## 0803: "Airfoil"

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michelcolman
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### Re: 0803: "Airfoil"

jpers36 wrote:
Karilyn wrote:FYI: You count to 100 on two hands using one thumb as a 5, and the other hand having fingers be 10 with the thumb being 50.

9 on the 100 scale looks the same as 5 on the traditional finger counting scale.

Forget that, I can count to 1024 on my two hands.

How do you represent zero then?

michelcolman
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### Re: 0803: "Airfoil"

Monika wrote:You realized this in middle school? Most adults answer this riddle wrong:
You take a lump of gold, get into a boat on a closed lake and row a bit. Then you throw the gold into the water. Does the water level of the lake sink or rise?

Or this one, which my physics teacher got wrong:

What happens to the water level if a floating block of ice melts?

This one is especially nice to use on uneducated global warming activists. (Of course the ice on land, like the south pole and greenland, will still make water levels rise as it flows off the land, but not the floating ice caps and icebergs)

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

thanksbastards wrote:does anyone know the Cooefficent of lift for a NASA or NACA0015 airfoile with a reynolds number of about 40-50,000? all the published data I can find starts at 80k or higher

You can use XFLR5 to get a really good approximation. (available at sourceforge)
With free transition, I understand why there is so little data at 50k Reynold number, because you get a laminar separation bubble on top, and that is completely not representative for anything that actually flies, and probably not something that you were supposed to learn about, as it's a bit more advanced than "how do we generate lift?"

So I've just done two small computations, one with natural transition (green), one with forced turbulent boundary layer (blue), at 50k Reynolds number. Results are behind the spoiler.
Spoiler:

You should have measured something in between both curves. Maybe you also have measured a smaller lift rise with angle of attack because you measured a finite wing. That depends on the experimental setup, though.
Cl is of course lift per wing area, divided by the stagnation pressure. You can either measure the latter directly with a Prandtl tube, or you can compute it as {density by two} times {reference velocity squared}. The latter isn't as accurate, but you might have to do it, depending on what measurement equipment you used.

Now, can anyone tell me why the imath tag doesn't seem to work here? Any formula I tried to type looked like this:
[imath]q = \frac{\rho}{2} \cdot v_\infty^2[/imath]

Code: Select all

[imath]q = \frac{\rho}{2} \cdot v_\infty^2[/imath]
edit: WTF? When I'm logged in, I get no math symbols, just the equation source. If I log out, all's fine.
Last edited by Zak McKracken on Sat Oct 09, 2010 6:48 pm UTC, edited 1 time in total.
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michelcolman
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### Re: 0803: "Airfoil"

Richard wrote:A little (imprecise) experiment to demonstrate the coanda effect and lift (or diffusers on race cars). Turn on your tap and dangle the backside (convex) of a spoon near it. Slowly move the spoon into the stream. When the spoon meets the stream it will be pulled further into the stream by the reaction to the water slung off the tip. I never really bought that bernoulli shit. He may make my carburetor work but I don't think he can hold an airplane in the air. I have seen a picture of a plane flying above clouds and it clearly makes a groove.

Another nice one is the experiment wher you blow over a hanging piece of paper so that it goes up. Lots of people will say this is due to Bernoulli (the air coming out of your mouth is moving faster, so it has a lower pressure). In fact many people use precisely this experiment to demonstrate Bernoulli's law. But then you ask them why it still goes up if you blow against the bottom, and you get something like "o, well, yeah, that's different, because, err... well, the air bounces into the paper, you know...)

Of course this experiment has nothing to do with Bernoulli: the only way you could use Bernoulli's law here, is by comparing the pressure in the air stream (which will be pretty close to the surrounding atmospheric pressure) to the air pressure inside your lungs (which is higher). There's absolutely no reason for the pressure in the air stream to be lower than that of the surrounding air, since you added energy to it.

The paper only goes up because of the Coanda effect.

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

airshowfan wrote: In fact, I wonder whether any structural components on the wing are sized by the negative-g condition, i.e. are stressed more highly by negative gs than, say, by a high positive-g turn.

Yes, there are. If the wing was massive, that'd be zero problem, but it's made up of stringers and ribs (and skin in between), and they can take a certain amount of stress when you're pulling, but under compression the usual mode of breakdown is buckling and folding, so you need to make sure there is no segment of skin too large and no piece of ribs or stringers too long without sideways support, even more so with fiber composites, as they can bear a lot more tension than compression.
But that does in fact not add a lot to the overall mass, especially since you need to take into account also the landing shock, where the airplane needs to be able to fly into the ground at nominal landing speed and 3° decent angle, with a certain amount of fuel in the wing tanks.
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Karilyn
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### Re: 0803: "Airfoil"

Faranya wrote:I always hated the significant digit system. It is all well and good for small numbers to avoid an illusion of precision, but it falls apart with large numbers. Like the 4 000 000*1.15=4 000 000 mentioned before. Even if it is avoiding some false precision, I normally wouldn't consider 600 000 of something to be negligible...

Uhhhh, there's 3 significant digits in that problem. 1 1 and 5. So even using significant digits, you still pull 3 of them... 4.60x10^6

Faranya wrote:As for the answer on the test, if there was no precision conventions given, I wouldn't call it wrong. However, I wouldn't call them 'smarter' for expressing it to a lower precision, they might have just been lazy or careless.
I think it's safe to assume that the people who did it were the "smart" kids who normally pull straight 100s, as opposed to the ones which are lucky to pull a 60 on most tests, which was why he was upset about having to mark their answers wrong.

