## 0803: "Airfoil"

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Time Kitten
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### Re: 0803: "Airfoil"

funda wrote:
picnic_crossfire wrote:Can anyone here actually answer that student's question?

-snip over the boring old parts-

The real details of how an object generates lift are very complex and do not lend themselves to simplification. For a gas, we have to simultaneously conserve the mass, momentum, and energy in the flow. Newton's laws of motion are statements concerning the conservation of momentum. Bernoulli's equation is derived by considering conservation of energy. So both of these equations are satisfied in the generation of lift; both are correct. The conservation of mass introduces a lot of complexity into the analysis and understanding of aerodynamic problems. For example, from the conservation of mass, a change in the velocity of a gas in one direction results in a change in the velocity of the gas in a direction perpendicular to the original change. This is very different from the motion of solids, on which we base most of our experiences in physics. The simultaneous conservation of mass, momentum, and energy of a fluid (while neglecting the effects of air viscosity) are called the Euler Equations after Leonard Euler. Euler was a student of Johann Bernoulli, Daniel's father, and for a time had worked with Daniel Bernoulli in St. Petersburg. If we include the effects of viscosity, we have the Navier-Stokes Equations which are named after two independent researchers in France and in England. To truly understand the details of the generation of lift, one has to have a good working knowledge of the Euler Equations.

I take it that means "No"

wbeaty
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### Re: 0803: "Airfoil"

Time Kitten wrote:
funda wrote:The real details of how an object generates lift are very complex and do not lend themselves to simplification. For a gas, we have to simultaneously conserve the

I take it that means "No"

No, wrong.

Yes, all the usual verbal explanations of lift ...basically suck decayed donkey testes. Seriously.

To come up with a simple, vastly improved verbal explanation, you first must understand how lift works. Work on it until the blinders fall from your vision. Einstein's assertion is only too appropriate: that if you can't explain something to your grandmother, it means you don't understand it. Handwaving about the complexity of the math is just a copout. Instead sit down and spend lots of time (years) in learning to see the difference between "system of equations" versus "sensible explanation," and learning to see the flaws in lifting-force explanations.

To eliminate your own misconceptions, longrunning arguments with physicists helps greatly. A skeptical approach to existing textbooks helps greatly.

Discovering the NASA GRC website helps greatly:

http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html
http://www.grc.nasa.gov/WWW/K-12/airplane/wrong3.html
http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html
http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html
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wbeaty
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### Re: 0803: "Airfoil"

Steve the Pocket wrote:Someone needs to compile a list of things they actually still teach in schools, even just in the lower grades, that are blatantly wrong.

If we go through these lists of common student misconceptions, we'll find some which teachers believe too, and some which are taught by K-6 science texts:

http://phys.udallas.edu/C3P/Preconceptions.pdf
http://amasci.com/miscon/opphys.html
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minetruly
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### Re: 0803: "Airfoil"

Did anyone notice that in the last panel, her fists are balled and she's standing in a slightly more aggressive pose?

I love how he manages to make simple stick figures convey so much.

Also, I don't understand how there can be confusion over the speed of air moving over a curved wing. This would be easy to test in a wind tunnel. Just take the measurements-- how fast was the air moving above and below the wing? What was the air pressure above and below the wing? Etc. Surely these tests have been done many times. Anyone have any ideas on how to find them?

airshowfan
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### Re: 0803: "Airfoil"

funda wrote:The proponents of the arguments usually fall into two camps: (1) those who support the "Bernoulli" position that lift is generated by a pressure difference across the wing, and (2) those who support the "Newton" position that lift is the reaction force on a body caused by deflecting a flow of gas.

I stopped reading right there, because you completely mischaracterize the debate.

NO ONE disagrees with Newton. Newton basically says that the wing deflects air downwards, so by the third law of motion, the air exerts an upwards force on the wing. (You can even do the math: The total mass of air influenced by the wing per unit of time, times the average downwards velocity that each unit mass of air gains through this influence, equals the impulse exerted by the wing onto the air per unit time, i.e. the lift force). NO ONE disagrees with this. The question is; HOW does the wing deflect air downwards? Practically everyone agrees that it's by inducing a decrease in air pressure over the wing (i.e. the top of the wing "sucks" air down) and by inducing an increase in air pressure under the wing (i.e. the bottom of the wing pushes air down). This can be easily verified in wind tunnels and in properly-instrumented test airplanes. The next step of the question - HOW is this pressure differential induced? - is where you see different simplified models battling it out. (And a non-simplified model, the Navier-Stokes equations, is enough to compute how much lift a wing will generate, and thus to predict aircraft performance quite accurately).

wbeaty wrote:If we go through these lists of common student misconceptions, we'll find some which teachers believe too, and some which are taught by K-6 science texts:
http://phys.udallas.edu/C3P/Preconceptions.pdf
http://amasci.com/miscon/opphys.html

minetruly wrote:What was the air pressure above and below the wing? Etc. Surely these tests have been done many times. Anyone have any ideas on how to find them?

These tests are done regularly as part of aerodynamics college courses, and as airfoil-development tests in industry (although the latter relies increasingly on computer simulations). A quick Google search reveals a tiny fraction of the bountiful data that exists about this:

http://www.mh-aerotools.de/airfoils/vel ... utions.htm

http://www.melmoth2.com/texts/CFD.htm

http://www.am-inc.com/NSAERO.shtml

http://fsae1000.blogspot.com/2009/04/cfd-revisited.html

http://paperplane.org/Aerodynamics/airfoil86P.gif

http://www.supercoolprops.com/articles/ ... rfoils.php

http://www.cham.co.uk/phoenics/d_polis/ ... .htm#fineg

jmorgan3
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### Re: 0803: "Airfoil"

wbeaty wrote:
Nope, instead they explain the flight of infinitely-wide wings. They're a very useful shortcut in calculation, but they offer no explanation.

To explore the hidden flaw in infinite-wingspan diagrams, just ask yourself where the other end of the 3rd-law force is located. There's an upward force on the airfoil, but where is the equal downward force? Answer: it's expressed as a pressure pattern on distant solid surfaces.

There's a downward force on the air. You can take any set of points in a 2D potential flow field, make them a control volume, and test to see if momentum is conserved. It will be.
wbeaty wrote:Whenever infinite wingspan is used, the distant Earth's surface (or the distant walls of the wind tunnel) could either be close by the airfoil, or light years distant, and the instant down-force remains the same. The down-force on the wind tunnel is independent of the tunnel's width. In other words, withdrawing the floor and ceiling to arbitrarily large distance is ineffective. You can't get rid of the floor and ceiling or the down force, all you can do is refuse to include them in the diagram. But that sets up a misleading situation which violates Newton's 3rd. I suppose you could try withdrawing them to infinity rather than to billions of miles, but it would create an un-physical situation: an infinite wingspan at infinite distance from a surface. Does the force on the distant surface suddenly go to zero when that distance hits infinity, yet the force remains constant for arbitrarily large values? Think hard, don't just choose an answer.

The boundaries in 2D potential flows around airfoils are at infinity (incidentally, so are the boundaries in non-ground effect finite wing models). It's a lot less arbitrary than setting a wall boundary condition some random distance below, and gives pretty much the exact same answer, as long as the altitude is more than an order of magnitude larger than the chord. It is an unphysical situation, but it gives an answer indistinguishable from an infinite wing at finite but large altitude. And an infinite wing becomes a better and better approximation as aspect ratio increases. Practical airplanes don't have such a high aspect ratio that one can ignore finite wing effects in airplane design, but I'm not arguing that 3D effects are useless, only that they aren't necessary to understand lift.
wbeaty wrote:As I understand it, the solution is simple: *always* include the starting vortex, and make sure the distance between the airfoil's bound vortex and the starting vortex is << than the distance between the airfoil and the Earth's surface. In that case the force on the Earth does go to zero as you pull the Earth away to arbitrarily large distance. That's complicated though. There's a much simpler version.

I'm not "excited about" vortices, it's just that vortices are a central feature of a simple explanation of flight. If you remove them, your explanation isn't simplified; it's just wrong. If you pretend that they're unimportant, you remove any hope of explaining lift. If you screw them up, e.g. by including the bound vortex while hiding the starting vortex, you violate Newton's 3rd, and remove any hope of explanation.

The starting vortex ensures that the total angular momentum of the atmosphere is constant at zero. That doesn't mean that it affects the region around the airfoil in any meaningful way. In fact, it's addition to the flow around the airfoil will vanish toward zero as distance increases. Just showing the bound vortex doesn't mean you're violating Newton's third, only that you're looking at a region with constant, non-zero angular momentum.
wbeaty wrote:One possible fix: remove the starting vortex but then include the Earth's surface. Keep 2D airfoil diagrams as they are, but add a "floor" which exhibits the instant downward force. This gives an explanation of "venturi flight," where the wing pushes down on the Earth via an instant force-pair. It explains WIG aircraft. In a 2D world where the starting vortex is more distant than the Earth's surface, you're explaining a WIG aircraft, even if the Earth's surface is hundreds of meters below.

If by "venturi flight" you mean that air changes pressure because it is squeezing between the airfoil and the earth's surface, I would like to know how this explains lift.
wbeaty wrote:My conclusion: to explain the lifting force in 2D, use a thin flat airfoil, include an infinite region of air, and then look carefully at the acceleration of mass carried by the paired vortices. Treat it much like you'd treat the reaction kick caused by the ring-vortex launched from an Airzooka. Take great care not to violate Newton's 3rd.

Better version: get rid of the infinitely-wide wing entirely. Instead come up with a simplified version of the 3D vortex-based explanation of lift with finite real-world wings ...like this one below which I aimed at little kids and grandmothers. (Well, it's for *my* grandmother. Maybe *your* grandmother is on an aerodynamics faculty.)

Airplane Flight Analogy 1997
http://amasci.com/wing/rotbal.html

Your link is actually a decent conceptual explanation of why finite wings produce drag when they produce lift, but it still does not explain why and how that lift is produced. How does that air under the wing get launched downward? Do airfoils always push the air down? Would a cylinder work? An ellipsoid? A rotating cylinder? A flat plate?
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Jonathan SCE
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### Re: 0803: "Airfoil"

On the upside down problem, I tested it with X-Plane in an A380-800 and I can keep it level, however it is hard not to accidentally put too much stress on the wing while doing a barrel roll. Also X-Plane cut out your engines in inverted or sustained negative-g flight unless you make the plane with inverted equipment (a check box in Plane Maker).

minetruly wrote:Also, I don't understand how there can be confusion over the speed of air moving over a curved wing. This would be easy to test in a wind tunnel. Just take the measurements-- how fast was the air moving above and below the wing? What was the air pressure above and below the wing? Etc. Surely these tests have been done many times. Anyone have any ideas on how to find them?

I could give you my old fluid mechanics lab which did this experiment on a NACA 2415 wing section inside of a FLOTEK (model 1440) wind tunnel with surface pressure taps to find the net lift force, surface pressure coefficient, and the lift coefficient. You could convert the pressures to air speed.

pyromosh wrote:Physics classes, military pilots, ROTC instructors, FAA texts, civilian pilots, and a variety of aerospace related text books have all got this wrong in my experience. Even flight school got it wrong (with instructors both young and old). The pseudo-quantum-entanglement explanation that the molecules "want" to arrive at the same time always struck me as wrong some how, but I assumed that there was something I just didn't understand. This comic actually makes me feel a lot better.

