User talk:Dolphin51/Sandbox

Hi Dolphin51, Three quick comments at this moment (I have to go in a few minutes) with regard to bluff bodies:

• ...are inefficient generators of lift: the oscillating lift is quite often a very undesirable side effect, which one tries to minimize, to prevent vibrations. This wording has the opposite taste.
• ...when moving through a fluid...: the object may as well be fixed and standing in the wind, stream or waves passing by. The 1st paragraph has the same limitation: the formulation should satisfy (at least) Galilean invariance (at the moment the lift article's 1st paragraph is).
• ...causing the object to vibrate: whether the lift causes the object to vibrate depends on many factors, e.g. stiffness, natural frequency, vortex shedding frequency, correlation of lift forces along the span, etc. Lift does not need to let the structure vibrate. -- Crowsnest (talk) 07:40, 20 March 2009 (UTC)

Thanks very much Crowsnest. I have amended my proposed text to take account of your comments, as far as possible. I deleted the final sentence about inefficient generators of lift. It was unnecessary; I could find no suitable citation; and it was not readily compatible with the notion that vortex-induced vibrations are usually a nuisance. Dolphin51 (talk) 02:58, 31 March 2009 (UTC)

Hi Mark. Thanks for your suggested amendment regarding lift and drag on non-streamlined bodies. You will see that I have deleted that sentence in its entirety. It was unnecessary, and Crowsnest alerted me to the problem of talking about inefficient generators of lift when alternating lift is the cause of vortex-induced vibration (VIV). VIV is usually undesirable and engineers try to avoid it or eliminate it. Consequently the less lift the better on any bluff body likely to suffer from VIV. Dolphin51 (talk) 03:10, 31 March 2009 (UTC)

Inspired by your work here, I already moved a sentence down from the intro to the section on bluff bodies . -- Crowsnest (talk) 10:35, 31 March 2009 (UTC)

Hi Dolphin51. Can you already move the last sentence of the 1st paragraph to the main article: "An airfoil is a streamlined body that is capable ...". I really like it and it is so to the point. The 1st sentences have still some friction somehow. For instance both mentioning fluid dynamics and aeronautics, and the fact that the lift is perpendicular to the oncoming flow is mentioned so late. -- Crowsnest (talk) 16:53, 31 March 2009 (UTC)

The 2nd paragraph is also OK, and improved with what it is now in the article. -- Crowsnest (talk) 17:20, 31 March 2009 (UTC)

Thanks Crowsnest. I have left the first sentence in place, and transferred everything from my Sandbox, except my first sentence, to the main article. I have retained your citation for vortex-induced vibration. Dolphin51 (talk) 23:16, 31 March 2009 (UTC)

Dynamic pressure

Made a few edits... let me know what you think. A full derivation of both dynamic and impact pressure can be made to make the physics clearer... I have a dozen or so of the equations on my talk page in preparation for such a derivation. (Weirpwoer (talk) 22:17, 2 December 2009 (UTC))

Thanks for your contributions to enhance the article. I have a few comments:

• You have cited both NACA Report No. 837 and NACA TN-1120. They have the same title and the same author. Are they different documents? I have converted your citation of Report No. 837 into a weblink. Is TN-1120 available on the web such that it also can be converted into a weblink?

http://aerade.cranfield.ac.uk/ara/1946/naca-tn-1120.pdf

Thanks. I will add that as a weblink

• Your statement While dynamic pressure is restricted to incompressible flows ... implies that the true meaning of dynamic pressure has been determined by some supreme authority. Some authors, academics, engineers and scientists give one meaning to the expression dynamic pressure, whereas other authors, academics, engineers and scientists give it a slightly different meaning. Neither group is more correct than the other. Certainly Wikipedia does not set out to declare that one meaning is more correct than the other - the same principle as applies to British and American spelling of various words, such as centre and center.

Do you care to show me which peer-reviewed literature is treating dynamic pressure as representing a solution to Euler's fluid equation where density is allowed to vary? I have browsed upwards of four dozen aircraft performance handbooks and I have never actually seen dynamic pressure being described in this way. Obviously a meta-analysis is needed. I look forward to seeing where the claim is being made that dynamic pressure uses a varying-density solution. I'll confess... I have not read Bernoulli's original literature (although, according to Professor Anderson, the equation "1/2 rho V^2" was never given by Bernoulli, but was left to Euler - so it would be necessary to check Euler's publications to establish the origin of the term "dynamic pressure" and precisely which solution it was associated with.) (Weirpwoer (talk) 21:12, 9 December 2009 (UTC))

See my comments below.

• You refer to a common streamline. It is not clear what you mean by a common streamline. Can the word common be removed without any loss of meaning?

How about we start off with the partial derivatives and show how Euler's equation arises, then show how it is transformed into "dynamic pressure" by holding density fixed? From an engineering perspective... it make virtually no difference whether you pick a neighbouring streamline so long as it is far enough upstream that it is unaffected by some moving body. For all intents and purposes the point-properties of interest, in the field upstream, will be more or less the same whether one takes 'the' streamline of interest or some adjacent one. The effect is probably no worse than neglecting effects to elevation. (Weirpwoer (talk) 21:12, 9 December 2009 (UTC))

You have not begun to deal with the question. The question is What do you mean by a common streamline? (Are all streamlines common streamlines? Or do you have a criterion by which some streamlines are common streamlines, and all other streamlines are not common.)

