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Example to visualise the falsity of the equal transit time theory.

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

This discussion is going too deep to be relevant to this article. It may be taken up again elsewhere, but the initial focus should be on whether there is any encyclopedic value to the proposed material. — Cheers, Steelpillow (Talk) 16:38, 11 December 2016 (UTC)

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I suggest making an example of the equal transit time theory to better visualise it.

Here in short: Cessna 172 - Source [1]

• Wing loading = mass / wing area = 1157 kg/16.17 m² = 71.5 kg/m²
• Stall speed = 89 km/h 98 km/h with flaps up [2]

The needed pressure difference at the wing to produce this lift is 71.5 kg/m² * 9.8 m/s² = 701 Pa Assume the lift is given by the length difference between the upper and the lower part of the airfoil. The needed pressure difference is given by the difference in dynamic pressure at the two sides. The dynamic pressure is

$q={\tfrac {1}{2}}\,\rho \,v^{2},$

In order to achieve this pressure difference at the stall speed of 89 km/h 98 km/h and at standard density, the required ratio of upper path to lower path is given by:

$700Pa={\tfrac {1}{2}}\,\rho \,(v_{upper}^{2}-v_{lower}^{2})$

where, assuming the optimal case of the lower velocity to be equal to the airspeed and the upper flow to be accelerated,

$v_{upper}=v_{lower}\cdot {\tfrac {l_{upper}}{l_{lower}}}=v\cdot {\tfrac {l_{upper}}{l_{lower}}}$

gives for the stall speed the ratio

${\tfrac {l_{upper}}{l_{lower}}}={\sqrt {1+701Pa\cdot {\tfrac {2}{\rho v^{2}}}}}=1.6$

So, the upper path should be at least 70%60% longer than the lower path, which is obviously not the case if you compare it with the used NACA 2412 airfoil.

Do you agree inserting this example in the section False explanation based on equal transit-time? -Eio (talk) 20:40, 6 December 2016 (UTC)

I corrected the figures for the flaps up configuration, i.e. stall speed 53 kts [3] and deleted the old figures. -Eio (talk) 07:26, 7 December 2016 (UTC)

There are several issues to overcome:

1. The equations for dynamic pressure would need sourcing.
2. The angle of incidence will affect the position of the leading-edge stagnation point and hence the path lengths. The effect is most pronounced near the stall. This position would need to be taken into account - and sourced.
3. It would be better to treat both path lengths relative to a straight line between stagnation points. Otherwise, you would have to source the claim that any simplification is valid.
4. Even with every calculation assumption sourced, I am not sure if the calculation might still fall foul of original research: you would at least need to demonstrate (i.e. to source) that similar calculations have been performed.

— Cheers, Steelpillow (Talk) 21:04, 6 December 2016 (UTC)

1. The equation for dynamic pressure is well known and can be found in the page dynamic pressure, so it does not need sourcing
2. If you take a more precise look to what I wrote, you'll notice that I made a new calculation just to avoid the criticism you brought on your discussion page. This calculation avoids assumptions about the stagnation points. The calculation shows, instead, that the stagnation point should be such aft on the lower side to have a 70%60% longer path above.
3. Of course the path lengths are between the stagnation points. One position is defined at the trailing edge. Indeed, there may be small variations of the position at the trailing edge. This calculation makes no assumptions here. (See above)
4. You will probably not find a reliable source with this calculation. It's the calculation to show that this theory is wrong. However, the steps are now such straightforeward that they do not need a source.

Apart from Steelpillow's concerns about insufficient sourcing of basic physics equations, I'd like to read from other users if this example may be helpful for the reader. -Eio (talk) 21:21, 6 December 2016 (UTC)

Supplement: I checked the position of the stagnation point with the NASA FoilSim III. The Foilsim, given the parameters (airfoil thickness 12%, camber 2%, critical angle of attack, 98 km/h) predicts the lift with good accuracy (11% less than real, which is probably due to the fuselage lift at high angle of attack). In the simulation you can see a ratio of upper path to lower path of only 132/121 = 1.09, so the real path is only about 9% longer instead of 60%. -Eio (talk) 07:49, 7 December 2016 (UTC)

Equal transit-time sets a constraint on the average velocities. You have set a constraint on the average of the square of the velocities, and so, are not disproving the theory. Nevertheless, this is all original research. I also second Dolphin51 in that a detailed de-construction of the theory is not needed: a short (sourced) statement that the theory is extremely weak should suffice. Ariadacapo (talk) 11:29, 7 December 2016 (UTC)

The equal-transit time model was never a model put forward seriously in scientific circles. It is an attempt to provide a simple and easily-understood explanation of how an airfoil generates aerodynamic lift. The intended audience was young people and newcomers to aeronautics. The world now sees that it is too simple, and that it can be easily demolished. There is nothing to be gained by yet another exercise to scientifically demolish it. The equal-transit time model is not the only imperfect model in this field. All simple explanations of aerodynamic lift have strengths and weaknesses. The equal-transit time model is not the only one with weaknesses; it is just that its weakness is more obvious than most of the others. We don't need to scientifically demolish these simple explanations; we just need to encourage young people and newcomers to move on to a more rigorous and satisfying explanation (for example, the Kutta condition.) Dolphin (t) 11:14, 7 December 2016 (UTC)

I totally agree that this theory can be easily demolished as with the water hose example in this wonderful explanation of lift generation or by asking how inverted flight works. However, on three points I do not agree:

• I did not set any constraint on the square average of velocities. I took the optimal case with the lower velocity being equal to the one of the free streaming, i.e. the case in which the highest lift is generated, showing that even in this case the equal transit time model is wrong
• It is not true that this model was never put forward seriously. This may be different in different countries. I frequented a scientific gymnasium in Italy, I got there my pilot licence, later I studied physics in Germany and later became flight instructor. Nowhere I found a significant amount of people with a clear idea about lift generation. The reason why I decided to make this calculation is that the equal transit time model is still widely used to explain lift.
• Finally, it is not original research. It is not a new theory, but a numerical example of the falsity of a widespread theory, a falsity which is documented by at least 10 sources in the section.

Therefore I suppose this calculation might find several interested readers and, if written in a short subsection, will not disturb the ones considering it as obvious. -Eio (talk) 14:12, 7 December 2016 (UTC)

In your 700 Pa (surface average) equation you should have the surface-average of the square of velocities, but you wrote it as the square of the surface-average of the velocities. In the equal transit time theory nothing says that the velocity is uniform over any side of the wing. For a given average velocity, being very fast over the first half, and very slow over the remaining half, yields lower average pressure than having uniform velocity. The above calculation only disproves an equal-transit-time-at-constant-velocity theory.

