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If I understand well, there is a positive net transfer of (upward) momentum from the particles striking the foil. Is this correct? Mark.camp (talk) 19:12, 6 February 2015 (UTC)

There is no transfer of momentum from anything to the foil. The net force on the foil is zero (unless the machine is manoeuvring). In a billiard-ball model, the balls are deflected downwards in accordance with L=dp/dt. The balls gain downward momentum but the foil does not gain upward momentum. The planet beneath gains the upward momentum as gravity attracts it towards the heavier-than-fluid foil, but the effect on the airflow and on the foil is negligible. Of course, net momentum change of planet + balls = 0. — Cheers, Steelpillow (Talk) 19:31, 6 February 2015 (UTC)

@Steelpillow, you wrote:

"There is no transfer of momentum from anything to the foil.

Are you saying that the collisions result in no transfer of vertical momentum? So, are you saying that the downward momentum transfer from air particles striking upward-facing surface subareas is equal in sum (over long enough time period) to the upward transfer of air particles striking downward-facing subareas from below?

" In a billiard-ball model, the balls are deflected downwards in accordance with L=dp/dt. The balls gain downward momentum but the foil does not gain upward momentum. The planet beneath gains the upward momentum as gravity attracts it towards the heavier-than-fluid foil, but the effect on the airflow and on the foil is negligible.

It is true that the foil does not gain upward momentum, but that is irrelevant because it is not disputed. The effect on the airflow and on the foil is irrelevant because it is not disputed. The question raised is only about whether there is a momentum exchange between foil and air, not about anything else. To believe that collisions with the air particles create lift equal to the net momentum exchange is not to say that either experiences a change in momentum, nor to say anything about the effect on the airflow or the foil.

Your statement that I've asserted that the balls gain downward momentum is correct if it is interpreted to mean that the balls (the body of air as a whole) gain downward momentum across the foil-air boundary. Obviously, the balls striking the upward-facing surfaces gain not downward but upward momentum. Obviously, in the whole system, the balls experience no change in vertical momentum: they gain in upward momentum from collisions with earth just what they gain from collisions with the foil.

Mark.camp (talk) 02:27, 18 February 2015 (UTC)

The net force on the foil is zero (unless the machine is manoeuvring). In a billiard-ball model, the balls are deflected downwards in accordance with L=dp/dt. The balls gain downward momentum but the foil does not gain upward momentum. The planet beneath gains the upward momentum as gravity attracts it towards the heavier-than-fluid foil, but the effect on the airflow and on the foil is negligible. Of course, net momentum change of planet + balls = 0. —

Thanks for the clarification. Is there a transfer of vertical momentum to the foil when a single particle with nonzero vertical momentum collides with the foil? Mark.camp (talk) 00:18, 7 February 2015 (UTC)

(Zapletal writes ->) Mark,

"Is there a transfer of vertical momentum to the foil when a single particle with nonzero vertical momentum collides with the foil?"

I recall this being discussed before, but can't remember where. The short answer is that there is a big difference between a "Kinetic Theory of Gases" description of Lift, and a "Continuum Mechanics" description. Both give the same end result, but in different ways.

In yours and the KToG descriptions, very soon after your particle bounces downwards off the underside of the foil it hits another particle below it, bounces back upwards off it, and then continues to bounce up-and-down between the underlying particles and the foil (this, of course, is greatly simplified...). There are a great many (squillions!) of these exchanges of momentum, and their net result, summed over the whole surface of the foil, is the Lift force.

However, in the CM description, these "collisions of particles against foil" are simply called "pressure". There are more frequent collisions on the underside of the foil, so "greater than ambient pressure" there, and less frequent collisions above, so "lower pressure". By definition, the Continuum cannot consist of individual particles, so the only way it can interact with other Bodies is via these "pressure" forces acting at the mutual boundaries. (This ignores Gravitational, EM, etc., interactions, and strictly speaking the interactions are via a "stress tensor", which also models "friction = viscosity".) (End Zapletal) 101.171.255.254 (talk) 04:47, 7 February 2015 (UTC)