• You have written When the density is allowed to vary in some way. This suggests to the first-time reader that there are numerous ways in which density can vary. Would it be sufficient to say When density varies along a streamline? Dolphin51 (talk) 02:14, 3 December 2009 (UTC)

There are many ways in which density can vary and it is not merely an academic point - does a streamline (or technically some elemental area bound within a streamtube) undergo an isentropic process, or a non-isentropic one? That's more or less the same as asking whether we're dealing with subsonic or supersonic flow. For subsonic flow density, in air, may be taken to vary isentropically with pressure. What if we're dealing with water? Or a highly imperfect gas? Then completely different rules will apply to how density varies, and so different solutions from Euler's equation will arise. Critical question then. The density (of an elemental area, in streamline-coordinates) does vary, and for air it may be said to vary isentropically if the flow is subsonic. The solution you'll find after integrating will be the so-called Saint-Venant equation. But it is a separate solution to the so-called Bernoulli one. Many more solutions exist. (Weirpwoer (talk) 21:12, 9 December 2009 (UTC))

I am convinced that you know what you mean when you write the density is allowed to vary in some way. However, Wikipedia is aimed at a general readership. Readers are entitled to say density can only vary in two ways - upwards and downwards. It is not sufficient for the author to know what he is writing about. It is necessary for the reader to also end up knowing what he or she has read. How can your statement When the density is allowed to vary in some way be changed so that a general readership finds out what is intended? Would it be sufficient for Wikipedia to say When density varies along a streamline?

• You have asked Do you care to show me which peer-reviewed literature is treating dynamic pressure as representing a solution to Euler's fluid equation where density is allowed to vary? I look forward to seeing where the claim is being made that dynamic pressure uses a varying-density solution. Good questions, but you have presented them in an ambiguous way. I will re-write them in a way that shows the ambiguity, and answer each of the two.

Q1. Do you care to show me which peer-reviewed literature is treating ${\tfrac {1}{2}}\rho v^{2}$ as representing a solution to Euler's fluid equation where density is allowed to vary? I look forward to seeing where the claim is being made that ${\tfrac {1}{2}}\rho v^{2}$ uses a varying-density solution.

A1. No-one has ever claimed that ${\tfrac {1}{2}}\rho v^{2}$ is significant in flow where density varies. If anyone made that claim, the claim would be incorrect.

Q2. Do you care to show me which peer-reviewed literature is treating dynamic pressure as representing a solution to Euler's fluid equation where density is allowed to vary? I look forward to seeing where the claim is being made that dynamic pressure uses a varying-density solution.

A2. I have cited two British authors (of highly respected text books on aerodynamics) who use the expression dynamic pressure where other authors use impact pressure. The information of primary importance is the so-called compressible Bernoulli equation and the following equation:

$q_{c}=P_{0}-P={\tfrac {1}{2}}\gamma PM^{2}\left(1+{\tfrac {M^{2}}{4}}+{\tfrac {M^{4}}{40}}+...\right)$

All authors agree on the above equation for $q_{c}$. However, different authors give it different names - impact pressure, dynamic pressure, kinetic pressure. The name is only of secondary importance, but Wikipedia's role is to explain what is meant by the different names. Wikipedia is neither a US-oriented dictionary, nor a British-oriented dictionary. Dolphin51 (talk) 22:10, 10 December 2009 (UTC)

Lead

Hi,

One line in the article claims that the term 'Dynamic Pressure' applies only to incompressible flows, then immediately says it is also applied to compressible flows. I'd never heard the term 'impact pressure' before reading this article, and this shows most links to the Dynamic Pressure article are from aerospace articles, dealing in compressible flows. I think either the claim that it refers to only incompressible flows needs to be solidly backed, or the whole article needs to be re-focused on both kinds of flows.

I think the new version needs a lead which deals with both incompressible and compressible fluids, and which is as non-technical as possible whilst still being accurate.

Perhaps something like:

Dynamic pressure (indicated with q, or Q, and sometimes called velocity pressure or kinetic pressure) is a phenomenon in fluid dynamics which causes bodies moving relative to a fluid to experience different fluid pressures to a stationary body. It is equal to the difference between the stagnation pressure and the static pressure. The concept is central to aerodynamics and high speed hydraulics, and is governed by Bernoulli's principle. In the United States, it is sometimes called Impact pressure when the flow is compressible.

It's still a bit short, but I couldn't think of anything else to add...

--Ozhiker (talk) 15:07, 22 December 2009 (UTC)

Thanks for those suggestions. They have given me some fresh ideas.

By now you have realised that the task of writing about dynamic pressure for a dictionary is not straight-forward. Many authors in the field of fluid dynamics, perhaps the majority, define dynamic pressure as ${\tfrac {1}{2}}\rho v^{2}$ and they explain that dynamic pressure is only significant in incompressible flows (and perhaps compressible flows up to about 0.3 Mach). They sometimes define impact pressure as the difference between stagnation pressure and static pressure, or between pitot pressure and static pressure. I have found two authors, both British, who define dynamic pressure as the difference between stagnation pressure and static pressure, or between pitot pressure and static pressure, for all isentropic flows, including compressible flows.

