> >
>

# Theory on lift

Tech Log The very best in practical technical discussion on the web

# Theory on lift

18th Oct 2012, 22:41

Join Date: Jan 2012
Location: Ontario
Age: 71
Posts: 81
Italia,
Thanks for a good overview of the complexities of trying to get to grips with the way air behaves.

I think the author shunned Bernoulli's relation completely by making a revolutionary claim that I have never seen before. It is not one of the regular myths/misapplications that he is repeating. Here's my way of explaining what I think he was saying, and I have repeated his statement at the end:

Focussing on just the wing surface, ie its own map of local curvature variations and static pressure distribution that goes with the curvature.
Knowing the free-stream condition and a measured static on the surface you can calculate the vel at the same point using conservation of energy, ie with Bernoullis relation.
If we now drop a ram air turbine into the flow we can no longer use the relation for points U/S of the turbine and D/S because of the work extraction in between.
We can, of course, use the relation for all points D/S once we have redatumed, if you like, with a new lower total pressure.
Now, just as we say the whole of the lift force occurs from the wing surface pressure distribution we also say the whole of the energy transfer to the air also occurs only on the wing surface.
So energy is not conserved in the airflow over the wing any more than it was with the RAT power extraction.

"As energy is not conserved the Bernoulli relation cannot be applied to airflow round a wing in flight."

Nobody else throws it out for this reason. It's a new one as far as I can tell.

Can you make any sense of it?
19th Oct 2012, 09:10

Join Date: Dec 2001
Location: what U.S. calls ´old Europe´
Posts: 941
This is one that he mentioned: Incorrect Lift Theory
Of course that theory is completely incorrect, it assumes that if the airsteam ahead of the airfoil is parallel to the airstream aft of the airfoil, then lift is produced. Of course bernoulli fails to explain a wrong assumption...

As energy is not conserved the Bernoulli relation cannot be applied to airflow round a wing in flight
Interesting aspect. However, as long as we ignore friction (which we usually do in all those theories), the force generated ("Lift") is perpendicular to the direction of movement, hence there is no work done, a force perpendicular to a movement does not produce work, hence energy is conserved. The same applies to any element of the wing surface, pressure (hence force) is produced perpendicular to the local surface, and therefore perpendicular to the streamlines, so along the streamlines energy is conserved.
But interesting to think about, how a Rat can then extract energy... Or how a propeller can inject energy with bernoulli (constand energy along a streamline) still being valid...
19th Oct 2012, 18:12

Join Date: Jun 2010
Age: 34
Posts: 382
Peter...

I just read the whole article word for word and I agree with his description of lift. It has added a new perspective to my understanding of lift and to me it makes sense.

I'm not sure exactly what you're trying to say but I think it has to do with not seeing where/how energy is added to the system?

Think of the air standing still with reference to the ground and an airfoil comes passing through it. If you look at the air you will see that it gets accelerated from rest (zero velocity) to a positive velocity (speed and direction of movement) as the airfoil passes by. Energy has just been added to the system. So to create lift, energy has to be added to the system to get the air to flow (start moving) around the wing and for downwash to be 'created'. That downwash is then what forces the wing upwards. There are two ways to add energy into the system (ie: accelerating the air): by adding propulsive power to the airplane which gets directly transferred to the airfoil and which transfers that power (energy) to the air, or you have no engine and you use gravity as the 'engine' as gliders do. In a glider, assuming that the air is still and there are no thermals, the glider (while flying at a constant velocity) will have a constant horizontal and vertical component of velocity. That vertical component of velocity is what is adding energy to the system and the factor responsible for that vertical component is gravity.