I think you are saying the answer is yes, there is a transfer of vertical momentum to the foil when a single particle with nonzero vertical momentum collides with the foil. Thanks, this confirms what I remember being taught. When you say that the net result, summed over the whole surface of the foil, is the lift force, (which is non-zero) are you saying that the net result (the net vertical momentum transferred to the foil) must be non-zero? Mark.camp (talk) 23:37, 7 February 2015 (UTC)

Mark, There is no net transfer of momentum to the foil in steady flight - that is pretty much the definition of steady flight. At an individual level, each ball imparts a small momentum to the foil depending only on where it strikes and the component of velocity at right angles to the surface of the foil at that point. In an elastic collision, which we assume here, perhaps surprisingly the direction of travel of the ball is not relevant. Meanwhile gravity provides a steady opposition to these brief bursts of lifting force. So although lift and gravity cancel each other out overall, there is a certain "noise" to the steady state. HTH. — Cheers, Steelpillow (Talk) 11:47, 7 February 2015 (UTC)

@Steelpillow, you wrote that there is a certain noise to the steady state. Noise is random by definition. Are you saying that the collisions are random, that they do not sum to an upward transfer of momentum? If the collisions are random, then over time the lift from the collisions, which is exactly equal to the average rate of momentum transfer from the collisions, is zero. But isn't it true that the lift is non-zero?

Mark.camp (talk) 02:50, 18 February 2015 (UTC)

Thanks, Steelpillow. You reference brief bursts of "lifting" force. But I think, to nitpick, you mean the net result of brief bursts of lifting force and brief bursts of downward force (particles impinging from above the foil surface at the point of impact). This is how I picture it, and I want to confirm that my picture is correct. I am trying to reconcile the micro and macro descriptions of lift in my mind. It seems that they should yield consistent answers about momentum transfers.

There is no change in momentum to the foil in steady flight, I think. True, one possibility is the one you mention, that there is no net transfer of momentum from particle collisions to the foil. But there is another, that there is a net transfer of momentum from these collisions, and that it is cancelled by another net transfer, from gravitational interaction. Mark.camp (talk) 00:36, 8 February 2015 (UTC)

(Zapletal Writes ->) Mark, Your last sentence pretty much nails it (in terms of this simplified "billiard ball" model...).

For an even simpler version, consider an aerofoil moving at constant horizontal velocity through a vacuum, and above a large massive body such as the Earth. The gravity force between Earth and foil pulls them together, and gives them both equal time-rate-of-change of inwards momenta (ie. d(m.V)). Of course, the lighter foil has the higher dV here, so follows a more curved path (roughly parabolic, concave down). Now picture something like a football bouncing up and down "elastically" (!) between the two bodies. Each time it hits the Earth and bounces back up, it "exchanges" twice its vertical linear momentum with the Earth, and gives it some downward dP (but of very tiny dV). Similarly, each time it hits the underside of the foil and bounces back down, it gives the foil the same upward momentum dP. So answer to your original question is, indeed, YES. End result is that the foil travels along a path a bit like "mmm".

The bouncing ball in this model is roughly equivalent to Lanchester's "pillar" from page 9 of his book, ie., "As a whole, the fluid, in the previous section, does not gain or lose momentum any more than does a cast-iron pillar supporting a load." .

Adding more detail to the model has many more balls bouncing every which way, which add, in Continuum Mechanics terms, an "ambient pressure" everywhere. But, for this BB model to work there MUST be a time-averaged increase in the number of these balls bouncing between each other in the zone between the Earth and foil. This "increased pressure zone" MUST ALSO travel steadily with the foil, much as the single football does above, or as does Lanchester's "cast-iron pillar". (End Zapletal)101.171.127.235 (talk) 03:01, 8 February 2015 (UTC)

@Zapletal: Thanks, good explanation! Mark.camp (talk) 19:56, 8 February 2015 (UTC)

