Theories of Flight.

[CaptainCargo]

When I was learning to fly, which was quite a while ago, I was told Bernoullis theory explained lift. However, for some time now it has been apparent that his theory (and it's still a theory) is wrong. It was developed by studying incompressible fluids in pipes. As explained at http://wright.grc.nasa.gov/WWW/K-12/airplane/right2.html Newtons second Law of Motion can be used to explain lift.
The next page (arrow on bottom of page) explains why Bernouillis Theorem is wrong. Is anyone still being taught this theory of flight, and if so, why? Or is this heresy?
Amazing that, a hundred years on, we're still not sure, 100%, why wings do fly.

[Genghis the Engineer]

I have an aeronautics degree, in the course of which I learned 3 or 4 different explanations of how an aeroplane flies. They were at-least to some extent contradictory, but also all worked in certain circumstances.

Bernoulli is a vital part of an aeronautical engineer's toolbox, but is only one of various principles used. The important question is "what do I want to know". That might be how much lift, how much drag, what will the effects of alpha / beta / flap / slat / bank angle / etc. be. When presented by such a question, you pick the theory that answers the question best.

For pilots, Bernoulli's theorem has worked very well for years, because they don't need an ability to accurately predict aircraft behaviour - they need a reasonably feeling for why the aircraft flies and what will stop it. It's not heresy, it's an adequate working model.


In the meantime, bear in mind what a scientific or engineering theory is. It is the best model, to predict what is happening, for a given situation. TRUTH is a concept that scientists and engineers don't work in, they work in good and bad models, and in probabilities. TRUTH we leave to priests who deal in unprovable certainties, in science and engineering certainties are usually unprovable. If you meet a scientist or Engineer who offers you a clear certainty of anything, distrust them, they are a poor member of their profession.

G

[john_tullamarine]

May a second engineer second the first engineer's post ...?

[Flathatter]

Genghis, where can I read up on these 3-4 different explanations?

[bookworm]

The next page (arrow on bottom of page) explains why Bernouillis Theorem is wrong.

It does nothing of the sort. It explains why the "equal transit time" assertion, which is sometimes used to explain lift to pilots by flight instructors, is wrong.

Bernoulli's theorem simply relates the pressure in an airflow to its velocity. It's correct for low-speed inviscid flow, which is a model that has been producing very consistent and accurate predictions of aerodynamic quantities for 90 years.

The air flowing over the top of the lifting wing is moving faster than that flowing below it, and the pressure is therefore lower. The fallacy is in the explanation for why the air over the top is moving faster.

You may not be sure why wings fly, but aerodynamicists and engineers have been for most of the last century!

[CaptainCargo]

It's not that I am unsure of why wings fly: I've read quite a bit on the subject. The whole thing is very well explained at http://wright.grc.nasa.gov/WWW/K-12/airplane/bernnew.html
What I was trying to point out is that very few pilots have heard anything beyond Bernoullis' Theorem. In three years sim training, I have only come across two pilots who'd ever heard of any other explanation.
I was merely making the point that this theorem appears to be used to make people learning to fly think that they understand the principles of aerodynamics. I was certainly never told of any Newtonian explanation when I wrote my ATPL exams. Surely this should be part of the curriculum. Or is it taught on a "need to know" basis? As long as pilots believe it will fly, they don't need to really understand why?

[Genghis the Engineer]

Flatthatt, if you go and find the bookshop at any University with an aeronautical Engineering department, you'll find a selection of textbooks with titles along the lines of "aerodynamics for engineers", most of which are a bit excessively mathematical but will usually cover a fair selection of theories.

When I was a student the standard book was "Aerodynamics for Engineering Students", by E.L. Houghton and N.B. Carruthers. I have my 10 year old copy in front of me which lists the following in the contents page...

- Bernoulli (2d inviscid flow theory)
- 2D viscous flow theory
- Finite aerofoil theory (using the simplified horseshoe vortex model)
- Estimation of pressure distributions from boundary layer theory.
- Mach number effects and supersonic flow / thin wing aerodynamics.
(so that's five methods, I'd forgotten the BL method, which is usually only used for drag estimation rather than lift).