Oddly, my flight ground class, Jeppesen Private Pilot book, and my Intro to Aerospace class got it right with both the air being compressed by the wing, speeding it up (Bernoulli) and Newton's third law. (I hope I got this right )

The funny thing is, I think it was the ground class that got rid of my conception of longer distance, although it could have been sooner.

Zak McKracken wrote:
ddxxdd wrote:We've all been taught that the force of friction equals Normal Force times coefficient of friction, right? And that the height, width, and length of the object don't factor into that calculation, right?

Well then why is it that wider tires on cars and trucks provide better braking power? Or is the fact that "wider tires procures better braking power" a myth?

The classical friction you learn about at school is not a myth, but it's not everything either. For train wheels for example, this works well, because you have two hard, relatively smooth surfaces. Shear stress is proportional to normal pressure there. Your mouse on the table for example, should also follow this pretty well, unless you use some sort of lubrication or some super-special mouse pad.

~Snip~

"If this was not true, then you would see drag racers with tires like bicycles, since they would be less massive and easier to accelerate." Taken from Physics Begins with an M... Mysteries, Magic and Myth. Although they get the wing part slightly wrong, they worded that part like it was only Newton's third law providing the lift and not both Bernoulli and Newton. I want to get the second book Physics Begins with Another "M"...Mysteries, Magic, Myth, and Modern Physics, but I need some more money first...

mcv
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### Re: 0803: "Airfoil"

ndu192 wrote:Airplanes can fly upside down because if you change the pitch, the angle of attack at which the wings fly at result in the same pressure difference capable of lifting the plane. If you look at fighter planes and stunt planes, they have nearly symmetrical airfoil shapes, and it's just the wings angle of attack which creates the pressure differential. Likewise, it's very hard to fly upside down in a 747 because the wings aren't designed to fly upside down. It's possible, but you would need to pitch up a lot while upside down to compensate for the inefficient airfoil. There's your answer

Thanks! This is exactly what I was thinking. Glad to see it confirmed without having to go into higher aerodynamics stuff. My physics-fu isn't good enough for that.

airshowfan
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### Re: 0803: "Airfoil"

Yesterday I had a chance to fly in a 747-8 simulator at Boeing Field. It's used by the stability-&-control/airplane-handling aerodynamicists to "test" conditions that are too risky to actually test-fly (such as really bad and almost-impossibly unlikely things happening during takeoff and landing, to see whether the airplane can still be kept within the bounds of the runway) so the engine performance and aerodynamics are extremely faithful to the real thing.

Guess what: I could sustain -1g flight. We flew inverted right over Puget Sound. If the airplane is relatively empty and lightweight (so you don't need quite as high an angle of attack to generate sufficient lift) and you're flying pretty fast through relatively dense air (greater dynamic pressure means you don't need quite as high an angle of attack to generate sufficient lift, and it also means the elevators can generate a greater force to keep the nose from dropping), it's actually possible to accelerate a little bit and climb a little bit with the airplane happily laying on its back in the air. (We didn't try higher weights or higher altitudes because, well, the people there had work to do and can only squeeze in so much fooling around).

Ok, "happily laying on its back in the air" is a bit of an exaggeration: The dihedral wings upside down become anhedral, so the airplane wants to un-roll towards whatever side is slightly lower, and it takes constant small adjustments of the yoke to keep the airplane level, kinda like balancing a broomstick (but not as difficult, since a 747 doesn't roll very fast). And, of course, you have to keep pushing the yoke pretty hard to keep the nose up (or, from our point of view, down) in the sky, at the right angle above (or, from our point of view, below) the horizon.

I'm also happy to report that I could land the thing without totally wrecking it. I had landed a (real) Cessna just a couple hours before, although to be honest I'm not sure whether that helped or not since it handles quite differently, especially how high you have to flare. At one point I thought I was flaring, but I was actually on the ground riding on the main gear. I noticed that the airplane wasn't sinking any lower and I asked "Wait, am I on the ground?" and my friend (who had taken me there) laughed and said "You've been on the ground for a while now", even though the cockpit was like 50 feet up in the air...

Time Kitten
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### Re: 0803: "Airfoil"

wbeaty wrote:
Time Kitten wrote:
funda wrote:The real details of how an object generates lift are very complex and do not lend themselves to simplification. For a gas, we have to simultaneously conserve the

I take it that means "No"

No, wrong.

Yes, all the usual verbal explanations of lift ...basically suck decayed donkey testes. Seriously.

Allow me a moment to facepalm, as after the quote skip is the supporting evidence for my point.

I understand it. Several answers, both correct, incorrect, ethical, and irrelevant have been given.

However it's very difficult to find one that could be implemented in a classroom, as for most I had to do over an hour of study to find out what the hell they were saying.

ndu192 did get the answer together concisely, and funda did not, pulling up a wordy debunking rather than an answer.

darknut
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### Re: 0803: "Airfoil"

reminds me of something that happened a few years ago while still in high school science
teacher is teaching and there was something was not fully explained
and i perhaps being the only one actually trying to learn something and not just trying to survive the next test started asking questions
the teacher appearently not very knowledgable in that particular subject was trying to placate me with half answers so she could move on
but not satisfied i tryed to get more information until another student yelled across the class "shut up i'm trying to learn"
i simply had no reply because at the time that was the stupidist thing i had ever heard
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Ghavrel
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### Re: 0803: "Airfoil"

darknut wrote:reminds me of something that happened a few years ago while still in high school science
teacher is teaching and there was something was not fully explained
and i perhaps being the only one actually trying to learn something and not just trying to survive the next test started asking questions
the teacher appearently not very knowledgable in that particular subject was trying to placate me with half answers so she could move on
but not satisfied i tryed to get more information until another student yelled across the class "shut up i'm trying to learn"
i simply had no reply because at the time that was the stupidist thing i had ever heard

Ah, yes. How dare somebody be aggravated with you taking time away from a lesson in a class dedicated to a cursory overview of scientific concepts? Why should you have to stay behind to ask questions far more specific than the teacher intends to cover in said class? Of course you shouldn't! The entire class should have to take extra time out of their day just to learn what they're supposed to be learning, because gosh darn it you are interested in something and that is more important.

A general rule: there is a certain amount of time given to you to ask questions in class. After a certain point, it becomes disruptive. Teachers are almost always willing to take time outside of class to go over concepts. If you do what you described above at a university, where professors are required to set aside time outside of class for exactly this reason (among others), you are officially "that guy," and you deserve all the nasty looks you get.

Look, I understand being interested in things; I really do. But it's just impolite to inconvenience everyone when you could take care of your curiosity after class. And if you're not willing to stay after (or go to office hours if you can't stay), maybe you aren't interested enough to be taking the time out of class? Please keep that in mind.

EDIT: This is my 42nd post, so I'm pretty sure you aren't allowed to argue with me. I think what happens now is everybody is shocked at my preternatural brilliance and tact, and then the paper I'm writing on sustainable development is magically finished and I get a perfect score on it.

EDIT2: Ah, crap.
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wbeaty
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### Re: 0803: "Airfoil"

airshowfan wrote:
funda wrote:The proponents of the arguments usually fall into two camps: (1) those who support the "Bernoulli" position that lift is generated by a pressure difference across the wing, and (2) those who support the "Newton" position that lift is the reaction force on a body caused by deflecting a flow of gas.

I stopped reading right there, because you completely mischaracterize the debate.

Then you're new to the debate. It appears in "Stick and Rudder," although the recent controversy extends back to 1990 with Weltner's papers. (Or perhaps you mean that no physicsts and aero professionals disagree with the Newton explanation? If so, I agree.)

The majority of old K-12 textbook illustrations clearly depict air behind the wing flowing horizontally, with zero downwash. Their explanations don't mention Newton or deflected air. I've watched fights break out on Usenet among crazed Bernoulli-ists over whether airfoils need to deflect any air at all; whether they can magically fly using pressure-difference alone. Actually, Weltner's papers were aimed at the people who believe in "pressure difference only." Only in the last decade have K-12 educators started taking Newton and air-deflection seriously. Back in the 1990s they were angrily insisting that the Newtonian explanation is simply wrong; no downwash is needed, and pointing to cambered airfoils at zero AOA as "proof" of this.

On Wings of Ignorance
http://www.textbookleague.org/105wing.htm

Note well that in a 2D flow diagram the net downwash is exactly zero, the airfoil performs no net work upon the air, and the airfoil flies by pressure difference! 2D diagrams accurately describe ground-effect flight, or a venturi. Unlike with helicopters and hovering rockets, airfoils in 2D diagrams are lifted by a 2D pattern of pressure, and no net down-momentum is deposited into the air. Instead, all the momentum ends up in a distant surface. The system is analogous to EM forces with an infinite wire supported over an infinite conductive surface, where the force is an image-force caused by the surface, and is independent of the distance between the wire and surface. On the other hand, helicopters and 3D wings are analogous to EM forces where some conductor-rings are each given a current and then thrown downwards. A 3D wing is almost identical to a hovering helicopter. A 3D wing is not a venturi which pushes instantly upon the Earth.

Time Kitten wrote:
wbeaty wrote:Yes, all the usual verbal explanations of lift ...basically suck decayed donkey testes. Seriously.

Allow me a moment to facepalm, as after the quote skip is the supporting evidence for my point.

Sorry, I was complaining about horrible explanations of lifting force found grade school textbooks. Even some aero texts have problems.

Time Kitten wrote:I understand it. Several answers, both correct, incorrect, ethical, and irrelevant have been given.

Agreed.
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jmorgan3
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### Re: 0803: "Airfoil"

wbeaty wrote:Note well that in a 2D flow diagram the net downwash is exactly zero, the airfoil performs no net work upon the air, and the airfoil flies by pressure difference! 2D diagrams accurately describe ground-effect flight, or a venturi. Unlike with helicopters and hovering rockets, airfoils in 2D diagrams are lifted by a 2D pattern of pressure, and no net down-momentum is deposited into the air. Instead, all the momentum ends up in a distant surface.

As I said in my last post, there is no boundary surface in 2D potential flow diagrams. There is a downwash created, as you can see here by playing around with the settings. In a true, physical situation on earth, the air forced downward by a wing (2D or 3D) would eventually be restored to having zero vertical momentum due to the influence of the earth's surface, but in practice that has no noticeable effect on the flow field near the wing. Changes do not propagate instantly, but are of course limited to the speed of sound.
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airshowfan
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### Re: 0803: "Airfoil"

wbeaty wrote:(Or perhaps you mean that no physicsts and aero professionals disagree with the Newton explanation? If so, I agree.)

I guess that's what I meant.

wbeaty wrote:The majority of old K-12 textbook illustrations clearly depict air behind the wing flowing horizontally, with zero downwash. Their explanations don't mention Newton or deflected air. I've watched fights break out on Usenet among crazed Bernoulli-ists over whether airfoils need to deflect any air at all (...) Back in the 1990s they were angrily insisting that the Newtonian explanation is simply wrong; no downwash is needed, and pointing to cambered airfoils at zero AOA as "proof" of this.

