How much effect does the Bernoulli effect have on lift?

I understand that the Bernoulli effect is a flawed explanation for the cause of lift, and does not cause much at all, but how much?

Is there any experimental data on the force caused by the Bernoulli effect? Maybe implicitly through data of the pressure difference between the top and underside of an aeroplane's wings. After that, I assume I could (crudely approximating the pressure to be acting perpendicularly to the flight direction) use $\Delta P A$ to work out the net force on the plane.

Perhaps there is another way to quantitatively analyse the extent to which the Bernoulli effect causes lift.

Edit: see this short cartoon (content similar to Mike Dunlavey's answer).

• Yeah, that video is pretty good. The only question is it refers to the Coanda effect above the wing. Denker explains why that's not right. – Mike Dunlavey Jun 21 '13 at 12:39
• – Ben Crowell Jun 21 '13 at 13:26
• Agree that the video is pretty good. Denker makes a very good point about the Coanda effect - in its strict definition, it requires a plume or jet of air, which is not present around a typical airplane wing. However, many people use a broader definition where it refers to the tendency of a swath of air to follow the curve of a convex surface. So it's really an argument over semantics. Personally, I don't like to explain lift that way, because calling it the "Coanda Effect" doesn't actually explain anything, it just gives it a fancy name. – Paul Townsend Aug 25 '15 at 14:58

There's no problem with the Bernoulli effect, only with the way it's understood and explained. It's usually explained with mistakes, like the need for asymmetrical airfoil and equal flow time above and below, and without mentioning the need to deflect the direction of airflow.

Here's the best light-math explanation I've seen. Also study this section that directly answers your question.

EDIT: It is easy to find wrong pictures like this:

as opposed to a correct one like this (from the link above):

So the answer to your question is: All of the lift depends on the Bernoulli principle, because speed and pressure are in trade-off, but the physics need to be correctly understood.

• It is equally true that all the lift depends on the change in airflow direction. You have to calculate one or the other but not both. – Marty Green Jan 18 '13 at 17:53
• @mike Thanks Mike. I'm not used to people agreeing with me. – Marty Green Jan 18 '13 at 18:46
• @Alyosha: There really isn't a larger thing. If you really want basics, you can go back to Newton's laws. Bernoulli's principle is just a consequence of Newton's laws. – Mike Dunlavey Jan 18 '13 at 19:47
• @Alyosha: Pretend you're a wing. You can only be lifting if the pressure underneath exceeds the pressure above. Then pretend you're a slug of air. This wing comes along, cuts you in half, then pulls/pushes you downward. Same thing. – Mike Dunlavey Jan 18 '13 at 22:05
• +1 Very good answer. I've seen many comments/answers on this site that unnecessarily bash Bernoulli because the author equates Bernoulli with the incorrect "equal time" explanation. Glad to see someone else trying to set the record straight. – OSE Jan 27 '14 at 20:17

Sometimes you will see statements like 'some of the lift is caused by Bernoulli's principle and some of it is caused by Newton's laws", but this is the wrong way to think about it. The fact is that 100% of the lift can be explained by Newton's laws and 100% can be explained by Bernoulli's equation. Both approaches explain 100% of the lift.

The problem is that popular explanations using Bernoulli's principle usually make a dog's breakfast out of things, so I understand why you think it's a "flawed" explanation - usually it is. However, applied correctly Bernoulli's equation can be used to predict 100% of the lift.

To grossly oversimplify things, classical aerodynamics calculates lift something like this:

• write down the differential equations expressing conservation of momentum, conservation of energy, and conservation of mass.
• solve those differential equations and apply boundary conditions to get a solution
• the solution is a vector field that represents the speed and direction of the airflow at each point in space
• Forget about the direction and just use the magnitude of the vector - this is the speed
• Now that you know the speed everywhere, use Bernoulli's equation to substitute pressure for speed
• integrate the pressure over the airfoil surface to get the lift.

