Why do air foils produce lift?

[stevepm]

Hello, I have recently joined with hope that I can find a straight forward answer to a question that has bugged me for so long. Why do air foils REALLY produce lift? I have heard and read of the most common explanation involving the bernoulli effect, but when I dug deeper I read that the bernoulli effect does not generate nearly enough lift for an airplane to fly, and that it partially relies on the theory of equal transit times. I also read that the bernoulli effect neglects density or pressure changes expressed in the ideal gas law. Every article or excerpt I read said that the upper body of air as no reason to reach the tail of the wing at the same time as the lower body, and after watching wind tunnel tests, I found this to be true, in fact, the upper body passed its lower counterpart. Now, even though the bernoulli effect does speed up the body of air above the wing slightly, the pressure difference is simply not enough, this is where I ran into a simpler explanation involving the redirection of air, Newtons Third Law, and the Coanda effect. That explanation said that with the redirection of air following the top of the foil by the Coanda effect, combined with the redirection of air off the bottom of the wing, then that would create downwash and take advantage of Newtons third law. THEN I read of the Kutto-Joukowski Theorem, which seemed to use downwash as a source of lift but then it began to mention Bernoulli, but if there are such large holes in the Bernoulli principle, then why is it still used? I apologize for such a lengthy question, but there are simply so many different answers which point to different reasons for support. So, is lift on an airfoil a combination of these theories/laws, is it one of them, or is there something I have not yet stumbled upon?

 

[mfb]

xkcd: Airfoil

It is a combination of those effects, and they are not completely separate anyway.

 

[russ_watters]

xkcd: Airfoil

It is a combination of those effects, and they are not completely separate anyway.

Yes. Somehow the internet has generated separate camps believing only one or the other work, which isn't true. Often it is because of false assumptions or associations, such as believing Bernoulli's principle and the equal transit time assumption are linked, when they aren't.

 

[Vanadium 50]

Every time I see a thread title with "really" in it, I want to delete it. It opens the door to a neverending sequence: "Thanks for telling my why airfoils REALLY produce lift. Now tell me why they REALLY REALLY produce lift!" Then REALLY REALLY REALLY. And so on forever.

Wings are pushed up, because air is pushed down.

That's it. Even the Bernoulli explanation does this (lower air pressure means fewer air molecules, so the net effect is to move air from above the wing to below the wing. So all these complications involve how air is pushed down.

 

[rcgldr]

Every article or excerpt I read said that the upper body of air as no reason to reach the tail of the wing at the same time as the lower body ...

That is called "equal transit" theory, which is different than Bernoulli principle, and as you've read, "equal transit" theory is not true.

Newton's third law applies, the pair of Newton third law pair of forces are the downwards and somewhat forwards force that the wing exerts on the air, and the upwards (lift) and somewhat backwards (drag) that the air exerts on the wing.

Newtons second law and the physics laws of impulse versus momentum apply. The downwards force from the wing corrersponds to the net acceleration of the affected air. In physics, an impulse (force x time or force x Δt) correspondes to a change in momentum m Δv, but if you divide this formula by the time interval Δt, you end up with Newtons second law, force = m Δv / Δt which is essentially mass x acceleration.

Bernoulli priniciple notes that air tends to accelerate away from higher pressure areas to lower pressure areas. Bernoulli equation defines a somewhat idealized relationship between the decrease in pressure and the increase in speed during this transition, assuming no exernal work is performed, and ignoring issues like turbulence, vortice flows, surface friction, ..., but the basic concept applies, and more sophicated mathematical models based on Navier Stokes, can predict how a wing will perform under a varity of conditions.

 

[DrDu]

It is called Kutta Joukowski theorem, not Kutto.
I think most of the explanations do not exclude each other.
That the lift is due to downwash follows from conservation of momentum. But the difficult part is to predict the correct amount of downwash.
In the same way, the Bernoulli equations are almost exact when used sufficiently far from the surface of the wing as the gas behaves ideal there.
However, the Bernoulli principle is not sufficient to calculate the velocity profile around the wing.
The Kutta Joukowski theorem is an exact theorem linking circulation to lift. However to find the correct circulation, one has to invoke the empirical Kutta condition which fixes the location of the stagnation point on the edge of the wing.
Hence the problem to derive the condition on where the flow will stall lies at the hart of the problem.
The Coanda effect may give an explanation why in some airfoil geometries the flow doesn't stall earlier.