The garden hose, the wings of a paper airplane or of a F-104 are illustrations that point out the weaknesses in the equal-time model. Going one step further and trying to disprove the theory requires considerable effort precisely because it is not obvious. I share your enthusiasm and interest for the problem, but not your conclusions. For such a piece of work, I think a solid reference is in order — I still can’t see how this is not WP:OR. -- Ariadacapo (talk) 15:40, 7 December 2016 (UTC)

This with the average velocity is indeed a good point. If the velocity change at the stagnation points is not instantaneous (finite acceleration), the velocity on the upper side is not constant, giving an higher average pressure difference. I'll search for a solution. -Eio (talk) 17:16, 7 December 2016 (UTC)

There is a published reliable source with a similar calculation. If we're going to include something like this in the article, then we should use the published calculation rather than doing our own. The treatment above goes quite far beyond the "routine calculations" allowable under the original research policy.

The material appears on page 15 of Anderson and Eberhardt's Understanding Flight:

Take a Cessna 172,which is a popular, high-winged, four-seat airplane. The wings must lift 2300 lb (1045 kg) at its maximum flying weight. The path length for the air over the top of the wing is only about 1.5 percent greater than the length under the wing. Using the popular description of lift,the wing would develop only about 2 percent of the needed lift at 65mi/h (104 km/h), which is “slow flight” for this airplane. In fact, the calculations say that the minimum speed for this wing to develop sufficient lift is over 400 mi/h (640 km/h). If one works the problem the other way and asks what the difference in path length would have to be for the popular description to account for lift in slow flight, the answer would be 50 percent. The thickness of the wing would be almost the same as the chord length...

http://ae.sharif.edu/~iae/Download/Anderson%20D.F.,%20Eberhardt%20S.%20Understanding%20flight%20(MGH,%202001)(249s).pdf

My take is that the article in it's present form treats the equal transit time fallacy sufficiently and that adding this material would be unnecessary "piling on". That said, I'll be fine with it if that's where consensus takes us. If we do add it, I'd much rather see a concise sentence or two of English prose rather than a whole page of mathematical symbols. Mr. Swordfish (talk) 20:26, 7 December 2016 (UTC)

I am happy you found a source with a similar calculation (and thank you for the link, I'll take a look at this interesting book!). However, this source evidently does not consider the non constant speed on the two paths pointed out by Ariadacapo and, differently from mine, does not even consider the shift of the stagnation point at high angle of attack, which was originally pointed out by Steelpillow, although he did not notice I corrected it. The 1.5% are the value you get from the standard NACA 2412 with stagnation point as foremost point. Considering a critical angle of attack of 10°, the stagnation point on the leading edge shifts backward making a path difference of 9% - still way too few. The needed 50% path difference (in my calculation 57%) are independent from this consideration.

Still, I think some readers may be interested in the calculation and the others will not lose more than 1 second to skip the equations in a subsection called "example" and jump to the next section.

By the way: I began with two sentences prose, but Steelpillow undoed my edit claiming it is original research, this was the starting point of the discussion.-Eio (talk) 22:25, 7 December 2016 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

origins of the wing shape

I think the Overview needs to mention the origin of the wing-shape, which I believe comes from nautical sails, where tacking is accomplished by the sail creating a wing-shape parallel to the ocean surface (making a horizontal "lift" to either port or starboard). Pb8bije6a7b6a3w (talk) 16:17, 5 January 2017 (UTC)

The sail in question is the lateen sail. Yes, I agree it should be mentioned here somewhere. But while it did inspire some pioneer aviators, the bird wing was of course far more influential to the wider development of aviation. I added a link. — Cheers, Steelpillow (Talk) 17:21, 5 January 2017 (UTC)

What's so special about the lateen sail that it warrants an "especially" link? The only thing special about it that I'm aware of is that some of the sail is forward of the mast which means it takes less force to trim it in than a Marconi rig. Not sure what that has to do with the article though. Care to explain or provide a reference? Mr. Swordfish (talk) 18:37, 5 January 2017 (UTC)

I was under the impression that the sail, not the bird, was the origin of the shape. It sure is easier to visualize with the sail, and the sail shape was actively being used and experimentally maximized on ships, where the bird wing is just an observation. I'm a fluids engineer, so the hands-on experimentation aspect makes sense to me. Pb8bije6a7b6a3w (talk) 18:53, 5 January 2017 (UTC)

@Mr Swordfish: The lateen sail was the first sail which made it easy for a ship to tack against the wind. It did so because, unlike the early square sail which was conceived as a simple baffle plate and optimised for a following wind, it was conceived as a lifting surface and optimised for a crosswind. The modern Bermuda rig (aka Marconi) is derived from it and perhaps that could be added too. I think that expanding a touch on which kinds of sail rely most on this kind of lift would be useful. — Cheers, Steelpillow (Talk) 19:09, 5 January 2017 (UTC)

@IP editor: I am not clear that the idea of a recognisable lift force was in the minds or early sailors. Perhaps a Classical scholar might know. — Cheers, Steelpillow (Talk) 19:09, 5 January 2017 (UTC)

I haven't been careful with my wording. I'm trying to say that the Wright Brothers and that guy before them with the glider pulled from nautical experience and experimentation, not ornithological observation. As a child I saw the Wright's little wind tunnel and thought "what made them try that particular curved shape in the first place?". Steelpillow, I 'm new and couldn't find your link, but would love to see it. Thanks for the talk guys! Pb8bije6a7b6a3w (talk) 19:17, 5 January 2017 (UTC)

I think you are correct about this. I just don't think the Overview is the place to discuss origins in any level of detail. There's an article on History of Aviation where this topic would be appropriate. Skimming it, I don't see anything about nautical sails being a model for airplane wings, but that doen't mean it couldn't be added if proper sources were cited. I'd suggest taking this discussion to the talk page there. Mr. Swordfish (talk) 19:44, 5 January 2017 (UTC)

@Steelpillow A common myth is that old-style ships (e.g. square riggers) did not use lift and could only go downwind with the sails stalled and drag as the only driving force. This is not the case - from ancient times sailors knew that their ships went faster when the wind was abeam and trimmed their sails to take advantage of aerodynamic lift. Of course, they didn't call it that, but they knew how to use it. It is a modern conceit that they didn't discover and exploit aerodynamic lift.