Regardless of what name they use, all authors agree that in isentropic compressible flows, the difference between stagnation pressure and static pressure, or between pitot pressure and static pressure, is given by equations similar to the following:

$q_{c}=P_{0}-P={\tfrac {1}{2}}\gamma PM^{2}\left(1+{\tfrac {M^{2}}{4}}+{\tfrac {M^{4}}{40}}+...\right)$

$q_{c}=P_{0}-P={\tfrac {1}{2}}\rho v^{2}\left(1+{\tfrac {M^{2}}{4}}+{\tfrac {M^{4}}{40}}+...\right)$ — Preceding unsigned comment added by Dolphin51 (talk • contribs) 21:51, 22 December 2009 (UTC)

Comments

I'll comment with references as I find them. As for example of downwash greater than upwash in the immediate vicinity of a wing, the "flow deflected down" image as seen on Lift_(force)#Explanation_based_on_flow_deflection_and_Newton's_laws, which has numerous references, and Downwash also with multiple references. Center of mass of a closed system center of mass Bird flying through wall of helium bubbles demonstrating downwash, scroll down to downwash calculations and results: "Trailing vortices behind the wing tips associated with downwash following the birds – and the momentum flux resulting in weight support – are not surprising, and entirely match expectations from aerodynamic theory and experience from aeronautics." lift from tail reduces drag. Sink rate of vortices from aircraft, "several hundred feet per minute", scroll down to section 7-4-4 Vortex Behavior FAA wake turbulence. Rcgldr (talk) 23:18, 22 February 2024 (UTC)

Rcgldr: Thanks for your comments.

When you look at Lift (force)#Explanation based on flow deflection and Newton’s laws you can read the statement:

As the airflow approaches the airfoil it is curving upward, but as it passes the airfoil it changes direction and follows a path that is curved downward.

Where it says “As the airflow approaches the airfoil it is curving upwards” it is referring to the upwash. In the accompanying diagram you can see the upwash of the flow immediately upstream of the airfoil leading edge.

The text and the diagram acknowledge that downstream of the airfoil there is downwash but nowhere do they suggest that upwash doesn’t exist or that the downwash is greater than the upwash.

I have stated numerous times that in two-dimensional flow the mass flow in the upwash is exactly equal to the mass flow in the downwash. (In three-dimensional flow around a wing of finite span it is a little more complex so to see the equality of the upwash and downwash we must look at the horseshoe vortex or lifting-line theory.) You have provided links to videos of an aircraft flying through cloud, and a bird flying through helium bubbles. Neither the aircraft nor the bird have an infinite wingspan - the flow around their wings is not two-dimensional flow so those videos cannot be used to draw any conclusion about 2-D flow.

The article Downwash presently contains five in-line citations. The article and the cited sources say little or nothing about upwash. I’m not aware of anything stated in the article or the sources that supports your view that downwash is greater than upwash. If you can see a statement that “downwash is greater than upwash”, please let me know exactly where to look to see what you are seeing.

You have quoted “Trailing vortices behind the wingtips ... aerodynamic theory and experience from aeronautics.” This quotation does not state that downwash is greater than upwash; in fact it does not even mention upwash.

Many pages have been written about downwash, and many diagrams have been drawn with a caption referring to downwash, but many fewer exist referring to upwash. Perhaps this is because the upwards force on an airfoil (and downwards force on the air) seems more directly related to the downwash than to the upwash. It would be easy to overlook upwash or even imagine that there is no such thing. However, the principle of continuity of mass tells us that upwash must exist, and overall it must be identical to downwash.

The physics of 2-D lifting flow around a uniform airfoil (of infinite span) tells us that half of the lift comes from receiving the upwash and turning it to flow horizontally. The other half of the lift comes from receiving this horizontal flow and turning it to flow with a downwards component of velocity. Dolphin (t) 01:40, 23 February 2024 (UTC)

Dolphin51Note that image in Wiki's Lift article does show upwash ahead of a wing, but a greater amount of downwash due to the relative air flow being diverted downwards. My focus is not on 2-D modeling, but on 3-D physics, including airfoils that span wind tunnels tall enough to allow for vertical flow in the immediate vicinity of an airfoil. I recall some articles from Dr Mark Drela (MIT), who designs airfoils for high end radio control gliders, that mention wings producing downwash (in the vicinity of a wing) in order to generate lift. Rcgldr (talk) 03:04, 23 February 2024 (UTC)

Dolphin51If half of the lift is due to diverting horizontal flow downwards, wouldn't that mean that in the immediate vicinity of a wing, that downwash is greater than upwash, and it's not until later on that recovery upwash equals the downwash? Is it always a 50% | 50% ratio? I'm wondering about something like M2-F2 video. Rcgldr (talk) 06:29, 23 February 2024 (UTC)

Don’t forget that when we say “upwash is equal to downwash” (or similar words) we are referring to two-dimensional flow (around a uniform wing of infinite span.) That is not your focus.