Done correctly, this number is 100% of the lift. So, Bernoulli's principle is responsible for 100% of the lift. The thing is, almost all of the physics is in step one - the rest is a bunch of hairy math and then a calculational trick at the end to use Bernoulli's equation to turn speed into pressure. This trick (mis)leads some into thinking Bernoulli's equation somehow "explains" the physics, but without the context of the rest of steps it makes little sense.

If you look at the overall context you'll see that Bernoulli's equation is a small and relatively unimportant part of the overall theory. But correctly applied, it predicts 100% of the lift.

I take it as self-evident that lift can be generated by a wing without any difference whatsoever in the shape of the top or bottom of the wing. After all, balsa wood gliders (or ones that are rubber band powered) fly just fine with completely flat wings. If you look at such a plane, you will see the wing is set at an angle relative to the longitudinal axis of the fuselage: the wing is tilted upwards at the front relative the rear. In normal flight, the relative wind strikes the bottom of the wing and pushes it upward (Newton's law). Curvature of the upper surface of the wind improves the lift due to the Bernoulli effect. (But from what Mike Dunlavey says above this is not necessary for the Bernoulli effect to operate.) I have understood that the other factor producing lift in a wing is "ram effect" caused by the wind striking the bottom of the wing due to the slight positive angle of attack the wing has in level (cruise) flight. Now planes can fly inverted, but since the wing's fixed angle of attack and the so-called Bernoulli effect (or whatever it is) now operate in conjunction with gravity to pull the aircraft toward the ground, the pilot must fly with an exaggerated nose-up attitude to maintain level flight. This allows the wind to strike the upper surface of the wing (remember, the plane is inverted) with sufficient force to compensate for these factors. This additional ram effect keeps the plane flying when inverted. I think M. Dunlavey might subsume what I am calling ram effect under his interpretation of a correct explanation using the Bernoulli effect. If so, I have no problem with it. But I find the concept of ram effect more accessible, and it has good lineage, going back to the Wright brother's concept of center of pressure of the wing.

• I clicked on the embedded link called "this-section" in Dunlavey's comment above, and found that it clearly explains all of the issues relating to lift, and how they are all simply different ways of addressing the effects of circulation patterns in the air flowing over the wing. My comment above is addressing the Bernoulli vs ram effect interpretations, but of course I am contrasting ram with the "incorrect" Bernoulli interpretation... – Adak47 Jul 22 '14 at 1:23
• Hey Adak47, you should space out your answer better so it's easier to read. – Brandon Enright Jul 22 '14 at 2:07
• Could you be more specific about what you mean by "space out your answer better"? Do you mean the physical spacing of the lines of text, the conceptual spacing of the ideas presented, or something else? – Adak47 Jul 22 '14 at 14:37
• Physical spacing - a little whitespace from a paragraph break or two would make it much easier to read. – Gregor Sep 1 '16 at 16:59

I cannot say exactly how much the Bernoulli Effect contributes to lift but it is not much. Cambered wings and barn doors fly inverted. Air speed increase is the same as the increased distance ratio. not enough to produce much lift. The wing tries to generate a ring vortex. This gets thwarted because the roll up around the trailing edge, called the "starting vortex" is shed before takeoff. This leaves, in plan view, a horseshoe shaped vortex consisting of the "bound vortex" and the two tip vortices. Stretch your mind here! The "Bound Vortex" is not convection, it is diffusion. It is a molecular knock on effect and travels at sonic speed around the wing forward underneath and stream direction on top and rolls up around the tips. Some air follows the diffusion around the tips and that is convection. The pressure above a wing is not reduced because of accelerated air, The pressure is reduced first by the bound vortex which then accelerates the air. The wing is a pump. Air from 18 feet above a Cessna 172 is accelerated down at 5 tons/second in normal flight. Thats how Newton is involved.. For every action..... Before responding check a text book on aerodynamics. See also www.newfluidtechnology.com.au "The Coanda Effect and Lift".

• ++ Your PDF is a much better explanation than your answer here. When you denigrate the Bernoulli Effect, you're referring to the version commonly and incorrectly taught. With some editing, this could be a nice answer. – Mike Dunlavey Jun 21 '13 at 12:54