I don't think leaving out density changes leaves out very
much that's relevant to lift, but I have to admit to not
being sure exactly what question this discussion is trying
to answer, so I'll hold off any comment.

The question was whether Bernoulli (did I get it right?) supersedes
Newton. I maintain that, while Bernoulli's equations are very useful,
they obscure something Newtonian about the source of the force. If you
have lower pressure above and higher pressure below, you get lift. But
you can't get to that condition without throwing air down. Consider a
"wing" with a flat bottom. Define the JAOA to be the angle the =bottom=
makes with the airflow. In this case the JAOA is zero. The top of the
wing is an arc. The air has to go a longer way around the top of the
arc, so the conventional Bernoulli argument would be that there is lower
pressure above for this reason alone.

I don't think that kind of wing, in that configuration, would generate
any lift. If it does, there will be downwash. Increase the JAOA and
you certainly get downwash, and you will also get lift. The two will
balance.

The argument of "no net downwash" has to do with whether the air comes
back up. It does not (completely) until the airplane lands.

I will grant that, once the plane is flying over the earth, there will
be no net accumulation of air below - the attempt at accumulating the
air will be counteracted by the increased pressure (which is also
causing the upwash ahead). But enough air will already have been
accumulated below (and will remain accumulated below until the end of
the flight) so that that increased pressure will support the aircraft.

In the (silly) configuration where there is no earth, and no gravity,
there will be no pressure accumulation. The high pressure below will,
in addition to pushing air ahead up, will continue to push air below
down. This flow will dissipate, but not disappear. The aircraft cannot
be supported by the earth (like sitting on a rock), so it has to be
supported by downward thrust (downflow). As far as the wing is
concerned, this is what happens anyway. The wing sees rising air,
flings it down, and keeps going.

Taken in its entirety, I'd say the [no net downflow idea] is false.
Pressure differences hold the plane up. Force holds the plane up.
Neither *requires* any net downflow.

Yes. But to get the plane flying there is some net downflow; enough to
increase the global pressure by (weight of airplane)/(area of earth).
When the plane lands, there is a net upflow to release this pressure.

Globally, because of the earth's surface, there is no net downflow
during steady state flight. (I believe that's the point you want me to
concede - I do concede that point). However, this is because of the
earth's surface. Locally, the wing is changing the vertical velocity of
the air it encounters. Locally, the wing is throwing air down. This
has the consequence (which the wing doesn't care about) that air rises
up to meet it, because the air density is mostly unchanged. But, that
tiny density change caused by the tiny pressure change is what
ultimately enforces the "no net downwash" because of the earth's surface.

So if I understand this, you are saying that if air were
incompressible, there would be no lift?

No. If air were truely incompressible, there would be no downflow at
all; the entire earth would be pushed away just as it does when I jump.

Jose
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