Interestingly I also recently acquired a 1930 reprint of a 1926 textbook by Glauert called "aerofoil and airscrew theory" which has Bernoulli's theory on page 10, basic aerofoil theory (the 2D viscous flow method) on page 117 and 3D viscous flow on page 125. He also lists the same two methods (momentum method and blade element method) as Houghton for how propellers work. What I really love about Glauert's book however is the separate chapters on monoplane and biplane aerofoil effects, the latter is sadly missing from most modern textbooks.


Hope that help, it's also fascinating that 3 out of the 5 methods I learned in the 80s and 90s were already published in the 20s.

G


N.B. Bookworm, Engineers and Scientists are most certainly not sure about why wings fly. We are pretty confident that we can predict whether they will and how well, but as to why - no. I asked this in my office (containing four qualified aeronautical Engineers from CEng to HNC) recently and nobody was prepared to say that they did.

[oxford blue]

I have decided to remove my original post from this slot, beause my argument over-simplified the case. There is some pretty sophisticated engineering further downstream on this thread and my simple model does not stand up to that sort of level of analysis.

Oxford Blue

[bookworm]

N.B. Bookworm, Engineers and Scientists are most certainly not sure about why wings fly. We are pretty confident that we can predict whether they will and how well, but as to why - no. I asked this in my office (containing four qualified aeronautical Engineers from CEng to HNC) recently and nobody was prepared to say that they did.

Oh c'mon Genghis...

That's tautologous. By that standard no one can ever say "why" anything in nature is the way it is, we can only explain it in a quantitative and predictive way in terms of other models.

If you see an apple fall to the ground, can you say "why" it fell? You can certainly predict whether it will and how fast, but "why"? That would seem to require the mind of God.

Low-speed aerodynamics is as well understood as any other area of applied physics, and to maintain that science has been baffled for 100 years by the nature of lift is simply daft!

[GoneWest]

Don't mean to hijack the thread - but whilst engineers are talking about information given to student pilots...I asked recently about the "engineering" view on "How many Forces" act on an aircraft in flight.

The purists seem to be starting to say Three Forces, not four...as taught to pilots.

Only answers I got were from pilots - who all said "four" - anybody disagree?

[bookworm]

CaptainCargo

I apologise if I misunderstood the motivation for your post. I did not interpret it from your original message. If your point is that this is an aspect of science that is both difficult and generally poorly taught, I wholeheartedly agree.

Before you start the campaign to strike out mention of Bernoulli's theorem in any elementary texts though, I would caution you to consider carefully the logic of the arguments presented.

The super little Java simulator in one of your links demonstrates very nicely that the flow pattern around an aerofoil is predictable. Once you know the flow pattern, you can calculate the lift. I'd be very surprised if the FoilSim applet does much integration of momentum fluxes in a Newtonian way -- more likely it uses Bernoulli's theorem to calculate the pressure at each surface knowing the velocity (you'll see they calculate the pressure coefficient).

The key part of the "why" that is so difficult to explain simply is "Why is the flow pattern the way it is?" The physicist's explanation is that it is calculable from the governing equations and the boundary conditions -- just do the sums.

But that's very unsatisfying for the layman, who doesn't want to be told, for example, that gravity obeys a relatively simple set of field equations if you'd just solve them for the earth and the moon, but rather prefers to be given Keppler's laws that describe the motion of the planets and satellites. So we're left with a need to give a simple explanation of why the flow pattern around a wing looks the way it looks.

The Equal Transit Time" assertion (http://wright.grc.nasa.gov/WWW/K-12/airplane/wrong1.html) (pleeeeeaaaaase don't call it "Bernoulli's theorem") is one little untruth designed to do just that. It gets the right result for the wrong reason.

So knowing that it's untrue, you understandably reach out for an alternative. How about "air gets deflected downwards"? That seems to be the gist of the "turning flow" argument that you want to prefer. But does that explain why so much airflow changes direction around the wing? Before you say "yes, it's obvious", take a look at the Skipping Stone theory (http://wright.grc.nasa.gov/WWW/K-12/airplane/wrong2.html), put your hand on your heart and tell me that this is not the picture at the back of your mind when you say "of course the air is deflected downwards". But as an explanation, it's just as wrong as the first one.

