So how do planes fly (no really)?

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

This is a good summary of how lift is created and what is right and wrong about the two popular explanations of lift.

Yes, any heavier-than-air craft must accelerate air downward in order to generate lift. Draw a control volume around the aircraft, and acknowledge conservation of momentum; if gravity is always exerting a downward pull on the aircraft, and air enters the control volume on a level trajectory, then the only way the aircraft can maintain level flight is for air to depart from the control volume with a downward trajectory. This is visibly obvious as rotor downwash in helicopter takeoffs and landings because it’s all concentrated in one spot (beneath the hovering helicopter), but it happens for fixed-wing aircraft, also.

I recall an article clearing up the common ‘partial vacuum’ mis-explanation of lift that may have been addressing this. But I think the conclusion was that a pressure differential between the top and bottom of the wing alone was insufficient to cause significant lift without air directed downward.

No argument here. And that doesn’t contradict anything I said. I was merely addressing what seemed to be a mistaken understanding on the OP’s part about what camber even is.

Others have already addressed the first paragraph, but I’ll concur: your flat-bottom, curved-top wing at zero AoA will generate lift, and will also cause air off the trailing edge to go downward. It has to. Conservation of momentum demands it.

As for the second part of that, Bernoulli’s principle doesn’t really care about gradients in a particular direction, except for gravity. A flow which is uniformly accelerated, as in a frictionless pipe, will experience the same pressure change across the entire cross-section of pipe. There will be a pressure gradient due to gravity in the vertical direction, but that’s the same regardless of the flow’s velocity. For an incompressible flow, the change in pressure is a function only of the change in velocity, and in no way depends on any spatial direction.

It is a bad approximation in all cases. It never even comes close to being true. Your “point mass” analogy is poor, because that’s a simplification that actually serves to make a problem tractable. Invoking equal transit times, on the other hand, allows nothing to be analyzed which wouldn’t be analyzed before. It only substitutes the unnecessarily complicated truth with an unnecessarily complicated lie.

If you want to gloss over details (which isn’t necessarily a bad thing), just say the air goes faster over the top. Because that’s what happens. Don’t add the unnecessary and factually incorrect statement that it takes just as long to go over the top as it does over the bottom. Adding that falsehood doesn’t allow you to do anything useful, and only perpetuates ignorance.

No you can’t. It does nothing to make the lesson more understandable, and it’s just flat-out wrong. There’s no reason to even introduce such an erroneous topic.

It’s more like those two things are distinct but inseparable manifestations of the same thing.

You can analyze the pressure field, integrating the pressures around the wing, and that will absolutely give the right amount of lift. Likewise, you can analyze the velocity vield, calculating the momentum of the air pushed downwards by the wing, and that will also give you the right amount of lift. They don’t add together…they’re two different ways of arriving at the same thing.

It’s a bit like trying to determine the the power consumption of a space heater. One option is to put it in a well-insulated space, and measure the temperature rise as a function of time. Or you can hook up instruments to its power supply and measure the current draw and voltage. Either method will (ideally) lead you to the same value for power. Either is valid because both are inseparable properties of the same physical process—the current draw for a given voltage and the heat addition to the room are linked by a functional relationship. Like the airplane, either can be validly measured, and either can provide the desired result. And neither one is the “cause” of anything…just a measureable result.

Okay, so it’s hard to come up with a great analogy off the top of my head, but the physical sciences are full of instances where multiple physical effects can be analyzed to independently arrive at the same answer. Why lift generation gets the special privilege of being questioned ad infinitum is beyond me.

To pile on, a wing that is not throwing a mass of air downward, is creating exactly zero lift. You can’t have lift without throwing air down.

The problem with the Bernoulli explanation is that it’s very non-intuitive. If the equal transit time assumption were actually true, then you could almost understand where the lift comes from. Students have already accepted that an accelerated flow has lower pressure. But without equal transit times, it’s completely non-intuitive. Why would the airflow over the top side be accelerated if there’s no equal transit time? And why on earth would the flow on the top side reach the trailing edge first?

