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I am an airline pilot, with more than 10 years of flying experience, and I would like to know how airplanes fly ;-) This may seem like a strange question for me to ask, so I will elaborate a bit:

The theory that was taught to me, and that is still taught to the vast majority of pilots all over the world (be it in airline pilot, private pilot, or paragliding training) is the following:

"An air parcel going over the curved top of the wing has to travel a longer distance, but it has to arrive at the trailing edge at the same time, hence it has to travel faster, and Bernoulli's law says that pressure decreases as speed increases."

This sounds like a good explanation at first sight, until you consider that there is no reason why this parcel would need to arrive at the trailing edge at the same time. Has it exchanged phone numbers with the parcel that went underneath the wing? Also, if you would calculate the lift based only on this theory and using the geometry of the wing, you would find a value that's about 2% of the actual lift produced by the wing. Finally, wind tunnel tests have shown that the air parcels indeed do not arrive at the same time. The air going over the top is not just going a little bit faster to arrive at the same time, it's usually going a lot faster and getting there well before the air that went underneath.

While trying to find an answer, I found a couple of other theories on the internet:

1. The simplest one, and rather obviously correct: the air leaves the trailing edge at an angle downward, and lift is simply the reaction force. Multiply the vertical speed component with the mass of air per second, and you get m/s times kg/s equals kg m/s^2, the force of lift.

2. The Coanda effect (Air "wants to" follow the curve around the top of the wing, which has to be caused by a pressure differential)

3. Circulation theory (lots of math)

The problem with the first theory (action/reaction) is that it's a bit too simple. It does a great job of explaining the very basic reason why the plane flies, but as soon as you want any more details, you get stuck. It does not say anything about pressure distributions, and it's not really clear how much air you should consider to be deflected by the wing. I suppose you should use an integral, but it's not clear how one would set it up.

The second theory, Coanda by itself, is just as flawed as the basic Bernoulli one. It, too, only accounts for 2% of the actual lift (disclaimer: that's just something I read somewhere, I never actually verified it).

The third, circulation theory, is way too complicated. Even if I could probably come to understand it with a few months of studying if I took the effort, I could never explain it to anyone without a good math background.

I finally settled on my own combined theory, which may be just as wrong as some of the others, but here it goes anyway:

Air going over the top has to indeed curve over the top of the wing. The Coanda effect makes it "stick" to the top surface, and this can really only be caused by a pressure differential. This means the pressure above the wing has to be lower than that of the surrounding air, to make the higher air curve downward. (In fact, air initially wants to go straight, which causes the low pressure that sucks it in). But this vertical pressure differential also results in a horizontal differential (air going through the low pressure area), which makes it speed up (Bernoulli's law). But as it speeds up, it will need more centripetal force to follow the curvature. Hence, the pressure becomes even lower, which again speeds up the air more, etc..., until an equilibrium is reached where the pressure is just right for both Bernoulli's law and the Coanda effect.

Meanwhile, at the bottom, air is deflected down which can only be caused by a higher pressure underneath the wing. This effect is small (even negligible) at small angles of attack, but becomes much more important at higher AOA.

Is this a bit closer to the truth already? Or is there any other way of explaining how a wing works without either oversimpiflying or resorting to complicated and unintuitive math?

Thanks,

Michel