Talk:Lift (force)/Archive 2

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Some figures that may be interesting

This article was contributed by --JayJayPlant 12:57, 5 August 2006 (UTC)

Interesting article that goes against what has been commonly taught and makes a case for what seems obvious, but maybe the simple physics should be shown....

The impulse of an air mass by the wings would be a large transfer of energy. Rough figures for an aeroplane with 100m wing span and a frontal area of lets say 200m² at say 80m/s (take off speed) would encounter ( an atmospheric density of 1.29kg/m³) approx 20 tonnes of atmosphere each second, The impulse that this mass would give is F=mv (actually Ft=mv-mv₀, but we're looking at 1s and an initial velocity of zero for the air), if the wings were able to give the air encountered a velocity of 80m/s (and that would be optimistic) then

20640kg_air X 80m/s= 1.65 megaNewtons of force

on the wings(this is the best case).

The force of gravity on this 400tonne aircraft is F=mg :-

400,000kg X 9.81ms^-2 = 3.92 megaNewtons.

(NOTES: Only the frontal area of the wings can carve out the atmosphere to impel downwards, so the surface area of the wings are irrelevant for moving air masses, and it should be noted that only the atmosphere that comes in direct contact with the aerofoils can have an effect in a momentum interaction.)

So how can this aircraft leave the ground?

Um? How indeed?

It is very easy to never notice what 1 atmosphere of pressure is. It is 14 pounds/ sq inch,or approx 1kg/cm². This is alot, and I really mean a lot. But, because we have evolved to be happy in this atmosphere we never notice this pressure.

So how does this help an aeroplane? Some one mentioned that a 747 had a wing area of 500m², okay. If you had a vacuum above the wings, then the atmosphere below the wings( and everywhere else around the vacuum) would exert 1 kg/cm² trying to fill the vacuum. On 500m² that would be a weight equivalent of 5 million kg, or 5000 tonnes. To keep a 747 of 400 tonnes in the air would require a mere 8% pressure drop above the wings to maintain altitude.(400/5000 =0.08)

The reason for laminar flow over the top of the wings is to stop the atmosphere above the low pressure volume getting in, so having the atmosphere exert its force on the underside of the wings only. A stall is when the laminar flow breaks down and the low pressure volume is filled from elsewhere.

As you can see there is a good reason that they claim that low pressure above the wing is what gives lift.--JayJayPlant 12:57, 5 August 2006 (UTC)

Anonymous, extemporaneous thoughts like this tend to display what is commonly held. The above comments are appreciated. For the record, though, notice the "clutching at straws" mentioned earlier seen here again, since air is so "insubstantial experienced up close as anything that can support heavy aircraft". What this is missing is an understanding of how large a quantity of air is given an impulse by the wings. The frontal area mentioned of only 200 m^2 for a wing span of 100 m is off. Conservation of mass, a requirement even for this most readily dismissible of substances, air, requires a much larger frontal area that is affected by the wings and given the impulse downwards. The value of the velocity downwards at 80 m/s need not be assumed to be so great either but merely about one tenth of that or 8 m/s. A frontal area adjusted to a value of 5000 m^2 readily puts everything in proper perspective and makes it all come out to be about right. This is air that is not just flowing within a meter nearby the wing surfaces but up to 25 meters both above and beneath them on average that is being affected by them and being given the "shove" downwards. Makes sense, no? This is quite a large amount of air and therefore quite a large amount of mass.

Much more than the 35 grams or so of one cubic foot of it, hopefully not mixing measurement systems more than necessary. No need to try to somehow find a "convenient vacuum" somewhere (I believe the laminar flow logic here does not hold - someone correct me if I am wrong), in pertaining to which something of this sort many have tried to do, to apply to the upper wing surface!!! Anthony Chessick 15:50, 3 August 2006 (UTC)

How does a fluid behave?

Contributed ny--JayJayPlant 13:14, 5 August 2006 (UTC) It has to be understood that the particles( atoms or molecules) that make up a fluid generally do not have a force component linking themselves to each other (See gas). A liquid is just a gas that has particles that are moving to slowly to escape gravity. (Note a liquid that can form a miniscus will behave differently to a gaseous fluid, because of the van de Waals force.)A particle of gas moves in its own little vacuum and occasionally hits something, either another particle or a surface, when it hits another particle it changes direction. If it hits a surface the surface experiences what is known as pressure. If the container is expanded the gas can only fill the newly created volume at the speed the particles are travelling at.

The Coanda effect must rely on surface friction to divert particles in the spin direction. But those particles that never contact the surface can only behave like a gas. The reason the ball diverts is because on the side spinning forwards, with its surface texture, will be hit/ and hit particles in the direction that the texture is moving, there will an increase in the number of particles collecting forward on this side, so building up pressure. The side spinning backwards is batting particles backwards , so reducing the number of particle of the front of this side. If you put more particles into a volume you have an increase in pressure, if you remove particles you have a decrease in pressure. I have never suggested that the low pressure is sucking, because a gas particle cannot pull, it can only push as it hits something, so the Coanda ball is being pushed by the atmosphere; which does not like the dis equilibrium of a local high pressure spotonto this high pressure zone. The low pressure side puts up less resistance to the gas trying to be in equilibrium, and so the ball gains a sideways component to its travel.

Now why would a fluid flow seem to attach to a curved surface:, because if the fluid flow took a tangential path there would then be a vacuum created between the surface and the straight lining fluid, that vacuum is going to have to be filled. It can be filled either by internal pressure within the flowing fluid , or the fluid and/or the surface is going to be pushed towards the vacuum by external pressures. I have been a bit shocked to discover that it might be thought that the fluid particles are some how rolling along the surface; all the particles can do is bounce and have their direction changed by collision.

A fluid's behaviour is just a generallisation of what many individual particles are doing on a microscopic scale, the fluid flow is just a macroscopic collection. As a flow passes a curved surface the mean free path of some particles have the opportunity to lengthen in the direction of the surface,so filling the void, but leaving a void behind them that will be filled when another particle happens to travel into the new void(now remote from the surface)and then that particle will leave another void, and so on. The fluid flow acts like a flow because most of the particles happen to be flowing in roughly the flow direction and as ; dare I say, a faster flowing fluid is at lower pressure so the flow column( if you like)will be contained, if it happens to be within another fluid, by that stationary fluid. If the flow is in a vacuum, it will disapate as the particles on the edge travel without collision to send them back into the flow, away from the others.

So why is there so much air affected above the wing, because as the flow over the wing leaves the curve(or the leading edge of a flat wing) in a tangent(macroscopically speaking), it will result in a vacuum that has to be filled, either by the surface/wing, or the surounding air, more likely and easier for the air to fill the void, hence the coanda effect, and this will have a knock on effect away from the wing surface, so a large volume of air will move towards the upper surface of the wing, remember this is filled just by the air particles that happen to travel into the void/ lower pressure zone, they do not pull particles with them. Now as these particles move towards the wing, the wing moves on, leaving air behind that has been effected by the lower surface of the wing, in most cases showing a deflection of paths downwards. This will effectively also leave a lower pressure region behind the trailling edge of the wing, that the upper particles are already moving towards, so the air will actually have downwards motion well behind the wing, but ....

The problem with the article is that it is, and can only be, the particles that hit the wing that can have an effect on the wing, (see gas), the particles of a gas do not interact except to bounce of each other or a surface. Granted the movement of air is a manifestation of just how much energy is being expended.

If you wish to see how this conflict in hypothesis has arisen and been maintained, look at the first link on the article page "How airplane fly", In the section "Wing Votices" there is a picture of an F-14 in high G , and the author has used this to support the air movement argument, to demonstrate the effect that the wings are having in moving so much air above the wing. What the picture is also showing, and not been appreciated (in what has been written, anyway) is that the condensation is produced by extremely low pressure above the wing, cooling the air above the wing so much that the gaseous water vapour condenses into liquid water. It is a visual showing of how large the low pressure zone is above the wing.

Because particles cannot pull on another particle, the apparent Coanda effect that creates streamlines over the wing, cannot pull a wing up, anymore than the wing is "sucked" into the low pressure area. A fluid can only push with pressure it cannot pull.--JayJayPlant 13:14, 5 August 2006 (UTC)

"Ne sutor supra crepidam" "Stick to your (and our) knitting here" An unsigned piece of some length on molecular movement in fluids only peripheral to the subject on an overly lengthy talk page (with a warning to this effect) is at risk for removal as I am sure is the consensus! A problem spotted with this is the need to understand inertia. Even molecules of gas have weight. Another problem is the need to understand differential pressures, that is, pressures relative to one another. You haven't even gotten yet to viscosity and other characteristics of fluids. Fluids are just a collection of bouncing molecules but they are much more than this as well. Anthony Chessick 03:31, 5 August 2006 (UTC)

Okay so now I've registered. The knowledge of how a fluid works is of vital importance to aerodynamics, and a little background in the discussion page has to be helpful, it gives readers an insight to where they may look if they want to get a fuller picture of the dynamics of the system as a whole. The air mass hypothesis requires a mass of air to be moved so an eplanation of how this may or may not happen is vital.

One of the reasons why the downwash hypothesis has a problem, is that in level flight there is no momentum change, so how does the aircraft stay in level flight? Could it be the bounacy of a low pressure zone created above the wing? It is going to interesting to see how this conflict turns out. I dont mind if my present view turns out to be wrong, but I will require a proper description of the fluid mechanics to support the air masses/ downwash hypothesis.--JayJayPlant 13:14, 5 August 2006 (UTC)

JayJayPlant, your User page does not tell us anything about yourself. I am not a perfect person, especially not a perfect teacher and readily back away from "conflicts", if there is one here. Another concept needing some thought is "average". Within the downwash is some faster moving molecules and some slower ones. They all have been given a push down as a result of the passage of the wing even though most did not contact it. This pursuit of level of detail is not helpful to understanding Lift but only gets into infinitely long discussions of flow details that are exceptions and not the rule and flow segments that fall outside of the average. Sorry to be so abrupt but it is simply incorrect to say that in level flight there is no momentum change! Please address these ideas to someone a little smarter than I am. Anthony Chessick 14:19, 5 August 2006 (UTC)

As a postscript here, the salient edge of the Newtonian view of Lift comes into focus with the following facts. The above example of the 747 taking off at 80 m/s on the airport runway with the wings seeing a frontal air flow of about 5000 m^2 that is given a momentum change downward into a "downwash" of an average velocity means that the air mass flowing over and under the wings is:

(80 x 5000 x 3.2808^3 x .0765) / 2000 = 540 tons per second

The weight of a 747 is less than 500 tons and so the wings are deflecting downwards an air flow that is significantly greater than its own weight every second. How much force is provided can readily be found by means of this fact together with how fast the air is moving downwards on average in the resulting downwash.

In the field of wind energy, the air mass flow seen by the 75 meter diameter rotors of the 1.5 megawatt turbines at the rated wind speed of 30 mph comes to 80 tons per second. The modest wind turbines sold for use by home owners rated at 10 kilowatts with 10 foot long blades and seeing just a 15 mph breeze (about half its rated wind speed) are being driven by about a quarter of a ton of air mass flow each second.

There is no mystery to these facts. It is time to make abundantly clear just what is happening that provides the Lift Force in no uncertain terms and, indeed, to actually calculate it using math based on Newton's Second Law, F = ma. Anthony Chessick 12:57, 6 August 2006 (UTC)

JayJayPlant, you suffer from a typical misconception: the idea that air behaves like a hail of bullets. No, air behaves like a fluid; very much like water, but of course with 1.2KG/M^3 density rather than 1000. And simple fluid mechanics is based on this central concept: for good reason it deals with fluids and not with clouds of flying bullets. Fluid behavior is an "emergent property" which by definition can never be seen if we examine populations of whizzing molecules. (In other words, we must deal only with "forests," and anyone who starts dealing with "trees" has lost sight of the fluid mechanics behaviors.) Any aerodynamics explanation which is based on visual pictures of gas molecules will often suffer from this "hail of bullets" fallacy, a fallacy which leads us away from seeing the "fluid" aspect of the air. If instead we imagine that all our explanations take place under water, it greatly helps fight the "bullets" misconception. (And if any aerodynamics explanation can't handle the underwater environment, yet works well for clouds of moving air molecules, then that explanation is almost certainly not based on fluid behavior, and is almost certainly wrong.) --Wjbeaty 22:50, 6 August 2006 (UTC)

Sorry, this is wrong. Gasses behave exactly like humongous amounts of billiard balls. And proper statistical analysis will yield the same results as those predicted by fluid dynamics. Except, of course for control volumes so small the continuity hypothesis is no longer valid -- and that is pretty small indeed. Thermodynamics are derived from considering gases as large amounts of molecules.CyrilleDunant 16:37, 7 August 2006 (UTC)

Read it carefully before commenting. (Perhaps I should have said hail of non-interacting bullets.) I'm discussing the difference between airfoils in gas at 760 Torr versus airfoils at 0.01 Torr. Do you know how a fluid behaves? Are you aware that gas at 0.01 Torr no longer acts like a fluid, but instead acts like a molecular beam? It acts like a hail of individual bullets which don't collide with each other. The effects of molecule-molecule collisions become insignificant at low pressure, but at 1ATM their effects are extremely significant, and it causes gas to take on fluid characteristics similar to that of water. At 0.01 Torr the inviscid/incompressible fluid model used in fluid dynamics fails. Crookes Radiometer starts spinning at that low pressure because the gas acts like non-interacting bullets, but Crookes Radiometer won't spin at high pressure because gas then behaves as a fluid. Gas at 1ATM acts like water because it acts like strongly-interacting billiard balls where any individual ball cannot move very far without being reflected back by a collision and thus communicating momentum change to other molecules. In other words, in a fluid-like gas, the billiard balls are essentially vibrating back and forth, and rapidly transferring momentum throughout the array of balls. No stats are needed to understand this, it's the "vibrating back and forth" which holds the key concept. (Of course an animation would help greatly!) But as I said above, it also helps if we move our explanations under water. That way the fluid nature of the medium is so obvious, that it becomes difficult to fall into misconceptions. (Or in other words, water is not like a hail of non-interacting bullets!) --Wjbeaty 02:25, 9 August 2006 (UTC)

Well, yes, you should have said "non-interacting". Because bullets interact. In a fascinating way. And not at all like billiard balls, I should say. What I was trying to say is that you can derive fluid behaviour from considering it like a statistically large amount of billiard balls. Note "statistically". Note that if "statistically" is not true anymore, the rest of my sentence drops. And "vibrating back and forth" is very incomplete: what about rotation? What about complex moecules having many degrees of freedom? BTW, yes, I know how a fluid behaves.62.167.50.249 05:50, 9 August 2006 (UTC)

Of course there is a situation where gases really do behave like a hail of bullets: when pressure is less than a fraction of a Torr and the mean free path is a significant percentage of the size of containers or of wings. Explanations based on the motions of separate air molecules are explanations of aerodynamics up in the Ionosphere. But down here near the surface of the Earth, air molecules rapidly and repeatedly collide with their neighbors, and this instantly transfers both momentum and viscous force. The repeated collisions act almost like chemical bonds, or better, like compressed springs connecting all the air molecules. And that's a good way to see the difference between fluids based on gas, versus fluids based on liquid: liquids have chemical bonds between the molecules, while gases behave as if there were compressed springs connecting all the neighboring molecules. The air is like a liquid, but a liquid which can only push. --Wjbeaty 22:50, 6 August 2006 (UTC)

Or push differentially. It is a temptation to try to understand the pressure distributions across the profile and all around it although aircraft wing designers rightly have a need to do so. For example, this is generally not necessary in wind energy technology and certainly finding the Lift Force, the subject of this Wikipedia entry, need not take this detour into the complexities of doing so. It is like starting in the middle of the flow problem (building up from a molecule by molecule analysis at the profile surface) rather than from the beginning - the averaged momentum change of a large quantity of air flow mass being applied to a deflecting surface. Even optimizing the Lift Force by means of profile designs can proceed without understanding the detailed pressure distributions but only how well the air flow mass deflection is being obtained. Anthony Chessick 14:46, 7 August 2006 (UTC)

It is strange that the defenders of the air mass movement hypothesis are so willing to insult those who they are trying to convince, and also to say that it is pointless to examine the mecanics of the system.

It is not a hypothesis, in the sense that conservation of momentum is not a hypothesis. It simply is a fact. Lift is produced because of the reaction of air.

If the mass air movement hypothesis dependes on inter-particle atraction to generate lift, then it means that lift cannot be experienced in a perfect fluid, which has no inter-particle forces.--JayJayPlant 11:51, 13 August 2006 (UTC)

1) There exists no such thing as a "perfect fluid". It is a hypothetical construct. A perfect fluid is one for which the behaviour law $pv=rT$ stands. This assumes not no interaction between molecules, but a) an infinitely small size for the molecules and b) no attractive behaviour between the molecules. It is a hypothesis valid for air around an airplane, for example.

2) If you write the Navier-Stokes equations for a fluid, the first thing you do is write the conservation of momentum equation. Which involves pressure.

3) The difference of pressure "above" and "under" the wing causes lift.

4) The difference of pressure "above" and "under" the wing is caused by the variation of speed. The variation of speed is caused by the deflection of the air by the wing. Because of the boundary condition introduced by the wing.

5) For the above to be true you need not make any assumption on the fluid other than continuum. If the pressure is so low that the continuum hypothesis is no longer valid -- well, you have so little fluid that lift is not really in order anyway :)

6) I suggest you go read Navier-Stokes Equations CyrilleDunant 15:11, 13 August 2006 (UTC)

I think you are on my side Cyrille, The last two sub sections of this discussion were started by me argueing against the air masses movement, which is an hypothesis that effectively abandons the notion that the pressure differential between the upper and lower surfaces of a "wing" is the source of lift.