I know it wouldn't be the first time a teacher over the years cut me corners cause they were like "Fuck it, you know your shit, hell you could teach this class. Not fair to count you off for this one."

michelcolman wrote:
jpers36 wrote:
Karilyn wrote:FYI: You count to 100 on two hands using one thumb as a 5, and the other hand having fingers be 10 with the thumb being 50.
9 on the 100 scale looks the same as 5 on the traditional finger counting scale.
F
orget that, I can count to 1024 on my two hands.

How do you represent zero then?

You count to zero on your hands?
Gelsamel wrote:If you punch him in the face repeatedly then it's science.

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

rhhardin wrote:Bernoulli reverses cause and effect in any case. The air goes faster because it ran down a pressure gradient from high to low pressure; the speed didn't cause the pressure change but rather responds to it.

No. It's just frequently misunderstood that way.
And yes ... air does respond to pressure.

1. Bernoulli says nothing about "air has to go faster because the upper side is longer" -- that's an invention of inept physics teachers. (you seem to know that, but just to be sure)
2. Bernoulli's law (actually there are several of thouse, there was even a whole family Bernoulli, several of whom were scientists) is the application of the first law of thermodynamics (energy conservation) to a flow.

Meaning: Kinetic energy can be converted to pressure and vice versa. As long as there's no friction involved (and no sonic shocks), there is no other way for energy to go. So if you're slowing down, pressure increases and vice versa. Or if pressure increases, you're slowing down (think golf course and sending a ball up a hill) and vice versa.
Bernoulli says nothing about which comes first, it's just a statement that the two always go together. Like a seesaw, you can say it moves because I'm lighter or because you're heavier, but those are equivalent statements. There's no "reaction" in this law, things happen simulateously.

Imagine a pipe with a tight spot. You know from mass conservation that the flow must be faster there, so you also know there's lower pressure. Argued the other way round: The tight spot is an obstacle, so it will slow the flow in the rest of the pipe, so upstream there must be increased pressure (compared to the same pipe with no obstacle), so flow will be accelerating into the tight spot. Both give the same result, just some find it easier to understand one or the other explanation. In this case, it's the first one for me, in the case of an airfoil, thinking about pressure first seems more obvious. But you could still argue that the tip of the airfoil is equivalent to a tight spot and the air from the stagnation point and upwards needs to squeeze around it, so it must be faster ... you can always argue both ways.
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Zak McKracken
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### Re: 0803: "Airfoil"

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 shool 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 mousepad.

But imagine putting two hairbrushes together. Even with zero normal pressure it gets really hard to move them at all. If you then take twice as large brushes with equal density, you're doubling the contact area and thus the force required to move them tangentialy, although the normal pressure can still be zero.

Now rubber tires are somewhere in between. The rubber "hugs" the small stones and uneven surface of the road. If you increase the normal pressure, the sideways force won't increase proportionally but less, because you're already gripping all the small stones (unless the pressure was too weak for your tire to begin with). If you reduce the pressure but increase the contact area (either by getting broader tires or by reducing tire pressure), the tire can "hug" more of those small stones and therefore stand a larger sideway force.
This is of course depending on the softness of the rubber, the roughness of the road and how your tires match it, whether there's loose gravel, water, sleet, snow ...

Note however that this is only while the tires are not slipping. As soon as the tires start slipping, it's completely different. If you are driving on snow, it's also different. Then broader wheels spell trouble. I'm not exactly sure, though, how that works.

Having said that, I understand why they only teach linear friction laws at school, because the whole truth is pretty complex, not completely understood afaik, and most practical examples of stickiness and friction are close to the linear relation between normal pressure and shear tension. It's most practical to learn the general rule first and the exception later. People didn't go all "the whole mechanics we were taught is moot!" when quantum mechanics were discovered, because to our daily lives, quantum mechanics is seldom relevant, although it is much more precise than and could completely replace good old Newton's laws. So it is usually treated like an exception to the rules, although it is of course a much bigger truth which Newton's laws are just a special case of.
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Monika
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### Re: 0803: "Airfoil"

Vulcanis wrote:I'm surprised that no one else has mentioned the fact that it is not "Your parents are Santa" but "Santa is your parents".

This, in fact, means Santa is actually... our parents.

Oh. Up to this post I thought that the evil teacher was indeed saying that the kid was begat by Santa Claus. Not that his parents are putting the gifts in the living room on the night from the 24th to the 25th.

BTW in Protestant and Atheist families in Germany Santa shows up in person in the afternoon or evening of the 24th. Usually a neighbor, friend of the parents or hired college student. In Catholic families it's the Christkind (Christ child, a woman for some reason) places the presents under the Christmas tree, but is not seen doing this.
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LatwPIAT
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### Re: 0803: "Airfoil"

jbo5112 wrote:5th grade field trip to planetarium (paraphrase): "We calculate how far away a star is based on how big it looks and how big it actually is. We calculate how big a star actually is based on how far away it is and how big it looks." The first time he made these statements were in different sections of his lecture, but I still caught it and called him on it. He then made both statements within a minute or two, apparently not realizing that you can't solve for 2 variables with his 1 pseudo-equation. The explanation from the planetarium employee was reduced to "we also have other methods we use", and he quickly moved on after a 5th grader exposed his stupidity.

You're being rather harsh on him. While it's true that you can't solve for 2 variables with one equation, it's entirely correct that "we also have other methods we use" is how they solve that problem. You didn't expose his stupidity as much as mention that he spoke wrong, and he explained very quickly what mistake he had made. I'll agree that it might not have satisfied you, but he's not being stupid.
merlanai wrote:I wonder if anybody else was taught how to taught how to count to 100 on their fingers, and use the same technique to be able to do a long series of simple addition/subtraction/multiplication/division as fast as a person could read it off to you.