 

[stevepm]

Thank you to everyone who clarified and corrected for me, I really appreciate your time and assistance.

 

[boneh3ad]

Bernoulli's equation is not wrong, it simply does not explain why the air moves faster over the top of the airfoil than under it. If you know a priori that the air is moving faster over the top, then Bernoulli's equation works perfectly well assuming incompressible flow (or by using a version corrected for compressiblility). This is often how lift is measured on an airfoil on large wind tunnel models.

The concept of downwash is similar and equally valid. It implies that a force has been imparted on the flow by the airfoil in order to change its momentum, resulting in the redirection of the flow. The existence of downwash signifies lift. If you have the means, you can measure lift based on measuring the wake of the airfoil, though this is not done in practice very often as it is less convenient than using a force balance or pressure distribution. Usually people using this explanation neglect to explain why the downwash is generated, however.

So really, both Bernoulli's principle and downwash are correct. Those using them simply don't often explain why they arise and often explain it incorrectly. The Kutta-Joukowski Theorem relates the net circulation around an airfoil to the lift generated, and any circulation superposed imposed over any 2-D shape in a flow will cause both a velocity differential on the top and the bottom as well as downwash, so the concepts are all related. You can generate this circulation a number of ways. A baseball, for example, uses the Magnus effect due to the ball itself rotating. An airfoil is slightly more complicated.

If you have a smooth shape such as an oval (functioning as a stand-in for an airfoil here), you have the flow meet up with the airfoil at the leading edge and then hug the contour of the shape. It will follow the surface even around the portion with the smaller radius of curvature until it either separates due to the pressure gradient or else meets up with the flow 180 degrees around the shape from the forward stagnation point and then leave the shape, creating a rear stagnation point. We will ignore separation here for a moment and only consider the unseparated case. In this case you have no lift since it is mathematically identical to a cylinder with no circulation in a flow, which has no lift.

Now take the case of real airfoils. Instead of having a rounded trailing edge, they have a sharp trailing edge. In the rounded case, the flow would navigate the curved trailing end and speed up while doing so, but may or may not ever separate from the surface. When you introduce a sharp trailing edge, the velocity would reach infinity if it tried to do this (or nearly so), which cannot happen, as the pressure gradient required would instantly separate the boundary layer from the surface... and it does. In effect, the sharp trailing edge forces the flow to separate at this point both over the top and under the bottom of the airfoil. What you are essentially doing is enforcing the location of the stagnation point and the direction of the flow leaving the airfoil. Mathematically, this is referred to as the Kutta condition.

By pitching the airfoil, you can effective control the angle at which the air leaves the surface and generate lift be redirecting it downward. Of course at larger angles the drag increases and you run the risk of separation of the boundary layer over the upper surface, leading to stall. This explains the downwash. The fast speed over the upper surface is a result of the governing equations governing the flow (continuity and Navier-Stokes). Since the two stagnation points are set, assuming no separation, the equations are only solved if the flow over the top is moving much faster than underneath. It is the sharp trailing edge enforcing the stagnation point combined with the angle of attack that leads to both of these phenomena.

Also, just as a note, scientific questions cannot be answered by poll.

vortice flows

Bernoulli's equation works perfectly well in vortical flows assuming all the other conditions are met and that you don't try to apply it at the actual point of the vortex, which is a singularity.

 

[rcgldr]

Now take the case of real airfoils. Instead of having a rounded trailing edge, they have a sharp trailing edge.

Although a sharp trailing edge reduces drag, it's not required to produce lift. The M2-F2 and M2-F3 pre-shuttle re-entry lifting bodies had somewhat blunt trailing edges (that's where the rocket nozzles were located on the M2-F3). The other unusual aspect of these models is that the "hump" is on the bottom of the air foil. Image of M2-F2 glider with F-104 chase plane following.

... vortice flows ...

Bernoulli's equation works perfectly well in vortical flows assuming all the other conditions are met and that you don't try to apply it at the actual point of the vortex, which is a singularity.

The point I was getting at is the speed of the spinning air in vortice results in more of the total energy of that air being kinetic as opposed to pressure x volume. That would have an impact on the relationship between net velocity (linear flow) versus pressure. I've read that part of the reason delta wings can operate at higher angles of attack, 20° or so, without stalling, is they take advantage of leading edge induced vortices, but I don't recall the details as to why.

