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> > The lift has to be provided
> > by the sum of momentum flux and pressures on the boundary that don't cancel
> > out.
> >
> > In the case of an aerofoil in an infinite continuum of air, you can draw
> > such a control surface where the pressures pretty much cancel and you can
> > equate the momentum change to the lift. But where there is a ground plane
> > or top/bottom surfaces of a wind tunnel, those pressures do not cancel.
> > There ground or bottom surface pushes up on the air above it, and you
> > cannot
> > identify a momentum flux that fully accounts for the lift.
>
> Actually, the ground plane is not necessary. If the control volume
> is a very large cube or sphere, with the wing at the center, we find
> that the net momentum flux through this control volume is zero.
>
> => In other words, the lifting wing imparts zero net momentum to the
> => atmosphere as a whole, with or without a ground plane being present.
>
> A simple explanation is that the downwash immediately behind the wing
> (between the tip vortices) is canceled by the upwash outboard
> of the tip vortices.
>
> One possible objection which follows is:
>
> Since the lifting wing pushes down on the atmosphere, why doesn't
> the atmosphere continually receive net downward momentum?
>
> Answer:
> The wing is not the only thing pushing on the atmosphere,
> or on the fluid inside a large control volume enclosing the wing,
> to be more precise. There is a pressure field extending far away
> from the lifting wing, lower pressure above, and higher pressure below.
> For any chosen large control volume surrounding the wing, this pressure
> field will push UP on the enclosed fluid, cancelling the wing's
> downward push. The net result is zero momentum change of the
> enclosed fluid. You can make the control volume arbitrarily large,
> and the net momentum change remains zero.
>
> We will get a nonzero momentum change only if we select a compact
> and selective control volume, such as one extending only out
> to the wingtips. But such a control volume ignores the upwash
> outboard of the vortices, so I'd argue that it inappropriately
> ignores some of the physics of the situation.
If there is no net downwash, why does downwash graves appear in the
upper surface of clouds flown over and why does it take 55 seconds for
the downwash/ wake turbulence to reach ground below and behind a
BAE146 flying at 800 feet at weight 35 tonnes?
I think Kutta, Prandtl and Max Munk showed the momentum influence
already 80 years ago and now totally forgotten.
Jan-Olov Newborg
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