Paper airplanes give aerodynamic insights

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Research unveils mechanisms that explain flight stability, inspiration for drones.

Trajectories of plates falling through water, where the different colors represent different degrees of front weighting. Only the right weight distribution leads to the smooth gliding shown in blue.
Photo credit: NYU’s Applied Mathematics Laboratory

Scientists discovered new aerodynamic effects using paper airplanes, enhancing understanding of flight stability and potentially inspiring new small drones.

Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences explains, “We discovered the aerodynamics of how paper airplanes keep level flight is very different from the stability of conventional airplanes.”

Since paper airplanes rely on gravity and proper design for movement, they’re good candidates for exploring factors behind flight stability.

Researchers launched paper airplanes with differing centers of mass through the air. To find the best design, team members placed different amounts of thin copper tape on the front part of the paper planes, giving them varied center of mass locations. Lead weights added to plates falling in a water tank served the same purpose.

In the experiments, researchers found flight motions depended on the center of mass location. If the weight was at the center of the wing or displaced somewhat from the middle, it underwent wild fluttering or tumbling motions. If the weight was displaced too far toward, the flier dived and crashed. In between, a sweet spot for the center of mass gave stable gliding.

Researchers coupled the experimental work with a mathematical model that successfully reproduced the different flight motions. It also helped explain why a paper airplane is stable in its glide. When the center of mass is in the sweet spot, the aerodynamic force on the plane’s wing pushes the wing back down if the plane moves upward and back up if it moves downward.

“The location of the aerodynamic force or center of pressure varies with the angle of flight in such a way to ensure stability,” Ristroph explains.

The effect found in paper airplanes doesn’t happen for traditional airfoils used as aircraft wings, whose center of pressure stays fixed. Ristroph says, “The shifting of the center of pressure seems to be a unique property of thin, flat wings, and this ends up being the secret to the stable flight of paper airplanes.”

“This is why airplanes need a separate tail wing as a stabilizer while a paper plane can get away with just a main wing that gives both lift and stability. We hope our findings will be useful in small-scale flight applications, where you may want a minimal design that doesn’t require a lot of extra flight surfaces, sensors, and controllers,” he concludes.

New York University