 

[boneh3ad]

Although a sharp trailing edge reduces drag, it's not required to produce lift. The M2-F2 and M2-F3 pre-shuttle re-entry lifting bodies had somewhat blunt trailing edges (that's where the rocket nozzles were located on the M2-F3). The other unusual aspect of these models is that the "hump" is on the bottom of the air foil. Image of M2-F2 glider with F-104 chase plane following.

They still have abruptly terminated trailing edges of some fashion. If the trailing edge is truncated such as with the M2-FX series, commonly called a flatback airfoil, it still performs the same function of fixing the trailing stagnation point, or in this case points. The roots of wind turbine blades are similarly designed.

 

[mmmcheechy]

As I'm not an expert in anything feel free to completely disregard any and all parts of my comment. I voted other in the poll for the following reason.
I personally believe that lift is generated via the boundary layer effect. (and that bernoulli's work is among the earliest experimental simplification and explanation of this process) that is the transition from laminar to turbulent flow allows for the creation of pressure differentials. the shape of the airfoil must then direct theses turbulent regions in a way that lowers the average pressure above the wing from average pressure below it.
also I am ignorant of both the Kutta-Joukowski Theorem and the Coanda effect and did no investigation into either of these before voting, but thought I would mention the boundary layer effect as something that could be taken into consideration

 

[boneh3ad]

I personally believe that lift is generated via the boundary layer effect.

What exactly do you mean by the "boundary layer effect"? There is no principle in fluid mechanics called the "boundary layer effect". There is the principle of the boundary layer, but that alone does not explain lift, though it is related.

(and that bernoulli's work is among the earliest experimental simplification and explanation of this process)

Bernoulli's principle has nothing to do with boundary layers, and is in fact invalidated in situations where a boundary layer develops on account of viscosity. In those cases it only holds along a streamline.

that is the transition from laminar to turbulent flow allows for the creation of pressure differentials.

No it doesn't. The pressure gradient vertically (normal to the wall) through a boundary layer is the same whether it is laminar or turbulent: zero. True, turbulent boundary layers are thicker and therefore can affect the pressure profile over an airfoil due to the additional displacement thickness, but they don't otherwise act any different than laminar boundary layers in terms of transmitting pressure from the free stream to the surface. This is, in fact, one of the fundamental tenets of boundary layer theory.

 

[stevepm]

I have sometimes seen the Coanda effect used to explain why air travels over the top of a wing is redirected downwards, is this correct, or is it more related to the boundary layer's effect on the air traveling over the wing? Or is the Coanda effect a result of the boundary layer tampering with air flow over top of the wing?

 

[SleepingTroll]

A simple way to look at this is that air has mass and so it has inertia. The air is directed upward creating a vacuum above the wing, the "pull" of this vacuum is more or less perpendicular to the aircraft travel and the resultant vector is airspeed converted to lift.

 

[rcgldr]

I have sometimes seen the Coanda effect used to explain why air travels over the top of a wing is redirected downwards, is this correct, or is it more related to the boundary layer's effect on the air traveling over the wing? Or is the Coanda effect a result of the boundary layer tampering with air flow over top of the wing?

If you use a volume of air as a frame of reference, then the upper surface of a wing with an effective angle of attack (one that produces lift), once past the peak part of the upper wing, recedes away from the air, and the air has to fill in what would otherwise be a void left behind that upper surface as it travels through a volume of air. If there is a reasonably attached flow, the stream of air follows that surface, but because air has momentum, the acceleration results in a reduction of pressure. If the angle of attack is too large for attached flow, then turbulent flow such as a very large vortice fills in that void, producing a lot of drag and reducing lift.

Viscosity is also required for this to work. Without viscosity, then a volume of air could simply follow the wing without interacting with the surrounding air, effectively changing the "shape" of a wing.

Surface friction along with viscosity also has an effect, but how much depends on the circumstance.

 

[Aero_UoP]

If you use a volume of air as a frame of reference, then the upper surface of a wing with an effective angle of attack (one that produces lift), once past the peak part of the upper wing, recedes away from the air, and the air has to fill in what would otherwise be a void left behind that upper surface as it travels through a volume of air. If there is a reasonably attached flow, the stream of air follows that surface, but because air has momentum, the acceleration results in a reduction of pressure. If the angle of attack is too large for attached flow, then turbulent flow such as a very large vortice fills in that void, producing a lot of drag and reducing lift.

