# Why an Airplane Flies (Bernoulli's Principle vs. Newton's Third Law)

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A few days ago I started reading Ira Flatow's Present At The Future (On a recommendation), and in the introduction it discusses his misconceptions about why an airplane wing keeps a plane in the air.

On the Bernoulli's Principle 'error':

"Newton, and his laws of motion. You can easily-and correctly-explain why airplanes fly from the first principles. No need to resort to Bernoulli...Airplanes fly because the wing makes the air go down, so the airplane goes up. Action-reaction. Newton's Third law. How hard is that to understand?"

Apparently this is a very common error made by physics teachers across America.

He says that:

[bernoulli] was created-really pulled out of a hat- around World War II when the airplane was becoming popular and people wanted a simple explanation. But in reality it takes more time to explain the complicated workings of Bernoulli's principle than it does the simple laws of Newton.

I'm not entirely sure this is true. The book doesn't give any math; just this explanation.

One of my questions is: How does an airplane's wing make air go down?

It doesn't really make sense to me. I have with me a physics textbook I permanantly 'borrowed' from my 8th grade science teacher, and in it it says:

The air above the wing must be moving faster. According to Bernoulli's Principle, then, the air above the wing exerts less pressure on the wing than the air below the wing. This creates an upward unbalances force that keeps the airplane in the air.

It seems that my textbook's explanation makes a bit more sense, but Flatow's also makes sense (with the exception of the 'air being pushed down by the wing'.

Can anyone shed some light on this?

(If this doesn't make sense, feel free to attribute it to the extremely high heat, and humidity, that's been preventing me from sleeping)

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I agree entirely with your points and will look into it...

I've always been taught the "air moves faster" approach.

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I was taught the same ideas rather recently, so reading that section of the book was interesting; it presented this idea I hadn't yet heard about.

However, after some thought it didn't really make much sense...

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Apparently this is a long-standing debate. I found a great overview of the issue in this article that I found via the Wikipedia article on Bernoulli's Principle, which looks at the issue from the perspective of aircraft pilots:

Bernoulli Or Newton: Who's Right About Lift?

In fact, if you look at five different aviation references, you’re likely to find five different explanations about how lift comes to be. Even worse, some sources advocate a specific theory, while rejecting the premises favored in others.

Those who prefer Newton’s ideas (i.e., Newtonian lift) believe that air is forced downward behind the wing. Simultaneously, the wing is forced upward with the famous “equal and opposite reaction” described in Newton’s third law. Then there are those who favor Bernoulli’s celebrated principle that as airflow accelerates, the static pressure within the airflow drops. We all know that the air flows faster over the top of the wing than the bottom. Bernoulli’s equation therefore concludes that the wing gets “sucked” upward by the reduced pressure.

You pull out the classic Stick and Rudder by Wolfgang Langewiesche and quickly find the statement “forget Bernoulli’s theorem.” Still unsatisfied, you reach for Aerodynamics for Naval Aviators. There you find nothing but Bernoulli and something called “circulation.” You find much of the same while inspecting Aerodynamics for Engineers by John Bertin and the more readable Illustrated Guide to Aerodynamics by Skip Smith. In fact, Newton isn’t even mentioned during the lift discussion in the latter book. To add more fuel to the fire, prestigious academic institutions seem to favor one theory over another. Portions of Harvard’s and Princeton’s Websites discuss Bernoulli as though his ideas are the only ones available.

He goes on to support Newton with several sources, though. Then he declares them both right and delves into some more history.

The truth is that, among the Newton-Bernoulli disputers, neither party is wrong. According to Dr. Jean-Jacques Chattot, professor of Mechanical and Aeronautical Engineering and director of the Center for Computational Fluid Dynamics at the University of California-Davis, the descriptions of lift advocated by Newton and Bernoulli “are actually the same thing, just from two different perspectives.” How is this possible? Take another look at the dates when Newton and Bernoulli lived.

He gets into some science on page 2:

Another common butchering of Bernoulli’s principle is the concept that a wing is a half of a Venturi tube. It’s true that Bernoulli’s equation accurately describes the pressure fluctuations that occur within a Venturi. However, no matter how you slice it, a wing simply isn’t a half of a Venturi! There’s always a tremendous amount of focus on the upper portion of the wing, but the lower surface also contributes to lift. Depending on the angle of attack, portions of the lower surface of the wing may also generate negative pressures. That, however, is hardly mentioned in most discussions of Bernoulli. Lift only occurs if there’s a positive net pressure difference between the bottom and top of the wing (commonly referred to as “high pressure on the bottom, low pressure on the top”).

Long story short:

Now you’re probably thinking, “Great, they’re both right—there’s even more to learn!” Don’t get bent out of shape. Since both concepts are true, you can pick the one with which you’re most comfortable. Bernoulli’s theory tends to be harder to understand and is favored by mathematicians and engineers. Newton’s is palatable to pilots because it’s more intuitive. Regardless of which philosophy you prefer, the important conclusion is that you realize there’s more than one correct way to explain lift.

