Why is the explanation of lift based on increased path incorrect?

[vivesdn]

Some research on wiki, google and this forum seem the state that planes fly because of Bernouilli, i.e., the acceleration of the air on the top of the wing because of the increased path.
Just to discuss a little bit, as other threads seem just dead.
Wings, sails and rudders work in the same way. This is clear. As a sailor, I think that increased path is negligible so it doesn't explain the power obtained from the wind. On the other hand, it is not possible to catch a sailship by following the same path (assuming close-hauled sailing), as second boat will receive the wind from the front.
It is not only that air is slower below the wing and faster over the wing. The air is changing direction both below and above the wing. The same for a sail or a rudder. Air is accelerated downwards (not meaning that v is increased, just a change in direction) to follow the obstacle (wing, sail or rudder). Importantly, above the wing air increases its velocity because cross section is increased to fill the space behind the wing. At the trailing edge, air is flowing downwards for both flows. I find strange that most pictures of these flows do not show this effect.

What do you think?

 

[Danger]

You are quite correct that it is deflection of the air, rather than a venturi effect, that creates lift and control surface effects.

 

[cesiumfrog]

planes fly because of Bernouilli, i.e., the acceleration of the air on the top of the wing because of the increased path.

Yeah, it seems the actual mechanism that produces lift is the lower air pressure just above the wing compared to that just below the wing.

You can use Bernoulli's principle to calculate the pressure difference based on how fast the air is flowing on either side of the wing.

However, the "increased path" (the airfoil shape) alone is insufficient to calculate how much faster the air moves above the wing (the flows don't match up again the way one naively expects). You could measure the speeds, or you could break out the Euler equations (accounting for energy and momentum simultaneously) to predict them.

Alternatively, you could take the holistic approach: The upward lift on the plane must be equal (in a more rigorous sense) to the downward deflection of the air. You could "just" measure that instead, but (as you noticed, a naive estimate won't account for how much air both above and below is deflected) you need the Euler equations to calculate it.

I understand there is a special class of shapes for which the Euler eq's have an exact solution, but I'm not sure what it's called.

 

[vivesdn]

So, what is is wrong on the usual explanation on lift is that the increased path is the cause of an accelerated flow. Bernouilli will apply as it is an energy-balance equation. But the increase of air speed is not due to increased path but to increased volume to cover (as bottom air is deflected to avoid the obstacle, more space has to be filled by upper flow).
Interesting reasoning that applying Bernouilli should one get the same lift that considering deflected flows. And the difficult part to be calculated still is the speeds/flows.

Thanks. I was confusing Bernouilli (general) with the idea that the difference in velocities is due to increased path.