I have to admit defeat here. I cannot come up with a good intuitive non-circular explanation of why the air moves faster over the top of a lifting aerofoil than over the bottom, or why a huge tranche of air is deflected in its vicinity, at least not one that stands up to detailed inspection. The best I can do is along the lines of asserting that the flow must be parallel to the trailing edge, and the only allowable flow that fits the symmetry of the situation is something that circulates around the aerofoil. But that's more of a qualitative explanation of the way the maths works than an explnation in its own right. Even so, the inability to provide a simplistic explanation is not, IMHO, the same as saying that we don't understand something. For anyone who wants to, the theory is there, and it's been perfectly well tested and proven over a hundred years of practial flight.

[CaptainCargo]

The skipping stone theory is obviously flawed, as it does not take into account the flow over the upper surface. Neither does the equal transit time theory work, as it does not explain
symettrical aerofoils.
I'm not saying ditch Bernouillis'Theorem, as it does work, and can be used to predict the lift generated by an aerofoil. I just find it a bit strange that the Newtonian explanation has not found its way into the piliots curriculum, at least it hadn't when I last saw a copy of the ATPL syllabus. Bernouillis' Theorem is taught as the only explanation of lift, when it is, in fact, exactly as its name suggests, a theory.
As I said in my first post, and genghis concurred,no-one is really sure what the correct explanation for lift is, they just have models that (usually)work. I think pilots should be taught this.

[bookworm]

I'm not saying ditch Bernouillis'Theorem

Oh I'm sorry -- I must have misunderstood your original post where you twice claimed that it is "wrong". :rolleyes:

To say that it's "just a theory" is all very well, but as Genghis conjectures, everything in science is "just a theory". Next time you want to find the length of the hypotenuse of a right-angled triangle, be careful when applying Pythagoras's Theorem -- it is, after all, "just a theory". :)

Ultimately, all the mechanics we do is derived from Newton's Laws of motion -- even Bernoulli's theorem. The Newtonian approach that you cite is fine as far as it goes, but I have two issues with it:

1) It's just another way of calculating the lift once you know the flow field. It's not a very direct one.

Imagine I placed a watepaper bin in a corridor (in a very litter conscious office :) ) and wanted to know the weight of the contents at the end of the day. Compare the following methods:

a) Weigh every person entering the corridor during the day as they enter. Weigh every person leaving the corridor during the day as they leave. Subtract the totals and deduce the weight of the contents added to the bin during the day.

b) Weigh the contents.

In principle, both are possible and correct. Applying Newton's Second Law (using the Momentum Theorem) to find the lift of a wing is a bit like method a). It's good to know it works, and perhaps it adds some insight to the understanding of the problem. But if you know the speed of flow at each point over the surface of the wing, why not use it directly to find the pressure? :)

2) It often leads to some incorrect assertions. For example, it's common to hear that the "lift of the wing is equal to the rate at which air momentum is tranfered downwards" or worse that "an aerodynamic force can only be generated by changing the momentum of air". Neither give a very complete picture of the physics -- for example in ground effect you have to add in the increased pressure on the ground as well as any momentum changes. Even in free flow, you have to be very careful about the way you add up the momentum to make it work. I note, BTW, that the Lift from Turning Flow page avoids any of these horrors.

I'm sorry to rant. I'm just a bit fed up with seeing a load of "Shock horror -- Established Aerodynamics Proved Wrong" headlines from people who don't understand the physics. I appreciate that yours was a genuine attempt to highlight some important shortcomings in the way pilots are taught aerodynamics. I hope you've enjoyed the debate.

[niallcooney]

Guys,

Check out this link... extremely detailed but easy to understand.

http://www.monmouth.com/~jsd/how/htm/airfoils.html

Nial

[John Farley]

Oxford

Sorry if it seems to cut across your ideas, but Mr Bernoulli actually has no trouble with generating lift regardless of the wing cross section or any airframe related angle of incidence. It may help you to visualise why if you consider the task of carrying a sheet of 8x4 chipboard (or MDF if you are richer than some) from the B&Q door to your car in a strong wind. Edge on it is not very aerodynamic and easy to carry. At an angle of attack (AOA) of say 20 deg you might just find it leaves your sweaty grasp.