That's CRAZY! Thanks for enlightening me about how widespread this impossible explanation has become. I guess I'm luckier than I had realized, having been sheltered (for the most part) from such bad models. (And not just when it comes to airfoils. Reading the lists of misconceptions that have been linked to on this thread, I'm amazed that anyone older than 9 or 10 years old could think that the seasons have something to do with the distance from the earth to the sun, etc. I mean, one thing is to not know enough physics to appreciate how Newton's laws always apply, or to not know why blue light is scattered by the air less than red light, but a whole other thing is somehow missing a very relevant bit of astronomy that's taught to every elementary schooler).

Zak McKracken
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### Re: 0803: "Airfoil"

funda wrote:
picnic_crossfire wrote:Can anyone here actually answer that student's question?

How is lift generated? There are many explanations for the generation of lift found in encyclopedias, in basic physics textbooks, and on Web sites. Unfortunately, many of the explanations are misleading and incorrect.

I could not agree more
funda wrote: Theories on the generation of lift have become a source of great controversy and a topic for heated arguments for many years.
No.
Not at all. Not within "the community". Every aerodynamicist worth his or her pay knows how it works and there is no debate.
That debate exists only among students and others who haven't actually studied it and are (understandably!) confused by the different types of explanations, some of which try to make it sound as if they were contradicting each other. Which is nonsense. As long as you don't make the "date at the trailing edge" assumption, you're probably good.

funda wrote:The proponents of the arguments usually fall into two camps: (1) those who support the "Bernoulli" position that lift is generated by a pressure difference across the wing, and (2) those who support the "Newton" position that lift is the reaction force on a body caused by deflecting a flow of gas.

1. Of course there's a pressure difference! How else can you apply an aerodynamic force to a wing in mid-air? And of course there's a reaction force! How can you accelerate mass without force and counterforce?
2. Those two are completely not in contradiction. It's just a matter of which seems easier to understand, and at what level of detail you're looking at the problem. You can regard either energy conservation (Bernoully) or impulse conservation (Newton) and come to the same conclusion. In fact, both together (put into appropriate form and with added viscosity terms) form the Navier-Stokes equations.
3. There's a third explanation of lift which uses circulation and potential flow theory, but the only people you'll want to explain lift that way are mathematicians and maybe some physicists. It's also true. It's just a different way of looking at it, and please do not construct a controversy from that. (Except maybe: How do I teach it best?)

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Zak McKracken
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### Re: 0803: "Airfoil"

wbeaty wrote:
jmorgan3 wrote:
wbeaty wrote:And then it gets WORSE: It's impossible to understand airplanes by only employing 2D flow diagrams. These diagrams depict an odd sort of "flatland flight" where no work is performed on the air, and an airfoil could ideally coast along forever.

While it's true that most 2D flow diagrams you see are inviscid simulations, they still give a good conceptual picture of how lift is produced.

Nope, instead they explain the flight of infinitely-wide wings. They're a very useful shortcut in calculation, but they offer no explanation.

The flight of an infinitely-wide wing is almost the same as a finite one. If you're just trying to see the principle, you're good. I know of one glider that was laid out using 3D methods. All the others usually don't do that because apart from the outer 5% of the wing and a small part at the wing root, air behaves precisely as in a 2D simulation, on a highly stretched glider wing.
wbeaty wrote: To explore the hidden flaw in infinite-wingspan diagrams, just ask yourself where the other end of the 3rd-law force is located. There's an upward force on the airfoil, but where is the equal downward force? Answer: it's expressed as a pressure pattern on distant solid surfaces.

If you go just a little closer to the airfoil: it's expressed on air mass being moved downwards by the airfoil. Look at potential theory. You are pushing air around and that results in lift.
In a CFD computation, you're usually using a "far field" boundary condition, which stets a constant velocity and inflow direction, but will accept any variables where the flow exits the simulated far field. Now you have to ways of determining the lift from the results: You either integrate the pressure distribution over the surface of the airfoild or you integrate the impulse (that's velocity times density) over the surface of the far field boundary (or any other closed path around the airfoil. If your simulation is good, they will always arrive at the same result. There is of course always some numerical error, because you computer uses a finite volume discretisation and numbers are of finite accuracy and so on, but if the grid is fine enough, you're good!

Why don't we need a ground? Why would we? An aircraft doesn't need one, either. It could fly on a planet with no ground (a gas planet) just the same. The thing you're exerting the opposite of the lift force on is the fluid around you. What that does with this force does not need to bother you. Lifting vortices will decay via friction, the downard movement is eventually stopped by the ground (or not, if there isn't one), but that's really a detail that can't keep lift from being generated and therefore is not important when it comes to explaining it.

wbeaty wrote:Whenever infinite wingspan is used, the distant Earth's surface (or the distant walls of the wind tunnel) could either be close by the airfoil, or light years distant, and the instant down-force remains the same.

That is physically correct! As long as the ground isn't really close, it has no effect. You're pushing air downwards. What it then goes on to do with the impulse you've supplied it with is no your business, unless the ground is so close that the reaction of the air hitting the ground (local pressure increase will still affect your airfoil. That's called "ground effect", and it creates additional lift. But let's not get distracted. I'm afraid I already am
wbeaty wrote: The down-force on the wind tunnel is independent of the tunnel's width. In other words, withdrawing the floor and ceiling to arbitrarily large distance is ineffective. You can't get rid of the floor and ceiling or the down force, all you can do is refuse to include them in the diagram. But that sets up a misleading situation which violates Newton's 3rd.

Oh no sir, you don't violate laws of physics. You can't.
The potential flow equations, the Euler and the Navier-Stokes equations are all built around energy and momentum conservations. If I make a computations using any of these models, and the result converges, than that means that the solution is in agreement with all of the equations and thus with all the laws of physics that went into them.
Also, you speak of "diagrams". If I'm drawing a diagram by hand, of course the result will be inaccurate because I can't draw very well. The thing is just, no engineer draws a diagram by hand and than changes it until he likes it better and calls the result an airfoil design (ok, some might do that, but their geniuses). You get a geometry, you build a grid, you specify boundary conditions (speed, angle of attack and so on), you wait for a solution. That solution includes values for lift, drag pitching moment and what will you. It's amazing how precise those results can be if you paid attention to what you're doing, and there's no floor or ceiling included.
wbeaty wrote: I suppose you could try withdrawing them to infinity rather than to billions of miles, but it would create an un-physical situation: an infinite wingspan at infinite distance from a surface. Does the force on the distant surface suddenly go to zero when that distance hits infinity, yet the force remains constant for arbitrarily large values? Think hard, don't just choose an answer.

Ahhh.... I think I understand your problem. A bit.
No, the force that the air you pushed around exerts on the ground does not "suddenly" go to zero. It gradually goes to zero.
In a two-dimensional potential flow (that's a simplified model with no friction and no solid body rotation) every disturbance decays like the inverse of the distance from its origin. If you do have friction (or in 3D, where it's the squared inverse), it goes even faster. Now if your ground is really far away, the pressure difference noticed there will be asymptotically approaching zero with increasing flight altitude.

This means of course that the force will only be distributed over a larger area of the ground. Which will be very far away from the airfoil. So the reaction that the air will have to the presence of the ground is extremely small already. The effect on the flow around the airfoil will be even smaller by the same factor, thus can be comfortably ignored.

Imagine a supersonic airplane (or a supersonic airfoil in 2D -- big difference in your eyes, but it's really the same principle). Anything the airfoil does to pressure travels at the speed of sound, so the ground below the airfoil isn't even "aware" of what's passing over its head, until it's gone and the sonic boom hits it. The ground will reflect the shock wave, in essence putting the air that the airfoil deflected back into a "normal" state, but that reflected shock will be far behind the airfoil, and since it's faster than the speed of sound, the reaction of the ground can never ever reach the airfoil. If someone makes a computation of a supersonic case, the volume taken into account behind the model can be very small since nothing that happens there can affect the flow anyway, so why bother?
You are still right in that the kinetic energy that I put into the air will not magically dissappear. But the thing is that this doesn't have any influence on whether the airfoil creates lift. It's probably harder to imagine because there's no fixed point to "hold on to", but who needs firm ground when you can fly? )
wbeaty wrote:As I understand it, the solution is simple: *always* include the starting vortex, and make sure the distance between the airfoil's bound vortex and the starting vortex is << than the distance between the airfoil and the Earth's surface. In that case the force on the Earth does go to zero as you pull the Earth away to arbitrarily large distance.

OK, we're in the mathamatician zone here. Anyone not wanting to get thoroughly confused (if you aren't already...), don't read this:
You need to formally include the starting vortex in a potential flow analysis, because the potential flow equations demand that a vortex cannot end inside the flow field.
The same reasoning explains the wing-tip vortices, which also strictly speaking cannot end within the flow field.
These are also of big importance when analyzing a configuration and trying to separate friction, wave and lift-dependent drag and so on. You can make a Navier-Stokes computation, get all the forces by surface integration, and then find out the single components of drag and lift by analyzing the vortices, supposed your grid is fine enough and the method good enough to represent them well.

However, in real life, where there is friction, these vortices and especially the starting vortex are being dissipated by means of friction. You cannot measure the stating vortex of an aircraft that took off somewhere three hours ago. If it's so weak you cannot measure it, and it's thousands of kilometers behind the aircraft, it stands to reason to assume that it doesn't actually still influence the aircraft, although mathematically it must still exist!
Even in potantial flow analyses, usually the wingtip vortices are assumed to be "infinite". There's an analytical solution for a semi-infinite votex (starting at the wing tip and going to infinity behind it).
The more elaborate methods use a "vortex sheet", because actually you are creating vortices wherever the wing lift is changing, because the lifting vortex that represents your airfoil is changing its strength. But still, these are modelled as semi-infinite vortices. And they can, too. Because the starting vortex that would tie up their ends, is so far away that although it mus exist, it is completely irrelevant to the actual flow around the model.

Another view: You are using your airfoil to push down air, which creates vortices (because face it: what goes down must come up in a continuous fluid), so the air gains kinetic energy while the airfoil passes through. This kinetic energy (equal to inviscid drag of the airfoil times distance traveled) is contained in the vortices. Once you leave a piece of vortex behind you, it does tell a story of what you did to it, and it does still influence the flow field you're in for a little while, but once you've left it behind for good, it cannot hurt you any more, except if you come back. It might to something to someone else coming its way, but apart from that, all it does is to contain the kinetic energy you left behind, and eventually fade to nothing. Sad fate, and I appreciate if people care for that. They're cruel things, airplanes, aren't they?

Ok, this post is so long I got logged out while writing it. So I'll just stop here. If you don't understand something or feel the need to disagree, PM me.

And congratulations to anyone who made it this far )

Zak
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### Re: 0803: "Airfoil"

jmorgan3 wrote:As I said in my last post, there is no boundary surface in 2D potential flow diagrams...

Oops, I posted a brief msg while working on a response to your earlier one. My words aren't clear enough so we need diagrams, perhaps an animation! Seriously. In the mean time here's the Anderson/Eberhardt explanation of flight. (Unfortunately they don't treat the specific misconceptions caused by 2D airfoil diagrams.)

A Physical Description of Flight (PDF)
http://www.allstar.fiu.edu/aero/Flightrevisited.pdf

.
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### Re: 0803: "Airfoil"

Zak McKracken wrote:Ahhh.... I think I understand your problem. A bit.
No, the force that the air you pushed around exerts on the ground does not "suddenly" go to zero. It gradually goes to zero.

Bingo, that's the problem ...because in a 2D world the net force on the ground doesn't gradually go to zero.

It doesn't decrease at all.