I'll concede your point that the lateen rig was the first to efficiently go to windward, but earlier ships could go to windward (just not all that well) and you don't need to sail above a beam reach to exploit aerodynamic lift. So I still don't see how singling out the lateen sail is relevant. From a readability standpoint, adding "especially the lateen sail" without saying why is odd, and stopping to explain why (if we could, and I'm not convinced that we can) would be a distraction. I'd support removing the phrase.

As for the origins of the wing shape, airplane wings certainly evolved from sails (and windmill blades) since new technology borrows from existing technology, but the overview section is not the place to delve into the history and origins in any depth. Mr. Swordfish (talk) 19:32, 5 January 2017 (UTC)

I have undone my edit because it obviously needs more care. The documented history of Early flying machines is littered with feathered wings and bat-like wings. The modern concept of an aeroplane wing was formulated by Sir George Cayley, the "father of modern aviation", and through workers such as Horatio Phillips led directly to the airfols developed by the Wright brothers. Airfoils evolved through dreams of birds, bats, kites and helicopters, followed by hard graft in the laboratory. Sail-like forms did not make any documented appearance (that I am aware of) until the twentieth century, and even then were too obscure a side issue to gain a mention in the article I linked to. I am aware that the present article is not about the history of development and that the lead should not be used to present material outside of the main content, but I did neither of those, I added a little more about the applications of lift to the Overview section and I still think that would be an improvement. — Cheers, Steelpillow (Talk) 20:16, 5 January 2017 (UTC)

Couple of uncited conclusions

I just removed a couple of subsections from the article, because the cited sources did not appear to directly state the claimed conclusion, that the explanations are false. Such unsupported claims constitute WP:OR and are not allowed on Wikipedia. I am putting them here so that if anybody can establish WP:RS for the claims of falsehood, they can be easily tidied and reinstated. — Cheers, Steelpillow (Talk) 13:40, 23 October 2017 (UTC)

Misconception regarding the role of viscosity

Explanations that use the term "Coandă effect" sometimes further assert that the viscosity of the flow in the boundary layer is responsible for the ability of the flow to follow the convex upper surface. However, the idea that viscosity plays a significant role in flow turning is not consistent with the physics of curved boundary-layer flows. Analysis of the momentum balance in the flow in the boundary layer shows that the flow curvature is caused almost exclusively by the pressure gradient and that viscosity plays practically no direct role in the ability of the flow to follow a curved surface.

Misconception regarding "pulling down" of the flow

Explanations that refer to the Coandă effect sometimes also refer to the flow over the upper surface as "sticking" to the airfoil and being "pulled down" to follow the surface. Taken literally, this description is not consistent with the physics of gasses. For air to be pulled in the literal sense, it would have to be put in tension (negative pressure). The kinetic theory of gasses shows that in a gas at a positive absolute temperature the pressure cannot be negative. Thus for the flow to curve downward over the upper surface, it must be pushed down by higher pressure above than below. The difference in pressure between the flow at the upper surface itself and the flow far above the airfoil is generally small compared with the background atmospheric pressure, so that the lowest pressure on the airfoil upper surface is still strongly positive in an absolute sense.

Flow deflection and Newton's laws

Towards the end of this section: this explanation does not explain pressure and velocity variations in the vicinity of the airfoil . This ignores the fact that flow deflection or curvature of a flow coexists with a pressure gradient perpendicular to the flow. The pressure gradient in turn coexists with pressure and velocity variations in the vicinity of the airfoil (which in turn tie into Bernoulli principle). The idea that curved flows coexist with pressure gradients perpendicular to flow should be included somewhere early on in the article. Rcgldr (talk) 02:32, 23 June 2016 (UTC)

The section includes a subsection on Limitations of deflection/turning. Your concern is already addressed there. — Cheers, Steelpillow (Talk) 08:16, 23 June 2016 (UTC)

The statements are already there, These pressure differences arise in conjunction with the curved air flow. and This direct relationship between curved streamlines and pressure differences was derived from Newton's second law by Leonhard Euler ... in Lift_(force)#Pressure_differences. Which would in turn seem to explain pressure and velocity variations ... . Rcgldr (talk) 09:39, 23 June 2016 (UTC)

Yes, the information is there and does not need repeating. I am sure it could all be better organised. — Cheers, Steelpillow (Talk) 11:37, 23 June 2016 (UTC)

The main point here would be removal of this explanation does not explain pressure and velocity variations in the vicinity of the airfoil, and optionally replaced with a reference to the statements in the pressure differences section. Rcgldr (talk) 14:46, 23 June 2016 (UTC)

I think I see your point, and tend to agree with it, at least partially. The thing is, the very simple explanation using Newton's laws does not even address pressure differences and speed changes. It is quite possible to explain lift at an elementary level without talking about pressure or speed changes, and when we talk about limitations of "this explanation", we are talking about such an explanation.

Agree that it's possible to derive Euler's formula for pressure gradients (dp/dz = rho * v^2 /R) from Newton's second law by simply applying the kinematic expression of centripetal force, and this explains the pressure differences. So, yes Newton's laws adequately explain pressure differences. But the simple explanation, which is aimed at people who don't even know what a gradient is, doesn't even address pressure. "Air goes down, plane goes up" is the simple explanation, and it's correct as far as it goes and probably enough for most people. A more detailed discussion involves pressure differences, and that goes beyond the simple one.

Anyway, that's what we're trying to present here. Maybe there's a better way to present the material. Mr. Swordfish (talk) 16:01, 23 June 2016 (UTC)

The title of the section includes the term flow deflection, and the section states that "The air flow changes direction as it passes the airfoil and follows a path that is curved downward." Then in the pressure differences section it relates a curved path (streamline) with pressure differences. My only issue here is the statement "this explanation does not explain ...", when it is explained later on in the same article. Rcgldr (talk) 04:55, 24 June 2016 (UTC)

I cannot understand your point. The section in question does not explain the pressure issue, another section does. The wording is entirely consistent with this fact. — Cheers, Steelpillow (Talk) 08:48, 24 June 2016 (UTC)

My point is that the section mentions curved flow, which does coexist with a pressure gradient, but then continues with "does not explain", which could be interpreted as stating that curved flow does not explain (or at least coexist with) pressure gradients. Rcgldr (talk) 07:51, 25 June 2016 (UTC)