@Mark, yes, "lift" can be negative if the ball strikes the upper surface. In such a thin medium where this model works, the foil has to be angled so that more of them strike the lower surface. But it is not directly transferable to a dense medium where the balls are a jumble constantly bouncing off each other, because then the balls start fighting each other for personal space and Bernoulli's analysis becomes significant. A carefully-shaped foil can generate lift through Bernoulli's principle, even when not angled upwards. At a microscopic level though, we are still simply summing the balls that hit from different directions, it's just that Bernoulli gives the balls above the foil attitude so they strike less often than one would otherwise expect (they prefer to hurry on past and don't have the time to). And in all cases, when we sum the net rate of change of momentum of the balls striking the foil it equals the lift. In fact, it is only because L=dp/dt that Bernoulli's principle works. — Cheers, Steelpillow (Talk) 10:23, 8 February 2015 (UTC)

@Steelpillow, you thought I was saying that "lift can be negative". I realize that it can, but that is not relevant to my point. I was saying that, even in the case of positive lift, the air particles striking much of the wing--all of the upward-facing parts--are imparting downward momentum.

Mark.camp (talk) 21:58, 17 February 2015 (UTC)

@Steelpillow--Thanks much, again. I'm starting to try to think now of the air as a single body comprising all the air particles. It has a single momentum, equal to the sum of the particle momenta. It is bounded by surface between the foil, the upper boundary of the air, and the earth.

Is it correct to say that the average rate of vertical momentum transfer to this body from the foil equals the average rate of vertical momentum transfer to the air particles striking the foil, i.e., the lift? Since the air as a single body cannot have a continuous net change momentum, I guess there would have to be also a continuous transfer of vertical momentum from the earth to the body of air as well, via collisions of air particles with the earth.

So if this is correct, then lift = rate of downward momentum imparted to particles striking the wing = rate of upward momentum imparted to the wing by particles striking the wing = rate of downward momentum transferred to the craft by gravitational attraction to earth = rate of upward momentum imparted to the air particles striking the earth.

Is all of this correct? If so, then I think I have for the first time a good picture in my mind of the microscopic, momentum-based view of lift. Thanks, Mark.camp (talk) 19:56, 8 February 2015 (UTC)

I would say yes, that is about right, as long as we remember that some of these are changes and not absolute values. You can round off the picture by adding that these also equal the rate of downward momentum imparted to the Earth by the air particles = the rate of upward momentum imparted to the Earth by the gravitational attraction of the foil. — Cheers, Steelpillow (Talk) 23:07, 8 February 2015 (UTC)

Thanks @Steelpillow. Good additions. Mark.camp (talk) 20:37, 9 February 2015 (UTC)

(Zapletal Writes ->) Mark, I feel obliged to add a clarification to the above discussion.

Fluid Dynamic Lift, of the type that is presented in the main article, is a subject that was developed in, and best belongs in, the field of Hydrodynamics. This is the study of idealised, inviscid, INCOMPRESSIBLE, fluids similar to water (hence "hydro"). The main article is currently written mostly from the point of view of Aerodynamic Lift. But, because gaseous air moving in what is commonly called "low-speed, sub-sonic flow" behaves very much like the incompressible liquids of Hydrodynamics, the original Hydrodynamic explanation of FDL works fine here.

But an important distinction needs to be made. Whereas gaseous fluids can be modelled as Billiard Balls that are mostly flying freely through a vacuum and only briefly bouncing off each other, in liquids the modelled BBs are ALWAYS in intimate contact with other BBs. (So picture the difference between 10 x BBs bouncing around a big billiard table, and 1,000 x BBs all in contact in a group on the table, but with this group freely deformable, or "fluid".) Thus the BBs in the hypothetical liquid can exert a force on a Body indefinitely, without the BBs ever moving, and without anything ever "exchanging momentum" (eg. "hydro-static" pressure forces). Note that the hypothetical particles that are assumed to make up a "real" liquid (ie. atoms, etc.) are thought to be in a constant "jiggling" motion related to their "heat energy". But so too are the atoms of a solid, and nobody pretends that the atoms of a cast-iron pillar ever need to "exchange momentum" to support a load.

