Theories of Flight.
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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.
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.
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!
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!
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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
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
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
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
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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!
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!
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).
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).
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<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).
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).
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...
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?
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?
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.
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.
bookworm, I may have oversimplified, but that is what instructors do! 
What I meant was:
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)
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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.
Checkboard
What's the source for your quote? I don't really follow the:
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.
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.
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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....
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....
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.
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.
My apologies, bookworm, the quote was from the Bernoulli Versus Newton page, which is about the fourth page deep in the nasa tutorial CaptainCargo showed as a link in the thread's first post.
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.
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.