Your focus is the physics of 3-D flow around a wing of finite span. Around such a wing the upwash upstream of the wing is a little less than the downwash immediately downstream of the wing due to the influence of the downwash between the trailing vortices. Every wing operates continuously in the downwash associated with its own trailing vortices. This downwash adds to the downwash associated with the bound vortex in the wing, but it reduces the upwash upstream of the wing. This causes the lift vector to be canted backwards through a small angle, and that results in lift-induced drag.

You mentioned “recovery downwash”. I’m not familiar with that expression. I don’t think it is a legitimate concept. What do you understand by “recovery downwash”? Dolphin (t) 14:53, 23 February 2024 (UTC)

Dolphin51When the air is disturbed, such as a wing producing downwash, the air eventually recovers, such as the earth stopping any downwash and redirecting the flow outwards and and eventually upwards. Eventually the air returns to it's previous state. I see this as two separate interactions, the wing inducing downwash, and later the earth stopping and reversing the downwash.(talk) 15:18, 23 February 2024 (UTC)

It is very common for lift on a wing to be explained by writing “the wing forces the air down as it goes past, so the air exerts an upward force on the wing” or words to that effect. This is a valid explanation of lift for any audience that is not looking for something rigorous. It is valid provided readers are only looking at the airflow close to the wing – from one or two chord lengths ahead of the wing to one or two chord lengths downstream of the wing. If a reader uses this explanation to imagine the downwash reaching far below the wing until it reacts with the Earth’s surface it becomes entirely invalid. To see the downwash more than a couple of chord lengths downstream of the wing a more sophisticated model of the airflow is necessary. The horseshoe vortex is a suitable model to take the reader beyond the elementary concept of “the wing forces the air down”.

In the horseshoe vortex model of the flow around a wing, the lift generated is due to the bound vortex. (The Kutta–Joukowski theorem states that the lift per unit span is equal to the strength of the bound vortex, the circulation, multiplied by the true airspeed and the air density.) A vortex is characterised by high velocities close to the center, and lower velocities the further we move away from the center. Good examples of vortices are the tornado, cyclone, hurricane and other revolving storms. Velocities are very high near the center but slower as we move away from the center. The flow around an airfoil is identical to a vortex embedded in the uniform flow provided by the relative motion of the atmosphere and the airfoil. People commonly ask “what makes the air flow faster over the top surface of the wing?” The best answer is that it is the bound vortex around the wing that makes the air flow faster over the top and slower under the lower surface.

Imagining that the downwash from the bound vortex reaches all the way down to the Earth’s surface is like imagining a tornado that produces 200 mph winds in Oklahoma producing that same wind speed all the way to California in the west and Maine in the east! The effect of a vortex quickly approaches zero as we look progressively further away from the center. The downwash from a wing does not extend very far below the altitude of the aircraft, as shown by the horseshoe vortex model. The downwash does not reach the Earth’s surface except perhaps for an aircraft taking off or landing. Your description of the recovery downwash as the downwash after it reaches the Earth’s surface is entirely invalid.

I suggest you study the horseshoe vortex and become fully acquainted with it. It will help your work in aerodynamics if you always write using the language of the horseshoe vortex (bound vortex, trailing vortices, starting vortex, upwash and downwash.) Dolphin (t) 13:02, 24 February 2024 (UTC)

Dolphin51"downwash ... reacts with the Earth’s surface" I only meant that as a simple example. The downwash reacts with the surrounding air long before it reaches the Earth's surface, but for the 3-D flow that I'm interested in, the downwash and the associated downwards moving vortices last much longer than just one or two chord lengths: FAA Wake Turbulence. Although downwash dissipates long before reaching the Earth's surface, the downward impulse through a volume of air eventually reaches the Earth's surface in the form of an temporary increase in pressure, and the Earth's surface supports the weight of the air and any aircraft in the air (assuming no vertical component of acceleration of the aircraft). Rcgldr (talk) 01:01, 25 February 2024 (UTC)

Rcgldr: We seem to have drifted a long way from your comments that you dispute the notion that upwash must be equal to downwash. You have written "the downwash reacts with the surrounding air ..." The science of aerodynamics tells me that the surrounding air, as you call it, is actually part of the vortex that contains the downwash.

When I wrote To see the downwash more than a couple of chord lengths downstream of the wing a more sophisticated model of the airflow is necessary I wasn't saying that the downwash only lasts for a couple of chord lengths, was I? I was saying that the simple "wing pushes the air down" explanation doesn't even begin to explain the presence of trailing vortices, or downwash between these vortices, or lift-induced drag. If the "wing pushes the air down" explanation is taken to its logical conclusion it suggests the down-going air must continue descending until either its velocity dissipates or it reaches the Earth's surface. There is an abundance of evidence to show that this is NOT the eventual fate of the bound vortex but you are writing as though this is an accurate description of the flow after it has imparted lift to the wing. The upwash and downwash that constitute wake turbulence are a consequence of the trailing vortices, NOT the bound vortex. When people write "the wing pushes the air down" they are describing the bound vortex within the wing.

