The flying wing has some horizontal momentum which is secondary here,
How much?

mv

The air thrown forward (or, if you will, the higher pressure ahead)
tries to reduce that, the engine presumably makes up for it.

Energy is 'pumped' into the air by the plane.

Yes, and what form does that energy take? I maintain that it takes the
form of a net increase in mv^2/2 over all the air molecules. Since m
doesn't change, and 2 only changes in a pentium, that leaves v to
change. This changes mv, thus momentum.

We agree that there is (microsocopic) momentum transfer at each
collision. We disagree as to whether the net is zero, and I think that
part of that disagreement has to do with just how much of the system we
are looking at.

The wing throws air down. If that causes other air to be squeezed up,
so be it - the wing will grab that air and throw it down again. The air
piles up in front of and below the wing, and ultimately pushes on the
earth. New (undisturbed) air keeps appearing in front of the wing
(where it is pushed up, and then back down). But if, instead of feeding
this system fresh air, we instead feed it the same air, say, by flying
around in circles, there will be a net movement of air. Air will be
sucked from the (infinite amount of) air above, and pushed down into the
(infinite volume of) air below. The next time the wing encounters this
area, there will already be downward movement of air from the first
passage... etc. etc. and so forth.

Momentum is conserved in elastic collisions

Low speed collisions between air molecules and aluminum sheets are to
first order elastic (although some energy goes into making molecules
wiggle and spin, and I suppose an electron is knocked out every now and
again).

Roll the airplane into a 90 degree bank. The weight is
now orthogonal to the lift. As teh airplane falls, it
banks even though there is no Earth 'under' the
belly. Why?

I'm not sure I understand the question. But if you put an airplane in a
knife edge and let it dive as it will, and maintain a lift-producing
AOA, the wing will push air in the belly direction, as it pushes itself
against that air in the antibelly direction. Some of that air will
swirl around the wing, but enough of it will dissipate the momentum that
the wing imparted to it over the entire atmosphere, and there will be a
(very) slight breeze blowing in the belly direction.

Jose
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