The reason that Mr Bernoulli’s explanation applies to this flat uncambered surface is thanks to something called the stagnation point (SP). The SP is that point (looking at a cross section of any wing) above which all air goes over the top surface and below which all air goes underneath.

If you are still bothering to read this, consider holding your board at a 90 deg AOA to the wind (no lift but plenty of drag) the SP is right in the middle of the board (this would be much easier with a pencil and paper) if you now rotate the board slowly back towards 0 deg AOA the SP moves slowly towards the leading edge (LE) but only gets there at 0 deg. At say 10 deg the SP is still a little way back from the LE (and of course on the undersurface of your board) and so the air that goes over the top actually has a longer journey than the air that goes underneath because it starts its journey from a little way back on the bottom surface.

Regards

[spudskier]

I'm actually a student right now at a major university working on my private. They are definitely teaching Bernouillis principle here... the venturi effect if you will. To me anyway, it doesn't completely explain flight.

I was an AP physics student in High School so I know there are other explanations, but I don't have nearly enough authority or knowledge to conest it.

['%MAC']

Wow this thread has really taken off, 2 pages already and it was only posted yesterday. Wonder if it’s due to Bernoulli, Kutta, Joukowski, or simply the Magnus effect. Coanda was discussed earlier.

That’s all, nothing useful

Oh, one more thing as G the E said, engineers, and scientists deal with probabilities and not certainties, or more precisely they do not deal with 100% probabilities. These theories you all are discussing on the thread were borne from consensus. Bunch of researchers sat around in a conference and said, yeah that sounds reasonable; the math and research supports the model, we’ll adopt it. Except it is not quite so clean and tidy; politics and personal egos always get involved. Clearly certainties can be part of engineering and the sciences, but only when it is defined as a probability as in p>.0001 or some such nonsense. A measure of conviction is required for prudent action, whether you call that a certainty or a p value. Anyway carry on, it's most entertaining. :)

[CaptainCargo]

I don't pretend to be an engineer, the reason I started this thread was to see if anyone could explain why only one theory of flight is currently taught to pilots. That, and to see what the techies on the site had to say about it. My apologies for being deliberately contentious when I made my first post, but it did elicit the response I was hoping. It's been most interesting. More interesting, perhaps, would be to run a poll, preferably on a different forum (less techies), asking what percentage of pilots have ever heard of more than one theory of flight.
The first I heard of a Newtonian theory was when I went on a performance refresher a few years ago. At the end of the session, the chap teaching us said that he had a few hours before his flight, and was anyone interested in seeing a different explanation of lift to that we were taught when learning to fly. Only two of us stayed (out of about twenty), which perhaps proves that the majority of pilots are not particularly interested in why their aircraft fly. Thanks for your replies.

[bookworm]

CaptainCargo

You may find David Anderson's Understanding Flight (http://www.amazon.co.uk/exec/obidos/ASIN/0071363777/) an interesting read , as well as his article (http://www.aa.washington.edu/faculty/eberhardt/lift.htm) and John Denker's critique (http://www.monmouth.com/~jsd/fly/lift.htm) of it.

Thanks for rattling the cage. :)

[Algy]

Over the years I've asked umpteen pilots, engineers, lecturerers, etc, etc the question - in nom-mathematical terms how does a wing work? I've never had the same answer twice but I've hugely enjoyed the discussion - and this latest one.

Line pilots inevitably give the old chestnut of longer distance/same time and are amazed if you suggest that it might not be entirely, how can I put this, true. Professors tend to start speaking and then suddenly stop as they realise the tricky ground ahead.

I was recently greatly impressed by the answer from a young, working engineer with a major airframer. A full and frank admission of the difficulties and a sketch of the prime competing theories. So impressed indeed that we are in the process of hiring him (for other reasons too I hasten to add).

[Evo7]

The issue that I don't understand is the apparant chicken & egg situation regarding high velocity/low pressure over the top of the wing.