If we are to look much beyond the trailing edge of the wing we must use a more sophisticated model such as the horseshoe vortex. When you mention wake turbulence you are actually alluding to the horseshoe vortex but you aren't yet using the language of this vortex system.

You have written "the downward impulse ... eventually reaches the Earth's surface ... temporary increase in pressure." Small pressure variations of this kind move through air at the speed of sound, and no movement of air is involved because we can treat the air as incompressible. We agree that the weight of the aircraft is supported by the Earth's surface regardless of whether the aircraft is stationary on the ground or airborne but this is not relevant to the debate about whether the mass of air participating in the upwash around an aircraft is equal to, or less than, the mass of air participating in the downwash. Dolphin (t) 13:05, 25 February 2024 (UTC)

• "dispute the notion that upwash must be equal to downwash". What I was disputing was that upwash just in front of a wing is equal to downwash just behind a wing. I might have worded it poorly before. What I agree with is over the long term there is no net vertical mass flow (upwash == downwash), and you already mentioned that the downwards momentum is greater than the upwards momentum due to the differences in speed. Rcgldr (talk) 08:23, 26 February 2024 (UTC)

  Rcgldr: It is potentially confusing. Upwash just in front of an airfoil is equal to downwash just downstream in two-dimensional flow (eg a uniform airfoil of infinite span.)

  However, in the flow around a wing of finite span (3-dimensional flow) the downwash just downstream of the wing is a little greater than the upwash just in front. This is a consequence of the wing operating in the downwash associated with its own trailing vortices. It is the origin of lift-induced drag which affects all airfoils of finite span including wings, tailplane, propellers and rotor blades.

  Let’s imagine 2-D flow around a wing of infinite span; with upwash angle and downwash angle equal at 5 degrees. Now let’s imagine two large pieces of wing disappear, leaving a wing of only 15 metres of span. A pair of trailing vortices immediately form, causing the wing to lie in the downwash associated with these two trailing vortices. This downwash must be subtracted from the upwash ahead of the wing so that the upwash angle is now only 4 degrees; but it must be added to the downwash just downstream of the wing so that the downwash angle is now 6 degrees. The 2 degree difference between upwash and downwash angles causes the lift vector to be canted backwards by 2 degrees, and the component pointing backwards (parallel to the velocity vector) is drag, and it is called lift-induced drag. The shorter the wingspan, the greater is the amount by which the downwash exceeds the upwash, and the greater is the lift-induced drag for a given airspeed and a given weight (or lift). Overall, upwash is still equal to downwash because of the extra upwash outside the pair of trailing vortices.

  When you say “downwash exceeds upwash” you are correct providing you are talking about the flow induced by the bound vortex around a wing of finite span (3-D flow). When I say “upwash is equal to downwash” I am correct providing I am talking about 2-D flow (around a uniform airfoil of infinite span.) We agree that there is no net vertical movement of mass associated with the horseshoe vortex system. Dolphin (t) 12:38, 26 February 2024 (UTC)

  For 3-D flow, lift force = downwards mass flow rate times downwards exit velocity. Is this not the same for 2-D flow? Rcgldr (talk) 18:51, 27 February 2024 (UTC)

  The idea that the force between two objects is equal to the mass of one of them, multiplied by the rate of change in its velocity, is both valid and used widely. It is an application of the law of conservation of momentum for a rigid body which says that the external force applied to a rigid body is equal to the time rate of change of the momentum of the rigid body. This law is an extension of Newton’s second and third laws of motion.

  This version of Newton’s laws is not applicable to fluids such as the air flowing around an airfoil, or the water flowing around a hydrofoil. Fluids are not rigid bodies - they are capable of experiencing different pressures at different points in the fluid body, and they are capable of deforming in response to the changing pressure.

  There are situations where a fluid exerts a force on a rigid body and that force is entirely due to the difference in pressure at the extremes of the rigid body; and not due in any way to a change in momentum. For example, consider water flowing through a long length of garden hose. The rate of flow of water is the same at every point of the hose, and the velocity of the water is uniform at each cross-section of the hose, so the momentum of the water within the hose does not change. However, the water does exert a force on the hose, and vice versa. This force is the drag force caused by viscous shear forces within the boundary layer that exists where the water is contacting the inside surface of the hose. The magnitude of this force is equal to the water pressure at the entrance to the hose, multiplied by the area of the cross-section of the hose at its entrance; reduced by the atmospheric pressure at the exit of the hose, multiplied by the area of the cross-section of the hose at its exit. In this example, the force on the hose (a rigid body) from the fluid (water) is due entirely to pressure differences, and not in any way due to the change in momentum of the fluid. Dolphin (t) 11:43, 28 February 2024 (UTC)

  Rcgldr You have written about 2-D flow and 3-D flow and asked if Lift is equal to the downwards mass flow rate multiplied by the [change in velocity]. A major problem with this approach is that the mass flow rate of the air influenced by the wing/airfoil is infinite - air close to the wing has its velocity changed significantly, and air a great distance from the wing has its velocity changed a minuscule amount, but clearly the amount of air affected is unknown but extremely large. Similarly the amount by which the velocity of a parcel of air changes as it passes the wing varies among the various parcels of air. It is not possible to specify the mass of air in the downwash, and the change of velocity in the downwash, and multiply them together.