36 divided by 6 plus 5 times 2 - 2 divided by 5 minus 2 minus 2 plus 10 times 5 plus 6 divided by 8 plus 2 EQUALS:

That might be a good way to teach quick arithmetic, but it anathema to good order-of-operations. When someone reads that out as fast as they can, they can't make indicative pauses, so the answer to that task ends up being 62.35, which I understand to be difficult to display with fingers...

Seriously, I hate that nobody bothered to explains order-of-operations to me in primary school. It was the particular brilliance of my teachers/the Ministry of Education to then insist on including that on the tests. For that matter, the clarity of mind that is required to give out a test three months before the year ends, that covers everything on the curriculum that year.

Of course, in the last year of primary school, I was outsmarting my maths teacher.
"How do I divide two decimal numbers?"
"For such difficult questions, we use a calculator."

Then I went home, complained to my parents, and was told how to do it. Difficult? DIFFICULT? I've never seen a simpler way to solve a question like that, and the knowledge of how to solve it would have been invaluable to the rest of the class once they started to learn algebra.
jpers36 wrote:Forget that, I can count to 1024 on my two hands.

Yes, yes, I guess you can if you want to, but it looks so much more beautiful if you stop at 1023.
Grant10k wrote:It's all fun and games until you get to 132.

People always looked strangely at me when I was counting something and reached 4 or 20. Eventually I learnt to just ignore it or keep my hands out of sight.

Fun story. A few weeks ago we were learning about electromagnetic induction and such things in class, and we were handed a stack of previous exam papers that we could use to study. I leaf through the thing and arrive at a question:

"induce a current in a copper ring, using only insulated wire, a variable resistor, and a cell"

So, I dig into the question and realize that I need to exploit Lenz' Law (where the change in magnetic field strength will be opposed by a proportional but opposite magnetic field) by creating a solenoid from the wire, and attaching the variable resistor and the cell to it. I can then aim the solenoid along the perpendicular to the plane of the copper ring, and by varying the resistor, I can create a varying magnetic field strength. This varying magnetic field strength will then create and opposed magnetic field along the perpendicular to the plane of the copper ring, and it will induce a current in the copper ring.

Simple, right?

Well, it turns out that the answer key just said to wrap the wire around the copper ring. Except that is wrong. That would induce a magnetic field in the copper ring, but no current. Peeved, I turn to the student next to me and raise the question, and he looks at it and has the same realization. The key is wrong. Completely utterly wrong. I even, still somewhat doubtful, talk to a theoretical physicist, and he tells me that the key was wrong.

Of course, he also had a much simpler solution: as long as you're not on the magnetic North or South pole, place the copper ring vertical on a table and spin along the axis normal to the Earth's surface...

rcox1
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### Re: 0803: "Airfoil"

markchd wrote:
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.

http://amasci.com/miscon/miscon4.html has some pretty shocking stuff.

Note that the comic was not talking about the fact that some science taught does not strictly match current understanding of the world, and some of it is shockingly out of data or simply wrong, but how to deal with a situation often referred to as a 'teachable moment'.

The best response is always to drop whatever else is going on and work off of the new tangent. In the real world the best response is not always possible, but that does not justify the less good responses. Many of the posts here illustrate this best response by engaging in a dialogue about our current understanding of the world. This is science.

The website cited is almost anti-science as it seems to begins from the proposition that a correct answer exists, that the purpose of science is finding th correct answer is the goal, and once that answer is found there is no further reason for debate. It appears to lack understanding of the process, or that things can be shown to be false in a situation, but not true.

Take the missive on the scientific method. If anything, the scientific method is based on the idea that observation should for the basis of the formation of new ideas, not just believing what people say. This idea of observation, not hearsay, is what makes science different from faith based demagoguery. The details of a scientific method may vary, but the idea of observation is constant.

So, for instance, one may say that scientist build new instruments, and this is the scientific method, but it is the process of building the instrument, not the final product, that is the science. For an STM, there is the hypothesis that tunnel current by keeping the current constant map a surface at that atomic level. The instrument is built, refined, and in the process we validate and refine the hypothesis. Focusing on the STM the common mistake of the layperson. The scientist is more concerned with what knowledge was created in the process of development, and what knowledge is being created by it's use. Specifically, we can now observe on an atomic scale. Therefore, science is observation, which is what is taught in school, and why the STM is a nobel worthy item.

Almost everything on the site suffers from this critical fallacy, that the results are more important than process in science. It is a common issue when communicating with people with no or limited science training. It is also an issue when trying to make science popular. For instance, Myth Busters does a good job communicating the process of experiment, but then has to mess it all up by reducing the process to a sound byte for popular consumption.

Karilyn
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### Re: 0803: "Airfoil"

LatwPIAT wrote:
merlanai wrote:I wonder if anybody else was taught how to taught how to count to 100 on their fingers, and use the same technique to be able to do a long series of simple addition/subtraction/multiplication/division as fast as a person could read it off to you.

36 divided by 6 plus 5 times 2 - 2 divided by 5 minus 2 minus 2 plus 10 times 5 plus 6 divided by 8 plus 2 EQUALS:

That might be a good way to teach quick arithmetic, but it anathema to good order-of-operations. When someone reads that out as fast as they can, they can't make indicative pauses, so the answer to that task ends up being 62.35, which I understand to be difficult to display with fingers...

If it makes you feel any better I could've wrote it as

(((((((((36 divided by 6) plus 5) times 2) minus 2) divided by 5) minus 2 minus 2 plus 10) times 5) plus 6) divided by plus 2 EQUALS:

It WAS a quick arithmetic thing, not order of operations. *sigh* People being silly and missing the obvious point. Pedantic.

