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# A "new" theory of lift ?

## A "new" theory of lift ?

(OP)
i'd like some more informed aerodynamists' opinion on Mr (Dr?) Johnson's opinion that lift is not caused by circulation.  From http://knol.google.com/k/the-spell-of-kutta-zhukovsky-s-circulation-theory# ...

"it is shown that the lift you experience when you fly, comes without circulation, as displayed in the following figure showing the lift and circulation of a Naca0012 wing as function of the angle of attack, computed by solving the Navier-Stokes equations for the flow around the wing:

pic doesn't show, sigh

We see that the lift increases linearly with the angle of attack up to 16 degrees, while the circulation stays
basically zero up to 10 degrees: Lift and circulation are not equivalent as in Kutta-Zhukovsky's formula"

there is an impressive looking pic showing lift increasing with AoA, as expected, but "circulation" remaining constant, and close to zero.  this sort of breaks the linkage between circulation and lift, but i'm smart enough not to take things I can't derive myself at face value.

As far as I've read Johnson doesn't propose a consistent new theory, but tries to explain lift and drag at near separation AoA.

opinions ?

### RE: A "new" theory of lift ?

In my limited understanding, circulation is a mathematical artifice, introduced in order to allow use of a closed system model to approximate the real system comprising an airfoil traveling in a free field, and the resulting upper and lower surface 'flows'.  Neglecting induced vortices, the only actual flows are of nominally stationary air molecules flowing 'vertically', away from and then back toward their original locations as the airfoil passes by.

The operative word here is the verb 'approximate', so I'm not surprised when different math models don't agree with each other or with reality.

Mike Halloran
Pembroke Pines, FL, USA

### RE: A "new" theory of lift ?

Is where they try to explain it.  Except they don't actually explain it.  At least not in any clear concise way.  Every time you think they're about to summarize they give a link to a different page and go on rambling.

Essentially they're saying it's 3D turbulent flow separating and causing a down wash if I understand correctly.

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### RE: A "new" theory of lift ?

Oh, and unless things have changed a lot in the last 11 years, which is possible, I thought all computer CFD were fairly unstable approximations.  They seem to be relying on CFD a lot to justify what they say.

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### RE: A "new" theory of lift ?

The circulation approach was a mathematical artifice to get the solutions to the equations to come out "correct."

I think the modern CFD programs can now run the full-blown Navier-Stokes equations.  Prior to that, I think they were running the Euler equations.

### RE: A "new" theory of lift ?

Oh, and the problem is supposedly that the Euler equations did not handle unsteady flow, which is supposedly what the actual mechanism boils down to, i.e., the steady-state solution is unstable, and unobservable in real life.

### RE: A "new" theory of lift ?

OK, So anyone know of a website with a coherent explanation of the current theory.  Equivalent to the 2 sheet (including diagrams) explanation we had to do in my first year fluids class for circulation theory?

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### RE: A "new" theory of lift ?

I'm a bit dubious about the stuff on Knol, since it's not unlike Wikipedia, and worse, since it's written be specific people who may, or may not, have agendas of their own, and there appears to be less peer review than even Wikipedia.

To wit, they claim that NASA is confused and offers 3 bad explanations "but offering no theory claimed to be correct."  And yet, the NASA site has, on each of the "wrong" theory pages, a link to the "correct" theory NASA page: http://www.grc.nasa.gov/WWW/K-12/airplane/eulereqs.html which then links to the unsteady NS equation page: http://www.grc.nasa.gov/WWW/K-12/airplane/nseqs.html

### RE: A "new" theory of lift ?

(OP)
yeah, that was were i was before the other thread was RF'd (apparently the OP was a student).  just as IR posts, yes NASA refutes 3 incorrect theories of lift, but then (not reported by Johnson) go on to say the Newton and Bernoulli are both correct.

Also i was going to say the Johnson doesn't prove circulation is wrong he just says it is (the way i read his paper).

### RE: A "new" theory of lift ?

I was lazy earlier, the NASA "right" page is here: http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html

The problem with circulation is that there is no physical mechanism by which it can occur, nor by which it can be observed.

### RE: A "new" theory of lift ?

http://www.onemetre.net/Design/Downwash/Circul/Circul.htm

Why is circulation = 0 ahead of the airfoil when we can see the streamlines deflecting upwards? Why is Vk equal but opposite on top and bottom?
Seems very idealised, close to the point of being incorrect...

### RE: A "new" theory of lift ?

As discussed elsewhere, the circulation theory is a mathematical construct used to solve the problem of having no downturning of air to generate the lift, so circulation was added to impart a downward momentum to the airflow at the trailing edge: http://knol.google.com/k/why-it-is-possible-to-fly#Kutta(2D)Zhukovsky_explanation_of_the_generation_of_lift_by_adding_large_scale_circulation_to_potential_flow

However, since this is a totally ficticious construct, the circulation can't even be constant around the airfoil, otherwise, it wouldn't correlate with other observable effects.

### RE: A "new" theory of lift ?

Which  is  pretty  much  what  I  was  getting  at.

### RE: A "new" theory of lift ?

(OP)
ok, circulation is an analytical construct that bridges analysis and the real world.  As a theory it matches observed behaviour, and makes predictions that have been validated (no?).  It is a theory with limitations eg does it predict stall behaviour ? (I don't think so).

CFD is possibly a better tool, depending on the mesh, etc (just like FEM).

To my limited understanding, the "problem" is related to potential flow models (eg predicting zero drag).  but this is for an ideal fluid, no?  How does potential flow theory stack up against Navier-Stokes (ie CFD) ?  I'd've thought it was reasonable to make a CFD model of an ideal potential flow "problem" to clarify the idealisation and the realities.

no ?

### RE: A "new" theory of lift ?

KZ theory is a zero-drag approach, and requires significant tweaking to make it work at different conditions and AoAs.

The issue is simply that there is no ideality, and CFD is the only way to get simulations to match reality consistently.

### RE: A "new" theory of lift ?

The google knol that started this thread has a few references that I checked into.  I have JD Anderson's book Introduction to Flight, and you can read a lot about the theory of how lift is produced there.  The basics are in an early chapter and much more detail in chapter 5.  Circulation is in the "alternative explanations" section, along with other trivia like the Magnus effect.