With regard to Bernoulli: he's basically saying that there is energy added to the system and Bernoulli describes the conservation of energy for a system (where energy is neither added or subtracted from a system) so Bernoulli doesn't apply. Bernoulli is a mathematical description of an effect that happens in a closed system. Bernoulli doesn't say this:
Think of two adjacent streamlines with different speeds. Since these streamlines have different velocities forces between them trying to speed up the slower streamline and slow down the faster streamline. The speed of air at the surface of the wing is exactly zero with respect to the surface of the wing. This is an expression of viscosity. The speed of the air increases with distance from the wing. Now imagine the first non-zero velocity streamline that just grazes the highpoint of the top of the wing. If it were initially to go straight back and not follow the wing, there would be a volume of zero velocity air between it and the wing. Forces would strip this air away from the wing and without a streamline to replace it, the pressure would lower. This lowering of the pressure would bend the streamline until it followed the surface of the wing. The streamlines are bent by a lowering of the pressure. This is why the air is bent by the top of the wing and why the pressure above the wing is lowered. This lowered pressure decrease with distance above the wing but is the basis of the lift on a wing. The lowered pressure propagates out at the speed of sound, causing a great deal of air to bend around the wing.
That is essentially what is happening on a real wing. Like others have said, you need to have viscosity to produce lift. If the molecules weren't 'connected' to each other then they would have no 'communication' between streamlines and you could end up with a condition where one streamline has a velocity of 10 m/s and the two adjacent streamline velocities are 200 m/s and 3000 m/s, all while travelling in a straight line! If that were the case you would not have the air bending, and you would therefore not have any downwash.... meaning no lift.

Last edited by italia458; 19th Oct 2012 at 18:28.
19th Oct 2012, 18:39

Join Date: Jun 2011
Location: france
Posts: 759

19th Oct 2012, 19:39

Join Date: Jun 2010
Age: 34
Posts: 382
Definition of Streamlines
19th Oct 2012, 19:43

Join Date: May 2010
Location: PLanet Earth
Posts: 836
Originally Posted by peter kent
"As energy is not conserved the Bernoulli relation cannot be applied to airflow round a wing in flight."

Nobody else throws it out for this reason. It's a new one as far as I can tell.

Can you make any sense of it?
Interesting thought!
However the problem of energy conservation only significantly applies in the lower parts of the boundary layer of the wing. If you look at the speed and thus energy above the immediate boundary layer it will be close to the free stream air speed and thus you still have accelerated air speed and therefore reduced static pressure.
The streamlines above the boundary layer might not be perfect anymore and you might loose some lift compared to the theoretical lift with no boundary layer. But the general effect (Air accelerated creating low pressure and thus lift) will still be there.

Therefore my appreciation of this is that the effect described in the article might spoil the result of a calculation based on Bernoulli under ideal conditions but it does not prove that Bernoulli doesn't explain lift. At least my picture is not completely ruined (yet).

Last edited by henra; 19th Oct 2012 at 19:44.
19th Oct 2012, 20:06

Join Date: Jun 2010
Age: 34
Posts: 382
If you look at the speed and thus energy above the immediate boundary layer it will be close to the free stream air speed and thus you still have accelerated air speed and therefore reduced static pressure.
True. But saying Bernoulli is responsible for this is exactly what this paper was highlighting as a 'myth'.

But the general effect (Air accelerated creating low pressure and thus lift) will still be there.
Not true. Lift is directly related to the downwash of air. The article also explained that the acceleration of air DOES NOT create the low pressure - the low pressure causes the acceleration of the air.

If you have air flowing around an airfoil that is producing lift you will have a relative high pressure on the bottom and a relative low pressure on top. If you are saying that since there is a low pressure on top and high flows to low, the wing will get pushed/sucked up - that's not really true. Air has to get deflected to create 'lift'. If air is not deflected by the airfoil, there is no net force and therefore, no lift. That's also why spaceships need retro rockets in space to maneuver because there is no surrounding atmosphere where a change in shape of the spaceship would produce a net force - they need to apply a net force by expelling mass at a high velocity (rocket). Putting those two together, if there is a low pressure, the air will flow in the direction of the low pressure - which is upwards. If the air flows upwards, according to Newton's 3rd law, there will be an equal and opposite down force on the wing. That's the opposite to lift!

Last edited by italia458; 19th Oct 2012 at 20:10.
19th Oct 2012, 20:21

Join Date: Aug 2011
Location: Grassy Valley
Posts: 2,123
Howdy Italia458

Just a comment, see what you think.

-" the low pressure causes the acceleration of the air." Not the way I learned it, for air flows into low pressure as the result of inhabiting a higher pressure in the locale. The air is acceleratd by the higher pressure which is created by, work.

Perhaps pedantic, though I don't think so. Professor Nicholson demanded that in Nature, there was no "pull" only push.

