## fredag 8 oktober 2021

### Styrs Skolan av Läromedelsföretagen?

Statistik från Läromedelsföretagen visar att Skolan till Läromedelsföretagen betalar 500-1000 kr (snitt 650 kr) ca 0.5% av totalkostnaden per år och elev. Det ger en stor läromedelsmarknad om minst 650 miljoner kr att dela mellan läromedelsjättar som Gleerups, Studentlitteratur, Liber och Natur och Kultur.

För huvudämnet matematik skulle då kanske varje elev per år få tillgång till läromedel för 200 kr. Hur mycket lärdom kan det rymmas inom en sådan ram? Räcker det? Inte i alla skolor tydligen, eftersom många lägger det dubbla, förmodligen för att det krävs. Men kanske inte ens det räcker för att ge alla elever tillgång till rikt material för utveckling och förkovran.

Skolans undervisning verkar styras av läromedelsföretagen som producerar och säljer läromedel med speciellt funktionalitet som gör att läraren i detalj kan övervaka varje elevs prestation uppgift för uppgift minut för minut, vilket då kan bli lärarens huvuduppgift eftersom det utmärkta läromedlet sköter själva undervisningen. Matematikämnet är särdeles lämpat för denna övervakade detaljstyrda utbildning. Men kanske är det inte det bästa för vare sig elev eller lärare.

Här erbjuder Leibniz World of Math ett alternativ i form av konkret realisering av den nya läroplanen i matematik+programmering i form av:

• open textbook fritt tillgänglig utan kostnad,
• ny skolmatematik som konstruktiv matematik för en digital värld,
• sammanhållet rikt program från förskola till högskola där eleven själv bygger matematik
• utvecklat av högsta akademiska kompetens.
Som Rektor, testa vad Leibniz WoM kan ge Dina Lärare.
Som Lärare, testa vad Leibniz WoM kan ge Dina Elever.
Som Elev, testa vad Leibniz WoM kan ge Dig själv.

## tisdag 5 oktober 2021

### Nobel Prize in Physics to Climate Models which Do Not Model Climate

The Nobel Committee in Physics has as an act of scientific political correctness today given half of the Nobel Prize in Physics in 2021 to Syukuro Manabe and Klaus Hasselmann for the physical modelling of Earth's climate quantifying variability and reliably predicting global warming.

In other words, the Prize has been given to Climate Models which Do Not Model the Climate, as is shown in the following graph of Global Warming over time comparing Climate Model predictions with Real World observations (second image from Roy Spencer Global Warming) :

These graphs must have been unknown to the Committee. What is the meaning of "reliably predicting global warming" when the prediction has nothing to do with the actually observed absence of observable global warming (0.2 C over 40 years)? Is the "reliability" that all climate models show too much warming, or that the spread is so big that even virtually no warming is included in the predictions?

## fredag 24 september 2021

### Kritik av Skolverket i Ny Avhandling om Matematik+Programmering

Peter Vinnervik ger Skolverket svidande kritik i sin avhandling om den nya kursplanen med programmering som del av matematikämnet, vilket tas upp i artikeln Forskare: Skolverket är otydliga om programmering i Läraren:

• Skolans styrdokument ger inte lärarna tillräckligt bra stöd för hur de ska undervisa i programmering.
• Man talar om att eleverna ska lära sig programmeringens grunder, men vad de består av kommuniceras väldigt kortfattat i kursplanerna, framför allt för ämnet matematikbudskapet om programmering kommuniceras via flera olika texter.
• Man är väldigt otydlig med vad det är för kunskaper som eleverna ska lära sig.
• Lärarna upplever budskapet som väldigt luddigt.
• Det behövs ytterligare en revidering av kursplanerna för att göra det tydligare för lärarna hur de ska arbeta med programmering i undervisningen.
Peter Vinnervik går så långt att han föreslår att programmering skall överföras till teknikämnet, eftersom reform av matematikundervisningen förefaller vara utsiktslös.

Vi får se om Skolverket kan lyssna på denna kritik. Skolverkets syn uttrycks av undervisningsråd Johan Falk, som i Läraren uttrycker Skolverket: Ge mattelärare tid att fortbilda sig i programmering:
•  Studiematerial och tillfällen till fortbildning i programmering finns.
• Flaskhalsen är tid och den är det bara skolhuvudmännen som kan skapa för sina lärare.
Innebörden är att Skolverket inte anser att Skolverket kan göra något mer än det som redan gjorts.

Det skall bli intressant att se om Skolverket är kapabelt att lyssna på något av den svidande kritiken från Vinnervik. Det är inte säkert. Som Skolverkets Generaldirektör Peter Fredriksson urskuldande brukar säga: "Matematik är inte Sveriges bästa gren".

From Vinnervik's Abstract:

The results show that teachers face several intrinsic and extrinsic challenges during the process of integrating programming in their teaching. A perceived lack of professional knowledge and understanding of programming among the teachers emerged as a prominent challenge both prior to and more than two years into the reform. Additional challenges are related to teaching materials, time for preparation and professional development. In technology education, teachers mainly see programming as a medium to explore and understand technological systems and construction work. They are uncertain of what programming means in terms of practices and concepts, and about learning progression and assessment. The results further reveal that the curriculum texts are sparse on details about what programming knowledge entails. Important strategic decisions are left entirely to the teachers without any clear guidance. In addition, the results indicate that many technology teachers work in isolation and that interdisciplinary work around programming, as intended in the curriculum, is generally lacking. It is concluded that there is a risk of inequality among schools and that the children’s experience of programming becomes fragmented, despite good intentions. The current implementation model needs to be improved, and this thesis presents two possible actions.

## måndag 20 september 2021

### New Math Education Site: Leibniz World of Math

I have changed the name of my mathematics education project to Leibniz World of Math from the previous DigiMat Encyclopedia. Take a look!

## fredag 17 september 2021

### Euler Was Right, Prandtl Was Wrong II

I am working on a new article to be expanded to a book with the title Euler Was Right, Prandtl Was Wrong  which can be seen as a summary of my work on fluid dynamics for 30 years together with former students Johan Hoffman, Johan Jansson and Anders Szepessy. In short, our work shows that the following prophetic declaration by Euler from 1755, indeed is fully correct:

• My two equations contain all of the theory of fluid mechanics. It is not the principles of mechanics we lack to pursue this analysis but only Analysis (computation), which is not sufficiently developed for this purpose...We have to wait until the age of the computer to solve the equations.
And yes, we now live in the age of the computer and then Euler's two equations as a parameter-free model can be solved in the form of Euler CFD (Computational Fluid Dynamics) and so open a whole new world of turbulent flow to prediction, analysis and control, without any further need of mathematical modeling with parameter fitting.

Euler CFD is to be compared with Prandtl CFD as the Standard CFD developed during the 20th century based on Prandtl's boundary layer theory including complicated wall and turbulence models with many parameters, which does not offer true predictive computation, as the legacy of the declared Father of Modern Fluid Mechanics

Take look and see what you think. This post directly connects to the discussion in recent posts with Doug McLean representing Standard CFD. See also previous post.

## onsdag 18 augusti 2021

### Corrections to Key Statements by Aerodynamics Expert McLean

Below follows corrections by Doug McLean to my attempt to collect Key Statements by Aerodynamics Expert Doug McLean. As before my comments are in italics in parenthesis.

Do the statements in your summary give correct expression of my views? For the most part, no:

"1. Flight is perfectly understood because fluid flow obeys the RANS equations."

Your comment: "1 is empty: Perfect understanding does not come from looking at RANS numbers. "

This isn't how I would put it. I'd say lift is perfectly understood in a scientific sense because the RANS equations with a no-slip BC and a good turbulence model correctly model the physics of the flow point by point, and solutions to the equations yield the right global flow patterns and flow details. The good agreement with reality verifies that the principles embodied in the equations are the right ones. Thus I say lift is perfectly understood in a scientific sense because we know what principles apply point-by-point in the flow, and we know that to make global predictions, all we have to do is solve a set of PDEs. So the understanding provided by RANS is based on a lot more than "looking at RANS numbers".

"2. Qualitative explanation(s) of lift (are) not essential to the science, and their faults don't contradict my assertion that the science is well understood."

This one is true.

"3. No-slip is enforced in physical terms because the required force arises naturally from the solution to the viscous-flow equations."

C"3 is misunderstanding of the difference between real physics and mathematics."

To conclude that I misunderstand this you have to misrepresent what I said. I was responding to your claim that the no-slip BC is "unphysical" because it contains no explicit reference to a force, and a force would be required to enforce the zero velocity. I replied "Of course forcing the fluid to have zero velocity at the wall requires some applied force, but the required force arises naturally from the solution to the viscous-flow equations." Any reasonable person would agree that both of us, in referring to "force" and "velocity", were referring to the theoretical world modeled by the equations, not to actual physical flows. To accuse me of saying that a mathematical equation can cause a force to arise in the real world is absurd.

"4. New Theory and RANS are equally "deficient" in the sense of failing to provide to a "qualitative" understanding of flow patterns."

Your comment: "4 is misunderstanding of New Theory."

I stand by this one. Your counterargument: "The New Theory comes with an explanation of the generation of large lift at small drag as a consequence of the general explanation of slightly viscous incompressible bluff body flow as potential flow modified by 3d rotational slip separation." is gobbledygook that explains nothing and fails to answer qualitative questions such as why pressure differences and changes in flow velocity appear in the field, and how "3d rotational slip separation" actually modifies the flow.

(Doug admits that New Theory of Flight to him is "gobbledygook", which means that he has not understood. To dismiss something on the only ground that one does not understand, is not the way science is to be performed. The New Theory is not hard to understand since it builds on (i) potential flow modified by (ii) 3d rotational slip separation. I ask Doug: What is it that is  "gobbledygook" with (i) + (ii)?)

"5. Headline of Scientific American 2020 (is) sensationalistic nonsense."

This one is true.  (This is a most remarkable statement.)

"6. There is no need of New Theory, even if it happens to be correct, because there are already many theories (for different audiences) which are (even if not correct) by the aeronautical/scientific community agreed in broad consensus to model lifting flow correctly to their respective levels of physical fidelity."

No. There is no need of New Theory, even if it happens to be correct, because RANS and all the simplified theories related to it (in retrospect derivable from RANS with simplifying assumptions) already provide our understanding in a scientific sense. The qualitative explanations for different audiences aren't really part of our scientific understanding, as I've explained to you more than once. (Also most remarkable)

"7. New Theory (might) make a contribution for (massively) separated flow."