This is playing on words: the pressure differential is caused by the variantion of the momentum of the air. Of course, the "direct" cause of lift is differential pressure, but the "engineered" cause is the wing shaped so as to displace the air in a suitable fashion.CyrilleDunant 10:16, 14 August 2006 (UTC)

I am trying to find out if the Coanda effect actually occurs for a fluid flowing through a vacuum to see if the "attachement" of a fluid flow to a surface is only possible if the flow and the surface exist within an environment with an ambient pressure. As yet I have found no periodical that has any info on an experiment such as this. ???--JayJayPlant 16:49, 13 August 2006 (UTC)

This is bacause you ccan't have a fluid flowing in a vacuum ? Because it would boil and make the vacuum not a vacuum anymore.CyrilleDunant 10:16, 14 August 2006 (UTC)

A Math Formula As Per Eberhardt and Anderson For Determining The Lift Force

It is briefly stated in the Eberhardt and Anderson reference of this subject article that an actual calculation of the lift force may be made (independent of formulas based on Bernoulli's Equation, the Batchelor Circulation Parameter, various Venturi considerations, Wing Edge Effect Vortices, Unequal Transit Times, and all the rest) by using a formula based on what these authors call the "rocket thrust" formula. This is correct but rockets are only a special application of this more general formula. Newton's Second Law, F = ma, may be rewritten in a different form for the case of all fluid flows as follows:

${\overline {F}}=\left({\frac {dm}{dt}}\right)\nabla {\overline {V}}$

This is a vector equation as is indicated by the over lines above the F and the V. It may be considered to be a short form of Navier-Stokes that has been integrated over the control volume and made applicable to the presence of a boundary condition - the wing or blade profile surfaces. The (dm/dt) factor in effect says, "the rate of fluid mass flow". For the case of rockets, of course, this is just the rate of burnup of the rocket fuel that is then propelled through the rocket nozzle. In some cases where, for example, flow in a pipe is involved this is just the same as $\rho \mathrm {AV}$ but for wings or blades the A is an undefined value. So an assumption that may be made is that a proportionality constant is used instead of A and this constant is left for other work, usually empirical (wind tunnels, etc.). In general it may be said that the rate of mass flow for air passing over a wing or blade is quite a bit higher than generally realized when taking into consideration that the value of A may encompass distances that are large both above and below it, reflecting the substantial incident area where flow is affected by its passage through it.

The second factor, $\nabla {\overline {V}}$, is the vector difference between the average flow vector before and after the passage of the wing or blade. Vector algebra is useful and vector subtraction (as here) is done by just placing both vectors at the same starting point and finding a new vector that extends from the tip of one vector to the tip of the other. In the case of rockets, the beginning vector is zero and so the result is just the same as the vector of the flow out of the nozzle. In the case of wings and blades, in general the magnitude of the vectors (the actual flow velocity) is unchanged but the directions are altered in a process called flow deflection. The new vector, then, is found by placing both the starting flow vector and the deflected flow vector at the same beginning point on a graph and drawing a line between the two tips (extending as they do in two different directions), which is a vector nearly at right angles to both of these vectors. This becomes the direction of the force vector, F. Note that sometimes the vector, F, has both a lift and a drag component to it - but this can be discussed elsewhere.

Notice also the parallel with bends in pipes where forces are seen by the pipe supports as a result of fluids flowing within them.

Notation is sometimes confusing. The upside down Greek letter delta used here is often also used to indicate a differential over space especially in dot or cross products of vectors as made clear with a dot or "x". Here no differential is intended and a simple "vector that is the difference vector" is meant.

Notice how quick and easy this is, using math to powerfully make the complex more understandable and to simplify calculations. No need to view what is happening at the airfoil surfaces either in terms of flow velocity bumps or pressure distributions or flow transit times. All that is needed is the beginning flow vector and the ending flow vector of the averaged flow mass seen by them. In wind energy, this is especially important because some of these details hold little interest compared to how much forces are being generated.

Then this formula can be worked to produce calculations making predictions of how changes in profile shape or attack angle create changes in performance of various parameters of interest. It is, in other words, just the beginning of lengthy computations that bear upon further design efforts.

It is important that this be mentioned here irrespective of any rules or policies of Wikipedia involving the handling of disputes over what are the correct formulas for the lift force. In effect, this is additional material upon which debate is taking place. Anthony Chessick 16:46, 21 August 2006 (UTC)

Er by my reading of Professor B, you need to account explicitly for the pressure variation in the momentum flux expression in at least two important cases 1) when taking the control surface directly over the wing (where the mass flux is zero, see eg Batchelor eqn 6.4.20) and b) in a 2-d system, evaluating momentum flux at large distances, where the pressure and momentum flux integrals are in fact equal (Batchelor, eqn 6.4.27 et seq.. And of course, it helps if you've got a technique to actually find the velocity variation, which the Kutta condition gives you. Linuxlad 20:27, 22 August 2006 (UTC)

It is with reluctance that I dismiss these thoughts and hold firm to what has been stated above. Batchelor and, before him, Prandtl, Joukowski, and Kutta are not saying anything earth-shaking, just trying to follow the flows on a streamline-by-streamline basis, even, sometimes, making use of the interesting variation of vortex-lines. The Kutta condition means only that the air mass "flux" turns a corner (in his terms, "circulates") at the trailing edge and then heads downwards by a small angle equal to an "effective" angle of attack that is often not determined as well as it might be. Further, it is plain wrong to say, as he does, that pressure variations of the necessary significance occur at distances far removed from the airfoil when in fact, for aircraft as well as wind turbines, we know they don't. (He also misidentifies his "airfoil" profile of Figure 6.4.1 as a "cylinder", a proof-reading error perhaps but a telling one in those earlier days when the Magnus Effect was such a byword.) Anthony Chessick 01:36, 23 August 2006 (UTC)

I think the reference to an airfoil as a "cylinder" is no "proof-reading error". Any 2D airfoil is a cylinder in the sense that it is a surface defined by an array of parallel lines ("generators") passing through a curve in 3D space. Anthony Chessick must think it referred to a "circular cylinder", which is a special case in which the defining curve is a circle in a plane perpendicular to the generators. --J Doug McLean 22:50, 30 October 2006 (UTC)

Some basic physics, and other missing pieces of the puzzle

Explaining lift qualitatively, without computation, has been an interesting topic to me for some time. It's a difficult problem, and prone to being misunderstood, so it's not surprising that this discussion generates so much disagreement. After years of mulling it over, I think I understand some of the reasons why it is so difficult, which I'll get to below.

I agree with Anthony Chessick that the fact that air has mass is an essential factor that is missing from much of the discussion. I will propose two other essential factors that I think help explain the difficulties we face and that suggest what we need to do to surmount them. But before I do that, I want to establish a couple of basic facts that I think are incontrovertible but that don't seem to be agreed upon by all our participants:

The available physical theory in principle "explains" everything nearly perfectly. It just doesn't make it easy to understand.

I'm not referring here to higher-level derived concepts like circulation and the Kutta-Joukowski theorem or to things that show up in phenomenological observations, like the existence of the starting vortex. I'm referring to the fundamental physical theory. Here is a very brief summary:

Air consists of mostly empty space with only a small percentage occupied by molecules flying around in random thermal motion. The kinetic theory of gasses provides a highly-accurate probabilistic description of these motions, not only when the gas is in thermodynamic equilibrium, but when some deviation from equilibrium is present. But in aerodynamics we needn't concern ourselves with the details of these motions. In ordinary air, the mean free path of the molecular motions is very small, and on a practical scale, air acts like a continuous material. Furthermore, its properties and behavior as a continuous material are relatively simple. In ordinary aerodynamic flows, local deviations from equilibrium are small, and under these conditions we can rigorously derive, from the kinetic theory, the continuum description of the physics that we call the Navier-Stokes (NS) equations. Historically, the NS equations weren't first derived this way, but we now know how to do it. So our continuum description of the physics is firmly tied to our understanding of the molecular physics, but it allows us to proceed to describe and analyze flows without having to know the details of the molecular motions.

In the NS equations the representation of molecular transport processes (transport of momentum by viscous "stresses", and the transport of heat by conduction) is highly simplified compared to the general possibilities, but for ordinary aerodynamic flows this simplified representation is highly accurate. For a complete definition of the physics governing the flow around an airfoil, all we need to add is the condition of no slip and no temperature jump at the interface with the solid surface (another approximation of the molecular physics, but highly accurate). Then if we could solve the full NS equations for the flow around an airfoil or wing, in sufficient detail to resolve the time-dependent details of the turbulence in the boundary layer and wake, I'm confident that the time-averaged flow would be predicted with an accuracy that would exceed that of the experimental measurements. We don't have the computing power to do this now, but a few decades from now we should be able to calculate the flow around a 2D airfoil this way, and maybe 70 years from now we'll be able to do a whole airplane. For now, we must settle for "modeling" the effects of turbulence. But even with turbulence modeling, the accuracy of predictions based on the NS equations is beginning to rival that of the experiments, if we limit our attention to the attached-flow regime. When separation is present, the accuracy of our current turbulence models is not that good, the effects of these inaccuracies on the predicted flow are larger, and the resulting predictions of lift and drag are not very accurate. We should view this not as a deficiency in the basic physics, but just as a result of the lack of computing power that forces us to model the effects of turbulence rather than compute them directly.

So in a quantitative theoretical sense the physics of lift is perfectly understood: Lift happens, and we can in principle predict it accurately, because the flow obeys the NS equations with a no-slip condition. There is no mystery or fuzziness in the basic physics. The fuzziness and misunderstandings arise when we try to explain things qualitatively.

The pressure is the only way the lift force can be transmitted to the airfoil.

An electrically neutral fluid can transmit force to a body only through direct contact in which the internal stress in the fluid is transmitted directly to the surface. At any point on the surface, the force transmitted to the surface can be visualized as a force vector, the force per unit area transmitted to the surface. This vector can be resolved onto a component parallel to the surface (the shear component) and a component perpendicular (the normal component). The shear component is of direct viscous origin, while the normal component generally has both viscous and non-viscous contributions. But in ordinary air flows, according the NS equations, the direct viscous contribution to the normal component is negligible, and the normal component is equal to the local hydrostatic pressure. The displacement effect of the boundary layer is often significant, but it is an indirect viscous effect and is felt as a change in the pressure, not as part of the direct viscous contribution to the normal component.

If we integrate these local forces over the whole body surface, we get the total aerodynamic force, which can be resolved into a drag component parallel to the freestream and a lift component perpendicular. On a 2D airfoil with attached flow, typically about 75% of the drag comes from the integrated local shear contributions, and about 25% of the drag (the form drag) comes from the integrated pressure, through the displacement effect of the boundary layer and wake. 100% of the lift comes from the integrated pressure, with only a negligible contribution from shear.

So whatever the deeper origin of the lift force is (and it must include the transfer of momentum that is going on throughout the field), the force is, for all practical purposes, transmitted to the airfoil only through the pressure acting at the surface.

The science is clear on these two issues, so I hope we can stop arguing about them. Now here are two key elements that have been missing from the discussion so far and that I think are crucial:

A flow field is a distributed, or "global", phenomenon, while the equations of motion (the NS equations) explicitly address only local interactions.

The NS equations are a set of field partial-differential equations (PDEs) that explicitly express only local relationships between the flow variables. Forces are exchanged only through direct contact between adjacent fluid parcels or with bounding surfaces, and there is no "action-at-a distance", as there would be if we had significant electromagnetic or gravitational forces.

A flow field, on the other hand, is a global entity in which the local physical balances expressed in the equations must be satisfied everywhere simultaneously. Determining what flow-field does this requires solving the equations for the particular situation at hand. This is a huge obstacle to intuitive understanding because we humans are not well equipped to solve PDEs in our heads. Nor is it easy for us to deal with corresponding problems of a qualitative nature, as for example in applying Newton's second law locally at points in a flow field and then trying to deduce what the overall flow pattern must be.

The equations enforce only implicit relationships between flow variables, not one-way cause-and-effect relationships. In particular, the cause-and-effect relationship between the pressure and the velocity is circular. Likewise, the cause-and-effect relationship between the flow field and force it exchanges with the airfoil is circular.

So it is obviously wrong to try to reason what the velocity will do first, without reference to the pressure, and then to deduce the pressure from Bernoulli's principle. Likewise it is wrong to invoke one-way causation in the other direction. Any argument based one one-way causation between pressure and velocity is at least partly wrong. A correct argument must acknowledge that causation runs in both directions simultaneously. In my attempts to deal with this issue, I've found that resolving circular causation requires looking not just at what is happening locally, but looking at what is happening over the extended flow field. Thus the issue of circular causation leads naturally back to the previous issue, that of a global flow field governed by local physical balances.

Because circular cause-and-effect is much more difficult to grasp than one-way causation, we tend to go to great lengths to find one-way causation relations, even when they don't exist. "Bernoulli-based" explanations of lift are obvious examples. Another example, in which the error is not so obvious, is the line of argument put forward by Dave (B.E.Mech) on this talk page, and by Weltner and Ingelman-Sundberg on their web site. It is noteworthy because it explicitly rejects the one-way causation from velocity to pressure that is usually invoked in Bernoulli-based explanations, but then it turns around and invokes one-way causation in the other direction. The argument goes as follows:

It is wrong to argue that the high flow speed over the upper surface of an airfoil "causes" the low pressure there because the pressure difference whose existence we're trying to justify must have been there in the first place to accelerate the flow to higher speed. So where does the pressure difference come from? It arises because the airfoil deflects the flow, or causes it to change direction. So the change in flow direction causes the reduction in pressure, which in turn causes the increase in flow speed.

This argument says, in effect, that it is not correct to invoke a longitudinal acceleration (a change in speed) as the sole reason for a pressure change, but in the case of an airfoil flow it is correct to invoke a normal acceleration (a change in flow direction). The implied justification is that the primary effect of the airfoil surface is to force the flow to change direction and that it is therefore logical for the normal acceleration to "precede" the pressure change in the chain of cause-and-effect. This idea has considerable intuitive appeal, but it is not entirely correct. The problem is that the interaction of most of the flow with the solid surface is not as direct as this argument implies. Only one vanishingly thin streamtube (the stagnation streamline) actually comes into contact with the airfoil surface, and the normal accelerations of all other streamtubes happen out in the field, just like the longitudinal accelerations do. For most fluid parcels there is no direct interaction with the airfoil surface, only with adjacent parcels, and in this situation there is no basis in the physics for making a distinction between the normal and longitudinal components of the acceleration. They are both just accelerations, and neither one has a one-way causal link to the pressure. We can correctly apply the same argument to the normal acceleration as the original argument applied to the longitudinal acceleration: The only thing that can cause a change in the velocity vector is a pressure gradient, so that for the normal acceleration to happen, the normal pressure gradient must already be there. And then if we incorrectly limit ourselves to one-way causation, we leave unanswered the question of what causes the pressure gradient.

These two issues, global behavior governed by local physical balances, and circular causation, are resolved naturally when we actually solve the equations: Global behavior arises naturally, and circular causation relationships are properly taken into account by the equations. But these issues do make the task of explaining lift qualitatively a difficult one. Our failure, so far, to face these issues has naturally led to errors and confusion.

We'd like to be able to start from first principles (the properties of air and the laws of physics), and using nothing else, predict that lift exists and explain what features of the flow contribute to the lift. But I've concluded that this is not a realistic expectation, and that we'll have to settle for something less ambitious.

As I've already argued, the flow around an airfoil must obey the basic laws of physics, in the form of the NS equations. These equations can be used to predict what the flow around an airfoil will do, including how much lift is produced and the detailed flow pattern that accompanies the lift, but to make such a prediction, we must solve the equations for each particular airfoil shape and flow condition we're interested in. Because the flow around an airfoil is a complicated phenomenon, this requires lengthy calculations that are practical only on a high-speed computer. So starting from first principles and predicting what happens requires solving a complicated set of equations on a computer, and is not something we should expect to be able to do in our heads.

To cut the problem down to size, so that we can approach it with simple words and diagrams instead of laborious calculations, we'll have to assume some things ahead of time, things that are consistent with the theory and that can be observed in real flows. There may be more than one viable approach to this, but the only satisfactory one I have found is to assume from the start that lift exists and that it is felt as a pressure difference between the airfoil's upper and lower surfaces. Then, applying the Newton's second law in a qualitative way that doesn't require calculations, I can deduce what the flow pattern looks like that accompanies and supports the lift, a flow pattern that is consistent with what is actually observed.

To summarize my proposed approach to a correct explanation: I start by noting that air has mass and exerts pressure. I then assume that the lift force exists and is transmitted to the airfoil by a pressure difference between the upper and lower surfaces. Then I explain the circular cause-and-effect relationship between pressure and velocity in as layman-friendly terms as I've been able to devise. This is not easy, but if I leave it out, I'm left with an explanation that is incomplete and, to my mind, not entirely correct. Now, with the correct local physics in hand, I am able to argue that an airfoil produces lift essentially by pushing air downward, turning part of the air stream downward and imparting downward momentum to it. To do this, the airfoil must exert a downward force on the air, and since every action has an equal-and-opposite reaction (Newton's third law), the air exerts an upward force (lift) on the airfoil. The pressure difference that transmits the lift is sustained by the changes in flow direction and speed associated with the downward turning of the stream. Both the momentum transfer and the pressure difference are necessary parts of the picture (not alternative ways of explaining the same thing, as has been suggested by some).

I've drafted a somewhat detailed explanation along these lines. It's longer and more detailed than the current version of the lift article (this page). I'd be happy to share the draft with anyone who's interested. --J Doug McLean 20:02, 30 October 2006 (UTC)

It suffices here to say in reply that the essential bones of this discussion are what are important, not lengthy - leading to book length - expostulations making more of this than is necessary here. The highly deductive approach from Newtonian theory vs. the more inductive traditional teachings handed down from aviation pioneers as characterized by correlations and graphs. If you favor one or the other, please say so. Your vote will be counted along with those of the others. In wind energy, which is the basis from which I come, the pressure, necessary though it may be, is almost meaningless and no one worries about pressure distributions across the profile rather than just skipping from descriptions of the airflow - before and after its encounter with the airfoil - right to the resulting forces in total generated on the blade. As far as deliberating whether a figure of a roundish object cross section in the book does or does not represent that of a cylinder, to what lengths does this go? If the figure were that of a square or a proper wing profile ( which it should have been ) could this still be referred to by Batchelor as a "cylinder"? One way or the other, it is an error. It is telling that minor errors such as this create comment but the larger error of outdated - and, by now, generally accepted as misleading - theories in the book does not. Anthony Chessick 16:19, 21 November 2006 (UTC)

We seem to have a disagreement as to what kind of explanation this article should provide. To design a turbine blade it suffices to know what happens when air flows over an airfoil section, but I think that when people look up lift force in Wikipedia, they probably want to know how it happens. To me, explaining the how of a complicated physical phenomenon requires breaking it down into pieces that can be related back to first principles, and showing how the pieces fit together, not so much how they might be logically related through the mathematics ("the highly deductive approach"), but what the physical cause-and-effect relationships between them are. This is my idea of what an "essential bones" explanation requires, and anything less is condescending to the reader.