Neverthless, the "particles" that make up a hypothetical Hydrodynamic fluid (continuously divisible, so not atoms!) are assumed to possess Inertial mass, so they DO require a force impressed upon them to change their "quantity of motion" (= Newton's term for "momentum"), as per Galileo's Law of Inertia, aka NI. So it takes a force acting over a distance to get this fluid moving, and the fluid then gains momentum and kinetic energy. But, again, these same hypothetical fluid particles can also transmit forces with NO MOTION, or NO "exchange of momentum", whatsoever. Picture a heavy boat floating in a quite pond of water. Or the same boat floating in a pond of very slippery, but stationary, billiard balls. Same-same. (End Zapletal)101.171.213.77 (talk) 02:19, 9 February 2015 (UTC)

Thanks. Your comments are very thought-provoking. The other cases you bring up (liquid statics, liquid dynamics, cast-iron pillar) baffle me...I am not able to come up with a unified picture in my mind that makes sense. But for now I will focus on this article, and explore whether there are possible suggestions for improvement coming out of the above discussion. I am aware that I'm barging into the middle of a long-running discussion by very knowledgeable people, so for the moment I am not ready to make any suggestions.

In fact, I still have a question about the airfoil case. Do the above simple conclusions about momentum transfers between the three bodies--earth, wing, and air--which apply to the discrete collision view (microscopic view) apply to the continuous fluid model? Mark.camp (talk) 21:22, 9 February 2015 (UTC)

They should be good for a continuous gas model, as the molecules remain well separted. As I remarked earlier, the jostling between balls invokes Bernoulli's principle but the same transfer mechanism applies. A liquid usually contributes static lift as well as dynamic, the "iron pillar" effect, but let's ignore that and focus on the dynamic. Because the balls are all in contact with each other, the momentum transfers are less easy to track, one can think of transfer "through" a ball "pushed by" the foil rather than "to" a ball "striking" it, and the momentum tends to disappear into the crowd, but the underlying principle is the same. I think it would not be a good model for liquid flow to describe on Misplaced Pages though, unless it can be well sourced. — Cheers, Steelpillow (Talk) 23:14, 9 February 2015 (UTC)

So, I think you are saying that even in the fluid dynamics view, not just the microscopic view, there is a non-zero rate of momentum exchange between the three bodies, equal in magnitude to the lift. Wing up, air down (associated with net force from air pressure); air up, earth down (associated with forces of gravity and air pressure); earth up, wing down (associated with force of gravity between wing/vessel and earth). (In the fluid dynamics view, it becomes not the average of many random transfers, but rather a continuous rate of transfer). Is this correct? So, even though (in the fluid dynamics model) the wing has zero change in vertical momentum, it is exchanging vertical momentum with the air as a single body. Here I get lost though. In the continuous model, there is a force between earth and vessel, but there is, unlike the microscopic model, no change in momentum of earth or vessel/foil. So the wing is getting upward momentum but there is no cancelling momentum. I am missing something still. A momentum can cancel a momentum, and a force can cancel a force, but how can a force cancel a momentum????Mark.camp (talk) 23:53, 9 February 2015 (UTC)

(Zapletal Writes ->) Two points to cover here.

1. Semantic quibble first. This "Lift" subject is part of a nested hierarchy, roughly;

Classical Mechanics = Rigid-Body-Mechanics + Fluid-Mechanics +...,

Fluid-Mechanics = Fluid-Statics + Fluid-Dynamics +...,

Fluid-Dynamics = Hydrodynamics + Aerodynamics +..., etc.

The explanations of "Lift" in this article come mostly from the field of Hydrodynamics, but they are couched, unfortunately IMO, mostly in Aerodynamic terms. So, the article uses the word "air" too much, rather than the more general "fluid". Note that anything that "flows" is a fluid. Anyway, "Fluid-Dynamics" covers both the individual-particle model (whether the particles be of liquid or gas) and also the continuum model (again, of both incompressible liquids and compressible gases). But "Hydrodynamics" generally only refers to the incompressible continuum model.

To stress it again, the Circulation Theory of Lift (ie. the main one presented in this article), is a Hydrodynamic theory.