As I understand it, the "disturbance" decreases in inverse proportion with distance from the airfoil, but the pressure pattern on the 2D Earth simultaneously increases in width (area,) and the effects cancel out. The down-force experienced by the 2D Earth remains constant with 2D airfoil altitude. A 2D airfoil can never fly high enough to escape from venturi-like Ground Effect mode.

I'm complaining because 2D potential flow diagrams explain ground effect, they don't explain flight. 2D diagrams fail because they miss the fact that 2D flight is an exotic anomaly. They fail because we try to remove the ground-effect by simply deleting the ground! That violates Newton.
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### Re: 0803: "Airfoil"

wbeaty wrote:
Zak McKracken wrote:Ahhh.... I think I understand your problem. A bit.
No, the force that the air you pushed around exerts on the ground does not "suddenly" go to zero. It gradually goes to zero.

Bingo, that's the problem ...because in a 2D world the net force on the ground doesn't gradually go to zero.
It doesn't decrease at all.

Hmm... correct. The disturbance decreases, but since it also widens, the force will stay constant, at least in inviscid flow. Yes, I didn't get that right first time.
The thing is just: If there is no ground in your control volume it will hardly be able to exert any forces on the airfoil, will it?
wbeaty wrote: As I understand it, the "disturbance" decreases in inverse proportion with distance from the airfoil, but the pressure pattern on the 2D Earth simultaneously increases in width (area,) and the effects cancel out. The down-force experienced by the 2D Earth remains constant with 2D airfoil altitude.

yes, agreed. I think we're slowly getting to the point.

wbeaty wrote: A 2D airfoil can never fly high enough to escape from venturi-like Ground Effect mode.

And this is where you are mistaken.
Take a simple potential flow model of a 2D-Airfoil. That's a constant flow overlaid with a vortex and a couplet (giving you a representation of a rotating cylinder). In an infinite space. No wall, no ground. The nice thing is that with potential flow, you can compute flows in infinite space, as long as the singularities you're using are in a finite space. Since this is a valid solution of the potential flow equations, this must obey momentum conservation. And it does!
The upward force on the cylinder surface, that you get from integrating the force over its surface does see an equivalent downwash of fluid behind the airfoil! If you take any closed path around the airfoil and integrate the momentum of fluid entering/leaving the enclosed volume, you'll see that it is being deflected downwards. Speed times density integrated over a volume gives momentum and in this case it's equal in value and opposite in sign to the lift created by the airfoil.

Now, about ground effect. The rule-of thumb is "half wingspan". If you're closer to the ground, you get significant ground effect. With an infinite wing, that would mean: always. Problem is that the rule-of-thumb is just that.

Back to our potential flow model. The boundary condition of a solid wall can be fulfilled by adding an "image" of the airfoil mirrored in the ground. This will cancel out all the vertical movement in the plane of symmetry, which is the ground (I hope you know enough about potential flow models to understand all this...).
Now, if the ground is close, the ground effect can be easily seen, because the mirror image below the ground not only cancels vertical fluid movement at the ground but also induces a certain additional velocity distribution at the location of the real airfoil. This will increase the lift (as the airfoil is facing its sibling's pressure surface, the velocity will be smaller the closer you go to the ground, due to the presence of the ground. That means overall pressure increase, but more so towards the presure surface, thus lift increase.
Now, lets move the ground away a bit.
The mirrored airfoil will always be twice as distant as the ground, and its influence will decay as the inverse of that distance. So even though we are regarding an infinite wing, the influence of the ground effect must be decaying! The mirrorred vortex below the ground doesn't get any stronger, and rather quickly the pressure gradient will be completely neglibile. A few cylinder diameters (equivalent to airfoil chord length) will be enough for that.
This teaches us that the rule-of-thumb for where ground effect occurs should be revised and rather be given as a certain multiple of chord length, at least for aircraft with large aspect ratio wings.

WTF? Didn't we just say that the force on the ground doesn't change? Right! But it's distributed over a larger area. Now the effect of that huge area of very very slight pressure increase on the ground is an even larger area of even slighter pressure increase at the height of the airfoil. So slight that you can completely forget about it. If you remove th ground even further, the force exerted on it actually doesn't change (you're right), but the influence that has on the airfoil still goes asymptotically to zero.

Another word on "venturi-like": The basic ground effect is what I described above. It can be explained with potential flow models without problem. Mind that there's no venturi-thing going on there, though!
That only becomes relevant when the wing is closer than one chord lentgh to the ground. The problem then is that not only the "far field effect" of the wing is reflected by the ground but you're actually building a channel below the wing, where the air at the trailing edge (given positive incidence) will be accelerated, and before that will be slowed down significantly more than in free air. This is something that cannot be modelled with just a simple lifting vortex. Potential flow can model this, but you'd need a lot more than just a vortex and a couplet.

I think the point you're missing is something like this: If you have a technical system, regarding any control volume must lead to correct results. You can make meaningless or overly complicated choices for the control volume, but in the end they cannot condradict each other. So if I choose to not include the ground in my control volume (which simplifies things a bit), I must still get the right result. Any physical model of a flow that would require the inclusion of a ground, however far away, and not allow me to just regard the area around the airfoil, cannot be quite right.

The following things are equivalent, and barring computational inaccuracies should yield the same result:
1. Integrating pressure over the surface of the airfoil
2. Integrating momentum over any closed path around the airfoil
3. Extending the simulation to include the starting vortex (and use a physical model that loses zero circulation!) and compute the kinetic energy in all the vortices (needs knowedge of starting point, distance traveled and so on. constant speed would make things easier, too)
4. Extending the simulation to include a ceiling and a ground and integrating pressure over those (You'll have to get drag from somewhere else then, though. And the presence of those walls will change the flow field, unless they're properly far away, and then you're intagrating a very small value over a large surface, which is inaccurate, unless you can do it analytically, meaning you do have to use potential flow)
5. Extend the simulation to include the complete atmosphere, then integrate over Earth's suface and upper atmosphere's surface ... now that's just plain stupid.

Oh, another point that may be a misconception: Your animated picture with the "flat balloons" (actually no bad way to explain lift in very general!) could create the misconception that the wing-tip vortices contain solid-body rotation. They don't. In a potential vortex (and vortices in fluids are like that, escept in the very center, where friction is dominant), the circumferential speed decays with the inverse distance from the center. So if you have a vortex at the wing tip, the center wing is pretty unimpressed by that, espacially since it faces only the end of a semi-infinite vortex.
In your animation, the circumferential velocity goes up with distance from the vortex core, so that might somewhat increase the perceived influence these vortices have on the flow. I whish I had some animation somewhere that illustrates the difference ... haven't

I hope this explanation makes more sense to you ... if not, feel free, this is actually really good exercise I'll just need to find out how to use fewer words.
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### Re: 0803: "Airfoil"

You're both wrong. Asians discovered America about 8000 years (+/- 6000...) before the Vikings.

That's also true, of course, but again, the Europeans didn't know about it, just like Columbus and his associates were unaware of the Vikings' discovery. If someone claimed that Columbus (or Erickson) were the _first_ human to discover the Americas, that would obviously be wrong, but he DID (inadvertently) discover them, and furthermore it is historically very important, because it lead more or less directly to European colonization of most of planet, which is why seven or eight of the top ten most important world languages today are European languages. Chinese and Arabic are really the only major world languages (widely important and widely studied as foreign languages significantly beyond their geographical region of origin) that are *not* from Europe. (Okay, arguments could also be made for certain dead languages, most notably Sanskrit, but they are at this point not important for the same kinds of reasons.) English, Spanish, French, German, Dutch, Portuguese, Italian, and Russian are all European languages. This is not a coincidence. With the possible exception of Russian, they are all important (beyond local importance in Europe) specifically because of European colonization that really got seriously underway directly because of Columbus and his discovery.

So yeah, it had been discovered before. But that's missing the point.

tucsonspeed6
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### Re: 0803: "Airfoil"

shotgun.shenanigans wrote:Gotta say, as a future high school physics teacher, I love this comic. In fact, I remember doing a science fair project on this very concept when I was in high school.

I think this will become a topic in my class at some point. Now to get through the rest of university.

By the way, this will never happen to you. No matter how engaging your methods are, most of your class won't be able to care less about what you try to teach them. While you go into the exciting details of science, all but a handful of your students will be trying to take a nap. You should prepare yourself more for questions like "I'm never going to use any of this, so why do I have to learn it?" They'll even ask questions like this when you teach them simple things like how to take accurate measurements with a ruler. And have a good answer prepared because they're all going to be future celebrity millionaires, rockstars, models, and professional athletes, and they'll have tons of money to pay other people to do everything for them. And no, I'm not a crotchety old teacher hanging out in the teacher's lounge. The state of today's education system has less to do with teachers who don't care enough and more to do with MTV.

Ghavrel
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### Re: 0803: "Airfoil"

tucsonspeed6 wrote:And no, I'm not a crotchety old teacher hanging out in the teacher's lounge.

Yes, you are.

tucsonspeed6 wrote:The state of today's education system has less to do with teachers who don't care enough and more to do with MTV.

While it's dangerous to put the blame of such a large problem on any one factor, unqualified and uninteresting teachers are certainly a large part of it. Uninterested students are another.
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### Re: 0803: "Airfoil"

tucsonspeed6 wrote:By the way, this will never happen to you. No matter how engaging your methods are, most of your class won't be able to care less about what you try to teach them. While you go into the exciting details of science, all but a handful of your students will be trying to take a nap. You should prepare yourself more for questions like "I'm never going to use any of this, so why do I have to learn it?" They'll even ask questions like this when you teach them simple things like how to take accurate measurements with a ruler. And have a good answer prepared because they're all going to be future celebrity millionaires, rockstars, models, and professional athletes, and they'll have tons of money to pay other people to do everything for them. And no, I'm not a crotchety old teacher hanging out in the teacher's lounge. The state of today's education system has less to do with teachers who don't care enough and more to do with MTV.

Makes me think of
"The children now love luxury. They have bad manners, contempt for
authority, they show disrespect to their elders.... They no longer
rise when elders enter the room. They contradict their parents,
chatter before company, gobble up dainties at the table, cross their
legs, and are tyrants over their teachers."

On the other hand US American high school students are - on average - two years behind e.g. German high school students in math and I don't know how much in science. What could be the cause? Certainly not MTV, we get that here, too. I have four theories about this, the first two I read in US American newspapers (can't remember which ones), the third one is my own from having attended a US high school for one year, and the fourth one is a combination of my experience in the US and a German newspaper article about the German school system.

#1 (from a newspaper): Malnourishment. Sure, American kids, even of the poorest parents, are not starving. They are even more likely to be overweight rather than underweight (just as German poor children). Nevertheless many children only get the free school (or preschool / head start) breakfast and lunch and the parents may not be able to buy dinner or provide sufficient and/or healthy food on weekends for some periods of the early childhood. The article went on to explain that this causes slight brain damage. This reduces the IQ by several points and, most importantly, severely impares the desire to learn.

#2 (from a newspaper, about math in the US compared to other countries): Concentration on fractions. That article blaimed the fact that US kids apparently spend several years of math classes mostly on practising fractions instead of going to higher-level math. This matches one thing I witnessed: US kids in elementary schools seem to be ahead of German students! Something must go wrong in middleschool / junior high that puts them so far behind. If this is fractions, no idea, I did not know any middleschool kids.

