel)    +    M(wing) * Accel(wing)  =  0

...therefor upwash creates negative lift.

>   3) The paper draws an analogy between a wing and a pump. This is a bad
>   analogy. Bernoulli's principle does not apply to the air in pumps, but
>   it does apply (to a very useful approximation) to the air near a wing.

Why does Bernoulli's principle not apply to air in pumps?  A propellor is
a pump, and is also a wing.  The example of the Helicopter springs to
mind.  A helicopter accelerates the air downwards, and by reaction forces
the rotor is forced upwards.  However, the rotor is clearly a wing.

>   4) The paper draws an analogy between a wing and a scoop. This is also
>   a bad analogy. The paper says that the ?the height [of the scoop] is
>   somewhat related to the chord length?. This makes a nice intuitive
>   picture, but it just isn't how wings work.

I agree partially with the above.  A wing is vaguely like a scoop, so it
is a distant (not a bad) analogy.  Because the flow of air around a real
3D wing is three dimensional, the paper's description of the two
dimensional scooping process is correct in general principle, but very
wrong in detail.  If the "scoop" is supposed to be the size of a chord
length, then any lifting force calculations will be incorrect.

   5) The scoop model predicts that ground effect should gradually become
   noticeable starting when the wing is within a chord-length of the
   ground. This is wrong. In fact, we know from standard engineering
   equations and common pilot experience that ground effect gradually
   becomes significant starting when the wing is within a span length of
   the ground.

Mr. Denker is totally correct about this.  Each wing accelerates a large
disk of air into vortex motion, where the center of the disk of air is at
the wing tip, and the disk stands on edge.  When the perimeter of this
disk approaches the surface of the earth, the "ground effect" becomes
   6) The paper cites the Coanda effect as a plausibility argument in
   favor of the scoop theory. Alas, for reasons spelled out at
   using the Coanda effect to explain the operation of a normal wing
   makes about as much sense as using bowling to explain walking. To be
   sure, bowling and walking use some of the same muscle groups, and both
   fundamentally rely on Newton's laws, but if you don't already know how
   to walk you won't learn much by considering the additional complexity
   of the bowling situation.
   Furthermore, if you actually carry out the experiment suggested in the
   paper, it gives evidence against the claim that the airfoil affects
   the fluid for a distance ?somewhat related to the chord length?. If
   you touch a chopstick or some other small object against a large
   stream of water, you will find that the thickness of water that
   follows the curve is much less than a chord length. In contrast, a
   real wing affects the air over a distance much larger than the chord.
   The Coanda effect is just not a good model for how wings work.
   7) In the paper and elsewhere, the authors have calculated estimates
   of the size of the scoop and the amount of air deflected. These
   calculations require assuming standard lift formulas that do not come
   from the scoop theory itself, but come from some other theory. Any
   attempt to use such calculations as evidence in favor of the scoop
   theory would be an invalid circular argument. To say it another way,
   the scoop theory could never be considered a complete theory; you
   would have to explain the other theory before you could begin to use
   the scoop theory.
   8) Although in one place the paper correctly says that ?there is
   nothing wrong with the Bernoulli principle?, in numerous other places
   it leaves the impression that Professor Bernoulli is somehow to blame
   for the "equal transit time" fallacy and/or the "curved on the top /
   flat on the bottom" fallacy. Any tool can be used properly or
   improperly. Millions of students have invoked Newton's laws
   improperly, but we don't let that stop us from applying them properly
   when we get the chance. By the same token we should not teach people
   to disrespect Bernoulli's principle.
>   9) The paper implies that friction plays a central role in making the
>   air follow the curve of the wing. For example, it says ?Why should a
>   fluid follow a curved surface? The answer is viscosity? This is
>   nonsense.

I find Mr. Denker's above assertion very unsettling, considering his
discussion of air flow detachment.  The boundary layer around a wing only
exists because of the viscosity of the air.  Without viscosity, there
would be no boundary layer, and there would be no reason for the air to
follow the upper surface of the wing. 

   The paper says ?We hope that the answers provided here will clarify
   many misconceptions about lift and that you will adopt our explanation
   when explaining lift to others.? I agree that the paper makes some
   valid points about common misconceptions. Alas, it goes on to replace
   those common misconceptions with a string of other misconceptions.

I agree that the authors have some misconceptions.  It also seems apparent
that Mr. Denker has misconceptions as well.

If we feel that it is far more important to be right than to find the
truth, then we will hotly defend our emotional investments in our
particular viewpoints, and the truth will suffer greatly.  Here's a quote
to live by:

It is a good morning exercise for a research scientist to discard a pet hypothesis every day before breakfast. It keeps him young. -- Konrad Lorenz
> By way of constructive counter-offer, a pilot-oriented explanation of > how wings really work can be found at > >
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