New Theory of Flight Submitted to JMFM

Our new article New Theory of Flight has now been submitted to Journal of Mathematical Fluid Mechanics, after having been rejected by AIAA Journal.

New Theory of Flight is a spin-off of our earlier article Resolution of d'Alembert's Paradox published in Journal of Mathematical Fluid Mechanics in 2008, which has been one of the 5 most downloaded articles and therefore now can be downloaded for free.

Take the chance to read this article, which finally after 256 years solves a problem preventing a fruitful interplay between theoretical and practical fluid mechanics, and then continue with the New Theory of Flight.  

The JMFM referee reports for Resolution of d'Alembert's Paradox, can be studied here.

Stefan Löfven: Matematik-Syndrom?

Trots flera påstötningar reagerar inte S på mitt förslag om uppföljning av mitt tidigare möte med Socialdemokraterna i Riksdagens Utbildningsutskott om av IT-Matematik för ett år sedan.

Kristina Persdotter, politisk S-sekreterare i Utbildningsutskottet, lovar att svara om S är intresserat av IT-Matematik eller inte, men svarar inget alls.

Nu är det ju så att IT-Matematik precis passar Stefan Löfvens satsning på modern utbildning och innovation, som är kärnan i den nya moderna S-politik som nu skall säljas.

Man frågar då fråga varför Löfven inte har begripit detta?  Kan det vara så att Löfven, i likhet med så många med erfarenhet från den traditionella skolan, lider av en mer eller mindre allvarlig form av det matematik-syndrom som gör att tanken lamslås när matematik och matematik-prov kommer på tal, så att säga?  Och om tanken är lamslagen kan man ju inte säga vare sig ja eller nej till en diskussion om IT-Matematik. Kan det vara så?

Björklunds Mattelyft verkar också lamslaget: Trots oändliga resurser för utveckling av material för omskolning av mattelärare har endast en liten 15 min video producerats hittills, som visar hur man skall lära elever efter 8 år av skolmatematik,  hur man utan miniräknare kan räkna ut vad 6 delat med 0.1 blir.

Efter att lagt upp denna post kommer så prompt ett svar från Kristina Persdotter:

Hej Claes,

Vi bjöd in dig och Trevor till ett möte som vi uppskattade mycket och vi tar med oss de lärdomarna i vårt fortsatta jobb. Socialdemokraterna är mycket intresserade av att undervisningen utvecklas och kvaliteten höjs, inte minst i matematik. Vi ser att det är lärare, skolledare och forskare som ska utveckla undervisningen, inte politiker och politiska partier, och därför har vi bland annat föreslagit betydligt större resurser till lärares kompetensutveckling och till att nytt institut för lärande som vi tror är rätt väg att gå för att höja kvaliteten på undervisningen och resultaten i skolan, se t ex Forskningsinstitut för lärande

Med vänlig hälsning,
Kristina Persdotter

OK, vad säger man då om detta? Uppenbarligen backar S från uppgiften att ansvara för att skolan är anpassad till det moderna IT-samhället. Björklund sätter ner foten med ett diktat att återgå till 1950-talets katederundervisning, medan S vill satsa 25 miljoner på ett Forskningsinstitut för Lärande, som förmodligen skall befolkas med samma lärare, skolledare och forskare som inkompetensförklarats genom samma S-förslag, som ju innebär att universitetsforskningen kringgås.

Varför är det så svårt att få till stånd en diskussion om matematikundervisningen i våra skolor, där inte alla är lamslagna av frågans oerhörda obegriplighet? Varför vågar Löfven inte tänka själv? Är det inte matematik-syndromet som spökar?  Och i så fall, är det bra för S? 

Lift from Unsymmetric Attachment-Separation

The lift of a wing in the form of a tilted flat plate with a certain angle of attack can be explained as an effect of

• unsymmetric attachment-separation in real flow (right picture),

which reflects different stability aspects of attachment and separation of symmetric potential flow (left picture) with the flow diverging in attachment and converging in separation. The result is downwash with redirection in real unsymmetric flow, which gives lift as a reaction, while in symmetric potential flow there is no downwash and the lift is zero. Since the downwash is proportional to the angle of attack, lift can be expected to be proportional to the angle of attack, which is also observed:

 

This is all explained in more detail in The Secret of Flight. 

Lifting Line Theory Illposed

Circulation theory in the form of the Prandtl/Lanchester Lifting Line Theory relies on the following theorems by Helmholtz concerning "vortex filaments" or lines of concentrated vorticity:

• Theorem 1: The strength of a vortex filament is constant along its length.
• Theorem 2: A vortex filament cannot end in the fluid; it must extend to the boundaries of the fluid or form a closed path.
• Theorem 3: In the absence of of rotational forces, a fluid that is initially irrotational remains irrotational. (Kelvin's theorem).

Here, Theorem is 3 is not wellposed and thus does not describe physics: An infinitesimal perturbation can give rise to substantial vorticity without rotational forcing, as shown in the Basic Principle of New Theory of Flight. 

