Re: a couple of points on flight

[William Beaty <billb@ESKIMO.COM>]

On Fri, 15 Jan 1999, JACK L. URETSKY (C)1998; HEP DIVISION,              ARGONNE NATIONAL LAB ARGONNE, IL 60439 wrote:

> 2.  2-d airfoil theory explains lift on a wing very well.  Wind tunnels (the ones
> I was introduced to 50 or so years ago) are set up to be 2-d and one has to
> correct the measurements for wall effects, etc.

Hi Jack!
 From what I understand of it, I would say that 2-d airfoil theory ALLOWS
CALCULATION of lifting force, but that is contains misleading features
which befuddle anyone who is attempting to explain airplanes.  See below.

> 3.  It is true that the ground effect is related to the wing span in
> 3-d.  In 2-d calculations one doesn't usually introduce a ground plane.
> If one did, I think the effect probably dies off either logarithmically
> or as 1/distance.  Airfoil theory is, after all, just the same potential
> theory that we came to know and love in electrostatics - except that
> circulation must be introduced in order to keep things finite.

Here is a central problem: in 2D, the air far upstream from the wing is
flowing horizontally, right?  And the air far downstream is also flowing
horizontally, correct?  These flows come about through the superposition
of circulation and constant horizontal flight.  It seems to me that this
guarantees a ZERO change in momentum of the air.  It looks as if the 2D
flow diagram is symmetrical about a vertical line, and upwash exactly
equals downwash.

If the wing lifts the air up, reverses the air's vertical velocity, then
pushes it down to exactly the same position again, leaving it with zero
vertical velocity, then no net momentum change occurred.  For there to be
net momentum change, the air would be lifted up at first, but then it
would be pushed down AND KEEP MOVING DOWN AFTERWARDS.  If wings were to
fly by deflecting a horizontal hail of bullets, then a "contrail" of
constantly-descending bullets would trail behind the wing.  The descending
contrail appears to be lacking in 2D circulation diagrams.  A
constantly-descending contrail appears to be incompatible with the
circulation field. This confuses me.

I have no idea on how to integrate the net change in the air's momentum in
the vertical slices as it passes the circulation field of a wing in 2D.
My assertion that the net momentum change is zero is based upon visual
reasoning and intuition.  Yet I still cannot grasp how a wing can create
lift unless either it acts directly against an immobile infinite mass of
air, either that or it takes in air having a zero vertical velocity
component and then leaves a contrail of air which moves constantly
downwards.  Can anyone here explain where I've gone wrong about the 2D
"potential field" analogy of circulation?

If this were electrostatics and a charged metal object was being
accelerated in an E-field, I would look to the distant "capacitor plates"
where the e-field flux lines ended, there to find the opposite mechanical
acceleration and the opposite quantity of momentum.  In 2D airfoil
diagrams, the opposite momentum seems to be stored on the infinite mass of
air which is behind the airfoil and extends to plus and minus vertical
infinity.  The airfoil trys to accelerate a long horizontal slice of the
air downwards, but this is impossible in 2D, therefor the airfoil reacts
against an "object" having infinite mass, and the lifting force resembles
a contact-force with zero momentum changes, rather than a downwards
ejection of massive air parcels (think of a hovering helicopter, then
think of a toy boat in a bowl of water resting on scales.)


> ps Anderson does not quarrel with conventional aerodynamics.  He just
> thinks that his explanation is more "physical".  I think that the
> essential physics is contained in the statement that the integrated
> pressure over the wing surface is related to the net change in airflow
> (the "downwash"), but that's just a matter of taste.

I agree in part.  My quarrel is with the folks on newsgroups who point out
that in 2D, upwash apparently equals downwash, therefor a pressure-
difference can be created without any overall deflection of moving mass
being required.  I strongly suspect that this argument is flawed because
this efect only arises in a 2D "flatland" world, and cannot be used to
explain why a 3d aircraft can fly.

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