Viscosity is also required for this to work. Without viscosity, then a volume of air could simply follow the wing without interacting with the surrounding air, effectively changing the "shape" of a wing.

Surface friction along with viscosity also has an effect, but how much depends on the circumstance.

But the lift of an airfoil can be perfectly predicted with potential flow theory, aka frictionless... no viscous phenomena...
It's the drag that demands viscosity to be taken into account in order to be predicted...
Maybe I haven't usterstood clearly what you said :(

 

[cjl]

But the lift of an airfoil can be perfectly predicted with potential flow theory, aka frictionless... no viscous phenomena...
It's the drag that demands viscosity to be taken into account in order to be predicted...
Maybe I haven't usterstood clearly what you said :(

Yes, except for one thing: without viscosity, there's no reason why the rear stagnation point has to be at the trailing edge. Potential flow adds in sufficient circulation to establish this condition (effectively, this is considered to be an additional constraint), but without viscosity, there's no physical reason why the stagnation point couldn't be somewhere else. In fact, if you solve a completely inviscid equation without this constraint, you'll find that the rear stagnation point on the airfoil is on the upper surface, and the net lift is zero.

 

[Aero_UoP]

Symmetric Airfoil - Potential Flow
c$_{l}$=2πα

Cambered Airfoil - Potential Flow

c$_{l}$=2π[α+$\frac{1}{π}$$\int\frac{dz}{dx}(cosθ_{0}-1)dθ_{0}$]

and for both cases at the trailing edge: γ(ΤΕ)=0 (kutta condition)

Where's the viscosity in that? All I can see is geometry...
Is it wrong what I say? What is your objection for?

 

[cjl]

Symmetric Airfoil - Potential Flow
c$_{l}$=2πα

Cambered Airfoil - Potential Flow

c$_{l}$=2π[α+$\frac{1}{π}$$\int\frac{dz}{dx}(cosθ_{0}-1)dθ_{0}$]

and for both cases at the trailing edge: γ(ΤΕ)=0 (kutta condition)

Where's the viscosity in that? All I can see is geometry...
Is it wrong what I say? What is your objection for?

As I said, both of those formulas come from the starting assumption that the airfoil will have sufficient circulation to establish the kutta condition. If you don't assume that the Kutta condition holds, you'll get the inviscid solution I mentioned (stagnation point on upper surface, no lift) if you actually solve for the flow. Viscosity is what establishes the kutta condition in a real flow.

 

[rcgldr]

Viscosity is also required for this to work. Without viscosity, then a volume of air could simply follow the wing without interacting with the surrounding air, effectively changing the "shape" of a wing.

But the lift of an airfoil can be perfectly predicted with potential flow theory, aka frictionless... no viscous phenomena...

From what I understand, that theory assumes that flow behaves as if there is viscosity. I'm not sure how you would predict a flow without viscosity, it would be based on collisions with a wings surface and momentum changes. Without viscosity, then a relatively narrow stream of air can flow through the surrounding air without any interaction at the sides, only a collision interaction at the leading edge.

 

[Aero_UoP]

From what I understand, that theory assumes that flow behaves as if there is viscosity. I'm not sure how you would predict a flow without viscosity, it would be based on collisions with a wings surface and momentum changes. Without viscosity, then a relatively narrow stream of air can flow through the surrounding air without any interaction at the sides, only a collision interaction at the leading edge.

Chapter 4, Fundamentals of Aerodynamics, 5th Ed., Anderson, McGraw Hill.

cjl,

I'm not sure about that, I have to look it up mate ;)

 

[boneh3ad]

cjl,

I'm not sure about that, I have to look it up mate ;)

He's right. Have you ever studied panel methods? Using those as example, you always add in an extra constraint to the equation that fixes the trailing edge stagnation point at the sharp trailing edge. The reason this was originally done was so that the flow was commensurate with reality, as without mathematically fixing it, potential flow theory would predict the trailing stagnation point to lie somewhere on the top surface of an airfoil at positive angle of attack. This is observed to not be the case in real life, and the reason for this, and therefore the real-world justification for the otherwise artificial Kutta condition, is that real flows have viscosity. Trying to navigate such a sharp corner like a trailing edge would require the local flow velocity to go to infinity in a potential flow. Under the influence of viscosity, however, the boundary layer essentially just separates there, as does the boundary layer on the top side, fixing the trailing edge stagnation point at that sharp trailing edge.

