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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.
Now they just need to solve the 8+ folds problem...
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!
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.
Paper is affected by air as it falls! Astounding. ;-)
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.
I'm not sure that researchers from Theoritical and Applied Mechanics can do much for cancer research.
Remember, Civil Engineers make the targets, Mechanical Engineers (or TAM nerds) make the bombs.
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.
Paperweight - stop it going floating in the first place.
Due to lack of disk space this user has been discontinued
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?
Finally, a possible answer to why Toast ALWAYS falls butter side down in uncontrolled experiments !
Of course, this still doesn't mean we can get a perpetual motion engine by strapping said toast to a cats back, but we can hope !
I see a new form of energy just round the corner, CatToastOnics !
A slashdotting - you get the stick first and then the carrot !
Just two words for you: Dumbass Retard.
Thank you.
Logic, macros, and more
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
No, it's easy ... just fold it about nine times and it should fit.
Sure a cure for cancer would be nice, but atleast I can use this to calculate how many of those leaves from my neighbor's damned tree are going to end up on my lawn.
Maybe now I can bill him for raking...
Brandon Petersen
Get Firefox!
They've problery already found the cure. Now they just try to calculate were it landed... Everything got an purpose...
Congratulations. Within the span of two words you have personally offended (along with the parent poster):
- people who can't speak
- donkeys
- mentally retarded people
In the future, I would kindly request that you try to be more politically correct and just say 'fuck you'.HTH. HAND.
?-|||-----x<*))))><
'fuck you' is offensive to people who have no or non-functional genitalia, you insensitive clod! That includes most of the slashdot editors, a large portion of the trolls, victims of ritual female genital mutilation, mules, and Barbie.
Phys Rev Lett. 1994 Sep 5;73(10):1372-1375. Related Articles, Links
_ 1
Behavior of a falling paper.
Tanabe Y, Kaneko K.
http://prola.aps.org/abstract/PRL/v73/i10/p1372
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'.
Because physicists study physics.. not disease and hunger. Not to mention the fact that having a world where veryone is equal, fat and happy is not ideal. Happiness is a relative thing. A major component of happiness is knowing that some other poor soul has things worse than ourselves. There will ALWAYS be winners and losers. Quit being such a bleeding-heart and accept life for what it is. It's been working for a billion years or so. Don't think you know better. Sheeshh..
What is your penile percentile?
What are you doing for a better world today?
How about selling your computer and feed some children in nigeria with the money?
Would have the nice side-effect that we wouldnt have to hear your wise-ass remarks.
HI O WISE PRINCE. WHT TOOK U SO DAM LONG?
It doesn't necessarily follow that this problem was solved now because of lack of funding. Rather, I'd say it's more likely that it means that the difficulty of the two problems is about equal.
...), and there's a lot of consideration being given to tricks to solve Navier-Stokes (and other more complicated models that include the fluid being conducting or charged, or in some GR framework). So it's reasonable to expect that with new algorithms popping up, and refinements on the old ones, suddenly some intractable problems become accessible.
We still can't solve the three-body problem analytically (except for some special cases), and thats been around for 400 years. And its not for lack of trying.
However, only within the last 50 years or so could we make approximations to the solution that work for long enough to be interesting and give insight into the problem. It's the availability of computers that makes it possible.
Fluid dynamics is a hot topic in astrophysics right now (simulating stars, gravitational collapse of nebulae, accretion discs and jets around blackholes,
So I don't think that this was a 'problem left behind', as much as a problem which is just now becoming solvable. (Part of) the reason we spend billions on particle physics and not on this sort of problem is that the minimal 'thing' to advance the science in particle physics costs billions, whereas nowadays one can run fairly large-scale simulations (of classical systems) on a $2000 laptop: the biggest cost for those problems is hiring students/postdocs/professors to work on them. So really there what funding enables is diversity in the problems being tackled (how many laptops can you afford? how many grad students?), rather than the speed at which any one particular problem is solved.
Of course, this isn't true of some problems (quantum systems) which you really do need 1000 cutting edge systems all networked together to solve even a simple problem. In that case, you're going to have to be willing to throw a fair amount of money at the problem before you can see any progress.
Smartass teachers like to give students tasks they think are impossible and offer bonus points. I'm sure for 85 dollars and gold foil, it was something like a free A in the class. When I was in eighth grade a teacher offered a A for the class if you memorized a few hundred digits of pi that were posted circleing the room near the ceiling. I wish I had know about Pseudonumbers then. I probably wouldn't have learned any algebra after that, but I would've shown that smartass.
Interestingly, when scientists were making progress in cancer treatments, I asked a similar question of "cancer? Dumbass scientists with nothing better to live for than proving evolution and curing cancer? Why not solve the falling paper dilemma you retards?
Neil is that you? Yeah yeah, it's me... Neil...
I think we may have a winner....
OTOH, curing cancer is a pseudoscientific attempt to interfere with the clear intention of the divine. In fact, by curing cancer, and going beyond the understanding of the divine to the prideful attempt to compete with the divine, we are surely condemning ourselves to eternal suffering. All to prevent a few years of suffering in this life. How gauche.
"She's a scientist and a lesbian. She's not going to let it slide." Orphan Black
"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.
I served in an Army psychological warfare unit in Viet Nam that had produced and delivered, by 1970, enough leaflets to cover the entire country of South Viet Nam to a depth of more than 6 inches. Delivery was divided between Army helicopters and Air Force planes.
It's not surprising to see the Air Force funding further study on this subject.
With any luck it will fly around a bit, swoopishly. The circulation caused by the back-spin generates lift, same as airfoil-shape induced circulation (faster airflow on top, slower on the bottom) as per that well known Kutta-Joukowski formula s * b * mu * gamma.
Which is apropos of nothing. Also, the Navier-Stokes equations can't be solved around a singularity like the edge without a simplification which usually takes the form of an assumed boundary layer of some sort (probably laminar at these Reynolds numbers which makes it a lot easier). Also, N-S is initial-condition sensitive because the solutions have bad scale missmatch, so you'll want to use your duodecaduple precision math library.
I didn't really understand from the blurb if they were talking about bendy things like paper pages. That would make it a fluid-structural coupled problem. Very tricky. The hardest part of that is getting the fluids guys to return the structures guys' phone calls.
Equine Mammals Are Considerably Smaller