How wings work

[blufive]

The latest Scientific American, explaining how wings work:

[...] because the wing top is curved, air streaming over it must travel further and thus faster than air passing underneath the flat bottom. According to Bernoulli's Principle, the slower air below exerts more force on the wing than the faster air above, thereby lifting the plane.

Scientific American, April 2006, P76

Everyone knows that that's how wings work. Unfortunately, it's bollocks.

While I'll let such inaccuracies pass in the non-technical press, I expect better of a magazine that regularly prints articles attempting to explain cutting edge of quantum mechanics, cosmology, immunology, and lots of other -ologies. Even if it's just a throwaway line in an item explaining something different.

The problems with that explanation can be demonstrated with a few fairly straightforward examples:

Firstly, in the course of aerobatics, it is quite common for aircraft to fly upside down (by which, I mean really fly upside down, in sustained level flight, not just a quick loop-the-loop or roll). For that to work, their wings must still be generating lift, despite the fact that the longest side is now on the bottom.

Secondly, not all wings are longer on top than underneath - there are many wing cross-sections that are symmetric, or have the same length on both top and bottom. Yet they still generate lift. For example: sails. Yep, a sail is a wing, turned on end. It's a bit of cloth. To all intents and purposes, both sides of it are the same length (let's not quibble over the tiny difference caused by the thickness of the fabric - trust me, it's irrelevant)

Finally: Two blobs of air approach a wing. One goes over the wing, the other under it. How does the air passing over the top know that it's got to go faster to keep up with the air passing underneath? They're not telepathic, psychokinetic entities. They're inert blobs of air. There's a big lump of metal between them. They cannot directly influence each other. While we're at it, who says that the air passing over the wing has to meet up exactly with the air passing under the wing?

So, how do wings generate lift? It's very straightforward, really: as air flows around a wing, the air is deflected downwards. That's it.

The Bernoulli Principle is a very real physical phenomenon, but it's the cause of lift in the same way as falling is the cause of gravity (which is to say: not much). So this is the last time it's going to get a mention in this post.

Let's consider a wing to be a simple flat sheet of metal, inclined to the airflow, with the leading edge higher than the trailing edge.

Returning to our hypothetical blobs of air, I'll introduce a third one and commit gross anthropomorphism by naming them (my brain can't cope with referring to several things as "it" in the same sentence). As the three blobs approach the wing, Alice is on course to pass over the top of the wing. Bob is on course to pass under the leading edge of the wing, but will collide with the wing itself. Carol is on course to pass under the wing.

Alice passes above the leading edge of the wing. Alice would like to keep going in a straight line (Newton's First Law of Motion, aka inertia). That would leave a vacuum immediately above and behind the wing, and air doesn't tend to leave vacuums lying around. So Alice expands into the space above the wing, reducing her density and pressure in the process. The pressure of the air above Alice also pushes her downwards. The overall effect is to create a low pressure zone above the wing and deflect Alice's course downwards.

Bob passes under the leading edge of the wing. Again, he'd like to continue in a straight line. Unfortunately, there's a big sheet of metal in the way. So Bob has to change course downwards to avoid it. As he does so, he has to shove Carol aside to make room to pass under the trailing edge. All this argy-bargy squashes them together, creating a high-pressure zone under the wing and slowing them down.

As the three blobs leave the trailing edge of the wing, they are all travelling downwards relative to their initial course. Newton's First and Second Laws imply that they have been pushed downwards by the wing.

Newton's Third Law implies that they pushed back - and they did. There's a high-pressure zone under the wing, and a low-pressure zone above it. That's your lift, that is. In practice, the overall effect also slows the air down a bit, causing drag.

So, if flat plates work, why do wings have more complex shapes? While a flat plate produces lift, it's not terribly good at it. Curved aerofoil shapes work better, producing more lift and less drag. They also work much better once you get beyond the simple case of straight and level flight.

Comments

[swisstone.livejournal.com]

Pardon my ignorance, but how does your model account for a plane flying upside down? Surely when a plan flies inverted, the wing is approaching the air in front at a different oblique angle, that compresses the air above the wing (relative to the ground) and causes it to expand below, thus creating pressure driving the aircraft towards the ground ...

[sbisson.livejournal.com]

There's also the issue of thrust - aircraft like the classic Geebee racer or the Harrier have enough thrust to fly without wing lift, and only use wings for stabilisation.

It's also why high alpha manoeuvers are feasible...