As I read the current phrasing, it is saying that the simple explanation based on Newton's F=ma does not explain how the forces arise, only what happens after they have arisen. It is clumsily phrased, no doubt about that, but I still do not read your interpretation into it. Probably the best thing is just to clean it up so it says what it means a bit more clearly and the problem goes away. I'll see if I can do that. — Cheers, Steelpillow (Talk) 11:38, 25 June 2016 (UTC)

When I looked at it, there seemed a lot of tangled verbiage in there trying to go way beyond the section topic in order to explain why the section topic did not go that far. So I cut most of it out. Is it any better, or have I cut too deep? — Cheers, Steelpillow (Talk) 11:52, 25 June 2016 (UTC)

I suggest removing all references to Coanda from this section. It's covered later on. As for why the air curves above the wing, that might belong in a separate section. No where in the entire article is there an accepted theory for why air curves above a wing, but I'll create a new talk section for this. Rcgldr (talk) 23:46, 25 June 2016 (UTC)

Hi, new contributor here. I believe that the article could benefit from an explanation of why air deflection is an efficient way for aircraft to generate lift to oppose gravity. The crux of this is the interplay between momentum and kinetic energy for an aircraft moving perpendicular to a gravitational field. By using a wing an aircraft is able to deflect a large volume of air, hence to produce the necessary lift force the velocity change of the deflected air is small. ( Impulse = Mass*VelocityChange ) With a large deflection mass the necessary VelocityChange can be small. A small VelocityChange is important as the energy requirements to accelerate this air downwards is governed by (Energy = 0.5*Mass*VelocityChange^2) A small VelocityChange minimizes the power requirement required to generate a given lift force when compared to using VTOL-esque engines(for which a smaller air mass is accelerated to a greater velocity to provide the same force).

Firstly I wanted to check if other editors thought that this point had educational merit? secondly is anyone interested in co-writing a more polished paragraph regarding this with me? CaptainAnalogy (talk) 14:34, 4 March 2017 (UTC)

If efficiency does get included, it would not be in the section this thread is discussing. Better to start a new discussion below. But really, I see efficiency as more related to design decisions than to the basic theory. — Cheers, Steelpillow (Talk) 12:45, 4 November 2017 (UTC)

Suggestion - Add a complete summary of the currently accepted correct theory of lift.

I made this change last night but was unaware of Wikipedia's rules. What do you guys think. Feel free to poke around and improve or add to it. I think it's a good addition because right now, the article is very stretched out and there is no obvious, clear answer to someone who just wants a concise explanation from start to finish.

The currently accepted correct explanation of lift

As a three dimensional wing begins moving through the air (from right to left), the effects of viscosity create a vortex sheet at the trailing edge. This vorticity develops into a starting vortex rotating counter-clockwise; to keep the net vorticity of the flow-field zero, an equal and opposite clockwise vortex is created that is bound to the wing as it continues to move. This bound vortex is responsible for the acceleration of the fluid parcels on the upper surface of the wing and the deceleration of those underneath, which by conservation of energy (and in simplified form, applied to a fluid, Bernoulli's Principle) causes the changes in pressure associated with lift. This pressure differential causes the air underneath the wing to 'push up' on the object moving through the fluid, and by Newton's third law, this applied force creates the vertical component of the aerodynamic force on the body.

The existence of the bound vortex was predicted very early on in fluid mechanics by early aerodynamicists, and Ludwig Prandtl later proved this theory by capturing the starting vortex on film. Capturing the existence of the starting vortex proved that of the bound vortex, as conservation laws state a static fluid has no vorticity; to keep the net vorticity at zero, an equal and opposite vortex is necessary.

This theory of circulation caused by the bound vortex is further backed up by the existence of wingtip vortices. A vortex line both physically and mathematically can not end in a fluid; Helmholtz's theorem maintains it must either end at a physical surface or connect to another open-ended vortex line. The vortex line of the bound vortex on a 3 dimensional wing cannot end at the wingtip; it instead curves into and becomes the wingtip vortex, which is in turn connected to the starting vortex. The starting vortices from each wing are also connected, forming one big loop. A common misconception is that wingtip vortices can be completely eliminated, when in reality wingtip devices are designed instead to reposition these vortices and increase the aspect ratio of a wing without increasing the span (reducing spanwise loading and bending). Wingtip vortices cannot be weakened; to lift the same amount of mass, the same amount of circulation is required, which will create the same amount of vorticity at the wingtip. Induced drag can, however, be reduced by increasing the span along which the trailing edge sheds vorticity, which winglets are designed to do.

Bndrylyr (talk) 21:36, 10 July 2017 (UTC)

I discourage the view that there is a single "correct explanation" of lift on an airfoil. The explanation favoured by one person will be dismissed by another. Lift can be used to illustrate a number of different principles of physics and math. Satisfactory explanations exist for people at all levels of prior knowledge. I can challenge your version of the correct explanation by saying it is only meaningful to readers who already understand such concepts as viscosity, vortex, vortex sheet, bound vortex, and so on. There are simpler explanations, no less correct than yours, that are understandable by readers with no knowledge of viscosity. For example, a reader who understands the concept of pressure can appreciate the following explanation: The average pressure on the underside of the airfoil exceeds the average pressure on the topside. But that simple explanation is inadequate as an example of the application of the Kutta-Joukowski theorem, or the Kutta condition. There is at least one correct explanation for every level of knowledge of physics, fluid dynamics and math, from young people and newcomers to the subject, all the way up to high-level specialists in each of these fields. Dolphin (t) 22:26, 10 July 2017 (UTC)

Personally I would have to respectfully disagree; while there are many simplified explanations of lift, they aren't a complete cause and effect, start to finish explanation. Sure, you can explain the pressure difference, and that's 'correct' and causes the vertical component of the force, but it doesn't explain where the fluid acceleration comes from. We have a section for this already in the article. It covers plenty of simplified explanations. The article lacks an explanation that goes from start to finish (and the transition from a static flowfield to a moving fluid is absolutely vital to lift generation!). I'm not sure what you mean when you say there is no single 'correct explanation'?... I would say there certainly is, and these simplified explanations just cover small pieces of the complete process. The most irritating thing for me when I first entered this field was reading and learning about all these scattered 'simplifications' of such a vital process and struggling to find anything that explained how it all pieces together. The physical process itself is well known and well understood (modelling it without numerical computation proves a different challenge!). I believe it deserves a spot somewhere on the page. And bringing up the concepts you mentioned might inspire readers to do their own research and learn more about aeronautics and external fluid mechanics; not many engineering undergraduate programs cover external flows! Wikipedia's intext links help with that. An entire wave of aging engineers is about to retire from the aeronautical industry; the more inspiration the better! Bndrylyr (talk) 04:41, 11 July 2017 (UTC)

In at least a couple of your edits you have referred to the correct theory of lift. In particular, you have used the singular theory, not the plural theories. From this, I infer that you believe there is only one correct theory of lift. I disagree with any suggestion that there can be only one theory of lift that is correct. Perhaps you agree with me - above, you wrote Sure, you can explain the pressure difference, and that's 'correct' ...