If it makes you feel any better, we were taught Order of Operations in like, first grade, and I myself started on College Algebra in 3rd.

Of course, in the last year of primary school, I was outsmarting my maths teacher.
"How do I divide two decimal numbers?"
"For such difficult questions, we use a calculator."

One of my favorites was in really really like, first grade, I seem to remember the teacher explicitly saying that it was impossible to subtract a larger number from a smaller number. And I was all like "But what about Negative Numbers?" And she was like "Fuck you."
Gelsamel wrote:If you punch him in the face repeatedly then it's science.

LatwPIAT
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### Re: 0803: "Airfoil"

Karilyn wrote:It WAS a quick arithmetic thing, not order of operations. *sigh* People being silly and missing the obvious point. Pedantic.

I perfectly understood what the purpose of the task was, thank you. I'm merely opposed to its use, on the grounds that it teaches bad form when it comes to order-of-operations.
Karilyn wrote:One of my favorites was in really really like, first grade, I seem to remember the teacher explicitly saying that it was impossible to subtract a larger number from a smaller number. And I was all like "But what about Negative Numbers?" And she was like "Fuck you."

Ah, you too, eh? I remember my math book for 4th or 5th grade had a set of simple arithmetic tasks that would sometimes result in positive numbers and sometimes result in negative numbers. The book said that because you couldn't subtract a larger number from a smaller one, our task was to cross out the tasks that "couldn't" be solved, and solve the rest.

I also distinctly remember a bunch of tasks in one of my previous math books by the same authors that had tasks involving a thermometer and word problems like "It is 2o C, and the temperature drops 5o C. What is the temperature?"

Are negative numbers really that hard to understand?

Monika
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### Re: 0803: "Airfoil"

I was also rather shocked in first grade when I was told that negative numbers would not be taught until 7th grade. But when I answered math problems with negative numbers instead of the expected "n.l." (nicht lösbar = not solvable) it was still marked right.
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Karilyn
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### Re: 0803: "Airfoil"

LatwPIAT wrote:
Karilyn wrote:One of my favorites was in really really like, first grade, I seem to remember the teacher explicitly saying that it was impossible to subtract a larger number from a smaller number. And I was all like "But what about Negative Numbers?" And she was like "Fuck you."

Ah, you too, eh? I remember my math book for 4th or 5th grade had a set of simple arithmetic tasks that would sometimes result in positive numbers and sometimes result in negative numbers. The book said that because you couldn't subtract a larger number from a smaller one, our task was to cross out the tasks that "couldn't" be solved, and solve the rest.

I also distinctly remember a bunch of tasks in one of my previous math books by the same authors that had tasks involving a thermometer and word problems like "It is 2o C, and the temperature drops 5o C. What is the temperature?"

Are negative numbers really that hard to understand?

I don't know. What would the answer be if it was in Kelvins? :
Gelsamel wrote:If you punch him in the face repeatedly then it's science.

LatwPIAT
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### Re: 0803: "Airfoil"

Faranya wrote:I always hated the significant digit system. It is all well and good for small numbers to avoid an illusion of precision, but it falls apart with large numbers. Like the 4 000 000*1.15=4 000 000 mentioned before. Even if it is avoiding some false precision, I normally wouldn't consider 600 000 of something to be negligible...

In that case, shouldn't it be 4*106 * 1.15 = 5*106? Anyway, the point is that when an accuracy is given to a single digit (n), the real value could fall anywhere within the range of n-(n/2) to n+(n/2), which means that for 5*106, the actual value could be anywhere between 4,500,000 and 5,500,000 - which you'll see that 4,600,000 falls well within.

serpret
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### Re: 0803: "Airfoil"

cs24 wrote:The explanation is wrong because the streamlines don't meet up after the trailing edge of the airfoil: http://www.youtube.com/watch?v=6UlsArvbTeo&t=0m17s

but isn't the explanation that the lift is generated by higher speed air above the wing? And doesn't that video clearly show the upper air moving faster than the lower?
Based on that video, their assumption that the two air molecules should meet up is wrong, however, that video seems to support their overall conclusion even more so.

rcox1
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### Re: 0803: "Airfoil"

Karilyn wrote:
LatwPIAT wrote:
Of course, in the last year of primary school, I was outsmarting my maths teacher.
"How do I divide two decimal numbers?"
"For such difficult questions, we use a calculator."

One of my favorites was in really really like, first grade, I seem to remember the teacher explicitly saying that it was impossible to subtract a larger number from a smaller number. And I was all like "But what about Negative Numbers?" And she was like "Fuck you."

So by this argument we should introduce imaginary number as soon as we introduce the root function.

While I can see the argument for that, the domain is explicitly limited so we can teach a concept. Addition and subtraction can well be taught within the domain of positive real integers. Later, negative and real numbers can be introduced. Those students that learned addition and subtraction of integers, and did not instead focus on a bit of trivia that they read in a book somewhere, can expand the definition of what they can do pretty easily. The reality is that with positive whole number one cannot subtract a larger number from a smaller number, any more than with real numbers on can take the root of a negative number.

Calculus books regularly give theorem that the limit of root function only exists for positive real numbers, without explicitly stating that we are limiting ourselves to real numbers. Anyone who takes calculus knows that this is not always true, and the kid that brings up the issue of imaginary numbers is probably not trying to improve the educational process, but showing off, kind of the like the five year old that knows about every dinosaurs, so thinks they know everything.

Akula
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### Re: 0803: "Airfoil"

Even in flight school they still try to pass this off...
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styrofoam
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### Re: 0803: "Airfoil"

Akula wrote:Even in flight school they still try to pass this off...