I see you like the paper. I especially am drawn to "air rest frame" and "wing rest frame". My apologies if I am thick....
19th Oct 2012, 20:52

Join Date: May 2010
Location: PLanet Earth
Posts: 836
Originally Posted by italia458
Air has to get deflected to create 'lift'. If air is not deflected by the airfoil, there is no net force and therefore, no lift.
I take it you are a 'Newtonian'

But if we assume we have high pressure on the lower side and low pressure on the upper side I fail to see why simple physics shouldn't apply:
F=p*A, p being the pressure differential and A the wing area.

...if there is a low pressure, the air will flow in the direction of the low pressure - which is upwards. If the air flows upwards, according to Newton's 3rd law, there will be an equal and opposite down force on the wing. That's the opposite to lift!
One word: Inertia.
Somewhere on the first pages of this thread I commented on how Bernoulli and Newton are somewhat linked.

That is why, if you have an airfoil where the camber at the TE points downward , the air molecules will continue downward even behind the Trailing Edge. Therefore you have a bigger 'expansion' and thus higher acceleration over the wing, reducing the pressure according to Bernoulli. This same effect gives you a bigger mass stream deflection according to Newton.
In my eyes Bernoulli and Newton are not really conflicting. they are different ways of looking at the same phenomenon, that is causing the lift.
This effect itself must be somehow linked to the behavoíour and interaction of the molecules in the air, because lift requires viscosity and mass.

Last edited by henra; 19th Oct 2012 at 20:54.
19th Oct 2012, 20:53

Join Date: Jun 2010
Age: 34
Posts: 382
Lyman...

Are you familiar with F=ma? If you are, you'll know that for a mass (ie: a book, car, computer, apple or air) to be accelerated, there must be a net force. A net force means an 'excess' or imbalance in the forces on the object. For example: When a book is resting on the table, there is no net force on the book, therefore the book is not accelerating. Since the start velocity was zero and there is no acceleration, the book will continue to lie on the table forever... unless there is a net force applied to it.

Pressure is essentially a type of force - think of it as the source of a force. This could be water pressure (force) from a firehose that knocks you off your feet. So for the air to be accelerated, there must be a net force applied to it. Just as a clarification, an acceleration is required to change either direction OR speed since acceleration is related to velocity and velocity is a vector quantity (meaning it has both a magnitude (speed) and direction). So in the case of the air flowing over the wing, it is the low pressure (force) that is applied to the air that accelerates it. If the air runs into a higher pressure area (like as it passes underneath the wing, close to the surface) it will experience a net force and accelerate in a negative direction (aka: slow down).

In all cases here we're dealing with static pressure and not dynamic pressure so the actual speed of the air does not change the pressure measured - don't think Bernoulli here! For example: most test airplanes will have a very long probe attached to the nose of the airplane to measure free stream attributes - this is before the air is affected by the airplane. It doesn't matter how fast the airplane flies, the static pressure measured will be the same as long as the airplane is flown at a constant pressure level such as FL050.

The air is acceleratd by the higher pressure
Professor Nicholson demanded that in Nature, there was no "pull" only push.
To me, all that is is relativity. High pressure pushes, low pressure pulls is the same thing. It's a property of fluids that they try to equalize so that there is no net internal force applied by itself. The reason there is higher pressure at sea level and lower pressure as you climb is essentially just because there is gravity.
19th Oct 2012, 21:14

Join Date: Jun 2010
Age: 34
Posts: 382
I take it you are a 'Newtonian'
I wouldn't call myself a scientist but I have essentially the same 'beliefs' as they do. I'm not on any one side, I'm all about exploring what the real answer is, regardless of what it is.

http://cdn4.explainthatstuff.com/air...ind-tunnel.jpg

Disregard the arrows in that picture. It might help to visualize the airfoil like in the picture above, except start with the airfoil pointing vertical (perpendicular to the air flow). With the airfoil stationary to the air, you'll measure that the static pressure around the whole airfoil is exactly the same as the ambient static pressure. As soon as you start moving that airfoil in one direction (not the band ) you'll see that a low pressure area develops on the side opposite to the direction of movement. The faster you move the more pronounced is this area of low pressure. You'll notice that the air wants to rush in and fill that void. That is exactly what's happening when air is flowing over the wing in normal flight - there is a slight void created (not as dramatic as the one you're visualizing) and the surrounding air expands to fill it, which decreases pressure and accelerates the flow.