Abbott and von Doenhoff are more to the point in Theory of Wing Sections:  they don't waste a lot of words on circulation, merely demonstrating how to use the mathematics.
Circulation is used in airfoil design - you can find it in section 3.7 of TOWS.  But even so, the theory needs modification to match experiments.

To the layman and the engineer, the momentum theory is likely the most intuitive and useful.  And valid.

Back to the google page:  I've never met a pilot who knows how a wing generates lift, or cares, except the university edjikated ones.  So I don't know why the author refers to pilot's concerns.  The text fails to explain streamlines, yet relies on the concept of the streamline for its argument.  No layman reading that will make heads or tails of it.  No engineer reading it will glean any useful information from it either.

Steven Fahey, CET

### RE: A "new" theory of lift ?

(OP)
so the "new" theory is navier-stokes equations (as solved by CFD) ?

"KZ theory is a zero-drag approach" ... i thought the whole point to circulation was that it fixed the zero drag prediction from potential flow solutions ?

### RE: A "new" theory of lift ?

My reading of KZ is that it's supposed to give you a downward momentum at the trailing edge only, but has nothing to do for the drag.

I think NS, and even the Euler equations with drag, allow you simply crank the basic momentum and stress relationships without regard to "what is lift", i.e., lift simply arises from the turning motion of the air around the airfoil.  It's more a description than a theory.

### RE: A "new" theory of lift ?

(OP)
that's sort of what i meant ... we don't need any theory beyond NS to explain lift.  mind you "lift simply arises from the turning motion of the air around the airfoil" sure sounds like circulation to me !?

### RE: A "new" theory of lift ?

Not exactly, but I get your point.  The circulation theory does not attempt to explain the phenomenon; it merely makes the math come out, without regard to any physical explanation, nor can it do with without tweaking by hand to "correlate" with reality.  Presumably, this is most readily apparent when comparing flow around a cylinder vs. around a normal airfoil vs. around a flat plate.  Each condition, and each location on an airfoil requires adjustment to make the results match reality.

NS simply cranks the math, based on recognizable and accepted physical behavior, and does not specifically require tweaking of the math itself, i.e., running cylinders, airfoils, and plates require no special processing.

### RE: A "new" theory of lift ?

Professor Johnson's 'theory' is unmitigated nonsense.  There is nothing new there, and you might as well spend your time explaining to someone that evolution doesn't violate the second law of thermodynamics.  Circulation is a physical reality, in the sense that a wing generation non-zero lift will indeed have non-zero circulation around it, and the two quantities will generally exhibit the relationship predicted by 'circulation theory'.

In numerical solutions that assume potential (inviscid, irrotational) flow, it is indeed necessary to indirectly specify the circulation to get the 'right' value of lift.  This is done by imposing the 'Kutta condition', which specifies that the flow departs at the trailing edge, and how it does so.  This is not really a mathematical artifice.  In reality, it is a way to impose the effects of viscosity on a non-viscous solution.  It works because the main effect of viscosity on an 'almost inviscid' flow, which is what the flow around an unstalled wing is, is to force the flow to depart at leading edge, rather than upstream of it.  Although this is expressed mathematically, it is an empirically determined way to make the potential flow equations solvable, and to make the solution physically meaningful, in the sense of predicting lift.

Euler flow solutions (inviscid but not irrotational), interestingly, have not typically required the imposition of the Kutta condition, although, since the solutions are inviscid, one might have expected that the lift could not be determined by such methods.  It seems that the numerical errors in Euler simulations have an effect similar to physical viscosity.

Navier Stokes simulations, of course, have no need for the Kutta condition.  A 'good' Navier Stokes solution will predict lift, and also will predict a circulation close to the 'idealized' circulation associated with that value of lift.

vortexman

### RE: A "new" theory of lift ?

"I think the modern CFD programs can now run the full-blown Navier-Stokes equations."

Yes, but.  Simulations of the full N-S equations, including length scales (grid size) small enough to capture turbulent motion have been run for very simple flow conditions (flat plates) up to Reynold's numbers of a few thousand or so.  Doing so requires many hours (weeks) of running on massively parallel supercomputers, just to conclude that the laminar flow boundary layer models (aka Von Karman equations) and the DNS simulations show very good agreement (surprise, they both agree with wind tunnel data too!).  Past that, and for typical airfoils at typical Reynolds numbers (10^5 and up), a turbulence model is typically run (k-e models or similar) to model small scale motions.  Good agreement can be found using these codes for certain conditions (quasi-2d airfoil flows are one), while for more complex 3d geometry, they can leave a lot to be desired.  Panel codes, essentially inviscid flow approximations that include circulation are still used for airfoil design.

### RE: A "new" theory of lift ?

(OP)
thx for your contribution vortexman, you appear to know way more about CFD than i do (not difficult).  it was interesting to read that CFD applies KZ (at least, in a way).

two observations ...
care to comment on Johnson's plots of circulation vs lift ?  as i remember it, he plots that circulation is constant but lift is increasing (and if lift depends on circulation, it should be increasing, no?).

care to comment on his CFD plots, particularly if his CFD code embeds KZ.

based on the last two posts, it seems circulation is alive and well and living inside CFD codes.  then it is more than just another thing i learned at school, but an active working theory.

### RE: A "new" theory of lift ?

It concerns me that we're talking about CFD as it' there are only one or two approaches to it.

There are many, many algorithms and formulas that people have tried to use for various applications.  My entire final year aero course was essentially a list of all the the different approaches my prof knew about and the math behind them.

I lost track of all the ones that were highly dependent on inputs & boundary conditions etc. to give a remotely meaning full answer.

I'm sure things have developed a long way from there, but I'll be honest, to this day I have trouble relying too much on CFD that hasn't been validated by wind tunnel or other testing.

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### RE: A "new" theory of lift ?

"to this day I have trouble relying too much on CFD that hasn't been validated by wind tunnel or other testing."

Spot on.

### RE: A "new" theory of lift ?

Hi rb1957,

I haven't read all of his text word for word, but I did look at the color plots of velocity, pressure, and streamwise vorticity, and read the paragraph immediately after.  I think this partially explains Professor Johnson's confusion.  There are three components of vorticity, just as there are three components of velocity.  Circulation, which is the line integral of velocity around a closed curve that encircles the wing, would be affected by the spanwise component of vorticity, not the streamwise component.  The streamwise vorticity is irrelevant, and this would seem to be the source of his disconnect from reality.  Those plots demonstrate nothing about his novel theory of lift.