#3 (my theory): Low expectations. Prohibit multiple-choice, true-false, fill-in-the-blank, open-notebook and open-book tests. Free answer only. See your kids' performance (true performance, not test scores) rise to unexpected heights. (With the exception of fill-in-the-blank all these test forms are unheard of in Germany, and I think I only ever had one fill-in-the-blank, not considering foreign language tests for grammar.)

#4 (combination of my theory and the German news article about German schools): Choice. Apparently it is a serious error to let middleschool students and young high school students choose their subjects and difficulty level. Naturally most of them will choose the easier and "more fun" classes.
In Germany it's even worse, the kids are sorted into separate schools (three levels) after primary school (i.e. after 4th grade). Some states have comprehensive schools. In some states these are really only schools with all three school types, i.e. separate classes, but in others the difficulty level can be chosen by subject, similar to the US school system. In these schools the kids on the highest of the three difficulty levels fare worse than those kids in the highest school type. One possible explanation is the negative effect of choice: They may have been in lower classes in some subjects by their own decision in earlier years. This is what that newspaper article suggested. But there are other possible explanations, it could be the statistic effect called stage migration or Will Rogers phenomenon. In a comprehensive schools more kids are likely to aspire the highest possible high school degree. So naturally there will be more kids who just barely make it, so the average score in this school type will be lower. Besides this, the kids with the highest scores in 4th grades are most often sent directly to "Gymnasium", the highest school type, so in the comprehensive schools there will be mostly kids who didn't make it in 4th grade.
Nevertheless I think that letting kids choose their subjects and difficulties on a large scale is an error because it results in choosing simple subjects and low levels. For example the only choice I could make in years 1-10 was whether I wanted to learn French or Latin as the second foreign language (after English as the first). Depending on the state and school type there is usually a second choice for a language or alternate subject in grades 9 and 10. But that's it. (Except for [some] comprehensive schools.)
However, in grades 11-13 we get to choose subjects (within restrictions). And of course I made the lazy choice to get better grades . E.g. I had to choose between biology and physics (I could have taken both only if I dropped Italian). I chose physics. There I was not going to learn much because I came from a school that focused on this. In biology I would have learned much more.
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### Re: 0803: "Airfoil"

Just to give some background, I have a Masters in Aerospace Engineering. I am a huge fan of this comic, but this one bothered me.

It is not totally correct to call this theory wrong. While the idea that the two particles on upper and lower surfaces meet at the trailing edge is not true, it is true that the local velocity on the upper surface is higher than the lower, resulting in lower pressure on the upper surface. This image (http://www.cartage.org.lb/en/themes/sci ... ldist2.gif) is a good example of a typical pressure distribution on an airfoil. The key point being that the lower pressure on the upper surface, relative to static pressure, has a larger effect on net lift than increased pressure on the lower surface.

The fact that aircraft fly upside down does not conflict with the theory of curved surfaces inducing faster moving air. The question is simply answered by the fact that wings generate steady-state lift from two sources: camber (A difference in curvature between the upper and lower surfaces) and angle of attack (the angle with which the wing meets oncoming air). A wing with camber will generate lift at zero angle of attack. Therefore, for a cambered wing to fly upside down it would have to compensate for this by increasing its angle of attack. Please see lift-curve slopes in Abbott and Von Doenhoff for more information about this.

A more commonly misunderstood principle, even among aerospace engineers, is the relationship between velocity and total and stack pressures. In a wind tunnel, increasing velocity means static pressure decreases, but total pressure remains constant. However, in an aircraft increasing speed means total pressure increases and static pressure remains constant. I had a high school teacher try to claim that while driving in a car the pressure outside the windows would decrease according to our velocity via Bernoulli's principle. This is definitely not correct and has bothered me ever since.

Technical Ben
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### Re: 0803: "Airfoil"

wbeaty wrote:To eliminate your own misconceptions, longrunning arguments with physicists helps greatly. A skeptical approach to existing textbooks helps greatly.

Discovering the NASA GRC website helps greatly:

http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html
http://www.grc.nasa.gov/WWW/K-12/airplane/wrong3.html
http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html
http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html

I should probably read the wall of text AFTER your post, but it seems to miss the point. You win the thread.
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### Re: 0803: "Airfoil"

I remember back in school I did all the sciences, physics, chemistry and biology.
We had a really good chemistry teacher who's I'm told confided in my parents at the parent teacher meeting that I was probably the person in the class most likely to end up in actual science (I have) she was worried that I'd score poorly in the leaving cert exams because i was far more interested in real chemistry and the stuff beyond the scope of the course than in the high school level course.
She was actually right, i scored bellow people who put their time into memorizing the book rather than understanding it but I got enough points for my course anyway so i'm not too bothered.

I was kinda lucky though.
both my physics teacher and chemistry teacher knew their subjects and were never afraid to explain the more complex version when I pointed out logical problems introduced by the nature of the simplifications in the schoolbooks.

I still remember the explanation my physics teacher gave when I complained about the books take on satalite dishes.
I'd extended the diagram a little to show how it clearly didn't work.

He explained how, yes the book is actually wrong, it was a simplification and then went on to show the difference between a section cut out of a circle and a parabola and did the calculations to show that while it was wrong it would still be incredibly close as long as you stuck to a 5% section of a circle for any reasonably sized dish.

Normally they seemed quite happy if I spotted such stuff.

My biology teacher wasn't so hot on his subject and tended to just sort of mumble and not really explain anything better.
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### Re: 0803: "Airfoil"

Zak McKracken wrote:
wbeaty wrote:
Zak McKracken wrote:Ahhh.... I think I understand your problem. A bit.
No, the force that the air you pushed around exerts on the ground does not "suddenly" go to zero. It gradually goes to zero.
Bingo, that's the problem ...because in a 2D world the net force on the ground doesn't gradually go to zero.
It doesn't decrease at all.

Hmm... correct. The disturbance decreases, but since it also widens, the force will stay constant, at least in inviscid flow. Yes, I didn't get that right first time.
The thing is just: If there is no ground in your control volume it will hardly be able to exert any forces on the airfoil, will it?

Thanks for sticking with this! I'm looking for errors in my amateur understanding of basic aero, and if I don't find them, probably I'll end up writing more articles aimed at the public. Translating irro flow and vorticity into terms easily understood by little kids! Sorry for the long delay. I was figuring out how to post quick little GIF drawings here as needed.

Zak McKracken wrote:
wbeaty wrote: A 2D airfoil can never fly high enough to escape from venturi-like Ground Effect mode.

Now, about ground effect. The rule-of thumb is "half wingspan". If you're closer to the ground, you get significant ground effect. With an infinite wing, that would mean: always. Problem is that the rule-of-thumb is just that.

Nope, it still applies here. See below.

Zak McKracken wrote:Back to our potential flow model. The boundary condition of a solid wall can be fulfilled by adding an "image" of the airfoil mirrored in the ground. This will cancel out all the vertical movement in the plane of symmetry, which is the ground (I hope you know enough about potential flow models to understand all this...).
Now, if the ground is close, the ground effect can be easily seen, because the mirror image below the ground not only cancels vertical fluid movement at the ground but also induces a certain additional velocity distribution at the location of the real airfoil. This will increase the lift (as the airfoil is facing its sibling's pressure surface, the velocity will be smaller the closer you go to the ground, due to the presence of the ground. That means overall pressure increase, but more so towards the presure surface, thus lift increase.
Now, lets move the ground away a bit.

Yep. You're talking about the interaction between circulation and a wall. There are two sources of "ground effect" here: an image-force caused by circulation alone, and a very large lifting force caused by superposing circulation with constant wind and then squaring the result to obtain a pressure pattern that connects the airfoil surface with the ground surface. (The 2D force-pattern causing the flow-turning looks like flux lines between groups of electric charges.) I agree that the circulation-image force is insignificant and falls with inverse proportion to distance. It's also attractive to surfaces, I think, so it's opposite of lift. In EM analogy it's the small interaction between the superconductive ground surface and the electric current inside the airfoil.

But on the other hand, the airfoil circulation superposed with constant wind is creating an upward force on the airfoil, and simultaneously causing an equal downward force on the ground. There's an instant pressure pattern connecting them. That's why I call it "venturi," even though the force is independent of the distance between airfoil and ground. This is an instant or "contact" force, because any change in wind velocity or in circulation will instantly alter the whole 2d pressure distribution and change both the lifting force and the downward average pressure. So, a direct force-pair exists between the airfoil and the ground. The two ends of the force-pair are created by the flow pattern, just as happens in a venturi. That's why I insist it be called "Ground-effect flight." Also, the airfoil injects momentum into the air, and the ground instantly removes it again. We have a momentum source and sink. It's just as if the 2D airfoil was pushed off the ground by magnetic repulsion.

We can remove the ground to finite distance and ignore it, but only as long as we accept that both the instant downforce and the momentum still end up on the ground. But we can't do as the 2D diagrams do: cannot delete the ground or discard it to infinite distance. That violates Newton's 3rd, and violates conservation of momentum. Sure, it's OK to delete the ground and replace it with a starting vortex. In that case the down-force really does land on the air, and the momentum really is injected into a region of air.

Zak McKracken wrote:I think the point you're missing is something like this: If you have a technical system, regarding any control volume must lead to correct results. You can make meaningless or overly complicated choices for the control volume, but in the end they cannot condradict each other. So if I choose to not include the ground in my control volume (which simplifies things a bit), I must still get the right result. Any physical model of a flow that would require the inclusion of a ground, however far away, and not allow me to just regard the area around the airfoil, cannot be quite right.

That's the mistake. In fact it actually is "quite right." Why?

The forces are instantaneous contact forces mediated by pressure patterns. On the whole, there is no "reaction engine" involved. If the ground was not there, then the momentum injected into the air by the airfoil does not end up deposited in the air. I see many texts which say the opposite, but they're simply wrong. Instead the momentum radiates instantaneously outwards to infinity. It never stops and sits on any air parcel. There is no momentum-sink local to finite space, so momentum conservation is violated. Also, if the ground was not there, then the lifting force's force-pair doesn't land on empty air. (Again, I've seen texts that say the down-force is on the air. They're wrong. They're teaching a misconception. That's important.) Instead the force and the pressure pattern radiates outwards to infinity. The airfoil deflects the air, but there's no ground to deflect it back again. As I understand it, vector "flux lines" of aerodynamic forces must terminate on vorticity sheets associated with surfaces (as with a venturi,) or must be associated with free regions of vorticity, as with propulsion by vortex-shedding. Neither of these appears in 2D diagrams, so these diagrams break all three of Newton's laws. But isn't this topic for advanced classes only? No. I'm convinced that these flaws have enormous educational consequences, but consequences which are hidden. The confusion they cause is obscuring their enormity. I'm certain about how large they are, because when I got past them myself, I ended up like Feynman running around yelling "Now I understand EVERYTHING!!!" The long-broken connections in my simple mental modeling were restored, and "aerodynamics" for me started running like a machine. Until that moment I had no idea how crippled it had been.

It's true that the weeping and teethgnashing of elementary airfoil controversy is mostly associated with "Bernoulli vs Newton" mistakes. But once I started staring at it unblinking, I found that some large portion of confusion had some mysterious origin. I tracked the conceptual flaws and found that they radiate (!) from enormous Newtonian violations built into 2D airfoil diagrams. The diagrams depict ground-effect flight, but they state that they're explaining flight at altitude. The diagrams depict single-ended forces, then wrongly state that the force-pair's downforce end lies on the air. They depict momentum-violations, then wrongly state that the airfoil deposits the down-momentum into the air.