Now that you're experimenting with that concept I should point out that at these extreme angles of attack the explanation of the origin of the force which pushes the airfoil upwards is different. At very high angles of attack there is a noticeable amount of lift that is generated by the deflection of air off the bottom of the airfoil. However, in normal flight, these extremes are not reached and therefore it is not really a valid explanation of lift of an airfoil in flight.

Last edited by italia458; 21st Oct 2012 at 20:23. Reason: Correction.
19th Oct 2012, 21:22

Join Date: Aug 2011
Location: Grassy Valley
Posts: 2,123
Thanks Italia, I do remember that...

Acceleration. May I leave that for now? I see the wing as an engine. It is an air compressor, a device that increases air pressure faster than the air can escape. This happens dynamically, and pressure is created, then maintained, in an open area.

The viscosity and pressure keep the air from moving fast enough to "escape". For simplicity, the area below the wing is high pressure, above the wing low.

The upper streamline and the wing itself trap the low pressure zone. From the link, "No Mass can penetrate a streamline". As long as the low is confined, the high maintained, the high pressure air wants to enter the low, it has no time to escape around the leading or trailing edges, this works as a dynamic lifting system, the system is created and destroyed thousands of times each Second.

I do apologize if this sounds stupid... But I am an amateur....

Last edited by Lyman; 19th Oct 2012 at 21:26.
19th Oct 2012, 22:01

Join Date: Aug 2000
Location: UK
Posts: 3,648
With regard to Bernoulli: he's basically saying that there is energy added to the system and Bernoulli describes the conservation of energy for a system (where energy is neither added or subtracted from a system) so Bernoulli doesn't apply. Bernoulli is a mathematical description of an effect that happens in a closed system.
Consider the dynamics happening on a pool table. If we simply ignore friction, we can make extremely accurate predictions of the behaviour of the balls using the conservation of momentum and energy. And that works because friction is low compared to the other aspects of the dynamics.

But hold on! The balls are rolling, not sliding. So there must be friction, right? Oh dear. The laws of conservation of momentum and energy can't possibly be used to explain the motion of the balls because it's no longer an energy conserving system. And yet still, we manage to direct the balls to the pockets with unfailing reliability. How can that be?

Consider the dynamics of a wing. If we simply ignore viscosity, we can make extremely accurate predictions of the behaviour of the wing using Bernoulli's theorem. And that works because viscosity is low compared to the other aspects of the dynamics.

But hold on! We need some viscosity for the Kutta condition and to explain the boundary layer etc.. So there must be viscosity, right? Oh dear. Bernoulli's theorem can't possibly be used to explain the motion of the air because it's no longer an energy conserving system. And yet still, we manage to predict the lift coefficients with unfailing reliability. How can that be?

Last edited by bookworm; 19th Oct 2012 at 22:02.
20th Oct 2012, 00:03

Join Date: Jan 2012
Location: Ontario
Age: 71
Posts: 81
bookworm,
I had a suspicion that the authors (Anderson and Eberhardt "Understanding Flight') were trying to throw something out because it wasn't accurate to the nth degree.
After all, the planemakers themselves use it OK.
Enough of them have written books based on their time in industry showing it's good enough for them.
eg Richard Shevell (Douglas) "Fundamentals of Flight"
Ed Obert (Fokker) "Aerodynamic design of Transport Aircraft"
20th Oct 2012, 00:52

Join Date: Jun 2010
Age: 34
Posts: 382
Lyman...

What you're saying makes sense.. but not to create lift - it makes sense to accelerate the airflow and deflect it downwards. It's the downwards velocity that creates an upward force on the wing that lifts it. The pressure isn't the direct cause to the lift.

In the article he describes how an airplane flying over a big scale would indicate the weight of the airplane - the earth does not get lighter when the plane takes off. It seems like you believe that the 'suction' created by that void on top of the wing is responsible for sucking the wing upwards. If you're sucking in air, you need to displace it somewhere - where are you displacing this air that you're 'sucking' up?

Bookworm and Peter...

It's not that Bernoulli is wrong with regard to pressures and velocities - it is correct that as the flow over the wing is accelerated, the static pressure will drop. The author seems to have a big deal with saying Bernoulli is involved for a wing in real life when it's clear that Bernoulli is for a closed system and it's also clear that lift in real life is an open system with energy added.