Perhaps where you have used the word correct you mean comprehensive. I agree that your description of lift, taking into account viscosity, starting vortex, bound vortex etc., is much more comprehensive than one that only takes into account the average pressures on top and bottom of an airfoil.

I think it would be naïve to imagine that your comprehensive theory of lift (viscosity, vortex etc.) is the ultimate in explanations of lift. It offers little in relation to lift in transonic flows, and nothing in relation to supersonic flows. Other theories, even more comprehensive, exist to soundly explain the complexities surrounding generation of lift in these high-speed flows. (Remember the difficulty in breaking the sound barrier.)

There are numerous theories of lift that are correct. Each one is ideal in particular circumstances. This situation is not unique to the concept of lift on an airfoil. Regardless of the topic, it is up to the readers to peruse the numerous theories and find the one that is best for their level of prior knowledge, and their current needs. Dolphin (t) 12:50, 11 July 2017 (UTC)

I agree with Dolphin here. Having read every work cited by this article, plus at least a hundred others that did not make the cut, my take is that there are a variety of "correct" ways to explain lift. The idea that there's one and only one "correct" explanation is at odds with what the reliable sources state. Since it's our job as wikipedia editors to represent the material found in the reliable sources, implying either directly or indirectly that there's one "currently accepted correct explanation of lift" would violate wikipedia policy. Furthermore, wikipedia is not the place to publish original research or synthesis.

By the way, the explanation that you derided as "entirely incorrect" is the one recommended by the American Association of Physics Teachers: "At least for an introductory course, lift on an airfoil should be explained simply in terms of Newton’s Third Law, with the thrust up being equal to the time rate of change of momentum of the air downwards."

All that said, that doesn't mean that your proposed addition has no place in the article. It would need some changes so that it adheres to wikipedia policies (proper citations, accurate reflection of those cites, no original research, etc.) In the past, major changes to this article have been implemented first in a "sandbox" and then presented on the talk page for discussion and review, with changes to the actual article only occurring after consensus is reached here on the talk page. Mr. Swordfish (talk) 14:43, 11 July 2017 (UTC)

To Mr. Swordfish and Dolphin; I apologize if I have been unclear. I'll try to explain what I mean. I'm certainly not dismissing any of the simplified explanations; my overall point is they aren't so much 'simplified explanations' as pieces of the whole process. Explaining to someone that lift is created by the pressure difference is just fine, until they think about it and ask, well where does the pressure difference come from? Well, then Bernoulli has to be explained. And someone might think on it and come back with, okay, well then why is the fluid moving faster on top? Then you explain circulation, and it goes on and on. Humans naturally think in terms of cause and effect. When I was learning this stuff, I had to go through this whole process until I finally got to sit down with one of my professors and just started asking questions. It shouldn't be that hard; it's nearly impossible to find a 'this happens, which causes this, then this, then this, and finally this' on the internet. The only online source I've ever found that did something like that was a paper by a well regarded research professor at Embry-Riddle in Daytona. I really wish I could find his paper again so I could use it as a reference if this makes it onto the Wikipedia article.

So I'm absolutely not trying to discredit anything (except that downturning theory and Newton's third law; this is a misconception and there is no change in vertical momentum in the far-field! See one of the sources; Doug McLean's 'Understanding Aerodynamics', page 427 (8.5.1) - this is a relatively new discovery (1987 & 1996 independently) as far as I'm aware and has not been well circulated yet, but lift is entirely pressure. Maybe we should consider modifying that section? The mathematical proof involved the discovery of a mistake in the integral that concluded there was a net downward flux through a Trefftz plane placed between the bound and starting vortices [it is nonconvergent]. However a modification could be made to describe action/reaction of the pressure differential on the body?). I am proposing we link all these pieces together into one big summary to spare others the experience I had. My choice of title was poor, sorry. Maybe something more like 'The complete process of lift generation by a 3-dimensional wing', or along those lines? Bndrylyr (talk) 21:19, 11 July 2017 (UTC)

Thanks Bndrylyr. I endorse Mr swordfish's suggestion that you activate your personal sandbox and work up your proposed additions, or your proposed alternative text for some or all of the existing text. When you think you are getting close to finished let others know and ask them to comment on it. Others will be able to help and it builds consensus. Dolphin (t) 21:59, 11 July 2017 (UTC)

Thanks; I'll start working on this. Ignore what I said about downturning; I'm incorrect there (misinterpreted the conclusion in the referenced book)! I'll get to work on a summary though. Bndrylyr (talk) 10:56, 13 July 2017 (UTC)

Just a head's up: we (the editors on this page) spent about a year arguing about momentum transfer in 2014, with the resulting consensus being the article (more or less) as it appears today. You might want to read the archives so as to forestall repetition of that debate. Mr. Swordfish (talk) 14:25, 13 July 2017 (UTC)

Haha. Will the debates ever end?

The doubt in that explanation I expressed earlier was my own misinterpretation of a conclusion in that book. The nonconvergence was a legitimate discovery but how it affected the understanding of lift is not related to what I had thought. My bad! Bndrylyr (talk) 20:31, 13 July 2017 (UTC)

I would endorse both that there is no single "correct" explanation and that the various principles all form part of a unified overall picture in which every principle interacts inseparably with every other (debunking any of these principles is therefore a foolish thing to try, but we have had that debate). In fact, I have begun recasting the introductory sections to help draw this out. See also my new thread below, on circulation. — Cheers, Steelpillow (Talk) 12:59, 4 November 2017 (UTC)

Article title

I am unhappy with the current title of this article. Lift forces in fluids are also generated aero/hydro-statically and by direct vertical thrust, and mechanically one also talks of the lift force exerted by a crane, hoist, etc. I think it needs to be less ambiguous. Should we change it to, say, the more correct Lift (fluid dynamics) or perhaps to a shortened Lift (dynamic)? — Cheers, Steelpillow (Talk) 12:31, 4 November 2017 (UTC)

By comparison, I notice that the equivalent drag force is dealt with at Drag (physics), with Drag (force) redirecting to it. — Cheers, Steelpillow (Talk) 18:01, 5 November 2017 (UTC)

The current title has been in use for so long I am accustomed to it and it doesn't offend me. However, I concede that the content is devoted to fluid dynamic lift rather than to the various forces that are given the name lift. Similarly, the content of the article Drag (physics) is devoted to fluid dynamic drag rather than to the various concepts in physics that are given the name drag.