Zak McKracken wrote:The following things are equivalent, and barring computational inaccuracies should yield the same result:
1. Integrating pressure over the surface of the airfoil
2. Integrating momentum over any closed path around the airfoil
3. Extending the simulation to include the starting vortex (and use a physical model that loses zero circulation!) and compute the kinetic energy in all the vortices (needs knowedge of starting point, distance traveled and so on. constant speed would make things easier, too)
4. Extending the simulation to include a ceiling and a ground and integrating pressure over those (You'll have to get drag from somewhere else then, though. And the presence of those walls will change the flow field, unless they're properly far away, and then you're intagrating a very small value over a large surface, which is inaccurate, unless you can do it analytically, meaning you do have to use potential flow)
5. Extend the simulation to include the complete atmosphere, then integrate over Earth's suface and upper atmosphere's surface ... now that's just plain stupid.

#5, not stupid, since in 2D we're dealing with a span which is infinitely wider than the atmosphere thickness. We have to include the complete atmosphere because, with 2D airfoils, the pressure-footprint on the ground integrates to a constant force, expanding or contracting in width depending on altitude. With real 3D wings this entire phenomenon is missing. It's a strange piece of "Flatland World" physics which is not present in our world. 3D wings are like dipoles with forces falling off rapidly. But the 2D lifting-force is crazy stuff; like magnetic attraction between wires and sheet-conductors of infinite length.

I think Number 2 above is key. A closed path around the airfoil will show the outward flow of the down-momentum injected into the air, correct? OK, increase the diameter of the closed path. Momentum stays constant, right? No momentum is left in the air, it all passes outward through the closed path. Increase the closed path to any finite diameter, and you find that momentum still goes outwards and none remains in the air parcels within the closed path: a momentum source but no sink. No momentum ever sticks to the air. That's how 2D flow diagrams violate momentum-conservation.

Zak McKracken wrote:Oh, another point that may be a misconception: Your animated picture with the "flat balloons" (actually no bad way to explain lift in very general!) could create the misconception that the wing-tip vortices contain solid-body rotation. They don't.

Yep yep, that's part of the original article. The animation is one figure from a simplified description which mentions solid body versus irro flow when calculating the work done in "throwing down air" to keep a 3D wing aloft. But the central issue is the downward-moving volume becomign the "exhaust" of a reaction engine. Any circular flows inside that volume are conceptually the same as rocket-exhaust turbulence. I guess I could have used solid non-rotating balloons, then painted them with frictionless paint for infinite surface slip, then cast them downward to lift the wing upward.

Zak McKracken wrote:I hope this explanation makes more sense to you ... if not, feel free, this is actually really good exercise I'll just need to find out how to use fewer words.

Excellent exercise, combing greasy knots out of my brain. Now I understand... (everything)^2 !!!
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### Re: 0803: "Airfoil"

Oh me yarm WBEATY IS HERE! :O I am a fan of you! You are so inspiring!

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### Re: 0803: "Airfoil"

wbeaty wrote:
Zak McKracken wrote:I hope this explanation makes more sense to you ... if not, feel free, this is actually really good exercise I'll just need to find out how to use fewer words.
Excellent exercise, combing greasy knots out of my brain. Now I understand... (everything)^2 !!!

I'm sorry to disagree there. But the full answer will need more time than I have today, so you'll have to wait.

I'll just give you an image for the time being:
A rocket in space. No ground, no atmosphere, no vortices. A planet? Maybe, somewhere. But does it influence the rocket at all, (other than by gravitation of course)?

Oh, and a second: You sit on a wheelchair, with a gun in your hands. You fire forward, propelling yourself backwards. Does it matter if you hit anything?
(apart from maybe if you hit someone, or what you hit was precious to anyone or maybe someone's dog which they loved very much, and now they're upset and call the police and they give you a good beating and stuff...I'm just talking about the impulse it gives you).
Would it matter if there was a black hole somwhere in the (safe for you) distance, and you hit that?

Cheers,
Zak

If a tree falls into a black hole, does it make a noise? ;o)
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### Re: 0803: "Airfoil"

wbeaty wrote:Thanks for sticking with this! I'm looking for errors in my amateur understanding of basic aero, and if I don't find them, probably I'll end up writing more articles aimed at the public. Translating irro flow and vorticity into terms easily understood by little kids!

This discussion is awesome. I dont know vorticity, but some things seem odd here on a more basic level.

wbeaty wrote:But on the other hand, the airfoil circulation superposed with constant wind is creating an upward force on the airfoil, and simultaneously causing an equal downward force on the ground. There's an instant pressure pattern connecting them.

So, I guess I dont know what 'constant wind' means, but how exactly would pressure affect anything instantly? I'd think the speed of sound would be a limit (or speed of light..).

There should be a time factor involved in transfering force or pressure from plane to ground, during which the plane travels some distance. If the ground is far away, no interaction?

wbeaty wrote:#5, not stupid, since in 2D we're dealing with a span which is infinitely wider than the atmosphere thickness. We have to include the complete atmosphere because, with 2D airfoils, the pressure-footprint on the ground integrates to a constant force, expanding or contracting in width depending on altitude. With real 3D wings this entire phenomenon is missing.

What's wrong with constant pressure footprint?

If we include the earth for a moment, we have gravity affecting both plane and planet. Plane keeps it's altitude because of lift and wings doing something to the atmosphere; why does the planet stay still? What I mean to say is that the pressure-footprint on the ground ought to add up to the same in either 2d or 3d or it wouldn't be a stable situation.

wbeaty wrote:Yep yep, that's part of the original article. The animation is one figure from a simplified description which mentions solid body versus irro flow when calculating the work done in "throwing down air" to keep a 3D wing aloft. But the central issue is the downward-moving volume becomign the "exhaust" of a reaction engine.

The balloon concept is a very neat illustration. However, in the example I could just run on top of the balloons without making them spin at all, and would be easier. Is there a reason rotating cylinders of air can carry momentum downwards, but nonrotating air cannot?

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### Re: 0803: "Airfoil"

Zak McKracken wrote:I'm sorry to disagree there. But the full answer will need more time than I have today, so you'll have to wait.

Very understandable! I barely have time to work on this myself. But I'm repeatedly sucked in because there exists a very irritating hole in my connected mental concepts. Dangling chemical bonds. Missing piece of the puzzle.

Zak McKracken wrote:I'll just give you an image for the time being: A rocket in space. No ground, no atmosphere, no vortices. A planet? Maybe, somewhere. But does it influence the rocket at all, (other than by gravitation of course)?

Yes, that's vortex-shedding: in miles-deep ocean, a ROV turns on a thruster. It presses upon no surface, yet propulsion occurs because water intake is radial, while water outlet is a narrow jet. Or instead, an abyssal jellyfish pulses once, accelerating itself forward while emitting a vortex ring backward. These illustrate how 3D aircraft fly.

But 2D airfoil diagrams don't describe vortex-shedding propulsion. Are they offered as an explanation of flight? No, instead they shatter any hope of attaining intuitive understanding of flight. At least they did so in my own case. Now a helicopter, if it hovers miles above the Earth, and turns it's rotor on and off, that's the stuff right there. A yummy concept, contains no poison pills which are toxic to brain matter. Give our constantly-hovering 'copter a brief sideways shove so it momentarily drifts along, and you've now explained a fixwing aircraft. The piece of the puzzle finally falls into place.

But those 2D airfoil diagrams are a misshapen piece which was hammered into the puzzle, and now the correct piece has no place to go. Why can't people understand the XKCD diagram that started all this? Simple: it's because it doesn't describe the basic process of vortex-shedding propulsion, and airplanes/jellyfish/helicopters/birds/insects all fly by vortex-shedding.
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### Re: 0803: "Airfoil"

wbeaty wrote:As I understand it, vector "flux lines" of aerodynamic forces must terminate on vorticity sheets associated with surfaces (as with a venturi,) or must be associated with free regions of vorticity, as with propulsion by vortex-shedding.

I think you're thinking of Helmholtz's theorems. If you are not, then please cite or prove your above statement.
Hermann von Helmholtz wrote:1.The strength of a vortex filament is constant along its length.
2. A vortex filament cannot end in a fluid; it must extend to the boundaries of the fluid or form a closed path.
3. In the absence of rotational external forces, a fluid that is initially irrotational remains irrotational.

Do 2D potential flow diagrams of wings obey these rules?
1. Yes, the vortex sheet (basically a smeared-out filament) along the airfoil is modeled as having no variation of vorticity with span.
2. Yes, the vortex sheet extends to infinity in the span direction, and fluid has bounds at infinity.
3. Yes, the fluid is irrotational outside of the airfoil.

wbeaty wrote:A closed path around the airfoil will show the outward flow of the down-momentum injected into the air, correct? OK, increase the diameter of the closed path. Momentum stays constant, right? No momentum is left in the air, it all passes outward through the closed path. Increase the closed path to any finite diameter, and you find that momentum still goes outwards and none remains in the air parcels within the closed path: a momentum source but no sink. No momentum ever sticks to the air. That's how 2D flow diagrams violate momentum-conservation.

Conservation of momentum does not require momentum "sticking" to any one object. If you think it does, please prove or cite. Alternately, draw control surfaces around some part of a 2D potential flow diagram of a wing and show that momentum is not conserved. For your convenience here is the control volume formulation of Momentum Conservation: http://en.wikipedia.org/wiki/Reynolds_t ... ormulation

EDIT: Because you never answered this from my last post, I'll ask it again:
Your link is actually a decent conceptual explanation of why finite wings produce drag when they produce lift, but it still does not explain why and how that lift is produced. How does that air under the wing get launched downward? How are those vortices (bound, starting, and trailing) produced? Under what conditions do airfoils push the air down? Would a cylinder work? An ellipsoid? A rotating cylinder? A flat plate? All of these questions are answered by 2D theory, but not by your balloon-pushing-down theory.
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### Re: 0803: "Airfoil"

Sorry for not answering. Too easily distracted!

jmorgan3 wrote:
wbeaty wrote:Nope, instead they explain the flight of infinitely-wide wings. They're a very useful shortcut in calculation, but they offer no explanation.
To explore the hidden flaw in infinite-wingspan diagrams, just ask yourself where the other end of the 3rd-law force is located. There's an upward force on the airfoil, but where is the equal downward force? Answer: it's expressed as a pressure pattern on distant solid surfaces.

There's a downward force on the air. You can take any set of points in a 2D potential flow field, make them a control volume, and test to see if momentum is conserved. It will be.

Agreed that parcels conserve momentum. That's not the problem. Because of weight force, the airfoil injects a constant flow of down-momentum into the air. Where does this momentum end up? Are there some parcels out there where down-momentum is accumulating? We look at a region local to the airfoil. Is down-momentum in the region constantly increasing? Doesn't seem to be. The airfoil injects it, but then each parcel transfers down-momentum to other parcels more distant. That seems obvious: the 2D diagram is a sort of static momentum-flow diagram with no slow accumulation of down-momentum injected by the airfoil (no slowly changing patterns.) The momentum constantly injected by the airfoil instead is flowing in a static pattern constantly outwards, right? So if it doesn't accumulate locally where does it all end up? (The answer had better not be "at infinity." The model cannot include infinity as a necessary element. But I see no other option.)