The measurements of the static pressure and velocity is important to plane makers because they can calculate lift/circulation around an airfoil and determine how the airfoil will perform in real life, with adjustments for accounting for viscosity (Computational Fluid Dynamics). I don't think the authors mean to say that, what the aerodynamicists that work on designing planes do is, ignore Bernoulli because it's not applicable - it sounds like the author wants to argue that a better 'overall' description of lift should focus on Newtonian laws, as it once did.

That's my take on it.
20th Oct 2012, 01:24

Join Date: Aug 2011
Location: Grassy Valley
Posts: 2,123
Italia...

"It seems like you believe that the 'suction' created by that void on top of the wing is responsible for sucking the wing upwards."

I have said, There is no pull, only push. How then do you read me thinking the air "pulls"? You have said the low-pressure accelerates the air, that is "suction".

The paper dismisses Bernoulli as supporting acceleration causing low pressure. The paper supports low pressure causing acceleration. I believe both are incorrect. Acceleration is caused by high pressure at the leading edge escaping aft over the wing, as I see it.... In any case, the major portion of the high pressure migrates below the leading edge, into a wedge shaped RAM (remember RAM)? The angle of the wing deflects airflow down, causing uplift, and this downwash meets the upper streamline and is increased thereby...

I understand that I may be a hard read, it frustrates me also. There are some medical issues...

I cannot thank you enough for your patience.....
20th Oct 2012, 08:55

Join Date: Jun 2011
Location: West of Offa's dyke
Age: 85
Posts: 476
This discussion has devolved into a debate on what Anderson and Eberhardt’s (A&E) article ‘Understanding Flight' really means. Having read it two or three times now it seems to me that it is a bit like the curate’s egg – ‘Good in parts’

They go to some pains to debunk the familiar “equal transit times” explanation which is fair enough because it doesn’t hold water, but that is because the basic assumption of equal transit times is wrong, not because of the subsequent attempt to link the undoubted fact that air flows faster over a wing upper surface than the lower generates a differential pressure which can be (in principle) calculated using Bernouilli’s equation. Their arguments on the invalidity of Bernouilli when applied to flow around a wing are tilting at strawmen I think.

Another fundamental problem with this description is that the air’s pressure and speed are not related by the Bernoulli equation for a real wing in flight! The Bernoulli equation is a statement of the conservation of energy. For it to be applied the system must be in equilibrium and no energy added to the system. As you will see in the discussion below, a great deal of energy as added to the air. Before the wing came by the air was standing still. After the passage of the wing there is a great deal of air in motion. A 250-ton jet at
cruise speed is doing a lot of work to stay in the air. Much of the fuel that is burned is adding energy to the air to create lift. Thus the Bernoulli equation is not applicable
I disagree. The energy added is used to overcome a side effect of lift generation – drag.

Picture in your mind several wings: an asymmetric wing in normal flight, the same wing in inverted flight, a symmetric wing and a flat plate. For each one, an orientation into the wind can be found which gives zero lift. We call this orientation the zero effective angle of attack. Now if one were to measure the lift of these wings as a function of the effective angle of attack, the results for all of them would be similar
Nobody will argue with that. Put another way it says that the lift curve slope of a wing of infinite aspect ratio is independent of camber.

But the consequence of using this definition of AoA is that each and every wing section has a different datum, making it impossible, or at least very difficult, to compare the characteristics of various sections – not a great idea!

There is another mistaken description of lift, which we will call the wrong-Newtonian description of lift, although those that teach it just call it the Newtonian description of lift. This description of lift states that diverting air down produces lift, and that lift is a reaction force. This part is true. Unfortunately, in the wrong-Newtonian description of lift the air is diverted down by impact with the bottom of the wing. .....
Although there is a little of this kind of lift for most wings, it is minimized for efficient wings. The amount of air impacted by the bottom of the wing is far too small to account for the lift.
No problem there either

Yet another common description of lift is that of circulation theory. Here the air is seen to rotate around the wing. This is sometimes used to explain the acceleration of the air over the top to the wing. There is a great deal of jargon, such as "starting vortex" and "bound vortices", associated with this description. Circulation theory is a mathematical abstraction useful and accurate for aerodynamic calculations. Mathematically, circulation is a non-zero curl in the airflow in a closed line integral around a wing, which
is simply a statement that the wing bends the air.
For sure circulation theory is usually expressed in complicated math, but it can also be explained in plain English (or even American!). Way back in post #33 of this thread I gave a url. for such an explanation. It does a lot more than just state that the wing bends the air.

