# What's wrong with this argument that aerodynamic lift really does rely on Bernoulli? [duplicate]

There is a grade-school explanation of how a wing works that goes approximately like this (although I'm leaving out an erroneous bit):

Because of the geometry of the way the wing meets the air, air accelerates as it goes over the top of the wing. There is something called Bernoulli's Principle that says that the pressure of a fluid decreases as its velocity increases. Because the pressure against the top is less than the pressure against the bottom, there is lift.

The oft-included erroneous bit is a claim about why the air speeds up over the top. The claim is that the air along the top has to make it over in the same length of time that it would have taken to go along the bottom. Since it has a longer trip over the top, the story goes, it has to go faster. This is not the right reason at all. There is no rule of equal transit time and, in fact, the air along the top of the wing takes less time to get to the trailing edge.

People often point to that error and say it shows that the Bernoulli effect is not a correct explanation for flight. For instance, this question makes the assertion that the Bernoulli effect is "at best a minor contribution to the actual lift", and none of the answers contradict this. But seems to me that the true situation only makes the Bernoulli effect even more important, because the acceleration of the air stream is greater than you would think if you believed the equal-transit-times story. Why is this wrong?

I also hear that it isn't the Bernoulli effect, it's that the wings redirect the air downwards. But it does not seem to me that those two explanations are mutually contradictory. If they are, I would like to understand that as well.

• possible duplicate of What really allows airplanes to fly? Commented Jul 19, 2015 at 15:50
• I really like your question! I think others might not read through everything because they are bored by the same question asked over and over again. However, you did not ask why airplanes would fly, but why Bernoulli is not capable of explaining it. Commented Sep 26, 2015 at 8:51

You are right, the two explanations are not mutually contradictory.

There are two ways of caluclation the lift on an airplane. You can look at the total mass of air being deflected downward by the wing, and equate the rate of change of momentum of the air to the upward force on the airplane. This is exactly what is going on, and for my money it is the real "reason" the airplane stays in the sky.

Or you can do an inch-by-inch analysis of the surface of the wing and calculate the pressure at each point by Bernoulli's equation. It turns out that the airflow velocities along the wing surface configure themselves so that, added up and integrated appropriately, the total pressure difference between the top and bottom surfaces equates to the same lifting force that you get from the other calculation...the overall downward thrust of the air.

But if you're trying to explain what holds an airplane up in the sky, the Bernoulli's analysis is ridiculous. It's the downwash from the air that holds the airplane up. Just like a helicopter beating the air downwards...would you try to explain that by Bernoulli's principle?

• I guess this is asking for detail beyond my original question, but how does the wing direct the air downward? Commented Jul 19, 2015 at 16:44
• I have to disagree with your last two paragraphs. You don't have to do piecewise analysis to understand that the wing pulls the air into a downwash because of Bernoulli's principle. The answer from BillOer, while he should have said more, points to the best explanation I've ever seen. (And I'm a pilot.) Commented Jul 19, 2015 at 18:08
• The wing pushes air down because of the angle of attack. But I don't know any way to calculate exactly HOW MUCH air gets pushed down, either from the angle of attack or by some kind of Bernoulli's Principle analysis. But assuming that the wing is actually functioning properly (not stalling or anything like that) I think you'd get a pretty good estimate by multiplying the effective cross section by the velocity of the airplane. Commented Jul 20, 2015 at 6:26
• @Dunlavey And yes, I've been a big fan of the John Denker website since I first saw it about ten years ago. Commented Jul 20, 2015 at 6:27

Put very simply: An airfoil produces lift because of angle of attack; the leading edge of the wing is higher than the trailing edge. This imparts momentum to the air through which the wing passes and also changes the potential energy of that parcel of air.

John Denker's website See How it Flies probably has one of the best and most straightforward explanation of lift I've ever seen. It is worth a read.

• Welcome to Physics! Whilst this may theoretically answer the question, it would be preferable to include the essential parts of the answer here, and provide the link for reference. Commented Jul 19, 2015 at 17:51
• Fair enough. I just didn't want to "parrot" another source. I will formulate a proper response and post it shortly. John Denker (the author) has changes his site more than once. Commented Jul 19, 2015 at 18:16
• That is a good source. I wasn't looking for a general explanation of flight, but this one basically answers my question, if I understand it correctly to say that Yes, Bernoulli's principle is key (but you can still think in terms of action/reaction). Commented Jul 20, 2015 at 1:49
• dmckee - I was under the impression that, even in the case of a jet airliner, the top of the wing was in some sense "more important" than the bottom, and that air extending some distance above the wing is redirected downward. I couldn't see how to make sense of that except to think that some variant of the Bernoulli effect was in play. Is that wrong? Basically, I didn't think "angle of attack" by itself was an explanation; I thought that once the right one was chosen, you would still get faster airflow and hence lower pressure over the top. Is there some other phenomenon? Commented Jul 20, 2015 at 2:37
• Bernoulli effect still doesn't explain lift; it's just the beginning of it. It's like saying soda gets sucked up your straw because you suck on the straw. What actually happens is the lower pressure inside the straw allows normal atmospheric pressure to push the liquid up the straw. Bernoulli equations can be used to predict the behavior of a wing, but it doesn't fully explain how. Bernoulli happens, but it is what redirects the air above the wing and imparts momentum to that air. And it doesn't happen because the wing is longer on top; it happens because of angle of attack. No AOA, no lift. Commented Jul 20, 2015 at 5:13