That's disturbing. The only thing that could be worse is teaching this in engineering school, training to construct planes.
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Zak McKracken
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### Re: 0803: "Airfoil"

Akula wrote:Even in flight school they still try to pass this off...

yep. I saw a documentary the other day, and they asked a test pilot (and former aerobatic national champion) to explain how an airfoild generates lift. He gave exactly this stupid explanation. Then they went and measured the upper suface of an aircrafts wing and took the result as proof that the explanation must be correct. What's worse: They also interviewed a professor from my town and mingled his answers with the test pilot's, as if they were in perfect agreement. This was then proadcast by a big public TV station.
Said professor was later reported by colleagues (who work with him) to have been extremely irate. He had some stern words with the guys from the TV station, but I doubt whether it helped.
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Zak McKracken
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### Re: 0803: "Airfoil"

rcox1 wrote:
LatwPIAT wrote: And I was all like "But what about Negative Numbers?" And she was like "Fuck you."

So by this argument we should introduce imaginary number as soon as we introduce the root function.

Actually, no. I had my share of these things in school, and I often got answers along the lines of "You're right, but we can't explain the details of that to everyone now, so until we treat it next year, we're going to ignore it, because I can't teach you everything at once." If a teacher does that, I think there's no need to look stupid. My math teacher in second grade even made an excursion (because someone asked) to explain (in simple terms) how you can calculate the area of a circle (and thus Pi), by subdividing it into very tiny squares, and even tinier and so on ... which is something we didn't see again before 11th grade. I find it great to see at least a hint of the things to come.
In higher grades, this happens less often because the difference between the student's and the teacher's knowledge is smaller there. I've seen physics teachers who know what they're supposed to teach plus very little. They're thankful if they can learn some more because right now they are with their backs against the wall if someone in class asks to many unforeseen questions, while they need to maintain a position of authority, because otherwise they can't hope to stay in control of a class of 30 17-year-olds.
rcox1 wrote:and the kid that brings up the issue of imaginary numbers is probably not trying to improve the educational process, but showing off, kind of the like the five year old that knows about every dinosaurs, so thinks they know everything.

Hmmm... I might have been guilty of that a bit That and wanting to get my teacher's back to the wall
But then probably everyone who posts in this thread to put things right acts the same way in a sense.
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CmdrWestside
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### Re: 0803: "Airfoil"

I was in DC last week and the National Air and Space Museum had a graphic (which I can't show you, apparently) titled something to the effect that 'lift is created by differences in air pressure... I was amazed, and then XKCD comes along with a comic with the same theme.

Seriously, the Smithsonian gets that wrong, the rest of us are doomed, doomed. Maybe I'll send them a letter (or a link to XKCD "Airfoil" might be better.

RogueCynic
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### Re: 0803: "Airfoil"

I don't know if its been mentioned or not but physics is not an exact science. Physics is based on the concept of mass, but what is mass? How is it measured? And why can physics not explain why the bumblebee flies?
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SirMustapha
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### Re: 0803: "Airfoil"

STUDENT: So how do planes fly upside down?
TEACHER: ... actually that's a good question! We should find out! *flips pages of book* Well, actually, it turns out that the wing must deflect air downwards so it can fly.
STUDENT: But how does that work:
TEACHER: ... hey! We should try to learn this! *flips pages* So here we have a chapter about aerodynamics. Here's what it says:

*2 hours later*

TEACHER: So, everyone understood it?
CLASS: ... ... ... ...
TEACHER: ISN'T LEARNING FUN??

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### Re: 0803: "Airfoil"

RogueCynic wrote:And why can physics not explain why the bumblebee flies?

This is a fallacy. Flapping wings have been successfully modeled using the Navier-stokes equations, and it's a very active area of research. The only way "physics" can't explain it is if you assume that the wings are like the stationary wings on a plane, but that's a moronic assumption.

pyromosh
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### Re: 0803: "Airfoil"

CmdrWestside wrote:I was in DC last week and the National Air and Space Museum had a graphic (which I can't show you, apparently) titled something to the effect that 'lift is created by differences in air pressure... I was amazed, and then XKCD comes along with a comic with the same theme.

Seriously, the Smithsonian gets that wrong, the rest of us are doomed, doomed. Maybe I'll send them a letter (or a link to XKCD "Airfoil" might be better.

I don't know what the specific display you saw said, but the Smithsonian's National Air And Space Museum web site has the correct explanation, and even points out the fallacy:

http://www.nasm.si.edu/exhibitions/gal1 ... EASERS.HTM

That said, the way you are explaining the display isn't necessarily wrong. It *is* from a pressure differential.

The fallacy isn't that there is a greater pressure area under the wing, and a lower pressure area over it. The fallacy is that this pressure differential is caused by air molecules magically having some kind of pact to arrive at the trailing edge of the wing at THE EXACT SAME TIME.

I have to admit, I didn't know this was wrong prior to this comic. 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.

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### Re: 0803: "Airfoil"

RogueCynic wrote:I don't know if its been mentioned or not but physics is not an exact science. Physics is based on the concept of mass, but what is mass? How is it measured?

Physics is an exact science, but aerodynamics stopped being about physics a long time ago.
All the laws required for aerodynamics are known. The much-quoted Navier-Stokes equations which describe viscous, compressible and continouus fluids, were set up 1822. Almost everything that's being done today in computational aerodynamics is "just" applying them or (and that's the biggest part) a simplification to a problem and determining the consequences. Or finding new ways of solving them. Or simply conducting experiments, which is sometimes a lot easier and more accurate.

The concept of mass ... well, if you really want, you can call everything except maths "not exact" because at some point it boils down to quantum physics, and there are still some things not completely understood in quantum physics. But that need not bother any biologist, chemist or aerodynamicist, because that is completely meaningless to their field of work.