Explaining lift correctly is treacherously difficult, as demonstrated by the numerous attempts at it that have gotten it wrong and by the confusion that characterizes much of the discussion on this page. An accessible explanation that meets my definition above and gets everything right would be a first, and developing one is going to take some work. The current Wikipedia article is better than most, but it has significant deficiencies that we should try to fix (see below). Given the almost unique difficulty of this topic, I don't think I was "making more of this than is necessary here". I think everything in my admittedly long posting above was relevant to the task at hand, and I'd appreciate some specific feedback on the issues that I raised. In any case, the problem certainly doesn't boil down to an either/or choice between "deductive" and "inductive" approaches.

So, what are the deficiencies of the current article? First, "Reaction due to accelerated air", "Bernoulli's principle", and "Circulation" are presented as separate, equivalent ways of explaining lift, the implication being that any one of them can stand alone as a logically complete explanation. The problem with this is that none of these can stand alone in that way. A complete explanation must include both reaction and pressure, at the least.

Most of what is said in the "Reaction" section is right, as far as it goes, but it fails to convey the idea that the airfoil influences a lot more air than just what flows close to the upper and lower surfaces. And this section by itself doesn't tell you that the pressure is what transmits the force or how the pressure difference arises as a result of the reaction.

The "Bernoulli's principle" section has several problems. Overall, it is confusingly vague. It describes Bernoulli's principle and makes an oblique reference to solving for the velocity and imposing the Kutta condition, but it does not make clear how Bernoulli's principle is supposed to explain lift. To do this it would need to describe and explain what actually happens in the flow around an airfoil. Then for the lay audience it does something unnecessarily intimidating: using a vector integral equation just to convey the idea that we get the total force by adding up local pressure contributions. And several things it says about the pressure integral are incorrect. The integral does not suffice "to predict both lift and drag". It doesn't "predict" anything; it just defines the total force in terms of contributions distributed over the surface. And it is not "always exactly true". For that to be the case, it would have to include the shear contribution, which is a major part of the drag and even makes an insignificant, but not exactly zero, contribution to the lift. Finally, saying that it excludes the "form drag" isn't consistent with the usual definition of form drag as the pressure drag due to the displacement effect of the boundary layer. This is separate from the direct shear contribution to the drag, usually called "skin-friction drag".

For a lay audience, the "Circulation" section contributes nothing to understanding, as the article itself admits. The article's discussion of circulation, the Kutta-Joukowski theorem, and the Kutta condition is too cursory to do anything but cause confusion. It would be better just to mention these things by name, informing the reader that they are elements of the mathematical theory, and to refer interested readers the technical sources.

The so-called "lift equation" is not really an equation in the sense of expressing an independent physical relationship. It is really just the definition of the conventional lift coefficient, which, among the many possible ways of non-dimensionalizing the lift, is the one that is usually most convenient. The lift coefficient represents the lift with the effects of speed, density, and area approximately removed, and is therefor more "portable" in a practical sense, but it is not somehow a more fundamental physical quantity than the lift itself. The lift equation doesn't "predict" anything, unless you consider scaling from one situation to another to be a form of prediction.

The "Coanda effect" section is right where it belongs, under misconceptions, but it too contains significant errors. The conventional explanation of lift does not make "verifiable predictions of lift using the lift equation" (see above). And it is not correct to say that "the effect is not fully understood". A correct and detailed understanding of it is available, though apparently there are many people who misunderstand it. It is also incorrect to say that "Coandă effect's force actually pushes in the opposite direction of the main lifting force". The fact is that the Coanda effect is not applicable to ordinary airfoil flows. We need to make clear the distinction between the Coanda effect and ordinary boundary-layer attachment, and to clarify these issues I am posting a separate entry in the discussion of the Coanda effect article.

Regarding Batchelor's "error", I agree it's a minor issue, but I stand by my statement that it wasn't an error at all. In Section 6.6 of An Introduction to Fluid Dynamics he uses "cylinder" to refer to any 2D body (constant cross-section), including a flat plate at angle of attack, which is mathematically correct usage, just not in line with current American vernacular. I agree that some things in the old books are misleading, for example the Prandtl and Tietjens explanation, which is repeated by Batchelor, that implies that the shedding of a starting vortex somehow causes the establishment of circulation around the airfoil. This is an example of establishing a connection that follows logically but gets the cause-and-effect backwards. J Doug McLean 20:23, 4 December 2006 (UTC)

Opening Illustration

Hello to everyone, As a flight instructor (but still learning a lot) I'd like to add something to the disscussion regarding the graphic on lift near the top of the main article. Where is the relative wind? And since when did lift have a forward component to the vector diagram? If anything, it has a slight rearward component, which contributes to induced drag. I think we could come up with a better diagram explaning lift. Anyone else feel the same way? Joe "Jetman"

Yeah, it isn't the greatest diagram. It takes the frame of reference of the airmass rather than the airfoil. So the airfoil is shown moving through the airmass rather than the airmass moving past the wing. It also is drawn with the wing in a "downward glide" rather than "straight and level." This give the forces their "funny" angles. I presume this choice was made in order to illustrate the fact the lift is not always opposite weight but is defined as being the force perpendicular to the relative motion of the fluid and body. I agree that it's a confusing picture. If you can find or draw a better one, I'd be more than happy to have this one replaced. Blimpguy 23:14, 16 November 2006 (UTC)

I wanted to comment on that image. There are many like it in many books (Including many basic ME textbooks), and there are some fundamental flaws. Primarily, it needs to be noted that lift is generated perpendicular to the chordline. If lift were generated forward of that perpendicular, as illustrated, then the total thrust of an aircraft would, in fact, be increased by the presence of lift. The reverse is actually the case, where lift induces a second vector, induced drag. and I'll agree that marking V(infinity)would be helpful

How do gliders overcome drag? Rolo Tamasi 21:23, 30 September 2007 (UTC)

Someone misspelled "angle of attack" in the illustration.

Thrust in diagram

Why is a thrust vector shown in the diagram of an airfoil at the top? This does not belong there. Dhaluza 13:57, 4 February 2007 (UTC)

It is okay to include the thrust vector, because the figure is trying to show the force balance on an airfoil. There is no reason for the thrust vector to be oriented such that it points in the direction of motion or is parallel to the chord of the airfoil. -Myth (Talk) 00:24, 5 February 2007 (UTC)

No, the thrust and weight vectors do not belong at all. These are not aerodynamic forces generated or acting on the wing, the force balance only applies to the whole aircraft. Dhaluza 11:06, 5 February 2007 (UTC)

Well, without the extra vectors showing force-balance the diagram violates Newton's Third. And in a 3D aircraft those vectors still are not aerodynamic forces, so the wing-vs-aircraft argument is not relevant --Wjbeaty 21:00, 18 February 2007 (UTC)

I think Dhaluza is right. The purpose is to explain the lift force on the airfoil. How it might be balanced, or not, by other forces on the airplane is a separate topic. The forces needn't always be balanced. Unbalanced forces just result in acceleration of the airplane.

Leaving the extra forces out of the diagram does not violate "Newton's Third". The balance or imbalance of separate forces on an object is not what Newton's third law is about. The third law deals with the individual forces that are exchanged between two objects, and states that the objects experience them as equal-and-opposite forces. If we wanted to show vectors illustrating this, we would have to show both the lift exerted on the airfoil by the air and the equal-and-opposite force exerted on the air by the airfoil. But this would be confusing unless we put the two vectors on separate diagrams showing the force on the airfoil and the force on the air. J Doug McLean 21:03, 19 February 2007 (UTC)

I have added the figure back (the reason that it is confusing is not clear to me). Without the figure it is even more difficult to follow the definition of lift. If you have a better figure please replace it, but till then let this figure be here.

I am fine if we do not show the force balance, but then atleast show the net aerodynamic force and its components perpendicular and parallel to the direction of motion and change the caption appropriately. That way it will be easier to explain that the component of the aerodynamic force perpendicular to direction of motion is lift. -Myth (Talk) 20:43, 22 February 2007 (UTC)

I am removing the image again. It does not support the definition of lift in the intro, which only refers to fluid dynamic forces. The diagram is actually specific to a heavier than air aircraft, and not generally applicable. Dhaluza 10:48, 28 February 2007 (UTC)

Instead of removing the figure, you can just add a comment in the caption. Its always better to explain with a figure. If you do not like the figure, replace it with a better one. No figure is not much useful. -- Myth (Talk) 21:15, 28 February 2007 (UTC)

Jef Raskin article is "controversial?"

User 80.221.34.208 added the word "controversial" to the Raskin external link. I've temporarily removed it for discussion. Besides contradicting the many supporters of "equal transit time" misconception, is Raskin'g writing actually controversial? If so, why? (If the controversy is over "equal transit time," then there is no controversy, just a widespread misconception which some authors have the temerity to point out.) --Wjbeaty 21:10, 18 February 2007 (UTC)

In an ideal world, Raskin's article would be labeled "not recommended". While debunking "equal transit time" is a good thing to do, much of the rest of Raskin's article is more confusing than enlightening. Specifically:

1) He devotes too much attention to demonstrations that involve blowing jets of air over pieces of paper or "airfoil" models. The pressure differences in these demonstrations are between flows with different Bernoulli constants, i.e. higher total-pressure in the jet than in the surrounding air. The pressure difference on an airfoil, on the other hand, comes largely from a flow with a single Bernoulli constant, i.e. the flow outside the boundary layer and wake. To really understand the jet demonstrations correctly one needs to take the jet total-pressure difference into account, which is an unnecessary complication and potential source of confusion when the objective is to understand the lift on an airfoil.

2) He refers to ordinary flow attachment (to an airfoil or a baseball) and to the water-faucet demonstration as examples of the Coanda effect. All of these are misleading (see my posting dated 4 December 2006 and the ensuing discussion on the Coanda talk page).

3) He mischaracterizes explanations of the Coanda effect when he says that "the airstream is 'entrained' by the surface". The Coanda effect is a result of the tendency of jets to entrain surrounding fluid. Solid surfaces don't entrain anything.

4) His "MENTAL MODEL OF HOW A WING GENERATES LIFT AND DRAG" is questionable on several counts. He refers to air molecules being "attracted to the surface" and being "pulled down" toward the upper surface. Air actually has no significant attraction to surfaces (The no-slip condition is not a result of attraction), and the air is pushed down by the air above it. His analogy of the air being "attached to the wing with invisible rubber bands" that pull the wing upward is a poor one because it encourages seeing the air as being under tension, which is not possible. J Doug McLean 21:26, 19 February 2007 (UTC)

Incorrect Lift Theory

I came across a few pages that provide a fairly lucid debunking of some of the incorrect theories regarding lift (equal transit, skipping stone, etc). They also have some helpful java apps that you can play with--nice. I plan to integrate some of the content one way or another at my first opportunity, but that may be a while. If anyone else would like to do it, feel free to. The site is http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html Click the "next" buttons at the bottom to continue viewing each successive incorrect theory and the respective rebuttals. Hope that helps. Davidmhaley 20:12, 21 February 2007 (UTC)

presence of force implies mass and acceleration?

It seems like a lot of people argue that airfoil lift is entirely caused by downward deflection of air according to f = ma. Their reasoning is that there is a force holding up the plane, so by f = ma it must come from mass under acceleration. But that's necessarily the case. Force can exist without mass under acceleration. A book sitting on a table is not held up by mass under acceleration. Nor is a hot air balloon, nor is a boat on the water.

I find the buoyancy arguments compelling. Force can also be created by differences in pressure, without accelerating masses, right? If we measure the air pressure above a 747 wing and find it to be 8% lower than the air pressure below, that fully accounts for the force holding up the plane (though I won't venture as to what causes that, perhaps the partial vacuum created by the shape of the airfoil).

I imagine that there's truth to many of the arguments laid out here. Some of the force holding a plane up comes from pressure differences, some of it comes from downward deflection of air. Is it the case that in a plane weighing 1500N, the pressure differences on the wing account for 1200N of upward force and the acceleration of air accounts for 300N of upward force? Is it the case that a plane can fly upside down only with much more drag because it relies more on deflection caused by extreme angle of attack and less on pressure differences (which might in fact be working against it)?

---

- Not correct. A book sitting on a table is mass under acceleration - away from the earth at 10m/s/s. That's why it stays on the table. Don't argue against f = ma. It is fact. (Nothing to do with the theory of lift here - just the physics). --Grinning Idiot 17:51, 15 April 2007 (UTC)

A book sitting on a table is not accelerating unless you want to bring some sort of relativistic equivalence in to this discussion which would be entirely irrelevant. We're dealing with Newtonian mechanics here. The velocity of the book is zero. The derivative of the velocity of the book is zero. I'm not arguing against f = ma, I'm arguing against the idea that f implies ma. Force can exist without acceleration. Let me give another example since you didn't see my point- consider a spring pushed to half of its rest length. It's causing a force on whatever is holding it back, right? Is there anything under acceleration? no. The fact that there is a force holding an airplane up does not imply that air is being accelerated downwards to keep it afloat.Jhhays 01:59, 25 April 2007 (UTC)

Jhhays, I'm assuming the previous post was yours (you didn't sign) but you are right. Downward deflection is not the explanation of lift. This discussion page is very good though. I think some people here might know what they are talking about. --Grinning Idiot 15:24, 4 May 2007 (UTC)

Wow. I have now read all the posts on this discussion page. They range from amazing to common sense to psychotically incorrect. Not getting involved - have fun!--Grinning Idiot 15:07, 5 May 2007 (UTC)

Lie-to-children

I think this article is begging for a link somewhere to the "lie-to-children" article. The reason there are half-correct theories out there concerning lift is that initial explanations to aviation students are simplified so they don't run away screaming. If they don't continue their aeronautical theory beyond the basic stages (beyond what is required to operate an aircraft) they will believe they have the whole story because they haven't heard any different and it sounds right. Check out the above mentioned article and give thoughts on whether it might be a relevant addition.--Grinning Idiot 19:58, 1 April 2007 (UTC)

The difference between "wrong" versus "lies to children" is that lies to children are easily recognized by adults (or at least by the experts.) Here's a common example: In grade school we are taught that atoms are little solar systems, with electrons orbiting the nucleus. Any chemistry student recognizes this lie, and probably sees why it's necessary. Chem instructors certainly recognize the lie. Yet the airfoil misconceptions were (until very recently) taught to pilots, and appeared on license exams. And in my experience, when I discussed these fallacies on newsgroups starting in ~1996, it created huge flamewars because most aviation people simply could not accept that the fallacies could contain any errors. The entire airfoil controversy caught fire only in the 1990s (though "Stick and Rudder" by Langewiesche is an early rare example of the correct, non-fallicious explanations.

Is there a concept called "lies to adults?" I'd say no, because if we must give misleading oversimplifications to advanced students, the teachers recognize the oversimplifications. And we also tell the students about the oversimplifications. It's a matter of respect. But if a textbook explains lift to student pilots by using the equal transit time fallacy, and if the textbook author really believes that fallacy is true, and if the pilot licence exams require fallicious answers on test questions, then it has nothing to do with "lies to children." Instead it's called "being wrong." Or its called "errors as infectious disease" where textbooks spread the errors to teachers. Think about it: if you gave a correct answer on a pilot exam, you'd be marked wrong. They REQUIRED the wrong explanation.

If the textbooks and authors and exam-creators all realized that equal-transit-time (etc.) is an error, then things would be different. They didn't. Instead they angrily defended it as being correct. If they told their students "this is extremely oversimplified and doesn't work well, but it's the only understandable explanation..." then things would be different. They didn't. Instead they really believed that parcels divided by the leading edge are required to join at the trailing edge. I watched over the last ten years as the physics teaching community and the aviation community confronted this error and slowly developed better explanations. But the errors still appear in older textbooks, so they won't rapidly vanish.

Apparently even Prandtl believed the equal transit time fallacy, and a diagram in an early aero math paper may have been one cause of this particular galloping error. Jeff Raskin points out that even Albert Einstein believed the same fallacy, and based a (failed) airfoil design upon it. --Wjbeaty 22:35, 1 July 2007 (UTC)

It is very difficult to believe that Albert Einstein believed in equal transit time. We can be pretty confident that he understood the theory of conservation of energy and that he could see that the only two energy variables with any significant part to play are pressure and velocity. It is therefore immediately apparent that lower pressure regions will have higher velocity. As the average pressure above the wing has to be lower than below the wing it would be obvious to him that the transit time above the wing must be less than below the wing.

I believe the observation that it is a “lie to children” is extremely valuable and accurate. I don’t regret that the “lie” may cause some to believe that the airflows have equal transit times as it is a misunderstanding that is unlikely to have any consequence (any more than thinking that atoms have valence “hooks” on them). However I do regret that fact that it causes many to believe that shape is the cause of lift rather than angle of attack. This misconception can be a barrier to understanding many things we may come across (e.g. How can a boats rudder work? How can anything fly upside down? etc.)Rolo Tamasi —Preceding unsigned comment added by Rolo Tamasi (talk • contribs) 13:16, 10 September 2007 (UTC)

--- Just to clarify, the shape (camber) is an important part of the lift and combined with the Angle of attack sets the lift. Tzickuhr 02:37, 12 September 2007 (UTC)

Just to clarify even further, camber is not important in generating lift in wings that have no camber and is even less important than that in the case of cambered wings flying inverted! Rolo Tamasi 14:58, 16 September 2007 (UTC)

Basic ideas

Here is a simple explanation for lift which I think most people will agree with. First of all what does a wing do to the air? The answer is the air flowing over one side of the wing is forced to follow a curved path. The greater the angle between wing’s path and the relative airflow the smaller the radius of the curve path the air will follow, up to a certain point after which, the smooth flow of air breaks down. This has been shown in wind tunnels and is easy to observe as passenger in an aircraft flying in cloud or humid air. Form basic physics we know that to make something move in a circle we need to apply a force towards the centre of the circle. The wing is providing that force by in effect pulling down on the air above the wing and in turn being pulled up in the process (Newtons 3rd law).

This is in complete accord with Bernoulli’s principle which states that if we accelerate a parcel of air the pressure will drop. The air follows a curved path as its passes over the lifting surface of the wing and therefore is accelerating for the full chord of the wing. From the equation F=MV²/R we know that the force must related to the velocity squared. Note that while we know that the speed of the air over the top surface does in fact increase it is only necessary for the air to follow a curved path for it to be defined as accelerating.