Perhaps. We'll see.

The no-slip condition also came up in a previous note where you said:

"You say that slip at the wall is fiction, yet you present in your book a turbulent bl in Fig 4.1.14 which meets the wall with effectively slip. Contradiction."

There's no contradiction. On an airliner wing in cruise, the thickness of the viscous sublayer is typically less than 0.2% of the thickness of the TBL, over most of the chord. So the sublayer is too thin to be seen on the scale of plots like fig 4.1.14. But the sublayer is real, and it obeys no-slip at the wall. Modeling it realistically with no slip, as most RANS codes do these days, is preferable taking the shortcut of a slip BC.

"You say that no-slip is a physical boundary but you do not answer my question how in physical terms you can control fluid particles to have zero velocity."

I did answer the question, but you twisted my answer beyond recognition in your response to item 3 above. In an actual physical flow, forces internal to the fluid arise naturally (pressure forces, viscous forces, and Reynolds stresses), and these forces can produce the accelerations needed to meet the no-slip condition. When we model this mathematically, these forces are modeled in the equations that apply throughout the field. This is the basis for my statement in item 3 above. I'm not saying that the equations "control" the flow; I'm saying that actual physical forces control the flow. No-slip is a valid BC for the equations. There's no need for force to appear explicitly in the BCs, as you seem to believe.

"What is the physics on a microscope level that realises no-slip? "

See p. 15 of my book for a simplified explanation. (Why simplified? What is a real explanation?)

Conclusion: Your blog page "Key Statements by Aerodynamics Expert Doug McLean" misrepresents most of my statements. Please revise it to reflect more accurately what I've actually said.

(Let me here try with a new short summary of McLean's views):
1. Lift is perfectly understood in a scientific sense because the RANS equations with a no-slip BC and a good turbulence model correctly model the physics of the flow point by point, and solutions to the equations yield the right global flow patterns and flow details.
2. Qualitative explanation(s) of lift (are) not essential to the science, and their faults don't contradict my assertion that the science is well understood.
3. Forcing the fluid to have zero velocity at the wall requires some applied force, but the required force arises naturally from the solution to the viscous-flow equations.
4. New Theory is gobbledygook.
5. Headline of Scientific American 2020 (is) sensationalistic nonsense.
6. There is no need of New Theory, even if it happens to be correct, because RANS and all the simplified theories related to it (in retrospect derivable from RANS with simplifying assumptions) already provide our understanding in a scientific sense.
7. New Theory might perhaps make a contribution for (massively) separated flow.
(Let's see if McLean accepts this as a summary of his views. On 7: All bluff body flow (wings, airplanes) is (massively) separated flow.)

Question to Doug:
You admit that New Theory of Flight is "gobbledygook" to you, which means that you have not understood. To dismiss something on the only ground that one does not understand, is not the way science is to be performed. The New Theory is not hard to understand since it builds on (i) potential flow modified by (ii) 3d rotational slip separation. What is it that is "gobbledygook" with (i) + (ii)?)

You've taken what I said our of context. This comes from my response to your item 4, which specifically referred to the fact that CFD calculations, including both RANS and your New Theory, don't provide any "qualitative" explanation of flow patterns, the kind of explanation that would be understandable to a non-technical person.

Your response was gobbledygook in the sense that a non-specialist would have no idea what you're talking about. I also stand by my statement that, even to a specialist, it doesn't explain anything about lift in a qualitative flow pattern sense.

No, I understand your New Theory just fine. I just contend that it hasn't added anything to our understanding of lift.

My new questions:
1. So the theory is not "gobbledygook" to you, only to a "non-technical person"?
2. Ok Doug, you say you understand New Theory. I then ask you: Do you think New Theory is correct or not correct? If not, what is wrong?
3. What qualitative flow pattern would you like to see explained, which you do not find in the New Theory? Attachment on top? Separation without pressure rise at trailing edge? Large lift at small drag?
Answers by Doug: (with new question (Q1)-(Q7) in parenthesis in italics)

Yes, I think I understand how the New Theory models the physics, and I think it's incorrect. I've given detailed reasons in previous notes, so I won't repeat them. Regardless of the details, one bottom-line result suffices to show that the New Theory is deficient: According to the New Theory, the pressure drag of a streamlined body without the induced drag associated with lift in 3D (e.g. 2D NACA 0012 at zero lift) is at least 80% of the total, with skin friction less than 20%. Experimental measurements of skin friction on many kinds of streamlined bodies, including airfoils and wings, contradict such a low level of skin friction and support the higher levels predicted by traditional models.

(Truth is that experiments for NACA0012 at zero angle of attack shows C_D = 0.006 without tripping and C_D = 0.008 with artificial tripping, while Euler CFD with zero skin friction gives C_D = 0.006 in close agreement with experiments without tripping. Now, a wing on an airplane does not have a tripping device (ribbon) on the leading edge, and so Euler CFD matches the real case. What is then the role of tripping in the experiment, when the real case does not have tripping? (Q1)

The motivation given in the standard literature is that the the ribbon is there to guarantee that the boundary layer is turbulent and so does not separate until the trailing edge, which follows from an expectation that a laminar boundary separates early. Is this also your answer? (Q2)

With tripping C_D increases with 0.002 which can be seen as an effect of changed geometry with a turbulent wake after the ribbon as additional form drag, which is identified as skin friction drag. Do you see that it is not so clear how to distinguish between form drag and skin friction drag in tripped experiments? (Q3)

If now the effect of tripping is to increase skin friction contribution to C_D with 0.002 as an effect of a turbulent boundary layer, what does that say about skin friction contribution without tripping? Still dominating? If tripping adds 0.002 skin friction, how much skin friction is there without tripping, smaller or bigger than 0.002? (Q4))

And here I'm talking about conventional calculations for which the turbulence model was calibrated to flat-plate TBL data and used unaltered for everything else, on whatever portion of the surface that the BL was predicted to be turbulent. Your claim that conventional methods can't predict drag correctly for wings, etc. unless the turbulence model is tuned on a "case-by-case" basis is false.

(No, Doug Standard CFD with wall and turbulence models contain parameters which are determined on a case-by-case basis. Do you really claim that there is one choice of parameters for all cases? If so, where can I find the values of these parameters? (Q5))

Your reasons for rejecting the conventional theories at other levels (circulation theory, lifting line, BL theory, etc.) are also false, in my opinion.

I'm not alone in this assessment. You've had some years now to make your case, and it seems you've convinced very few, if any, of the cognoscenti in the field. As a counter to this general line of argument, you could cite the example of plate tectonics, which was widely rejected in its field for many years before finally becoming the dominant paradigm. Given the evidence I've seen, however, I'd say the New Theory has practically zero chance of becoming the plate tectonics of high-Re aerodynamics.

What qualitative flow pattern would I like to see explained, which I do not find in the New Theory? Just about any qualitative feature of the flow: flow turning, changes in flow speed, differences in pressure, etc. You can observe these things in your numerical solutions, but that doesn't explain in a qualitative cause-and-effect sense how they come about. The New Theory is similar to conventional CFD in this regard.

(No Doug, if you do not see that New Theory explains large lift at small drag in physical terms as (i) attachment because the flow is potential before separation, and (ii) 3d rotational slip separation without pressure rise at trailing edge, then you have not understood the physics of New Theory. What is it with (i) and (ii) that you do not understand? And if you understand (i)+(ii), what is it that you do not understand concerning consequences of (i)+(ii) on lift and drag? (Q6))

You know where I stand. I think the other Wikipedia editors have already made a valid case for not including the New Theory in the lift article. I hope that their arguments prevail and that I won't have to take part in that discussion.

(You did not take part in the Wikipedia discussion, where only so called hobbyists participated, which prevented any form of technical discussion. Why did you not participate, when you effectively serve as expert behind the Wikipedia article? (Q7))

You continue to misread and ignore my answers. Regarding the NACA 0012, the New Theory predicts C_D = 0.006, which agrees with experiment. But you also claim that skin friction represents only 20% of that total drag. That would be an average skin friction of 0.0006 on each surface, about the same as attached laminar flow on a flat plate. When I point out that such a low value is contradicted by "Experimental measurements of skin friction" under turbulent conditions, you deflect the conversation back to the total drag. On the airfoil we know from experimental measurements that the boundary layer becomes turbulent, either at a trip or farther aft by natural transition (untripped case). In both cases the average skin friction is significantly higher than the laminar flat-plate level. The fact is that the new theory gets the total drag right but apparently misses the average skin friction part badly for the untripped case. Conventional CFD gets both parts right, for both the tripped and untripped cases.

(Euler CFD with zero skin friction gets untripped C_D correct (=0.006) within measurement accuracy, with thus form/pressure drag = 0.006. Standard CFD claims 50-80% skin friction drag which with the same total  drag means that form drag is max 0.003 = max 50 percent of form drag from Euler CFD. The reason is probably that Standard CFD does not catch the correct separation (too high pressure at the trailing edge) and so gets too small form drag. Standard CFD in this respect resembles potential flow separation with pressure rise at separation and zero form drag.)

And you're wrong about turbulence models needing to be adjusted "case-by-case". Turbulence models vary widely in quality. There are bad ones that probably do need case-by-case adjustment. Perhaps this is what misled you to think that this is generally true of turbulence models. But it isn't. Good turbulence models don't require case-by-case adjustment. I know this from decades of experience using several different turbulence models.

(How do you distinguish good turbulence models from bad?)

Your new questions Q1-Q7 have easy answers, none of which would support your arguments. But, given that you don't seem to actually read my answers, I think continuing to answer your questions would be pointless, so I'm stopping here. My joining a technical discussion on Wikipedia would be equally pointless.

(Ok, it seems that our discussion has come to an end since you do not want to answer my Questions Q1-Q7. But the question "what keeps planes in the air" remains to be answered and this will form next headlines in Science and Nature. I want to thank you for your participation displaying the state of modern fluid mechanics, which will serve an important role as reference in the scientific discussion, which will continue until basic questions have found answers. This is the way science works, or is supposed to work. Best regards, Claes.)