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But how does a wing push air down? It doesn't really make sense.

You'd expect the wing to 'cut' through the air, not force some of it down, so it gets pushed upwards.

Bernoulli's still makes the most sense...

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Because it's moving past the wing and has to go somewhere. Neither Bernoulli nor Newton address the issue of why the air is moving past the wing. It's really beside the point.

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The airfoil "pushes the air down" due to the Coanda effect.Wiki

Edited by honestdude14
grammar
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So both laws can be used?

Edited by antimatter
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So both laws can be used?

Yes. Bernoulli is a statement of conservation of energy. Newton is conservation of momentum. They both hold. If someone disagrees, ask which conservation law is being violated.

I suspect the controversy arises because in some scenarios it's easier to see that one is true but the other is not at all obvious, e.g. the asymmetric wing usually uses Bernoulli but a symmetric wing uses angle-of-attack. And the standard explanations often get some details wrong (like how continuity is explained) and that is used as an argument to invalidate the whole concept.

———

regarding Coanda: A link from an aeronautical engineer. Read all of 18.4

http://www.av8n.com/how/htm/spins.html#sec-coanda

"You may have heard stories saying that the Coanda effect explains how a wing works. Alas, these are just fairy tales. They are worse than useless."

I don't have the background to vouch for it, though.

Oh.

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In a way, both explanations are both right and wrong.

Newton's third law is key in the sense that any wing that does not push air downward offers zero lift. Bernoulli's law when misapplied (i.e., the pressure differential explanation) doesn't say anything at all about redirecting the airflow.

Bernoulli's law when properly applied is key in the sense that in a well-designed wing, it is the upper surface of the wing that does most of the work in redirecting the air flow downward. Newton's third law doesn't say a thing about why a flat sheet of plywood held at some angle with respect to horizontal makes for an incredibly bad lifting surface. Bernoulli's law does. With the hunk of plywood, it is the bottom surface that does the work, and it accomplishes this through friction (i.e., drag). The same thing happens when a kid sticks his hand out of a car window and pretends the hand is an airplane. That is not what happens with an airplane wing.

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The "air moves faster" approach implicitly assumes one thing -- that the air on the top of the wing and the air on the bottom of the wing have to rejoin. That a volume of air that was split in half by the leading edge reforms into the same volume as the two halves slide off the back of the trailing edge. That actually isn't true. Yes, the air on the top does move faster, but it isn't because it has a farther distance to go and has to "catch up" to the bottom air.

In practice, the way things like life on an airfoil are calculated usually involves the circulation http://en.wikipedia.org/wiki/Circulation_%28fluid_dynamics%29

The circulation is calculated on a wide circle around the wing (usually nowhere near the surface itself to make the calculations/measurements easier). So long as the integration is performed along a continuous closed loop, you can choose any path you want.

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Imagine in a theoretical plane design that a wing is mounted to the plane that moves downwards from the plane. The air is compressed under he wing, the molecules of air squashing together pushes the other surrounding molecules and they bunch up resisting the downwards movement of the plane. The wing gets to it's fully downward point and the molecules have time to move around and spread out evenly again at which point the plane will start to fall. An insect would then tilt it's wing and bring it back up with less resistance for another go.

A real plane however is simpler. It is moving forward in the air. It's wing is at a constant angle and moves forward, the molecules at the front of the wing can easily slide above and below the wing. The molecules below the wing are compressed (squashed together) and as the molecules don't move instantly (momentum) you get a bunching below the wing called lower pressure and higher pressure due to the same mechanism above the wing and the plane is pulled up, fundamentally by pushing air and having the air push the plane.

I understand that mechanism. Is there another plausible one?

Edited by alan2here
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Imagine in a theoretical plane design that a wing is mounted to the plane that moves downwards from the plane. The air is compressed under he wing, the molecules of air squashing together pushes the other surrounding molecules and they bunch up resisting the downwards movement of the plane.

This is exactly the piece of plywood I talked about in post #11. An object whose lower surface accounts for the majority of the lift makes for an incredibly lousy lifting body. A good lifting body maximizes lift and minimizes drag. A wing whose lower surface provides the majority of the lift does exactly the opposite.

Here are three models of force that NASA deems to be incorrect:

• The "equal transit" model. This explanation incorrectly invokes Bernoulli's principle to explain the pressure difference between the windward and leeward surfaces as a result of different transit times. One problem with explanation is that it fails to explain how a plane can fly upside down.
• The "skipping stone" model. This explanation incorrectly invokes Newton's third law to explain lift as a result of action by the windward surface of the wing. One problem with this explanation is that it ignores the action by the leeward surface of the wing, and it is this surface that does most of the airflow deflection in a well-designed wing.
• Venturi effect. This explanation incorrectly invokes Bernoulli's principle to explain the pressure difference between the windward and leeward surfaces as resulting from a constricted flow along the upper surface of the wing. One big problem with this explanation is that an airfoil is not a Venturi nozzle.