To simplify and paraphrase Bernoulli, the sum of the static and dynamic pressures is constant, so if the flow velocity is high then the dynamic pressure increases and the static pressure will drop. Fine.

Why is velocity of air over the wing faster? Well, the pressure above the wing is lower than the static pressure away from the wing - there must therefore be a force acting on a parcel of air passing over the wing and thereby accelerating it (the force is just proportional to grad(P) / rho -> larger pressure gradient = stronger force). However, the pressure is low because the velocity is high - the arguement seems circular.

Hopefully I've explained my confusion - but what am I missing? After this point I can understand splitting the airflow into equal velocity & circulatory components, that Kutta-Zhukovsky tells you that lift is proportional to circulation (amongst other things) and the rest of it. It may not explain everything, but I'm happy with it. It's just the origin of the pressure and velocity fields that I'm having trouble understanding.

:confused:

[bookworm]

Evo7

I don't think you're missing anything at all. You've laid out the the dilemma nicely, and I've never seen a "nice" explanation I've liked.

If you're happy with explanations that are fairly mathematical in nature, try the following. Forget pressure and concentrate on velocity for now. The only flows that can be constructed to satisfy the basic equations of incompressible, inviscid fluid mechanics are:

- trivial uniform flows
- vortices
- source-sink dipoles (and higher orders)

Dipoles have the the wrong symmetry (though you need them to match boundary conditions for a wing of non-zero thickness), so the only way to get a downward component of flow at the trailing edge (Kutta condition) is to have a vortex, or collection of vortices.

That leads inevitably to the concept of circulation around the wing -- you can't have a downward component at the trailing edge without an upward component at the leading edge, a downstream component above the aerofoil and an upstream component below it. It's a consequence of the incompressibility.

Is that an "explanation"? At some level I suppose, but it doesn't exactly get the Feynman award for intuitive communication!

[4PON4PIN]

The theory of flight is complex, even to the point of take-off. However, it is essential to remember that it is the theory that provides the lift to keep an a/c airborne. If you took away the theory, even for a moment, the thing would plummet like a stone.

Again, pencil and paper would be useful, but please use your imagination to follow me through....

Imagine a basic aerofoil shape, in cross-section, and I'll explain how it is all to do with the pressure differences between the top and the bottom of the wing. (Some people think pressure difference is the reason why a cricket ball swings through the air, but in fact that is just sheer fluke).

Ok, so the top of the wing has a nice STEEP curve, so let us call that S for steep. But the bottom of the wing has a much more SHALLOW curve so I'll label that S for shallow. Now if you imagine two identical particles of air travelling towards the wing, one I will call A and the other one I'll call...... A as well.... because they're identical.

Right, now these two particles of air are going to be divided when they hit the leading edge of the wing (which is in the front, so let me label that point F for FRONT.) However, they have to meet up again at the rear of the wing (which is where the FLAPS are.. so let us call that F for FLAPS).

So.. particle A has to pass over S to point F, in the same time that it takes particle A to pass over S to point F. But... one of those particles has to travel a greater distance to get from point F to point F, than the other. Which is it? Is it particle A or particle A?

I think MOST of you got it spot on.. it is of course particle A.

OK, so now we know that particle A has to pass over S to point F in exactly the same time as it takes particle A to pass over S to point F. But particle A has a greater distance to travel than particle A, so how does it achieve the same time?

NO! Cornish Jack it does NOT set off earlier!!!!

If you lot are not going to take this seriously, then I won't waste any more of your time. Goodbye

with acknowledgements to "Roy Mallard" - Other Peoples Lives

[Genghis the Engineer]

Many years ago a very young Genghis and several other then wannabee Engineers were sat in a tutorial with Professor Robin East (now allegedly retired, although I still see him at RAeS lectures occasionally) who was one of the driest lecturers and most clear and lucid tutorial supervisors I've ever known.

Prof. East asked us this very question, and we all gave various versions of Bernoulli, 2D, 3D, viscous, inviscid - you know the drill.

