Turbulence Required For Lift

  • #27
Suggest looking at the web book by Dr. John S. Denker, "see how it flies": https://www.av8n.com/how/
Check chapter 3.
Also checkout his web page on physics topics.
 
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  • #29
Very good article. I have read quite a bit of Denker's works. Also, emailed him a couple of times. The first time an instructor put me into a spin my first thought was "this could kill me", it looks like you are going straight down, you aren't but it seems like it. You certainly don't have time to analyze the situation - just react.
 
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  • #30
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Yes, that's exactly what I'm referring to.
I thought that was what was referenced by "circular flow". My understanding is that it isn't actually physically true. That circular flow is just a conceptual model of relative flow velocities once you remove the average flow velocity. I am not convinced the conceptual model is correct at the trailing edge as the 2 streams join there. The real flow is always downstream however. It has been a useful concept historically though.

Also, my understanding is that Bernoulli does not account for the sum total lift measured in practice. It seems to me this and accelerating the flow downwards both contribute to the total lift force.
 
  • #31
russ_watters
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Also, my understanding is that Bernoulli does not account for the sum total lift measured in practice.
It actually does. It's common to represent lift and a pressure profile over/under the wing, along with the associated velocity profile per Bernoulli's principle.
 
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  • #32
I thought that was what was referenced by "circular flow". My understanding is that it isn't actually physically true. That circular flow is just a conceptual model of relative flow velocities once you remove the average flow velocity. I am not convinced the conceptual model is correct at the trailing edge as the 2 streams join there. The real flow is always downstream however. It has been a useful concept historically though.

Also, my understanding is that Bernoulli does not account for the sum total lift measured in practice. It seems to me this and accelerating the flow downwards both contribute to the total lift force.
Denker specifically mentions the physical laws are not cumulative, that is, you don't get some lift because of one law and some from another. All the physical laws are operating simultaneously. So you have event called lift and when that event, a fluid motion problem, is in effect you have Bernoulli's equation available and Newton's various laws. You choose the equations that make solving a particular problem easiest. As a corollary you could look at an electrical circuit - you don't get some current in a branch due to Kirchhoff's voltage law and some due the current law; they are both in effect simultaneously and you use whatever combination of associated equations needed to solve the problem. Denker does show a nice example of Newton's conservation of momentum as related to a wing but that in no way affects the Bernoulli effects - both are just there simultaneously.
 
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  • #33
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Also, my understanding is that Bernoulli does not account for the sum total lift measured in practice.
That would mean Bernoulli is wrong. Lift always needs (or is) a force acting between airfoil and air in addition to buoyancy. This force requires (or is equivalent to) a pressure difference between top and bottom side of the airfoil in addition to the static pressure difference and corresponds to different velocities according to Bernoulli. This is always the case as long as the Bernoulli equation holds.

It seems to me this and accelerating the flow downwards both contribute to the total lift force.
Whereas there always needs to be a pressure difference according to Bernoulli, there doesn't need to be a downward acceleration of the air. This is just the usual case for airplanes because there is nothing below or above the airfoil that excerts additional forces on the air. In that case the force from the airfoil is equal to the net force acting on the air around it and therefore accelerates it downward according to Newton 2. But this is not the only possible case. Exceptions without or with reduced downwash have already been mentioned above (flying within a tube or near the ground). In these cases the downward acceleration of the air doesn't correspond to the force between air and airfoil.

The downward acceleration of the air is not only not a necessary condition for lift. It actually is an unwanted side effect because it reduces the lift. When air flows out of the high pressure zone below the wing or into the low pressure zone above the wing the pressure difference and therefore the lift is decreased. At normal conditions only the direct air flow from the bottom to the top side around the wing tip can be reduced (e.g. by winglets). But at very low altitudes it is also possible do reduce the downwash because the gound prevents the air from escaping downward. If lift would be supported by the downwash, it should be reduced under these conditions. But instead it is significantly increased (ground effect).
 