On the bottom of the wing the air for the most part will just collide with the under side of the wing and be defected down. The lift will be equal to air mass times the velocity which in the case of my aircraft would be only 10 % of the lift needed to sustain level flight. The important difference here is the velocity is not squared and so the lift produced is only a small part of that needed.

Now if we consider a wing as just a flat plate at an angle to the air flow. We can see that the only air which is directly affected is a rectangular block of air of which the wing chord becomes the diagonal. The block of air will be divided into two equal parts. We can determine the volume of the whole block and what its mass will be from the air density, the area of the wing, and the vertical height of the block of air. You can then derive the well know equation for lift.

Lift =Cl * ½ ρV²*S Using the metric system Lift will be in Newtons Cl is the coefficient of lift which is a number between 0 and about 2. ρ is the air density which is about 1.225 kg/cubic meter at sea level. V is air velocity in meters a second. S is aerofoil surface area in sq meters. Cl will be related to the amount of air moved and how much the air is forced to bend not to mention a host of other minor factors.

Now we get to the bit where lots of people will disagree. A popular site refers to physical description of lift .I am of the view that this particular physical description of lift is just plain wrong. I think for it to be correct the equation for lift would have to be proportional to the velocity not velocity squared. Below are some of the problems I see with the idea.

If you really think that the physical description of lift is correct try and use it to explain how the tail plane produces a strong down force despite the fact that under certain conditions it may have a positive angle of attack of as much as 12 degs!

A biplane's a lower wing which would be just about useless!

The idea that downwash is the cause of lift was disproved way back in the 1930’s by experiment. It was found that the speed and angle of the up flow in front of the wing was the same as the down flow at the trailing edge.

So where does all the turbulence from a large aircraft come from. A simple analogy is what happens at the start of a game of pool. You hit the white ball which in turn transmits its momentum to all the other balls causing them to go all over the place. The force applied to the system all comes from the single blow to the white ball. Trying to work out the amount force applied to the system by just adding up the mass of all the balls will not yield any useful information. In other words the wing may well disturb a large mass of air but the bit that matters is the air that directly interacts with the wing. PR 27 July 07

I have had a careful look at the above link to the physical description of lift. It appears to be full of errors and mistakes. There are too many to list but here are a few examples. The picture of the Cessna flying over the fog is claimed to be an example of a wing producing a large downflow. I think not, there are two jet turbines blasting 1000's lbs of hot air at the fog bank.

The article also claims that power is needed to generate lift, as an aircraft in level flight is not gaining or losing height this is not true. In physics for work to be done a force must move its point of application in the direction of the force. If the plane is flying level the lift force is not moving in the direction of the force and so work is not being done. This is a serious error. On the other hand a plenty of work is being done overcoming drag. This is an important distinction and negates much of what is claimed in the article.

Under conclusions he states that lift is proportional to the amount of air diverted times the vertical velocity of the air. I don’t know where any one has proved that, it seems to be an unwarranted assumption. I also don’t think that it can be reconciled with the fact lift is proportional to the amount of air moved times the square of the horizontal speed.

Is there any reason why the lift force has to be solely generated by an exchange of linear momentum? I would argue that it is in fact mostly generated by giving the air angular momentum. Remember we only need to generate a force to balance the weight of the plane not a force to accelerate the plane higher.

Further to the above I would add that the explanations of how ground effect and winglets work are also very dubious and certainly not the accepted view. PR 5 Aug 07

There are to my mind two areas in which the main article could be improved.

The first is to get rid of what I call the rocket engine analogy of lift. That is the idea that the wing must accelerate an amount of air directly downwards to balance the weight of the aircraft. In fact lift for the most part is generated by changing the direction of the air flow by making it take a curved path. This again should be obvious from experimental results. In a wind tunnel the amount of lift from an aerofoil can be found by measuring the up force on the tunnel itself. If air moving vertical down was the cause of lift it would push the floor of the wind tunnel down and so make it impossible to get a reading for the lift force.

The next area which needs attention is the section on the Coanda effect. The way in which wing generates lift was fairly well understood before Coanda noticed that the hot exhaust from the engine was some how increasing the amount of lift that wing produced. He was then given the credit for finding and explaining this phenomenon. If you are to claim that Coanda effect is the source of lift you are in effect saying he did not discover anything. The Coanda effect specifically requires a source of high pressure air to be injected into the air flow.

In the Coanda effect energy has to be added to the airflow and the air flows along the curved surface due to various forces of attraction between the surface and the air molecules. On the other hand in ordinary lift the air follows the curved surface at first because it has no choice and subsequently in order to fill the void that the wing would otherwise create on the lifting side of the wing. In both cases the lift force is generated by the air being forced to change direction but the reason the air follows a curved path is quite different. The forces can be added together so the can hardly be considered one and the same.

I think the section on the Coanda effect should be restricted to explaining that it is way to increase the amount lift a wing produces, or if you like another way of producing lift. It should not be under the heading of misconceptions.

I would also suggest the section referring to Raskin be removed. The Coanda effect is a separate phenomenon and not a generally accepted explanation of ordinary lift. PR 24 Aug 07

Question to PR

Quoting PR: The idea that downwash is the cause of lift was disproved way back in the 1930’s by experiment. It was found that the speed and angle of the up flow in front of the wing was the same as the down flow at the trailing edge.

Dear PR. Can you provide any reference to the experiment you mentioned? Wouldn't it seem that the case of generated lift without net downwash violates Newton't 3rd law? Integrate total momentum flux of air along the vertical planes some distance ahead and behind the wing. If there is no total change of vertical momentum of the air (i.e. no net downwash), then there is no total vertical force acting on the air as it passes the wing, or, from Newton't 3rd law, no vertical force by the air on the wing. N.P. Aug 07

I will answer this question in some detail later as I don't have time just at the present, but in the mean time I would like you to think about this. The Earth stays at pretty much the same height above the sun so where is the change in vertical mommentum coming from and will it upset Newton ? PR 29 Aug 07 —Preceding unsigned comment added by 124.180.147.246 (talk) 22:37, August 28, 2007 (UTC)

Newton's 3rd law is not violated.

The pressure field of the wing is reacted. Recall the 2 dimensional case mentioned earlier. The upwash in front of the airfoil is exactly the same as downwash behind the airfoil. The force on the airfoil is reacted against the wind tunnel walls by pressure. I verified this with a 2-d Navier-Stokes CFD code. As I moved the walls further from the airfoil, the pressure change on the walls was lower, but acting over a larger region. Each time I integrated the pressure on the airfoil (the lift) and the pressure on the walls, they were the same in opposite directions.

From a very far distance, the vortex structure of a wing is somewhat like a doublet, so I realized that a 3 dimensional wing must do the same thing (I'll explain this better later if you're interested). So I set up a 3 dimensional wing and did the same N-S analysis, again changing the outer boundaries to solid surfaces instead of far-field conditions. I got the same result. When I integrate the lift on the wing (by integrating the pressure on the surface) and then I integrate the pressure on the top and bottom walls I get the same number (in opposite directions). The lift of the wing is reacted against the wind tunnel walls. I moved the walls further from the wing and got the same results, with a smaller pressure over a larger area.

So, the lift of a wing is reacted against the ground and against the outer boundary of the atmosphere. This took a little thought, but I would compare it to a hydrofoil in water. The low pressure on the upper surface of the hydofoil causes a wave on the surface of the water. A wing will do the same on the outer boundary of the atmosphere, causing a wave. The distances are so large relative to the wing that these disturbances will be imperceptible.

An equal and opposite force, so no violation of Newton's 3rd law. TZ 29 Aug 07

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Hmmm, interesting. What about hypersonic flight in upper atmosphere? Before disturbances reach any distance in the vertical direction, the vehicle will be long gone. By the way, to calculate lift numerically it is sufficient to do 3-D Euler simulation, without wind tunnel.

That the downwhash exists in situations of realistic Reynolds number flows can easily be observed from experiments; for example, see visualizations in the following paper: Aircraft Trailing Vortices and Downwash Phenomenon by Hiroshi Higuchi; the paper can be downloaded from Physics of Fluids Journal at http://pof.aip.org/pof/gallery/1993toc.jsp.

The lift still can exist without downwash, however, provided that trailing vortices are shed from the tip -- a process which generates circulation around the wing. N.P. 30 Aug 07 —Preceding unsigned comment added by 128.186.104.222 (talk) 15:39, August 30, 2007 (UTC)

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With hypersonic flight the pressure still reacts against the ground and space. There's just a delay due to the pressure wave (shock). I don't see a problem here.

Yes, I could have done an Euler calculation, but I already had the N-S model complete, so I just changed the boundary conditions on the outer box. It was easier. If you don't change the boundary conditions to be solid walls like a wind tunnel, there will still be a disturbance at the computational boundary, so you will not have reacted the force. The walls must be solid to understand how the force is reacted.

More on the downwash later. TZ 30 Aug 07 Tzickuhr 02:46, 31 August 2007 (UTC)

Newton 3rd law and lift

Here are my views on Newtons 3rd law and how it applies to lift.
It is necessary to be clear on the definitions of the following terms:-
Velocity is speed in specific direction that is to say a vector quantity.
Acceleration is a change velocity over time that means a change in speed or direction is acceleration.
Mass is a measure of how difficult it is to accelerate an object.
Momentum is the product of Velocity and Mass and is therefore also a vector quantity.
Force is a directly related to any change in momentum a body undergoes.

Newtons 3rd law is normally stated as follows:

A/ To every action there is an equal and opposite reaction.

This only covers a dynamic situation that is where both bodies are moving so an alternative definition which includes the static situation is typically stated as follows:

B/ For every force acting on a body there is an equal and opposite force acting on another body.

If we apply definition A to an aircraft in level flight we know that the vertical velocity is Zero and the product of Mass times velocity must also be zero which in turn leads us to conclude that the net vertical momentum of the air must also be zero and therefore we can not account for lift by considering vertical movement of the air.

On the other hand if we apply Definition B to an aircraft in level flight we can say that there is a force of mass times gravity pulling the aircraft down and the air must be providing an equal and opposite force on the wing. If we accept that the air flowing over the wing follows a curved path, then the wing must be producing a centripetal force on the air, which is equal and opposite to the weight force of the aircraft.

To help clarify the above I will quote some numbers for an aircraft.
Weight 350 Kgs
Stall speed 20 meters /sec (40 knots)
Force required to support aircraft =Mg = 350 * 9.8 =3430 newtons
If force provided by turning airflow then F=MVh²/R where M will be the amount of air moved and Vh is the true airspeed over the wing.
Assume r =1 (this is guess but it is in the right ball park)
Using Newton 3rd and solving for air mass required to provide lift
3430=MVh²/1
M=3430/Vh² = 3430/20*20
M=8.5 Kgs of air or about 6.9 cubic meters of air

If we think that the vertical momentum of air is responsible for lift then F=½MVd² where Vd is the net vertical velocity of the air and will be no greater than .25 of the horizontal airspeed. Using Newton 3rd and solving for air mass required to provide lift
3430=.5*M*5*5 =12.5*M
M=274 kgs of air or 220 cubic meters of air at sea level

Now I will leave to those who are interested to calculate what happens when the lift has to be doubled as in a 2 g turn. PR 10 Sept07. PatRobot 02:10, 26 September 2007 (UTC)

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Ooohh, a trick question and you almost got me. If you're already at the stall speed you can't pull 2g in a turn!

I see no aerodynamics in your equations. It looks more like the equation for a ball on a string. Can you please show the force and moment diagram that includes a centripetal force? What about the upwash in front of the wing?

Are you saying the air is only disturbed one meter from the wing (r=1)? Even for an A380?

How did you determine that Vd=0.25*Vh? That's a lot of downwash!

So is it 6.9 or 220 cubic meters of air? How can there be two different answers?

Tzickuhr 03:30, 12 September 2007 (UTC)

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Sorry it was not meant to be a trick question. In a 2 g turn the new stall speed can be easily be determined knowing that the lift goes up by the square of the airspeed. The stall speed will typically occur at about 15 degrees angle of attack and just before the stall occurs is the maximum lift the wing can produce at any given speed.
This implies that air mass moved must remain constant at any given angle of attack, and moves across the wing in a shorter time at higher speeds. If we base our calculations on vertical movement of air we get an impossible answer for air mass on the other hand if we base our calculations on the curved airflow we get an acceptable answer that is the air mass moved remains constant at the stall angle regardless of speed.
The justification for saying that the vertical speed of the air can be no more than .25 of forward speed is that airflow from the highest part of the of the wing to the trailing edge represents the maximum vertical height that the air has to move in unit time and is Tan 15 degs just before the stall angle is reached.
If Vh=30 m/s and angle =5 degs then Vd=2.6 m/s or 5 knots which might be more typical for a light aircraft in cruise mode.

I'm slightly confused by this working, it appears not to recognise that the air is accelerating all the time it is in the pressure gradient and that it is the final speed that is important, not the average as this appears to estimate. 11:01, 29 September 2007 (UTC) —Preceding unsigned comment added by Rolo Tamasi (talk • contribs)

The values calculated by me under Newton 3rd and lift are simply to demonstrate the scale of the problem and may well be off by some margin. The results showed I hope how improbable it was that vertical momentum could account for lift especially as I ignored up flow upwash in front of the wing which of course makes the vertical calculation invalid.
Applying the principle that bending the airflow causes lift then we can say that up flow upwash contributes to the overall lift. So the answer is much closer to 7 cubic meters of air than it is to 220 as in the example given previously.
The value I used for the radius should I think be of the same order of magnitude as the chord of the wing in use. The radius does not determine how far above the wing the air is disturbed. Of course to get the correct answers you would have to integrate the various radii over the whole wing but using F=mv2/r does give an idea the much greater forces involved in bending the flow rather than just pushing air vertically down.
As a pilot my main interest is to explain how lift works to others in a way that I hope complies with conventional aerodynamics and physics.PR 13 sept 07 PatRobot 02:10, 26 September 2007 (UTC)

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It was a joke.

It's obvious by your description that you don't have a clue how a wing works. You're just making up numbers and plugging them in equations that have nothing to do with aerodynamics. Your ability to pilot an airplane does not lead to any understanding in how a wing works. I've read that many pilot training programs use incorrect descriptions of lift. You haven't even acknowledged that you understand what upwash is.

A wing lifts because the surface curvature and angle of attack cause the pressure on one side to be lower than on the other side. And this has nothing to do with the bogus equal transit time nonsense. It's physics.

When we do a CFD analysis, we integrate the pressure on the surface to calculate the lift. If we want loads distributions from a wind tunnel model or an airplane, we measure the surface pressures and integrate them to calculate the lift. The only forces that can be applied to an object by a fluid are the pressure normal to the surface and the shear stress tangential to the surface.

We never use the vertical velocity in any way to calculate the lift of the wing.

As a professional aerodynamicist who designs wings for a major business jet manufacturer, my main interest is to explain how lift works that is correct. If you have any questions, please ask.

Tzickuhr 02:16, 14 September 2007 (UTC)

Do I see a possibility that you may agree with each other? PR says that the total lift cannot be explained only by vertical acceleration of the air (whether or not you agree with his maths). I think that below Tzickuhr says something similar viz. “The lift is the integral of the rotational velocity (the vorticity) of the wake, not the integral of the vertical velocity.” Rolo Tamasi 23:51, 14 September 2007 (UTC)

Absolutely correct Rolo. Oh and by the way as pressure is force per unit area what is the origin of the lift force Tzickuhr? Pr 16 Sept 07 PatRobot 02:10, 26 September 2007 (UTC)

I’m surprised you don’t understand that PR. The answer is that the origin is the relative movement between the wing and the air. That creates pressure differences that have the equal and opposite effects of lift on the wing and acceleration of the air. Rolo Tamasi 09:38, 16 September 2007 (UTC)

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It is the airflow changing direction that is the origin of lift force.

I disagree, I would say that the acceleration of the air and the lift have a coincidental rather than a causational relationship. For me there is a clear, undeniable, logical sequence. The origin is the relative movement between the wing and the air, angle of attack is a condition and pressure differences are the result. The pressure differences in turn cause two coincident effects, lift on the wing and acceleration of the air.Rolo Tamasi 20:12, 1 October 2007 (UTC)

The mistake that is made by a number of people on these pages is their failure to understand that acceleration is a vector quantity. When an object moving at speed changes direction, large forces are produced and that acceleration is often greater than either it’s starting speed or its final speed.

I suggest it is safer to assume that people in here have an intimate understanding of acceleration and of vector mathematics.

A speed cannot be smaller or larger than an acceleration, they have different dimensions and are therefore incomparable.Rolo Tamasi 20:12, 1 October 2007 (UTC)

If we consider an object moving horizontally at 16 meters/sec and 1 second later it is moving vertically at 9 meters/sec what is the acceleration? If you really understand acceleration you will know the answer straight away. If you have difficulty working this out you will have to study up on vectors.

If we consider an object moving at 16 metres/sec and 1 second later it is moving at –9 metres/sec what is the acceleration it has experienced? Rolo Tamasi 20:12, 1 October 2007 (UTC)

When you have worked out the acceleration you can then find the size of the force that caused the change by multiplying it by the mass.
In the case of air flowing over a wing we need to know the acceleration at every point around the wing and the mass of air involved then we can determine the total lift force. It sounds simple, but is difficult to actually calculate, for this reason an easier method is used to calculate the lift forces. That is to measure the different pressures at a large number of points around the wing and add them all together to find the total lift force.
If you want to demonstrate the effect next time you are at supermarket push a loaded trolley directly away from you and let go, you will notice you can not get much of a push force in the opposite direction. On the other hand try to swing the trolley through an arc of say 180 degs and you will find that the pull force you have to provide is large and lasts much longer than the simple push case. Now suppose instead of swinging the one trolley through 180 degs we swing a succession of trolleys through say 30 degs of arc we would experience a powerful and continuous force pretty much in one direction. I don't need to point out that the trolley has to allow all wheels to steer for this to work. That it I’m going shopping! PR note name change last name got cancelled by Wiki PatTwace 05:56, 1 October 2007 (UTC)

The secret of the difference here is the instruction to let go in one and not the other. This does not demonstrate that it is possible to transfer more energy by continuingly changing the direction of acceleration. It only shows that you can you transfer more energy if you are able to hold on longer!

The only difference between the curved flow of air and a linear flow of air is the viewpoint of an observer (you are in the aircraft, I am on the ground). The same energy is required in both and the maths for both is essentially identical other than the approach needs to be consistent throughout the frame of reference.

