Even in the most thoroughly tested area – orbital mechanics – of plain old Newtonian physics, not everything is known. Newton’s law of gravity has never been completely solved as a calculus problem for a universe with more than two objects in it.
See, that’s the problem with the universe. It’s got too many objects. 
Thanks for the reply aerodave!
#4: Why does air have any viscosity whatsoever? Do different gases have different viscosities, or does it tend to vary with another sort of quality?
#2: In the present day, what is the role of flight tests? Where do CFD and WT fail us?
#1: Let me attempt a re-phrase; I apologize in advance for the imprecision and verbosity.
B
______A_________
-> / \
E -> / \
-> < |
-> ------------------------
-> C
D
E represents a given volume of air, headed towards the wing sketched above. The volume is divided between areas A and C, above and below the wing. (I ignore areas B and D.)
If E is evenly divided between A and C, and area A (above, including the front and rear of the wing) is greater than area C (below), then the air pressure in A will be less than the air pressure in C.
This story seems similar to, “Equal transit times.” That is, if n air molecules travel distance A in the same amount of time that n different molecules travel distance C, and A>C, then it seems that A indeed will have lower air pressure than C.
Why is this wrong or confused?
Just to be sure I understand this, you’re saying that the static pressure immediately in front of a electric fan is lower than that of the surrounding environment. Hm, I would have thought that it would be higher. 
I guess it depends on your dubies? 
Your initial interpretation is correct; in airplanes, at human scale and reasonable speed, Coanda is driven mainly by air pressure.
The inertia of a fluid mass over a separating wing creates low pressure in the separation between the mass and the wing. Higher pressure from the mass above the wing presses the fluid mass downward along the curve of the wing. Higher pressure under the wing pushes the wing upward. Downwash and lift; equal and opposite; due to mass, due to inertia.
I find the concept of viscous air quite intriguing. Imagine flying if air had the viscosity of warm molasses. In my experience air viscosity is only a consideration for planes the size of insects. Flat plate wings seem to work just fine for them.
rwj.
Not at all! Viscosity is critical in the analysis of flight in almost any speed and size regime. Boundary layers are the areas near moving bodies where viscous effects are important, and BLs get a lot of attention, for good reason. And if you’re familiar with the concept of Reynolds number, you realize that no viscosity leads to infinite Re, and a flow that is completely dominated by its own inertia. Random motions are never damped out by viscosity, and flow won’t follow the paths you want (like around a curved wing!).
In fact, it can be safely argued that fixed-wing flight would be impossible without viscosity. We spend so much time trying to avoid friction in real systems, but in the case of flight, friction and viscous losses in the air are the only thing that lets us fly in the first place! Then again, without friction, we’d have never gotten to the point of walking, much less flying.
MfM
#4: Air has viscosity because of the internal interactions between its molecules. As nearby parts of a “chunk” of air try to slide past each other, the molecules interact in much the same way that gives solid objects friction. All fluids have viscosity (okay, except for superfluids, but let’s not go there), and it’s different for each fluid. Viscosity is also somewhat temperature dependent (directly proportional for gases, inversely for liquids).
#2: Flight tests are important mainly because of scaling. Putting a 10%-scale part ina wind tunnel at Mach 0.8 isn’t the same as moving a full-scale piece through the air just as fast. That’s because it’s usually impossible match all the parameters that you need for what’s called “dynamic similarity.”
For example, simply scaling a part down geometrically and maintaining the speed will alter your Reynolds number (Re), which is dependent on your object’s length. It’s important to match Reynolds number for a lot of things, or to at least recognize that you’re compromizing that parameter. But it’s hard to match Re at small scale. That’s because to compensate for the changed length, you have to change one of the other things that it depends on: density, viscosity, or velocity. The first to are hard to change unless you are pressurizing the air or not using air at all. The velocity is easy to change, but you affect a ton of other things if you mess with that.
In short, scaling things for wind tunnels results in necessary compromises. The only practical way around them is to build something full-scale and fly it around. This happens late in the development process, of course.
CFD falls short only in that it’s based on numerical approximations and can’t model everything perfectly. Maybe one day we’ll be at the point where we can do design on computers only and jump straight to building planes. But the computers need to be a lot faster and the codes need to be a lot smarter. Give it a few decades. The other big hurdle is trust…would you fly in something that never had an experiment validate some dude’s computer program?
#1: you’re thinking of all that air getting “smeared” across the top of the wing. But it doesn’ have room to smear out, because there’s air just ahead of it and behind it trying to do the same thing at times t-1 and t+1. Those arrows you drew will stay in pretty much the same vertical plane as they make their way from one end of the airfoil to the other. Just try to focus on the “sticking” and “turning down” that the top-surface air has to do, and you’ll be well on your way to understanding lift better than 99% of the people out there.