  • #34
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It actually does. It's common to represent lift and a pressure profile over/under the wing, along with the associated velocity profile per Bernoulli's principle.
I have seen a few lectures where a contra view is presented. Who should I believe and why? Certainly, lift can be explained by the pressure gradients across surfaces. Can you mathematically show that those pressure gradients are totally explained by Bernoulli's principle, even for a symmetrical wing near CLcrit? The reason I ask is that the difference in length of the 2 surfaces is only very slightly different due entirely to the change in stagnation point on the LE with AOA. The rest of the curve is the same. If the flow splits at the stagnation point and re-joins at the TE, then the 2 flows have almost the same mean velocity.

While I have an interest, I can not work the proof myself so must rely on technical articles etc. If they disagree on this point, it seems a controversial topic with no clarity as to the truth.
 
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  • #35
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Can you mathematically show that those pressure gradients are totally explained by Bernoulli's principle, even for a symmetrical wing near CLcrit?
The lift can be calculated by integration of the pressure over the surface (and than subtracting buoyancy). But in order go get the pressure profile according Bernoulli the velocity profile must be given. If you are looking for a general proof, not only for a special case with known velocity profile, then Bernoulli alone is not sufficient. I'm not even sure if such a proof is possible because we don't have general solutions of the Navier-Stokes equations. But we can check it for every special case. Do you have an example for a velocity profile that doesn't match the pressure profile according Bernoulli?

The reason I ask is that the difference in length of the 2 surfaces is only very slightly different due entirely to the change in stagnation point on the LE with AOA. The rest of the curve is the same. If the flow splits at the stagnation point and re-joins at the TE, then the 2 flows have almost the same mean velocity.
Why should that be a problem? Lift results from the velocity profile over the whole surface of the airfoil and not from the velocities at two special points only and with different velocities you get different forces even if top and bottom side of the profile have the same length.
 
  • #36
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The lift can be calculated by integration of the pressure over the surface (and than subtracting buoyancy). But in order go get the pressure profile according Bernoulli the velocity profile must be given. If you are looking for a general proof, not only for a special case with known velocity profile, then Bernoulli alone is not sufficient. I'm not even sure if such a proof is possible because we don't have general solutions of the Navier-Stokes equations. But we can check it for every special case. Do you have an example for a velocity profile that doesn't match the pressure profile according Bernoulli?



Why should that be a problem? Lift results from the velocity profile over the whole surface of the airfoil and not from the velocities at two special points only and with different velocities you get different forces even if top and bottom side of the profile have the same length.
No, I don't have example velocity profiles. I am just going by statements in lectures and technical notes that I have come across over the years. The nature of this is that I do not have references either. I am not insisting anything here, it just seems to me a point of some controversy that I’d like to better understand. In truth, I probably don’t have a high enough technical background to do so but why not ask and see if I can learn something at least.

“Why should that be a problem?....” Well, that whole concept of upper surface greater distance in the same time, just always seemed too schoolboy simple and convenient. So, I’m fishing to for enlightening comment.

Ken
 
  • #37
A.T.
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...Well, that whole concept of upper surface greater distance in the same time, just always seemed too schoolboy simple and convenient. ...
Same time is wrong. The upper time is usually shorter, despite greater distance.
 
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  • #38
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Well, that whole concept of upper surface greater distance in the same time, just always seemed too schoolboy simple and convenient.
It is at least strongly misleading. Of course higher speed results in greater distance at the same time. But the flows on top and buttom side don't pass the profile in the same time.
 
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  • #39
russ_watters
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I have seen a few lectures where a contra view is presented. Who should I believe and why?
Without seeing those lectures myself, I can't respond to them directly - I don't know what they said or how it was interpreted. What I will say is that it seems a relatively recent internet phenomena (10-15 years) where teaching lift by attacking fallacies has become popular, and unfortunately when you focus so strongly on fallacies without teaching the realities, it creates new, opposite fallacies. Bernoulli has been incorrectly tied to the most popular fallacy, which has lead people to believe even if just by implication that Bernoulli's principle itself is a fallacy. It isn't.