## tisdag 17 augusti 2021

### Encounter with Wikipedia Culture on Theory of Flight

Here is an account of my encounter with Wikipedia concerning the article Lift (force) which continued on the Talk page  and from there was lifted to the Physics page. The Lift (force) article starts with:

• There are several ways to explain how an airfoil generates lift. Some are more complicated or more physically rigorous than others; some have been shown to be incorrect.
Then follows an account of popular "theories" (Newton, Bernoulli, Coanda) all carefully shown to be incomplete/trivial and thereby incorrect as scientific explanations of lift. But no scientific theory commonly accepted to be correct is presented. The general reader of the article is thus left in confusion from double-speak: There are several ways to explain lift, but they are all incorrect. This is disinformation.

This is the starting point for giving a reference to New Theory of Flight, which I add, and which is then quickly deleted by eager Wikipedians to be followed by lengthy discussions on the Talk and Physics pages.

Nowhere in these discussions do I meet any professional scientist, only what one Wikipedian describes as people made editing Wikipedia their hobby. In particular, not Doug McLean with whom I have have a long discussion on theory of flight recorded in recent posts, and who serves as scientific authority behind the hobbyists doing the editing of the article.

What I meet is a swarm of Wikipedians trying all possible tricks to silence my voice, without ever getting to the point of disinformation/double-speak in the claim that "There are many ways to explain lift, all wrong". What strikes me is that is that the swarm is so well coordinated, like a bee swarm with objective to kill the intruder, but with unknown coordinator. I do not meet a single Wikipedian willing to take a look at a possible case of misinformation. Read the interchange on the Talk and Physics pages and build your own conception of how Wikipedia functions and how articles are coordinated by some coordinator without name and beyond contact. I do not think this is how Wikipedia was originally conceived as an open objective service to the people, not steered by hidden special interests.

PS  There is already a process started at Wikipedia to replace the point of departure:
• There are several ways to explain how an airfoil generates lift... some have been shown to be incorrect.

The flow around a lifting wing is a complex fluid-mechanics phenomenon that can be understood on essentially two levels:

1) The level of the mathematical theories, which are based on established laws of physics and represent the flow accurately, but which require solving partial differential equations, and

2) The level of qualitative physical explanations without math. Correctly explaining lift is difficult because the cause-and-effect relationships involved are subtle. A comprehensive explanation that captures all of the essential aspects is rather long. There are also many simplified explanations, and most readers will likely already have been exposed to one or more of them. But simplifying the explanation of lift is inherently problematic, and no simplified explanation has been devised that's completely satisfactory. Each of the simplified explanations presented below is therefore accompanied by a discussion of its shortcomings or errors.

We no longer see any claim that There are several ways to explain how an airfoil generates lift, and instead we are offered physical explanations without math, which McLean admits is not true physics and in additions admits are problematic. It is not clear that McLean's proposal is a step forward, but at least it acknowledges that the present version is not ok. Maybe an opening to mention New Theory of Flight, maybe under a new section with title Challenge to Old Theory: New Theory Published in Leading Scientific Journal ?

## fredag 13 augusti 2021

### The Secret of the Pythagorean vs Aerodynamics Communities

The Phythagorean Society was founded on the scientific principle that the World can be described in terms of natural numbers and quotients of natural numbers as rational numbers = All is number. It was discovered that the length of the diagonal of a square with side 1 being equal to $\sqrt{2}=1.41421356...$ by Pythagoras theorem, is not a rational number (a so-called irrational number with a non-repeating infinite decimal expansion), which was to be kept as a secret within the society. But it was revealed by Hippasus who then the story goes was drowned in a cover-up, but it did not help and the Pythagorean Society quickly collapsed to be replaced by the Euclidean School based on geometry = All is form.

The community of modern aerodynamics is built on the principle that Navier-Stokes equations with a no-slip boundary condition contains all there is to say, including an explanation of how a wing generates large lift at the expense of small drag as a theory of flight. However, the fact is (as clearly demonstrated in last posts supported by the fact that NS with no-slip is uncomputable and so tell nothing directly) that there is no commonly accepted scientific theory of flight. This is a known fact within the aerodynamics community but is withheld as a secret from the people of the World e.g. in the Wikipedia article on Lift (force) coming with a claim that there is such a theory. But no such theory is presented. As a remedy only a collection of theories all shown to be incorrect/incomplete is offered to the people in a cover-up unprecedented in the history of science, after Pythagoras.

The New Theory of Flight challenges this secret revealed by Scientific American as: No one can explain why airplanes stay in the air. The discussion with aerodynamics expert Doug McLean shows an expected reaction of denial of the aerodynamics community. What will the price be to tell the truth? What will happen to the aerodynamics community when the secret is fully revealed?

PS1 The discussion with Wikipedia on Lift (force) article has now been lifted to next level (Physics).

PS2 As just one example of the confusion concerning the physics of flight/lift, consider the explanation in Understanding Flight by Anderson and Eberhardt based on the Coanda effect (supposedly caused by viscosity), which is refuted in the Wikipedia article on Lift (force) as one of many incorrect theories (without presenting any correct theory).

## tisdag 10 augusti 2021

### Key Statements by Aerodynamics Expert Doug McLean

Here are key statements (marked by headings starting with "On") by aerodynamics expert Doug McLean recorded in the preceding post, in his book Understanding Aerodynamics, in Physics Teacher and proposed update of Wikipedia article on Lift, with my comments in italics in parenthesis. Comments by McLean will be posted as soon as they arrive. Headlines from articles in NYT 2003 and Scientific American 2020 claiming that "nobody can explain flight", are also included.

(The net result will show to be that there is no scientific theory of flight commonly agreed to be correct, which is demonstrated by the fact that no such theory is presented in the literature, only a bunch of theories which are all viewed to be incorrect/incomplete/empty. This is a major failure of modern physics/aerodynamics, unbelievable to the general public and fiercely denied by aerodynamics experts. It is the ultimate expression of Nobel Laureate Hinshelwood's characterisation of modern fluid mechanics as being split into practical fluid mechanics (hydraulics) observing phenomena which cannot be explained (lift), and theoretical fluid mechanics explaining phenomena which cannot be observed (zero lift of potential flow), in other words a complete collapse as science. )

### On Standard Theory of Flight:

So in one sense, the physics of lift is perfectly understood: Lift happens because the flow obeys the NS equations with a no-slip condition on solid surfaces. On the other hand, physical explanations of lift, without math, pose a more difficult problem. Practically everyone, the nontechnical person included, has heard at least one nonmathematical explanation of how an airfoil produces lift when air flows past it. Such explanations fall into several general categories, with many variations. Unfortunately, most of them are either incomplete or wrong in one way or another. And some give up at one point or another and resort to math. This situation is a consequence of the general difficulty of explaining things physically in fluid mechanics, a problem we’ve touched on several times in the preceding chapters. (from the book Understanding Aerodynamics: Arguing from the Real Physics by McLean)

The conventional mathematical theories can all be traced back to established laws of physics and have evolved over the years, from potential flow with the Kutta condition, through boundary-layer theory, lifting-line theory, and so forth, to the present RANS/DES state of the art. In the aeronautical/scientific community there is a broad consensus that these theories model lifting flow correctly to their respective levels of physical fidelity.

The qualitative physical explanations are something else altogether. We devise them to help us with our intuitive understanding and to communicate with non-technical audiences, but they're not an essential part of our scientific understanding. I don't even like to refer to them as "theories". No one yet, to my knowledge, has devised objective criteria for choosing which aspects of the physical phenomenon to include in such an explanation, and which to omit, leaving the choice largely to subjective taste and to perceptions of what the target audience will understand. Given the complexity of the phenomenon, the subtlety of the cause-and-effect relationships involved, and the subjectivity of decisions as to how to proceed, I'm not at all surprised that numerous explanations have been circulated, that some of them are wrong, and that not everyone agrees on which one, if any, is actually correct. ... this state of affairs doesn't justify the conclusion that "no one knows what keeps airplanes in the air." The early mathematical theories settled that question a century ago, and the current state of the art carries on the tradition.

I don't think seeking qualitative physical explanations implies that our real scientific explanation based on no-slip NS needs any "fix". In my previous note I made clear how I see the distinction between the science and the qualitative explanations.

By “physical explanations without math” I mean explanations that appeal to physical principles but don't depend on solving equations or making any other kind of quantitative determination. I'd agree with you that such explanations are, in a sense, "not true physics". In my previous note I tried to provide some rationale for why we pursue qualitative explanations at all, but I also argued that they aren't essential to our scientific understanding and that they shouldn't even be called "theories".

(Doug sends here a double message: (i) There is a scientific explanation/theory of flight. (ii) There is no satisfactory scientific explanation of flight. Doug makes a distinction between (i) quantitative explanation by math (NS with no-slip) and (ii) qualitative physical explanation without math, with the double message that (i) is settled, while (ii) is not settled. But NS with no-slip is uncomputable so (i) is empty and so none of (i) and (ii) is settled. Besides, the very idea of physics without math is acknowledged as not true physics. Why then pursue such an idea? It can only be done if there is no scientific explanation of flight.)

### On No-Slip vs Navier's Friction Boundary Condition:

I understand that a BC enforcing a relationship between wall shear stress and slip at the wall is mathematically permissible, but I don't think it's an actual "physical BC" because slip at the wall is a fiction. No-slip, on the other hand, is a physical BC imposed on us by the physics at the microscopic level. Of course forcing the fluid to have zero velocity at the wall requires some applied force, but the required force arises naturally from the solution to the viscous-flow equations. There's no need for the BC to address force explicitly, and no need to revert to Navier's condition.

(We read that Doug knows that slip is fiction, but in Fig 4.1.14 in his book he displays a turbulent boundary layer with a sublayer which effectively is slip. Doug states that the physical force required to keep a fluid particle at rest (no-slip) naturally arises from the solution of viscous equations as if mathematics has physical power. Strange!)

### On New Theory of Flight:

RANS/DES doesn't do as well as we'd like on cases with massive separation, though it's improving as our DES capabilities and turbulence models improve. So maybe your New Theory can make a contribution there. (Here is a little opening to the need of something new. Good!)

### On Computability of NS with No-Slip:

Of course I don't claim DNS is computable for an airplane, as I explain on p. 51 of my book. I'm referring to RANS. And that's what I meant here. I apologize if my choice of wording confused you. So in one sense, the physics of lift is perfectly understood: Lift happens because the flow obeys the NS equations with a no-slip condition on solid surfaces = RANS.

(Doug claims that lift is perfectly understood because the flow obeys RANS. But RANS includes both wall and turbulence models and so is not true flow physics and so the claim of perfect understanding is empty. It does not explain lift better than the model $L=C\alpha$ with $L$ lift and $\alpha$ angle of attack and $C$ a constant to be determined by observation for one $\alpha$ and $L$.)