~o0o~

2. Mark, I think you are asking,

" there is a non-zero rate of momentum exchange between the three bodies , equal in magnitude to the lift. ... So, even though (in the fluid dynamics model) the wing has zero change in vertical momentum, it is exchanging vertical momentum with the air as a single body"

Simple answer, NO. There is NO "exchange of momentum" between wing<->fluid, or between fluid<->ground, in the CToL continuum model (which happens to be the best model available for last ~120 years). But you are not alone in this misunderstanding. Certainly most of this Talk page, and some of the others, are devoted to arguing this issue.

In brief, in the CToL model of steady flight of a wing, the NET FORCE acting on the wing, namely the sum of downwards-forces (eg. gravity) + upwards-fluid-pressure forces, is ZERO. The force system acting on the wing is in EQUILIBRIUM. Hence "steady" flight. Same for the ground. However, there ARE changes-of-momentum of the various different parts of the continous fluid. These are a result of the pressure field that travels with the wing and supports it. This pressure field terminates at the fluid's boundaries, which include the wing and ground surfaces.

The above misunderstanding is, IMO, a result of "fluid" being slippery stuff that offers little resistance to being pushed, so it simply moves out of the way whenever you push it. But then, because of the fluid's slipperyness combined with the MOMENTUM it picked up when you first pushed it, it manages to circle around behind you, and push you forward so you fall flat on your face! <- This is a very non-technical description, but it is the gist of how the CToL maintains the pressure field so it travels unchanged with the wing. (End Zapletal)101.171.127.229 (talk) 05:15, 10 February 2015 (UTC)

@Zapletal, are you saying that the surface integral of vertical component of momentum transfer across the air-wing boundary is zero? If so, then there must be some other interaction between air and foil other than these collisions that accounts for the non-zero lift. I cannot think of any, other than by taking into account the fact that there is some interaction being ignored in saying that air particles are precisely elastic particles, with no distant interactions. But this is a small error. Am I missing something?

Here is my new thinking:

You wrote:

"There is NO "exchange of momentum" between wing<->fluid, or between fluid<->ground, in the CToL continuum model (which happens to be the best model available for last ~120 years). But you are not alone in this misunderstanding."

You heard what I did not say. I don't think that there is any exchange of momentum in the CToL contuum model. If there is a continuous force between air and foil, and no change in momentum of foil or air, then it follows that there is no change in momentum.

It is certainly true that CToL continuum theory requires that there is no momentum exchange across this surface. It is certainly true that the momentum of the air is constant, in both the continuum and the discrete particle models. But it doesn't follow that there is no momentum exchange across the air-wing surface, only that if there is, then there must be something in the approximation that is made in deriving CToL continuum from the discrete model which results in the former giving an incorrect result for momentum transfer. (And of course, there must be an opposite transfer, which we agree on at the earth-air boundary.)

This is what seemed impossible to me at first. If anything is inaccurate about CToL, it would have to be infinitesimal, since the difference between the theories is infinitesimal. It vanishes with larger and larger numbers of collisions.

It also seemed unlikely that there would be a consensus here to the contrary, with so many knowledgeable contributors and so many references from the literature.

But since it seemed unavoidable, I started to think about how, at a microscopic level, the two theories could produce such startlingly different results.

It turned out to be easy (just a week or so of agonizing day-and-night thinking) to see, once I looked at the other "force" involved. Gravity is a continuous Newtonian force. I did a thought experiment. What if there were two opposing continuous forces, say gravitational and electrostatic) on a rigid motionless body, call it "X"? Would there be any momentum transfer between the earth and X? Would there be any momentum transfer between the charged body which was the source of the lift force and X? No! So, in terms of momentum transfer, there are two kinds of physical phenoma producing net forces over time: particle collisions, and continuous forces. The former type results, if there are many collisions over time, in continual (but not continuous) momentum exchanges which integrate to a potentially non-zero value; the other does not predict any momentum transfer at all, at any instant nor over time. Both produce net force over time. So, as soon as we approximate the effect of many real collisions with an imaginary continuous force (from air pressure) we change from a model which predicts momentum transfer to one which predicts none! No matter how long you integrate the momentum for in the continuous model, you will never get any momentum because the momentum exchange was continuously precisely zero.

Would like your thoughts.