The other thread that is active in this forum right now (recently resurrected from February) is an example of this problem. But the OP, to his credit, recognized that he was being misled:
https://www.physicsforums.com/threa...ift-current-vs-historical-discussions.984585/
Certainly, lift can be explained by the pressure gradients across surfaces. Can you mathematically show that those pressure gradients are totally explained by Bernoulli's principle...
Of course. Here's an explanation of how it works:
https://www.mh-aerotools.de/airfoils/velocitydistributions.htm
...even for a symmetrical wing near CLcrit?
What does that have to do with it? Bernoulli's principle doesn't explain why the speed changes, it only explains how speed and pressure are related. That's it. Anything else is a mis-application/over-reach.
The reason I ask is that the difference in length of the 2 surfaces is only very slightly different due entirely to the change in stagnation point on the LE with AOA. The rest of the curve is the same. If the flow splits at the stagnation point and re-joins at the TE, then the 2 flows have almost the same mean velocity.
That's too qualitative to be easy to respond to, but it sounds vaguely like the equal transit time fallacy. But regardless of the cause of the velocity profile being what it is, the relationship between velocity and pressure follows Bernoulli's principle..... But sure, if the velocity profiles aren't much different, the pressure profiles won't be much different.
The reason I ask is that the difference in length of the 2 surfaces is only very slightly different due entirely to the change in stagnation point on the LE with AOA. The rest of the curve is the same. If the flow splits at the stagnation point and re-joins at the TE, then the 2 flows have almost the same mean velocity.
You don't seem to be mentioning that the airflow above the wing gets "squeezed" by this process, not unlike in a Venturi tube (but without the exact area ratio to calculate it). So the air over the top ends up going faster than just the "path length" difference would imply. But again, how the velocity profile is established has nothing to do with Bernoulli.
While I have an interest, I can not work the proof myself so must rely on technical articles etc. If they disagree on this point, it seems a controversial topic with no clarity as to the truth.
There is no actual controversy in the field. It is well understood that both ideas (Bernoulli's and Newton's) have value. And they're related anyway; both use the velocity of the air.
 
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  • #40
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“Why should that be a problem?....” Well, that whole concept of upper surface greater distance in the same time, just always seemed too schoolboy simple and convenient.
The others pointed out that that's wrong, and I'll name it: that's the "equal transit time" fallacy, which is often incorrectly associated with Bernoulli's principle.

In my opinion, while the "equal transit time" fallacy is wrong, the over-correction that frequently takes down Bernoulli's principle with it is much worse.
 
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  • #41
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I have a few comments to add:
  • The answer to the original question is a definitive "no." Turbulence is not required in order to generate lift.

  • The existence of vortices does not imply a flow is turbulent. Laminar vortices are absolutely possible and fairly common.

  • Having said the above, the concept is turbulence is inherently linked to the generation of vortices. The key point is that turbulence features a variety of scales of vortices that are generated by larger vortices breaking down into smaller vortices, which break down into even smaller vortices, and so on until the energy is dissipated. We call this the turbulent energy cascade. This concept was enshrined in a limerick by L. F. Richardson: " Big whorls have little whorls Which feed on their velocity, And little whorls have lesser whorls And so on to viscosity."

  • Veritasium just did a segment on turbulence that is a pretty good low-level introduction to the topic. I would say his discussion is fairly easy to follow and largely technically correct (a few minor gripes).

  • The entirety of lift can absolutely be accounted for by integrating the pressure over the surface of a body, and this pressure can, in many cases, be calculated using Bernoulli's principle provided the velocity profile is already known.

  • The latter point is the important one. Knowing the velocity profile a priori is not trivial and the lack of a simply explanation for how to derive it is a big part of why arguments like this persist. At the end of the day, Bernoulli's principle actually says absolutely nothing about lift. It simply relates velocity and pressure in an incompressible flow subject to several limitations. It can successfully be applied to calculating lift, among many other methods.

  • Fluid mechanics is complex. It generally is not conducive to simple answers. This leads many people to struggle with it and, once they find an answer that they feel is intuitive, they have a hard time moving toward something more comprehensive. The bottom line is that fluids are ultimately governed by a complicated form of Newton's laws and all of the various explanations for lift are effectively one possible result of Newton's laws out of many. There is no reason there needs to be only one correct answer here. You can calculate the lift based on the pressure distribution. You can calculate the lift based on the downwash. You can calculate the lift based on circulation. When applied properly, they are all effectively different sides of the same multifaceted coin.
 