Or more specifically: can we enclose the 2D airfoil in a circular boundary of very large diameter, a diameter where the increasing down-momentum is all stored in air contained within the boundary, rather than all of the down-momentum just flowing outwards through it?

jmorgan3 wrote:The boundaries in 2D potential flows around airfoils are at infinity (incidentally, so are the boundaries in non-ground effect finite wing models).

But in a non-ground effect finite wing model, if the increasing down-momentum being injected by the airfoil is ending up trapped on some local parcels of air, then infinite boundaries are then OK. In that case, as the boundaries are moved out to great distance, the amount of momentum flowing out through boundaries will fall to zero. The 3D airfoil is then injecting momentum into the air, not into infinity. In that case the other end of the force-pair for the lifting force lands upon a region of the air, rather than landing upon infinity.

My suspicions about unnoticed flaws in 2D flow diagrams were triggered by Electromagnetic analogy: In a static model (no EM waves,) a current-carrying wire cannot apply a force to a pure b-field: currents can only apply forces to b-fields associated with some other pattern of currents in distant wires. The first wire pushes on the others, and vice versa, so Newton's 3rd is OK. In particular, if we tried filling all of space with a constant b-field and having a wire experience a force, we'd have created a single-ended force and a broken model with open non-circular b-field lines, where no other distant wires experience the first wire's reaction force, and where field-momentum flees outward to infinity but never lands on any particular region of space. In a static situation, b-fields mediate forces between wires, but cannot themselves behave as wires. Now I look at a wind tunnel and see that upper and lower walls are like current-carrying surfaces with opposite currents (a very wide solenoid,) with the airfoil being a single current-carrying wire being forced away from one wall and towards the other. It's like a venturi, with instant-forces connecting the airfoil to the walls. Can I remove those walls? No. Removing the walls violates Newton's 3rd. So then I wonder, is my conceptual trouble with 2D airfoil diagrams actually based on an analogous flaw? Hmmm. Seems so. The airfoil system seems to be violating momentum conservation by injecting down-momentum into infinity, rather than injecting it into particular parcels of air. The airfoil seems to be violating Newton's 3rd by terminating the lift reaction force on infinity, not upon some local parcels of air. The 2D diagram might be useful for engineering calculations, but it seems to require that the airfoil's lift be a single-ended force not part of Newton's laws. The airfoil isn't pushing against air, instead it's "pushing against infinity."

jmorgan3 wrote:It's a lot less arbitrary than setting a wall boundary condition some random distance below, and gives pretty much the exact same answer, as long as the altitude is more than an order of magnitude larger than the chord. It is an unphysical situation, but it gives an answer indistinguishable from an infinite wing at finite but large altitude. And an infinite wing becomes a better and better approximation as aspect ratio increases. Practical airplanes don't have such a high aspect ratio that one can ignore finite wing effects in airplane design, but I'm not arguing that 3D effects are useless, only that they aren't necessary to understand lift.

But I don't want to calculate lift, I want to *understand* lift. As with the Einstein quote, I want to understand lift sufficiently that I can explain it to my grandmother. I want to add it to my high-traffic website but without misleading tens of thousands of children. So ...an airplane flies by constantly dumping it's down-momentum into parcels of air, and these momentum-bearing parcels must be constantly growing as the airfoil proceeds horizontally. Down-momentum is stored in a wake behind the airfoil. In a 2D diagram this isn't happening. Where is the region of constantly growing momentum? If the lift equation somehow breaks Newton's laws, then it's only a convenient engineering trick for calculating lift, and is not an explanation of flight.

jmorgan3 wrote:The starting vortex ensures that the total angular momentum of the atmosphere is constant at zero. That doesn't mean that it affects the region around the airfoil in any meaningful way.

If I understand correctly, the starting vortex also ensures that the airfoil isn't injecting momentum to infinity, or applying any forces to a group of infinitely distant air parcels. At great distances the effects of opposite circulation from an airfoil and from a starting vortex will cancel out, (where "great distance" means >> than distance between airfoil and starting vortex.) But remove the starting vortex, and now the effects of circulation remain undimnished at infinity. That's very bad. If a model requires a forcepair-interaction with infinity, that model is broken.

jmorgan3 wrote:
wbeaty wrote:One possible fix: remove the starting vortex but then include the Earth's surface. Keep 2D airfoil diagrams as they are, but add a "floor" which exhibits the instant downward force. This gives an explanation of "venturi flight," where the wing pushes down on the Earth via an instant force-pair. It explains WIG aircraft. In a 2D world where the starting vortex is more distant than the Earth's surface, you're explaining a WIG aircraft, even if the Earth's surface is hundreds of meters below.

If by "venturi flight" you mean that air changes pressure because it is squeezing between the airfoil and the earth's surface, I would like to know how this explains lift.

It doesn't explain lift. By "venturi" I mean "has a force-pair connected between airfoil and a solid wall." Squeezing is irrelevant: if the airfoil is pushing against the floor, if a force-pair extends from floor to airfoil, then that's an example of a venturi. If instead we look at a wing flying in three dimensions at altitude, and the wing presses against a region of air, while in 2D the airfoil presses against the distant ground, then the 2D version doesn't explain flight.

jmorgan3 wrote:
wbeaty wrote:Airplane Flight Analogy 1997
http://amasci.com/wing/rotbal.html

Your link is actually a decent conceptual explanation of why finite wings produce drag when they produce lift, but it still does not explain why and how that lift is produced. How does that air under the wing get launched downward? Do airfoils always push the air down? Would a cylinder work? An ellipsoid? A rotating cylinder? A flat plate?

My link is a crude explanation of Newtonian flight concepts. It explains how lift against that human foot is produced: the foot goes up and the balloon goes down.

We're taught that airplane wings are supposed to gain lift by throwing air down? Yet the horseshoe-diagram of vortex lines associated with a 3D wing shows this, but it gives a very poor picture of the down-momentum stored in air, and it gives a very poor feel for the origin of the action-reaction forces. My animation above is a crude grade-school version of the essential parts of 3D lifting-line theory: don't use it for engineering calculations, instead just use it to replace the bad diagram in the XKCD comic. But then as you say, *HOW* does the airfoil push the air downwards? Streamline-curvature or flow-turning theory supposedly explains this without requiring that airfoils press against infinity.
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### Re: 0803: "Airfoil"

jmorgan3 wrote:
wbeaty wrote:As I understand it, vector "flux lines" of aerodynamic forces must terminate on vorticity sheets associated with surfaces (as with a venturi,) or must be associated with free regions of vorticity, as with propulsion by vortex-shedding.

I think you're thinking of Helmholtz's theorems. If you are not, then please cite or prove your above statement.

No, I mean "force fluxes" not vortex lines. I'm trying to visualize the pressure-gradients and then follow the propagating aero forces through space as if they were EM flux lines. The forces can terminate on walls of course, but in the examples I've looked at, when they terminate on the air, that air is associated with vorticity. Watch a single pulse being launched from an "airzooka" smoke-ring launcher. Look at a pump (a ducted turboprop.) Both of these create a propulsive effect by dumping momentum into parcels of air, and thereby gaining equal and opposite momentum. They push against air, not against distant surfaces. The same appears true of a 3D wing and it's down-moving vortex wake. A lifting force can be created, but the rule seems also to be that vorticity must also be created. So, flight by a process of vortex-shedding. So, is vortex-shedding REQUIRED? Can a lift-producing device operate without vortex-shedding? If not, then perhaps viscous models are always required, since inviscid models cannot handle the process of vorticity-creation. (And note that my crude balloons-animation is an illustration of vorticity-creation.)

jmorgan3 wrote:
wbeaty wrote:A closed path around the airfoil will show the outward flow of the down-momentum injected into the air, correct? OK, increase the diameter of the closed path. Momentum stays constant, right? No momentum is left in the air, it all passes outward through the closed path. Increase the closed path to any finite diameter, and you find that momentum still goes outwards and none remains in the air parcels within the closed path: a momentum source but no sink. No momentum ever sticks to the air. That's how 2D flow diagrams violate momentum-conservation.

Conservation of momentum does not require momentum "sticking" to any one object.

Agreed, momentum can flow independent of air flow.

My complaint is that we can't include infinity as a necessary part of any model: injecting momentum into air but then having the momentum not end up in air, but instead fly instantly off to infinity. Where has that injected momentum gone? It isn't stored in the atmosphere. It has vanished, since at any place in the atmosphere we look for it, it's not there but has gone infinitely farther out. It's not accumulating in the atmosphere because it's not stored in any parcel anywhere. We cannot draw a boundary large enough to enclose the constant increase in down-momentum which demonstrates that the airfoil is constantly injecting down-momentum into the atmosphere. Momentum isn't conserved, because "infinity" isn't a location.

jmorgan3 wrote:EDIT: Because you never answered this from my last post, I'll ask it again:
Your link is actually a decent conceptual explanation of why finite wings produce drag when they produce lift, but it still does not explain why and how that lift is produced. How does that air under the wing get launched downward?

jmorgan3 wrote:How are those vortices (bound, starting, and trailing) produced? Under what conditions do airfoils push the air down? Would a cylinder work? An ellipsoid? A rotating cylinder? A flat plate? All of these questions are answered by 2D theory, but not by your balloon-pushing-down theory.

Um. 2D inviscid theory explains flow attachment? Vortex creation? Since when? But I agree that 2D inviscid diagrams are very useful as part of a complete explanation. Their flaws and limits just need to be avoided or at least acknowledged.

For those needing a break, here's a weird fascinating paper:

Secret of Flight Hoffman / Johnson 2008 (NOTE loads slowly)
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### Re: 0803: "Airfoil"

PS, in all of my stuff above, and in this message, don't take anything as being literally correct textbook stuff. I'm trying to work out a method to correctly explain viscous vortex airplane flight without using any math. I might be blind to a huge flaw that screws everything up. Someone here might find it. It's vaguely the same as trying to explain the gravitational 3-body problem: if you ignore the experts who say 3-body problems have no general solutions, you might end up in failure, or you might end up stumbling into Deterministic Chaos and cool 2D fractal maps.

not baby Newt wrote:This discussion is awesome. I dont know vorticity, but some things seem odd here on a more basic level.

The short description: vorticity is like current in a wire, with circulating parcels of air being like the b-field flux lines surrounding the wire, with the inner parcels spinning faster. Vorticity is made out of thin lines of "mathematical singularity" where the rules of non-viscous flow aren't obeyed. Lines of vorticity must be connected in circles, but two lines of opposite vorticity are allowed to end upon a solid surface. In an ideal tornado in frictionless fluid, the circulating air has zero vorticity, but there is a thin core of high vorticity running down the center. (I think Cosmic Strings are supposed to behave similar to this as well, with Einstein-ian torsion being the "spinning gas" that surrounds the line-like core of Spacetime Defect.)

not baby Newt wrote:
wbeaty wrote:But on the other hand, the airfoil circulation superposed with constant wind is creating an upward force on the airfoil, and simultaneously causing an equal downward force on the ground. There's an instant pressure pattern connecting them.

So, I guess I dont know what 'constant wind' means, but how exactly would pressure affect anything instantly? I'd think the speed of sound would be a limit (or speed of light..).

I don't know the technical term for constant wind. Free stream? In the XKCD airfoil diagram, what do we call those horizontal streamlines that approach the airfoil?