This is a classical example of why it is important to ensure an understanding of the principles informs the use of the maths and why it is dangerous to allow the maths to inform your understanding of the principles.Rolo Tamasi 20:12, 1 October 2007 (UTC)

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The lift is due to the pressure on the wing. The wing pressure (due to the circulation) extends out to the walls so that the integrated pressure on the walls equals the wing lift. F=F. The summation of the forces equals 0. I have proven this with a CFD calculation. If anyone else does this calculation and gets a different answer, please let me know.

The lift is related to the downwash behind the wing based on the circulation. However, the circulation also induces an upwash in front of the wing that is equal to the downwash. There is no net downwash. The air is not accelerated in the way this page describes F=ma. This "physical description of lift" ignores the upwash in front of the wing and is wrong and is in no way equivalent to pressure. There is not an "equal and opposite" acceleration of the air. I'm going to try to do this calculation in the next couple weeks by integrating the vertical velocity on a cut plane in front of the wing and behind the wing and showing that they are equal and opposite.

The pressure on the wing is due to the curvature of the surface. This is hard to explain, which is why there are so many incorrect explanations. I'll see if I can put together some pictures that explain this visually.

I'm working with a professor to complete my understanding of a few details of the far field lift derivation, but I'm confident I'm right. If anyone would like to discuss these details, please let me know.

PR, I do not understand your question. The origin of the lift is the pressure.

Tzickuhr 02:22, 19 September 2007 (UTC) TZ

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TZ The statement “The pressure on the wing is due to the curvature of the surface” is meaningless what I hope you are trying to say is “the air flowing over the curved surface of the wing causes a reduction of pressure” in which case we would seem to agree on number of the relevant points.

I can’t go along with the repeal of Newtons second law as pressure is simply an example a force spread over an area therefore we are stuck with F=ma. Please explain A why it is not applicable or B how it should be applied PR 20 Sept 07.PatRobot 02:10, 26 September 2007 (UTC)

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This appears to be a problem about definitions rather than a difference of substance.

I prefer to ditch the jargon in a public forum as it confuses rather than informs and is unnecessary.

For example, air does not circulate around an aerofoil when it generates lift. The variable named “circulation” in the Kutta-Joukowski equation may well be non-zero but that does not mean that there is any pattern of flow that could be called circulation in any normal meaning of the word. It is a little like the difference between saying “For some purposes all the mass of a body can be considered to be acting at the centre of gravity” and “All the mass of a body is at the centre of gravity” – lazy use of jargon that could lead to a big misunderstanding.

Likewise, while it may be important to take account of any curvature of a wing in order to accurately calculate lift, curvature is not required in order to generate lift.

I am always surprised that some people’s curiosity is satisfied by the explanation that lift is caused by accelerating the air. That, as Basil Faulty would say, is a statement of the bleeding obvious. It explains no more than saying the air is accelerated because there is lift. Neither of them gives any indication at all what the mechanism actually is – and that mechanism is the formation of pressure differences. Rolo Tamasi 15:43, 20 September 2007 (UTC)

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Acceleration of air over an aerofoil.
In the following discussion my remarks apply to aerofoils moving at speeds below about 300 meters per second.
Air molecules at room temperature are moving at speeds in the range of 500 m/sec or close to 1000 knots.
When an object moves through the air there is a relationship between the speed of the object and the speed of the air molecules. Suppose we have a wing moving at 50 m/sec then any air moved out the way by the wing will be replaced by air from the immediate surroundings and not from some more distant location. In other words the potential void at the back of the wing will not be filled by air from the front of the wing; it will fill from close by long before it can have any influence over the more distant air near the front of the wing.

The question then arrises as to the reason the air flow accelerates over the front section of the wing. To keep it as simple as possible let us consider an aerofoil which is a curved plate, (and part of the arc of a true circle) where the chord is at zero degrees to the air flow. A small parcel of air striking the top surface of the leading half aerofoil will attempt to leave at a tangent this will produce an area of lower pressure both below and ahead of the parcel, thus causing an acceleration of the air along the surface of the wing but only up to the mid point of the aerofoil beyond this point the horizontal component is reversed. The air then starts to slow down which in turn causes the air pressure to rise. A similar situation occurs on the underside of the wing but the situation is reversed so that the net result is an increase in pressure in the first part of the aerofoil and the pressure starting to fall towards atmospheric after it passes the mid point of the aerofoil. You can understand this in terms pressure differences, Bernoulli or acceleration as you wish. These effects take place over very short distances, not over longer distances as the air molecules are just too quick.

As they are taking place instantaneously along the entire pressure gradient and the pressure gradient is propagating at close to the speed of sound they are actually taking place over quite large distances (typically expressed at between 1 and 2 wing spans).Rolo Tamasi 17:32, 12 October 2007 (UTC)

The acceleration I referred to was in the vertical plane not the horizontal (I was contrasting the deflection explanation of lift and the pressure explanation), the accelerations in the horizontal plane broadly cancel out and thus their effects do also. Many people have, from an early understanding, been seduced into the trap of perceiving that horizontal speed increases create lower pressures and thus lift. It is just a perceptual fallacy, the relationship is coincidental not causational. Rolo Tamasi 17:32, 12 October 2007 (UTC)

Now I hope it will be clear why the nose of an aeroplane or airship is rounded and the tail tapered to a narrow point.

A flat plate at an angle to the air flow produces lift because the airflow changes direction and as it is impossible for it to change direction instantly it follows a curved path. --PatTwace 07:37, 12 October 2007 (UTC)

I think the above sentence illustrates the problem perfectly. Whether the air is moving or stationary is merely a matter of the frame of reference of the observer. Most see aircraft moving in stationary air – the perception of curved path caused by the acceleration is a purely matter of choice. It is possible to accelerate along a straight path if it starts as stationary. It is thus confusing to say that lift is caused by the path being curved. Rolo Tamasi 17:32, 12 October 2007 (UTC)

The frame of reference is unimportant the air flow is still curved the air is accelerated both backwards and vertically thus giving a curved path compared to the more distant air.--PatTwace 22:36, 14 October 2007 (UTC)

It is only because of a particular frame of reference that you were able to say "it is impossible for it to change direction instantly". In any event, the air is accelerated backwards and then decelerated. Both of these events are perpendicular to the plane of the lift and thus have no effect on lift. In addition the horizontal acceleration and deceleration cancel out, there is no residual horizontal momentum. Rolo Tamasi 18:57, 15 October 2007 (UTC)

In any event, the air is accelerated first upwards and then downwards. Both of these events are in the same plane as the lift and thus have no effect on lift. In addition the vertical acceleration and deceleration cancel out; there is no residual vertical momentum.--PatTwace 03:09, 19 October 2007 (UTC)

So you don’t believe that fans work?

Consider, for example, the high-pressure region on the under surface of the wing. This creates pressure gradient from the high-pressure to the ambient with a component that inevitably accelerates the air downwards, where is the reverse gradient that decelerates it back to stationary?

Pressure works equally in all directions, if part of the pressure works on the wing as upwards lift, there must be a reverse net effect working on the air accelerating it downwards. Rolo Tamasi 11:59, 20 October 2007 (UTC)

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Yes, it is the curvature of the air flow that creates the low pressure, but the curvature of the surface causes the air to turn. I tend to focus on the surface because that is what I have to change to get the air to turn to get the pressure I want. You are correct in that the physics is all about the air.

But wings with no curves also generate lift. There is no need for the air to turn, just for it to accelerate. I find it far clearer to consider that the pressure difference causes the acceleration of the air rather than the other way round. The pressure difference is caused by the wing moving and vacating space. Rolo Tamasi 18:33, 24 September 2007 (UTC)

A simple aerofoil can be made by taking a flat sheet and bending it into an arc of a circle. An aerofoil made like this works fine but once the camber exceeds a value of about 7% the aerofoil will only work at positive angles of attack. Such a wing will not produce lift at negative angles of attack or if you like it will not allow the aircraft to maintain level inverted flight. So curvature is kinda important. I will leave it to the reader to figure out why.--PatTwace 06:20, 8 October 2007 (UTC)

Rolo

I will try to explain why the idea that the void that you think should form over the back section of the wing is not responsible for lift. First of all when you move an object through the air it simple flows around it and no voids are formed. The next point to consider is this, if a void were indeed formed in this region, the air would fill it from the rear of the wing not the front and would slow the air down over the top of the wing not speed it up. The air does in fact start to slow down once it passes over the thickest part of the wing, but this has more to do with fact that the air is no longer turning so quickly and therefore the acceleration is less. This all shows up clearly when you look at the pressure around a wing at least half of the lift is generated by the first ¼ of the wing. That’s why they put mainspar around that position.

To understand circulation think of it this way suppose we take a hollow cylinder and spin it. The air on the outside of the cylinder will be flung outwards thus creating and area of low pressure right around the outside wall, on the other hand the air on the inside will be flung from the centre of the cylinder to the wall creating a higher pressure on the inside wall.PR PatRobot 02:10, 26 September 2007 (UTC)

I don’t think a void should form over the back of a wing, but it would if the air did not flow. The reason the air accelerates is because of a pressure gradient. In steady state conditions equilibrium is established where the pressure gradient is sufficient to cause the flow rate necessary to maintain the pressure gradient. This is the mechanism by which any fluid flows round any body.

On the top of a wing the pressure gradient exists in all directions but the horizontal accelerations cancel out. I would be interested to understand why you feel the air would accelerate from the back and not the top. The air accelerates horizontally before the maximum low pressure and decelerates horizontally after it.

The simple answer is that it that’s not what happens anyway, but even if it did the air would fill the potential void from all available directions but as the wing is in the way some of the area to the front is unavailable and we are left with a net acceleration of the air towards the front of the wing and by newton 3rd a net rearward force on the wing.PR PatTwace 05:42, 1 October 2007 (UTC)

You appear to believe that the air on top of the wing is slower than the free stream speed and that it gets relocated forwards (and indeed continues moving forwards). I have never come across these ideas before. Can you explain? Rolo Tamasi 21:25, 1 October 2007 (UTC)

Which proves the reason the air speeds up is not due to a low pressure area behind the wing. The air speeds up because it has to follow a longer path around the curve than the straight line path. Just like the water skier who moves out the side of the boat will move much faster. If you have ever flown a plane you will be very familiar with consequences of the air trying to move from the back of the wing to the front it’s called a stall.

I am afraid I don’t see that is an attempt answer to my question.

The air velocity is not due to the longer path. It is due to the curvature of the path. The length of the path for the air around a sail is the same on both sides, but the pressure on the concave side is higher and the pressure on the convex side is lower. Tzickuhr 03:21, 11 October 2007 (UTC)

I agree point taken --PatTwace 07:37, 12 October 2007 (UTC)

However, I have two issues with what you do say: -

1)You don’t need a curved surface to generate lift (as you said yourself).

The benefit of a curve is an optimisation of the acceleration along the aerofoil; it is not an essential element for lift. My concern is that any definition of lift that says it is caused by the curvature of a wing will confuse the reader, as they will take it to imply that wings have to be curved and also that inverted flight is impossible.

2)Only a pressure gradient can cause a fluid to accelerate.

I am exceptionaly familiar with the behaviour of a wing at the stall. I see no value in describing a stall in the terms you do. As long as there is a low pressure region the air is "trying" to flow towards it. In most real life stalls the air is not flowing backwards. Rolo Tamasi 16:21, 8 October 2007 (UTC)

See this link http://www.youtube.com/watch?v=zrwlpHE7P8Q It shows the air flowing forward at the stall and its fun.PatTwace 03:04, 10 October 2007 (UTC)

You are confusing the issue with separated flow. That is a very complicated subject and is beyond the scope of this topic. It's hard enough to get people to understand lift with attached flow. Let's stick with that.

I dont agree that it is hard to get people to understand lift. It is just hard to get those who don't understand it to stop confusing people! Rolo Tamasi 17:32, 12 October 2007 (UTC)

Likewise, when you say you don't need to have a curved surface. True, it's the curvature of the air flow path that generates the pressures that create lift, but if the surface is not curved, you will not get much lift before the flow separates. Again, more complicated than needed for this topic. Tzickuhr 03:21, 11 October 2007 (UTC)

Agreed! Rolo Tamasi 17:32, 12 October 2007 (UTC)

To quote from a Martin Simons a well know aerodynamics professor “Every diversion from the straight path is associated with interdependent velocity and pressure changes.” --PatTwace 06:20, 8 October 2007 (UTC)

Obviously, a change of direction is an acceleration, which can only be created by a pressure difference. I don’t se any reference to curve. Rolo Tamasi 16:21, 8 October 2007 (UTC)

I understand circulation very well thanks. It’s a shame that name was used for the variable as it confuses so very many people. If you are saying that the layman would see any pattern of flow with a non-zero line integral around the shape as a circulation I must disagree with you.

A curved acceleration can be resolved into two perpendicular linear accelerations. There is little point in arguing that there is a substantial difference between the two. If you consider a vertical acceleration of the air from a moving wing frame of reference you will see a straight line. If you consider it from a stationary wing frame of reference you will see a curve. They are both the same.

The simple world of lift is being completely confused by people who believe that mathematical models define the principles. They don’t, it is the other way round. There are many ways of mathematically modelling the same lift.Rolo Tamasi 23:15, 28 September 2007 (UTC)

Personally I find it very disappointing when a perfectly good theory has to be discarded because of the failure of the facts to cooperate.In the above case the facts are as follows:-

The pressure above the wing drops to near its minimum value in the first 5 % of the wing chord and remains close to the minimum until it reaches about the half way point on the wing and then starts to rise rapidly. In fact a pressure higher than normal is reached before the air the leaves the trailing edge of the wing. This has been measured countless times in wind tunnels.

I can’t see a logical reason for a low pressure zone to relocate to any place other than where it was created. I add these comments with some trepidation as I have not fully digested your comments above EG A curved acceleration can be resolved into two perpendicular linear accelerations.PatRobot 01:00, 30 September 2007 (UTC)

We appear to failing to communicate effectively. – I have not made any reference to the nature of the pressure profile along the top of the wing, that changes significantly on shape, speed, angle and chord length. But in all cases when a wing is generating lift it is, on average, below the ambient pressure that exists before and after the wing. What is the relevance of its profile?

I am interested to understand why some consider there to be a significant difference to the energy input required to accelerate air along a curved path rather than a linear one. I suggest that this is just an artefact of a particular mathematical approach and, in particular, the frame of reference that happens to be chosen. It may be misleading to call it a theory. Rolo Tamasi 14:35, 30 September 2007 (UTC)

I'm not trying to repeal any of Newton's laws. The pressure (force/unit area) on the surface area of the wing integrates to the lift force. This has nothing to do with F=ma. The pressure on the upper and lower walls of a wind tunnel also integrate to the lift force in the opposite direction. Pressure acts on an area to create a force.

A book on a table applies a pressure (force/unit area) on the table. The table applies a pressure back on the book. F=F. Or more technically, Fbook-Ftable=0. Fwing-Fwalls=0

Rolo, air does circulate around a wing, but it is superimposed by an onset flow and therefore does not look like the circulation you mention. Picture a spinning cylinder, with and without an onset flow. A wing needs the onset flow to create the circulation.

Tzickuhr 22:47, 20 September 2007 (UTC)

Hi, Tzickuhr. My point is that Wikipedia is here to inform rather than to confuse.

Some of us in here have a thorough understanding if lift but Wikipedia has far more to offer those who do not and have looked up Wikipedia in order to learn. They have to be the primary target audience.

Unfortunately, while the former group understand the substantial difference between circulation and circulation, to the target audience the two words appear identical and thus they can only be confused, it has to be avoided.

Your justification is subject to two fundamental flaws in logic.

Just because Γ is non-zero when the air is circulating it does not mean that whenever Γ is not zero the air must be circulating (all men are human but not all humans are men). It is a shame it was ever given that name – rotation would have been better but has different conflicts.

(Modified on re-reading my reply.) When you say the flow “does not look like the circulation you mention.” You are recognising that the flow does not at all resemble circulation in any normal use of the word, i.e. that the actual flow is not circulating.

By subtracting the free stream speed and direction from every part of the flow you are changing it hugely from that which actually takes place. Once you do that I accept that you would have a flow pattern that might be said to look more like a circulation than the actual flow does but even then I would say it is not even close to what most laymen would consider to be circulation.

Why cant people just accept that Γ can have a value without the flow actually being a circulation?

And why are there so many contradictory and flawed diagrams all over the Internet struggling to demonstrate the impossible?

I understand the concept of circulation; it is straightforward but is continually presented in a way that completely confuses people who are trying to understand lift a little better. Let us not add to the confusion. Rolo Tamasi 11:55, 22 September 2007 (UTC)

Correction required to Coanda Effect opening sentence

The opening sentence currently reads: 'A common misconception about aerodynamic lift is that the Coandă effect plays a no part.' What's being said?? This obviously requires correction, please! —Preceding unsigned comment added by 206.47.191.132 (talk) 12:20, August 29, 2007 (UTC)

Lift Equation only provided as algerbraic restatement of Lift Coefficient

Since this article's intent is to explain and define 'Lift', I believe it would be preferable to have a short review of the Lift Equation near the start of the article which defines lift in the classical formula: L =0.5*Cl*r*V^2*A. The restatement of this formula in the latter part of the article as the definition of Lift Coefficient should be secondary to the principle definition of lift i.m.h.o. —Preceding unsigned comment added by 206.47.191.132 (talk) 13:03, August 29, 2007 (UTC)

Thoughts on downwash

As Mr. McLean mentioned earlier, the equations of motion are simplified to get the Navier-Stokes equations, which is the best flow simulation used on a regular basis. By eliminating viscosity, the N-S equations are simplified to the Euler equations. Eliminating the rotational terms yield the Full Potential equations and eliminating compressibility finally gives the Potential flow equation.

The Potential Flow (Laplace) equation does a wonderful job of predicting the lift of a wing. It is typically solved using a Panel Method or a Vortex Lattice method.

Working with the simplest form, the Vortex Lattice method uses a series of vortices to simulate the flow over a wing. These are arranged as a series of horseshoe vortices to model the spanwise lift distribution. Each vortex induces a symmetric flow field which results in an equal and opposite velocity distribution on each side of the vortex (see Figure 3 of http://web.mit.edu/2.016/www/handouts/2005Reading4.pdf). Therefore, looking at the vertical component of velocity, each individual element of the vortex lattice model will induce an equal and opposite vertical flow. The upwash in front of each wing element will be equal to the downwash behind the element. The upwash outside of each wake element will be equal and opposite of the downwash on the other side of the element. The Superposition principle says that the effect of each of these vortex elements can be summed together to calculate the velocity at any point in the flow field.