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  • #42
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Ok, a lot to break down here... Vortices, vorticity and turbulence are all different things:

Vorticity:
The rotation of a fluid parcel. Take a fluid parcel (= a tiny bit of fluid) and ask if it rotates: yes, then this fluid has vorticity. Vorticity is a vector field, just like velocity, and therefore defined at every point in the flow. Note that a laminar boundary layer also contains vorticity. This is a mathematically well defined quantity. Further more, in 2D, if you take the integral around a closed line of the flow velocity tangent to that line, the result will be non-zero if the fluid captured in this closed line has vorticity.

Vortex:
This is a flow feature where fluid is rotating around a central point (or line in 3D, called a vortex filament, which is actually a potential flow concept). It is less well defined. In the book of Green called 'Fluid Vortices' I remember him (don't have the book with me right now...) saying something along the lines of "A vortex is defined as such when most fluid dynamicists agree it is a vortex!", although he said this a bit with tongue in cheek.

Turbulence:
Even harder to really pin down. But generally speaking it is a random-ish fluctuation of velocities on top of a mean flow. It often starts from an instability in the flow, meaning that a small perturbation grows into large flow features. I'm actually not sure if a vortex is inherently instable such that it will always generate turbulence, or that laminar vortices exist...? But a shear layer (two layers of flow on top of each other with each a different direction) I believe is inherently instable and thus transitions to turbulence rather quickly (but I'm not a genius in stability theory...). Let's not bother with the question about what happens if the fluctuations become as large or larger than the mean flow.

So, is turbulence required for lift? Hmm, turbulence in the boundary layer is not necessary since fully laminar flow around a wing can also generate lift, albeit (much?) less efficient. But, directly behind the wing, at its trailing edge there is a shear layer generating turbulence. This is however not needed for lift I guess.

Is vorticity needed for lift? Yes it is. I see a wing more as an 'air-bender'. Imagine in 2D a strip of air hitting a wing. After it has passed, the strip is 'bend' or rotated downward. This is only possible if you have vorticity in the flow. Try generating a flow field where part of it is 'bend'when there is no vorticity anywhere in the flow, it is not possible. It is captured in 2D in the Kutta-Joukowski theorem stating that lift is equal to the density times free stream velocity times circulation (circulation and vorticity are directly related). No circulation, no lift.

Are vortices needed for lift? Well, Helmholtz second theorem states that a vortex filament cannot end in a fluid. It needs to either end on a surface or form a closed loop. Along the span of a wing there are these 'bound vortices' (as @russ_watters already showed with a picture) since the line integral around an airfoil of the flow tangential to this airfoil*) is not equal to zero (thus there must be vorticity). These bound vortices cannot end in the fluid and thus continue downstream, roll up in two trailing vortices (see picture) and connect through the starting vortex. At least, in potential flow theory where there is no viscosity dissipating these flow features. So I guess vortices are inherently coupled to wings...

Tip-vortex-roll-up.jpg





Just a few extra remarks about things I have an opinion on:
  • A 'partial vacuum' above the wing is not necessary for the wing to function, and in fact does not really exist for airplanes going below mach 0.3-ish. Or, even more relevant, wings work absolutely fine in water and water is incompressible for all intents and purposes here (think of these hydrofoil boats).
  • Also, the 'greater speed on top of the wing' is misleading with regards to lift generation. Although true, many then continue to say: 'well, speed is higher, Bernoulli says that pressure is thus lower, and hence lift!'. But why then! Why is the pressure lower if speed is higher... This doesn't really explain anything in my opinion.
  • A wing generates lift because air (or water) is 'pushed' downwards, for which a force is needed according to Newtons (real**)) second law: the change in (vertical) momentum is equal to a force. Newtons third law states that an equal but opposite force is thus necessary, which is the lift on the airfoil.
  • Bernoulli, although absolutely correct and useful, is the most misleading and misused law there is in fluid dynamics, certainly for the laymen. It does not generate any intuition to understand flow. Pressure decreases if velocity increases... I've wondered very long about why this would be true, maybe that's why I studied fluid dynamics later on :).
  • An airplane making use of the 'ground effect' still generates downwash, and in fact this downwash makes the ground effect a thing. The downwash 'hits' the ground generating an extra pressure which gives kind of an extra push upward to the plane (the post already too long for more explanation).
  • The more interesting question about wings is this: why would the flow not separate from the upper side? Why would it follow the surface at all? This has more to do with the Coanda effect. So a plane doesn't fly because of Bernoulli, but because of Coanda! :)
*) ón the airfoil the flow has zero speed due to no-slip. So take the flow just outside of the boundary layer.

