Aircraft lift - is it all Bernoulli's principle?

[PeterPeter]

I find it hard to believe that the only factor important in computing aircraft lift is Bernoulli's principle.

Doesn't good old Newton's Second Law play an effect? In other words simply deflecting the airflow downwards.

Does anyone know the relative importance of these factors? (EG for a Jumbo which weighs say 333 metric tons. Area of wings 511 sq m according to Wolfram Alpha. I'm not sure what the slowest speed is a 747 can fly in level flight or the angle of the wings.)

 

[Matterwave]

Yes, Newton's third (I think you meant third) law certainly plays an effect. That is why wings on airplanes are angled, and that is also how some airplanes can fly upside down.

I don't know off the top of my head the relative importance of the two factors.

 

[A.T.]

Does anyone know the relative importance of these factors?

These aren’t additive factors. These are different models on different levels of abstraction. Both must account for 100% of the generated force in their own way.

 

[rcgldr]

I find it hard to believe that the only factor important in computing aircraft lift is Bernoulli's principle.

To use Bernoulli, the wing is used as a frame of reference and there needs to be some method obtain the relative speeds of the air flow over and under a wing, which is complicated (a simplified version of Navier Stokes). Given the speeds, then Bernoulli equation is a close approximation.

If using the air as a frame of reference, Bernoulli is violated, since the air is accelerated mostly downwards (lift) and somewhat forwards (drag), resulting in an energy increase. Although using the air as a frame of reference is valid for explaining how lift is generated, it's not good for trying to compute lift.

 

[sophiecentaur]

That puts it rather well, I think.
This (regular) topic often turns into a big-endian vs little-endian dialogue of the deaf and doesn't acknowledge the difference between basic principles and the pragmatic need to design wings. It always amazes me that people ignore that ultimately air (or something) needs to be forced downwards in order to produce a lift force.

 

[Jozsef]

That puts it rather well, I think.
This (regular) topic often turns into a big-endian vs little-endian dialogue of the deaf and doesn't acknowledge the difference between basic principles and the pragmatic need to design wings. It always amazes me that people ignore that ultimately air (or something) needs to be forced downwards in order to produce a lift force.

Indeed, the principle of Bernouilli is not the only lift generating mechanism. Differential pressures, resulting from differential speeds of airflow above and under the wing, refer only to asymmetric wing designs. ( upper cross section distance > lower cross section distance). With such wings, inverted flight should result in a downward force, making level fight impossible. A wing also deflects the incoming airflow downwards in respect with its angle of attack. This is the angle that the plane of the wing makes with the horizontal airflow on its border of attack ( = the front of the wing). The larger the angle of attack, the more mass of air is deflected downwards. The action - reaction law of Newton postulates that the force (momentum) with which the air is forced downwards must result in an equal but opposite force (momentum). It is this opposite force that pushes the wing upwards. This last is a very important lift generating mechanism especially in acrobatic airplanes with more symmetric wing designs ( upper cross section distance = lower cross section distance). It also explains the possibility of sustained inverted flight.

 

[D H]

These aren’t additive factors. These are different models on different levels of abstraction. Both must account for 100% of the generated force in their own way.

Exactly. They are just different ways of looking at it, and both are rather simplistic ways of looking at lift. If you want to design a wing you need to use considerably more advanced mathematics than conservation of momentum and Bernoulli's principle.

Conservation of momentum doesn't say a thing about what causes that air flow to be turned downwards, and because of that, it doesn't say a thing about what constitutes a good versus bad wing. Bernoulli's principle doesn't explain why air flows faster over the top of the wing compared to the bottom, and because of that it too doesn't say much about what constitutes a good versus bad wing.

 

[CWatters]

The reply by A.T. gets my vote.

Its interesting to look at plots of lift vs angle of attack. For many normal looking wing sections the "zero lift angle" is actually negative. Eg they produce positive lift even at small negative angles of attack.

I point this out just for interest not as evidence for or against B or N models of lift.

 

[cjl]

Indeed, the principle of Bernouilli is not the only lift generating mechanism. Differential pressures, resulting from differential speeds of airflow above and under the wing, refer only to asymmetric wing designs. ( upper cross section distance > lower cross section distance).

Not at all. Symmetric airfoils only generate lift at a nonzero angle of attack, and the speed of the airflow over the top of a symmetric airfoil at a positive angle of attack is much greater than the speed of the air below the wing. Also, your parenthetical comment seems to indicate that you subscribe to the equal transit time assumption (that the air traveling over the top of the wing goes faster because it must travel farther in the same amount of time). This is false - the transit time of the air over the top of the wing is actually shorter than the transit time beneath the wing for a wing generating lift. There is no physical mechanism that would force the air to take the same time traveling around both sides of the airfoil.

With such wings, inverted flight should result in a downward force, making level fight impossible. A wing also deflects the incoming airflow downwards in respect with its angle of attack. This is the angle that the plane of the wing makes with the horizontal airflow on its border of attack ( = the front of the wing). The larger the angle of attack, the more mass of air is deflected downwards.