(Navier-Stokes with slip without wall/turbulence models = DNS for an airplane requires more than $10^{16}$ mesh points way beyond present computational capacity.)

### On Separation:

The standard theory does not lead to "early separation (at the crest of wing)", provided the boundary layer is turbulent. (What if the boundary layer is laminar?)

The idea that laminar-bubble reattachment is a fiction that we dreamed up because we need it is also off-base. The existence of laminar bubbles with turbulent reattachment is amply documented experimentally. They're typically associated with separation at low R_x and so don't show up on airliner wings at cruise, but sometimes appear near leading edges of deployed slats and flaps, and on wings of smaller airplanes at lower speeds (gliders, HPAs, etc.) (So laminar bubble reattachment does not explain lift of wings.)

### On Proposed Update of Wikipedia article on Lift force:

The flow around a lifting wing is a complex fluid-mechanics phenomenon that can be understood on essentially two levels:

1) The level of the mathematical theories, which are based on established laws of physics and represent the flow accurately, but which require solving partial differential equations.

2) The level of qualitative physical explanations without math. Correctly explaining lift is difficult because the cause-and-effect relationships involved are subtle. A comprehensive explanation that captures all of the essential aspects is rather long. There are also many simplified explanations, and most readers will likely already have been exposed to one or more of them. But simplifying the explanation of lift is inherently problematic, and no simplified explanation has been devised that's completely satisfactory. Each of the simplified explanations presented below is therefore accompanied by a discussion of its shortcomings or errors.

Over the last hundred years or so, many different simplified explanations have been proposed. Most follow either of two basic approaches, based either on Newton's laws of motion or on Bernoulli's principle. But neither approach, by itself, is a completely satisfactory explanation.

(We read that McLean/Wikipedia sends the message all the people on Earth traveling by air that there is no scientifically satisfactory explanation of lift. This is nothing but a monumental failure of modern aerodynamics, unique in the history of science. But McLean also serves as a key authority for Wikipedia to give the false impression that everything is OK
• There are several ways to explain how an airfoil generates lift...For example, there are explanations based directly on Newton's laws of motion and explanations based on Bernoulli's principleEither can be used to explain lift.
No they cannot and this is acknowledged = DoubleSpeak.)

### On Need of New Theory:

1. The science of lift is not in dispute.
2. Correctly explaining lift qualitatively isn’t easy.
3. Over the last 100 years or so, many different explanations have been put forward for various audiences, and the apparent incompatibilities among the different approaches has been a source of confusion and controversy.
4. In the aeronautical/scientific community there is a broad consensus that these theories model lifting flow correctly to their respective levels of physical fidelity.
5. Your take on the standard theories of aerodynamics is outside the mainstream, as is your proposed New Theory.
6. Do I think there's any need for a new theory? Not at a conceptual level, but perhaps at the practical prediction level.
7. Even if this New Theory were also correct, there's no way that it's the first.
8. I don't think seeking qualitative physical explanations (of lift) implies that our real scientific explanation based on no-slip NS needs any "fix".
9. I don't think Euler/NS with slip is useful for cruising flight with attached flow, but it might be useful for modeling massively separated flow.
10. Calculating a no-slip TBL with a good turbulence model represents the physics in a physically realistic way, which is preferable to an ad hoc fix like a slip BCIt seems to me almost guaranteed that a slip BC won't get it right.
11. RANS/DES doesn't do as well as we'd like on cases with massive separation, though it's improving as our DES capabilities and turbulence models improve. So maybe your New Theory can make a contribution there.

### On Headlines of Scientific American and NYT: Nobody can explain flight:

Those headlines are sensationalistic nonsense. Immediately after the NYT 2003 article came out, I wrote to Kenneth Chang at NYT to try to set the record straight, but he didn't reply

The NYT and SciAm headlines were written by people under the same misapprehension as you are, i.e. that the qualitative explanations reflect the state of the science as a whole. In aero engineering circles those headlines are considered to be nonsense.

(Doug acknowledges above that nobody can explain flight, and thus that the title is not nonsense, but anyway makes efforts like Wikipedia to cover up this undeniable factThis is serious and will be the topic of the discussion with Wikipedia on the next level beyond Talk page. )

### Closing Words by Doug:

OK, let me back up and comment on one part of your question: "How can something which is well understood be difficult to explain and boil down to confusion?" Well, the part that's well understood, in my opinion, is that a lifting flow at high Re obeys the equations of continuum fluid motion with turbulence accounted for, say by RANS. This is a set of field PDEs that enforce the relevant physical principles locally, point-by-point. The local balances that are enforced are pretty simple. Determining how the flowfield behaves, on the other hand, requires solving the set of PDEs. Aspects of a solution (pressure distributions, drag, etc.) can be compared with experiment to evaluate the quality of the simulation it provides. A solution can also be interrogated at as many points as you like to verify that the physical balances embodied in the equations were honored, point-by-point. From a pure science perspective, I would argue that this is all the "science" we need, and, given the generally high quality of the simulations, I think it justifies my statement that the science of lift is well understood.

But of course our natural curiosity pushes us to go beyond what the actual science requires and to try to devise global, qualitative explanations that answer questions such as "why is the flow above and below the airfoil deflected downward?" or "Why is the pressure reduced in a region above the airfoil?" With such questions we're really asking how the solution to a complex set of field PDEs behaves, and we're asking for answers that illuminate physical cause-and-effect. Extrapolating from local principles to global behavior is naturally difficult (Doing it rigorously requires solving PDEs, after all). And the cause-and-effect relationships involved are subtle. It's not surprising that such qualitative explanations have been error-prone. But, as I've argued before, the qualitative explanations aren't essential to the science, and their faults don't contradict my assertion that the science is well understood.

In this connection I would point out that the proposed New Theory is similar to RANS in the sense that it requires solving a set of PDEs. It's also similar to RANS in the sense that solutions don't provide intuitive qualitative explanations for global flow patterns. The New Theory and RANS are thus equally "deficient" in the sense of failing to provide to a "qualitative" understanding of flow patterns. (No: The New Theory comes with an explanation of the generation of large lift at small drag as a consequence of the general explanation of slightly viscous incompressible bluff body flow as potential flow modified by 3d rotational slip separation).

Your take on the standard theories of aerodynamics is outside the mainstream, as is your proposed New Theory. You maintain that Prandtl was wrong about BL physics and that K and J were wrong about circulation theory. I disagree. Nothing in this discussion has convinced me that there's anything wrong with the standard theories. Nor has anything you've written convinced me that your New Theory has any more than a possible peripheral niche application calculating massively separated cases. At this point, I don't know what kind of resolution you're hoping for. I don't expect that you'll convince me or convince the editors (or arbitrators) at Wikipedia to see things your way. With regard to Wikipedia, if you had a growing group of followers writing peer-reviewed papers based on your approach, it would be a different story, but that doesn't seem to be happening. (Yes it does!)

So I've answered your questions, and I think my answers have been devastating to your side of the argument. But you don't really seem to pay attention to my arguments. Whenever I point out what I think is an error in your reasoning, you change the subject instead of offering a rebuttal. Given how all of this has devolved, I really don't see any point in further discussion. I ask you please to stop the emails. If you carry on the discussion on Wikipedia, I may join in.

### Summary:

Doug says that:
1. Flight is perfectly understood because fluid flow obeys the RANS equations.
2. Qualitative explanation of lift is not essential to the science, and their faults don't contradict my assertion that the science is well understood.
3. No-slip is enforced in physical terms because the required force arises naturally from the solution to the viscous-flow equations.
4. New Theory and RANS are equally "deficient" in the sense of failing to provide to a "qualitative" understanding of flow patterns.
5. Headline of Scientific American 2020 sensationalistic nonsense.
6. There is no need of New Theory, even if it happens to be correct, because there are already many theories (for different audiences) which are (even if not correct) by the aeronautical/scientific community agreed in broad consensus to model lifting flow correctly to their respective levels of physical fidelity.
7. New Theory can make a contribution for separated flow.
(1 is empty: Perfect understanding does not come from looking at RANS numbers. 2 is misunderstanding of the purpose of science. 3 is misunderstanding of the difference between real physics and mathematics. 4 is misunderstanding of New Theory. 5 is cover-up. 6-7 There is and there is not any need of New Theory.)

### From Staying Aloft: What Does Keep Them Up There?:

NYT 2003: To those who fear flying, it is probably disconcerting that physicists and aeronautical engineers still passionately debate the fundamental issue underlying this endeavor: what keeps planes in the air?

''Here we are, 100 years after the Wright brothers, and there are people who give different answers to that question,'' said Dr. John D. Anderson Jr., the curator for aerodynamics at the Smithsonian National Air and Space Museum in Washington. ''Some of them get to be religious fervor.''

The answer, the debaters agree, is physics, and not a long rope hanging down from space. But they differ sharply over the physics, especially when explaining it to nonscientists.

''There is no simple one-liner answer to this,'' Dr. Anderson said.

### From No One Can Explain Why Planes Stay in the Air:

Scientific American 2020: In December 2003, to commemorate the 100th anniversary of the first flight of the Wright brothers, the New York Times ran a story entitled “Staying Aloft; What Does Keep Them Up There?” The point of the piece was a simple question: What keeps planes in the air? To answer it, the Times turned to John D. Anderson, Jr., curator of aerodynamics at the National Air and Space Museum and author of several textbooks in the field.

What Anderson said, however, is that there is actually no agreement on what generates the aerodynamic force known as lift. “There is no simple one-liner answer to this,” he told the Times. People give different answers to the question, some with “religious fervor.” More than 15 years after that pronouncement, there are still different accounts of what generates lift, each with its own substantial rank of zealous defenders. At this point in the history of flight, this situation is slightly puzzling. After all, the natural processes of evolution, working mindlessly, at random and without any understanding of physics, solved the mechanical problem of aerodynamic lift for soaring birds eons ago. Why should it be so hard for scientists to explain what keeps birds, and airliners, up in the air?

