## Crumpled paper is an unpredictable projectile

In graduate school I had a desk next to the trash can at the end of a long row of desks. Often several grad students were writing or studying at the same time, and you would frequently hear someone crumple up paper to throw at the trash can.

Of course, this was pre-computer days.

This was very irritating because sometimes they didn’t hit the trash can. Often I thought they didn’t even try to. In fact, sometimes I think they even tried to hit me. Have you ever tried writing a doctoral thesis while being pelted with crumpled-up paper?

I am not sure which is more surprising: those serious, mature graduate students engaged in such trivial pursuits, or how sturdy crumpled-up paper can be. I have no explanation for the lack of maturity in graduate students.

Crumpled paper, on the other hand, does have surprising rigidity. Isn’t it interesting that we don’t have a clue as to how that works? How does a flimsy sheet of paper become an unaccountably tough projectile simply by the act of crushing? Narayanan Menon and Anne Dominique Cambou, physicists at the University of Massachusetts, have been investigating this question. Don’t ask me why!

Paper has no uniform structure. It is a matrix of cellulose fibers. It is, so far, impossible to mathematically predict how it will crumple. In other words, the strength of crumpled paper is not designed into the crumple. It just happens.

Another interesting thing ... did you know that no matter how tightly paper is crumpled by hand it cannot be made into a structure composed of less than 90 percent air? Smaller volumes of air can be achieved, but only through applying extreme pressures, like maybe that applied by a steamroller. Anyway, this may partly explain why paper makes such good packing material.

It has been extremely difficult to peer inside a crumple of paper to discern its properties. Some investigators have tried reverse engineering by unfolding the crumple and analyzing the lines. Sadly, those investigators are no longer with us. Now, whenever biologists can’t see inside something, we just cut it open. Maybe physicists are just more sensitive.

So, typically, physicists tried examining paper balls with X-ray tomography, which costs quite a bit more than a good pocket knife. Tomography is usually used to hunt for tumors or to look inside delicate artifacts from archaeological digs. It bounces X-rays off the internal surfaces of an object to create thousands of 2D cross-sections that can be reassembled into a 3D image by computer.

Anyway, it didn’t work. The X-rays sailed right through the paper. So they switched to sheets of aluminum foil although that raises the question as to whether or not aluminum foil crushes in the same manner as paper. According to their research on foil, the ridges and multilayered walls act as numerous, short, structural pillars.

Because of paper’s matrix-type construction, paper has considerable tensile strength. For example, it’s difficult to stretch paper sufficiently enough to tear it. When it is folded, the energy of creating the fold is added to the tensile strength. Then the walls of the numerous, enclosed cells act as support columns. Numerous short columns are stronger than one long column in the same way that a collection of short sticks is stronger than one long stick.  This makes paper projectiles unyielding.

Tensile strength appears to be the reason why it is commonly thought that paper cannot be folded more than seven times. Each fold adds to the strength of the paper in a manner that the force required to compress the fold is proportional to the cube of the number of sheets.

So, assuming a crumple has at least five folds within it, my graduate school colleagues attacked me with scientifically created projectiles whose strength had been increased by 125 times.

Even hand-crushed paper can be surprisingly distracting to someone writing a doctoral thesis.

Gary McCallister, .(JavaScript must be enabled to view this email address), is a professor of biology at Colorado Mesa University.

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