While it is true that the larger the angle of attack, the more air is deflected, it is also true that the larger the angle of attack, the greater the speed differential between the top and bottom surface of the airfoil (and thus, the greater the pressure differential).

The action - reaction law of Newton postulates that the force (momentum) with which the air is forced downwards must result in an equal but opposite force (momentum). It is this opposite force that pushes the wing upwards. This last is a very important lift generating mechanism especially in acrobatic airplanes with more symmetric wing designs ( upper cross section distance = lower cross section distance). It also explains the possibility of sustained inverted flight.

As A.T. said, these are not two separate, additive mechanisms that generate lift. Each must account for the entirety of the lift. If you draw a control volume around the aircraft right at the surface of the aircraft, the pressure distribution (which can be calculated from a known velocity field by using the Bernoulli equation for a sufficiently subsonic aircraft) on the skin of the aircraft must account for 100% of the lift, since the pressure on the aircraft skin is the only force acting on the aircraft. Similarly, if you draw a large control volume around the entire aircraft including a signficant amount of air, there must be a net momentum flux downwards out of the control volume in order to account for the force required to keep the aircraft flying.

 

[A.T.]

Differential pressures, resulting from differential speeds of airflow above and under the wing, refer only to asymmetric wing designs.

Why "only"? Differential pressures and differential speeds happen at symmetric profiles too, if the angle of attack is not zero.

 

[D H]

Indeed, the principle of Bernouilli is not the only lift generating mechanism. Differential pressures, resulting from differential speeds of airflow above and under the wing, refer only to asymmetric wing designs.

Bernoulli's principle still explains inverted flight. That it doesn't is a canard.

Here's a link to the hyper physics page on airfoils: http://hyperphysics.phy-astr.gsu.edu/hbase/fluids/airfoil.html. Note that it clearly resolves the Bernoulli's principle vs Newton's laws debate:

If the question is "Which is physically correct?" then the answer is clear -- both are correct. Both are based on valid principles of physics. The Bernoulli equation is simply a statement of the principle of conservation of energy in fluids. Conservation of momentum and Newton's 3rd law are equally valid as foundation principles of nature - we do not see them violated.​

The only problem I have with that discussion is that the so-called Newton's third law route doesn't invoke Newton's third law! It would be better titled the conservation of momentum argument. To invoke Newton's third law you would have to be looking at third law force pairs. The lift on the aircraft and the downturning of air flow do not constitute a third law action-reaction pair.

The nice thing about the conservation laws is that they provide a very powerful tool for hand-waving all the nitty-gritty details away. Sometimes that's great. But when you want the nitty-gritty details (e.g., "Is this a good wing design?"), they're not so great.

 

[rcgldr]

To invoke Newton's third law you would have to be looking at third law force pairs.

Newton third law pair, the wing pushes downwards and a bit fowards on the air, the air pushes upwards and a bit backwards on the wing. If not in a ground effect situation, then the force that the wing exerts onto the air results in acceleration of the air (in level flght, gravity prevents the aircraft from accelerating upwards).

 

[D H]

Newton third law pair, the wing pushes downwards and a bit fowards on the air, the air pushes upwards and a bit backwards on the wing. If not in a ground effect situation, then the force that the wing exerts onto the air results in acceleration of the air (in level flght, gravity prevents the aircraft from accelerating upwards).

That works quite nicely in my regime, drag and lift on a spacecraft in low Earth orbit. The spacecraft is long gone by the time a molecule that has hit a spacecraft interacts with other air molecules in the extremely sparse atmosphere at that altitude. The mean free path is so very, very long up there. All I have to do is model the density, mean mass, and mean relative velocity of those molecules, and model their interaction with the spacecraft statistically. Some fraction of the colliding molecules bounces off specularly, another fraction bounces off diffusely, and a third fraction collides inelastically, eventually sliding off at near zero relativity velocity. The various fractions are a function of the surface. Lift and drag on an orbiting spacecraft is easy. No Bernoulli's principle, no Reynold's number nonsense, no modeling of fluid flow, no modeling of flow separation, no modeling of shock and turbulence.

That explanation doesn't work for a plane flying through a dense atmosphere. That redirected air flow is many, many third law interactions removed from the molecules hitting the bottom of the plane's wing (and not so many hitting the top). Conservation of momentum is a more appropriate name for that explanation of lift rather than Newton's third law.

 

[cjl]

That works quite nicely in my regime, drag and lift on a spacecraft in low Earth orbit. The spacecraft is long gone by the time a molecule that has hit a spacecraft interacts with other air molecules in the extremely sparse atmosphere at that altitude. The mean free path is so very, very long up there. All I have to do is model the density, mean mass, and mean relative velocity of those molecules, and model their interaction with the spacecraft statistically. Some fraction of the colliding molecules bounces off specularly, another fraction bounces off diffusely, and a third fraction collides inelastically, eventually sliding off at near zero relativity velocity. The various fractions are a function of the surface. Lift and drag on an orbiting spacecraft is easy. No Bernoulli's principle, no Reynold's number nonsense, no modeling of fluid flow, no modeling of flow separation, no modeling of shock and turbulence.