In brief, the lift of a wing is a reaction force and is proportional to the amount and vertical velocity of air is diverted from the horizontal to the vertical, with almost all of the air diverted from above the wing.
Again, no problem with this as an overall explanation, but it doesn’t really tell us much about how it all happens. A&E go on to say that

Lift = mdot * vv

Where mdot is a mass flow rate and vv is the vertical downwash velocity imparted by the wing measured in the air’s rest frame. That is a trivial statement unless we can understand a bit more about the two terms.

They suggest:

We would first like the reader to view the wing as a kind of "virtual scoop" as illustrated in figure 5. The amount of air intercepted by the wing is related to the lift distribution along the wing. The shape of the virtual scoop is half of an ellipse with the major axis equal to the wingspan and the minor axis proportional to the chord length (distance from leading to trailing edges) of the wing. The air intercepted is diverted down with the highest downward velocity near the wing and the deflection speed tapering to zero as the distance above the wing increases, as shown in the figure. This is not intended to imply that there is a real, physical scoop with clearly defined boundaries, and uniform flow. But this visualization aid does allow for a clear understanding of how the amount diverted air is affected by speed and density
The amount of air intercepted by the scoop, mdot, is proportional to the
• area of the wing
• wing’s speed
• air’s density
To a good approximation, neither the angle of attack nor the load on the wing affects the
amount of intercepted air.
In one respect this is wrong. mdot is the flow leaving the TE and is proportional to wing span not wing area. We still have no idea how much air is affected though. A&E calculate that the deflected air might be drawn from as much as a semispan above the wing, but this is based on some assumptions rather than any definite scheme of things.

So far as I can see, apart from saying that it is proportional to AoA and airspeed they give no guidance on how the vertical velocity is generated – a fundamental piece of knowledge so far as our understanding of lift generation is concerned.

Moving on to their strictures on the (mis)use of Bernouilli, they are of course correct when they say that the general application should be:

Static pressure + 0.5 rho*V^2 = Total pressure

Their argument is that if energy is added to the flow then total pressure will increase and Bernouilli’s equation will be invalidated. Equally true of course if energy is extracted from the flow. But let us look a little deeper.

There is abundant evidence from wake survey experiments that total pressure is not constant behind a wing producing lift, so in broad terms they are right, although not because energy is added – rather it is subtracted. However, it is also true that this loss of total pressure is confined to a small area just behind the TE – in the wing wake in fact.

The NASA site that Italia 458 referenced to define streamlines says:

A streamline is a path traced out by a massless particle as it moves with the flow. ........ Since there is no normal component of the velocity along the path, mass cannot cross a streamline. ............. We can use Bernoulli's equation to relate the pressure and velocity along the streamline. .............. Since no mass passes through the surface of the airfoil (or cylinder), the surface of the object is a streamline.
The wing surface may be a streamline, but since the streamwise velocity is zero everywhere on the wing surface applying Bernouilli there would be silly. Close to the wing the streamwise velocity increases steadily through the boundary layer, but in a turbulent boundary layer (as exists over 90% plus of the wing’s surface) there is a constant, if random, exchange of mass from the high energy outer regions towards the regions close to the surface. It is this energy transfer that permits turbulent boundary layers to accept higher adverse pressure gradients before separation. However, this exchange of mass means there can be no streamlines inside the boundary layer and consequently Bernouilli’s equation cannot be applied there.

At the outer edge of the boundary layer (where there is no more mass transfer) there will be a bounding streamline and from this point out Bernouilli may be applied. This is confirmed by all those wake surveys, which show that outside the wing wake the total pressure is constant.
What does this mean for the application of Bernouilli to the flow around a lifting wing? It means that it can be used to calculate pressures and velocities around a shape that is close to, but not exactly the same as, the basic wing. This does not mean though that the equal transit time explanation can be retained!

I think I can safely say that none of this bothers practising aerodynamicists who are perfectly happy to use pressures measured on the wing surface and go from there via 0.5rhoV^2 to get to wing loading.

