Here's something that was buried in my un-sent messages from a couple of
weeks ago. Perhaps this will supply a way for Mr. Denker to see my own
errors, and to see how they lead to a split between the "Bernoulli" and
"Newton" paradigms.
Do airfoils throw mass downwards?
No.
No?!!!!!!!!!!
Well, if we want to imagine an airfoil as being like a baby in a shopping
cart who grabs boxes of Cheerios off the grocery shelf and flings them
downwards in
passing, then airfoils do fling mass downwards. But the physics is not
quite so simple. The supermarket is entirely filled with "frictionless
Cheerios!: :) Here's a better analogy.
Go underwater in the nearest ocean. Now make a "baseball" underwater by
freezing a sphere of water solid. We'll ignore the slight density change
in ice and assume that the ice-ball is now hanging in front of us.
Now grab the ice ball and fling it downwards. It goes whizzing off, and
the reaction force propels us upwards. But think for a moment. Globally,
was any water(ice) thrown downwards? Well, no. But how can this be?
When the ice-ball is moving, the water is parting in front of it and
allowing it to pass. Behind it the water closes together again. (There
is also a toroidial vortex trailing behind it, but we'll ignore this extra
complexity.) The total distribution of water (and ice) in the ocean is
remaining constant, yet the ice-ball is flying downwards! There is no
overall circulation-loop being created by the moving ice-ball. Yet it
certainly does move.
And finally, imagine the ice-ball to have melted. Never throw any ice in
the first place, instead throw an organized "water ball".
We must confront the fact that while the ice-ball or the water-ball is
moving downwards, no mass is moving on average. Each bit of water gets
out of the way by moving from the front of the ice-ball to the back, but
simultaneously the ice-ball moves downwards to replace it. In a global
sense, matter has circulated, but it has not moved in a net forwards
direction. For every bit of matter moving downwards, there is an equal
parcel elsewhere which moves upwards. But something has moved. Momentum
has moved.
If we are underwater and we fling a neutral-density ice-ball, or if we
fling an underwater smoke-ring, then we have actually just flung a parcel
of pure momentum!
This is not the case with a baseball in air or a machine gun in vacuum.
In that case there is a genuine transportation of matter from one location
to another. It's only when the entire atmosphere is packed with
frictionless baseballs that the matter-transport aspect of the situation
vanishes, and only a hunk of momentum is moving. And, when the
"Machine-gun hovercraft" is flying over the earth, we should imagine the
atomsphere to be replaced with liquid lead, so that the bullets are
neutrally bouyant.
When an airplane flys, it throws down a spinning pattern of air in the
form of two long counter-rotating cylinders. These cylinders transport a
pattern of momentum, but globally there is no mass being transported,
since for every parcel of air that moves downwards, there is another
parcel nearby which is moving upwards. It's an obvious feature of the
"disk balloons" model of airplane flight.
As the old Ranier Beer ads used to say: PRETTY COOL, EH?