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Re: Judgement on opposing airfoil views, pt. 1

I'm back from vacation and itching to cause trouble! :)



On Fri, 27 Aug 1999, JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439 wrote:

Hi Bill-
I think that you are misunderstanding John, and clearly misunderstanding
the underlying physics.
The point is then in the relevant fluid dynamics context it is
incorreect to make microscopic arguments of the nature of "this piece of
wing here is related somehow to that parcel of air over there". What one
does in fact is to solve the Laplace equation in a infinite reqion subject
to certain local boundary conditions and conditions "at infinity".

I hope I've already incorporated the above concepts into my thinking: if
we look at the parcels of air far in front of an airfoil, we see they are
accelerated upwards only slightly... but also that there are a lot MORE OF
THEM distributed vertically at that horizontal location, and therefor the
momentum in a vertical slice of the atmosphere in front of the wing might
not decrease with distance in the way we'd first imagine. Closer to the
wing, each moving parcel has greater acceleration, but there are fewer of
them having the large vertical accelerations. I agree that if we track
just one parcel, then we will totally miss this aspect of the problem.

However, even knowing this I *DO* track only one parcel. Why? Simple
answer: because when an aircraft flys in 3-D, the pattern of circulation
ahead of the aircraft cancels out at a distance. Therefor I can observe
one parcel of air and watch what happens as the aircraft passes close by
it.

The pattern of circulation around an aircraft is analogous to a small loop
of wire with an electric current inside: the magnetic field drops off
rapidly with distance, and at large distances we assume that it is zero.
On the other hand, in the traditional 2-D mathematical model of an
airfoil, the physics resembles the magnetic field surrounding an INFINITE
wire. With an infinite wire, the "near field" region extends to infinity,
and we cannot assume that electromagnetic forces are zero at a great
distance from the wire. With a small loop of current in 3-D, the
situation is different, and this shows that the 2-D simulation has major
differences from the flowing air around a 3D aircraft.


I am lead to realize that when a real 3-d aircraft is flying high above
the earth, we can say that the parcels of air which lie far in front of it
are *stationary,* just as we can say that the field at a great distance
from a magnetic dipole is zero. It is never *exactly* zero, but it is so
small that it can be ignored. Even if we integrate the vertical momenta
of all the parcels in an infinite vertical plane which lies far in front
of the aircraft, the vertical momentum there will still be insignificant
if the aircraft is still far away. Except for the region around the
trailing wake-vortex pair, air which is at a distance from the aircraft
which is >> than a wingspan, is not moved by the wing and doesn't
participate in "circuilation." Obvious, no?


Whatever
the conditions at any part of the region affects the solution everywhere
else. Until one grasps this essential mathematical truth, the subject of
aerodynamics is guaranteed to remain mysterious.

This is true, but nevertheless there is a profound difference between the
magnetic field surrounding an infinite conductor, versus the magnetic
field surrounding a small current loop. At a great distance, the field
from the current loop becomes insignificant because the individual
contributions from different parts of the loop cancel out. This is not
true of an infinite wire. If EM is a complete analogy for vorticity and
for the non-turbulent velocity fields in a fluid, then the solution is
obvious, and the subject does *NOT* remain mysterious.

I made this point with John Denker in private communications long ago:
circulation surrounding a 3-D airplane cancels at a distance. I think he
was taken aback. Then he agreed. But it appears that he did not
incorporate this concept into his mental model of flight. If he had, he
wouldn't be saying the things he is saying.


I suggest that you acquire a good book on aerodynamics and study some
of the solutions.

I essentially can see the wing flying in my mind, and watch the flows take
place around and behind it. The image is fuzzy, but the global details
are quite sharp. It doesn't look so nasty at all. The devil might be in
the details though.

I knew I was on the right track when I realized that an electromagnetic
analogy makes perfect sense (and may in fact explain everything, as long
as we assume that the flows are laminar.) It does appear that viscosity
cannot be removed without shattering the entire mechanism which makes
flight possible.


Two dimensions is easy, three dimensions cannot be done
in closed form except for some simple shapes (that also can be done in
electrostatics).

Could this also be true of an electromagnet where the wire is wound in a
sort of pancake, but as a square loop rather than round? That's the EM
analogy for the lines of vorticity surrounding a wing, and if the
"conductors" run across the span of the wing and also trail off of the
rear edge, then the b-field of such a coil is (similar? Identical?) to
the velocity field of the flowing gas around a wing in 3D. At a great
distance the field is insignificant. And so I conclude that, at a great
distance in front of the aircraft, the parcels of air are motionless.
This is not true in the 2D flow analysis of an airfoil section.


My view is that there is no easy road to undeerstanding -
that is the point of my message - which you might wish to reread.


You wrote, incorrectly:
******************************************************************************
Correct me if I'm wrong, but John Denker disagrees with me. Instead he
says that, over time, a 3D wing in high-altitude flight DOES NOT need to
impose a net downwards momentum-change upon the air-parcels it passes.


Umm. I think you have a major suprise in store. Please get John Denker
to comment to you about this issue. (He's stopped talking to me. I
suspect that he sees that my arguments do have weight, even though they
come from a non-degreed lowly engineer.)

John's recent arguments have gone like so:

Wings don't have to deflect air downwards

Upwash causes positive lift

downwash also causes positive lift

if the wing has exactly equal upwash and downwash, then
there is a significant lifting force even though there is
no net deflection of the air.

This is the basis of his critique on the Anderson/Eberhardt paper. Again,
if the continuing miscommunication has given me a totally false idea about
the nature of John's arguments, then I am stuck, because when I ask him
questions to get further clarification, something always happens and the
subject winds up on an entirely different track (this occurs again and
again and again, and I cannot see why I can't just get some straight
answers.)


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William J. Beaty SCIENCE HOBBYIST website
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