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Most books and science resources say it's because of Bernoulli's principle. That is incorrect.

The correct answer is Newton's 3rd law of motion, with help from the Coanda effect.

The Coanda effect is most easily explained by running some water onto the back of a spoon. If you try that, you will see that the water does not simply run off the spoon in its original path, but will follow the way the spoon curves.

An airplane wing is just like the back of a spoon. As the wing moves through the air, the air above the wing has to travel along a curved path, going up, across, and down while moving back. As the air leaves the wing, it is moving downwards (partially). Since the air was initially just moving across the wing, a downwards force is exerted on the air by the wing.

Newton's 3rd law states that for every action, there is an equal and opposite reaction. For the wing, this means that the air is also pushing the wing up. Since the wing is attached to the airplane, the airplane is pushed up.

You should notice that if the airplane is not travelling fast enough, then it will not fly. This is because even of the air is moving downwards, there is not enough of it to overcome the airplane's weight. Once enough air, larger than the equivalent of the airplane's weight, is pushed down, then the airplane can fly.

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