Lift can be explained in terms of pressure differences (http://www.grc.nasa.gov/WWW/K-12/airplane/right1.html) or from a downward deflection of the airflow (http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html)

of the airflow, and it is this downward deflection that ultimately gives the body lift.

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And it wouldn't work if air immediately adjusted to moving things in the same way swimming wouldn't work if water immediately adjusted to moving things, you would fall to the bottom like there was no water there.

There must be a more sciency way of putting that.

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The "air moves faster" approach implicitly assumes one thing -- that the air on the top of the wing and the air on the bottom of the wing have to rejoin. That a volume of air that was split in half by the leading edge reforms into the same volume as the two halves slide off the back of the trailing edge. That actually isn't true. Yes, the air on the top does move faster, but it isn't because it has a farther distance to go and has to "catch up" to the bottom air.

This is the "bad continuity equation explanation" I alluded to earlier.

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• 10 months later...

The simplest way that I can explain why you should primarily "believe" Newton's explanation is to look at a helicopter or at an aircraft propeller. Simply put, helicopters fly because they accelerate a mass of air downward. Likewise, propellers accelerate a mass of air backwards to produce thrust. Airplane wings accelerate air downward in exactly the same way. Airplane wings are relatively large and therefore less acceleration is taking place on a larger mass of air than with a propeller.

I was recently reading Skip Smith's "Illustrated Guide to Aerodynamics" and was very disappointed to only see three short paragraphs that dealt with lift due to momentum change.

Edited by oisiaa
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A typical clark y airfoil starts generating lift at about -3.5 degrees angle of attack.

A symmetrical airfoil is used for maximum speed and low drag.

I was taught both principles are correct.

Here is a neat airfoil simulator.

http://www.grc.nasa.gov/WWW/K-12/airplane/foil2.html

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I was taught both principles are correct.

Within the limits of applicability, this is true. Bernoulli's principle assumes certain things about fluid flow, so once those assumptions fail, it no longer applies.

The bottom line is that fluid dynamics is complicated, and these arguments arise from people trying to simplify it.

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I'm pretty sure you can fly a stunt plane upside down until the blood runs to your head.

That means that, at least, not all of the lift is due to the "Bernoulli effect".

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I'm pretty sure you can fly a stunt plane upside down until the blood runs to your head.

That means that, at least, not all of the lift is due to the "Bernoulli effect".

The Bernoulli effect is based on Newton Mechanics. Even wings designed to work "upright" can create lift upside down at the right angle of attack, as can a sheet of plywood. Unless they are totally stalled, they all use the Bernoulli effect to some degree, just not as efficiently. Stunt planes use the effect quite efficiently upside down or right side up, either way.

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• 4 years later...

This is a little late, but 50 years ago I began to doubt the basic Bernouli explanation of pressure difference between the top and bottom of the wing. That doubt was easy to validate by taking 15 psi (max atmospheric pressure at sea level), multiplying it times the the wing area of a cargo plane, and finding the resulting force was not even in the ball park of the max payload to be lifted. Obviously there are a lot more forces generated by other phenomena. Seems to me the only way you can get the lift (force) numbers you need to match payload is the downward redirection of the mass of air above the wing (F=ma). I just can't see any of the pressure differential answers noted by others reaching the magnitudes necessary to multiply times wing area to match payload.

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Let's see, a Lockheed F-104 Starfighter, with one of the highest wing loading of military aircraft ( ie. small wing, high weight ) has a wing area of approx. 190 square feet. That comes out to over 27000 square inches. which means that apressure difference between top and bottom of the wing would be equal to its max take-off weight !

I think you may have made a mistake in your math gnerosy.

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sorry meant to say that a 1 pound difference in pressure would be equal to max take-off weight.

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Lift and weight are forever seeking each other in balance. Lift is an upwards force opposed by weight, the downward force. The airplane MAY develop more lift or more weight in a short time span, but they will balance each other out. If the airplane weighs 100 pounds, it needs to generate 100 pounds of lift. No more, no less. An airplane is 'buoyant' in the air. It displaces the air to remain 'floating'. Excess engine power allows an aircraft to climb or descended. Not lift.

There is not a "Law of Lift", we have some good ideas, but no one actually knows how lift works. There is airflow being turned down off the trailing edge of all airfoils, this is known as Downwash. This downwash is often used to show Newtan's 3rd law. Airflow goes down, airfoil gets lift. Bernoulli is used to describe what happens above the wing. There is a massive low pressure above an airfoil, due to the increased airflow, 'sucking it up.'

Since lift is still considered a mystery, and argued passionately, many flight instructors and pilots simply don't like to bring this topic up. They know that their answer isn't completely right, so we leave it alone. (Like politics and religion!)

I am a flight instructor, to keep things as simple as I can I like to use water to describe what happens to a airfoil. After all, it is fluid dynamics.

The airfoil simply 'floats' in the air, displacing the air to do so. It displaces the air in one of two ways, with a really big engine or it induces it with a really curved airfoil. As the engine gets smaller, the wings get bigger. Compare the SR-71 to a glider.

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