He heard us out, then said - "you're making it far too complicated",

"Look at it this way", he said. "An aeroplane travels forwards, whilst doing so it has a shape which continuously deflects air downward. Since it takes a force to do this, and every force has an equal and opposite reaction, you get lift".

If you use prof.East's basic premise, and establish that the rest are all simply means to predict how the lift behaves, it makes some kind of sense.

G

[Keith.Williams.]

Genghis,

Your professor is my kind of teacher.

When dealing with the subject of lift I start by telling the students that "The wing of an aircraft is simply a tool used to accelerate air downwards. Everything else that we will look at regarding this subject is concerned with how it achieves this downward acceleration and the consequences of it doing so".

Bernouli gives an exellent explanation of how a low pressure area is created above the wing. Once the students accept the fact that this low pressure area holds up the wing, I ask "so now what holds up the low pressure area"?

This brings us nicely on to the newtonian effects of air above the low pressure area being drawn down into it. This in turn leads to an entirely intuitive explanation of downwash and lift-induced drag. It is surprising how many of the more experienced students (usually ex CFS QFI types) are completely stumped by the question "so what holds up the low pressure area"?

I realise that this approach does not explain the minute details of every possible aspect of the airflows around wings, but we must be careful that our explanations are actually intelligible to the students. When I first started in the business of teaching POF to CAA students, I sat in on a course presented by another instuctor. He was particularly keen on circulation theory, so this is what he used. Towards the end of the lesson on lift, a maltese student sitting next to me looked across to me and asked "Is he really saying that the air flows over the wing from the leading edge to the trailing edge, then flows back to the leading edge underneath it"? when I shook my head he collapsed into his seat.


Captain Cargo,

You are correct in saying that the Newtonian explanation of lift is not included in the JAR ATPL syllabus. But strangely enough they have asked questions about it!

[Checkboard]

The difference between the explainations are because aeronautical engineers and physists are looking for a theoretical model that allows them to calculate the amount of lift a given airfoil will produce under a given situation - which is handy if you are designing an aircraft.

That is why they "complain" about the Bernoilli explaination of lift - it is difficult to apply Bernoilli's equations (developed for fluid flow in tubes) to freestream airflow over a wing, and calculate the amount of lift the wing will produce.

As pilots, we really don't care about that - we want to know how the wing will react in flight to changes of angle of attack, camber (flaps), damage, airspeed etc etc. The "Bernoilli explaination" allows us to set up a reasonable (albeit simplified) mental model that permits us to intuit the wing's response in flight. That is why it is by far and away the most popular method taught to pilots to "explain" lift. It's an instructor thing - instructors who rattle on about circulation and newtonian physics may be presenting a more accurate picture - but their students will never be able to build a mental model useful in flight from that explaination (evidence the post above).

[Evo7]

<snipped>

It's an instructor thing - instructors who rattle on about circulation and newtonian physics may be presenting a more accurate picture - but their students will never be able to build a mental model useful in flight from that explaination (evidence the post above).


Checkboard - assuming that you're referring to my post, my instructor has nothing to do with it. It's just my curiosity. I've got a PhD in Physics, and the explanation of the principles of flight that comes at PPL level is so obviously flawed (it isn't even dimensionally correct) that I went in search of a better one.

However, so far I've just used Denker's "See how it flies" and Barnard & Phillpot's "Aircraft Flight" (even with a PhD I find books without equations lighter reading...), neither of which deals with my query above - so I'm still not happy. However, I understand exactly what bookworm is getting at, so when I get the time I'll go find a book that doesn't leave the equations out and work through it.

I do like Genghis's Professor's version - I'll remember that next time I'm getting ready for a lecture on circulation... :)

[bookworm]

Einstein said: "Everything should be made as simple as possible, but not simpler."

I can't argue for a moment with the line Genghis quotes from East. We need explanations at a number of different levels, provided they don't mislead. But it is important to be able to peel back the layers of the onion when the need for a more sophisticated model arises. That's the nature of physics.

For me what's special about lift, and what helps aeroplanes fly, is not that air is deflected by an aerofoil, but rather what a huge amount is deflected. And an explanation that doesn't approach that aspect doesn't fully satisfy my curiosity as to why it took more than two centuries after Newton before man mastered flight.