One existing category of articles is Category:Fluid dynamics which is a sub-category of Category:Dynamics (mechanics). There is no existing category called Dynamics (without a qualifier such as mechanics.) For this reason, if the title Lift (force) is to be changed I favour Lift (fluid dynamics) rather than Lift (dynamics).

If the title of this article is to be changed, I am in favour of simultaneously changing Drag (physics) to Drag (fluid dynamics) and making both of them members of the category Fluid dynamics.

The following articles already make use of the qualifier (fluid dynamics):

Characteristic number (fluid dynamics)

Circulation (fluid dynamics)

Eddy (fluid dynamics)

Peniche (fluid dynamics)

Plume (fluid dynamics)

Rayleigh's equation (fluid dynamics)

Seeding (fluid dynamics)

Shock (fluid dynamics).

I can find three articles that use the qualifier (fluid mechanics):

Foil (fluid mechanics), Splash (fluid mechanics) and Trajectory (fluid mechanics) but I'm not in favour of using this qualifier for fluid dynamic lift and/or drag. Dolphin (t) 07:22, 6 November 2017 (UTC)

I'm ok with either Lift(force) or Lift(fluid dynamics). One practical implication of a name change is that any link to a section within this article will break unless someone finds and corrects all of them. Unless that happens too I'm not in favor of changing the title. Mr. Swordfish (talk) 21:15, 7 November 2017 (UTC)

Lift is a concept almost coincident with aerodynamics of flight, never confused with rocket propulsion. The disambiguation page Lift calls this article "A mechanical force generated by an object moving through a fluid", which sounds right. Notice that the concept of this article so dominates the namespace that lift coefficient needs no disambiguation. Apart from the philosophical realization that other forces might also be called lift, there does not appear to be good motivation for moving the page, unless one wishes to be disruptive. — Rgdboer (talk) 02:03, 8 November 2017 (UTC)

Article reorganization

I have just done a major reorganization of the article, added some elementary remarks to give context and trimmed some of the mathematics that is better treated in the relevant linked article. I have tried in particular to remove some of the scars and "protective editing" it picked up during the deeply embroiled controversies it suffered a while ago. I hope folks think I have moved it in the right direction. I am sure there is still more to do, but it's time for me to step back and see how much of it sticks. — Cheers, Steelpillow (Talk) 17:18, 5 November 2017 (UTC)

Past practice has been to first offer a draft of major re-orgs in a sandbox and invite comments. Or at least to discuss the reasoning and objectives of a re-org here on the Talk page. I'm disappointed that we did not follow that practice here.

As for the changes, I do not find the new version to be an improvement. That said, many of the changes are positive, so I'm reluctant to just revert it all. I'm going to spend some more time with it to absorb the changes and try to understand why they were made. Not sure whether the right move is to revert and discuss or edit from here. Other opinions? Mr. Swordfish (talk) 16:24, 6 November 2017 (UTC)

Considering the extensive consultation and re-write done in a sandbox a few years ago by Mr swordfish and others, I am in favour of the same process being used again if extensive changes are considered warranted. Our experience has been that, if the task is tackled as a project carried out off-site, such as in a personal sandbox, it attracts the assistance of numerous others. Conversely, if the task is tackled by multiple amendments to the main article, that attracts fewer helpers.

My memory of the previous consultation and re-write is that it was done in one of Mr swordfish's personal sandboxes. I'm sure Mr swordfish can refresh our collective memories as to exactly where it was that he carried out his project. I then suggest we follow a similar procedure to examine the improvements recommended by Steelpillow.Dolphin (t) 06:27, 7 November 2017 (UTC)

If you look at the Circulation thread above, you will see that I asked for comment. None was offered. That has not stopped Mr swordfish (talk · contribs) from undoing the edit I asked for discussion on, still without any explanation. Prior to that, his personal sandbox draft referred to above (User:Mr swordfish/Lift) appears to have had little if any input from anybody else before it was moved over here. On that basis, I find calls for doing collaborative processes "my way" to ring somewhat hollow and endorsements of such methods hard to understand. I am taking this article off my watchlist, you needn't bother to reply to me personally. — Cheers, Steelpillow (Talk) 08:14, 7 November 2017 (UTC)

Steelpillow is correct that the last major re-org was at User:Mr swordfish/Lift in the Summer of 2014, with a small flurry of edits in December 2015. The discussion did not take place on the talk page of the draft article; it took place here. See Archive #8 for details. Prior to that, a major re-write occurred Summer of 2012, again with lots of comments here. See Archive #6. My first crack at re-organizing this article was June/July 2009. See Archive #4.

Additionally, Dolphin has used his sandbox for proposed changes, and Doug McLean had a draft version or two that was integrated into this article. So I'm a bit puzzled by the assertion that these major re-revisions "appears to have had little if any input from anybody else before it was moved over here." The discussion was extensive and took place over many weeks each time.

Wikipedia editing is supposed to be a collaborative process based on consensus. The consensus seems to have been to deal with major revisions by proposing them off-line and discussing here before making them live. That's not "my way" or "Dolphin's way", it's the consensus of the editors. Or at least it seemed to me that it was - consensus may change and that's why I didn't just summarily revert the recent major rewrite.

Moving forward, we have a choice to make: revert to the last version or move forward from here. Is there consensus to accept the changes of the last few days, or should we move it off-line for discussion? If we choose the second approach, I will volunteer my user space unless someone else would like to host it. Mr. Swordfish (talk) 16:04, 7 November 2017 (UTC)

@Mr swordfish: I think the way ahead is to sort Steelpillow’s changes into a manageable number of major changes, and then examine each of those major changes to decide whether it is compatible with the plan and layout developed in the recent major re-writes, and whether it represents an improvement (or at least whether it should remain.) You have already done that for Steelpillow’s relocation of the section on Circulation.

Steelpillow’s edits were made in good faith so I am inclined to leave the article as it is at present and only make changes or reversions after each major change has been assessed and a decision made.

