A few weeks ago, my office was invaded by cardboard. It was a stealth assault, the flattened boxes piling up as the deliveries of equipment, tools and other sundries for a research project flowed in. It all just kept stacking up, and only when a student came to my door did the embarrassment of having to clamber over the pile force me to really look at it. This small mountain of cardboard had done me the service of protecting expensive, precious deliveries, but it barely weighed anything and it's just paper: flimsy and weak. How could something so insubstantial have any structural benefit?
Paper is something that we habitually underestimate. Members of the laboratory where I did my doctoral work at Cambridge had a favorite demonstration to impress audiences on open-house days. They'd hang up a large roll of printer paper, scroll it partway onto a suspended second roll below, with a single sheet of paper bearing the weight in between, and hang more than 150 pounds of extra weight from the lower roll.
Then they would dramatically stab through the single sheet of paper with a scalpel. The audience would gasp, but nothing moved. As they cut the hole wider, eventually the paper would rip. But the demo showed that the bonds of paper's cellulose fibers are strong in tension in one direction, despite how thin the sheet may be in another direction. The critical factor is how you arrange the paper—for instance, by pressing it into the folds and waves of corrugated cardboard.
Billions of dollars worth of goods are regularly transported in corrugated cardboard boxes, so it's no surprise that there are many scientific papers on the material's strength—equations, computational modeling and detailed consideration of humidity, temperature, paper type and box shape. They are the sorts of structural calculations you would do to design a building. It's like paper architecture.
Corrugated cardboard is made of a wavy internal layer that's sandwiched between two flat layers. The outer layers are important because they make it harder to bend—to curve that structure, you've got to stretch the outer layer, and as the experiment with the weight demonstrates, that's very hard to do. The farther apart those layers are, the harder it is to make it curve, so the first job of the corrugations is to hold the sides apart and stop them from sliding over each other.
But the most interesting bit is the corrugations themselves. They're made of a flat surface that has been bent back and forth repeatedly as it moves laterally. It's a useful and fundamental rule for anything that starts as a flat sheet: It may be easy to bend it in one direction, but you can't also bend it in the other direction at the same time without stretching or squashing it.
Pizza-lovers will be familiar with the consequences of this idea. If you pick up a slice of pizza by its crust, the point will generally flop downward, because the crust can't hold it up. But if you fold the pizza, bending it along the axis of the slice, the point of the slice can't flop down, or bend, in the other direction—at least, as long as the crust doesn't stretch. In the cardboard, the paper won't stretch, so the corrugations make the structure strong by effectively stopping it from bending.
It's a clever idea, and I almost felt guilty about stamping on my pile of boxes hard enough to destroy the structure and flatten them beyond reprieve. It was a relief when someone finally came to collect it all. But next time I see a cardboard box, I'll at least give it the nod of appreciation that it deserves.