Nevertheless, Lifting Line Theory is based on Theorem 3 with a closed lifting line of vorticity formed by (i) transversal vorticity along the wing, (ii) streamwise vorticity extending from the wing tips (iii) transversal starting vortex, formally adding to zero as illustrated in the above left picture. The right picture shows Prandtl's conception of streamwise vorticity from the trailing edge compensating variation in transversal vorticity again from an idea of closed circuits of vorticity summing to zero

The streamwise vorticity emerging from the airfoil compensating variation of transversal vorticity in Lifting Line Theory superficially connects to the counter-rotating vortex lines of 3d rotational slip separation of the New Theory attaching to the trailing edge, but the physics is entirely different:

In the New Theory "vortex filaments" are really created on the surface from opposing flow instability, while in the Lifting Line Theory they appear formally from variation of transversal vorticity as a consequence to Helmholtz's (illposed) Theorem 3.

Note that the "vortex filaments" of streamwise vorticity attaching to the trailing edge in the New Theory conforms to Helmholtz's Theorem 2 with "vortex filaments" allowed to start from the boundary, as a correct statement. Helmholtz Theorem 1 is questionable, Theorem 2 is ok and Theorem 3 is illposed. Lifting Line Theory is based on Theorem 3.

One may say that the New Theory is based on unstable physics, while Lifting Line Theory is based on illposed formal mathematics. Unstable physics is real, while unstable formal mathematics is unreal.

Clarification by Dover

Here is the reaction from Dover upon my request to see the review of The Secret of Flight.

Dear Claes,

In response to your recent messages, a few comments:

In Dover's 70-year history, the company has published perhaps 20 or 25 books on aerodynamics.  This is a minor yet important category for us and we have no contacts in the aerospace industry. As far as we know, no one in that industry is aware of the projects we are considering, including yours, nor are they pressuring us in any way concerning them.  How anyone would try to do that is, frankly, beyond our comprehension.

I've discussed your request for our review with my department head and regret that we must decline.  All of the reviews we obtain concerning projects under consideration are requested by us under a strict belief that anonymity must be preserved, not only the identities of the reviewers, but the content of what they say. We are not engaged here in scientific debate or discussion, we are making publishing decisions. We ask qualified people to tell us what they think secure in the knowledge that they will not later find their comments posted on the Internet without their permission.  This system works well for us-- your first Dover book was reviewed the same way--and we are unwilling to make any exceptions to it.

While we must decline to go ahead, I wish you every success in finding a publisher for your manuscript.

Best regards,

Rochelle Kronzek
Engineering, Science and Mathematics Editor
Dover Publications, Inc. 


OK, so Dover is not engaged in "scientific debate or discussion", only publishes, or not publishes, scientific books based on "publishing decisions". This gives material to the current discussion concerning the role and functioning of publishing companies as a service to science. The system with secret reviews "works well for Dover" but is against the basic principle of science of open discussion.  

Dover Pushed to Not Publish The Secret of Flight

I took a risk by putting up a post announcing that Dover had approached me through Rochelle Kronzek with a proposal to publish my upcoming book The Secret of Flight.  I was well aware of the risk that Dover could be put under pressure from the aerodynamics community to suppress the book, since the book questions the established thinking of this community, but I did not expect Dover to be overly sensitive. After all it was a "delightful book" that could give Dover good money, in addition to the good money from my finite element book, which I gave away to Dover.

But I was wrong, as evidenced by today's message from Rochelle:

• Unfortunately, the reviewer feedback that we've received about your project was very negative and my publisher has decided to back away from the project. I'm sorry that "The Secret of Flight" is not a good fit for our list. I wish you every success in finding a suitable publisher for your book manuscript.

We see Rochelle changing from 

• What an absolutely delightful book, Claes!!  We at Dover are very interested in publishing this work for you and your co-authors when you feel ready to do so. 

to

• The Secret of Flight is not a good fit for our list.

I have asked Rochelle to get to see the reviewer feedback and will report. Stay tuned...Scientific publication can be tricky business...What pressure was put on Dover to not publish the book?
What would Dover risk by publishing the book? What was stronger than good money and good service to science? 

Otto Lilienthal: The Flying Man

Otto Lilienthal, German aviation pioneer named the Glider King and The Father of Flight, reported in Birdflight as the Basis of Aviation measurements during 1866 - 89 of The Carrying Capacity of Arched Surfaces in Sailing Flight collected in a set of diagrams giving the lift L for different angles of attack.

The above legendary Table IV shows a lift coefficient C_L= 0.1 x alpha, with alpha = angle of attack (in degrees), of an arched wing with camber 1/12, up to stall at 15-20 degrees (compared to a plane wing with much smaller C_L as the dotted curve).  This is close to the generic formula found to describe many wings, also captured by the basic lift formula of circulation theory.

Lilienthal computed from the diagram that a wing of area of A = 15 m2 should be able to carry himself in sustained flight at a speed V = 10 m/s powered by 2/3 hp. It took 100 years for Lilientahl's dream to come true in the form of the Gossamer Condor on 60 m2 wings at a speed of 5 m/s powered by human 1/3 hp.