**) Newton's second law is often quoted as ##F = ma## or force is equal to mass times acceleration. But this is only true if ##m## is constant. The 'real' law is ## F = d (mv) / dt##, or force is equal to the change in momentum. If you apply the chain rule this can be written as ## F = vd(m)/dt + md(v)/dt = v\dot{m} + ma## if ##\dot{m}##, or the mass flux is zero only ##ma## remains. But in fluid dynamics the first term is usually more important.
 
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  • #43
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Oh, one last soapbox remark:

The longer path fallacy is indeed a fallacy. The path length doesn't matter since if you would follow two parcels separating at the stagnation point at the leading edge, one taking the upper route, the other the lower one, they do *not* meet at the trailing edge. So the increase in velocity is not explained by the longer path.
 
  • #44
boneh3ad
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Turbulence:
Even harder to really pin down. But generally speaking it is a random-ish fluctuation of velocities on top of a mean flow. It often starts from an instability in the flow, meaning that a small perturbation grows into large flow features. I'm actually not sure if a vortex is inherently instable such that it will always generate turbulence, or that laminar vortices exist...? But a shear layer (two layers of flow on top of each other with each a different direction) I believe is inherently instable and thus transitions to turbulence rather quickly (but I'm not a genius in stability theory...). Let's not bother with the question about what happens if the fluctuations become as large or larger than the mean flow.
You need to really emphasize the "-ish" part of this, because according to most modern thinking on the topic, turbulence is entirely deterministic but essentially a form a spatiotemporal chaos, i.e. it is so sensitive to initial conditions that modeling it stochastically is the only tractable solution in most cases.

It always starts with some form of instability in the flow, though sometimes the initial perturbation is so large that it breaks down essentially immediately in a process often called bypass transition. Generally speaking, fluctuations do not grow anywhere near the magnitude of the mean flow before a boundary layer breaks down. In subsonic flows, the unstable waves reach perhaps a few percent in magnitude in velocity fluctuations. At the other end of the spectrum, they can reach ~50% in terms of pressure in hypersonic flows.

So, is turbulence required for lift? Hmm, turbulence in the boundary layer is not necessary since fully laminar flow around a wing can also generate lift, albeit (much?) less efficient.
Less efficient? At its most fundamental level, turbulence is dissipative and therefore will tend to decrease efficiency. The caveat here is that turbulent boundary layers are also more resistant to separation, so in cases where they delay separation, the losses due to inducing turbulence can sometimes be less than the gains due to delaying separation (or in the case of wing stall, the losses are an acceptable price to pay for keeping the plane in the air).

But, directly behind the wing, at its trailing edge there is a shear layer generating turbulence. This is however not needed for lift I guess.
This isn't always doomed to be turbulent, though. You can certainly have everything laminar and maintain lift.

  • Bernoulli, although absolutely correct and useful, is the most misleading and misused law there is in fluid dynamics, certainly for the laymen. It does not generate any intuition to understand flow. Pressure decreases if velocity increases... I've wondered very long about why this would be true, maybe that's why I studied fluid dynamics later on :).
Well that is easily answered using ##\vec{F} = m\vec{a}##. You need a force to accelerate the flow, and that force is due to pressure on a fluid element. An element that is accelerating must have a higher pressure upstream of it and so be entering a region of lower pressure. The converse is also true.