If you’re going to explain how a wing works, just take the explanation that’s intuitive while still being correct. The wing blows air downwards like a fan blade, and the top side is shaped so that it throws the top-side air downwards as well as the bottom side, so you get much more lift.

I think this is the most important part of the explanation. Lift is the reaction to throwing air downward. Until that’s understood, it doesn’t help much to get into the very, very detailed explanations of how a wing causes that to happen.

Not really. aerodave has the best explanation so far. Lift is just the sum effect of the air moving over the wing. Whichever theory you use is merely a method of summing the individual molecular interactions of the fluid passing by the solid. You can look at the effect the wing has on the air (momentum theory), the effect the air has on the wing (summing the pressure), more complex methods like circulation theory, or the equations of motion of the flow itself in the Navier-Stokes equations. Each of these are just ways of viewing the sum effect of many microscopic interactions, and they are all inseparable. You cannot deflect the flow without changing the pressures on the surface of the wing and you cannot change the pressures on the surface of the wing without deflecting the flow. Thus neither is more correct, they are just more or less useful to use in given circumstances.

The only caveat here is that the equal transit time idea is bullshit.

Are you saying a plane can fly without the effect of Newton’s Third Law? I really don’t see how a plane can go up if an equivalent mass is not going down.

No, I specifically said that the effect is inseparable from the pressure variation on the wing. Perhaps you are confused because I said momentum deflection, which just means the the air going down. And it is not an equivalent mass, which is why the term momentum deflection is more accurate.

Neither the pressure nor the air going down is the cause or the effect, they are both part of the same process. One cannot happen without the other.

Yes, I understand that. But one causes the other. The end result of air going down, to me, is where the discussion should start. Most people asking this question get lost in the explanations about pressure and flow. But you don’t need to understand that part to understand the simple part that the reaction to downward airflow makes a plane go up. And I’ve seen detailed explanations of pressure variation that neglect to mention in the end that air is being sent downward.

As for the second part of that, Bernoulli’s principle doesn’t really care about gradients in a particular direction, except for gravity. A flow which is uniformly accelerated, as in a frictionless pipe, will experience the same pressure change across the entire cross-section of pipe.*

Transverse to the direction of flow, which is what I said.

  • There will be a pressure gradient due to gravity in the vertical direction, but that’s the same regardless of the flow’s velocity. *

And irrelevant to bernoulli’s principle

For an incompressible flow, the change in pressure is a function only of the change in velocity, and in no way depends on any spatial direction.

Flow in air is not incompressible flow.

Strictly speaking, this is true - but given that lift can be generated at very low airspeeds, the compressibility of air is not a factor in explaining lift.

Note also that it is possible to generate lift in an incompressible medium, as via the foreplanes and tailplanes of a submarine.

I’ll concede that I may not have read that they way you meant. But it certainly seemed that you were implying a pressure gradient normal to the flow direction. That’s what I was responding to.

Not irrelevant at all. Bernoulli’s equation contains a gravitational potential term. A flow that does nothing but change altitude will change pressure due to hydrostatic forces. You HAVE to account for that when performing a calculation using Bernoulli’s principle.

You’re fixating on the wrong operative words. Of course air is never perfectly incompressible; nothing is. However, for speeds below a certain threshold (Mach 0.3 is a common dividing line in aeronautical practice) the compressibility of air is perfectly negligible. If you can turn your car into a point mass, I can give my air zero compressibility. And besides, using the compressible form of the Bernoulli equation doesn’t fundamentally change any of this discussion.

I hate to quote myself, but I’m pretty sure laminar flow is important. How is this aspect captured in the equations? What I mean is, the equations simplify down to an ideal, as I think was already mentioned. You then have to add back in certain “realities.” Isn’t this one of them?

That depends, of course, on what level of detail you’re using. The statement “the airplane gets lift because it’s throwing air downwards”, for instance, is absolutely 100% true, even though it doesn’t explicitly mention laminar flow. With that said, the effects of laminar flow will cause some wing designs to be better than others at throwing air downwards, so it’s definitely something that an aeronautical engineer would need to take into account. But you don’t need to mention it at all in response to “Daddy, how do airplanes fly?”.