## måndag 9 augusti 2021

### Discussion with Aerodynamics Expert Doug McLean on Theory of Flight

Here is an account of a discussion with aerodynamics expert Doug McLean on the subject of scientific explanation of flight, more precisely how it is possible for wing to create a lift force at the expense of small drag with typically a lift to drag quotient of 15 for an common airplane (and bird) up to 70 for a glider. This account will be referred to when I now bring the Wikipedia article on Lift (force) to higher levels beyond the Talk page where Doug will serve as expert. The key issue is that both Wikipedia and Doug tell the World that there is a commonly agreed upon theory/scientific explanation of flight, while no such theory is presented, only a collection of theories which are all shown to be deficient in one way or the other, in other words that the World is misinformed on a scientific question of important concern to very many. It is against this background that the New Theory of Flight has been developed, a theory that is actively suppressed by Wikipedia.  I will comment key statements by Doug in a following post.

Of particular concern is that Doug abruptly ends the discussion without answering key questions about the information he is sending to the World in his book, articles in The Physics Teacher and as reference for Wikipedia. A scientist taking a role of authority carries responsibility to answer serious questions.

### Claes 0804:

Your book is excellent! Are you open to a discussion connecting to the Wikipedia talk page on Lift (force): New Theory of Flight presented at secretofflight.wordpress.com?

### Doug:

The talk-page debate over your work came to my attention yesterday. I was already aware of your work from reading a paper a few years ago. My reaction then was negative, but I know I carry some built-in bias as a member of the aeronautics "establishment". Yes, I'm open to a discussion on the talk page. I'd like to study your website and take a few days to think about it before joining that discussion, however.

### Claes:

I am glad you are open to discussion, and I look forward to your input to the Lift force talk page. Issues are important. The fact that there is no commonly accepted explanation of how a wing generates lift at small drag, is a truly remarkable deficiency of modern fluid mechanics, unbelievable to the general public, yet understood by all experts in the field. I hope you can get around bias and give the New Theory a fair chance to explain itself and I am ready to explain whatever needs more explanation.

### Claes:

Do you follow my discussion with Mr. swordfish and Dolphin on Talk: Lift force? Any comment? What would your answer be to the question if there is a commonly accepted scientific theory of lift, and if so which is this theory? I think we can agree that it is a very important question.

### Doug:

I've skimmed your discussion on the talk page. I'm not surprised that the editors took you to task for not observing Wikipedia standards. The standards can seem overly fussy, but I think they're there for good reasons. Claims like yours are a problem for an encyclopedia. You claim to have revolutionized a major field of engineering science, but the only available sources apparently are primary reports of your own work. Even if your claims are correct, an encyclopedia would have a hard time presenting a verifiable account. Regarding the question of a commonly accepted theory of lift, I'm working on a response to that, and I'll post it soon. Meanwhile, I'm having trouble reconciling your flow model with some aspects of the physics as I understand them. You say a laminar boundary layer "transitions to slip", but you don't elaborate on what this would mean in the real world. It can't mean that the air actually slips along the surface. Of course a slip velocity can be assumed in the computational world of your New Theory, but in the world of real air and real solid surfaces, the kinetic theory of gasses tells us that the effective slip velocity at the surface must be practically zero and that the spatial distribution of velocity off the surface will be continuous. Whatever flow field a New Theory computation predicts, the corresponding real flow field would have to have some sort of sublayer in which the velocity goes from zero at the wall to whatever slip velocity was used in the calculation. If the skin friction is indeed "very low" as you claim, the velocity gradient at the wall would have to be much smaller than the corresponding gradient in a Prandtl TBL, and the sublayer would presumably have to be much thicker than a Prandtl sublayer. This raises the question of how such a flow would resist separation of the classical kind in an adverse pressure gradient. We know how resistance to separation arises from the eddy-viscosity distribution in a Prandtl TBL (see sec 4.1.4 of my book). And presumably resistance to separation in the New Theory computational world arises through the slip BC, by which low-velocity air is omitted from the computation. Can you explain to me how this would work in a corresponding real-world flow with the no-slip condition that we know must be there? Continue this discussion by email?

### Doug:

The standard theory does not lead to "early separation (at the crest of wing)", provided the boundary layer is turbulent. For the cruise condition of any well designed wing, conventional no-slip CFD with a turbulence model predicts full-chord attached flow. The flow details predicted by such calculations are supported by ample experimental observations from both the wind tunnel and flight (BL mean-velocity profiles, near-field wake surveys, oil-flow photos showing the extent of attached flow, etc). So you "question" the standard theory in the face of overwhelming supporting evidence.

There are various routes by which the turbulent boundary layer (TBL) is established. Transition from a laminar BL can be by strong disturbance (trip wire or skin joint, etc.) or growth of small disturbances through natural instabilities (Your rejection of the existence of natural TS waves is unfounded. TS waves and other instability modes have been amply documented in experiments without artificial stimulation. For a qualitative example showing TS waves see fig 2.1 c of my book, and for an example of subsequent nonlinear disturbance growth see fig 2.1 d). Transition can happen with or without a laminar separation bubble. The fact that transition in a separation bubble often leads to turbulent reattachment is well documented. On a large-enough swept-wing airplane, the boundary layer in the spanwise flow along the leading edge attachment line is naturally turbulent, so that these wings don't even have a laminar starting condition (See sec 8.6.2 of my book). All of these modes by which a TBL can be established have been observed experimentally in full-scale flight.

You say that "the assumption of no-slip on a macroscopic level lacks solid physics, Or?" Or, as I believe, the physics is quite solid. If we accept the idea of continuum flow on a macroscopic scale, as you do in your New Theory, and if the physics on a microscopic scale leads to no-slip, then we have to accept no-slip on the macroscopic scale. As I've stated before, the kinetic theory of gases leads to no-slip. This isn't just a result of non-zero viscosity. Viscosity results from interactions between gas molecules. No-slip involves additional interactions between gas molecules and the irregular solid surface, i.e. it involves more physics than just viscosity. I discuss this, albeit on a superficial level, on p. 15 of my book.

Which brings me back to the question I asked before, and which the "Euler was right" paper doesn't answer. If your New Theory is correct, and the real-world flow must have no slip, as I believe it must, how do you reconcile the two? Does the real-world flow have a sublayer with zero slip, but somehow different from Prandtl's version of a sublayer, or does the real flow over a wing at high Re actually slip at the microscopic level? If you're saying that you've discovered new molecular physics, I don't think you'll have many buyers.

This is the kind of question I think you must answer if specialists are to accept your New Theory. I also think you'll have to provide more detailed comparisons with experiments: surface pressure distributions, drag polars, flow-field velocity profiles, etc.

As you can probably tell, I'm already inclined not to accept your New Theory. But I might be more favorably disposed if you could provide a satisfactory answer to my basic physics question above.

### Claes 0804:

You raise the basic questions of slip vs no-slip. Euler said slip with the Euler equations, and Prandtl said no-slip in order to “resolve” d’Alembert’s paradox by asking for no-slip, thu potential flow with zero drag and lift.  But the physics of no-slip is unclear because it requires some kind of atomistic resolution. On the the other hand viewing slip as a model for very small skin friction is very natural and this is what we do. This is exposed in more detail in the draft enclosed of Euler was Right, Prandtl was wrong, which I hope you will take a look at and comment.

### Claes 0805:

Concerning slip vs separation, it is precisely slip which makes the flow stay attached because with slip separation requires stagnation, which only can appear towards the trailing edge before stall. This a crucial component of the New Theory. The other is the role of slip in separation without pressure rise. My question: How can you be so sure that macroscopically the correct physics is no-slip with the consequence of making flight inexplicable? So slip is the key and so an important point for discussion.

### Claes 0805:

It is exactly your section 4.1.4 which is the key point of standard theory, which I question, and which leads to early separation (at the crest of wing) and small lift. Again the assumption of no-slip on a macroscopic level lacks solid physics, Or?

### Doug 0805:

The standard theory does not lead to "early separation (at the crest of wing)", provided the boundary layer is turbulent. For the cruise condition of any well designed wing, conventional no-slip CFD with a turbulence model predicts full-chord attached flow. The flow details predicted by such calculations are supported by ample experimental observations from both the wind tunnel and flight (BL mean-velocity profiles, near-field wake surveys, oil-flow photos showing the extent of attached flow, etc). So you "question" the standard theory in the face of overwhelming supporting evidence.

There are various routes by which the turbulent boundary layer (TBL) is established. Transition from a laminar BL can be by strong disturbance (trip wire or skin joint, etc.) or growth of small disturbances through natural instabilities (Your rejection of the existence of natural TS waves is unfounded. TS waves and other instability modes have been amply documented in experiments without artificial stimulation. For a qualitative example showing TS waves see fig 2.1 c of my book, and for an example of subsequent nonlinear disturbance growth see fig 2.1 d). Transition can happen with or without a laminar separation bubble. The fact that transition in a separation bubble often leads to turbulent reattachment is well documented. On a large-enough swept-wing airplane, the boundary layer in the spanwise flow along the leading edge attachment line is naturally turbulent, so that these wings don't even have a laminar starting condition (See sec 8.6.2 of my book). All of these modes by which a TBL can be established have been observed experimentally in full-scale flight.

You say that "the assumption of no-slip on a macroscopic level lacks solid physics, Or?" Or, as I believe, the physics is quite solid. If we accept the idea of continuum flow on a macroscopic scale, as you do in your New Theory, and if the physics on a microscopic scale leads to no-slip, then we have to accept no-slip on the macroscopic scale. As I've stated before, the kinetic theory of gases leads to no-slip. This isn't just a result of non-zero viscosity. Viscosity results from interactions between gas molecules. No-slip involves additional interactions between gas molecules and the irregular solid surface, i.e. it involves more physics than just viscosity. I discuss this, albeit on a superficial level, on p. 15 of my book.

Which brings me back to the question I asked before, and which the "Euler was right" paper doesn't answer. If your New Theory is correct, and the real-world flow must have no slip, as I believe it must, how do you reconcile the two? Does the real-world flow have a sublayer with zero slip, but somehow different from Prandtl's version of a sublayer, or does the real flow over a wing at high Re actually slip at the microscopic level? If you're saying that you've discovered new molecular physics, I don't think you'll have many buyers.

This is the kind of question I think you must answer if specialists are to accept your New Theory. I also think you'll have to provide more detailed comparisons with experiments: surface pressure distributions, drag polars, flow-field velocity profiles, etc.

As you can probably tell, I'm already inclined not to accept your New Theory. But I might be more favorably disposed if you could provide a satisfactory answer to my basic physics question above.

### Claes:

Thanks Doug for response, which I will answer shortly with details. Before doing that I think you have to answer the question if there is a scientific theory of lift which by the fluid mechanics community is accepted as scientifically correct explanation of lift at small drag of a wing in physical mathematical terms? If you answer yes, I ask you where in the literature it is exposed, and I will conclude that you see no need for any new theory. Is this your answer?  Is there no need of a new theory of flight? Is current theory satisfactory?