Before I get to that explanation, let me explain something fundamental about pressure, since it’s vital to the rest of this long-ass post. There are really two kinds of pressure: static and dynamic. Static pressure is what’s in a soda can, or the atmospheric pressure a barometer measures. Dynamic pressure isn’t something you can feel directly, it’s sort of a measure of the kinetic energy of the air (and it’s dependent on the speed of the flow). But you can feel the effects of dynamic pressure, like if you stick your face out the car window. The force you feel is a result of DP turning into SP. You can interchange the two types of pressure, all by changing the speed of the air. Bernoulli’s Principle merely states that the sum of the two remains the same, a quantity known as “total pressure.” Fluid at rest is all staic pressure, no dynamic. But moving air has lots of dynamic pressure. WHen you stick your face out the window, you cause some of the air to slow to nearly a halt, and it gives up its dynamic pressure by changing it into increased static pressure…and you can feel that.
A fan, however is a bad example, for a couple reasons. One, the fan is a compressor, which means its job is to add to the total pressure of the air. ( a household fan can only do this by a miniscule amount, but in only take s a tiny pressure difference to get a nice breeze). It does this by doing mechanical work, and dumping more energy into the air. The increase in total pressure is added to dynamic pressure (the flow is accelerated) and static pressure (the flow is compressed a little). The other problem is that you can’t get much out of measuring the flow immediately in front of and behind an open fan, because the free slipstream it creates is sort of self-smoothing. The speed of the air going into the blades is about the same as that coming out, because the air must go in and out at the same rate (conservation of mass and all that).
But, let’s say you can speed up a piece of air without adding work. Say you have a big 100-psi air compressor tank with a shop hose on it. If you open the valve and let the air spray out, the air inside the tank and coming out the hose have the same total pressure, 100 psi. But inside the tank, it’s all static. In the free jet hitting you in the face, the static pressure is the same as atmospheric, 14.7 psi. The other 85 psi shows up as dynamic pressure now. So it may not feel like it, but the jet has much lower static pressure. The reason you can’t feel it is because any air you’re feeling is slowed down some, and therefore the static pressure goes back up.
Are you dizzy yet?
Yeah, I’ve got a massive headache. And I gotta moderate this stuff?
Let me remind everyone of what aerodave said up front – there’s been a small hiccough in communication with the editing on this Staff Report*, so there may be some minor revisions before it’s appearance on Tuesday.
*It’s summer, after all.
Yes, I’m quite dizzy.
And interested. Thanks for all your work, aerodave. This is rather neat stuff.
Those who share my ignorance of this subject might want to plod through NASA’s website:
Beginner’s (Ha! -ed) Guide to Aerodynamics
Guided Tours
Ok. After partially digesting Bernoulli’s equation (Ptotal = Pdynamic + Pstatic), where P is pressure and staring at this page (especially the top right diagram)[1], I think I’m partway there.
The velocity of the gas above the wing is greater than the velocity below the wing, implying that the dynamic pressure is higher above the wing, and the static pressure is higher below the wing. The imbalance in static pressure creates lift. (There are also the Newton effects, but I’m ignoring them here.) I assume that total pressure is identical above and below the wing.
----- For complex reasons we needn’t get into (other than to say they have little to do with equal transit times), air moves faster over the top of a wing than beneath it.
I think we need to get into that now. Why does air move faster over the top of the wing (for reasons that have little to do with equal transit times)?
[1] My intuition for Bernoulli’s equation: for 2 systems with constant total pressure, if one system has a disproportionate number of molecules bouncing off one side of the box (higher dynamic pressure), it will have fewer molecules bouncing off other sides of the box (lower static pressure). Said box is hypothetical. Said intuition gleened by M4M: you have been warned.
Please identify the property of viscosity that counters the effects of pressure as described. Are you able to demonstrate an airflow that does not follow a curved surface in a non-viscous fluid at STP?
I am still not convinced that viscosity is more than a footnote in How airplanes really fly.
Usually when I see this statement, the authority is referring only to the under the wing deflection caused by the angle of attack.
Of course this falls short.
In my experience, it is the over the wing air mass deflection and the angle of departure that is the key to how airplanes really fly.
Peace
rwj
I think Peter Garrison agrees with you.
If I ever get my hands on an inviscid fluid, I’ll let you know.
And I’m not sure what you mean by “countering the effects of pressure.” Pressure and viscosity are not antagonistic properties.
You’re quite right. Total pressure can change due to weird effects at high speeds…like supersonic. But that’s nothign critical to following this discussion.
A great question, and one that really turns out to be a key part of the confusion. The drawn-out answer was taken out of the published article for the sake of brevity and clarity. The damn thing’s long enough as it is.
Remember the Coanda effect? If the flow has to make the turn, it creates low static pressure on the inside of the turn (the whole centrifugal force analogy, described very well in Craig’s book). If the static pressure drops, the air must necessarily speed up. Forget cause and effect…it’s not proper to talk about the acceleration causing the pressure drop or vice versa. They’re really just two mutually necessary happenings, which are the end result of an airplane wing getting in the way of the air.
