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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?

jaysonpowers
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    There's obviously no way anyone can comment without seeing the actual content of the book. –  May 02 '13 at 12:33
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    http://www.airspacemag.com/flight-today/Upside-Down.html: "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 02 '13 at 12:39
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    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 May 02 '13 at 12:40
  • That does help, and he did mention airfoils in his book. – jaysonpowers May 02 '13 at 12:58
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    related: http://physics.stackexchange.com/questions/290/what-really-allows-airplanes-to-fly –  May 02 '13 at 13:13

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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.

user1247
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    If you downvote, please comment. My answer is correct and canonical. – user1247 May 02 '13 at 12:40
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    Ramming the air downwards is totally wrong: http://www.av8n.com/how/htm/airfoils.html#sec-fluid 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 May 02 '13 at 12:46
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    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 May 02 '13 at 12:49
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  • 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 02 '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 03 '13 at 01:34
  • @Michael Brown, you are just plain wrong. What matters, as I said in my post, is "directing air flowing over the wings downward". This is obvious by conservation of momentum. There can not possibly ever be any other explanation, unless you don't believe in Newtonian mechanics. The camber of the wing plays a minor role, but to first order the role of the wing shape, in addition to the angle of attack, is merely to direct air downwards and thus produce positive lift by momentum conservation. Bernoulli's principle is one way of thinking about an aspect of this, but to focus on it is naive. – user1247 May 03 '13 at 01:38
  • @user1247 Jeez, that's what I said! You're acting like Bernoulli's principle is a completely seperate thing. It's not. Your assertion that a wing rams air downwards implies a physical picture which is visually appealing but very wrong (see the link I posted), even if it's not what you meant, so it is still a bad explanation. Of course air goes downwards, I never argued against that. Bernoulli's principle is one of the laws of fluid motion. Without it you couldn't solve for the flow field. To de-emphasize it is naive. – Michael May 03 '13 at 01:58
  • Let me put it this way. Is the pressure on the top surface of the wing lower than on the bottom? Yes. This is not controversial among aerodynamicists! How do you expect the momentum flow in the downwash to be balanced by a force on the wing if not by a pressure gradient over the surface of the wing? There is simply no other possibility. You could imagine that air recoils from the bottom surface of the wing. This is the bullet picture in the link I sent and it is wrong because air is a fluid. Downwash implies Bernoulli and vice versa. AOA is necessary to set up the flow field but that is all. – Michael May 03 '13 at 02:17
  • @Michael Brown, I think you over-reacted to my use of the term "ram". I am in no way advocating the "bullet picture." The use of the term "ram" is meant to emphasize the principle reason air is being directed downward. It is due to the wing's angle of attack. The camber is meant more to keep the flow laminar than to produce via Bernoulli a lower pressure on top due to air travelling faster. I think we essentially see things the same, however I think that to emphasize the word "bernoulli" at all when discussing wing lift can give a completely wrong impression to the lay person. – user1247 May 03 '13 at 11:13
  • @Michael Brown, in other words, there is not some magic "lower air pressure on top, higher on bottom" produced by the camber that causes lift. The main principle is simple: use angle of attack to direct air downward. As you say yourself, the Bernoulli effect is secondary, or at the very least both pictures exist. But if you invoke Bernoulli as the primary explanation, you can leave one with completely wrong impressions such that a wing with 0 angle of attack (and atypical tailing edge) that does not direct air downwards and yet could somehow produce lift by making air go faster over the top. – user1247 May 03 '13 at 11:23
  • @user1247: Please read. – Mike Dunlavey May 03 '13 at 11:47
  • @Mike Dunlavey, I don't see anything in your link (I have no idea why you would consider it authoritative, btw) that contradicts anything I have said. – user1247 May 04 '13 at 03:23