There can be no net downwash.

Everywhere there is downwash in the flow field, there is a corresponding equal and opposite upwash due to the other side of each vortex element. If you look closely at the pictures in <http://pof.aip.org/pof/gallery/pdf/1993/S5_1.pdf>, you will see the upwash extending outward from the wing tips. Note the location of the core of the vortex in Figure 2. Note how the smoke line outboard of the tip vortex is completely above the core.

The lift force (the pressure on the wing) is reacted against the walls (ground and space). The lift force cannot be reacted out in two different ways.

One more thought experiment. When an element of fluid is displaced downward, what fills the space that it used to occupy? How did it get there? Are those forces equal and opposite?

TZ 30 Aug 07 Tzickuhr 03:18, 31 August 2007 (UTC)

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> The lift force (the pressure on the wing) is reacted against the walls (ground and space)

Thinking out loud here... I believe we need some thought experiments to help zero in on critical concepts.

When a ship's prop suddenly starts turning, it experiences a thrust force... but where is the "wall" upon which it reacts? The narrow jet of water being created by the prop becomes longer over time. But must it strike a "wall" in order for the ship to begin accelerating? Does an aircraft require such a "wall," or could it still produce a lifting force if the distant Earth's surface was not present? Or do you believe that an underwater propeller obeys fundamentally different physics than a wing in flight?

This line of thinking demonstrates that you do not understand pressure. The "narrow jet" you speak of is the downwash behind the propeller due to the spiraling trailing vortices. The force that accelerates the boat is due to the pressure on the surface of the propeller. The downwash behind the propeller does not have to reach a wall but the pressure field created by the flow over the propeller will. Tzickuhr 10:41, 3 October 2007 (UTC)

Another example: a water-filled rubber balloon can accelerate forwards via F=mA, by ejecting a jet of water out the rear. If we immerse this balloon in a large water tank, is the physics fundamentally different? (In the water tank all the flow lines are closed, but does the balloon suddenly STOP being a reaction engine?!!

If I'm sitting in a rowboat, I can scoop up a bucket full of water from the lake. In doing so, I take water in from all directions. I then fling that water rearwards in order to accelerate the boat forwards. By injecting momentum into the water, I inject opposite momentum into the rowboat, just as with a rocket engine. Is this fundamentally different than using a paddle or a propellor immersed in the water? (Flinging a bucket full of water does not require any distant "wall" to react against... but is a propellor or a paddle or an airplane wing somehow different?)

In all these examples all streamlines must be closed, so in a global sense "upwash" must always equal "downwash." Yet if a pump should draw in mass-bearing fluid parcels from all directions, but eject the fluid in a narrow jet, that pump will accelerate itself as a reaction engine, and it will experience a reaction force proportional to the momentum-change given to those parcels over time. Isn't it similar to a rocket with momentum deposited into the "exhaust?" Or do you believe it's like a venturi problem where the force cannot exist unless there is a distant "wall" upon which an equal opposite force appears? --69.29.211.201 04:48, 24 September 2007 (UTC)

These cases are irrelevant to the lift on a wing. A fluid can only exert force on a body in one of two ways. A pressure acting normal to the surface and a shear stress acting tangential to the surface. Tzickuhr 10:41, 3 October 2007 (UTC)

It is an example of taking something simple and making it appear complex through muddled thinking. Of course a force can be reacted more than once. I am sitting on a chair; my weight is being reacted by the chair. The floor is reacting the weight of the chair and also my weight. Imagine a tall beaker of water on some scales. Then introduce an object heavier than water and with a very "draggy" shape, the scales will register the additional weight of the object as soon as it is placed in, long before it reaches the bottom of the beaker. The weight is being reacted by the drag as well as by the scales. The air exerts a pressure on the ground representing the air plus everything in it (adjusted for any acceleration effects of course). Rolo Tamasi 18:26, 24 September 2007 (UTC)

A force cannot be reacted in more than one way. This is fundamental physics. If a body is not accelerating, the sum of the forces must equal zero. You have combined two different control volumes. The chair reacts your weight. When you include the floor in your control volume, then the floor reacts the weight of the chair and you. Your weight is always being reacted through the chair. In all cases the sum of the forces must equal zero since there is no acceleration.

The drag force of the object dropped in the beaker is due to the pressure field in the fluid, which gets reacted against the walls of the beaker. It is always the pressure. Tzickuhr 10:41, 3 October 2007 (UTC)

Hi Tzickuhr, I was agreeing with you and your reply is agreeing with me! (worrying eh?)

As an aside, it is interesting to consider what the mechanism is that transfers the weigh of my object to the pressure on the floor and walls of the beaker. Clearly once the object reaches terminal velocity the pressure difference between the top and bottom of it equals its weight. However this pressure difference is due to an increase underneath it and a decrease above it. It is easy to see how the increased pressure below it has the effect of increasing the pressure in the entire beaker.

Would anyone like to explain if and how the decreased pressure above the object results in and increased pressure in the bulk of the beaker??? Rolo Tamasi 18:40, 3 October 2007 (UTC)

PS to get back to disagreeing, I believe my chair example is a useful illustration of multiple reactions to a single force. I also agree with you that if all the reactions don’t balance you will get acceleration. However, as the air is accelerating why are you unhappy with the multiple reactions? Rolo Tamasi 18:40, 3 October 2007 (UTC)

Do you understand control volumes? This is sophomore engineering. For your chair example, there is no acceleration therefore the sum of the forces must equal zero for any control volume. The chair reacts the weight of the person. The floor reacts the combined weight of the chair and the person. These are two different control volumes. The weight of the person is not reacted out in two different ways.

For the control volume we really care about of a wing in air, the induced drag is reacted out by the angular momentum (what you seem to be calling acceleration but is more accurately called conservation of momentum) in the wake and the lift on the wing is reacted out by the pressure on the upper and lower walls. The lift cannot also be reacted out with a change in vertical momentum. The far field momentum derivation proves this. Please read the paper by Cummings (AIAA-96-2482, purchase at www.aiaa.org) and tell me where they are wrong. The "downwash" theory is wrong ("Lift is generated when an object turns a fluid away from its direction of flow." and the whole section on "Reaction due to deflection" need to be removed). Tzickuhr 02:43, 4 October 2007 (UTC)

Please Tzickuhr, don’t allow your frustration to turn into personal remarks. I was trying to tease the discussion out in a direction that would lead to a resolution of our little conundrum.

Yes I believe I understand what you mean by control volume.

Following your red herring for a moment - Are you saying that a change of angular momentum does not involve acceleration? (Before you ask, I am familiar with the conservation of energy principle.)

Wow, how many times can I indent? Of course any change in momentum involves an acceleration, but when you're working with a fluid in a control volume you use the conservation of mass, momentum and energy equations to determine what's happening. For a control volume as described in Cummings' AIAA paper, there is no acceleration on the boundaries. You only look at the pressure and momentum on the boundaries. The only momentum being angular momentum (vorticity) on the downstream face. Tzickuhr 03:10, 5 October 2007 (UTC)

I am a free man. YOU may choose to use conservation of momentum but, when I describe my point of view, I use the terms I feel best help my point to be understood. We will find at the end of this journey that the conundrum you struggle with is all about clear understanding of language and not about physics at all.Rolo Tamasi 08:47, 5 October 2007 (UTC)

Let us just keep it simple.

Your hypothesis is that all lift forces on an aerofoil are explained by pressure differences (I agree, in a friction free environment it is the only way a fluid can have any influence on a solid body). You then go on to say that these pressure differences are reacted on the walls/floor and there cannot be any other reaction and thus it is not possible for an aerofoil to also result in a movement of the air.

This isn't a hypothesis. It has been proven by Maskell, Cummings, Kusunose and others. I never said there is no movement of the air, just that there is no _net_ change in vertical momentum. And I'm just passing on what these others have proven. Tzickuhr 03:10, 5 October 2007 (UTC)

For you it is an absolute truth that, even though you cannot fully explain it, you accept as such. A little like religion and no the less valid an approach for that. I, on the other hand, see an idea being described with a stated conclusion clearly at odds from my experience. You say we must stop talking about downwards deflection because it is impossible but I still feel the breeze from my propeller. Please excuse me for calling it an hypothesis until you have explained.Rolo Tamasi 08:52, 5 October 2007 (UTC)

I ask,if that is so why can I feel the air moving under a helicopter rotor, a fan, an aircraft propeller and I can see and feel the movement of water from a ships propeller?

Treat me as a dumb 14 year old physics student and explain it to me simply please. I am here to learn. Rolo Tamasi 08:13, 4 October 2007 (UTC)

This is a much different control volume than a wing in steady flight. I have never studied helicopter aerodynamics, so I can't be definitive, but I can point out the obvious differences. The wing wake extends (mostly) straight to the downstream face. The rotor wake spirals down below the rotor. Because the wake spirals down, the tip vorticies have an additive effect which creates a higher velocity below the rotor. However, there is still air moving up outside of the wake. Put your ceiling fan on high and hold a thread outside of the blade tips. The air is moving up. If the same amount of air doesn't move up as down, you would have to compress the air below the rotor, which is impossible.

I think we begin to see the end of the tunnel! A force can be reacted more than once but, at any boundary, the total net effect must equal the original force. You started by implying there can be no acceleration of the air as it is “all pressure”. You then become happy to accept a rotational acceleration and now your description clearly includes a linear one!

What you are describing includes a downward deflection of the air. So why do you say we should drop it?

No one is saying that every time an aircraft flies there is a permanent downward movement of the air so that the top of the atmosphere is getting lower and the air more dense.

The conundrum is in your understanding of the meaning of the words used. You pray to your god and deny the existence of other peoples gods. The truth is we are praying to the same god but describing him in different, yet equally valid ways.Rolo Tamasi 08:57, 5 October 2007 (UTC)

In the end the lift on the rotor is because the pressure on the upper side of the blades is lower than the pressure on the lower side. The control volume for a rotor is very complicated and mathematically may have problems with the wake. It's not even steady. I understand wings, not rotors. Let's stick with wings. Tzickuhr 03:10, 5 October 2007 (UTC)

Both you and I agree that, for a large number of reasons, the “Lift is caused by Pressure” conceptual model is far move valuable than the “Lift is caused by Deflection” conceptual model which tells us very little and is, in the end analysis, totally tautological. However that does not mean that the pressure does not cause a deflection. You cannot have a pressure differences in a fluid without causing the fluid to accelerate. Rolo Tamasi 08:59, 5 October 2007 (UTC)

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Rolo,

Here is what I hear from you. I explain myself but you don't understand, therefore I am wrong. I cite references that prove my point but you don't read them much less understand them, therefore I am wrong. I do calculations to prove my case and you do nothing but say "F=ma is true" but I am wrong.

Please tell me your background that explains why it is me, an Engineer, who does not understand the meaning of technical words explaining aerodynamics, but you do.

You do not even seem to understand the simple concept that a force cannot be reacted out in two different ways. You do not understand that the complicated flow of a moving rotor is not the same as a steady level wing.

I have explained upwash but you have not acknowledged that you understand what it is much less that you believe that it exists. I explained the wake structure of a rotor but you just say "I feel air moving" so I am wrong and you are right. If you reverse the ceiling fan, how come you don't feel the same strong air movement going into the fan? Because the wake structure is on the other side. Do you understand any of this? Everywhere in the room, outside of the fan wake, the air is moving the opposite direction. Do you know why? It's the pressure. Air moves toward low pressure.

Please show some proof that a wing deflects air down to create lift (don't forget the upwash). Find a reference. Show me the math. Use your "F=ma" to prove your case, don't just say it must be.

Have you studied far field momentum theory? Where am I wrong? Please read Cummings' paper and tell me where they are wrong. Prove something.

Tzickuhr 00:06, 6 October 2007 (UTC)

Dear Tzickuhr. I am impressed by your infallible engineer status and reading list. However this is a discussion and an ability to offer clear explanation is the only relevant qualification.

If you are unable to answer the relevant questions I don’t think we should agree with your proposal (that “Lift is generated when an object turns a fluid away from its direction of flow." and the whole section on "Reaction due to deflection" need to be removed.).

Those questions remain-

If there is no deflection why can I feel it? (Helicopter rotor, propeller etc etc)

If the pressure regions can have no other reaction except the pressure on the ground how is the air within the pressure gradients prevented from accelerating?

I think these are perfectly reasonable questions to ask. I am not trying to persuade anyone of anything, you are. Rolo Tamasi 19:44, 6 October 2007 (UTC)

Reasonable, but not relevant. And I already explained why a propeller is different, but you don't understand. This should be a discussion area for experts, not for a 14 year old to argue about things he doesn't fully understand. You still have not acknowledged you understand what upwash is. You don't understand that a force cannot be reacted out in two different ways.

Tzickuhr, you appear frustrated by my sluggishness in agreeing to your proposal and clearly attribute my reluctance to assumptions about my capability, knowledge base and experience. There are alternative possibilities.

You attempted to describe why a propeller is different but failed because what you did was to describe different behaviours but not to explain “why”. I continue to suggest we are lost in interpretation and fear the use of undefined jargon is not helping.

You claim there is no deflection at a wing but accept that a desk fan causes the air to circulate round a room. What is it that causes this difference in the behaviour of the two aerofoils? If the fan aerofoil can exhibit this behaviour why do I have to accept your proposition that a wing cannot? Rolo Tamasi 18:05, 11 October 2007 (UTC)

I'll try that one again. The complete equation is $\sum F=ma$ so if the sum of the forces on a control volume of air is zero, as I have calculated, there can be no NET acceleration. Obviously, the air accelerates as it moves around the wing, but the wing causes just as much upward acceleration (upwash) as it does downward acceleration (downwash). Tzickuhr 03:22, 11 October 2007 (UTC)

I suggest the problem may lie in the following areas – Your use of the word “if”; the definition and application of “control volume”; the definition of “upwash” and “downwash”; and, possibly, some missing factor. Rolo Tamasi 18:28, 11 October 2007 (UTC)

If I'm holding a book and let go, one of two things will happen. If I let go after setting it on a table, the table will exert a force on the book so that the sum of the forces is zero and therefore there is no acceleration. If it is not on a table, then the sum of the forces is not zero and the book will accelerate based on F=ma. Both cannot happen at the same time. Tzickuhr 17:32, 11 October 2007 (UTC)

This is because a book cannot be both touching the table and not touching the table at the same time, they are mutually exclusive. However you have already accepted that there are pressure differences at the wing, lift, air accelerating downwards, air accelerating upwards, air circulating in the room (fan example), and pressure and momentum changes at the boundary to the system. No mutual exclusivity here. Now, which of these do you consider deflection in reaction to lift and which do others consider deflection in reaction to lift? Rolo Tamasi 18:28, 11 October 2007 (UTC)

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Fluid dynamics text books would give you the quantitative expression of the lift force as directly proportional to the integral of vertical velocity component actoss the laminar/tubulent wake behind the body (e.g. Landau and Lifshitz, par. 21). The wake with flow caracteristics different from those of the incoming mean flow (e.g. vortices or downwash) is what makes possible the lift. I would like to end my posts here. N.P.

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The lift is the integral of the rotational velocity (the vorticity) of the wake, not the integral of the vertical velocity. Kusunose of Boeing integrates the vorticity in the wake region of a wind tunnel model to calculate the lift, and actually shows that the contribution of vertical momentum is a small correction that decreases the calculated lift. (Kusunose, K., "Lift Analysis Based on a Wake-Integral Method," AIAA-2001-0420, January 2001.) TZ Tzickuhr 12:56, 31 August 2007 (UTC)

That is interesting. I have difficulty comprehending it but I am not arguing with it. Surely (irrespective of the relative proportions of energy between vertical and rotational) if the impact of the vertical momentum decreases the calculated lift the air must be deflected upwards from the wing on average? I can confirm that the fan in my office and the propellers on aircraft work in the reverse sense. What am I misunderstanding? 15:38, 10 September 2007 (UTC) —Preceding unsigned comment added by Rolo Tamasi (talk • contribs)

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First let me clarify that there is downwash behind the wing. There is also an equal amount of upwash in front of the wing. I believe the correction term in the Kusunose paper is a slight decrease in the downwash due to the viscous wake momentum deficit. I'll try to look at the paper again to see if I have explained it correctly. Tzickuhr 02:51, 12 September 2007 (UTC)

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In answer to the last part of the above question. Most ceiling fans use flat blades and reverse the flow by reversing the direction of the blade which is the same thing as picking the whole fan up and turning it upside down. On an aircraft the flow from the prop can be reversed by changing the angle of the blade to the airflow from positive to negative. An aerofoil is designed to work with the airflow only flowing across it in one direction i.e. from the front which has a obvious radius on it to the back which tapers to a sharp edge. PR 14 sept 07

Indeed but no one was contemplating reversing the pitch and thus it cant be the answer. Rolo Tamasi 18:03, 24 September 2007 (UTC)

Major flaw in the downwash/momentum theory

I have copied this from the article – it appears to have been posted there by mistake as it is clearly a discussion item. Rolo Tamasi 12:25, 20 October 2007 (UTC)

There is a major flaw in the downwash/momentum theory of lift. Whilst downwash and downward momentum may be produced as a consequence of lift (through induced drag for instance), it is however not the cause of lift. In two dimensional airfoil theory (potential flow), there is no net momentum produced in the fluid by the airfoil. Anecdotally, there can be no net flow of fluid in any direction because fluid cannot accumulate anywhere. The flow that goes down, must circulate upward somewhere else, hence zero net momentum. Since there is no net momentum produced in the fluid by the action of the airfoil, there can be no lift generated by this mechanism. There must be another explanation of lift other than the "downward momentum or deflection-reaction theory". I am apparently not permitted to publish the "Curvature Theory of Lift" in this forum because it is classed as Original Work by Wikipedia. It is a faily simple theory and only takes ten lines of simple mathematics to prove. The result however is the same as produced by the Bernoulli Equation.Markosvincios 05:53, 20 October 2007 (UTC)

I agree that whenever any air is displaced, by whatever mechanism and in whichever direction, it must eventually result in flows so that the atmosphere recovers to its original condition. (With the added complexity of a net energy increase due to the work done.)

