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Physicists Finally Solve the Falling-Paper Problem
neutron_p writes "The so-called "falling paper" problem has long intrigued scientists. James C. Maxwell pondered the tumbling motions of playing cards in 1853. Why don't flat things fall straight down? Pieces of paper fall down, then rise into the air, then glide along, then again rise... It occurs in a seemingly chaotic manner. Now researchers at Cornell University have solved the falling paper problem by calculating the motions of a scientific journal page in flight and there were a few surprises." There's also a story in the Cornell Sun.
better save it here for posterity :-)
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Image: The seemingly chaotic motions of this page from a scientific journal became part of a computer modeling exercise to show why flat things don't fall straight down., J. Wang and U. Pensavento/Cornell University. Copyright Physical Review Letters 2004
The same falling-paper principles apply, the physicists believe, to naturally flat things like leaves. If they are right, Wang and Pensavento may have finally solved the mystery of why autumn leaves depart from a neighbor's tree on a windless day . .
. . . rise into the air . . . . . . rise again . .
. . . glide along . .
. . . and have to be raked from yards that don't contain a single tree.
As Wang explains, "Leaves and paper fall and rise in a seeming chaotic manner. As they fall, air swirls up around their edges, which makes them flutter and tumble. Because the flow changes dramatically around the sharp edges of leaves and paper, known as flow singularity, it makes the prediction of the falling trajectory a challenge."
Among the first scientists to be intrigued by the behavior of falling paper was Scottish physicist James C. Maxwell, who pondered the tumbling motions of playing cards in 1853. But while Maxwell was a brilliant mathematician, he lacked the today's computer-modeling techniques, not to mention access to fast, powerful computers. Wang and Pensavento put those advanced tools to good use to show why the falling trajectory of thin flat things -- and the behavior of airflow and other forces -- is not predicted by the classical aerodynamic theory.
"There were a few surprises," Wang notes. "We found the flat paper rises on its own as it falls, which would not happen if the force due to air is similar to that on an airfoil. Instead, the force depends strongly on the coupling between the rotating and translational motions of the object."
Wang and Pesavento also showed that the falling-paper effect is almost twice as effective for slowing an object's descent, compared with the parachute effect (that is, if an object falls straight down). And that evidently benefits trees and other plants that need to disperse seeds some distance from the point of origin. Plants with flattened seedpods also take advantage of the falling-paper effect.
The research was funded by National Science Foundation, the U.S. Air Force Office of Scientific Research and the Packard Foundation.
Says the professor who does not use the falling-paper effect to grade student essays and forecast their future: "What is predictable is that as the autumn leaves tumble down, they drift in particular directions, depending on the way they turn. This may explain, Wang adds, "why you are getting the leaves from your neighbor."
Source: Cornell University
With great numbers come great responsibility!
This seemingly simple problem like many other (more important problems like understanding air turbalance) is an exercise in solving the navier-stokes equation for a fixed set of boundary or initial conditions. The Navier-Stokes equation is the equation that describes the flow of fluids on the large scale. It is a non-linear partial differential equation and is in some cases extremely difficuilt to solve (There is a $1,000,000 prize for the answer to the question: Do smooth initial conditions always lead to smooth solutions?). This may not seem very significant but it is probably very difficuilt to solve.
Actually, this problem is important for aerodynamic theory. Items like airfoils, and spheres are well understood, but other shapes are confusing because of chaos. Understanding how paper falls is one step in understanding how different aerodynamical surfaces operate. The article states that falling paper is twice as effective at slowing down a falling object. Surely thats not minor concern. Additionally understanding the aerodynamical properties of low profile objects can help us understand aircraft (or spacecraft) failures.
And it's another physorg dead-end. Rather than mirror it or anything, a little googling will find the original material. Here's The original spam-free press release and Professor Wang's home page with a full citation for the paper.
Plants with flattened seedpods also take advantage of the falling-paper effect.
A specific example of this is the sycamore seed. As a matter of fact, landing a helicopter without motor assistance is called "the sycamore landing". It utilizes the exact same theory these phycisists has explained. So - It's not the theory that's new - it's the level of detail.
Underholdning.info
Phys Rev Lett. 1994 Sep 5;73(10):1372-1375. Related Articles, Links
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Behavior of a falling paper.
Tanabe Y, Kaneko K.
http://prola.aps.org/abstract/PRL/v73/i10/p1372
WTF are you on about? If you butter one side and then make a Mobius strip it'll have one side, half buttered. Nothing complicated about it.