RogueCynic wrote: And why can physics not explain why the bumblebee flies?

That's another stupid myth.
Some guy who thought he knew everything applied some realy simple empirical design rule based on passenger airplanes from the 1960s to bumblebees and found that it somehow didn't fit. O wonder. He told that to some journalist, who misquoted him, and the rest is history.
I've seen computations of flapping insect wings, and they can definitely fly
The thing that the guy above didn't take into account was:
1. Bumblebees fly at such low Reynolds numbers that they are hardly comparable with the type of lifting surfaces we construct ourselves.
2. Insects in general flap their wings so fast that the downbeat meets the vortices shed by the wing during upbeat. The flapping pattern (unknwon in the 1960s due to lack of highspeed cameras and trained bumblebees) is such that it uses those vortices to create even more lift.

Please never again say that "physics say bumblebees can't fly". It's complete bullshit.
Also, recurring theme: Just because some scientist is wrong doesn't mean science is stupid. People are wrong all the time, including everyone. Science is only wrong if scientists are wrong and all other scientists agree. Luckily, in science this is usually corrected much faster than in politics. And fewer people die of it.

I read a recent paper by some retired physicist stating that archaeopterix can't have been able to fly because they couldn't have enough propulsion power to stay in the air. Obviously he never heard about sailplanes. They need zero power if the winds are good and can stay in the air virtually indefinitely, as long as there is wind and a hill. Mark that this say nothing about physics in general, only about the person making that ridicoulous claim.
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Pfhorrest
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### Re: 0803: "Airfoil"

SirMustapha wrote:STUDENT: So how do planes fly upside down?
TEACHER: ... actually that's a good question! We should find out! *flips pages of book* Well, actually, it turns out that the wing must deflect air downwards so it can fly.
STUDENT: But how does that work:
TEACHER: ... hey! We should try to learn this! *flips pages* So here we have a chapter about aerodynamics. Here's what it says:

*2 hours later*

TEACHER: So, everyone understood it?
CLASS: ... ... ... ...
TEACHER: ISN'T LEARNING FUN??

When I'm not in any kind of urgent hurry, I like to do this whenever young kids try to annoy me with endless strings of "why". It's kinda of like a staring contest, really just a matter of patience, and of course it helps to be generally knowledgeable enough to usually have an answer to each "why" (and if not, to be able to explain why you don't know, and from that point on they're only asking questions about your life and what lead to you not knowing, so it's easy to know the answers to those).

The kids usually get bored of it before I do and leave frustrated. Or occasionally the smart ones will actually be intrigued by something and start asking genuine questions instead of just inane "why"'s, and then it's fun for both of us.
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a34
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### Re: 0803: "Airfoil"

When I was in high school, I actually asked my physics teacher this question. His response was: "They don't."

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### Re: 0803: "Airfoil"

RogueCynic wrote:And why can physics not explain why the bumblebee flies?

That's a rather old saying. In the meantime, experiments with insects have been done and it is known why bumblebees stay in the air. Larger insects that move their wings more slowly are preferable for the experiments: Put them in a wind channel with smoke to make the air movements visible. Unfortunately I don't know a whole lot of terms (a) related to insects (b) related to physics and air movements in English, so I can't explain it, but you can probably find it on Google in English, too ... I vaguely remember that the experiment was first done in the US, with moths or similar, some time in the 90s.
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CmdrWestside
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### Re: 0803: "Airfoil"

pyromosh wrote:
CmdrWestside wrote:I was in DC last week and the National Air and Space Museum had a graphic (which I can't show you, apparently) titled something to the effect that 'lift is created by differences in air pressure... I was amazed, and then XKCD comes along with a comic with the same theme.

Seriously, the Smithsonian gets that wrong, the rest of us are doomed, doomed. Maybe I'll send them a letter (or a link to XKCD "Airfoil" might be better.

I don't know what the specific display you saw said, but the Smithsonian's National Air And Space Museum web site has the correct explanation, and even points out the fallacy:

http://www.nasm.si.edu/exhibitions/gal1 ... EASERS.HTM

That said, the way you are explaining the display isn't necessarily wrong. It *is* from a pressure differential.

The fallacy isn't that there is a greater pressure area under the wing, and a lower pressure area over it. The fallacy is that this pressure differential is caused by air molecules magically having some kind of pact to arrive at the trailing edge of the wing at THE EXACT SAME TIME.

I have to admit, I didn't know this was wrong prior to this comic. 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.

I can't post links but if you went to imgur dot com slash gCf0z you'd see it. Dear moderator it's a picture showing a misleading picture in the National Air and Space Museum, it really applies to the comic.

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### Re: 0803: "Airfoil"

http://imgur.com/gCf0z

The Smithsonian tells kids that airplanes are carried through the air by invisible men

(Actually the sign talks about air pressure differences.)
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pyromosh
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### Re: 0803: "Airfoil"

CmdrWestside wrote:I can't post links but if you went to imgur dot com slash gCf0z you'd see it. Dear moderator it's a picture showing a misleading picture in the National Air and Space Museum, it really applies to the comic.

I see now. Thanks for that.

There's nothing wrong with that explanation. Lift *is* caused by differences in air pressure. The fallacy that the comic is talking about is when you try to explain what causes the differences in air pressure. Other people in this thread have explained the reason fare more succinctly than I can, but it is *NOT* caused by the common fallacy called "equal transit time".

The poster in your image doesn't mention "equal transit time", it never goes into the level of detail that attempts to explain the cause the pressure differential. It's a rather simple explanation, but it's not wrong. Incomplete perhaps, but not wrong.