The same is true of the air in a closed room being propelled by a desk fan; the water in a lake being propelled by a boat’s engine and even a cup of coffee being stirred with a spoon.

However I do not accept that these flows have no momentum, they all do. Rolo Tamasi 12:53, 20 October 2007 (UTC)

I suggest to those who believe that there is a net momentum developed by a 2d airfoil in potential flow - to calculate the net linear momentum produced over a control volume containing the airfoil. A simple equivalent mathematical model can be contructed by the superposition of a uniform velocity field (representing the freestream velocity), and a point vortex velocity field (representing the airfoil with circulation).

Furthermore, an airfoil in 2d potential flow does not perform any work on the flow. The net force (lift) of the airfoil is perpendicular to the freestream velocity. The dot product of the lift vector and the motion vector is zero. Therefore no work is performed by the airfoil on the fluid, or by the fluid on the airfoil.'Markosvincios 13:27, 21 October 2007 (UTC)

There is no net change in momentum in any closed system. The action of firing a gun does not change the net momentum in the system but it does change momentum.

Consider a fan on a desk in a sealed room with stationary air. Turning the fan on will cause the air to circulate around the room. The total kinetic energy in the air will increase, the total net momentum will remain the same, the centre of mass of the air will remain the same and there will be a resultant force on the fan, which will be reacted through the desk. Rolo Tamasi 14:56, 21 October 2007 (UTC)

PS a 2D aerofoil does nothing. Rolo Tamasi 18:02, 21 October 2007 (UTC)

I am confining my discussion to the 2d theory of lift for an airfoil. The concepts I am discussing refer to a single airfoil moving in a straight line. The same kind of airfoil motion that is representative of aircraft wings and lift. These concepts can be extended to three-dimensional flows, and for ease of understanding are limited to 2d. Why be concerned about complex flow situations when a satisfactory theory of lift has not been arrived at even by using a simple flow situation such as 2d potential flow. As a Professional Mechanical Engineer, I have put some thought into what I am saying, and its not my job to lecture others who have unsupported arguments or questions which have not been thought out very well. I am trying to be informative, however, if I am wrong about something then provide the solution for others to see in the discussion section.Markosvincios 11:03, 22 October 2007 (UTC)

It could be confusing if we were to describe the behaviour of 2D systems without explaining how these may be different to real life. Particularly if your conclusions are that no work needs to be done in order to generate lift and that lift generating aerofoils do not deflect the air. 2D systems only exist in order to help us understand.

I am interested in your comment “Since there is no net momentum produced in the fluid by the action of the airfoil, there can be no lift generated by this mechanism.” Can you justify this statement? After all, there can be no net momentum change in any closed system. It appears to be implying that it is impossible to support a body in a fluid by accelerating the fluid downwards by any mechanism at all.

Of course the mechanism has other elements as well (notably pressure differences) but I am quite happy that, in my desk fan example, the reaction from the fan is equal to the acceleration the fan imparts to the air and yet there is no net momentum change in the room. Rolo Tamasi 12:50, 22 October 2007 (UTC)

I plan to elaborate on the Curvature Theory soon, but I want it make sure it can be explained fairly clearly. The theory does involve first year University level calculus and it should be understandable in principle to high school level physics students. So, I will be justifying the theory.

Basically, the source of lifting forces on an airfoil is the "centrifugal acceleration" of fluid particles as they move along the curved path of the streamlines. The "centrifugal lines of force" act at right angles to the flow streamlines and cause a net lifting force on the airfoil. Because the lifting forces act at right angles to the flow, there is no mechanical work being performed.

That is all I will say for the time being.Markosvincios 15:56, 23 October 2007 (UTC)

I have never come across the term "centrifugal acceleration" before and presume your reference to centrifugal force is in the real sense rather than the more usual fictitious sense.

While I’m sure your maths will be just fine I look forward to the justification that the air moves only along the arc of a perfect circle in an inertial frame of reference and does not change speed. Rolo Tamasi 18:21, 23 October 2007 (UTC)

---

In the curvature theory posting in the article the use of equation 3 appears to be unjustified. It only addresses force components normal to the streamline and we know that, as pressure and speed changes occur along the streamline, that there are parallel components.

It is interesting to consider that, if there were to be no components of force parallel to the free stream flow then the motion of the air particles in the inertial air frame of reference would be linear and vertical. Rolo Tamasi 10:15, 28 October 2007 (UTC)

Streamlines Curvature and lift (Removal of Article)

Thanks to the vandalisation of my contribution from (Personal attack removed). Others may revert or review the article if they care to do so. I have other dragons to slay.

It appears the Bernoulli Theory has had 300 years of publicity and it still wrong, yet someone proposes a mathematically sound theory which provides a better explaination of lift, and its then taken down from Wikipedia in a day. Fools.

You may want to follow up with a cited reference from an independent source which was also removed.

See http://www.scribd.com/doc/247213/How-do-wings-work-Babinsky

The abstract quotes:

" The popular explanation of lift is common, quick, sounds logical and gives the correct answer, yet also introduces misconceptions, uses a nonsensical physical argument and misleadingly invokes Bernoulli’s equation. A simple analysis of pressure gradients and the curvature of streamlines is presented here to give a more correct explanation of lift."

Now, two quotes from me

[1] "If some people choose to be ignorant, let them be"

[2] "Whilst some people go to church on Sunday to be closer to God, others study Physics."

Markosvincios 08:26, 29 October 2007 (UTC)

For Your Information: Wikipedia is not a place to advertise your own research (a). It has a (fairly extensive) style manual (b). Your explanation of lift is for example, not truer than, say, solving NS for free surfaces (c). It is not done to sign your contributions on main articles (d). Personal attacks are not accepted (e).CyrilleDunant 09:48, 29 October 2007 (UTC)

Hi, I just found the article on the theory of lift with streamline curvature, on google. The overall results looks correct but for some small mathematical errors in the calculations presented. The sign conventions in the middle of the "proof" need to be rationalised. The static pressure equation in line 2 needs to be made negative. There may be another negative arising with respect to the conventions for the positive direction of radial acceleration, curvature, radius of curvature, or velocity gradient along the line integral. Its a tricky bit of calculus.

I also note that one external link on the article for lift(force) "Physics of Flight-Reviewed" http://user.uni-frankfurt.de/~weltner/ , attempts to prove the same thing, but they stop short by stating "Curved streamlines within a flow are related to pressure gradients. Unfortunately this equation cannot be integrated directly. The integration requires the knowledge of the total flow field." Apparently the deleted "proof" did integrate the pressure gradient without knowledge of the total flow field. Its a shame this article was pulled down. Luckily it will live on in googles database.

JohnBono 14:45, 29 October 2007 (UTC)

Related edit war

Looks like an edit war is breaking out over this issue, and I'd like to nip it in the bud. While the curvature of lift section that's been repeatedly added and removed is malformed, I'd like to see some discussion here as to its actual merits and legitimacy. It contains a citation, which I checked out and which seems to me to back the concept, so as cited material, it is properly discussed here as to its inclusion. Let's keep it civil, free of personal opinion, and focus on whether the material has legitimate source backing. Remember, NPOV requires that even if we disagree with something personally, if it is a cited viewpoint, it can be represented in an article. Having looked over the material in question, its length leads me to ask, additionally, whether it would be better for this material to be contained in its own article and referenced from here with a {{main}} template. AKRadecki^Speaketh 17:17, 29 October 2007 (UTC)

I have several things against this section, most of them being of an aesthetic nature. But I also object to the explanation.

1. it is not widespread (and thus is not really a candidate for WP)
2. it is not, as claimed "true". "True" is solving Navier-Stokes around the wing and integrating the stress on the surface. But then, no model is "true"...
3. Bernouli assumes a potential flow, incompressible and irrotational, true, but when those hypotheses hold, it is a good model. It will model the flight of a paper airplane, for example, but not that of a jet.

I don't believe I need to explain why the shape of the section in unacceptable.CyrilleDunant —Preceding comment was added at 17:44, 29 October 2007 (UTC)

I appreciate your comments, but they seem to revolve around you opinions of what is true and not true. The point here is: do others (ie, published references) discuss this as one of the explanations for lift? There is at least one reference, the one included in the edit, that does. Rather than express your opinion of its truthfulness, it would be more helpful for you to point us to external references that say such an explanation isn't valid. As to "widespread", that is not the same as "notable". If the aesthetics can be cleaned up, is there any policy reasons for not including the information? AKRadecki^Speaketh 18:27, 29 October 2007 (UTC)

No, no, my point was that this "theory" is presented as an explanation for lift. Which assumes that lift needs to be explained (in the sense "proven") somehow. This is not the case: lift stems from the conservation of momentum, the constitutive law of the fluid, and the boundary conditions set by the lifting body and the relative airspeed thereof. This yields the Navier-Stokes equations, which can be solved numerically, and the integral of stress over the surface of the lifting body projected along x and z axes yields drag and lift.

There is no mystical reason for lift, or mathematical demonstration to be made except perhaps to establish the NS equations. This is not my opinion of what is true, that is the state of the art since more than a century -- except then there where no computers and solving such equations was impractical.CyrilleDunant 20:15, 29 October 2007 (UTC)

But to someone who's not familiar with lift, it does need to be explained. That's what an encyclopedia is for, after all. You still haven't pointed to any refs that discount this theory. AKRadecki^Speaketh 20:25, 29 October 2007 (UTC)

I don't need to. There are many models for fluids, they do not all predict lift. Those that do not predict lift do not predict lift because in those models the integral around a closed boundary is always nil. This stems from the following two assumptions 1) the complex function describing the flowlines derives from a potential, 2) there are no singularities in the integration domain.

This is interesting from a mathematical, abstract point of view. But it is not rooted in physics (it is more a kind of "hmmm, what can we solve analytically" kind of reflection). None of those models, however "explains" lift. Lift is a feature of (some) of those models.

The purpose of an encyclopedia is to explain stuff, not wave equations around and pretend they explain something. So basically, there is lift because momentum is conserved, and that is all. CyrilleDunant 21:12, 29 October 2007 (UTC)

You are missing the point. You are approaching this from a philosophy/opinion point of view, not from a Wikipedia policy/guideline point of view. Actually, from a policy point of view, you do have to. You've removed cited material and provided no other reason than your own opinion that it is unnecessary. If style is an issue, fix it. If OR is an issue, either remove only the OR parts or tag those parts with {{fact}} tags and give the contributor a chance to further back up his/her points. This looks like a case of WP:OWN, with you deciding what can and what cannot be in this article, with your opinion being the only guide. One person does not have final authority as to the content of an article, and if you're going to remove cited material, you have to provide a valid reason for doing so. Your opinion by itself is not a valid reason for removal, that is acting in a POV manner. If you don't provide a valid reference stating that the cited material is a hoax, fraud or in some other way inappropriate here, I will work out the presentation issues and re-add it. AKRadecki^Speaketh 23:07, 29 October 2007 (UTC)

No, I am approaching this from the "this has to fit somehow in what is known of fluid mechanics", which is the majority point of view. This section gives undue weight to something that is not useful or interesting or even relevant to understanding lift. It is WP policy not to give undue weight to minority point of view. And I can tell you it is minority point of view because no aircraft is designed today without being modelled using NS, and guess what, they actually fly -- so much for "proving" lift... It is not a question of removing only the OR (which would be all of it), or because the layout is so bad (which would be sufficient grounds for removal as vandalism, even if well meaning vandalism). As for OWN, I'll have you note this is my first foray on this page in over a year, and it is not like it is not the seat of heated debates. Question: what do you think about the presented theory? Does it work? is it physically and mathematically sound? is it intelligible? can you design a wing profile with it? CyrilleDunant 06:50, 30 October 2007 (UTC)

Yes, it is WP policy to not put undue weight on minority theories, but that's not the same as including minority theories. If this was the lead explanation, you would have a point. But it isn't, so you don't. How can it be OR if it is referenced to an outside source? And who are you to judge what it helpful or interesting, two very subjective and opinion-based conclusions? Have you forgotten that we have a broad range of readers here, and not everyone fully understands fluid mechanics the way you do? Have you not considered that multiple math models that demonstrate lift are actually a good thing when it comes to teaching someone? Again, you still have not justified, by WP policies or guidelines, why a section of sourced text should be deleted, other than it isn't interesting to you, and it doesn't fit your view of things. AKRadecki^Speaketh 13:53, 30 October 2007 (UTC)

Because it puts undue weight on a minority point of view. That is WP policy. The pasting of extremely badly formated stuff on pages is also against WP policy. You have not provided a "well-formated" version of the text, as far as I know, which renders any discussion moot. From an encyclopedic point of view, explaining lift with potential flow as a starting point is a Bad Idea™(fluid modelling yes -- for historical reasons, lift no). As for fluid mechanics, I believe less people actually understand what potential flow is than have an intuitive grasp of fluid mechanics. CyrilleDunant 14:09, 30 October 2007 (UTC)

(reset indent)Akradecki, I would encourage you to step back and take another look at this. The introduced content was equivalent in length to the rest of the entire article. A google search of "Babinsky + lift" produces an entirely underwhelming 1,000 hits. There are not many cases where one could make such a clear determination of undue weight. Also note that this was added by a SPA; it sure looks like POV pushing. Maralia 14:43, 30 October 2007 (UTC)

I feel the article should not have been removed although clearly it would have benefited from some editing. However it is better dealt with here until we have some degree of consensus. Anyone who cannot site references and has to ask others to either find some or remove the posting cannot possibly be posting incompliance with Wiki rules. But once others had cited references we moved into the area of substance and style – a more subjective realm and good faith should have been assumed.

I suggest there is a substantial point that needs addressing in the post, that the method ignores all components of force parallel with the streamlines. If the justification is insufficient than it should not be included.

However there remains a further, far more significant issue. There is a view, stated by several in here and very more widely, that lift does not involve a net deflection of the air (upwash=downwash). This view is not expressed within the article. Should it be? If so, how should we address the conflict with the current content? While I would argue against the hypothesis (at least to start with) I do feel that there is sufficient reason to consider a reference to it. Rolo Tamasi 19:40, 30 October 2007 (UTC)

In respect of upwash versus downwash, refer to http://www.arvelgentry.com/origins_of_lift.htm "Origins of Lift"

"And on the 'deflecting the air downward' idea, that is a three-dimensional effect. In our 2-D case, the circulation flow field causes the air out in front of the airfoil to be directed upward around the airfoil and then back down to about the same level as it started out in front. Yet due to viscous effects and resulting circulation, lift is generated. Yes, we can't fly with a two-dimensional wing and, therefore, are influenced by three dimensional effects caused by a complex trailing vortex system. We can reduce these 3-D effects by using very long wings such as on gliders or the around the world aircraft design by Bert Ruttan. On an infinitely long wing, the 3-D effects are gone and we are essentially back to looking at two-dimensional airfoil aerodynamics. If we can reduce the 3-D effects, then 'deflecting the air downward' is not essential to the origins of lift."

The problem with this reference is that it has little authority. It is a private webpage merely asserting something to be the case while providing no argument as to why. Further, the links it provides are to sources that disagree with the notion that there is no net downwash. Rolo Tamasi 11:39, 4 November 2007 (UTC)

It appears to me, as a casual observer, there is a case for discussing the merits or otherwise of streamline curvature and the generation of airfoil lift. Firstly there are credible cited references for the material. This is not new thinking. Secondly, there is debate of style over substance. Not all new contributors to wikipedia are knowledgeable or experienced in its requirements, nor are they necessarily interested in providing a polished article initially. I would rather see substance than puff, and I would like to see the curvature/streamline theory given a proper forum for expansion. The principle that individuals can censor public knowledge because that information is not consistent with their internal beliefs, goes back to the middle ages. Consensus means exactly that.

If the same critical appraisal of this article were extended to all the other contributor articles, then there would be nothing left to read. Lets be fair and consistent in standards.

Which credible cited references do you have in mind? Rolo Tamasi 11:40, 4 November 2007 (UTC)

Circulation Lift Theory and Momentum Reaction/Downwash/Deflection Theory are Incompatible

I do not know why anyone has not seen this contradiction before.

In the derivation of the Lift equation for circulation, $L=\rho V\Gamma$, there are certain assumptions made.

The key assumptions are:

1. The Bernoulli equation is correct, and

2. No contribution to lift arises from momentum effects, because there is no change in momentum across the control volume containing the airfoil.

So, anyone who says that changes in momentum cause lift cannot say circulation causes lift too - because the derivation of the lift circulation equation, (not shown here), says so.

Alternatively, and correctly so, anyone who says the circulation theory of lift is correct cannot say the momentum theory of lift is correct too.

It appears the momentum theory of lift is based on false concepts or false assumptions. —Preceding unsigned comment added by 58.110.94.188 (talk) 17:05, 13 November 2007 (UTC)

Calculation of the momentum equation (not shown here) DOES show a contribution to lift force from momentum effects. Although not obvious, or intuitive, the momentum equation does show that half of the total lift force is developed from the rate of change of momentum across the control volume, and the other half of the lift contribution is from static pressure forces acting externally on the control volume.

What is harder to understand, is what this really means in practice.

Why?

1. If the control volume is drawn around the surface of an actual airfoil then all of the lift force arises from pressure effects and no momentum effects.

2. If the control volume is taken out toward infinity then there is no net circulation, because the starting vortex and bound vortex around the airfoil cancel out. Therefore there seems to be no far-field lifting force in so far as circulation is concerned.

3. Where does momentum actually produce lift? The momentum equation as applied to circulation is vague about the connection between airfoil lift and the rate change of momentum in the flow causing it. Something very important is missing from these arguments .... —Preceding unsigned comment added by 58.106.36.163 (talk) 15:38, 5 December 2007 (UTC)

Whether or not momentum produces lift is moot. That they absolutely always occur at the same time is undoubted.

Lift is a force on a wing, the only way a fluid can exert a (non frictional) force on a solid is by pressure differences.

The existence of a pressure difference in a fluid will always cause the fluid to accelerate (momentum change) down the pressure gradient.

Pressure in a fluid always works equally in all directions, if there is no wing present the fluid accelerates equally in all directions – no net effect.

If part of the pressure acts on a wing as part of the lift, that part does not act on the air. Thus, in this case, there is a net acceleration on the air equal and opposite to the pressure effect on the wing. If the lift effect is upwards, the acceleration of the air is downwards.