The curves below showing drag, lift, and 'circulation' as a function of angle of attack are unlabeled, and thus hard to interpret, but I suspect that he has chosen to refer to streamwise vorticity and circulation interchangably, which is incorrect.  I can't say it emphatically enough: nothing this guys is saying is correct.  If he understood aerodynamics at the undergrad level, he wouldn't be making this mistake.

The only way that "KZ is built into" CFD methods is the application of the Kutta condition in potential flow CFD codes, as far as I know.  This is an expediency required to get approximations to a "slightly viscous" flow with a fundamentally invisicid, irrotational computational method.  No assumptions about "circulation theory" are built into other CFD methods, because they're not needed.

Kenat,

No argument about that, there are many different approaches to CFD.  All of them are dependent on 'inputs and boundary conditions' to give valid results.  Moreover, virtually all of them have limitations that must be accounted for by the user in order to produce useful results.  Having said that, wind tunnel results aren't a sure-fire thing either.  My favorite saying on that topic: "The only guy who believes CFD results is the guy who ran them, and the only guy who doesn't believe wind tunnel results is the guy who measured them".  It's really hard to get good wind tunnel results.  Just like CFD, it takes a good understanding, and there are limitations.

CFD is now used fairly routinely for some problems without experimental verification, particularly early in the design process.  This requires a good understanding of what the CFD codes can and can't do, which has been acquired through long experience.

vortexman

### RE: A "new" theory of lift ?

Vortexman,
while I appreciate your comments on Johnson's theory, in section of your comment below on the effect of the spanwise component of vorticity on circulation;

"... Circulation, which is the line integral of velocity around a closed curve that encircles the wing, would be affected by the spanwise component of vorticity, not the streamwise component.  The streamwise vorticity is irrelevant, and this would seem to be the source of his disconnect from reality.  Those plots demonstrate nothing about his novel theory of lift"

How does this explain the constant Lift generated by planforms with tapered ends.
(P.S: I am in agreement of your explanation and I also have the opinion that Johnson's theory has many flaws, however, I also think His theory shold not be dismissed by a wave of a finger, rather it should be examined in the light of the fundamentals of physical laws)

### RE: A "new" theory of lift ?

(OP)
"How does this explain the constant Lift generated by planforms with tapered ends."

sorry aeroafrix2 but i don't get you you're referring to, care to explain.

and i welcome all comments about this, though i too didn't see anything new in Johnson's "theory" which seemed to me to be plots of CFD ... but maybe i missed something ?

### RE: A "new" theory of lift ?

Hi aeroafrix2,

I'm not sure I understand what you mean by "constant lift of planforms with tapered ends", but I assume you mean a constant spanwise distribution of lift.  Tapered wings don't necessarily have constant spanwise lift distributions, and I don't think anything I said has a bearing on that issue.

Regarding Johnson's "theory", there may or may not be many flaws, but there seems to be one huge one, recognized by examining it in the light of the fundamental laws of physics.  That flaw is that he attempts to "disprove" so-called "circulation theory by means of an incorrect observation.  His observation is that the lift generated by a wing doesn't vary with circulation as "circulation theory" would predict.  His huge mistake is that he uses stream vorticity rather than circulation around the wing.  Dismissing his theory on this basis doesn't constitute "the wave of a finger".

vortexman

### RE: A "new" theory of lift ?

Hello Vortexman,
sorry I was refering to the spanwise lift distribution of tapered planform.

If I may ask which Johnson are you refering to? the C. Johnson or the A.D. Johnson (the popular aerodynamis text author?)

I did ask that question because C. Johnson justified his circulation theory explaination of Lift by infering that the reduction of the chord in tapered planform accounts for the constant spanwise lift distribution in tapered planforms (elipitical wings)! What got me thinking was his assumption that if very "complex mathemtaics stuff" is used to solve his 3D model of Lift generation by circulation using his 2D model as a basis the conclusion arrived at would be the same as for the constant spanwise distribution of Lift seen on tapered planforms.

### RE: A "new" theory of lift ?

(OP)
as i understand it, tapered planforms don't have a constant airload distribution ... elliptical ones are supposed to (won't mention the Spitfire as 1/2 the world believes that the planform was chosen to accomodate the machine guns, as opposed to aerodynamic efficiency)

### RE: A "new" theory of lift ?

Err...I learnt it that the ideal (most efficient) lift distribution is elliptical, and the elliptical plan gives this most effeciently (in terms of metal weight required).  Other planes use varying section and varying AOA across the span to achieve the same results...

### RE: A "new" theory of lift ?

Hmm, I was taught ellipse is most aerodynamically favorable, but has a structural mass penalty; inverse ellipse (not sure that's quite the right term) was structurally most efficient but with aerodynamic draw backs; variations on 'tapered' are a compromise between the 2 extremes.

As to the Spit, nah, it was for the steam cooling of the Goshawk.

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### RE: A "new" theory of lift ?

@rb1957,
I thought tapered planform was a compromise between aerodynamic efficiency and structural (i.e. weight)penalty? at least that was what we were told some years ago in our aerodynamic lectures!

As for the source of lift being justified through the circulation theory, do we agree that C. Johnson's explanation are in order? Mathematical formulation of the theory appears o be order, though some of the assumptions might be questionable, but then, can anyone come up with reasons why this theory shouldn't be?

### RE: A "new" theory of lift ?

(OP)
yes, it is (a compromise) ... it only came up as people started talking about tapered planforms having constant lift (spanwise distribution) ... which i think we agree it doesn't.

as for Johnson's "theory", i don't think (IMHO) we agree it's in order, or that it's much of a theory ... scanning the posts i see a theme that there isn't much new in it (just seemed to be a bunch of CFD plots).  clearly your take is different, what do you see in his paper ?

### RE: A "new" theory of lift ?

I agree with vortexman:

That flaw is that he attempts to "disprove" so-called "circulation theory by means of an incorrect observation.  His observation is that the lift generated by a wing doesn't vary with circulation as "circulation theory" would predict.  His huge mistake is that he uses stream vorticity rather than circulation around the wing.  Dismissing his theory on this basis doesn't constitute "the wave of a finger".

