“If you take a plain piece of paper and try to make it fly, it will flutter, tip over, turn around in the air and make all sorts of crazy movements,” says Leif Ristroph, an associate professor of mathematics at New York University. But if you fold it into a paper airplane, “the magic of it is that it does not do all those things,” he says. “It will fly smoothly.” This amazing ability is the reason he is so keen on paper airplanes. His office is full of books about them.
But how easily can they fly? Ristroph and a team of other scientists decided to test this for the benefit of science.
“To try to understand the math and physics involved, we decided to go simple,” says Ristroph – so simple that their “paper planes” were only small sheets of paper, two inches long by six inches wide, sometimes left completely flat and some times. folded a little bit on each side to give them fins.
They experimented with aligning the “mass center” of each aircraft, the place where it would balance on the edge of a ruler without tipping over. On their paper plane, this happened right in the middle of the sheet, but the plane did not fly well.
They wondered what would happen if they adjusted the center of mass forward? To do this, they placed a thin strip of copper tape on the plane, always keeping the plane balanced on its left and right sides (otherwise it would turn). They discovered that if the strap was too far towards the front of the plane, the plane nose-dived. If it was too far back, the plane jumped.
Then they hit the right spot: “exactly halfway between the center of the sheet and the front of the sheet.” Not only did this provide the smoothest glide, but it allowed the aircraft to fly the farthest horizontally before landing.
They also found similar results by making thin plastic sheets “fly” underwater, as water is governed by the same physics and mathematics as air. And they made a computer model that let them predict how different paper planes would fare.
But why study paper airplanes?
The great thing about them, says Ristroph, “is that there is no tail needed.” Most birds and planes rely on their tails to maintain the level while flying. Their wings are used to generate “lift”, which is the force that overcomes the tendency of gravity to pull objects down. Unless it has a fancy, tailed design, “a paper airplane does it all in one,” he says.
“I doubt our discoveries will change the way passenger planes are designed,” says Ristroph. But “it could be more useful when we start thinking about very, very small flying planes,” such as flying robots and small drones to help search and rescue teams or monitor air quality over cities. Because they may be too small to fit separate lifting and stability mechanisms, they may be able to offer them together, as a simple paper airplane does.
Children can also benefit from Ristroph’s research. For the typical paper airplane – with paper folded into a triangular shape – Ristroph suggests experimenting as he did to make it fly smoothly. Put a paper clip on the body of the plane, the place where you hold it to launch it. Try putting the clip in different places, back and forth.
“For every location you place it, you have to see what you get in terms of flight – whether it’s smooth and stable, or whether it’s some kind of tension up and down or doing something else.” Sooner or later you should hit the perfect position and the plane will elegantly soar.