### Doug:

OK, I'll share part of what I've drafted for the Wikipedia talk page, though it may change before I post it.
The conventional mathematical theories can all be traced back to established laws of physics and have evolved over the years, from potential flow with the Kutta condition, through boundary-layer theory, lifting-line theory, and so forth, to the present RANS/DES state of the art. In the aeronautical/scientific community there is a broad consensus that these theories model lifting flow correctly to their respective levels of physical fidelity. So I think we already have an agreed upon theory that's physically correct, and even if this New Theory were also correct, there's no way that it's the first.

The qualitative physical explanations are something else altogether. We devise them to help us with our intuitive understanding and to communicate with non-technical audiences, but they're not an essential part of our scientific understanding. I don't even like to refer to them as "theories". No one yet, to my knowledge, has devised objective criteria for choosing which aspects of the physical phenomenon to include in such an explanation, and which to omit, leaving the choice largely to subjective taste and to perceptions of what the target audience will understand. Given the complexity of the phenomenon, the subtlety of the cause-and-effect relationships involved, and the subjectivity of decisions as to how to proceed, I'm not at all surprised that numerous explanations have been circulated, that some of them are wrong, and that not everyone agrees on which one, if any, is actually correct. I happen to think that my own contribution ("The Physics Teacher", November 2018) explains lift pretty well, except that some people seem to think it's too long. In any case, this state of affairs doesn't justify the conclusion that "no one knows what keeps airplanes in the air." The early mathematical theories settled that question a century ago, and the current state of the art carries on the tradition.

Do I think there's any need for a new theory? Not at a conceptual level, but perhaps at the practical prediction level. RANS/DES doesn't do as well as we'd like on cases with massive separation, though it's improving as our DES capabilities and turbulence models improve. So maybe your New Theory can make a contribution there. I don't think the New Theory makes sense for attached flow because I still think its representation of drag in attached flow is demonstrably wrong, and getting the drag right is crucial for designing transport wings to today's standards of performance. Besides, to predict the cruise drag of a Mach 0.8 airliner you don't just have to get the BL physics right. You also have to be able to calculate transonic flow with shocks.  Best, Doug

### Claes:

This is not what you write in your book and try to fix:

So in one sense, the physics of lift is perfectly understood: Lift happens because the flow obeys the NS equations with a no-slip condition on solid surfaces. On the other hand, physical explanations of lift, without math, pose a more difficult problem. Practically everyone, the nontechnical person included, has heard at least one nonmathematical explanation of how an airfoil produces lift when air flows past it. Such explanations fall into several general categories, with many variations. Unfortunately, most of them are either incomplete or wrong in one way or another. And some give up at one point or another and resort to math. This situation is a consequence of the general difficulty of explaining things physically in fluid mechanics, a problem we’ve touched on several times in the preceding chapters.

We read that generation of lift of a wing is a secret deeply hidden in the Navier-Stokes equations with no slip (unfortunately uncomputable because of very thin boundary layer), while scientific understanding in physical terms is a difficult problem, apparently unresolved. This is not the content of your Wikipedia article. Questions:

1. Why do you intend to write something on Wikipedia which does not reflect what you write in your book, and try to fix there by filling in a new theory/explanation in Chapter 7?

2. Navier.Stokes with no-slip is uncomputable and so reference to what what such solutions would show has no content. What do you then mean by saying that from these unknown solutions lift is "perfectly understood”? So turbulence and wall models are needed and one wall model is slip which models observed very small skin friction. What is that makes it impossible for you to at least open the possibility that Euler/NS with slip which is computable could be useful?

3. Are the (headlines of) the articles in Scientific American 2020 and NYT 2003 incorrect?

4. What do you mean by “physical explanations without math”? Physics without math is not true physics, right?

I hope you will give clear answers.The matter is serious.

### Doug 0806:

"1. Why do you intend to write something on Wikipedia which does not reflect what you write in your book, and try to fix there by filling in a new theory/explanation in Chapter 7?"

I see no contradiction. I don't think seeking qualitative physical explanations implies that our real scientific explanation based on no-slip NS needs any "fix". In my previous note I made clear how I see the distinction between the science and the qualitative explanations. Please read it more carefully. I don't think it contradicts anything in my book.

"2. Navier.Stokes with no-slip is uncomputable..."

This is simply not true. No-slip NS is computed routinely all over the world. When users do it correctly, they are careful to use grids that completely resolve the viscous sublayer. We know a lot about the physics of the sublayer, and no-slip NS predicts the mean-velocity distribution there well enough. The sublayer is thin, but it's not "uncomputable".

"So turbulence and wall models are needed and one wall model is slip which models observed very small skin friction. What is that makes it impossible for you to at least open the possibility that Euler/NS with slip which is computable could be useful? "

Yes, both approaches depend on models, though true no-slip NS doesn't use wall models that impose slip. Your claimed "very small skin friction" on streamlined bodies is observed only in your New Theory calculations. You haven't presented any measurements that directly support this claim. No-slip NS with conventional turbulence models predict skin-friction levels and flow details that are supported by ample experimental data from the wind tunnel and flight. For reasons given in my previous note, I don't think Euler/NS with slip is useful for cruising flight with attached flow, but it might be useful for modeling massively separated flow.

"3. Are the (headlines of) the articles in Scientific American 2020 and NYT 2003 incorrect?"

Yes. Those headlines are sensationalistic nonsense. Immediately after the NYT 2003 article came out, I wrote to Kenneth Chang to try to set the record straight, but he didn't reply.

4. What do you mean by “physical explanations without math”? Physics without math is not true physics, right?"

By “physical explanations without math” I mean explanations that appeal to physical principles but don't depend on solving equations or making any other kind of quantitative determination. I'd agree with you that such explanations are, in a sense, "not true physics". In my previous note I tried to provide some rationale for why we pursue qualitative explanations at all, but I also argued that they aren't essential to our scientific understanding and that they shouldn't even be called "theories".

I've answered your questions as well as I can. I'm guessing you won't agree with the answers.

Finally, back to the issue of the New Theory versus the Old. As part of your justification of the New Theory, you present arguments for rejecting some major pillars of modern fluid mechanics: our understanding of the various routes to transition from laminar to turbulent flow, including transition in a laminar separation bubble followed by turbulent reattachment, the relevance of the theory of turbulent boundary layers to wing flows, and the circulation theory of lift (the K-J theorem). I found the arguments presented to be counterfactual strawmen. For example:

"If lift of an aeroplane wing was critically depending on reattachment after the formation of a separation bubble without lift, then secure air transportation could not be a reality."

This is nonsense. A separation bubble with reattachment doesn't preclude lift. To take just one example, the design of the Daedalus human-powered airplane purposely used a laminar bubble as the upper-surface transition mechanism. The predicted turbulent reattachment was verified by flow visualization in flight. For an illustration of the kind of CFD used to design the airfoil, see fig 7.4.26 of my book. The Daedalus flew at low Re, but it achieved a very high L/D nonetheless, with laminar flow on about 60% of the wing upper surface and 100% of the lower surface. In flight at higher Re, such as air transport, other modes of transition I described in an earlier note are more common.

"We see that Standard CFD with wall and turbulence models can be fitted to given measurements of total drag CD, while the decomposition into pressure and skin friction drag lacks experimental support."

And elsewhere you imply that the fitting of turbulence models is generally done on a case-by-case basis. That's simply not true, and neither is your contention about drag. The standard decomposition into pressure and skin friction drag is supported by numerous measurements of local turbulent skin friction in the wind tunnel and flight.

In your arguments against the K-J theorem, you state that a wing cannot generate circulation. Nonsense. A laminar or turbulent BL with no slip naturally produces "bound" vorticity (see sec 4.2.4 of my book). Match that BL with an effectively inviscid outer flow that has circulation compatible with the lift, as required by K-J, and the BL automatically contains the integrated vorticity required by Stokes' theorem.

So I didn't find the arguments convincing. In my opinion the pillars still stand, and I don't see much justification for a New Theory.

I'm thinking that further discussion is unlikely to be fruitful. We've reached very different conclusions from the available evidence, and neither of us is going to convince the other. Regarding the Wikipedia discussion, it appears to be dying naturally, and I'm inclined to let it. But if it continues, I'll probably join in by posting the responses I've drafted.

### Claes 0806:

PS We know that flow with a laminar boundary layer will separate at the crest because the pressure gradient in the normal direction is small, and so standard CFD claims that a separation bubble forms and then the flow "reattaches with at turbulent boundary layer" which has “better resistance to adverse pressure” and so can stay attached. Concerning “resistance to adverse pressure”, if you think this a desired/needed property, slip is even better than a turbulent boundary layer. Ok?

### Doug 0806:

No, not OK. It shouldn't be decided by what we want or need, but by what theory and experiment say actually happens. For devices that normally operate with attached flow (wings, engine inlets, etc.), mountains of evidence support the fact that the separation resistance of TBLs is crucial.

Your idea of what causes laminar separation isn't supported by the BL equations or by NS. The normal-direction pressure gradient and the centrifugal force on a fluid parcel are both proportional to u^2/r, so reduced u in the BL doesn't change the balance. Separation isn't brought about by normal-direction dynamics. It's triggered by reversal of the streamwise flow by an adverse streamwise pressure gradient.

The idea that laminar-bubble reattachment is a fiction that we dreamed up because we need it is also off-base. The existence of laminar bubbles with turbulent reattachment is amply documented experimentally. They're typically associated with separation at low R_x and so don't show up on airliner wings at cruise, but sometimes appear near leading edges of deployed slats and flaps, and on wings of smaller airplanes at lower speeds (gliders, HPAs, etc.). Doug

### Claes 0807:

No Doug, the scientific discussion with Wikipedia is “not dying naturally”, instead it has just started and I will lift the question to the next level, where you will certainly come to
express your views. I also plan to make the discussion public on my blog. Ok?

The undeniable fact is that there is no commonly accepted scientific explanation of flight and both the Wikipedia article and your book clearly express this fact: If there was such
a theory, it would be presented, but instead only a bunch of incorrect theories are presented together with arguments showing how (miserably) they fail. Your section 7.3.3 is an expression of
the same thing: If there was a correct theory, then your “physical theory without math” would serve no role. You even agree that a “physical theory without math” is not a true physical theory,
and what is it then? Metaphysics? Or psychology?