IRstuff wrote:

The problem with circulation is that there is no physical mechanism by which it can occur, nor by which it can be observed.

I think I disagree here.  There is a very significant, and measurable, pitching moment coefficient generated by a wing, or even a 2d foil section, and the pitching coefficient varies pretty much proportionately to the lift coefficient, both in circulation models and in real airfoils (why else do airplanes need tails or other pitch control surfaces?).  The airfoil pitching moment is also in the correct direction to counteract the circulation predicted by theory, and from what I gather, is one of the reasons the potential flow plus circulation theory for airfoils has been around so long.  A lot of the NACA profiles, esp the low-drag laminar profiles, were generated using potential flow models as the basis for the shapes, backed up by subsequent wind tunnel testing.

### RE: A "new" theory of lift ?

(OP)
well not really (again, IMHO) ...the pitching moment is only due to the convention of having the lift act at 1/4 chord.

it's really 6 of one, 1/2 a dozen of another ... whether you fix the position of the lift force and add a moment to adjust, or let the lift act where the cp would have it; but i think we've gone down the fixed force approach for long enough.

### RE: A "new" theory of lift ?

Umm.  No, the center of lift is at the 1/4 chord point, for ANY airfoil producing lift - even a flat plate or a perfectly elliptical section.  You can do a moment analysis to figure that out, the pitching moment minimizes when the counter torque is applied at the center of lift...

But, the pitching moment, even on a flat plate, is non-zero at any non-zero angle of attack, and it doesn't matter where you restrain it.  The pitching moment acts to return the airfoil to a zero-lift position, which is why tailplanes produce negative lift.

### RE: A "new" theory of lift ?

There is no physical mechanism for getting air to move forward against the flow of the atmosphere across a wing.  You might get half of a circulation, but that's just the normal flow.  A counterflow cannot physically exist.

### RE: A "new" theory of lift ?

(OP)
nah ... don't buy that "the center of lift is at the 1/4 chord point, for ANY airfoil producing lift" ... if i had an airfoil i could resolve the aero forces as a single vector (by integrating the surface pressures) and i wouldn't need a moment to balance the free body.

and as for tailplanes producing -ve lift (which of course they do), it is because they have -ve camber and -ve AoA.

### RE: A "new" theory of lift ?

"nah ... don't buy that "the center of lift is at the 1/4 chord point, for ANY airfoil producing lift" ... if i had an airfoil i could resolve the aero forces as a single vector (by integrating the surface pressures) and i wouldn't need a moment to balance the free body."

So all NACA airfoil reports are wrong?  That's exactly what 2D airfoil section data (generated in a 2d tunnel) give, an integration of the chordwise pressure distribution.  And, in better tunnels, a direct measurement of the pitching moment, about the center of pressure.  So, you could resolve the forces to a single vector, yes - but the point of action of that force would be somewhere outside of the airfoils' surface - how can that be?

"and as for tailplanes producing -ve lift (which of course they do), it is because they have -ve camber and -ve AoA. "

Uh, yeah.  But WHY do they have a negative camber and/or AoA?

"There is no physical mechanism for getting air to move forward against the flow of the atmosphere across a wing.  You might get half of a circulation, but that's just the normal flow.  A counterflow cannot physically exist.  "

I can't quite follow your arguement.  The atmosphere is quite big, and the counter flow does not have to happen at the wing, it can be distributed as a small flow disturbance some distance away.  In real wings, the tip vortices carry some of the rotation.  In 2d section wind tunnels, (or even in pipes with 90 degree bends, you can measure the axial vorticity carried in the fluid due to the turning imposed on the flow.  Indeed, if you measure forces on airfoils in wind tunnels, you need to account for the upwash effect in order to account for differences seen from 2d pressure integration calculations.

### RE: A "new" theory of lift ?

(OP)
sorry, i believe that the NACA reports do exactly what i've said ... integrate the pressures, assume lift acts at 1/4 chord, and create the moment to balance the airfoil.

whay do you think the resultant force would act outside the airfoil ?  the typical pressure distribution peaks towards the nose ... and see that it follows that the resultant force is beyond the airfoil ?  and so what if it is ?  if this is equivalent to the original cm data then what's the problem.

and tailplanes have ... oops i "mis-spoke" ... conventional tailplanes produce +ve lift (i typed without thinking); the lift of a conventional plane is W+Lh.

### RE: A "new" theory of lift ?

If you can buy the concept of counterflow at a distance, then you can buy momentum transfer, and it's a much easier concept to buy.

Otherwise, you have to accept that there are air currents, wherever, that are moving faster than the wing and going around it somehow.  What's the physical mechanism and why hasn't it ever been observed?  Moreover, you have to buy into the concept that the air ahead of the wing is somehow anticipating that the wing will move through it at a later point in time, and the air will move in anticipation of that.

### RE: A "new" theory of lift ?

(OP)
as i understood it there is a pressure wave ahead of the wing, which gets steeper as the plane approaches mach 1, ultimating becoming the sonic shock for supersonic planes.

### RE: A "new" theory of lift ?

Yes, but none of that is going in the counterflow direction

### RE: A "new" theory of lift ?

aerofrix2:

I'm referring to the same Johnson referenced in the original post.  I already commented that the spanwise lift distribution of a tapered wing is not necessarily constant.  Beyond that, I didn't see any discussion on his pages about the lift distribution.  After discovering that he was mistaking streamwise vorticity for circulation around the wing, I didn't read any more of his text.  His 'theory' is not 'in order', it is clearly not valid.

IRstuff:

Counterflow, or upstream flow, is not necessary for non-zero circulation to exist.  Circulation is the line integral of velocity around the wing.  Aerodynamics textbooks often have an illustration showing the superposition of the non-lifting flow field (which has zero circulation) and an idealized circulating flow.  The resulting flowfield doesn't need to have any regions of upstream flow, or counterflow, near or far, and yet the circulation is non-zero.  The circulation of a lifting wing is physically measurable, and is very well known to conform (approximately) to the value predicted by "circulation theory", even though that theory is an idealized approximation.  This is not a controversial topic in aerodynamics.  Actually, the air ahead of the wing DOES know that the wing is coming, for subsonic flow, and behaves appropriately.  Your old aerodynamics textbook will have all this stuff in it, nicely explained.

vortexman

### RE: A "new" theory of lift ?

I understood that it was slower; that's what was interpreted as due to circulation.  It's mathematically a simple paradigm to account for the velocity differences, but that's what's physically not plausible.

the latter

### RE: A "new" theory of lift ?

Phew.