Then there is the bit:

In other words, the pressure difference drives the acceleration of the air, not the other way around.
Yup! But I don’t see it as any pressure difference along a streamline. Think in their air-rest frame. If the air is obliged to follow a curved path as the wing passes through it there must be a centripetal force making it do so. This has to be some sort of pressure differential. But the total pressure of the air at rest is equal to the ambient static pressure. The pressure differential therefore has to come from a drop in pressure at the wing surface (or more strictly I suppose at the outer edge of the boundary layer). Since Bernouilli applies at the outer edge of the boundary layer this drop in static pressure will be accompanied by an increase in velocity. Pressure difference across streamlines is the driving force.

Rather grudgingly, A&E say:

Although circulation theory can be used for accurate calculations of lift, it does not give a simple, intuitive description of the lift on the wing. We have also shown that the pressure and velocity of the air over a real wing in flight at not related by Bernoulli’s equation. Newton's laws hold without exception for both subsonic and supersonic flight, and can be used to yield an understanding of many concepts without complicated mathematics
From my pov. Newton’s laws as expressed by A&E do give a simple quantification of the lift on a wing, but it is if anything oversimple. It tells us nothing of how lift is actually generated nor how it might be distributed over the wing. If that is all you want, then fine, but if you want a bit more depth then I can only refer you back to the Arvin Gentry article I referenced in post#33 – plain English but realistic and informative.

Last edited by Owain Glyndwr; 20th Oct 2012 at 08:56.
20th Oct 2012, 08:59

Join Date: May 2010
Location: PLanet Earth
Posts: 836
Originally Posted by italia458
So what we see is air entering a BIGGER area and expanding to fill the area, and hence, decreasing the static pressure. But Bernoulli says that if air in a closed system goes into an area of bigger dimensions the air will expand to fill the area and INCREASE static pressure! The difference being that air over an airfoil in flight is not in a closed system, energy IS being added to the system and that energy is added to the air.
Yes, expansion means increasing pressure. But increasing can mean increasing back to free stream static pressure. No discrepancy to the 'closed' system here. The same applies for the energy. Also in a closed system you will convert energy if viscosity and friction exists. Those two don't care much if there is a tube around. You still have boundary layer, speed gradient, etc.
So I still do not really see where the fundamental difference between a closed system and an open system lies that would conflict with the general principle.

The expansion happens as any gas is always looking for equilibrium. So does air. That makes gases try to fill voids.
Re: Push vs. Pull: Pull is the consequence of less Push on ine side than on the other.
Knowing that we don't live in a vaccum we consider any pressure lower than ambient pressure as Pull although technically it is simply less Push as ambient.
Still in an ambient pressure of 1013 HPa we generally consider anything below as Pull or Suction in daily life.

Last edited by henra; 20th Oct 2012 at 09:00.
20th Oct 2012, 12:20

Join Date: Aug 2011
Location: Grassy Valley
Posts: 2,123
That is fundamentally the point I try to make, the wing compresses air, and does so in such a way as to create a very real and bordered system. Because air has mass, and seeks to equilibrate, a dynamic force lifts the wing. The system is constantly being destroyed, and created.

The zone of low pressure above the wing is a byproduct of compression up stream, and as a result of process, cannot be said to be its initiator. Bernoullians want folks to look at the magic of low pressure, and at its captivating creation by "accelerating" the air mass, locally. Fine, so far, but there is no "magic", lift takes work, hard noisy work, and if one wants to lift, one must stay moving. One must look at Newton to describe the system, Bernoulli describes local artifacts not the system.

The 'held in place' cambered section diagram is the recipient of airflow, not its creator. A flat plate is no different, they both produce lift by compressing air at the leading edge, both above and beneath it.

"A and E", in their paper, completely destroy the arse-about paradigm that the "shape" (section) of an airfoil makes some kind of basic difference in the fundamental Laws that create Lift.

Last edited by Lyman; 20th Oct 2012 at 14:23.
20th Oct 2012, 12:56

Join Date: Jul 2009
Location: France - mostly
Age: 81
Posts: 1,688
Originally Posted by Owain Glyndwr
A&E calculate that the deflected air might be drawn from as much as a semispan above the wing, but this is based on some assumptions rather than any definite scheme of things.
According to A&E, L = mdot*vv. Assuming that all the mass captured in the "virtual scoop" uniformly gets a downwash velocity vv, the power required for this is Pi=0.5*mdot*vv^2. Equating this to the power Pi=Di*V to overcome the induced drag Di, it can be shown for an elliptic lift distribution that the area of the scoop is equal to a circle with a diameter equal to the wing span.