Spokane, Washington  Est. May 19, 1883

Paper airplanes could help with design of drones or flying robots

By Galadriel Watson Special to the Washington Post

“If you take a regular piece of paper and try to make it fly, it will flutter, tumble, flip around in the air and do all sorts of crazy motions,” said 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 doesn’t do all those things,” he said. “It will fly smoothly.” This awesome ability is why he’s so keen on paper airplanes. His office is filled with books about them.

But how smoothly can they fly? Ristroph and a team of fellow scientists decided to test this for the benefit of science.

“To try to understand the math and physics involved, we decided to go simple,” Ristroph said – so simple that their paper airplanes were just small sheets of paper, two inches long by six inches wide, sometimes left perfectly flat and sometimes folded a wee bit on each side to give them fins.

They experimented with adjusting each plane’s center of mass. On their paper plane, this occurred exactly in the middle of the sheet, but the plane didn’t fly well.

They wondered what would happen if they adjusted the center of mass forward? To do so, 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 tape was too far toward the front of the plane, the plane nosedived. If it was too far back, the plane bounced.

Then they hit the right spot: “exactly halfway between the middle of the sheet and the front end of the sheet.” Not only did this produce the smoothest glide, but it enabled the plane to fly the farthest horizontally before landing.

They also found similar results by making thin plastic plates “fly” underwater, since water is governed by the same physics and math as air. And they made a computer model that let them predict how different paper airplanes would perform.

But why study paper airplanes?

What’s amazing about them, Ristroph said, “is that there’s no tail that’s needed.” Most birds and airplanes rely on their tails to keep level while flying. Their wings are used to generate lift, which is the force that overcomes gravity’s tendency to pull objects down. Unless it has a fancy, tailed design, “a paper airplane does this all in one,” he says.

“I doubt our discoveries will change the way passenger airplanes are designed,” Ristroph said. However, “it could be more useful as we start to think about very, very small flying aircraft,” such as flying robots and tiny drones for helping search-and-rescue teams or monitoring air quality above cities. Because they may be too small to fit separate lift and stability mechanisms, perhaps they can offer them together as a simple paper airplane does.

Kids can also benefit from Ristroph’s research. For the typical paper airplane – with paper folded into a triangular shape – Ristroph suggests experimenting like 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 various spots, forward and backward.

“For each location that you put it at, see what you get in terms of the flight – whether it’s smooth and steady, or whether it’s kind of bucking up and down or doing something else.” Sooner or later, you should hit the perfect position and the airplane will gracefully soar.