But yes, Newtonian force diagrams assume that systems are static, with no propagation delays or radiation loss. We just eliminate the complexity by making the speed of sound very fast, and limit our system to have slow changes, with objects being close-spaced. Then the two ends of any force-pairs are communicating back and forth repeatedly in zero time. It's the same motivation that leads to our use of non-viscous fluid in place of real air.

not baby Newt wrote:There should be a time factor involved in transferring force or pressure from plane to ground, during which the plane travels some distance. If the ground is far away, no interaction?
But in 2D we can't escape ground interaction at all. For distant ground and slow speed of sound, the ground-surface flow induced by the airfoil's image will be delayed in time. What does that do? Maybe it's a new kind of frictional loss, with energy being radiated as sound waves? It's interesting, but a distraction. Just keep your aircraft a few hundred feet up, so all the propagation-delay effects are small.

not baby Newt wrote:
wbeaty wrote:#5, not stupid, since in 2D we're dealing with a span which is infinitely wider than the atmosphere thickness. We have to include the complete atmosphere because, with 2D airfoils, the pressure-footprint on the ground integrates to a constant force, expanding or contracting in width depending on altitude. With real 3D wings this entire phenomenon is missing.
What's wrong with constant pressure footprint?

If we include the earth for a moment, we have gravity affecting both plane and planet. Plane keeps it's altitude because of lift and wings doing something to the atmosphere; why does the planet stay still? What I mean to say is that the pressure-footprint on the ground ought to add up to the same in either 2d or 3d or it wouldn't be a stable situation.
That's certainly true! I think I have this right... go deep underwater. Now whip out your Airzooka and start firing vortex rings at a high rep rate. You're propelled by the reaction-force "kick." You deposit momentum into yourself, and deposit opposite momentum into the stream of vortex rings. Now, is there any kind of venturi force, where some distant surface instantly experiences a pressure footprint? (Well, never instantly, but after a speed-of-sound delay.) Or are you truly "pushing off" from the water itself? Notice that the intake cycle of the Airzooka is creating a radial inward flow, like an enormous contracting sphere. At the center of this giant sphere, the inward flow is converted into a thin jet in a single direction (the marching line of vortex-rings.)

Now do the same thing high in the air while moving fast sideways. Add enough gravity so the lifting force doesn't drive you upwards. The line of downward-moving vortex-rings becomes spread out horizontally as a wide diagonal pattern: a pair of counterrotating wingtip vorticies.

not baby Newt wrote:The balloon concept is a very neat illustration. However, in the example I could just run on top of the balloons without making them spin at all, and would be easier. Is there a reason rotating cylinders of air can carry momentum downwards, but nonrotating air cannot?
A single chain of balloons would work fine. But if the balloons in the chain are made of air, and you try to push each one down in the center, what happens? The balloons are supposed to represent regions of air in an aircraft wake. The wing tries to drag down a 'solid' cylinder of air (a single chain of balloons.) But because air is fluid, instead the flow will wrap around upwards at the outside of the wings, and it ends up forming one big cylinder which contains two smaller spinning cylinders. The big cylinder descends, and the two smaller ones spin in opposite directions. The two balloons go downward, but in reality they are dragging a bit more air along with them, so the downward moving air looks like a single chain of balloons. (It's much like when an Airzooka tries to launch a sphere of air, but instead the moving air ends up as a sphere with a small ring-vortex embedded in the center, and a backwards-moving skin out the outside.)
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jmorgan3
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### Re: 0803: "Airfoil"

wbeaty wrote:Because of weight force, the airfoil injects a constant flow of down-momentum into the air. Where does this momentum end up? Are there some parcels out there where down-momentum is accumulating? We look at a region local to the airfoil. Is down-momentum in the region constantly increasing? Doesn't seem to be. The airfoil injects it, but then each parcel transfers down-momentum to other parcels more distant. That seems obvious: the 2D diagram is a sort of static momentum-flow diagram with no slow accumulation of down-momentum injected by the airfoil (no slowly changing patterns.) The momentum constantly injected by the airfoil instead is flowing in a static pattern constantly outwards, right? So if it doesn't accumulate locally where does it all end up? (The answer had better not be "at infinity." The model cannot include infinity as a necessary element. But I see no other option.)

Or more specifically: can we enclose the 2D airfoil in a circular boundary of very large diameter, a diameter where the increasing down-momentum is all stored in air contained within the boundary, rather than all of the down-momentum just flowing outwards through it?

Because of Gauss's Law, the point charge injects a constant flow electric flux into its surroundings. Where does this electric flux end up? Are there some parcels out there where electric flux is accumulating? We look at a region local to the charge. Is the electric flux accumulating in this region? Doesn't seem to be. The point charge injects it, but then each parcel transfers electric flux to other parcels more distant. That seems obvious: the 2D diagram is a sort of static electric flux diagram with no slow accumulation of electric flux injected by the charge (no slowly changing patterns.) The electric flux constantly injected by the charge instead is flowing in a static pattern constantly outwards, right? So if it doesn't accumulate locally where does it all end up? (The answer had better not be "at infinity." The model cannot include infinity as a necessary element. But I see no other option.)

Or more specifically: can we enclose the 2D point charge in a circular boundary of very large diameter, a diameter where the increasing electric flux is all stored in space contained within the boundary, rather than all of electric flux just flowing outwards through it?

wbeaty wrote:But in a non-ground effect finite wing model, if the increasing down-momentum being injected by the airfoil is ending up trapped on some local parcels of air, then infinite boundaries are then OK. In that case, as the boundaries are moved out to great distance, the amount of momentum flowing out through boundaries will fall to zero. The 3D airfoil is then injecting momentum into the air, not into infinity. In that case the other end of the force-pair for the lifting force lands upon a region of the air, rather than landing upon infinity.

Only in your solid-body model will this occur. In a physically possible potential flow situation where the tip vortices are irrotational, the momentum will also be transferred between parcels of air out to infinity.

wbeaty wrote:The airfoil system seems to be violating momentum conservation by injecting down-momentum into infinity, rather than injecting it into particular parcels of air. The airfoil seems to be violating Newton's 3rd by terminating the lift reaction force on infinity, not upon some local parcels of air. The 2D diagram might be useful for engineering calculations, but it seems to require that the airfoil's lift be a single-ended force not part of Newton's laws. The airfoil isn't pushing against air, instead it's "pushing against infinity."

It only "seems" like it to you. It is not violating momentum conservation. No law of nature requires that momentum stay in any one object or any one parcel of air. The airfoil is pushing against air, and that air is pushing against other air, and this continues out to infinity.

wbeaty wrote:If I understand correctly, the starting vortex also ensures that the airfoil isn't injecting momentum to infinity, or applying any forces to a group of infinitely distant air parcels. At great distances the effects of opposite circulation from an airfoil and from a starting vortex will cancel out, (where "great distance" means >> than distance between airfoil and starting vortex.) But remove the starting vortex, and now the effects of circulation remain undimnished at infinity. That's very bad. If a model requires a forcepair-interaction with infinity, that model is broken.

The velocity caused by an irrotational vortex is proportional to (1/r), where r is the distance between the point of interest and the center of the vortex. It obviously diminishes at infinity. If you include the starting vortex, then, at distances much larger than the distance between the vortices, then the induced velocity due to the two vortices will probably be proportional to (1/r^2) (I haven't worked it out mathematically, but it's most likely analogous to a dipole in EM). In no matter the number of vortices, the effect will go to zero as distance increases.

wbeaty wrote:By "venturi" I mean "has a force-pair connected between airfoil and a solid wall."

Then you are using a different definition of "venturi" than anyone else.
wbeaty wrote:My link is a crude explanation of Newtonian flight concepts. It explains how lift against that human foot is produced: the foot goes up and the balloon goes down.

We're taught that airplane wings are supposed to gain lift by throwing air down? Yet the horseshoe-diagram of vortex lines associated with a 3D wing shows this, but it gives a very poor picture of the down-momentum stored in air, and it gives a very poor feel for the origin of the action-reaction forces. My animation above is a crude grade-school version of the essential parts of 3D lifting-line theory: don't use it for engineering calculations, instead just use it to replace the bad diagram in the XKCD comic. But then as you say, *HOW* does the airfoil push the air downwards? Streamline-curvature or flow-turning theory supposedly explains this without requiring that airfoils press against infinity.

So you feel that "The airfoil's sharp trailing edge requires that the flow travel smoothly downward off the trailing edge" is more complicated and less accurate an explanation to give to children and grandmothers than "The airfoil is like a foot pushing down and rotating a bunch of balloons."?

If someone non-technical asked me to explain flight, I would start by showing that fluids tend to follow along surfaces. Then, I would draw an airfoil in a lifting configuration and show that the trailing edge is pointed downward. For the flow to follow the surface of the airfoil, it has to be pushed (or pulled) downward by the airfoil. By Newton's third law, then, the airfoil experiences an upward force from the air. If they then wanted to know about how drag happens, I would explain viscous drag and point them toward your site for a good explanation of induced drag. My explanation would gloss over a few technically important details and wouldn't be enough for that person to estimate the lift and drag of a given wing, but it would give what I would consider to be a conceptually accurate and fairly simple understanding of why aerodynamic forces exist.
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eran_rathan
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### Re: 0803: "Airfoil"

Maybe this is just me, but I always thought it could be explained fairly simply by using vector geometry.
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Zak McKracken
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### Re: 0803: "Airfoil"

wbeaty wrote:Note well that in a 2D flow diagram the net downwash is exactly zero,

Ha, gotcha!
That's wrong. It's not zero, and it shouldn't be. The flow leaves the trailing edge of the airfoil at an angle, so there must be a certain downwash. If you draw parallel streamlines, they should end up slightly lower behind the airfoil than they were before it.

I'll try to whip up a physically correct image ... it seems that most people who draw them for explanation purposes don't pay a lot of attention to those details. These are small details, too, and most people don't even bother, not even ones that should know better.

And also:
wbeaty wrote: So if it doesn't accumulate locally where does it all end up? (The answer had better not be "at infinity." The model cannot include infinity as a necessary element. But I see no other option.)

I wouldn't know why it could not.
Actually, potential flow theory gives solutions that do extend to infinity. Of you do anything to a fluid, it will have effects everywhere in that fluid. You throw a stone in your side of the ocean, something is gonna happen on my side of it. Immeasurably small, but present. Also: negligible. But for sake of completeness of the model we would need to recognise that. But if you were to make a simulation of ripples produced by a stone thrown into water, you still wouldn't need to include the whole world, because the effect fades away with distance, and (more important to your line of thinking) have no way of changing what is happening around the stone's impact point. So you can just pick a distance and say that anything beyond that point is not of interest. Wave energy is leaving the domain there, and it does not come back. You only need a boundary condition that will "swallow" anything that comes. You could make programming that boundary condition easier, though if you have a fluid model that will slowly dissipate the waves (add some friction) and then impose constant and undisturbed conditions in the distance distance. That's kind of cheating, but will also give you correct results if you don't overdo it.
Fact is: In a perfect inviscid medium, the influence does in fact extend to infinity. Fact is also that this does not change anything for the near field.

In a 2D flow, however, you are adding momentum to the medium that is passing by the airfoil, so you leave it behind the airfoil. If you gradually increase the control volume, the changes at the airfoil will go to zero. beyond a certain radius it will simply not matter at all.
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