Making of the Prandtl Myth by John D Anderson

We cite from the book Fundamentals of Aerodynamics by John D Anderson addressed in a previous post, concerning Ludwig Prandtl, the father of modern aerodynamics:

• The first practical theory for predicting the aerodynamic properties of a finite wing was developed by Ludwig Prandtl and his colleagues at Gottingen, Germany, during the period 1911-1918, spanning World War I. The utility of Prandtl's theory is so great that it is still in use today for preliminary calculations of finite-wing characteristics.
• The modern science of aerodynamics rests on a strong fundamental foundation, a large percentage of which was established in one place by one man-at the University of Gottingen by Ludwig Prandtl. Prandtl never received a Noble Prize, although his contributions to aerodynamics and fluid mechanics are felt by many to be of that caliber.
• By the 1930s, Prandtl was recognized worldwide as the "elder statesman" of fluid dynamics. Although he continued to do research in various areas, including structural mechanics and meteorology, his "Nobel Prize-level" contributions to fluid dynamics had all been made. 
• Prandtl remained at Gottingen throughout the turmoil of World War II, engrossed in his work and seemingly insulated from the intense political and physical disruptions brought about by Nazi Germany. 
• In fact, the German Air Ministry provided Prandtl's laboratory with new equipment and financial support. 
• Prandtl was considered a tedious lecturer because he could hardly make a statement without qualifying it. However, he attracted excellent students... 
• Prandtl died in 1953. He was clearly the father of modern aerodynamics-a monumental figure in fluid dynamics. His impact will be felt for centuries to come.

Anderson captures the essential quality of Prandtl's theory as a practical method for preliminary calculation of wing characteristics (lift),  and not a physical theory describing the true aerodynamics of the generation of lift of a wing. Anderson further emphasizes the strong connection between Prandtl's work and German war efforts, and thus gives the reason why Prandtl was not near to get a Nobel Prize.

Svar från Ulf Persson 2

Nedan följer svar från Ulf Persson på min fråga i Matematikes Existentiella Ångest 2. Jag delar Ulfs syn på betydelsen av programmering av matematiska metoder från grunden inom matematikutbildning. Detta är det ena benet av BodyandSoul (Puffin inom FEniCS), det andra bestående av kraftfulla datorprogram byggda på matematiska principer för simulering av komplexa fenomen (Dolphin/Applications inom FEniCS).

Men Ulf svarar inte på min fråga om den existentiella ångestens orsak. Kanske det inte är så lätt att analysera, med matematisk metodik.

                                              

Låt mig kortfattat kommentera din uppföljande fråga. Jag vill minnas att du vid något tillfälle skrev att det finns ingenting så praktiskt som en god teori. (Detta med någon specifik hänvisning till Leibniz). Jag hävdar att på ett naturligt och givande sätt kunna uppskatta den moderna kraftfulla datortekniken måste man ha en viss matematisk bildning. 

Problemet är att den nya tekniken är för kraftfull, man får för mycket gratis, och jag ser detta som ett grundläggande pedagogiskt problem. Att bara trycka på en knapp och få fram en lista på alla primtal till en miljon. So what? Helt annat blir situationen om man som liten först har gjort Erathostenes såll för hand för talen upp till säg hundra (en gång en kväll i slutet av 70-talet sållade jag fram primtalen mellan 10'000 och 11'000 och använde olikfärgade pennor, bara för att 'äga' dessa tal mer personligt) sedan programmerar sållet i Basic eller C eller något liknande program där man tvingas att implementera själva sållningsförfarandet. 

Därefter om man vill göra någon större undersökning kan man använda ett programpaket, eller utnyttja sitt eget skrivna program man har ju redan gjort jobbet. Vitsen med att programmera är ju att man då förvissar sig om att man 'är med' hela tiden, något som inte är fallet när man använder ett programpaket.

Paradoxical Circulation Theory of Lift

The New Theory of Flight presented on The Secret of Flight shows that the classical circulation theory of lift by Kutta-Zhukovsky is unphysical and thus incorrect, which is also supported by the fact that it builds on a paradox:

• Kutta-Zhukovsky lifting flow around a 2d airfoil is obtained by augmenting non-lifting potential flow by large scale circulation around the airfoil.
• The sharp trailing edge of an airfoil is supposed to be necessary for generation of lift.  
• The lift is proportional to the circulation, and the circulation is determined so as eliminate the singularity of potential flow arising from the sharp trailing edge.
• Lift is thus paradoxically obtained by elimination of what has been introduced, that is by eliminating the singularity introduced by the sharp trailing edge. This is like obtaining an effect by first introducing something and then removing it, as if (+ 1 - 1) could be greeter than zero. 
• The paradox is supposedly resolved by claiming that the singularity is eliminated by effects of viscosity. 

The New Theory shows that lift is generated, not by a sharp trailing edge, but by wings with smoothly rounded trailing edges with diameter up to 10% of the chord length.