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quick note on air-parcel motion



My contention is that no lifting force can occur against a wing if that
wing forces the air-parcels to describe hump-shaped trajectories as it
passes, and also it leaves the air-parcels with no vertical motion
afterwards. In other words, if it doesn't throw them down, then the wing
cannot experience a net upwards force. Sounds simple.

However, the classic 2D simulation of an airfoil contains a difficulty.
If we measure the surface velocity of the air across the airfoil and use
this to calculate the lifting force, we obtain a positive value rather
than the zero value obtained above. Momentum is being delivered into the
wing in order to counter gravity. Yet no corresponding downwards momentum
is being delivered into the air. The chordwise flow is circular, and in
2D it is impossible for the wing to leave the parcels of air having a net
downwards motion. It would violate continuity, I think. I don't see how
it cannot.

In this situation Newton and Bernoulli make opposite predictions... and
Newton loses! The Newton-based prediction would say that, because the net
downwash is zero, the momentum transferred to the air is also zero, and
the upwards force upon the wing is zero. No lift.

How can we resolve such a huge contradiction? Do we declare that Newton's
laws don't work in two dimensional aerodynamics, yet the Bernoulli
equation still is valid?!!!!! Or is there something funny about the
infinite extent of the 2D world? Perhaps the wing is trying to impress a
permanent vertical deflection on a streamline and therefor drive an
infinite amount of mass ahead of it. This would lead to a misleading
event: forces might appear, but they apparantly would cause zero net
vertical acceleration of the air.

Just thinking aloud...

More like remaining confused, aloud.

There is certainly more to the "religious battle" than first meets the
eye.

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William J. Beaty SCIENCE HOBBYIST website
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