Slashdot Mirror
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.
Now they just need to solve the 8+ folds problem...
better save it here for posterity :-)
.
.
.
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!
Prof. Wang from TaM was my math teacher. Smart lady. She went crazy explaning the use of hyperbolic trig functions. At the time I had no idea what she was talking about, but now I see it actually has a use. Her other research is in the fields of insect flight. Looks like Calculus isn't useless after all.
air currents? Dumbass scientists with nothing better to live for than proving evolution and why pieces of paper fall slowly. Why not cure cancer you retards?
You know, when they finally do find the cure for cancer through a process that involves falling paper, I bet someone is going to feel awfully silly.
This is just a rehash of an old study showing why open-faced peanut butter sandwiches always land face down.
Sheesh, evil *and* a jerk. -- Jade
Has anyone combined this with other falling-object problems?
For example, if one butters one side of the paper, will it still land face down, even if it's floating about?
Since cats fall on their feet, what happens if you wrap playing cards on each of their legs? Will their happy flight downwards be interrupted by randomly flying limbs?
What if you wrap the cat in a piece of paper that has been formed to make a Moebius strip, butter the other side of the animal, then tie it together to another cat? I suspect this may be the way to create time travel or a perpetual motion machine.
I hereby ask everyone to funnel funds towards this dynamic Cat, Toast, and Paper Research. I approximate we have about 4 years to prepare to salute our new Paper Machie Strawberry Jelly Cat Overlords.
Small potatoes make the steak look bigger.
The article says that the slowing-down effect for paper-like objects is much larger than normal "parachuting" effect. I wonder if this could be used in some way for parachutes.
by calculating the motions of a scientific journal page in flight
... they still need to repeat the experiment with different types of journals; psychology, home decorating, sports and paranormal to be absolutely sure.
..and it was well behaved and obeyed the laws of physics. I want to see what happens when they repeat it with a bible page.
Physicists Finally Solve the Failing-Paper Problem
Oh, if only :~(
<mutter>back to studying I guess.</mutter>
A government is a body of people notably ungoverned - AC
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.
This might be useful for future Rover missions (or, um Beagle missions). You'll lose accuracy, but at least you wouldn't hit the ground like a falling rock.
Logic, macros, and more
Notice the "Related Stories" section. It is blank. This doesn't relate to anything. Does that tell you something?
And physicists are supposed to do what about cancer? Please, let physicists do physics, and physicians do medicine!
Logic, macros, and more
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
If you're on the moon, where there is little or no atmosphere, they will fall straight down. Has anyone seen the video of the feather falling straight down without fluttering around at all?
"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."
Anyone who has ever thrown playing cards, frisbee, venetian blind bomerang (you have to be old enough to have had wooden venetian blinds as a kid) would not be surprised at the quoted 'surprise'.
That was already answered a while back. It has to do with the speed of rotation, combined with the height of the average table. If you were at a different height, the toast would fall butter side up.
Care about electronic freedom? Consider donating to the EFF!
"If we took the money that the physicists receive"
/. in *your* free time and get to work on that cure for cancer.
There is no evidence that the physicist and the mathematician received any extra money here. They probably are both lecturers (someone already posted about having the mathematician for a class). They may well be doing the research part in their free time. If you have a problem with that, maybe you should stop reading
For that matter, why aren't you criticizing smokers? Not only do they make themselves more likely to get cancer, they also take frequent breaks to smoke. I wouldn't be at all surprised to find out that smoke breaks take more time than the sum total of cancer research. Eliminating smoking would free up physicians who are currently working on cancer to do research and provide more time for non-physicians to do maid work, etc. to free up physicians to concentrate on their cancer research.
The results of physics research also free up people by cutting costs in other areas. If we still had a hunter/gatherer economy, we wouldn't be able to waste people on non-essentials like medicine, much less medical *research*. Not to mention the point that the advances in understanding chaotic systems may be applicable in areas other than physics (e.g. medicine). While statistical analysis (from mathematics!) suggests possible causes of cancer, we still don't understand what actually happens.
--Mark
"It is nice to know that the computer understands the problem. But I would like to understand it too." --Eugene Wigner