Anyway, until someone comes up with a decent coherent explanation with diagrams to convince me otherwise, I'm sticking with bound vortexes/circulation theory and quarter chord lift.

I'll make the significant assumption that the various profs & doctors at uni who taught me aero/mechanics of flight & related subjects, knew more or less what they were on about.

However, given that some senior guy at BAe Airbus once said on TV that lift was generated because the surface of the top of the wing was longer than the surface of the bottom of the wing and so the air over the top had to go faster to get to the rear at the same time as that on the bottom, I may well end up being the donkey.

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### RE: A "new" theory of lift ?

KENAT,

I'm not quite sure how you see the quarter chord point being involved, but the bound vortex is exactly what the circulation around the wing is.  Again reaching back to Fluid Mechanics 101, the Helmholtz theory says that a vortex can't end in 3D space, so it has to be a ring vortex.  When a wing starts moving from rest and generating lift, it starts to generate circulation around itself, which can be though of as a 'vortex'.  This vortex is continued in the form of the tip vortices, and the ring is completed by an imaginary vortex at the starting point of the wing.  That 'starting' vortex is imaginary, in the sense that the equivalent vorticity is actually spread out over a wider area, but the total amount of vorticity can be thought of, conceptually, as being a single vortex back where the wing started.  You probably have a picture showing this in your old Fluids or Aerodynamics book.  While this image is a bit idealized, the circulation is real.

IRstuff,

I guess I don't know what else to tell you.  It always strikes me as odd when someone declares that something can't be true, when he could simply look it up in a readily available book, or with a trivial Google search.  Suit yourself.

vortexman

### RE: A "new" theory of lift ?

Just because the air is slower on the bottom does not mean there is circulation.  Correlation does not prove cause.  Aside from the fact that one can come up with a number that makes the flows more balanced, that does not make for a physical reality or fact or phenomenon.  There is no physical phenomenology that explains how air can be moving along the bottom of the wing in the same direction.

### RE: A "new" theory of lift ?

(OP)
v'man, i think kenat was coupling a pair of thread that have arisen.

as far as i know, the CoP is not at the 1/4 chord.  for early NACA airfoils it was a good approximation and it became a convention ... apply the lift at 1/4 chord, and add a moment term to complete the balance ... i'm going to have dig out my Abbott and von Doenhoff or the early NACA reports to find the reference.

ir, if the flow is slower under the the airfoil, then logically it must be faster above it (incompressible momentum requires this, no?).  if it is faster above and slower below, that looks like a circulation flow to me.  is that causing the lift, or caused by the lift ... i guess that is the question.  my 2c is that if you start with fliud flows you're going to determine that thare is a net force (lift) from bernoulli, and if you start with the lift force which implies a pressure field then you'd determine the velocity field.

### RE: A "new" theory of lift ?

IRstuff,

Actually, the air on the bottom of the wing moving slower than the air on the top DOES mean that there is circulation.  Circulation is a well-defined quantity, and the situation you describe, slower flow on the bottom of the wing, is exactly what will cause that quantity to become non-zero.  Again, it is easy to find good illustrations of this on a wide variety of websites.

This is not just a number, it is a physical reality.  Air really does tend to depart the wing at the point of the sharp trailing edge as the angle of attack varies, until separation occurs (this is the Kutta condition).  This is the physical mechanism that results in circulation, because there is a value of circulation that will result in that departure point of the air for each angle of attack.  This isn't a mathematical expediency, it is a behavior of the air that is caused by the fact that it has nonzero viscosity.  When the air departs the wing at the trailing edge, it results in a flow field that has the 'necessary' circulation.  You can't really pin down the cause and effect; it doesn't work that way.

I don't understand what you're trying to say in your last sentence, so I can't respond to it.  I recommend that you look at the Wikipedia page on the Kutta Condition; it is nicely written and correct.

vortexman

### RE: A "new" theory of lift ?

My bad, the original link used "circulation," particularly in the pictures to imply that there is a counterflow.  "Circulation" to mean that there is a non-zero line integral of velocity around the object is consistent with the velocity being slower on the bottom.

### RE: A "new" theory of lift ?

I'm gonna have go back and read up too, when I get the chance.  I was taught, I thought, that you can't get the (correct, 3D) moment coefficient from a 2D wind tunnel test with pressure taps only...but that doesn't make sense now the way you put it, Rb.  Whatever.  I like vortexman's explanation, and agree with Kenat, I'll live comfortably with circulation theory.

Glad to have helped stir the pot.

### RE: A "new" theory of lift ?

(OP)
here's what wiki had to say on the Movement of center of pressure for aerodynamic fields ...
"The center of pressure on a symmetric airfoil typically lies close to 25% of the chord length behind the leading edge of the airfoil. (This is called the "quarter-chord point".) For a symmetric airfoil, as angle of attack and lift coefficient change, the center of pressure does not move. It remains around the quarter-chord point for all angles of attack and lift coefficients. The role of center of pressure in the control characterization of aircraft takes a different form than in missiles.

"On a cambered airfoil the center of pressure does not occupy a fixed location.[8] For a conventionally cambered airfoil, the center of pressure lies a little behind the quarter-chord point at maximum lift coefficient (large angle of attack), but as lift coefficient reduces (angle of attack reduces) the center of pressure moves toward the rear.[9] When the lift coefficient is zero an airfoil is generating no lift but a conventionally cambered airfoil generates a nose-down pitching moment, so the location of the center of pressure is an infinite distance behind the airfoil. This direction of movement of the center of pressure on a conventionally cambered airfoil is de-stabilising, necessitating a horizontal stabiliser to provide the aircraft with longitudinal static stability. Aircraft tend to use cambered wings because they have relatively benign flights with preferred flight orientations as compared to missiles.

"For a reflex-cambered airfoil, the center of pressure lies a little ahead of the quarter-chord point at maximum lift coefficient (large angle of attack), but as lift coefficient reduces (angle of attack reduces) the center of pressure moves forward. When the lift coefficient is zero an airfoil is generating no lift but a reflex-cambered airfoil generates a nose-up pitching moment, so the location of the center of pressure is an infinite distance ahead of the airfoil. This direction of movement of the center of pressure on a reflex-cambered airfoil is stabilising, and a horizontal stabiliser is not necessary. A tailless aircraft with a straight wing can be designed to have positive longitudinal static stability if the wing has reflex camber.