  A few scientists grappled with this problem in the early years of the twentieth century - among them Frederick Lanchester, Martin Kutta and Nikolay Zhukovsky. Independently, they each arrived at the concept of the circulation of the fluid flowing around the wing/airfoil; they discovered that the lift per unit span on a wing/airfoil is equal to the circulation of the fluid flow multiplied by the velocity of the fluid in the freestream remote from the wing/airfoil, multiplied by the density of the fluid. This is known as the Kutta–Joukowski theorem. To apply this theorem it is not necessary to know the mass of the flow around the wing/airfoil; it isn’t necessary to know the change of velocity that occurs in each parcel of air as it flows past the wing/airfoil, and it isn’t necessary to know the pressure at any point in the flowfield.

  These scientists also discovered that the value of the circulation around a spanwise slice of wingspan is always the circulation that causes the flow to satisfy the Kutta condition. Dolphin (t) 12:21, 28 February 2024 (UTC)

  "upwash ... downwash ... same angle" - doesn't upwash that is accelerating towards low pressure just ahead of a wing have higher velocity than downwash that is decelerating to ambient pressure just behind a wing? In 2-D flow, where is the momentum change in air that coexists with lift force? Rcgldr (talk) 05:23, 4 March 2024 (UTC)

  Rcgldr: To get a good understanding of the fundamentals of lift in two-dimensional flow without resorting to a lot of math, it is useful to look at a couple of diagrams. The first diagram shows a circular cylinder (of infinite span) in an inviscid, incompressible flow. Here is a suitable diagram taken from Potential flow around a circular cylinder:

  

  Potential flow with zero circulation

  This diagram depicts zero lift on the cylinder because circulation is zero.

  Notice that in this diagram of streamlines there are two axes of symmetry. One is horizontal through the center of the circular cylinder; and the other is vertical through the center of the circular cylinder. For both of these axes of symmetry, the flow speed and pressure at a point on one side of an axis of symmetry are identical to the flow speed and pressure at the similar point on the opposite side of the axis of symmetry. The flow directions at the two points are slightly different - if one direction vector is, say 25 degrees upwards, the other one is 25 degrees downwards.

  Now, we have to look at a second diagram. This is similar to the one above but there is circulation of the flow around the cylinder, and the cylinder is experiencing lift. Wikipedia doesn’t yet have the required diagram but I can direct you to a suitable diagram as follows:

  Google for “Flow past a cylindrical obstacle Fitzpatrick”

  You should get a hit on a document by Prof Richard Fitzpatrick of the University of Texas. This document contains a lot of math but ignore it. Scroll down to the diagram of streamlines around a circle. This diagram represents a circular cylinder generating lift such as the Magnus effect where circulation is induced in the flow by a spinning cylinder.

  Most importantly, notice that there is still one axis of symmetry - it is vertical through the center of the circle. This shows that speeds and pressures on the left of the axis of symmetry are identical to speeds and pressures on the right of the axis. Flow direction vectors are similar, but in the opposite direction.

  In this diagram we can see the symmetry of the flow around a cylinder even though the flow has circulation and the cylinder is experiencing lift.

  The situation with a two-dimensional airfoil is very similar. Even though the airfoil is oriented with an angle of attack, and there is no axis of symmetry, the momentum in the upwash ahead of the airfoil is equal in magnitude to the momentum in the downwash downstream of the airfoil. Consider a streamtube that contains the airfoil - the streamtube has a finite span. If the momentum entering the streamtube at the upwash end is pointing, say 5 degrees upwards above the horizontal, the momentum exiting the streamtube at the downwash end is pointing 5 degrees downwards below the horizontal. The rate of change of momentum in going from 5 degrees upwards to 5 degrees downwards is equal to this streamtube’s contribution to the lift on the airfoil. Dolphin (t) 11:18, 6 March 2024 (UTC)

• In the case of an airfoil that spans the width of a tall wind tunnel (no tip vortices) using smoke to track air flow, the air flow sufficiently ahead of the airfoil is horizontal, and behind the wing for quite some distance, the flow is angled downwards, as seen in one of the videos I linked to previously. Is this different than 2-D flow? Rcgldr (talk) 16:02, 8 March 2024 (UTC)

  Rcgldr: I have watched the videos you nominated on Talk:Wing. They certainly show downwash, but they also show upwash. It isn’t possible to see accurately whether the downwash exceeds the upwash, or whether the two are the same.

  If the videos show a wing that completely spans the wind tunnel with no leakage of air between the model wing and the wall of the wind tunnel, then the flow is two-dimensional. In two-dimensional flow around an airfoil, there are no trailing vortices so, in any streamtube in the vicinity of the wing, the momentum in the upwash matches the momentum in the downwash, and there is no lift-induced drag. Experimental evidence has always shown that the greater the wingspan, the closer to zero lift-induced drag, and the closer to upwash exactly matching the downwash - that is why high-performance gliders have large wingspans.