  • The more interesting question about wings is this: why would the flow not separate from the upper side? Why would it follow the surface at all? This has more to do with the Coanda effect. So a plane doesn't fly because of Bernoulli, but because of Coanda! :)
It actually has nothing to do with the Coandă effect, which is based on the phenomenon where a jet clinks to a nearby surface. This is not what is occurring around an airplane wing. It is more appropriate when discussing planes whose engines are embedded in the wing and produce a jet of air that blows over the wing. See: Boeing YC-14
 
  • #45
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Oh, one last soapbox remark:

The longer path fallacy is indeed a fallacy. The path length doesn't matter since if you would follow two parcels separating at the stagnation point at the leading edge, one taking the upper route, the other the lower one, they do *not* meet at the trailing edge. So the increase in velocity is not explained by the longer path.
That's not "longer path", that's "equal transit time". It is generally true - not a fallacy - that the parcel taking the longer path arrives at the trailing edge first. But it is popular to mix them together inaccurately (including the oft-cited NASA lift explanation for kids). This is part of what I pointed out earlier: overly aggressive debunking of "equal transit time" that takes other concepts down with it.

I can't imagine how confusing it must be for kids to read/see something so obviously true be claimed as false.
 
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  • #46
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You need to really emphasize the "-ish" part of this, because according to most modern thinking on the topic, turbulence is entirely deterministic but essentially a form a spatiotemporal chaos, i.e. it is so sensitive to initial conditions that modeling it stochastically is the only tractable solution in most cases.
You're absolutely right, that's indeed why I added the '-ish'. But I wasn't going to give a Turbulence lecture here :) Maybe I should have said 'seemingly random' to be more clear.

It always starts with some form of instability in the flow, though sometimes the initial perturbation is so large that it breaks down essentially immediately in a process often called bypass transition. Generally speaking, fluctuations do not grow anywhere near the magnitude of the mean flow before a boundary layer breaks down. In subsonic flows, the unstable waves reach perhaps a few percent in magnitude in velocity fluctuations. At the other end of the spectrum, they can reach ~50% in terms of pressure in hypersonic flows.
Thank you for the clarification. I was trying not to get into the details, but what I was referring to is when the classical approach of separating the mean flow and the turbulence fluctuations break down. Sometimes it is not clear how to separate the mean flow from the turbulence fluctuations and these fluctuations cannot be called 'small' anymore such that you can neglect these terms.

Less efficient? At its most fundamental level, turbulence is dissipative and therefore will tend to decrease efficiency. The caveat here is that turbulent boundary layers are also more resistant to separation, so in cases where they delay separation, the losses due to inducing turbulence can sometimes be less than the gains due to delaying separation (or in the case of wing stall, the losses are an acceptable price to pay for keeping the plane in the air).
Ok, you're right, a laminar boundary layer causes less frictional drag making it more efficient. I indeed had the separation issue in mind.

Well that is easily answered using ##\vec{F} = m\vec{a}##. You need a force to accelerate the flow, and that force is due to pressure on a fluid element. An element that is accelerating must have a higher pressure upstream of it and so be entering a region of lower pressure. The converse is also true.
I really wasn't trying to say that todays me doesn't understand how Bernoulli works, I do. But back in the day, when I still didn't know about this I was puzzled by it. And then Bernoulli simply does not help with getting an intuitive understanding of how wings work. It just replaces one unknown (why does a wing generate lift) with another (why does higher velocity means lower pressure).

I forgot to touch upon the question why the upper part of the wing even has a higher velocity in the first place. This is a lot less obvious when you realize that jet-planes can fly upside down and cardboards can also generate lift and all that.

It actually has nothing to do with the Coandă effect, which is based on the phenomenon where a jet clinks to a nearby surface. This is not what is occurring around an airplane wing. It is more appropriate when discussing planes whose engines are embedded in the wing and produce a jet of air that blows over the wing. See: Boeing YC-14
So how would you explain why the flow over the top part of the wing stays attached onto the surface? Maybe the original Coandă effect is just about jets, but the reason a jet clings to a surface is comparable to why flow over a wing stays attached. It has a lot to do with the wall normal direction of momentum transport. If there is enough of that the flow clings to the surface, if not you have separation (or the jet does not cling to the surface).
 