[blufive.livejournal.com]

The Harrier does (obviously) have the thrust to fly on engines alone, but once it's doing more than about 50mph, most of its lift will be coming from the wings. At real flight speeds over 150mph, it'll be pretty much all wing lift, simply because it's so much more efficient.

The Geebee might have had power-to-weight greater than 1 (wouldn't like to bet on it, though) but, again, it would have been using wing lift once it got up to any sort of speed whatsoever. If the prop were canted at 30° above the horizontal (which would be silly) you'd need a thrust-to-weight of 2:1 to stay up, and slowing down (by reducing thrust) would be... problematic. Wikipedia even suggests that the Gee Bee's fuselage acted as a lifting body in itself.

(Someday, I'll try to write up why that helicopter slicing up a street in The World Is Not Enough is mind-bogglingly ludicrous, but that needs more diagrams, and I think I've inflicted my artistic skills on people quite enough this evening...)

If you ain't got wings, you need to be a helicopter, a gyrocopter or a flying bedstead, I'm afraid. (and two of them do have wings, they just go round and round)

Really high angle-of-attack maneuvers are actually more down to having sufficiently advanced control systems to be able to keep control of the plane while it's travelling at angles where the aerodynamic forces are all over the place, but thrust (or more particularly, thrust vectoring*) is a big factor, yes.

*Which brings us back to the Harrier...

[luna-the-cat.livejournal.com]

First off, ::APPLAUSE::! This is one of the best, briefest and most coherent explanations I've ever seen. Thanks.

Re: Harriers and the like -- my impression was that, unlike most aircraft, all jet fighters were pretty much designed to be unstable in the air; to rely on simple speed to keep them going, and use the instability to enable high maneuverability.

[blufive.livejournal.com]

Thanks.

Many (most?) modern fighter aircraft do have Relaxed Stability. This allows the aircraft to be designed for pure aerodynamic efficiency - a lot of the natural stability of older designs rely on "weathercocking" - creating drag behind the center of gravity which acts to turn the nose into the airflow. It's simple, it works very well, but it increases drag and hinders maneuvering, particularly the sort of highly vigorous maneuvering that fighters tend to be designed for.

This is a relatively recent phenomenon, however. The key innovation that allowed it was active fly-by-wire control systems. In essence, the pilot isn't flying the plane - it would be like trying to balance three chairs on top of each other, on a broomstick, on your forehead. Instead, a computer (which has much better reactions and probably much better awareness of the immediate aerodynamic situation) flys the plane, with the pilot providing instructions via the flight controls.

The first plane to really use this sort of system was the F-16, though it is now common on most front-line fighter aircraft. It's also appearing (in a more restrained way) on many modern airliners, to improve fuel efficiency.

[luna-the-cat.livejournal.com]

Hmmmm.

Very different from what I'm used to. The only thing I've ever flown (aside from a brief stint in a paper cup, er, Piper Cub) was a glider, which is pretty much the essence of low-speed stability. You really have to work to stall them, and a soon as you stop making them stall, they stop stalling. I wonder what it would feel like to fly something made with almost the opposite in mind...

[blufive.livejournal.com]

You're right, having wheeled out the counter-arguments to the common explanation, I really should have addressed them, shouldn't I?

The magic sentence I should have included above is: It's all about the angle at which the wing meets the air.

The essence is simple - when a plane is flying inverted, it's actually meeting oncoming air at a different angle, relative to the aircraft body. The leading edge of the wing is still higher than the trailing edge, relative to the ground. So the compression is still below the wing. The actual change in angle is pretty small (probably on the order of about 5°, maybe as much as 10°) so it won't be obvious.

For most real wings, inverted flight is pretty inefficient, but it works well enough for a quick crowdpleaser. I suspect most purpose-built aerobatic aircraft use wing cross-sections that work pretty well both ways up.

[richc.livejournal.com]

Shouldn't that be 'The leading edge of the wing is still higher than the trailing edge, relative to the airflow'.

[blufive.livejournal.com]

Yes, that's also true (and more important, in lift terms). If the plane's upside down, however, then it's same difference, really.

[mutter, mutter, cold light of morning, mutter, posted at near midnight, grumble </muttley>]

[blufive.livejournal.com]

Actually, I've fumbled that question.

If the lift is to be "up" relative to the ground, which is the question Tony asked, then the leading edge must be higher relative to the ground. (assuming horizontal inverted flight)

The lift goes more-or-less perpendicular to the wing, away from the side facing into the airflow, so "relative to the airflow" is pretty much a tautology, as the airflow has no "up".