Our discussion is not ended by a statement that "further discussion will to be fruitful”. In science you continue until some form of agreement has been reached. Key points
for discussion are 1. Is NS with no-slip (DNS) computable, today, tomorrow? 2. Is Navier’s friction boundary condition more physical than no-slip?.

1. Parviz Moin in Tackling Turbulence with Supercomputers states that DNS for an airplane is way beyond present computational power. You state the opposite. Where is DNS for an airplane presented?

2. Section 6 in Euler was Right, Prandtl was Wrong discusses Navier’s friction boundary condition which describes the whole spectrum from no-slip to slip through the size of the friction parameter
C_f: If C_f>1 then basically no-slip, and if C_f < nu^0.5 then basically slip. Observations show that C_f is around 0.001-3 for Re > 10^6, connecting to drag crisis around Re = 10^6 with C_f = 0.001
and effective slip.

I argue with Navier that the friction boundary condition is a physical boundary condition being an expression of force balance with possibility of imposing force, while the full no-slip when imposed by simply setting u=0 on the boundary in math or code, is a non-physical condition which does not express force balance. Do you agree that u=0 is a non-physical boundary condition in the sense that it does not express force balance, which is the only one which can be controled: You can expose a fluid particle to a (viscous shear in the flow and a friction force on the boundary) but you cannot control it by simply telling it to have zero velocity (it does not listen to such commands in reality, only in math and code). Right? This a key point which we can settle in discussion. If I ask you how no-slip is imposed, what do you answer? If I ask you if you view Navier’s friction boundary condition to be more physical than no-slip, what is your answer?

The issues we discuss are very important and so discussion must continue, here and there. One way to proceed is to start from your statement: RANS/DES doesn't do as well as we'd like on cases with massive separation, though it's improving as our DES capabilities and turbulence models improve. So maybe your New Theory can make a contribution there where you admit that RANS/DES does not fill the whole picture and that there the New Theory/computation can have a role. What is it with RANS/DES which is not satisfactory? Best Claes

### Claes 0807:

Ok Doug, you refer to your article Aerodynamic Lift, Part 1: The Science in The Physics Teacher, where you start out:

1. The science of lift is not in dispute. It is well understood in terms of a quantitative mathematical theory that is based on established laws of physics, produces accurate predictions, and has been agreed on by the science and engineering communities since the early 20th century.

2. Confusion arises only in connection with explaining lift in qualitative terms.

3. But neither the basic equations nor the CFD solutions provide us with an intuitive physical explanation for how lift actually comes about. Correctly explaining lift qualitatively isn’t easy, for reasons discussed below, and the explanations that are typically offered tend to oversimplify and can be misleading. Over the last 100 years or so, many different explanations have been put forward for various audiences, and the apparent incompatibilities among the different approaches has been a source of confusion and controversy.

Here you are speaking with double tongue: 1. Science of lift is well understood. 2-3. Explaining lift is not easy = Confusion.

To me the statement 1 and 2-3 are contradictory. How do you reconcile this contradiction? How can something which is well understood be difficult to explain and boil down to confusion?  Best Claes

### Claes 0808:

1.Why can a turbulent boundary layer better resist adverse pressure gradient than a laminar, and so stay attached?
2. Can you show the BL equations for laminar flow along a curved boundary with the scaling of u^2/r you claim?

### Doug 0812

1. I've already referred you to sec 4.1.4 of my book. Just read it.

2. The u^2/r relationship isn't restricted to laminar BL flow. In any steady flow the normal-direction acceleration is u^2/r, where r is the radius of curvature of the local streamline. That's just simple kinematics. As for the dynamics, normal-direction viscous/turbulent forces are usually negligible, leaving only the pressure gradient to force the acceleration. So the normal-direction pressure gradient must also go as u^2/r.

### Claes 0812

Doug: If you assume that the normal pressure gradient balances normal acceleration, then the flow stays attached. But this is to assume what you want to prove. The question is why the flow stays attached, and my answer is slip. What is your answer?

### Doug 0812

Come on, Claes, think again. All I'm assuming is steady flow and no significant viscous force. The balance between pressure gradient and convective acceleration that remains is just the normal-direction component of the Euler momentum equation. Are you saying that separation involves a violation of the Euler equation? I wouldn't think so.

The fact that the normal-direction pressure gradient balances the normal-direction acceleration is always true for steady flow without viscous forces, regardless of whether the flow follows the curved surface or not. Separation isn't determined by the normal-direction dynamics. My answer is that it's determined by a tug-of-war in the streamwise direction, between an adverse pressure gradient and a favorable viscous or turbulent shear force that always arises at the bottom of the BL in conjunction with an adverse pressure gradient. Whether the flow separates or stays attached is determined primarily by the streamwise dynamics, and whichever happens, the normal-direction dynamics adjust so as to stay in balance. This is the established science. Read sec 4.1.4 again.

### Claes 0812

Ok we agree that separation requires some form of stagnation and my point is that no-slip invites to stagnation while slip does not. Do you agree?

Related question: Why does a turbulent bl stay attached when a laminar does not?

I read in section 4.1.4 that a turbulent bl has a sublayer next to the wall with small eddy viscosity= slip! Do we then agree on slip for a turbulent bl?

I understand what you say in 4.1.4 and to me it gives support to my idea that slip is the effective boundary condition beyond drag crisis. Do you see that you give strong arguments for slip in the form turbulent bl which stays attached much better than a laminar, because it effectively means slip? Do you see that, or do you not see that? This is a key point which needs to be settled. What is your answer?

### Doug 0813

Yes, separation requires reversing the flow near the wall. but it's misleading to refer to that as "some kind of stagnation". In a real flow with no slip the flow is stagnated along the whole surface. Yes, a calculation with slip doesn't invite reversal. But to me that just means that a calculation with slip is almost guaranteed not to predict the onset of separation correctly.

I'll ignore the turbulent-vs-laminar question. I've already answered it more than once.

No again. We don't agree on slip as a substitute for a TBL. A no-slip TBL and a slip BC both resist separation more than a laminar BL, but the similarity ends there. It's also important to get the amount of separation resistance right. Calculating a no-slip TBL with a good turbulence model represents the physics in a physically realistic way, which is preferable to an ad hoc fix like a slip BC. It seems to me almost guaranteed that a slip BC won't get it right.

### Claes 0813

Doug, In Fig 4.1.14 you show cross cuts through a laminar boundary layer in progress to separation and a turbulent boundary layer which starts with a “thin sublayer next to the wall in which the eddy viscosity is effectively zero” in other words with a slip bc. So you effectively agree with me that a turbulent boundary layer acts like slip, as depicted in the figure. I take this to the notes and do not expect any confirmation from you.

The discussion will continue on Wikipedia. As of now this article seeks to give the message that there is a commonly accepted scientific theory of flight and at the same time present only theories which are shown to be incorrect/incomplete. This is contradictory information to the World written to cover up that there is no commonly accepted scientific theory of flight, which is monumental failure of modern aerodynamics. See you in the Wikipedia discussion, where you as authority of aerodynamics will have to explain the contradiction.

### Claes 0808:

1. You claim NS with no-slip (=DNS) for an airplane is computable, right? Point me to a reference
showing that this has been done. What about Moin's estimation that at the very least 10^16 mesh points are required, which seems way beyond present computer power. How can you get around this limit without wall and turbulence modeling?

2. Are you familiar with Navier’s friction boundary condition which I speak about? If yes, do you agree that this is a physical boundary condition in the sense of expressing force balance? Do you agree with me that no-slip is a non-physical boundary condition as a condition which you can easily implement in math or code, but not by physical means, because there is no way you can force a fluid particle to follow a prescription to be zero, except by some force and then you are back to Navier’s condition with a certain choice of friction parameter C_f. Right?

3. Massive measurements show that for large Re (>10^6 beyond drag crisis and up) C_f = 0.001-0.003 which gives a very small contribution to a drag coefficient C_D which for a cruising airplane can be of size 0.03 or more, thus less than 10%. Are you familiar with these numbers? For the very extreme case of a NACA0012 at zero angle of attack (of no interest for flight), Euler CFD with slip gives C_D = 0.006 in close agreement with observation of non-tripped flow (by Ladson), thus with very small contribution from skin friction (effectively C_f = 0 within measurement accuracy). What do you say about these numbers? Don’t you agree that C_f is small for Re beyond drag crisis?

I really think that at this point of our discussion these are questions that you have to answer, if our discussion is a serious discussion about important scientific matters, right? Looking forward to your answers.

### Claes 0808:

Doug, you take the role of scientific authority in your book, Physics Teacher and lift article and on Wikipedia. In this role you have to answer questions relating to what you say. Science builds on the possibility to pose questions to leading scientistsand to get answers. You thus have a responsibility to answer. My questions will be posed on the next level at Wikipedia, where you will act as expert, so they will not simply fade away. Public media (Scientitfic American NYT…) question if scientists can explain flight and get no clear answers. The questions are independent of New Theory of Flight. So I expect answers in particular to the question about computability of NS with no-slip (DNS) for and airplane.  Because you take the role of authority. Ok?

### Claes 0809:

As a preparation for the upcoming discussion with Wikipedia I have put up our correspondence on my blog: I again ask you to answer the questions I have posed! The matter is serious.

### Doug 0809:

Meanwhile, a discussion should be a two-way exchange. You still haven't answered the question I raised early on as to how your slip BC is reflected in corresponding flows in the real world, in which I think the no-slip condition must apply. Is there some sort of sublayer that obeys no-slip, or do you think the flow actually slips at the microscopic level, i.e. do you think there's significant slip at distances from the wall on the order of a mean free path?

### Claes 0809:

Good to hear that you are intending to continue (important) discussion. I am ready to explain the virtues of slip, of course. Yes, there may be a sublayer connecting with no-slip, but my idea is that this does not matter if the sublayer is thinner than about 0.1% of main dimension which connects to a Re beyond drag crisis, that is say Re>10^6. The idea is thus to connect drag crisis to the appearance of slip as an effective macroscopic boundary condition as compared to no-slip before drag crisis. The idea is supported by the observation that indeed C_f is very small beyond drag crisis, of size 0.001-3. OK?

PS A turbulent boundary layer has a thinner sublayer than a laminar and so may reach the 0.1% drag crisis switch to effective slip at a lower Re than a laminar and thus stay attached better, because slip is favorable for attachment because separation requires some form of stagnation less possible for slip.

