So how do planes fly (no really)?

[Bemused]

@aerodave

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.

OK

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.

Really? But the flow separation at the leading edge of the wing has the air column moving up a distance that is measured in feet. That has to have a negligible effect on the pressure.

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’ll agree that for low Reynolds numbers we don’t need to worry about compressibility. At high Reynolds numbers we do. The .3 mach velocity “boundary” is a rule of thumb that works for man carrying aircraft operating (i.e. aircraft above a certain size) not too far above the surface of the Earth. Many types of aircraft fit that profile.

And, yes. The difference is not fundamental.

[flight]

@Bemused

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.

I think your trouble here is thinking about the trailing edge only. The cambered airfoil also causes the air to rise up as it approaches the airfoil. This solves your center of lift conundrum. Think of how the stagnation point of a cambered airfoil at zero angle of attack is on the lower part of the leading edge.

For your question about air moving up causing negative lift, you are confused about fluid entering and leaving your control volume. Air going up when entering makes positive lift, and air going down when leaving also makes positive lift.

@Bemused

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.

I could not reach your site from work, but I believe you are referring to circulation theory, or more specifically lifting line theory. This is not tied to CFD, but has been around for quite a while. In fact, CFD is trying to replace it in a lot of places.

I suggest you look at the post I submitted while you were typing yours. You are looking at this as a one-causes-the-other scenario or a separate-effect scenario, when the are completely interrelated.

[flight]

@Bemused

I’ll agree that for low Reynolds numbers we don’t need to worry about compressibility. At high Reynolds numbers we do. The .3 mach velocity “boundary” is a rule of thumb that works for man carrying aircraft operating (i.e. aircraft above a certain size) not too far above the surface of the Earth. Many types of aircraft fit that profile.

And, yes. The difference is not fundamental.

Aside from the mixture of Reynolds and Mach numbers, yes. Density (what you are talking about when we mention compressibility) is an intrinsic aspect of the developing flow field, but once you get to the point of measuring pressures on the wing or the velocity of the flow around the wing, the effect has already been accounted for, just like the difference between laminar and turbulent flow.

[Bemused]

I suggest you look at the post I submitted while you were typing yours. You are looking at this as a one-causes-the-other scenario or a separate-effect scenario, when the are completely interrelated.

Well of course they’re interrelated.

[flight]

Oh, and one thing that was missing from my earlier explanations. If you are going to measure lift based on momentum deflection, the air moving up and down into and out of a control volume around the wing, you need to also know the pressure along the edge of that control volume as well. Just the velocity and density is not enough. When you measure the pressures around the surface of a wing you are doing the same thing, with the control volume being the wing itself. You just have the benefit in this case of knowing that the flow both in and out of the control volume is zero there.