Mark.camp (talk) 19:35, 17 February 2015 (UTC)

@Mark, Zapletal here sets up his favourite straw man - an opponent who does not exist - in order to evangelise his own mantra. We all agree that there is no overall transfer in a steady-state condition, despite Zapletal's protestations nobody has ever begged to differ. What I describe as "disappearing into the crowd", he describes as "changes-of-momentum of the various different parts of the continous fluid". His pressure field is of course just the jostling of the crowd seen as a whole. Please do not be misled into thinking that our explanations differ. — Cheers, Steelpillow (Talk) 11:14, 10 February 2015 (UTC)

@Steelpillow, this debate is technically over my head for now, though I am eager to study it later. I am still stumbling in the dark, and taking one step at a time. On another subject, making posts more pleasant to read: A trick that works well for me, when I think of it, is to let my notes cool overnight before sending them. Your post seems a bit confrontational for a Misplaced Pages post, to be candid ;-) Mark.camp (talk) 17:11, 11 February 2015 (UTC)

@Zapletal, here is my tentative conclusion as of the moment.

1. Fluid dynamics is a statistical approximation of the kinetic theory of gases.

2. Question: "What is the average rate of positive vertical momentum transfer across the closed boundary between foil and air, due to mechanical interaction between air and foil, if the lift is 10,000 N?"

Answers:

Per precise theory:

10,000 N

Per approximate theory:

0 N

Which is correct, with respect to physical reality?

My current thinking: the more precise theory must be correct than the approximation. How to resolve the apparent contradiction with what you said about no momentum transfer? Perhaps you meant "per CToL theory, but not in physical reality". Or perhaps there is an error in my logic or facts.

Pls comment or correct any errors in my thinking? Mark.camp (talk) 17:11, 11 February 2015 (UTC)

(Zapletal Writes->) Mark, Steelpillow's and my explanations most certainly DO differ.

Steelpillow, my explanations are based on a long study of the works of the many people who founded this body of knowledge, together with careful checking of the implications of those works to determine how well their predictions correlate with measured observations in the real world. Your explanations, from what I have seen so far, are based on a narrow ideology (eg. "TS"), that is founded on a meager understanding of fundamental principles, that gives NO quantifiable predictions, but which you nevertheless promote by attempting to suppress all alternative viewpoints. I could also mention that your tone is decidedly "uncivil", you seem to be "not-here" to educate or build a better encyclopedia, etc. But I doubt it will make any difference...

Doug, I must apologise to you that I am finding "Wiki" a thoroughly futile exercise. Thank you for your (excellent!) efforts so far. But, s jwe;ifgvyubwe w;adly, I think good education is impossible under these conditions. (End Zapletal) 101.170.127.248 (talk) 02:55, 11 February 2015 (UTC)

@Zapletal, above you wrote to me that your and @Steelpillow do indeed disagree. I think you may be confusing my question with some other. I didn't make a statement to the contrary, nor ask a question about this subject. I don't have any knowledge or opinion about it. Currently I have just asked for comments and corrections to my most recent conjecture about the comparison between conclusions of kinetic theory of gases model (billiard ball) and fluid dynamics. Mark.camp (talk) 16:01, 12 February 2015 (UTC)

@Mark, my apologies for coming across a bit strong at being accused of certain incorrect statements, but I had my reasons. Sadly, there is a long history behind it. I will tolerate no more of Zapletal's accusations of ideology and suchlike ranting (I use the term advisedly - I'll post the diffs of this guy's first two contributions to this page if you need convincing) and I leave the above remarks in place only for your education. If Zapletal posts again, I will see it summarily deleted and if necessary I'll ask for the page to be protected. — Cheers, Steelpillow (Talk) 19:13, 11 February 2015 (UTC)

@Steelpillow: no problem! but thanks, I very much appreciate your apology. I am not familiar with the history, sorry. My opinion, as a newcomer: I would try to separate the two things--my public posts on the technical subject at hand, and my administrative appeals or approved editing actions to seek to enforce Misplaced Pages standards of conduct. I believe that all of us would do well to respect the rules against personal attacks very strictly in our posts, even if we believe that others have not. Mark.camp (talk) 16:01, 12 February 2015 (UTC)