Thanks for volunteering your User space as a place for the assessment and discussion. I think it would be best located at your User space because it is really only you who has a clear view of the plan and layout of the article as it has been for recent years. Dolphin (t) 21:17, 8 November 2017 (UTC)

Agree that the edits were in good faith, and I'm saddened to lose another editor due to misunderstanding. Moving forward, if I may be so bold as to characterize the bulk of the edits, I think the misunderstanding is based on a disagreement on the intended audience. The SP version https://en.wikipedia.org/w/index.php?title=Lift_(force)&oldid=808858410 (for lack of a better name) seems aimed at the freshman undergraduate engineering student. It proceeds logically from basic ideas in fluid mechanics and applies them to a lifting body, asserting at the outset "Some of the basic ideas involved in lift apply generally in fluid dynamics. A general understanding of these is necessary before the specific conditions applying to lift can be clarified."

While organizing the article this way is is consistent and logical, I don't think it's the right approach given our audience. My assumption is that the vast majority of readers do not have an engineering background and will be put off by telling them that they have to understand fluid dynamics first. Chances are, they've never heard the term "fluid dynamics". So, it's incumbent on us to provide an explanation that the average reader can read and understand, without insisting that they have to learn a bunch of complicated other stuff first. WP:TECHNICAL explains this in detail.

Applying this advice to this article, I've restored the simple explanations to their rightful place at the beginning of the article, i.e. the simple explanations based on Newton's laws and Bernoulli's principle. This is followed immediately with the idea of pressure differences due to flow turning (the approach advocated by NASA) in the basic attributes of lift section. This is in turn followed by the "more comprehensive" section and then the math section. The article now proceeds from the more easily understood ideas to the more complex. I've taken the liberty of moving Lift Coefficient and Pressure Integration subsections from the "basic" section to the "math" section. Likewise for Circulation and Kutta-Jaukowski.

I've now gone through each section and scanned the changes, reverting those that seemed obvious candidates for reverting based on WP:TECHNICAL. I think I'm following the advice given at WP:BRD. Many changes seemed positive and I've left those as-is. Mr. Swordfish (talk) 17:04, 9 November 2017 (UTC)

Serial comma

Re-reading the page today I noticed that the use of the serial (Oxford, Harvard) comma was inconsistent. The Manual of Style allows for either using it or omitting it, however we are supposed to be consistent within an article. I have added the serial comma where it was missing to remain consistent with the usage in the rest of the article. My take is that it makes that material more readable, but I'm open to other opinions. Mr. Swordfish (talk) 19:48, 4 December 2017 (UTC)

I have looked at your changes. I like the serial comma in the places you have used it. Consistency is most important. Dolphin (t) 03:39, 5 December 2017 (UTC)

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Circulation

The circulation theory of lift is not a complete theory, because the quantitative circulation has to be derived independently. For this reason among others, authors such as Clancy introduce it during the early stages of their explanation, alongside discussions of Newton, Bernoulli, etc. I have taken the liberty of doing so here, and of refactoring the explanation a little to make it more readable in this context. I think that some further refinement is needed, such as mention of the Kutta condition and perhaps trimming some of the more technical stuff present in the topic's main article on the Kutta–Joukowski theorem. Meanwhile, if anybody has any problems with what I am doing, please do bring them up here. — Cheers, Steelpillow (Talk) 11:23, 4 November 2017 (UTC)

Circulation certainly should be treated somewhere in this article, the question is "where?". Many readers may find it confusing as the term seems to imply that the air circulates around the wing much like the earth revolves around the sun. But this isn't the case - mathematically, it's the sum of two vector fields, one of which is circulatory, but no air molecule actually makes a complete circuit of the wing. So, we have to be careful that our readers don't come away with the wrong idea.

My take is that circulation is a mathematical abstraction and therefore belongs under the mathematical theories of lift, so I've moved it back there. The recent edits removed some of the math; I haven't formed an opinion yet whether that's an improvement of not so I haven't reverted those edits. Other opinions? Mr. Swordfish (talk) 16:23, 7 November 2017 (UTC)

Wikipedia provides some guidance at Wikipedia:Make technical articles understandable. In particular, this guidance suggests the least obscure parts of the article should be upfront; and the more obscure parts should be further down the page - see WP:UPFRONT. The concept of circulation, and the Kutta condition, are rather obscure so for that reason they shouldn't be too close to the lede. I am inclined to agree with the view that circulation is a mathematical abstraction and so should be included with the other mathematical theories of lift. Dolphin (t) 02:34, 8 November 2017 (UTC)

Since this sub-section has been moved back to the "maths" section, does it make sense to restore the mathematics? The previous version is here:

https://en.wikipedia.org/w/index.php?title=Lift_(force)&oldid=808585728#Circulation_and_the_Kutta-Joukowski_theorem

and the current version is here:

https://en.wikipedia.org/wiki/Lift_(force)#Circulation_and_Kutta-Joukowski

My preference would be to merge the two versions since there's some material in the current version worth keeping. Other opinions? Mr. Swordfish (talk) 13:48, 12 November 2017 (UTC)

@Mr swordfish: My apologies for not seeing this one earlier. My preference is the same as yours - merge the two. Dolphin (t) 21:43, 5 April 2018 (UTC)

Unsupported explanation under "Momentum balance"

Checking this article after a long absence, I see that a section that I drafted several years ago under the heading "Analyses of the integrated momentum balance in lifting flows" has been split, with most of it now under "Control volumes" (not a very informative heading), and the part that deals with the pressure footprint on the ground under a lifting wing moved forward in the article and given the new heading "Momentum balance". This part has been substantially edited since it first appeared in the article. The original version simply described the pressure footprint and noted that it's part of the balance of force and vertical momentum in the atmosphere as a whole, without trying to explain a mechanism for its formation. The current version gives a new explanation in the first three sentences, interpreting the pressure footprint as being a result of "downward momentum of the air in the wake", and further saying that "When it meets the ground, the downward-moving wake establishes a pattern of higher-than-ambient pressure, as shown on the right", citing Prandtl and Tietjens' book and Lanchester's book.

This idea of some vaguely defined portion of the flow having downward momentum imparted to it by the wing and subsequently having that downward momentum absorbed in a sort of impact interaction near the ground might seem intuitively plausible to some, but it's not supported by the sources cited, or by any other published source that I know of. Prandtl and Tietjens use the classical horseshoe-vortex model for a wing and its vortex wake to deduce a detailed theoretical pressure distribution for the footprint on the ground. The pressure disturbance far from the airplane is found to be entirely associated with the bound vortex and its image under the ground; the vortex wake is found to make no contribution. P&T don't mention "downward momentum" in the wake or anywhere else as being part of the mechanism. Lanchester also concludes that lift must be reacted by overpressure on the ground, but his analysis is less detailed, and he doesn't deduce a distribution for the overpressure. He also says nothing to imply that downward momentum is part of the mechanism of formation of the overpressure.