  The science related to generation of lift by an airfoil is well understood, and has been well understood since the early 1900s. If your assessment of upwash and downwash is not the same as the science found in reliable published sources, it is unlikely that Wikipedia can accept that your observations of some on-line videos have proved the long-established science to be incorrect. Dolphin (t) 13:06, 11 March 2024 (UTC)

  On a large scale, upwash equals downwash, but in the near vicinity of a wing, air approaches horizontally, and exits with a downwards component, similar to one of the images from the Wiki lift article: airfoil . However, I'm interested in 3-D flow, such as planes flying though smoke or better still birds gliding through a wall of bubbles, where you can see the momentary upwash before the downwash and related downwards moving vortices. Rcgldr (talk) 19:54, 11 March 2024 (UTC)

  Rcgldr You linked to a flow diagram at Lift (force). It is claimed that this diagram is a graphic copied from a video by Holger Babinsky. Whether this graphic shows the flow around a wing that completely spans the wind tunnel from wall to wall (2-dimensional flow) or whether the graphic shows 3-dimensional flow around a wing of finite span is undisclosed. It is my assessment that the graphic shows the latter - 3-D flow around a wing of finite span. This diagram should not be used to draw any conclusion, and certainly not any conclusion regarding the flow field around an airfoil in 2-D flow.

  The flow diagram at Lift (force)#Obstruction of the airflow is more useful. We know how it was produced so we have a good idea of its accuracy. It is generated by a computer program so we can have confidence in the details it shows. In particular, we know that this computer program finds solutions that represent 2-dimensional flow. The flow pattern is not one found around a wing of finite span. As you can see, this diagram cannot be described by saying “air approaches horizontally...” The flow in the upwash is directed upwards at the same angle as the downwash is directed downwards. Exactly the same conclusion must be drawn when using the diagram I described in my post on 11 March - the diagram by Prof Richard Fitzpatrick.

  However, you are interested in 3-D flow around wings of finite span. In this case, the downwash downstream of the wing is a little greater than the upwash upstream of the wing. The small difference between the two translates to the lift-induced drag on the wing. (As you know, in 2-D flow around an airfoil of infinite span, there is zero lift-induced drag.) Dolphin (t) 12:37, 13 March 2024 (UTC)

  My issue with 2-D flow is the idea that lift is being generated without some corresponding change in momentum. The idea of the momentum being due to upwash being diverted downwards conflicts with the fact that sufficiently ahead of the wing, the relative flow is horizontal. So what is the source of lift for 2-D flow? Rcgldr (talk) 23:29, 15 March 2024 (UTC)

  Rcgldr: Your question is a good one and I have spent a month contemplating the best way to answer it. You have written that you have an issue with the idea that lift is being generated without some corresponding change in momentum. Perhaps you are thinking that the only way momentum can change is if there is a change in the magnitude of the momentum - a change in the length of the momentum vector. That is only half correct - momentum can also change if there is a change in the direction of the momentum vector. Think of a vehicle moving at constant speed around a circular track; the magnitude of the vehicle's momentum is constant but its direction is changing continuously as the vehicle is constantly changing direction as it progresses around the track. The change in direction of the momentum vector is associated with the centripetal force. If the vehicle enters a slippery patch so that the centripetal force falls to zero, the momentum vector stops changing direction and the vehicle moves in a straight line off the outer edge of the track!

  

  Flow around an airfoil. Air arrives at the airfoil with an upwards component of velocity, and departs from the airfoil with a downwards component of velocity. The change in direction of the momentum vector for a streamtube is associated with the lift on the airfoil attributed to that streamtube.

  When lift is being generated by a wing or airfoil, the air reaches the leading edge moving with an upwards component of velocity. By the time that air reaches the trailing edge it is moving with a downwards component of velocity. See the adjacent image. The change in direction of the air entering that particular streamtube and then exiting is associated with the change in momentum, and therefore the lift generated by that portion of streamtube.

  Consider a wing (3-D) or airfoil (2-D) immersed in a uniform flow. At a significant distance upstream (and downstream) of the wing or airfoil, the flow is mostly determined by the uniform flow so it is horizontal. Close to the wing or airfoil, the predominant influence is the bound vortex that causes circulation around the wing or airfoil, as shown in the adjacent diagram. The flow leaves the trailing edge smoothly in accordance with the Kutta condition.

  At a significant distance downstream of a 2-D airfoil, the flow is again part of the uniform flow and its velocity is horizontal. At a significant distance downstream of a 3-D wing the predominant influence is the downwash associated with the trailing vortices - the flow is not horizontal but has a slight downward component at an angle called the downwash angle determined by the trailing vortices. Dolphin (t) 14:22, 15 April 2024 (UTC)

  By change in momentum, I only meant a change in direction (ignoring drag). Assume that the only interaction with the air is a wing, no ground below to prevent any downwards flow. The wing diverts the air flow, changing the direction of momentum from horizontal to slightly downwards. Since there is nothing else that interacts with the air, then that slightly downwards momentum of air is conserved. I assume that this momentum would still be conserved in 2-D flow? Rcgldr (talk) 22:32, 6 May 2024 (UTC)

  From the air's inertial frame of reference, energy is added. Initially the velocity is zero, and after a wing passes through, the exit velocity (the velocity when pressure returns to ambient) is non-zero, with a mostly downwards component and somewhat forwards component. I don't know if a 2-D flow can be modeled using the air as an inertial frame of reference. Rcgldr (talk) 22:32, 6 May 2024 (UTC)

  Rcgldr In Understanding Aerodynamics by Doug McLean, section 7.3.3.2 is titled “The Airfoil Reference Frame” and begins:

  The phenomenon of lift generation is the same regardless of what reference frame we view it from. We could watch the airfoil move through the air, but everything is easier to understand if we imagine ourselves moving along with the airfoil, so that the airfoil appears to us to be standing still and the fluid appears to flow past.”