"The way the center of pressure moves as lift coefficient changes makes it difficult to use the center of pressure in the mathematical analysis of longitudinal static stability of an aircraft. For this reason, it is much simpler to use the aerodynamic center when carrying out a mathematical analysis. The aerodynamic center is a slightly more difficult concept to comprehend, but the aerodynamic center occupies a fixed location on an airfoil, typically close to the quarter-chord point.

"The aerodynamic center is the conceptual starting point for longitudinal stability. Providing the center of gravity of an aircraft lies forward of the aerodynamic center the aircraft will have positive longitudinal stability. The horizontal stabilizer contributes extra stability and this allows the center of gravity to be a small distance aft of the aerodynamic center without the aircraft reaching neutral stability. The position of the center of gravity at which the aircraft has neutral stability is called the neutral point."

but i'll look into NACA 'cause i'm sure using the 1/4 chord is a convention

### RE: A "new" theory of lift ?

Vortexman, I meant to imply that bound vortex & circulation were the same thing (or at least closely related).  I have no confusion about my understanding of it.

As to 1/4 chord, I think that was rb1957 mixing things up, I was just saying that I'm fairly confident it's correct and not just an arbitrary convention.

Posting guidelines FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm? (probably not aimed specifically at you)
What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?

### RE: A "new" theory of lift ?

Yes, there are some graphs in the latter part of the book that appear to show the CoP wandering across the chord.

### RE: A "new" theory of lift ?

Just curious, has any one observed this circulation phenomenon in a closed lop wind tunnel either using "white smoke" or "white bubbles" instead of air? And for those that have, how far the chord length does the circulation go? Does the circulation go around the wing and if this is the case how does this circulation differ in the case of "slat" and "flaps" in a full wing assembly -- (sorry its doing my head in ;D)

Granted this theory is not new. However, most Aerodynamic lectures hardly dwell on it rather they go straight into the Momentum theory of Lift.

### RE: A "new" theory of lift ?

I think that one needs to separate the the fact that the velocities are different on the top and bottom, resulting in a nonzero line integral of velocity around the wing, from an actual air flow going around the wing.

### RE: A "new" theory of lift ?

(OP)
IR ... i don't know how you can separate the velocities near the upper and lower surfaces of the wing from circulation around the wing ??

aero ... "how far the chord length does the circulation go?" ... certainly it is 100% of the chord, and i think 100% of the span, with varying strength ... i think strongest at the tip.

### RE: A "new" theory of lift ?

@IR, vortexman & rb1957, how does this 100% chordwise circulation playout during take off and/or landing of an aircraft when the slats and flaps are fully deployed. Take for example during take off the flap is fully extended, and there would be a certain 'gap' between the leading edge of the the flap and the trailing edge of the wing. Now how does this 100% chordwise  circulation around the flap and the wing playout at the leading edge of the flap and at the trailing of the wing?

See the attached sketch (excuse my freehand drawing in word) if that would help explain what I mean.

### RE: A "new" theory of lift ?

Circulation, mathematically, is a line integral of the velocity around the wing, so a non-zero result means that the velocities between the top and bottom are different, as discussed.  HOW that arises is the question.  The obvious explanation, is that there is a "circulation" of air around the wing satifies the mathematical model.  But, my argument is that there is no physical basis for claiming that there is an actual circular flow around the wing, moving in counterflow on the bottom side of the wing.

Both the "new" theory and the momentum theory basically throws away actual air "circulation" and replaces it with other physical phenomenon.

### RE: A "new" theory of lift ?

IRstuff,

Start by considering all the different shaped bodies that could be placed in a uniform flow.  Would you expect all of them to result in a flow field with zero circulation?  If so, why?  This is just as valid as to ask for the physical mechanism that results in non-zero circulation.  It would also be just as valid to ask why some shapes deflect the air downward, which would be, in effect, questioning the so-called momentum theory.  So why would one seek the mechanism behind "circulation theory" and not seek the mechanism behind "momentum theory"?  Are you comfortable that you could explain the mechanism that results in downward deflection of the air?  If so, you will have identified the mechanism responsible for non-zero circulation, because the same mechanism causes both.  If you're OK with 'momentum theory' but not with 'circulation theory', you could respond now with your explanation before you read any further.

The short, shallow and unsatisfying answer is that some shapes will exert a combination of normal and shear stresses on the fluid that will cause non-zero circulation.  One could say the same about 'deflection'.

More to your point, the mechanism that causes the circulation is the fact that non-zero viscosity prevents attached flow from going around the sharp corner of the trailing edge.  This is, in essence, the Kutta Condition.  This fact is what resolves D'Alembert's Paradox (check Wiki), and makes it possible for any body to generate lift, and circulation.  Of course, this works for bodies that don't have sharp trailing edges as well, because non-zero viscosity inhibits the fluid from going around less-than-sharp trailing edges.

Picture a symmetric airfoil at zero angle of attack.  The air hits it and leaves it at the leading and trailing edges, so the flow is symmetric, and results in zero lift and zero circulation (and zero 'deflection').  If you start to bend the trailing edge down, the viscosity will force the flow to continue to depart the airfoil at the sharp trailing edge.  Intuitively, you can see how this causes the flow to be downstream over a larger and larger portion of the upper surface, and a lower and lower portion of the lower surface, essentially because the upper surface is being stretched, and the lower surface is being squished.  If you were to draw a closed curve fairly close to the wing surface, you can see how the line integral of velocity would become nonzero, and larger, as the trailing edge is bent down more and more (in other words, the wing is given camber), because the portions of the line integral from the upper and lower surface regions no longer cancel out.  The same effect would be observed if you simply give the symmetric wing a positive angle of attack.  To get a visual on that, you need to picture what happens to the leading stagnation point as the angle of attack is made positive.  Many pictures of this are to be found via Google.

vortexman

### RE: A "new" theory of lift ?

I have never said that there isn't an imbalance of velocities.  What you're describing is the physical basis for momentum theory, not circulation of air around the ENTIRE wing, only around the trailing edge.  That's the only distinction I've made or intended to make.

