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.

Yup

[by Anonymous Coward]

Now they just need to solve the 8+ folds problem...

Re:Yup

[discordja (612393)]

Okay
http://www.sciencenewsforkids.org/pages/puzzlezone /muse/muse0704.asp [sciencenewsforkids.org]

Re:Like many firsts .. this one's been DONE BEFORE

[tonsofpcs (687961)]

That report you cite is based upon chaotic motion, the new one seems to be based upon truely predictable motion.

The site is already getting quite slow...

[IversenX (713302)]

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

Re:The site is already getting quite slow...

[R.Mo_Robert (737913)]

The site is already getting quite slow... better save it here for posterity :-)

Or use the Coral cache version (remember, just appennd .nyud.net:8090 after the domain--I don't know why Slashdot doesn't do this more often): http://www.physorg.com.nyud.net:8090/news1630.html [nyud.net]

Re:The site is already getting quite slow...

[big tex (15917)]

I don't know why Slashdot doesn't do this more often)

Well, being the curious guy that I am, I tried both the original link and your coral link at the same time. (well, pretty close.)

Funny thing is, the original link opened, slowly, but much quicker than the coral link.

So, to get back to your question:
Q: Why don't we coral?
A: Because it's as effective as pigeonrank [google.com].

That's my prof!

[beefstu01 (520880)]

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.

NewsFlash!!

[thegoofeedude (771803)]

Paper is affected by air as it falls! Astounding. ;-)

Re:NewsFlash!!

[xsupergr0verx (758121)]

The real news is that they actually found an interesting use for those "pages of a scientific journal."

Re:NewsFlash!!

[Mark_in_Brazil (537925)]

The real news is that they actually found an interesting use for those "pages of a scientific journal."

There was a joke among physicists - I first heard it in the early 1990s- that said that a certain physics journal (I believe it was Physical Review Letters, or "PRL") was growing so quickly that its expansion was actually faster than the speed of light. There was, however, no violation of relativity, because no information was being conveyed.

--Mark

Bah.

[Black Parrot (19622)]

This is just a rehash of an old study showing why open-faced peanut butter sandwiches always land face down.

Paper!

[The-Bus (138060)]

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.

Re:Paper!

[techno-vampire (666512)]

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.

It's probably been asked before, but this gave me an idea: take a long strip of bread, butter one side of it, twist it and connect the ends to make a mobius strip, then drop it. What happens?

Re:Paper!

[lawpoop (604919)]

It lands on the outside.

Re:Paper!

[RedWizzard (192002)]

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.

Re:Paper!

[Jonas the Bold (701271)]

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.

You're theory is good, except that it fails to take into account the sheer impossiblity of attaching anything to a cat.

Usefulness

[ornil (33732)]

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.

Re:Usefulness

[26199 (577806)]

Probably not, since it's unpredictable... which could translate to, say, random 30ft drops. Which would be rather unpleasant if you happened to be 29ft from the ground.

You'd need a parachute to deploy when you got close to the ground ;-)

Re:Usefulness

[ajna (151852)]

if you on the other hand had a parachute which somehow was made up of thousands or maybe millions of small pieces of flat objects which could rotate independently

Again your caveat about not fully understanding the issues involved after reading a single non-technical article applies, but I got the impression that the phenomenon requires rotational and translational motion to be decoupled. Thus rotating independently may well be insufficient to allow for the effect of falling slower than via "parachuting".

Re:Usefulness

[Aglassis (10161)]

This effect isn't completely new (at least I don't think so). The space shuttles would roll and yaw back and forth a few degrees on reentry to slow down faster. If you ignore the horizontal speed of the spacecraft, this is somewhat similar to a piece of paper falling (but obviously more controlled--sometimes). Seems to me that the two items might be conceptually related. That being the case, I wouldn't be suprised if we saw a new style of atmospheric slowdown in future space probes.

Re:Usefulness

[PerpetualMotion (550623)]

It's called a hand glider. Unfortunatly, it cannot be packed into a backpack and deployed after falling 1,000 feet out of a plane.

Kites do not work well as parachutes.

Re:Usefulness

[UniverseIsADoughnut (170909)]

Parachutes made of paper?

Re:Usefulness

[JeanPaulBob (585149)]

I wonder if this could be used in some way for parachutes.

Step 1: Flatten self into a 1mm-thick sheet.

Step 2... Uh, actually, we seem to be running into a problem at step 1.