 

[A.T.]

...the real-world justification for the otherwise artificial Kutta condition, is that real flows have viscosity...

What would happen in a super fluid at the trailing edge?

 

[boneh3ad]

What would happen in a super fluid at the trailing edge?

Mathematically speaking, there would be no boundary layer and te flow would act like a potential flow and there would be no lift. Of course until someone decides to put an airfoil in a superfluid flow, we won't know how accurate that mathematical description is, and there is no reason for anyone to actually perform that experiment.

 

[A.T.]

the flow would act like a potential flow and there would be no lift

But what about the local flow velocity at the trailing edge in a super fluid? And would there be any drag in a super fluid? For example on a cylinder.

 

[boneh3ad]

In theory, no drag. You wouldn't get infinite velocity because you can never manufacture a perfectly sharp trailing edge and so far most superfluid studies that I know of haven't been perfect superfluids. But, if you had a perfect superfluid then in theory no drag, infinite speed.

 

[A.T.]

But, if you had a perfect superfluid then in theory no drag,

So if you had a super fluid planet, you could fly though it easily. Only entering the surface would create drag.

 

[boneh3ad]

You couldn't fly through it with airfoils. They wouldn't generate lift.

 

[rcgldr]

... if you had a perfect superfluid then in theory no drag, infinite speed.

Even without viscosity, wouldn't there still be momentum related issues contributing to drag of an object moving in a super fluid (assuming the super fluid has some amount of mass per unit volume)? Seems like there would still be something similar to a "wake" aft of a moving object.

 

[A.T.]

Even without viscosity, wouldn't there still be momentum related issues contributing to drag of an object moving in a super fluid (assuming the super fluid has some amount of mass per unit volume)?

In an ideal potential flow the fluid doesn't lose any momentum, so the density of the fluid is irrelevant for the drag. But it looks like density and velocity affects the pressure on the object:
http://en.wikipedia.org/wiki/D'Alembert's_paradox#Zero_drag

Is that correct?

 

[boneh3ad]

Assuming th flow is steady then there is going to be no drag (see D'Alembert's Paradox). If there is an unsteady component then drag is nonzero.

 

[rcgldr]

Assuming th flow is steady then there is going to be no drag (see D'Alembert's Paradox). If there is an unsteady component then drag is nonzero.

The paradox could be indicating an issue with the assumptions made about the flow. I'm not sure why a possible outcome of a an object flowing through a super fluid couldn't be a head and/or tail of super fluid that simply flows along with the object, rather than flowing around the object as it flows through the surrounding super-fluid. With zero viscosity, it's not clear what the path of least resistance would be for the fluid that the moving object collides with.

 

[boneh3ad]

With zero viscosity the system is entirely conservative and in a steady flow, the air parcels would end up exactly where they started before the object passed through. The only assumptions made in deriving D'Alembert's paradox are inviscid, incompressible and steady flow. All of these are met in the above example involving a perfect superfluid. It was called a paradox because, at the time of its discovery, potential flow was the state of the art in fluid mechanics analysis and the results were not in line with reality.

A superfluid is one with, among other things, zero viscosity. Without viscosity there is no way for a passing object to drag fluid along with it. Instead it just neatly pushes the fluid out of the way and, given the potential nature of the system, the fluid then neatly falls back into place where it started.

Flows in fluids with zero viscosity are very well-studied phenomena. Many, many books have been written on the subject and the mathematics are straightforward. Most if not all of the books discuss this very phenomenon.

 

[rcgldr]

A superfluid is one with, among other things, zero viscosity. Without viscosity there is no way for a passing object to drag fluid along with it. Instead it just neatly pushes the fluid out of the way and, given the potential nature of the system, the fluid then neatly falls back into place where it started.

Take the case of a flat plate moving through a super fluid. Why would there be any more of a tendency for the fluid to flow around the plate, as opposed to some portion of the fluid simply moving along with the plate?

 

[boneh3ad]

On the contrary, why woul it move with the plate. Even with viscosity it wouldn't. Shoot a hose at an inclined plate and water won't tend to build up, it will just be deflected.