### RE: A "new" theory of lift ?

(OP)
aeroafix,  to me 100% chord means the airflow is circulating around the airfoil.  if it is a multi-element airfoil, then it'd be circulating around each one and/or around the envelop ... there'd be stronger circulation around the element causing the most lift/with the highest Cl ... ther'd be flow thru the slot (between the elements) in one direction only.

do you have an alternate idea about circulation around <100% chord ??

### RE: A "new" theory of lift ?

@vortexman:

"Euler flow solutions (inviscid but not irrotational), interestingly, have not typically required the imposition of the Kutta condition, although, since the solutions are inviscid, one might have expected that the lift could not be determined by such methods.  It seems that the numerical errors in Euler simulations have an effect similar to physical viscosity."

Your assumption is right. Euler CFD gives the right lift, only because of the discretisation itself. It's the hidden numerical velocity that makes the flow leave at the trailing edge. If an analytical solution of the Euler equations would exist, you'd need a Kutta condition again to get it working.

### RE: A "new" theory of lift ?

IRstuff,

I'm kind of running out of ways to explain it.  As I said before, the physical basis of one 'theory' is also the physical basis of the other 'theory'.  You don't get to pick which phenomenon you think is really happening; they both are.  There is downward deflection of the airflow, and there is also circulation.  They are just different manifestations of the same phenomenon, and neither of them happens just at the trailing edge.

In particular, circulation must be evaluated around the entire wing section, and the curve on which you evaluate the line integral can't go through the wing.  There is a 'velocity mismatch', as you call it, and it isn't limited to the trailing edge.  Recall that we could invoke yet another 'theory', the Bernoulli Equation, which reminds us that the velocity on the upper surface of a lifting wing is higher than that on the bottom surface.  It all fits together, and if it didn't, something would be very wrong.

vortexman

### RE: A "new" theory of lift ?

@rb1957.Sorry I asked that question 'cos I remember doing some wing tunnel experiment some yars ago using 3D wing and one of the things we were hoping to observe was this 100% chord wise circulation and we also wanted to know how far off the "circulation flow field" was from the chord line of the wing and unfortunately it wasnt so easy to observe in the closed loop recirculation wind tunnel we were using.I am not completely convinced of this "circulation theory" even though mathematically it seems to add up, in reality it raises more questions than answers.

@vortexman
"....There is downward deflection of the airflow, and there is also circulation.  They are just different manifestations of the same phenomenon, and neither of them happens just at the trailing edge..."

care to explain further how these two phenomenon then combine to produce Lift? bearing in mind that the bottom line of either theory is thier attempt to justifiy (or explain)pressure differential between the top and bottom of the airfoil which in return results in lift. Also, I disagree that all the theories all fits together in an attempt to explain how lift in generated on airfoil and Bernoulli theory can be faulted 'cos it realies so much on the "continuity equation" i.e. in a nutshell can be explained as smaller area, higher pressure and bigger area lower pressure which may not be completely true in the case of flow over a body surface.

### RE: A "new" theory of lift ?

aeroafrix2,

I don't think I can explain these things to your satisfaction, especially in this limited forum.  I can only recommend reading some standard Aerodynamics texts.  All this stuff is there, and is standard theory that is widely understood and commonly used in practice.  To say "I am not convinced of this 'circulation theory'", and "Bernoulli theory can be faulted" based on your evidently uniformed intuition is a little bit silly.  What about that ridiculous "Force equals mass times acceleration" theory; do you have some problems with that too?

If you want understand this stuff, you'll probably have to do it the way Aerodynamics undergraduates have been doing it for decades.

vortexman

### RE: A "new" theory of lift ?

(OP)
maybe i'm being a bit slow this morning ... earlier in this discussion i thought it was (often) said that circulation was a mathematical artifice as opposed to a physical phenomenon ?  this looks to be the crux of discussion.

it would appear that Johnson's paper (incorrectly) uses spanwise circulation ... yes?

one thread i pick up is is circulation caused by lift or lift caused by circulation ??

### RE: A "new" theory of lift ?

rb1957,

Circulation is a real physical phenomenon.  The only context in which you could view it as a "mathematical artifice" is the use of the potential flow approximation to predict real flows.  In this situation, one is required to specify the circulation, because the potential equations have an infinite number of solutions for a given body and far-field flow conditions.  The trick to choosing which of these solutions corresponds to physical reality is to select the "right" value of the circulation.  This isn't really a mathematical artifice, it's the use of empirical knowledge to choose the physically meaningful solution.  We know, by experimentation, that the flow departs a wing at the sharp trailing edge (for the meaningful range of angles of attack).  We also know that this phenomenon is due to the fact that the air has non-zero viscosity.  So, specifying the departure point of the flow (imposing the Kutta condition) has the effect of choosing the value of circulation that corresponds to viscous flow.  I would call this an empirical adjustment, not a mathematical artifice.  The bottom line is that if you were to experimentally measure the circulation around a lifting wing, it would be very close to the "theoretical" value.  It's a real physical phemonenon that comes along with lift.  It isn't very easy to measure, so no one does.  No one measures momentum either.  Engineers directly measure the lift, and visualize the flow to learn more about the details, when necessary.

No, this was made clear in at least one previous post.  Johnson made reference to streamwise vorticity, which is NOT the same thing as circulation.  It's in the wrong dimension, and it's not a line integral.  This is why his "thory" is nonsense.

We humans like the idea of causation, but the question doesn't make sense.  There is no such thing as causation between lift and circulation.  If you move a wing-shaped body through the air, the resulting flow field will exhibit lift, and circulation, and deflection of the air, and a bunch of other characteristics.  It would be completely arbitrary to say that some of these are causing the others.  The assignment of causation to assist our intuition really is an artifice.

vortexman

### RE: A "new" theory of lift ?

@vortexman,

And by the way,I wouldn't want us to derail the topic, however I will like tosay categorically that Bernoulli Equation can and has been be faulted. Mind doing a little research on that in your spare time? Remember no man is an island when it comes to knowledge!