CmdrWestside
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### Re: 0803: "Airfoil"

pyromosh wrote:
CmdrWestside wrote:I can't post links but if you went to imgur dot com slash gCf0z you'd see it. Dear moderator it's a picture showing a misleading picture in the National Air and Space Museum, it really applies to the comic.

I see now. Thanks for that.

There's nothing wrong with that explanation. Lift *is* caused by differences in air pressure. The fallacy that the comic is talking about is when you try to explain what causes the differences in air pressure. Other people in this thread have explained the reason fare more succinctly than I can, but it is *NOT* caused by the common fallacy called "equal transit time".

The poster in your image doesn't mention "equal transit time", it never goes into the level of detail that attempts to explain the cause the pressure differential. It's a rather simple explanation, but it's not wrong. Incomplete perhaps, but not wrong.

Drat, I've discovered that my latest update on the lift theory, the Coandă effect, wasn't the true explanation. Thanks to another XKCDer and How Stuff Works (and you) I've updated my brain, thank you, I never really did see how Coandă effect explained lift, now I see it doesn't (exclusively).

There's a fountain downtown that does illustrate Coandă effect that got stuck in my head...

Tormuse
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### Re: 0803: "Airfoil"

This comic reminds me of my grade 10 science class in which the teacher stood at the front of the class and had us all hold up thermometers and wave them around and he said, "Notice that when you wave your hand around, it feels cooler, but waving the thermometer around doesn't change the temperature reading. Now, why would that be?" to which I answered "Isn't it because of sweat evaporating?" I was sitting at the front of the class and he patted me on the shoulder in a patronizing manner and whispered, "You're getting ahead of me there, buddy," and then continued his demonstration as though I hadn't said anything, having us dip the thermometers in water and wave them around again, and *eventually* getting to an explanation that water evaporating cools things down.

Now, I realize that he had the whole lesson planned out in advance and he didn't want anyone to interrupt his train of thought, but it would've been nice if he had at least acknowledged that I gave the right answer.

EDIT:

michelcolman wrote:
jpers36 wrote:
Karilyn wrote:FYI: You count to 100 on two hands using one thumb as a 5, and the other hand having fingers be 10 with the thumb being 50.

9 on the 100 scale looks the same as 5 on the traditional finger counting scale.

Forget that, I can count to 1024 on my two hands.

How do you represent zero then?

Personally, when counting in binary on my hands, I represent zero with no fingers up. Of course, this means I can only count up to 1023. (210-1)

Karilyn wrote:You count to zero on your hands?

Sure I do!

*Holds up fists*

Want a demonstration?

(Kidding! Kidding! No violent intentions here! You'd probably kick my ass anyway)
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wbeaty
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### Re: 0803: "Airfoil"

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.

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.

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.

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.

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.

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

Last edited by wbeaty on Mon Oct 11, 2010 12:08 am UTC, edited 1 time in total.
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### Re: 0803: "Airfoil"

FYI, I have never discovered America.
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### Re: 0803: "Airfoil"

rcox1 wrote:the kid that brings up the issue of imaginary numbers is probably not trying to improve the educational process, but showing off, kind of the like the five year old that knows about every dinosaurs, so thinks they know everything.

If you read XKCD, you were probably guilty of this at some point. I know I was!

Akula wrote:Even in flight school they still try to pass this off...

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.

You'd be AMAZED how poor an understanding of physics you need in order to be a flight instructor. My flight instructors have said infuriatingly wrong things not just about aerodynamics (which, I'll admit, most people don't learn in any systematic way unless they take engineering courses in college) but about basic Newtonian mechanics, the kind of misconceptions that a high schooler is supposed to NOT have. Grrr. Then again, as infuriating as that was, it's not a real problem: My flight instructors were there to help me understand airspace restrictions, how to troubleshoot problems with the airplane's systems, how to look stuff up in the FAR-AIM, how to talk on the radio, how to interpret weather reports, and all kinds of other things... and they did teach me all those things. A pilot doesn't really need to understand the nitty-gritty of aerodynamics or meteorology or even Newtonian mechanics as long as they can fly the airplane in a competent and safe way. Yes, you'd fly better if you understand physics, but you'd also DRIVE better, and we certainly don't expect people to be able to explain F=ma (or a(centrip)=v²/r or x=vt+½at² which are actually quite pertinent to driving) before they can get a driver's license.

(And when it came time for me to get a new flight instructor for my new certificates, I went to a flight school where I knew that some of the instructors are fellow Boeing engineers and wouldn't try to teach me bad physics).

Zak McKracken wrote:I often got answers along the lines of "You're right, but we can't explain the details of that to everyone now, so until we treat it next year, we're going to ignore it, because I can't teach you everything at once."

That sounds very reasonable. As long as the teacher doesn't really pretend that the model being taught is complete (as if any model could be really really complete...)

RogueCynic wrote:I don't know if its been mentioned or not but physics is not an exact science. Physics is based on the concept of mass, but what is mass? How is it measured? And why can physics not explain why the bumblebee flies?

You're joking, right? (F'ing bumblebees, how do they work?)

SirMustapha wrote:STUDENT: So how do planes fly upside down?
TEACHER: ... actually that's a good question! We should find out! *flips pages of book* Well, actually, it turns out that the wing must deflect air downwards so it can fly.
STUDENT: But how does that work:
TEACHER: ... hey! We should try to learn this! *flips pages* So here we have a chapter about aerodynamics. Here's what it says:
*2 hours later*
TEACHER: So, everyone understood it?
CLASS: ... ... ... ...
TEACHER: ISN'T LEARNING FUN??

It's a good thing I'm not a science teacher, because I'd probably do stuff like that ALL THE TIME.