Re:Usefulness

[3770 (560838)]

The flattening is not the problem. That will be achieved. Timing is the problem.

You need to flat yourself _before_ you hit the ground.

Re:Usefulness

[mdfst13 (664665)]

"You need to flat yourself _before_ you hit the ground."

I think that the bigger problem is that you would want to *unflat* yourself afterwards...

Of course, if you could do that you could probably do without the parachute.

But ....

[by Anonymous Coward]

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.

They used a scientific journal page...

[by Anonymous Coward]

..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.

Failing paper??

[nightfire-unique (253895)]

Hmm.. was I the only one who read that as:

Physicists Finally Solve the Failing-Paper Problem

Oh, if only :~(

<mutter>back to studying I guess.</mutter>

Navier Stokes Equation

[Sipos (731917)]

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 [wikipedia.org] 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.

Re:Navier Stokes Equation

[Timesprout (579035)]

Do smooth initial conditions always lead to smooth solutions?

Well from personal experience I know that if she has not waxed then there will be a major reluctance to be a smoothie on my part. So the answer is yes.

Where's my million bucks?

Re:Navier Stokes Equation

[by Anonymous Coward]

"There is a $1,000,000 prize for the answer to the question: Do smooth initial conditions always lead to smooth solutions?"

Hmm. Tell you what... I'll submit a "yes" and you submit a "no" and whichever of us wins will split the money with the loser. Sound like a good deal? :)

rolloverrover

[Madcapjack (635982)]

"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)."

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.

Related Stories

[SuperJason (726019)]

Notice the "Related Stories" section. It is blank. This doesn't relate to anything. Does that tell you something?

Re:Related Stories

[Mikail (817047)]

I immediately thought of the applications for games. Say you throw around a stack of papers to befuddle your opponents. I can see the headlines now... "Doom 4: Now with realistic falling paper motion!!"

Original pages...

[argent (18001)]

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 [cornell.edu] and Professor Wang's home page [cornell.edu] with a full citation for the paper.

A bit of clarification

[Underholdning (758194)]

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.

Re:A bit of clarification

[polecat_redux (779887)]

landing a helicopter without motor assistance is called "the sycamore landing".

For those interested, I believe the maneuver is more commonly referred to as an autorotation [fact-index.com].

Re:A bit of clarification

[Kiryat Malachi (177258)]

Not quite... sycamore seeds fall with a twirling motion, much like a helicopter rotor. But autorotation (the proper name for that maneuver) doesn't rely on the physics they're talking about at all - heli blades are shaped such that the movement of air around the blades forces them to rotate, and the rotation generates lift. Not enough to keep the copter flying unpowered, but enough to prevent it from falling straight to the ground. The motion in the article is definitely not related to rigid airfoils with a fixed axis of rotation - the motion described in this article is that of a thin unconstrained flexible flat sheet.

Some people have made comments about using tumbling motion to build better parachutes - it probably wouldn't work for a parachute because a parachute requires some attachment of the load to the sheet, and that attachment will prevent the tumbling motion from happening, both by preventing the tumbling and also by loading specific points on the sheet instead of having the load effectively equally distributed.

Now I Can...

[brandonp (126)]

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! [spreadfirefox.com]

They do fall straight down...

[by Anonymous Coward]

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?

I'm surprised at what surprised these guys...

[by Anonymous Coward]

"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'.

Experiment with a Ruler

[florescent_beige (608235)]

Take a regular 12" ruler preferably one of those wooden ones or stiff plastic. Hold it on the long edges between your thumb and middle finger (I mean, your thumb on the 6" mark and your index finger on the 15cm mark). Heave it into the air at about 45 degs (up not down), trying to give it some backspin.

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.

Re:Umm...

[M51DPS (757403)]

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.

Re:Umm...

[beefstu01 (520880)]

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.

Re:Scientests figure out how paper falls.

[by Anonymous Coward]

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.

Re:Scientests figure out how paper falls.

[Madcapjack (635982)]

And physicists are supposed to do what about cancer? Please, let physicists do physics, and physicians do medicine!

Re:Scientests figure out how paper falls.

[mdfst13 (664665)]

"If we took the money that the physicists receive"

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 /. in *your* free time and get to work on that cure for cancer.

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.

Re:Better Parachutes?

[B3ryllium (571199)]

No, it's easy ... just fold it about nine times and it should fit.

Re:buttered toast is flat

[Lally Singh (3427)]

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.

Re:Classic problems

[NichG (62224)]

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.

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, ...), 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.

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.