### RE: A "new" theory of lift ?

"categorically that Bernoulli Equation can and has been be faulted. "

Um, grammatical errors make interpreting that statement a bit difficult, but if you are saying the Bernoulli equation is wrong...then you need to supply quite a bit of proof yourself before many people will take you seriously.  Certainly there are limitations to Bernoulli's equation, but it's basis is simply a simplification of the same Navier Stokes equations used for CFD, and is adequate to model a rather enormous variety of flows.  Similarly, potential flow with circulation is adequate to model the lift characteristics for wing sections, at far lower computational cost and better accuracy than fully viscid RANS CFD modelling, all things being equal.

### RE: A "new" theory of lift ?

aeroafrix2,

The original post sought an aerodynamicist's opinion about the "new theory" that lift is independent of circulation.  That issue, and the related issues that arose in the discussion are very straightforward to deal with the use of very well-established aerodynamic theory.  By well-established, I mean that there is no reasonable doubt about the elements of theory I'm referring to.

I have no comment about your educational background, but you have made a claim that I would like to ask you to support.  Specifically how has the Bernoulli Equation been faulted?  Please explain this very clearly so that I can understand it.

Thanks,

vortexman

### RE: A "new" theory of lift ?

I don't remember in which one, but in one of those classics
either:
Prandtl & Tietjens, "Applied Hydro- and Aeromechanics"
or:
Prandtl & Tietjens, "Fundamentals of Hydro- and Aeromechanics"

Not only the existence of circulation in case of lift, but also the whole proces of how it comes actually into being, is demonstrated by experiments in those books.

They usually come in a pack and are not expensive. The fact that flying without the proper circulation, i.e. without viscosity, is not possible, becomes also clear in those texts.

### RE: A "new" theory of lift ?

(OP)
i've dredged up this site for further research ...
http://www.desktop.aero/appliedaero/potential3d/liftingline.html ... it discusses a how bunch of fluid dynamic theories.  i found it interesting that it says most CFD programs solve linearised approximations of Navier-Stokes ... hence different programs could give different results due to different assumptions.

i too would love to know how/why bernoulli is wrong ...

### RE: A "new" theory of lift ?

Vortexman,
I believe "Faulting the Bernoulli Equation" refers to not accepting it is being used "backwards" i.e. airspeed causes a drop in pressure but saying: Pressure differential causes airspeed.

Much of the new theories of lift center on this.

### RE: A "new" theory of lift ?

Dan320,

I'm not positive that I understand what you mean, but I'll offer the following comments:  1) The Bernoulli Equation "works", in the sense the it always gives the right answer, when used correctly.  There is nothing about causality in the Bernoulli Equation or in its application.  2) This notion of causality makes no sense; you can't say what causes what, and you don't need to.  3)  There are no "new theories of lift".  There are perhaps some "new" methods, such as numerical ones, but none of them replace or disprove the "old theories", which all remain valid.

vortexman

### RE: A "new" theory of lift ?

(OP)
how does an airfoil create lift ?

lift is created by the low pressure on the upper surface and the high pressure on the lower surface.

why ? how are these pressures created ?

the airflow above the airfoil is faster and below it is slower, as required by bernoulli.

why ?

it just is.  experiment shows this.  CFD, for what it's worth, shows this.

or maybe, it is a result of circulation around the airfoil.

why ?

it just is.

### RE: A "new" theory of lift ?

how does an airfoil create lift ?
lift is created by the low pressure on the upper surface and the high pressure on the lower surface.
why ? how are these pressures created ?

By means of viscosity. The air follows the shape of the airfoil, because it sticks to it. The only way to do so is by means of a centrifugal force, which in turn can only be caused by pressure gradients in the radial direction of the curve

the airflow above the airfoil is faster and below it is slower, as required by bernoulli.
why ?

Because the air does not disappear nor gets created around the airfoil and because of the statement above. If there is less place, and the amount of air going in (between infinity and your airfoil) is equal to the amount going out, it must go faster, because the cross section is smaller. (Compare internal flow)

it just is.

See above, it is not "just"

experiment shows this.  CFD, for what it's worth, shows this.
or maybe, it is a result of circulation around the airfoil.
why ?

CFD just solves your equations, either complete or not, on such a small scale that they can be linearised, just like any finite something method on any problem in physics or engineering.

Not only the experiment shows this, the theory also shows this, the experiment of Prandtl only confirmed it.

it just is.

No it is not "just"
The circulation and the lift ar both a result of the air following the shape of the airfoil, for being sticky

### RE: A "new" theory of lift ?

Whatever you say, Vortexman.
Old lift explanations state that pressure drops when airspeed increases. If you think about this for a while you will find it makes no sense, even if it is seemingly in accordance with Bernoullis conservation of energy equation.
When you realise that differences in air pressure is what causes the air to move, and not the other way around, everything becomes more understandable.
That is what I think people mean when they "disprove Bernoulli".

### RE: A "new" theory of lift ?

@Dan320.

It makes perfect sense, see my previous post.

What you say is not true. If I throw a stone through air at rest, there's no pressure drop moving any air, it's the stone that is moving. Any further existing pressure gradient is a local distortion caused by the presence of the stone itself not by any pressure drop in the farfield (remember that the stone flies through air at rest).

The fact that one may consider an equivalency by holding the stone and moving the air doesn't change anything to the situation.

Vortexman is right when he states that you can't say what causes what. The only thing you can say is that if one of the variabls changes, the other ones will change in accordance with Bernoulli as long as you fulfill the conditions for the law's validity.

### RE: A "new" theory of lift ?

(OP)
dan,

what causes the pressure difference in the first place ?

you can create it by say opening a can of pop/soda/soft drink ... as we know the pressure difference between the contents of the can and the outside atmosphere causes the can contents to rush out untill the pressure is equalised.  the can had a higher total pressure than the surrounding atmoshpere.

i guess we could create a similar set-up with a wind tunnel, such that the total pressure is increased due to airspeed (ie static pressure remains the same) and then open the tunnel to the outside ... the tunnel contents will rush out the same (because they have a higher total pressure than the surrounding atmosphere.

i don't think you can say pressure gradients create velocity ... i think bernoulli says static pressure and dynamic pressure are exchangeable, in the same way that potential and kinetic can be exchanged.  i don't think you can say potential energy causes kinetic energy ...

### RE: A "new" theory of lift ?

This discussion has gone off in so many directions the forum seems insufficient. Why can't we all meet in say, Rio for a conference?
Sign me up.

### RE: A "new" theory of lift ?

(OP)
great idea, but i think we'd only be able to afford Rio, North Dakota

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