Checkboard

Using Bernoulli's theorem is the way that the amount of lift from a wing is calculated. Consult any text that offers a quantitative model.

Keith

I too am thoroughly stumped by your question "so what holds up the low pressure area?". :) What do you tell your students as an answer?

[Tinstaafl]

What holds up the low pressure?

Air above/beside/infront/behind being accelerated into the low pressure region, leaving in turn a continually reproducing low pressure area in the region those particles have just left.


I'll stick with Bernoulli. As Checkers says, it's gets enough of the message across to pilot students to be easily comprehended & still be useful.

[Checkboard]

bookworm, I may have oversimplified, but that is what instructors do! ;) What I meant was:
The lift and drag forces on a body can be found by integrating the pressure times the area around the body if the pressure is known. The pressure can be determined from Bernoulli's equation as long as none of the assumptions of the equation are violated and the velocity variation is known. How is the velocity variation determined? A simple one dimensional, Venturi flow relation could be used. But this gives the wrong answer since a wing section isn't really half a Venturi nozzle. A similar incorrect answer is obtained if the velocity is set to the velocity necessary for air molecules to separate at the leading edge and meet at the trailing edge of the airfoil. The best way to get the velocity variation is to use the "Newton" theory and determine the flow turning caused by a given shape. It isn't easy to determine the velocity variation for a general shape. But for some simple shapes, the velocity variation can be determined. In order to use the "Bernoulli" theory to solve a practical problem, we usually use the "Newton" theory to determine the velocity distribution. (emphasis mine)

[Prof2MDA]

Surprised that nobody has jumped on Oxford's post, where another classic misconception is put forth, that of implying that the Newtonian model for lift and Bernoulli each explain part of the lift and that they two parts of the whole, rather than just being alternative models for the same thing. There is no such thing as being "part Newton" and "part Bernoulli". I like the description above to measure waste paper, that's a good analogy.

[bookworm]

Checkboard

What's the source for your quote? I don't really follow the:

The best way to get the velocity variation is to use the "Newton" theory and determine the flow turning caused by a given shape.

The velocity field is found by solving the partial differential equation that governs it (Laplace's equation for the velocity potential). I don't see how the "Newton theory" as it has been presented here (macroscopic application of Newton'd second law) helps with that, except in the sense that all fluid mechanics, including Bernoulli's theorem, is ultimately an application of Newton's laws at the microsopic level.

[CaptainCargo]

Maybe I'll stick with Bernouiliis' Theorem after all..it's getting far too complicated here....
Seriously, though, I've been amazed at the response this thread has received...obviously, not everyone agrees on how a wing works, or what is the best explanation of how it does. It's been very interesting, and I've now got loads of reading to do....thanks!

As far as only teaching Bernouilli to students, I still think they should be taught the Newtonian theory, even if it is more difficult to explain, which I don't think it is.

Or perhaps, if pilots are not 100% sure what's keeping their aircraft in the sky, they will plummet earthwards.......maybe wings only fly because we think they can....

[Tinstaafl]

Not quite, Capt. Cargo.

We all agree that a wing produces lift. There is just discussion over which model best describes it.

Remember a model is just that: a representation of observed, calculated or hypothesised phenomina. They're not the event themselves & all suffer some degree of error &/or approximation.

Newton's theories of motion aren't the 'be all & end all' when it comes to describing motion. Einstein's relativity theory is a further refinement on it and accounts for discrepancies between observed facts & the Newtonian theory.

Even Einstein's theories are still not necessarily the end of the story eg they don't account for quantum effects.

[Checkboard]

My apologies, bookworm, the quote was from the Bernoulli Versus Newton (http://wright.grc.nasa.gov/WWW/K-12/airplane/bernnew.html) page, which is about the fourth page deep in the nasa tutorial CaptainCargo showed as a link in the thread's first post.

[bookworm]

Thanks CheckBoard. I should have realised it was a passage from there.

Generally I've found those pages to be very good and carefully written to avoid any misinterpretation. I've emailed the author asking for more detail on what he means by that part. I'll report back if I get a response.