The Physics of Paper Planes

We’ve seen many different gliders from the animal world throughout this course. But as children, our first experiences with gliding probably came from paper planes. As a kid, I remember learning lots of different designs for planes, in an effort to make them fly farther and stay in the air longer.

But there are actually people who study paper airplanes and compete for the world record for longest time in the air. In 1998, Ken Blackburn set a world record for a paper plane flight that lasted 27.6 seconds! In order to design the plane that did this, Blackburn studied the physics of real airplanes.

One of the keys to reducing drag on the paper plane is to have thin wings. This has to do with a paper plane’s Reynolds Number, which indicates the significance of the viscosity of the fluid (air) on flight. Paper planes have a very low Reynolds Number, which means the air’s viscosity has a much larger effect on a paper planes than on airplanes. With thick wings, the boundary layer of air tends to separate from the wing, resulting in large amounts of drag. So as far as reducing drag goes, the thinner the better. We see this in nature as well. Insects, which have low Reynolds numbers, have thin, flat wings (like flies or butterflies). Meanwhile birds, which have higher Reynolds numbers, have thicker, curved wings.

Another design key is to have dihedral wings, or wings that are angled upwards (pictured below). This is a technique many airplanes use to improve stability. During flight, disturbances may cause the plane to roll in one direction. This results in different angles of attack for the two different wings. With dihedral wings, the lower wing will have a greater angle of attack. Because lift is proportional to angle of attack, there will be more lift on the lower wing, so the plane will roll in the opposite direction, returning to level flight. This stops paper planes from spiraling out of control and quickly falling to the ground.

Dihedral wings

One more of Blackburn’s techniques is used to slow the plane horizontally, lengthening the flight. He calls it an “up elevator” on the end of the wings (shown below). He folds the back end of the wings upwards, causing the back end of the plane to pitch slightly downwards, and the nose to pitch upwards. With more of the bottom surface area of the plane exposed to the oncoming air, there is more horizontal drag. Incidentally, the larger angle of attack would lead to more lift as well. Airplanes also use this technique. Pilots are able to control the back edge of the tail wing to change the speed.

Putting all these techniques together helped put Ken Blackburn in the record books. Maybe you can also use these the next time you have some spare paper lying around.

References

One Comment

posted on October 21, 2011 at 7:42 pm

I find it kind of funny how the cameraman and mic-bom guys run to the “airplane builder” at the end of the demo. It’s a PAPER airplane, guys!
Nice post — though a bit off-topic to the course focus on bio-inspired engineering and bird flight!