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I'm a computer scientist that likes to read about math and physics occasionally. A local author at a nearby aviation center brought bernoulli's flight equations into question.

It was clear enough logic, but I didn't understand all the math involved. He basically said that the lift equations don't account for why a plane can have lift while it's still upside down and took some sample data on his small aircraft to show.

Anyhow, I didn't know what to make of it, my only point of view and my first acquaintance with flight physics.

How much effect does Bernoulli's equations play in flight, especially when an aircraft is upside down?

He suggested that Newton did some early work on lift equations, is this true?

What is a sufficient way to view Bernoulli's lift equations?

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marked as duplicate by Ben Crowell, Waffle's Crazy Peanut, Qmechanic May 2 '13 at 19:05

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

There's obviously no way anyone can comment without seeing the actual content of the book. – Ben Crowell May 2 '13 at 12:33
2 "Most airfoils are cambered, or curved, on top but flat on the bottom. As a result, they fly better upright than inverted. Symmetrical airfoils, which have the same curvature on both surfaces, perform exactly the same upright or inverted, and so are favored by aerobatic pilots. In order to fly at all, however, a symmetrical airfoil must be positioned at a slight positive angle—leading edge high—with respect to the flight path; otherwise the airflow around the upper and lower surfaces would be the same, and no lift would be created." – Wandering Logic May 2 '13 at 12:39
Can't really address the book without clearer info, but try here for a good accessible discussion of the aerodynamics of flight. Short story: Bernoulli works perfectly well, though the shape of the wing doesn't come into it in the way a lot of people think it does, and a lot of other things people say don't work at all. – Michael Brown May 2 '13 at 12:40
That does help, and he did mention airfoils in his book. – mathacka May 2 '13 at 12:58
related:… – Ben Crowell May 2 '13 at 13:13
up vote 2 down vote accepted

It is absolutely true that the Bernoulli effect is not necessary in order for a wing to produce lift. Ultimately a wing produces lift by directing air flowing over the wings downward. The can be achieved by ramming air downward through the wing's "angle of attack" with respect to the air flow. This is why an airplane can fly upside down: the Bernoulli effect plays only a minor role, and the angle of attack is the primary force in guiding air downwards. The shape of the wing is not simply designed with the Bernoulli effect in mind: the goal is to produce smooth laminar flow of air over the wings so that the angle of attack (along with the shape of the tailing edge of the wing) can efficiently direct the air downward. A stall is when that laminar flow is disrupted such that the air no longer follows the shape of the wing and so can no longer be directed downward by the wing's shape and angle of attack.

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If you downvote, please comment. My answer is correct and canonical. – user1247 May 2 '13 at 12:40
Ramming the air downwards is totally wrong: The Bernoulli effect is indeed the operative principle for an airfoil, but the shape of the wing doesn't come into it like a lot of people think. It works just fine for symmetrical airfoils if they are at a nonzero angle of attack. – Michael Brown May 2 '13 at 12:46
Actually the more proper way to think about it is wing induced circulation, but that's getting into a whole other level of fluid mechanics. There is air going downwards, of course, by conservation of momentum. But "ramming air downwards" is the wrong way to get there. – Michael Brown May 2 '13 at 12:49
+ You're right to say "produces lift by directing air ... downward". You're not quite right to de-emphasize the Bernoulli effect. The page Michael Brown linked to explains it quite well. You can't really separate the downwash effect and the Bernoulli effect. The only problem with the Bernoulli effect is that it's badly taught. – Mike Dunlavey May 2 '13 at 12:52
@Mike Dunlavey, actually, no, you are both wrong. To some extent this comes down to the semantics of whether you refer to my description as a dual description of a Bernoulli effect. But it is plain wrong to imply that the camber of a wing (which would produce lift via Bernoulli) is primary. This is, indeed, why a plane has no trouble flying upside-down. This is simply a fact. The camber is not very important. What is important is directing air downwards (by whatever means). What I said in my answer is absolutely and unequivocally correct. – user1247 May 3 '13 at 1:34

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