### Claes 0812

Connecting to your question on crest separation of a no-slip laminar boundary layer, I have
added Section 8 to Euler was Right, Prandtl was Wrong.

### Doug 0812

This new section claims that the normal-direction pressure gradient is key in determining separation of a BL. This isn't consistent with the physics. Separation is determined by reversal of the streamwise flow. So it's the streamwise dynamics, not the normal-direction dynamics that determine separation.

I've written this to you before. If you disagree with me, why don't you tell me why? This is supposed to be a two-way discussion.

### Claes 0812

Yes, you are right that separation involves some form of stagnation with zero tangential velocity, and what I say is that with slip stagnation does not appear as easily as with no-slip which is a form of stagnation. Therefore slip does not separate as easily as no-slip. Ok?

### Claes 0812

The key question is why the flow does not separate right after the crest of the wing. My answer is slip. What is your answer?

### Doug 0813

"1. You claim NS with no-slip (=DNS) for an airplane is computable, right?"

Wrong. Did I say "DNS"? No. If I walk into any aero engineering office and start talking about "NS with no slip", and I don't specify "DNS", they'll assume I'm referring to RANS. And that's what I meant here. I apologize if my choice of wording confused you.

Of course I don't claim DNS is computable for an airplane, as I explain on p. 51 of my book. But I do stand by my claim that RANS with a turbulence model and no slip (and no "wall model" that uses slip) is routinely computable and that it also agrees quite well with experiments for attached-flow cases. So the implication in some of your writing that your New Theory is the only viable choice isn't true.

Please remove from your blog any implication that I think DNS is computable for an airplane.

"2. Are you familiar with Navier’s friction boundary condition which I speak about? If yes, do you agree that this is a physical boundary condition in the sense of expressing force balance? Do you agree with me that no-slip is a non-physical boundary condition as a condition which you can easily implement in math or code, but not by physical means, because there is no way you can force a fluid particle to follow a prescription to be zero, except by some force and then you are back to Navier’s condition with a certain choice of friction parameter C_f. Right?"

I understand that a BC enforcing a relationship between wall shear stress and slip at the wall is mathematically permissible, but I don't think it's an actual "physical BC" because slip at the wall is a fiction. No-slip, on the other hand, is a physical BC imposed on us by the physics at the microscopic level. Of course forcing the fluid to have zero velocity at the wall requires some applied force, but the required force arises naturally from the solution to the viscous-flow equations. There's no need for the BC to address force explicitly, and no need to revert to Navier's condition.

"3. Massive measurements show that for large Re (>10^6 beyond drag crisis and up) C_f = 0.001-0.003 which gives a very small contribution to a drag coefficient C_D which for a cruising airplane can be of size 0.03 or more, thus less than 10%. Are you familiar with these numbers? For the very extreme case of a NACA0012 at zero angle of attack (of no interest for flight), Euler CFD with slip gives C_D = 0.006 in close agreement with observation of non-tripped flow (by Ladson), thus with very small contribution from skin friction (effectively C_f = 0 within measurement accuracy). What do you say about these numbers? Don’t you agree that C_f is small for Re beyond drag crisis?"

Of course I'm familiar with such numbers, but they don't conflict with the conventional drag breakdown. Yes, skin friction on one surface of the wing can be about 10% of airplane drag. But wings have two surfaces, which puts the total skin-friction drag of the wing close to 20% of airplane drag. Then there's the pressure drag caused by the displacement effect of the BL. At the profile-drag minimum (at or near zero lift, depending on the airfoil), the "form factor" by which we traditionally bookkeep this effect is about 1.2 (i.e. the viscous-related pressure drag adds an amount equal to about 20% of the total skin friction), but at sectional max L/D, where an airfoil tends to operate at cruise, the form factor is typically around 1.5 (see fig 7.4.10 of my book). That brings the total viscous-related drag of the wing to around 30% of airplane drag. Then there's the rest of the airplane (fuselage, tail surfaces, struts, nacelles, junctions). When it's all added up, the total viscous-related drag of a transport airplane in cruise is in the neighborhood of 55-60% of the total. The rest is induced drag due to lift.

Yes, the measured profile C_D of a NACA 0012 at zero lift is about 0.006. Actually, at 9x10^6 Re it's a little lower, about 0.0056 according to the NACA measurements reported by Abbott and von Doenhoff. Let's compare that with the traditional picture of laminar and turbulent skin friction. I don't have the tools at hand to do a real transition prediction, but looking at the pressure distribution and taking Re into account, I'd guess natural transition would take place at about 25% chord, giving a transition Re of about 2 million. Fig 4.3.1 of my book gives a flat-plate C_fbar of about 0.0024 under those conditions. In this and the previous paragraph I don't distinguish between flat-plate C_fbar and actual airfoil C_fbar because they're typically almost the same. So the form factor would be about 1.2, similar to the example of fig 7.4.10, meaning that about 83% of the profile drag would be skin friction of the laminar and turbulent BL. As I understand it, your interpretation of the situation would have skin friction as a much lower percentage. As I pointed out in an earlier note, experimental data support the conventional picture on this matter.

On 7 August you quoted three statements from my TPT paper and say "To me the statement 1 and 2-3 are contradictory. How do you reconcile this contradiction? How can something which is well understood be difficult to explain and boil down to confusion?" I already explained why I see no contradiction here. Only statement 1 addresses the actual science. Statements 2 and 3 are about qualitative explanations, which I don't see as being essential to the science. The NYT and SciAm headlines were written by people under the same misapprehension as you are, i.e. that the qualitative explanations reflect the state of the science as a whole. In aero engineering circles those headlines are considered to be nonsense.

OK, let me back up and comment on one part of your question: "How can something which is well understood be difficult to explain and boil down to confusion?" Well, the part that's well understood, in my opinion, is that a lifting flow at high Re obeys the equations of continuum fluid motion with turbulence accounted for, say by RANS. This is a set of field PDEs that enforce the relevant physical principles locally, point-by-point. The local balances that are enforced are pretty simple. Determining how the flowfield behaves, on the other hand, requires solving the set of PDEs. Aspects of a solution (pressure distributions, drag, etc.) can be compared with experiment to evaluate the quality of the simulation it provides. A solution can also be interrogated at as many points as you like to verify that the physical balances embodied in the equations were honored, point-by-point. From a pure science perspective, I would argue that this is all the "science" we need, and, given the generally high quality of the simulations, I think it justifies my statement that the science of lift is well understood.

But of course our natural curiosity pushes us to go beyond what the actual science requires and to try to devise global, qualitative explanations that answer questions such as "why is the flow above and below the airfoil deflected downward?" or "Why is the pressure reduced in a region above the airfoil?" With such questions we're really asking how the solution to a complex set of field PDEs behaves, and we're asking for answers that illuminate physical cause-and-effect. Extrapolating from local principles to global behavior is naturally difficult (Doing it rigorously requires solving PDEs, after all). And the cause-and-effect relationships involved are subtle. It's not surprising that such qualitative explanations have been error-prone. But, as I've argued before, the qualitative explanations aren't essential to the science, and their faults don't contradict my assertion that the science is well understood.

In this connection I would point out that the proposed New Theory is similar to RANS in the sense that it requires solving a set of PDEs. It's also similar to RANS in the sense that solutions don't provide intuitive qualitative explanations for global flow patterns. The New Theory and RANS are thus equally "deficient" in the sense of failing to provide to a "qualitative" understanding of flow patterns.

Your take on the standard theories of aerodynamics is outside the mainstream, as is your proposed New Theory. You maintain that Prandtl was wrong about BL physics and that K and J were wrong about circulation theory. I disagree. Nothing in this discussion has convinced me that there's anything wrong with the standard theories. Nor has anything you've written convinced me that your New Theory has any more than a possible peripheral niche application calculating massively separated cases. At this point, I don't know what kind of resolution you're hoping for. I don't expect that you'll convince me or convince the editors (or arbitrators) at Wikipedia to see things your way. With regard to Wikipedia, if you had a growing group of followers writing peer-reviewed papers based on your approach, it would be a different story, but that doesn't seem to be happening.

So I've answered your questions, and I think my answers have been devastating to your side of the argument. But you don't really seem to pay attention to my arguments. Whenever I point out what I think is an error in your reasoning, you change the subject instead of offering a rebuttal. Given how all of this has devolved, I really don't see any point in further discussion. I ask you please to stop the emails. If you carry on the discussion on Wikipedia, I may join in.

### Claes 0813

1. Ok, so you now say that NS with  no-slip = RANS and so that your statement that the physics of lift is perfectly understood: "Lift happens because the flow obeys the NS equations with a no-slip condition on solid surfaces " should thus be interpreted as “Lift happens because the flow obeys RANS”.

But RANS involves both wall and turbulence models and the fact that these models are adjusted to give results in accordance to observation on case by case basis, does not explain anything. You can as well say that a model with lift scaling with angle of attack after adjustment of scaling parameter explains lift. It does not. At best it can predict lift after parameter adjustment, which is not really prediction because parameters have been adjusted to fit observation. On the other hand, Euler CFD with slip is parameter free and the fact that lift is accurately predicted in bond tests is very remarkable, very remarkable. You will get the chance to explain the meaning of your claim that "lift is perfectly understood by RANS”. I have not claimed that you say that DNS for an airplane is computable. I have asked you if it is, and you now inform me that you do not think it is.

2. You say that slip at the wall is fiction, yet you present in your book a turbulent bl in Fig 4.1.14 which meets the wall with effectively slip. Contradiction.

You say that no-slip is a physical boundary but you do not answer my question how in physical terms you can control fluid particles to have zero velocity. How can you do that? What is the physics on a microscopic level that realises no-slip? You say that slip is fiction but show it Fig 4.1.14. Explanation?

3. We compute C_D = 0.0060 of NACA0012 at aoa=0 with Euler CFD/slip which agrees with observation within measurement error. We have have massive data showing that parameter free Euler CFD accurately predicts bluff body flow (including wings and full airplanes) beyond drag crisis (HiLift 3). We have shown that Euler CFD for bluff body flow can be understood as potential flow with 3d rotational slip separation and from this understanding explain the generation of large lift at small drag of a wing.

What you want to do is to hide this information (published in the scientific literature and presented in leading works shops) to the World, in a situation when Standard CFD cannot deliver anything of this sort. You will get the chance in the Wikipedia discussion to explain why you want to suppress New Theory of Flight.

Anyway, I appreciate that you have been open to discussion, which will continue.