If so, then during the time it is in freefall, it acquires a downward
velocity. Small, no doubt, but nonzero.

Sometimes it does, sometimes it does not. I'll allow as the vertical
component of velocity decreases during that time, for a positive up
coordinate system and a plane in (macroscopic) level flight.

Ok. (I was sloppy - it doesn't "acquire a downward velocity", it really
"endures a downward acceleration", which depending on the initial
vertical velocity may or may not end up with the plane going downward.)
So we are saying the same thing here.

Do you agree that in each collision momentum is transferred to the
air molecule that is equal and opposite to the momentum transferred
to the wing?

Yes I do. This is what I call "throwing the air down". That downward
momentum will remain with the air (dissipated across many other
molecules as it keeps colliding, but never disappearing) until it is
transferred to the earth, which has been accelerating upwards in the
same fashion.

I agreed quite some time ago that the theoretical basis for
macroscopic gas laws is to be found in statistical mechanics.

Ok.

On a macroscopic level, the vertical component of momentum of the
wing is zero.

Yes.

Therefor on a macroscopic level, the sum of the
momenta transferred to the air molecules, integrated over all of
the air molecules must also be zero by Newton's third law.

Right?

Only in a nonaccelerated frame. We are dealing with an accelerated
frame. Consider a rocketship hovering over the moon. The (macroscopic)
vertical component of its momentum is zero also. However it has to
continually throw down rocket exhaust to stay there. So, without
looking at the rest of the picture, your conclusion about momentum is
flawed.

In the case of the wing, the momentum is transferred a few times... once
when the wing hits the air molecule (throwing the air down), again when
that molecule hits the earth and bounces back (throwing the earth away
from the wing), and then again when that air molecule (or its proxy)
hits the wing on the way back up.

Think about a person sitting on a stool. No momentum transfer (or so it
would seem). But then think about a person supporting himself by
dribbling a basketball. There is a lot of momentum transfer, but no
=net= change. The reason there is no net change is that the basketball
keeps pushing the earth away too.

Jose
--
Money: what you need when you run out of brains.
for Email, make the obvious change in the address.