  • #47
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That's not "longer path", that's "equal transit time". It is generally true - not a fallacy - that the parcel taking the longer path arrives at the trailing edge first. But it is popular to mix them together inaccurately (including the oft-cited NASA lift explanation for kids). This is part of what I pointed out earlier: overly aggressive debunking of "equal transit time" that takes other concepts down with it.
I think the argument usually goes like this: two air parcels arrive at the leading edge, one goes up, the other goes down, when they arrive at the trailing edge the parcel that took the upper route had to cover a longer distance compared to the lower one and therefore the velocity of the upper parcel had to be higher. Higher velocity means lower pressure, hence lift.

So the fallacy is about the two parcels arriving at the same time, and indeed the parcel taking the upper, longer, route is usually earlier at the trailing edge than the other one, which I guess is counter intuitive. I guess you can better call this the "equal transit time" fallacy indeed.

I can't imagine how confusing it must be for kids to read/see something so obviously true be claimed as false.
If you thought I was denying that one path is indeed longer than the other, mea culpa, that is not what I intended to say. The idea here was more that you don't need the longer path to generate lift. A flat plate can also generate lift, planes can fly upside down, etc. That's what I meant by calling it the "longer path" fallacy.
 
  • #48
russ_watters
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If you thought I was denying that one path is indeed longer than the other, mea culpa, that is not what I intended to say. The idea here was more that you don't need the longer path to generate lift. A flat plate can also generate lift, planes can fly upside down, etc. That's what I meant by calling it the "longer path" fallacy.
See, now both of those common/popular examples are, in fact, fallacious. If you look at the actual airflow paths you will see that due to the moving stagnation point and redirection of the air up toward/at the leading edge, you will see that the air over the top does indeed take a longer path. And I particularly dislike the flat plate example because a flat plate makes a really poor airfoil. We should not be teaching how lift works based on bad examples/exceptions except where necessary for the math (it is part of aerodynamics calculations to break the airfoil into plates, starting with 1).

What bothers me about this quite typical approach you are taking is that rather than trying to explain the fact, you are trying to explain it away -- with progressively worse and worse examples. It's not your fault; these discussions always go the same way because that's how the issue is taught/presented. We should be teaching/learning lift by explaining how/why a good/typical airfoil produces lift, not by trying to find exceptions that don't behave the same way. The next example is usually a sailboat...

[edit]
Here's my take on how the "equal transit time" fallacy should be dealt with, (if at all):
The supposed irrelevance of the "path length" difference isn't why the equal transit time fallacy fails. The equal transit time fallacy fails because it forces the air to do something it can't do; behave as a solid vertical column.

Typically the fallacy is presented for debunking by using a common/simple flat-bottomed airfoil. A good choice. The parcel of air traveling under the wing on a flat bottom is barely moving from the perspective of the surrounding/freestream air. This means that the parcel of air moving over the top of the wing is moving vertically; it just bobs up and back down vertically as the wing passes, to meet the parcel moving across the bottom. This doesn't happen, but the debunkings don't usually explain why or what actually does happen.

The parcel moving over the top of the wing has another parcel directly above it, in the way. It can't bob up and down because other air is preventing it from doing so. If we followed the logic up, it would have the entire column of air, up to space, bob up and down together. Even if air is considered incompressible, it wouldn't be possible or necessary for the wing to lift the entire column of air above our selected particle vertically and then drop it back down because distortions only travel through the air at the speed of sound, and pressures eventually wants to equalize - and there's another direction our parcel of air can go instead. So instead of lifting the entire column of air, our parcel on the top surface is "squeezed" somewhat, and is driven backwards due to its interaction with the airfoil and the air above the airfoil. It arrives at the trailing first because of, not in spite of its upwards deflection.
 
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  • #50
russ_watters
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Why not driven forwards somewhat?
The "other" air is in the way of that. The parcel of air eventually has to go from in front of to behind the airfoil. If it gets slowed down, it piles up in front of the airfoil.

This is one of the reasons I like using a Venturi tube as an analogy, though it is criticized for being mathematically imperfect (for an airfoil there is no defined throat area for calculating an area/velocity relationship). "Squeezing" the airflow in a Venturi causes the the flow to speed up, not slow down, because otherwise it would pile-up at the throat and violate continuity.
https://www.princeton.edu/~asmits/Bicycle_web/continuity.html

[edit] Another way: the airfoil is a "hole" in the air. Air ahead of the hole has to move backwards to fill the hole as the airfoil passes.
 
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