Very interesting - I took a PhD level course in college on molecular gas dynamics/DSMC, and I wish I'd had more time to study it in greater detail. What fraction do you usually assume for the inelastic collisions? I was under the impression that very nearly 100% either reflected diffusely or specularly (with the outgoing velocity of the diffusely reflected molecules dependent on the temperature of the surface and the level of thermal accommodation), but it's been a few years, and I may have forgotten some portions of what I learned. I assume from your description that you're dealing with knudsen numbers >>1?

 

[A.T.]

That redirected air flow is many, many third law interactions

There are as many third law interactions, as you choose there to be. Including the choice of just one, between the wing and the airmass.

 

[WhatIsGravity]

The general angle of attack on a wing for non-compressible flow aircraft is about 20 degrees, tapered towards the fuselage to ensure they don't go into a spin if they stall. Funny, I'm actually just quoting a pilot who flew me around for a while. The Bernoulli effect of lift is not much, unless you''re talking high velocity... 700km/hr or so.

 

[D H]

Very interesting - I took a PhD level course in college on molecular gas dynamics/DSMC, and I wish I'd had more time to study it in greater detail. What fraction do you usually assume for the inelastic collisions? I was under the impression that very nearly 100% either reflected diffusely or specularly (with the outgoing velocity of the diffusely reflected molecules dependent on the temperature of the surface and the level of thermal accommodation), but it's been a few years, and I may have forgotten some portions of what I learned. I assume from your description that you're dealing with knudsen numbers >>1?

We take whatever numbers the people who model the objects using CFD and/or study behaviors in vacuum chamber tell us to use. As far as Knudsen number: At least 10, typically 100 or more.

There are as many third law interactions, as you choose there to be. Including the choice of just one, between the wing and the airmass.

Put a book on a table in a vacuum chamber at the south pole. The downward force the book exerts on the table is equal but opposite to the upward force the book exerts on the Earth. By most definitions, those forces do not constitute a third law pair.

There's but one intermediary, the book, that stands between the force on the table and the force on the Earth. There are many, many intermediaries that stand between between lift and the downturned air flow. By my book, neither my example nor the lift and downturned air flow qualify as a third law action-reaction pair.


Note well: I'm not saying this is an invalid explanation of lift. It most certainly is valid. Conservation laws are very important precisely because they let us bypass all those intermediary interactions. I'm just quibbling over the name of this explanation.

 

[D H]

The general angle of attack on a wing for non-compressible flow aircraft is about 20 degrees, tapered towards the fuselage to ensure they don't go into a spin if they stall. Funny, I'm actually just quoting a pilot who flew me around for a while. The Bernoulli effect of lift is not much, unless you''re talking high velocity... 700km/hr or so.

That's exactly backwards. Bernoulli's principle works fine for low velocity flight. Bernoulli's principle doesn't apply to high speed flight because the simplifying assumptions that underlie Bernoulli's principle don't hold at high speeds.

 

[cjl]

The general angle of attack on a wing for non-compressible flow aircraft is about 20 degrees, tapered towards the fuselage to ensure they don't go into a spin if they stall. Funny, I'm actually just quoting a pilot who flew me around for a while. The Bernoulli effect of lift is not much, unless you''re talking high velocity... 700km/hr or so.

Bernoulli is most applicable at low speeds (below mach 0.3ish, which is around 100m/s). Above that, compressibility effects start to impact its accuracy. As for the angle of attack? 20 degrees is above stall for most wings, and high angles of attack create enormous amounts of drag. Most aircraft fly around with a few degrees of AoA, not ~20.

 

[sophiecentaur]

This has gone the way I predicted. There is no end to it if people can't accept that the two ideas are not contradictory.
If you want an object to stay in the air, there has to be an upward force on it and that can only come, when the object is in a fluid, by the constant reaction against fluid being moved downwards. If this were not true then we could have sky hooks and many other things, impossible in the real world. Bernouli works but it doesn't (need to) take into consideration what is happening to the air at a distance from the wing. The pressure difference gets smaller and smaller as you get further away - but it doesn't mean that there isn't a net downwards movement of a mass of air.
And it is merely quibbling to say that Bernouli is an approximation and that there is a 'better' pressure argument. The only pressure argument that will work is one that includes the pressure exerted on the whole of the Earth's surface - which, in total, must produce a force equal to the weight of the object.

 

[boneh3ad]

Ha, I'd argue this has gone better than most of these threads do.

 

[D H]

I agree. Most of them are the old "Great Taste...Less Filling" debate revisited.

 

[A.T.]

Put a book on a table in a vacuum chamber at the south pole. The downward force the book exerts on the table is equal but opposite to the upward force the book exerts on the Earth. By most definitions, those forces do not constitute a third law pair.

There's but one intermediary...

There are as many intermediaries, as you define there to be. You can define the objects such that there are only two of them, so no intermediaries anymore. The same is valid for wing and air mass.