If anything, the air going down is where it ends. Make a box around the wing (control volume for you engineers). Analyze the momentum of the air going in and out. You will see a net bias in one direction that will give you lift and drag. The pressure stuff that happens inside where the wing interacts with the air causes this.

In reality though, they are all interrelated. You can completely get the right answer with just looking at pressure and not air flow, and vice versa. But, and here is where we get to the “whys”, that is if you MEASURE it. If you are not measuring, but calculating, you must look at both the flow and the pressures, because they each affect each other. The equations that govern the flow, the Navier-Stokes equations, take both of these into account and both the flow and pressures must be solved for at the same time or neither can be solved.

Even when you measure the results, you can think of physical reality doing the calculations to solve for both pressure and flow simultaneously, and then you measure whichever is more convenient for you to see what the answer is.

The shape of the wing affects the way air flows over it. It is the complex interaction of the motion of the air past this shape that causes lift and drag. The velocity of the flow and the pressure affect each other at every point along the wing and in the air surrounding it to create the final flow field and pressure field that determines lift. The only cause and effect is that the wing causes and changes both of these fields simultaneously and interdependently.

It is very important if you are calculating the flow field from scratch. However, it is completely irrelevant if you know (have measured) either the surface pressure on the whole wing or the velocity field around it. Either of those things will give you lift without knowing if the field is laminar or turbulent. Whether the field is laminar or turbulent will determine what the pressure and velocity fields are.

Others have already addressed the first paragraph, but I’ll concur: your flat-bottom, curved-top wing at zero AoA will generate lift, and will also cause air off the trailing edge to go downward. It has to. Conservation of momentum demands it.

I pondered this statement for a bit, and found myself looking at the Navier-Stokes equations (which I have not done for a long time), and also considering some of the mechanisms described by statistical mechanics. I’ve also been pondering the fact that Bernoulli’s principle requires conservation of energy, but not conservation of momentum.

I’m also remembering the fact that I have watched airfoil streamlines in wind tunnels, and - while I agree that air flows off of the trailing edge of the kind of wing I described with a downward component, I don’t recall and don’t agree that a sufficient mass of air flows with a sufficient vertical velocity to account for the lift generated.

Momentum is conserved, yes. But in a real wing environment, this conservation has to take into account the formation of vortices and turbulence behind the wing.

So, ultimately, I’m going to flatly disagree that in the specific case I provided (flat bottom wing, top airfoil shape, and zero angle of attack) the lift is provided by a conservation of momentum argument where the air is flung down off the trailing edge. Also, if this were true, we would find the center of lift on the wing to be aft of where it actually is, and I am far from convinced that we’d see lift at all since the same conservation of momentum argument would require that the air being moved up at the front of the wing would cause a negative lift mechanism on the wing.

Now, matters here are not completely simple. If there is a positive angle of attack to this wing, then there is a tendency for the bottom of the wing to move air downward and Newton’s Laws can be used directly. In this case, quite obviously at least some significant component of the lift comes from the wing directly moving the air downward.

In fact, even a flat plate can be made to fly if it has a positive angle of attack, and this can be done without reference to bernoulli’s principle.

Now, I have not looked at this subject in a considerable period of time, though there was a time when I did a lot with it. One of the explanations I was looking at for lift clearly has its roots in computational fluid dynamics work and is therefore relatively recent, and it shows a model of an airfoil working that I have not seen before but which, when I think about it, sure looks like it is correct.

Basically, it says (of course) that conservation of momentum requires that a wing can only generate lift by forcing an air to move down at a velocity that satisfies the momentum equation; either a large mass at a low velocity or a smaller mass at a higher velocity. This article states - and supports with streamline drawings - that this air that is moved down is pulled via bernoulli’s principle from above the wing, and the vast majority of the lift comes about due to vertical air motion above the wing. This is referred to as a bound vortex.

http://www.allstar.fiu.edu/aero/airflylvl3.htm

I haven’t looked at this stuff in a very long time and I’m rather glad I was given a reason to. Good question.

More properly, compressibility need not be invoked to consider lift. However, at speeds commonly encountered by modern aircraft above the level of a single engine Cessna, compressibility needs to be taken into account and does affect the lift.