How, exactly, does an airplane wing work?

dimensionless

The conventional explantion is that the wing is curved on top. This curve means that the air has to travel farther than the air on the underside. Because the air is less dense on top there is greater air pressure on the under side of the wing and this is what gives the wing lift.

I see one potentily serious flaw with this line of reasoning. In order for the molecules to move up and over the wing they must first strike the wing and then bounce upwards. This collision will mean that a downward force will be exerted on the wing. I would think that this downward force would cancel out any potential vacuum that is created in the above explanation.

Is the theory more complex than this? Are there other forces, such as Van der Waals forces, involved? What am I missing?

pervect

There's some infomation on this at

http://travel.howstuffworks.com/airplane7.htm

n the late 1600s, Isaac Newton theorized that air molecules behave like individual particles, and that the air hitting the bottom surface of a wing behaves like shotgun pellets bouncing off a metal plate. Each individual particle bounces off the bottom surface of the wing and is deflected downward. As the particles strike the bottom surface of the wing, they impart some of their momentum to the wing, thus incrementally nudging the wing upward with every molecular impact.

Note: Actually, Newton's theories on fluids were developed for naval warfare, in order to help decrease the resistance that ships encounter in the water -- the goal was to build a faster boat, not a better airplane. Still, the theories are applicable, since water and air are both fluids.

Why is it not entirely correct?
The Newtonian explanation provides a pretty intuitive picture of how the wing turns the air flowing past it, with a couple of exceptions:

1. The top surface of the wing is left completely out of the picture. The top surface of a wing contributes greatly to turning the fluid flow. When only the bottom surface of the wing is considered, the resulting lift calculations are very inaccurate.

2. Almost a hundred years after Newton's theory of ship hulls, a man named Leonhard Euler noticed that fluid moving toward an object will actually deflect before it even hits the surface, so it doesn't get a chance to bounce off the surface at all. It seemed that air did not behave like individual shotgun pellets after all. Instead, air molecules interact and influence each other in a way that is difficult to predict using simplified methods. This influence also extends far beyond the air immediately surrounding the wing.

While the "pellet model" of lift that you suggest can work in some applications (such as space-shuttle rentry) as mentioned on this webpage, it does not work well for normal subsonic flight at sea level. In this regime, significant "flow attachment" to the upper side of the wing occurs. Because of this, the upper wing generates significant lift. Another way of putting this - in sea-level subsonic flight, Euler's equations (of fluid dynamics) are a much better way of estimating lift.

To "fix up" your pellet model, you'd need to model the pellets as interacting significantly. Modelling the pellets as ideal hard interacting spheres should give you an ideal fluid, which should reduce to Euler's equations (IIRC, anyway).

This level of modelling still isn't perfect, because it ignores effects such as viscosity. When viscosity is included, things starts to get really complicated fast - one can write down the appropriate partial differential equations (Navier Stokes), but solving them is another matter.

There are some more resources on this question at

http://www.grc.nasa.gov/WWW/K-12/airplane/bernnew.html
http://www.amasci.com/wing/airfoil.html#L1

rcgldr

At the big picture level, a wing has an effective angle of attack, as it passes by a volume of air, it introduces a void, that is mostly moving downwards and a bit forwards, which causes air to accelerate downwards (lift) and a bit forwards (drag). In the typical case where angle of attack is small, most of the downwards acceleration occurs above the wing. This is mostly because the lower pressure area above the wing draws some of the airstream away from the air that would otherwise flow below the wing, which lowers the seperation point where the airstream splits up, and because at the seperation point the air stream that flows under a wing is already deflected downwards at the seperation point so the wing's defelection of the air doesn't add that much more downwards velocity (less downwards acceleration), as opposed to the uppper airstream which starts off being deflected upwards, and then curves (acclerates) back towards the low pressure area caused by the moving void left by the wing as it passes through the air.

Surface friction, visocity of the air, laminar versus turbulent flow, ... affect the amount of lift generated.

Another link:

http://www.aa.washington.edu/faculty/eberhardt/lift.htm

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