Pfhorrest wrote:When I'm not in any kind of urgent hurry, I like to do this whenever young kids try to annoy me with endless strings of "why". It's kinda of like a staring contest, really just a matter of patience, and of course it helps to be generally knowledgeable enough to usually have an answer to each "why"
...
The kids usually get bored of it before I do and leave frustrated. Or occasionally the smart ones will actually be intrigued by something and start asking genuine questions instead of just inane "why"'s, and then it's fun for both of us.

You're gonna love this:

http://youtalkto.me/post/81106509/sarah ... -professor

CmdrWestside wrote:Drat, I've discovered that my latest update on the lift theory, the Coandă effect, wasn't the true explanation.

The Coanda effect isn't irrelevant. Given that air flows in a certain path (along the curvature of the wing), the reason why that generates lift has to do with Bernoulli and Euler-N and other simplifications of Navier-Stokes. But why does air flow along that certain path to begin with? The cause - or at least the FACT that it often sticks to a surface that curves away from the flow - is called the Coanda effect. So if the question is "Why does the air keep hugging the surface of the wing, and thus ends up flowing downwards and pulling the wing up, instead of just flowing straight back?", then the answer is the Coanda effect, and you wouldn't get lift out of the top of a wing if the air flowed straight back instead of hugging the surface and following it downwards. (And yes, it has to do with the pressure gradient not being adverse enough for long enough to decrease the air speed to zero... So just saying "It's the Coanda effect" doesn't really answer the "Why" question, you do have to dig a little deeper)

wbeaty wrote:
jmorgan3 wrote: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 very useful in calculation, but they offer no explanation.

I'm going to have to think about this more, but my first impulse is to disagree. I think the 2D / infinite wing illustrations do help people gain an intuition for what airflow is like around a wing and why the air ends up moving downwards even when the wing isn't at some obviously high angle of attack (e.g. when the bottom is horizontal). It's like the discussion of negative numbers and complex-number calculus: That initial picture is incomplete, but it gets some effects across, without the messy influence of other effects that can be covered later.

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### Re: 0803: "Airfoil"

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

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

Lift is the force that holds an aircraft in the air. 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. Theories on the generation of lift have become a source of great controversy and a topic for heated arguments for many years.

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. Notice that we place the names in quotation marks because neither Newton nor Bernoulli ever attempted to explain the aerodynamic lift of an object. The names of these scientists are just labels for two camps.

Looking at the lives of Bernoulli and Newton we find more similarities than differences. On the figure at the top of this page we show portraits of Daniel Bernoulli, on the left, and Sir Isaac Newton, on the right. Newton worked in many areas of mathematics and physics. He developed the theories of gravitation in 1666, when he was only 23 years old. Some twenty years later, in 1686, he presented his three laws of motion in the Principia Mathematica Philosophiae Naturalis . He and Gottfried Leibnitz are also credited with the development of the mathematics of Calculus. Bernoulli also worked in many areas of mathematics and physics and had a degree in medicine. In 1724, at age 24, he had published a mathematical work in which he investigated a problem begun by Newton concerning the flow of water from a container and several other problems involving differential equations. In 1738, his work Hydrodynamica was published. In this work, he applied the conservation of energy to fluid mechanics problems.

Which camp is correct? How is lift generated?

When a gas flows over an object, or when an object moves through a gas, the molecules of the gas are free to move about the object; they are not closely bound to one another as in a solid. Because the molecules move, there is a velocity associated with the gas. Within the gas, the velocity can have very different values at different places near the object. Bernoulli's equation, which was named for Daniel Bernoulli, relates the pressure in a gas to the local velocity; so as the velocity changes around the object, the pressure changes as well. Adding up (integrating) the pressure variation times the area around the entire body determines the aerodynamic force on the body. The lift is the component of the aerodynamic force which is perpendicular to the original flow direction of the gas. The drag is the component of the aerodynamic force which is parallel to the original flow direction of the gas. Now adding up the velocity variation around the object instead of the pressure variation also determines the aerodynamic force. The integrated velocity variation around the object produces a net turning of the gas flow. From Newton's third law of motion, a turning action of the flow will result in a re-action (aerodynamic force) on the object. So both "Bernoulli" and "Newton" are correct. Integrating the effects of either the pressure or the velocity determines the aerodynamic force on an object. We can use equations developed by each of them to determine the magnitude and direction of the aerodynamic force.

What is the argument?

Arguments arise because people mis-apply Bernoulli and Newton's equations and because they over-simplify the description of the problem of aerodynamic lift. The most popular incorrect theory of lift arises from a mis-application of Bernoulli's equation. The theory is known as the "equal transit time" or "longer path" theory which states that wings are designed with the upper surface longer than the lower surface, to generate higher velocities on the upper surface because the molecules of gas on the upper surface have to reach the trailing edge at the same time as the molecules on the lower surface. The theory then invokes Bernoulli's equation to explain lower pressure on the upper surface and higher pressure on the lower surface resulting in a lift force. The error in this theory involves the specification of the velocity on the upper surface. In reality, the velocity on the upper surface of a lifting wing is much higher than the velocity which produces an equal transit time. If we know the correct velocity distribution, we can use Bernoulli's equation to get the pressure, then use the pressure to determine the force. But the equal transit velocity is not the correct velocity. Another incorrect theory uses a Venturi flow to try to determine the velocity. But this also gives the wrong answer since a wing section isn't really half a Venturi nozzle. There is also an incorrect theory which uses Newton's third law applied to the bottom surface of a wing. This theory equates aerodynamic lift to a stone skipping across the water. It neglects the physical reality that both the lower and upper surface of a wing contribute to the turning of a flow of gas.

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.
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