As a different example, think of squeezing a spring. Does the force exerted by the spring increase because you make it shorter, or does it get shorter because you’re pushing on it? Cause and effect aren’t the issue, it’s just that length and force are two quantities that are linked together by a relationship.
As far as ignoring Newton in favor of Bernoulli, or the other way around, don’t worry about it…you’re right either way. My assertion is that they’re just two ways of getting a gut feel for the same phenomena. You’re looking at two different, but inextricably linked models. They are necessary consequenses of each other, so it’s not wrong to use either model.
If you measure the momentum change given to the air as the plane passes, the force required to cause it is equal to the lift. So a Newtonian description is right. If you sum up all the pressure variations above and below the wing (the ones that correspond to the flow turning the way it does), the net force is equal to the lift. So Bernoulli is right, too.
The moral? Pick whichever description makes sense, because they’re both right. Understand it intuitively enough, and you find that they’re really the same.
In the realm of human flight, the weight of the atmosphere, following the laws of mass, presses the airflow to follow the curve of the wing. Although the effects of viscosity can be beneficial, it seems clear that it is the fluid pressure of the atmosphere that is the major component of airflow around a wing.
rwj
aerodave: Please understand that these nits are miniscule compared to our agreements. It is just that I have been battling the Bernoulli Believers for so long that I [del]sometimes[/del] invariable have difficulty backing off.
Keep up the good work!
Peace
rwj
Well, rw, that’s because the “Bernoulli believers” are usually very wrong. So you and I may agree even more than you think.
I’m not a proponent of using Bernoulli to explain where lift comes from. I only assert that it is a perfectly valid way of describing the flow around a wing, if you know the right inputs into the equation. It has to be right, becuase it’s an incontrivertible physical law that precisely describes the interplay between the pressures and velocities we see. The problem is that it doesn’t provide the “why,” and that’s where people get into trouble. If you use the right data, you can very easily correlate the pressures and velocities around the wing using BP. But to use it as a the reason for lift, people end up making some bad assumptions, (like the equal-transit-time hypothesis), because you can’t get the right velocities or pressures easily given only the wing’s shape.
But it can be used for good. Any properly-formed model of lift based on pressure distributions must include the Bernoulli Equation. And bear in mind, a pressure-based lift argument is just as valid as a momentum-based “Newtonian” model. They’re just approaching the same flowfield from two different points of view. The caveat is that either model for lift requires putting the right numbers and assumptions into it.
Bernoulli gets a bad name only because it’s so easy to misuse…mainly because it’s well-known and perfectly valid. The problem occurs when people try to turn the description into a reason. It’s not the cause, any more than Netwon’s Law of Universal Gravitation is the reason we stick to the earth. But in both cases, the equations are great at describing the effects.
I do not doubt that.
Agreed.
It seems to me that the problem is that “Bernoulli” has become synonymous with all aspects of fluid dynamics – even the non-Bernoulli aspects. Saying “airplanes fly because air travels faster over the top of the wing” is like saying “cars go forward because the wheels turn”. While true as far as they go, they both fall short of reality.
[hijack]Are you aware of the ”Reverse Magnus Effect”? A slippery ball curves toward the side that is rotating into the airstream. This opposite to the direction baseballs curve. The Bernoulli Believers have warped the understanding of Bernoulli’s formula to fit this Magnus (Newtonian) Effect. The fact that this is the predicted and actual Bernoulli effect eludes their comprehension. Therefore they call it the “Reverse Magnus Effect”.[/hijack]
Peace
rwj
:smack: The fact that this (the “Reverse Magnus effect”) is the is the predicted and actual Bernoulli effect eludes their comprehension.
rwj
and you call yourself an engineer!
Your idea with ruffles has a bit of a problem. Even if the physics work just as you think they do, the effect of every peak ridge causing positive lift is cancelled by every trough causing negative lift, and all the time resulting in extra drag.
Hey, how did you guys see the staff report before it came out? I have been waiting for this for a while.
As to Newton, has anyone actually created a model that can acurately predict lift using just Newton? The inputs being the unperturbed flow field and the airfoil geometry. I was not aware of that having been done. In fact, I am aware of some people conducting research in an attempt to disprove it as the mechanism of lift, but rather an avoidable side effect of current methods. I am very interested in seeing their work once they publish. I was under the impression that, as has been stated above, they are both natural consequences of the same interactions.
Oh, and lastly the question of what CFD cannot do. It is very good at a lot of things, but the one thing it sucks at is predicting drag. Things are improving, but most codes tend to dramatically underpredict drag in most situations.
That’s exactly what the Bernoulli equation is. Newton’s laws are the entirety of classical mechanics; everything else is just special cases. If you apply Newton’s equations to an ideal gas, you get Bernoulli’s equations.