  McLean would respond to your comment by saying that if energy is added or subtracted, it conforms to the laws of physics regardless of which reference frame we choose.

  The actual displacement, velocity and kinetic energy of a parcel of fluid are strongly dependent on our choice of reference frame; but any change in kinetic energy, and the work done to cause that change, will always conform to the work-energy theorem regardless of the reference frame, providing it is an inertial frame. Dolphin (t) 22:38, 10 May 2024 (UTC)

  I forgot to mention that Chapter 7 is titled “Lift and Airfoils In 2D at Subsonic Speeds”. Dolphin (t) 22:41, 10 May 2024 (UTC)

  For a simple energy analogy, consider a glider at a constant speed, as it descends, the decrease in gravitational potential energy corresponds to an increase in energy of the air (a small part of that in the form of heat). Rcgldr (talk) 07:11, 11 May 2024 (UTC)

  Initially the reduction in potential energy is matched by an increase in the kinetic energy of air in the glider’s wake. As the velocities in the wake subside to zero, all the kinetic energy is transformed into heat (more correctly called internal energy.)

  Consider a large airplane flying at 40,000 feet and Mach 0.8. Its potential energy is very large, and so is its kinetic energy. An hour or two later, the airplane is stationary on the ground. The law of conservation of energy tells us that the energy of this airplane has been conserved. How is this possible?

  Initially the drag on the airplane transforms its energy into the kinetic energy of the air in the wake but that kinetic energy is eventually transformed into internal energy (or heat) as the wake subsides to zero. The law of conservation of energy tells us that 100% of the energy of the airplane eventually ends up as internal energy (ie heat). Dolphin (t) 22:50, 13 May 2024 (UTC)

  Momentum (angular momentum about the earth) is conserved. If the initial state is the aircraft moving at mach 0.8, and the aircraft land and slows to 0 using reverse thrust and assuming no braking from the tires, then the decrease in the aircraft's momentum coexists with an increase in the air's momentum. Momentum never dissipates, but since a very large mass of air is eventually involved, the change in velocity is very small. Rcgldr (talk) 02:50, 20 May 2024 (UTC)

  Why do you assume no braking from the tires? All airplanes rely on wheel braking. Reverse thrust is typically discontinued at about 60 knots, and then wheel braking is the sole means of retardation until the airplane stops. Dolphin (t) 08:39, 20 May 2024 (UTC)

  No wheel braking so the only interaction is with the air. Instead consider the case where the aircraft slows from mach 0.8 to mach 0.3. The total momentum of air and aircraft is conserved, regardless of how much energy is converted into heat. Rcgldr (talk) 06:07, 21 May 2024 (UTC)

  I'm glad we agree that the total momentum of the air and the aircraft are conserved. It will help clarify at least one point.

  On March 11 you wrote "... air approaches horizontally and exits with a downward component, ..." Also, on May 6 you wrote "... changing the direction of momentum from horizontal to slightly downwards." Both of these descriptions suggest the vertical component of momentum is not conserved!

  If the air approaches a wing horizontally the vertical component of its momentum is zero. If the air then exits with a downward component of velocity, the vertical component of its momentum is not zero. So momentum has not been conserved because the momentum of the aircraft has not changed, either vertically or horizontally.

  There is a better explanation of the flow in 2-D (or around a wing of high aspect ratio) in which momentum is conserved. Immediately in front of the wing the air has an upwards velocity, sometimes called upwash. Air entering each streamtube has an upwards component of momentum. Immediately behind the wing the air has a downwards velocity, sometimes called downwash. Air leaving each streamtube has a downwards component of momentum. The vertical components of momentum in front of, and behind, the wing are equal in magnitude but opposite in direction. Therefore they cancel and the momentum of the air within each streamtube remains constant.

  As the air passes adjacent to the wing its momentum is changed from vertically upwards to vertically downwards. This shows that a downwards force is acting on the air; we know that an upwards force must be acting on the wing. This seems to explain why a steady force can act upwards on the wing without causing an increase in the vertical momentum of the air - the air flows past the wing and its momentum changes temporarily but is not changed permanently - all momentum changes at one point are cancelled by momentum changes at another point. Dolphin (t) 13:12, 23 May 2024 (UTC)

  "suggest the vertical component of momentum is not conserved!" - When a wing passes through a volume of air, it exerts a downwards force over some period of time, and the change in momentum = force x time. Once the momentum has been changed and absent any other forces, then the momentum is conserved. Rcgldr (talk) 19:11, 23 May 2024 (UTC)