The net takeaway for me is that I still can't be sure why airplanes fly and there is no general agreement on an authoritative source that will explain this.
Now, some answers to why wings work are just plain wrong (like the original wrong answer -- the Bernoulli effect). However, when one person says "Wings work because they push air down, and the air pushes the wing up", and another person yells "No, that's all wrong! It's because of <insert-fancy-effect-here>", they can both be right. They are answering the question at different levels of abstraction. They also can be right in different cases -- the source of lift for wings, and the strength of different effects, can change with wing and flow conditions (at low speeds, one effect dominates, and at high speeds, another does. At supersonic speeds, a totally new effect takes over. and so on...)
Here's my attempt at an answer aimed at an appropriate level of abstraction, though of course it is doomed to failure: - Air striking a wing is divided by the leading edge into two streams, one that flows over the top, and one that flows under the bottom.
- Assuming the wing has some positive angle-of-attack, the stream under the bottom of the wing will be deflected downward, and therefore pushes back against the bottom surface of the wing. This part is reasonably uncontroversial.
- The stream flowing over the top of the wing tends to follow the surface of the wing, even when the surface is curving down and away from the stream. Why this happens is subject to the multiple levels of abstraction problem that I mention above. If the curvature of the top surface is too severe, the flow cannot follow the surface, and it separates. This is "stall". Again, why this happens is complicated, and there are multiple effects and levels of abstraction at work, and I only understand the basic levels, so I won't try to go any further. The net result for a typical wing in typical flight conditions is that the flow over the top surface is also deflected downward.
- You can get the amount of lift on the wing by integrating the pressures over the surface of the wing or by examining the curvature introduced to the flow by the wing -- both methods will give you the same answer (and they damn well better!). This is if you have modeled the airfoil and flow in a CFD software package with a reasonably tight mesh so that you know the flow conditions at every point in space near the airfoil. Or, you can pick a standard airfoil whose properties have been determined experimentally! There are exhaustive tables of NACA airfoils to pick from. [2]
Still confused? Yeah, so am I. This is about as deep as I'm prepared to learn this topic, considering that I've given up my former life as a thermo/controls specialist in mechanical engineering, and am now trying to stuff as much understanding of software engineering and computer science into my tired brain as I can. :-)
[1] https://www.quora.com/Why-couldnt-Feynman-answer-the-questio... [2] https://en.wikipedia.org/wiki/NACA_airfoil
* edit for typos
But arguably "Wings work because they push air down, and the air pushes the wing up" doesn't really answer the question because air being pushed down is as much an effect of wing working as is airplane flying, but the cause why wing works would remain mystery.
You: "But that doesn't answer the question. WHY does the air get pushed down?" They: "Because of such-and-such effect..." You: "But that doesn't answer the question. WHY does such-and-such effect happen?" They: "Because of fluid viscosity and boundary layers and navier-stokes blah blah blah..." You: "But that doesn't answer the question. WHY does fluid have viscosity?" They: "Because a such-and-such bonds between the molecules of the fluid..." You: "But WHY..."
See how it goes? Turtles all the way down.
Different levels of abstraction are presented to explain "why", they're understood differently by different people (due to varying expertise), which causes discussions to eventually spiral into what appears to be disagreement, but is actually different layers of detail. The layers may seem to be contradictory but are often related. Hence the term "arguing in circles".
Now, if you want to know why wings are snapped the way they are that's Flid Dynamics and you generally use a combination of simulation and wind tunnel testing to 'get it right'.
PS: You can't pull a fluid. Straws work by having the air push down harder outside your mouth than inside. In much the same way the air above the wing is pushed down by the air above that.
What you propose as a solution is the skipping stone theory which is not entirely correct and is mentioned as one of the incomplete/incorrect theories on the NASA site.
Edit: I forgot but a typical counterargument to the skipping theory is the question of how can planes fly inverted then, if the wing in the standard configuration pushes the air down?
Further, you will note they use F=MA on their correct page: http://www.grc.nasa.gov/WWW/k-12/airplane/right2.html
The issue is modeling individual particles is several orders of magnitude beyond our best computers so even the most accurate models used by supper computers are still approximations. Further simply measuring pressure on various places on a wing. However, that is somewhat pedantic it might be true that's why they fly, but it's not a useful model for building an aircraft. People talk about flow, boundary separation layers, turbulence, and vertices but there all just analogy's that break down.
Anyway, wings don't have a fixed shape. Aileron's allow a plain to rotate. http://en.wikipedia.org/wiki/Aileron But, Flaps and slats are used to adjust angle of attack. http://en.wikipedia.org/wiki/Flap_(aeronautics).
While inverted the flaps are pushed down which changes the angle of attack. This of course ignores things like thrust vectoring etc. And most aircraft are much more efficient flying normally, with inverted flight basically just a brute force solution.
PS: So yes. F=MA (and enough processing power to handle 10^30th particles) is really all you need, but we just don't have enough processing power to physically model what's actually going on.
Note that potential flow calculations are significantly oversimplified; they work only for thin airfoils at low angles of attack (so they will correctly model basic flight, but not anything beyond that)[1].
So lets say you get an intuition of flow separation and turbulance on a 2D cross-section (which is already a bit of a stretch) you now still can't explain how a delta wing works.
Really smart people who know a lot about how flight works and have expensive computers still need to test their ideas in wind tunnels.
[1] Here's an example of something that actually happens, but isn't predicted correcty by potential flow: http://en.wikipedia.org/wiki/Lift_(force)#mediaviewer/File:F...