The downwards-flowing air displaces other air upwards. The net pressure and fluid momentum effects result in the pressure differences at the boundary. Thus the sum total of the air pressure on the ground is equal to the total weight of the air plus the lift being applied to the aircraft.

None of this describes the mechanism by which the pressure differences are created, only the inevitable consequences once they do.

The pressure differences are created by an inevitable need for the air to move out of the way of the oncoming wing and to flow into the void left behind after it passes. If the air did not flow the inevitable result would be a rapit tendency towards infinite pressure immediately ahead of the wing an a total vaccum immediately behind it.

In fact a steady state is reached in these two regions where the pressure gradients are sufficient to accelerate exactly the quantity of air away and towards the wing in order to maintain exactly the pressure gradients causing the acceleration.

There are many and varied ways of mathematically modelling the different parts of the flow. The so-called different theories of flight are just different approaches to creating mathematical models. They are not mutually exclusive.

Rolo Tamasi (talk) 19:24, 5 December 2007 (UTC)

Control-volume analysis and momentum transfer

In recent exchanges there is a lot of confusion as to whether lift involves momentum transfer or not, culminating in the entry by Mr. Tamasi, 5 December 2007, which finds a non-existent contradiction between the Kutta-Joukowski theorem (lift per unit span = rho*V*Gamma) and the presence of any momentum transfer. Of course lift involves momentum transfer, and the Kutta-Joukowski theorem is correct. I think the confusion over momentum transfer in general arises because the momentum is either visible or not, depending on where you look. However, if you include all the right pieces in the analysis and do the sums right, it all works out, and there is no mystery or contradiction. The purported contradiction found by Mr. Tamasi is the result of leaving out one of the pieces, as I hope to make clear below.

I don't think I described any contradiction at all. I certainly see none.

I believe you are referring to contradiction seen by 58.106.36.163, to whom I was responding. The sense of my response was, I believe, similar to yours other than I question the value of attempting to attribute causational relationship. Within the system you can inevitably find pressure differences that equate to the lift and you can find momentum changes that equate to the lift. Equally you can net off both all pressures and all momentum changes to zero if you wish. These are just simple principles that we would not waste any time discussing in the dynamics of solids but once lift becomes involved we appear to make the simple mechanism appear as complex as possible. Most of the discussion tends to be about artefacts of a particular analytical model chosen to apparently assist in an explanation rather than features of lift. Why do we do it? Rolo Tamasi (talk) 00:37, 16 January 2008 (UTC)

Control-volume analysis is a powerful tool, and using control volumes of different shapes and sizes can provided insights into different aspects of the problem. In fact, if you want to gain a full understanding of what happens in the flow field when lift is generated, you have to look at multiple views that slice the atmosphere in more than one way.

Control-volume analysis can be applied to either 2D or 3D flow, and the outer boundaries of the volume can be either flow-through or solid walls. Correct results can be derived for any of these situations, and if things are done right there will be no contradiction between them. Some have insisted that only a closed system makes sense, but whether you enclose the atmosphere in a box or not needn't alter any general conclusions. If I assume the box is large, I can draw a control volume around a small subset of the interior and have an open system that isn't significantly affected by the walls. In the real atmosphere, the only real wall is the ground. If the height above the ground is large compared to any dimension of my control volume, it is as if the ground weren't there. And if there is a starting vortex, I can put it out of the picture by assuming that my airfoil or wing has been in flight over a large distance compared to the altitude, so that the effect of the starting vortex is cancelled by that of its image in the ground.

To do a momentum analysis in a control volume you have to take into account the time rate of change of the total momentum in the interior and the forces (pressures, if we ignore viscosity) and momentum fluxes at the boundaries. For my discussion I'll assume steady flow, for which the time rate of change of total momentum in the interior is zero. For analyzing lift, we take the surface of the airfoil or wing as the interior boundary of our control volume, where we need only to consider the pressure, whose integral gives the lift. The outer boundary encloses the airfoil or wing, and if the boundary is flow-through, we must consider both the pressures and the momentum fluxes.

Consider the 2D flow around an airfoil of infinite span. More than a few chord lengths away in any direction, the only flow disturbance outside the viscous wake looks as if there were a point vortex located somewhere on the airfoil (If you're far enough away, it doesn't matter exactly where), superimposed on the uniform freestream.

Now consider a tall, skinny rectangular control volume with vertical (front and back) faces far enough ahead and behind the airfoil so that the point vortex is a good approximation to the flow. In the vertical force/momentum balance that will tell us the lift on the airfoil, the pressures on the vertical faces make no contribution. If we move the horizontal (top and bottom) faces far enough away, keeping their lengths the same, the pressure contributions on them become negligible. The final result is independent of exactly how far ahead and behind we place the front and back faces, as long as the vertical dimension of the box is large compared to the horizontal. What we find is a flux of upward momentum through the front face that accounts for half the lift and a flux of downward momentum through the back face that accounts for the other half. If we calculate the circulation on the outer boundary, we get lift = rho*V*Gamma, and we have just carried out the simplest derivation of Kutta-Joukowski that I know of.

So in a tall, skinny control volume we find the lift totally accounted for by momentum fluxes at the outer boundaries (and to be consistent with Kutta-Joukowski). This disproves Gentry's (Origins of lift) contention that "deflecting air downward" is significant only in 3D flows. It also contradicts assumption 2 in Tamasi, 5 December 2007. I think where Mr.Tamasi went wrong is that he considered only the momentum content in the interior and left out the fluxes at the boundaries.

Now for a different view, consider a thin, flat rectangular control volume. Put the top and bottom just far enough away so that the vortex approximates the flow well, and move the front and back much farther away, but still a small fraction of the height above the ground. Now the fluxes of vertical momentum through the front and back effectively vanish, and fluxes through the top and bottom cancel by symmetry. Half the lift is now accounted for by overpressure on the plane below the airfoil, and the other half is accounted for by underpressure on the plane above, even though these planes are flow-through boundaries.

So for a tall, skinny control volume the lift is accounted for by momentum fluxes, and for a thin, flat control volume it is accounted for by pressures in the field. For situations between these two extremes, the lift is accounted for by combinations momentum fluxes and pressures that depend on the proportions of the control volume. Of course both the pressures and the momentum fluxes are always there at the same time. Which accounts for the lift just depends on how we choose to slice up the atmosphere.

Now for another view, to pacify those who insist that the ground is an essential part of the picture. If we take the thin, flat control volume that we just considered and increase either of its dimensions so that it is no longer a small fraction of the distance to the ground, the effect of the vortex at the airfoil no longer dominates over the effect of its image under the ground. The integrated pressures that account for the lift then shift toward more than half being accounted for by the overpressure under the airfoil. If we move the bottom boundary to the ground and make the control volume much longer than it is high, the lift is completely accounted for by the overpressure on the ground. Note that this doesn't contradict anything we concluded before. We can still account for lift in terms of momentum fluxes, and we can still find the underpressure above the airfoil to be significant, if we look in the right places.

This kind of analysis can be extended to 3D, with the wing and its wake modeled by a horseshoe vortex. The starting vortex doesn't last long in the real world, and in the ideal world where a vortex never dies, we can always put it out of the picture as I argued earlier. There are additional details to take care of and mathematical traps that some classical texts fell into, but if you do it right you find that lift can be accounted for by varying combinations of momentum fluxes and pressures, including pressures on the ground, very much like the above examples in 2D.

So considering only the pressures or only the momentum fluxes can lead you astray. To understand the relationship between the lift and the flow field that goes with it, you must consider both the pressure field and the momentum fluxes. --J Doug McLean (talk) 22:35, 14 January 2008 (UTC)

Possible sources of the Lifting Force Controversy: Vortex-shedding, Ground Effect, etc.

I've been observing the long-running battle over the Lifting Force explanation. I notice that certain unstated concepts are the source of distorted conceptions, and may provide the driving force for various sides in the battle. But these concepts are rarely highlighted or brought out for explicit discussion. Let me list some of them.

1. Flight in ground-effect mode is somewhat different than flight at higher altitude. Most importantly, all two-dimensional "infinite wings" remain forever in ground-effect mode. Perhaps infinite wings provide misleading examples for explaining the flight of real-world aircraft. The mathematics of 2D infinite wings is the mathematics of ground-effect flight, where the ground is an essential component of the system, and where the distance to the ground is much shorter than the (infinite) wingspan. This differs from the conventional flight of aircraft, where the wingspan is much smaller than the distance to the ground, and where some of the obvious "venturi" phenomena associated with infinite-wing descriptions are missing.

2. An airfoil in constant-altitude flight against a gravity force is a special case, and may be a misleading example. Alternatively, if we consider the accelerated-trajectory flight of neutrally-bouyant submarines, or aircraft moving in a "zero-G" environment, or if we examine the horizontal "lifting forces" created by sailboat hulls and ships' rudders, this may help remove some of the conceptual distortions which produce long-running "Swiftian battles," and which block our understanding of flight.

3. The creation and ejection of ring-vortices can supply a force useful for fluid propulsion. For example, a ring-vortex launcher produces a strong reaction force which drives the launcher backwards relative to the ejected ring-vortex. In recent years, detailed consideration of the forces involved in vortex-shedding provided key insights into the functioning of flapping insect wings. I remain convinced that the same insights also apply to fixed finite-wing aircraft, and a good explanation of the lifting force must involve the forces produced by vortex-shedding. Let me say it differently: airplanes can fly in ground-effect mode, or they can fly via vortex-shedding. Our most common mistake is to analyze the ground-effect flight required in a 2D world, then assume that we've explained the vortex-shedding flight of a 3D real-world aircraft. The lifting force will be difficult to understand as long as flapping-wing insect flight remains poorly explained.

4. The rudders on ships and the blades of rotary fluid pumps are airfoils which produce fluid mechanical forces. If our explanations of the lifting force apply only to fixed-wing aircraft in constant-altitude flight against gravity, but contains no obvious application to rowboat oars or to helicopters, then our explanations are deeply flawed. The best explanation should offer general connections to many different cases, rather than explaining only narrow special cases. --Wjbeaty (talk) 20:58, 18 January 2008 (UTC)

The Article does primarily address lift in the general form.

Just because some people don't understand lift does not mean that it has not been well understood for a few hundred years and is not extremely simple. Rolo Tamasi (talk) 01:02, 19 January 2008 (UTC)

This article is a start, but still has problems

The "physical description" of lift reads like an old argument by another name. There's only one right answer: both. Neither momentum nor pressure explain lift on their own, yet are both tremendously important to it. This should be obvious, since each section talks about the other.

Unfortunately, an accurate physical description of lift is not a trivial task and not even perfectly understood by anyone. A more correct description might talk about viscosity, the starting vortex, pressures, and momentum. Mostly it all comes out of the Navier-Stokes equations (which come from Newton's second law).

The mathematical models section has similar problems. The three “models” are convoluted and not explained very well:

• There is no such thing as the "Lift coefficient model". It's just a nondimensionalization for convenience, allowable thanks to the Buckingham π theorem. I temporarily deleted this, but a link to Lift coefficient would be a good addition somewhere since it comes up frequently.
• Bernoulli's principle is not a model of lift, but it does factor into lift calculations: for example, it's used when deriving the Kutta-Joukowski Lift Theorem. The integrals used here to calculate aerodynamic forces do not follow from Bernoulli's equation and should not be labeled as such, so I retitled this section to “pressure integration”, but there's probably something better. This section seems to confuse a variety of concepts.
• The Kutta-Joukowski Theorem section needs to be cleaned up and better explained.

I'll return to this when I have time. Mbelisle (talk) 05:00, 19 April 2008 (UTC)

New physical description

I started a more complete physical description of lift production. Until I find a good general reference, it's unreferenced and almost certainly has some problems. It would also benefit from diagrams showing the stages of lift production, which might save some of the verbiage. I acknowledge that it may be overly technical at the moment, which I'll work on once I'm sure it's correct. It think it is, at least, better than NASA or The Straight Dope, and who seem content to conclude "Why the flow moves faster over the upper surface is complicated, don't worry about it."

The "Newton" and "Bernoulli" explanations of lift should be added to the common misconceptions section, perhaps as “Newton vs. Bernoulli”, and/or to a section on ways to measure lift. If you know the details of the flow field (or are making measurements in a wind tunnel), then sure either

• the “Newton” way: a direct measurement of the force (via a force balance) or
• the “Bernoulli” way: integrating the pressures (via pressure taps on the surface of the airfoil)

will give you a reasonably accurate value for lift. But neither answers the real question a physical explanation should address: “Why does a wing generate lift?” Michael Belisle (talk) 00:38, 20 April 2008 (UTC)

We must bear in mind that Wiki is a general encyclopaedia and not a technical treatise, it should be written in language and style that is accessible to all. After all, the formulae are derived from principles not the other way round. The article, in my view, should not primarily be a description of the detailed physics or of the derivation of mathematical models but sections on these can be included. I agree that the physical explanation has to focus on addressing the question "why does a wing generate lift" but it should first do it in layman’s terms.

The value of many Wiki articles are effectively destroyed by us technicians expounding nuances that are absolutely irrelevant to the general user.

Your idea that aspects of the Newton and Bernoulli debate would sit very well in the misconceptions area is an excellent one.

I believe it is relatively straight forward to explain why the flow moves faster over the upper surface to a layman and without once mentioning Bernoulli or conservation of energy. I will give it some thought. Rolo Tamasi (talk) 08:24, 20 April 2008 (UTC)

John D. Anderson says “You cannot get more fundamental than this, conservation of mass and Newton's second law” (JDA, Introduction to Flight, p. 355). I use JD Anderson as a reference because, as Curator of Aerodynamics at the Smithsonian and a standard in Aerodynamics texts, he is quite possibly the most authoritative person on the subject. His explanation cannot be presented on equal footing with eskimo.com.

Bernoulli's principle, as applied, comes from Newton's second law while conservation of mass (in 2-D) is simply $\rho VL$ is a constant. In the equal transit-time explanation, people have no trouble accepting that that air moving faster has lower pressure than slower moving air, which is an application of Bernoulli's principle. True, the form of Bernoulli's equation applied is actually “Bernoulli's equation for inviscid, incompressible, steady flow along a streamline”, but in some ways that's more information than is necessary. It's the most common form of the equation and the only way to explain lift without mentioning Bernoulli is to not give the principle a name.

That said, I admit that what I put in there is temporarily not written in laymen's terms. I tried to first to put something in there that is correct and referenced (what was there was understandable but misleading). We can go back and make simplifications as appropriate, especially adding pictures.

After I wrote the section on viscous flow and lift startup (from memory), I searched for references in books by reputable aerodynamicists and I came across JD Anderson's explanation, where he explains lift in steady-state terms with conservation of mass and Newton's second law, neglecting viscosity. Technically, this is correct: if you started up a viscous Navier-Stokes solver and solved only for the steady-state flow field, you would never see the starting vortex. You could then describe the flow field as he has done. So I threw in a sloppy version of his explanation. JD Anderson also explicitly describes downwash (i.e. Newton's third law) as an effect of lift and circulation as a mathematical model of lift. His reasoning there is sound.

I have since located a good explanation of the stages of lift production in K Karamacheti, Principles of Ideal-Fluid Aerodynamics and clear diagram in FM White, Fluid Mechanics. The stages are inclusive of the foregoing. I think a good argument could be made to move the stages to another article. But, if I had looked up lift before I was an Aerospace Engineer, I would have wanted to know about viscosity. Failing to mention the starting vortex or viscosity is hand-waving. “The generation of [lift] depends on entirely on the nature of viscous flow past certain bodies.” (Karamacheti) Michael Belisle (talk) 22:18, 20 April 2008 (UTC)

I think what we need to do here is rewrite the article in a way that it conforms in some way to Wikipedia:Make technical articles accessible, without loss of information. It is unavoidable that, like special relativity, a variety of readers will come here, including aerospace engineers who don't understand how a wing produces lift. (Strange but true: I can guarantee that this article will show up in undergraduate lab reports on airfoils. Back when I was a TA, I mostly solved this problem by taking off points for citing Wikipedia because it was often wrong: for example, see Image:LiftCurve.svg or “At a zero angle of attack, no lift is generated,” which was in this article yesterday. I'd prefer not to have to do that.)

Lift, on its own, isn't significant enough to warrant its own article like Introduction to special relativity, but there is certainly a way to organize it in such a way that laymen don't feel it's overly technical, while aerospace engineers don't feel it's overly simple. Perhaps we need something like an Introduction to flight article, but that should involve a team effort within WP:AVIATION about what to include and how to present it.

The physics community is way ahead of aeronautics in communicating technically correct ideas to both general and technical audiences. I think it's a good model to follow. Michael Belisle (talk) 03:36, 21 April 2008 (UTC)

Wow, being a layman I read this article and understood nothing. Then I read the The Straight Dope page as mentioned above and I'm feeling happy again. Even if I don't understand fully and the Straight Dope has cut corners (which it probably has), at least I feel I understand 'lift' now. So can someone please make this page make me feel like that? Then I'll truly be a happy (lay)man.... Malick78 (talk) 16:49, 9 October 2008 (UTC)

I honestly think that a 'lay explanation' based around action-reaction is more intuitive to most people. The problem we experience when explaining lift is that one group of people try to explain how you would calculate lift, which almost always goes the pressure route; and the other group is trying to "explain" lift, without much focus on ease of calculation. Pressure integrals are used to calculate lift because it is easier to use the well-defined boundary of the wing, but it is possible to calculate lift from the deflection of the air as well. In my experience with students (I am a lecturer at a university), the explanation that wings experience an upward and backward force by deflecting air downwards gels with their experience of things like fans. The question of why airfoils are shaped the way they are then largely becomes related to how to deflect the most air, which involves delaying flow separation on the top surface. The pressure integral approach leaves some very interesting questions about why the air is moving faster on the top surface than the bottom one. Of course these two things are different ways of looking at the same phenomenon, but the flow deflection argument requires less build-up about Bernoulli. Chthonicdaemon (talk) 05:05, 4 December 2008 (UTC)

It might be more "intuitive" to some readers, but others will disagree. Like you said, “these two things are different ways of looking at the same phenomenon”; WP:NPOV therefore says we should include both. This article tries to write one explanation that does that, encouraging readers to recognize that the Bernoulli and Newton are equivalent and related. I disagree that airfoil design is a question of how to deflect the most air. You still have to deflect the air in a certain way. The related fact that a rotating cylinder in a free stream generates lift has nothing to do with deflecting the most air. Michael Belisle (talk) 18:49, 9 January 2009 (UTC)