In addition to not being supported by the sources, the new explanation isn't consistent with the details of the flowfield. The isobars of the footprint pattern on the ground are circles centered directly under the airplane. Very little of the pressure disturbance extends to large distances downstream (I made the graphic accompanying "Momentum balance", so I know it's an accurate plot of a slice through the theoretical pressure distribution). The only "wake" that can "reach the ground" is the vortex wake, and it descends at a very shallow angle. If it reaches the ground at all before breaking up, it does it far downstream of any significant remnant of the pressure footprint. Furthermore, a descending vortex wake carries with it equal integrated amounts of upwash and downwash, and thus has no net downward momentum to lose.

There is an integrated flux of downward momentum behind a lifting wing, associated with the bound vortex and its image under the ground, not the trailing vortices. Close behind the wing the flux integral corresponds to half the lift, and farther downstream, when a ground plane is present, it gradually decreases to zero. So the total flux of downward momentum lost behind the airplane corresponds to only half the lift, while the pressure footprint corresponds to all of it. Just as much of the loss of flux takes place above the wing's altitude as below. The lower boundary of the region where the loss takes place does touch the ground, but not until well downstream of the bulk of the pressure footprint.

Thus the details of the flow aren't consistent with the wake impact mechanism implied by the new explanation. The pressure footprint is really just part of the overall pressure field around the wing, which extends into the farfield. The pattern the pressure footprint is part of doesn't just appear near the ground. Every horizontal plane more than a few wing chords below the airplane has an overpressure pattern that integrates to 100% of the lift. As we move toward the ground, the pattern becomes increasingly spread out horizontally, and the maximum overpressure monotonically decreases, all the way to the ground. If the ground footprint were due to an impact mechanism, the maximum pressure would increase as the ground is approached, as in a stagnation-point flow.

The above argument against the new explanation is based on flow details that are documented in multiple sources, but I admit that putting it together involved some synthesis. Actually, that's OK because I'm not proposing including the argument in the article. I just want to see this section revised so as not to include the unsupported and misleading explanation. The lack of support in the sources should suffice to justify this.

The simplest option would be to revert it to what it was when treatment of the pressure footprint was first added to the article. At least I know that version was both correct and supported by the sources. The only downside to the original version is that it's purely descriptive and doesn't say what the mechanism is. This may be what motivated someone to embellish it with the new explanation. Unfortunately the embellishment has no basis in the sources or in the physics.

So, what would a correct explanation look like? P&T aren't much help in this regard. Their analysis of the footprint is based on vortex "induction", which amounts to a valid logical inference about the velocity field and allows them to calculate the pressure distribution, but it isn't a physical explanation in a cause-and-effect sense. At a basic physical level, the pressure disturbance on the ground exists because a lifting wing produces a pressure field that dies out only asymptotically with distance. So we could describe the footprint as simply the extension of the pressure field explained in the previous section (the horseshoe-vortex model supports this if you look at the pressure field it predicts), replacing the current version with:

A lifting wing (or airfoil) is always surrounded by a pressure field, as explained in the previous section. The pressure differences associated with this field die off gradually with increasing distance from the wing, becoming very small at large distances, but never disappearing altogether. Below the airplane, the pressure field persists as a positive pressure disturbance that reaches all the way to the ground, forming a pattern of slightly-higher-than-ambient pressure on the ground, as shown on the right (reference Prandtl and Tietjens, Figure 150). Although the pressure differences are very small far below the airplane, they are spread over a wide area and add up to a substantial force. For steady, level flight, the integrated force due to the pressure differences is equal to the total aerodynamic lift of the airplane and to the airplane's weight. According to Newton's third law, this pressure force exerted on the ground by the air is matched by an equal-and-opposite upward force exerted on the air by the ground, which offsets all of the downward force exerted on the air by the airplane. The net force due to the lift, acting on the atmosphere as a whole, is therefore zero, and there is thus no integrated accumulation of vertical momentum in the atmosphere, as was noted by Lanchester in 1907(reference Lanchester, sections 5 and 112).

This goes a bit beyond what the sources explicitly say, but perhaps it qualifies as allowable interpretation. At least it doesn't violate verifiability nearly as badly as the current version does, and it has the added virtue of being correct.

I'd also suggest changing the heading of the footprint section to "Lift reacted by overpressure on the ground under an airplane" and the heading "Control volumes" to something more informative such as "Analyses of the integrated momentum balance in lifting flows", both to better reflect the content of the sections.

Perhaps it would also be an improvement to replace the footprint graphic with one that provides a perspective view of the footprint like that in Prandtl and Tietjens' Fig 150, if a version can be found that doesn't infringe.

In summary, the new explanation in the current version of "Momentum balance" isn't supported by the sources and is physically incorrect to boot. If we're going to keep a footprint section, it really needs to be changed. I've offered suggestions for this change.

I "retired" from helping to edit this article several years ago, and I don't intend to return as a regular. I plan to retire again as soon as this issue is settled.

J Doug McLean (talk) 01:29, 17 March 2018 (UTC)

Welcome back Doug! I understand your concerns. I have had numerous experiences in which one of my statements has been amended, without my citation being changed, in such a way that the published text is no longer supported by the citation.

Wikipedia places great emphasis on verifiability. The expectation is that any reader should always be able to use the published citation to check the veracity of a statement. If the published text is not supported by the cited source it is grounds for editing the text or, at the very least, erasing the citation. In your case, you have substantial grounds to edit the text so that it is again compatible with the cited source(s).

You have raised your concerns on this Talk page so you are now at liberty to edit the offending sections to make them compatible with cited sources; and to go beyond that and make changes simply to improve the quality of the article. If you have any doubts about the acceptability of this approach, be bold and see WP:BE BOLD! Dolphin (t) 04:32, 17 March 2018 (UTC)

Thank you for the supportive response. Because bold edits haven't typically been well received in the past, I've been waiting to see if consensus would develop. Now I suppose we have a consensus of two. If no one else chimes in in the next week or so I'll go ahead and make my proposed edits. J Doug McLean (talk) 18:55, 5 April 2018 (UTC)

Since no one has expressed opposition, I have gone ahead and edited the title and text of "Momentum balance" and the title of "Control volumes". J Doug McLean (talk) 04:09, 20 April 2018 (UTC)