Paper Airplane Science

Just floating on Air

Introduction

After they are launched, paper airplanes fall through the air, pulled down by gravity. As they fall wings deflect air backwards and so the plane glides forward. An efficiently designed wing also throws air down to produce lift.
In addition, in order to fly well paper airplanes must be stable.

Material

• An 8.5 by 11 sheet of paper
• a manila folder or other thin stiff cardboard
• a pair of scissors
• a pencil

To Do and Notice

Build a paper airplane such as the one shown on my site, the Nakamura Lock, or in the Online Exploring Paper Magazine or in the Klutz Paper airplane Guide known as the Nakamura lock.

The basic forces of flight

Initial observations

Notice how the airplane flies.
Try to fly it backwards.
Notice that it definitely has a front end and will not fly backwards.

Air pushes on moving objects.

Hold the manila folder vertical, wave it back and forth rapidly through the air so that the flat faces of the folder hit the air.
Feel the force that the air exerts on the folder.

Balancing on air

Balance the paper airplane on a finger. The center of gravity of the plane is located directly over your finger when the plane is in balance. All the forces of gravity on individual atoms which make up the plane add up to one force at the center of gravity. You can model gravity as pulling down on the plane through the center of gravity.

A plane balanced between two fingers.

When the plane falls through the air, air pushes on its shape. The sum of all the pushes acts as if it were one force through the center of pressure.

Hold the plane with its wings in a vertical plane and the length of the plane horizontal, hold the plane with the wings perpendicular to the wind, or in the gentle blast of air from a fan. Allow the plane to pivot around. If you hold it by the nose the tail blows downwind, If you hold it by the tail the nose blows downwind, there is only one place along the plane where you can hold it so that it is not pivoting, that place is the center of pressure.

Alternate technique for finding the center of pressure

Trace the outline of the paper plane onto the manila folder. (This is easiest if you put the plane upside down on the folder.)Cut out the shape of the airplane. (You have just made a cut-out with the shape of the shadow of the airplane.) Balance the cut-out on your finger. The center of pressure of the plane is located over your finger.
Airplanes are designed so that their center of gravity is near, but slightly in front of, their center of pressure. This is why airplanes have a front and a rear, the center of gravity is in front of the center of pressure.

Hold the plane flat and drop it. Notice that the nose drops down. This is because gravity is pulling down on the center of gravity, while the air is pushing up on the center of pressure. This pair of forces twists the plane so that it dives toward the ground.

What’s Going On?

When you launch the paper airplane you give it kinetic energy.
If you throw it upward, the initial kinetic energy is converted into potential energy and some energy is lost due to air resistance.
After its initial launch a well balanced airplane will settle into a uniform glide at a constant speed. It is then powered by gravity as it falls through the air.
(To a physicist the plane turns gravitational potential energy into kinetic energy which is dissipated into heat by air resistance forces.)
The trick is to fold paper so that it falls through the air stably, converting the downward fall into forward motion.
The role of the wings is to convert the fall into forward motion.

Stability and Control

A well designed airplane will be stable, it will fly in a straight line of a gentle curve.
Stability means that if the airplane encounters a disturbance such as a wind gust, that attempts to turn it over it will right itself.

An airplane needs to be stable against three separate rotations.
Right-left called yaw.
Nose-up vs. nose down called pitch.
and right-wing-down versus right-wing-up called roll.

Airplanes are made stable against yaw, right-left rotation, by giving them a "vertical stabilizer" or tail. In many paper airplanes the rear of the body is made taller than the front. The plane will always pivot about its center of gravity, if it pivots to the left, the larger tail behind the center of gravity is hit by moving air and pushes the nose back to the right.
Wings that sweep backwards also help to give a plane yaw stability. If a plane turns left then the swept back right wing hits the air more straight on, while the left wing hits the air at more of an angle. The drag forces on the right wing will be greater than those on the left and will act to pull the plane back around.

Planes are made stable against roll by folding the wings up so that when viewed from the back of the airplane they look like a Y, This is called dihedral. The angle from the horizontal to a wing is the dihedral angle.) If the plane is gliding and rolls so that the right wing goes down and the left wing goes up then the right wing hits more air than the left as it falls, and the plane is twisted back to level. Without dihedral the plane will roll as it flies.

Pitch stability is gained by placing the center of gravity close to, but in front of, the center of pressure. The plane rotates about its center of gravity. If the nose goes up, the tail drops, wind hits the larger area of the wing behind the center of gravity and pushes the tail back up.

Control

You can control your airplane by folding the rear edges of the plane. The rear vertical edge of the plane is the rudder. Twist the rudder to the right and air hitting the rudder pushes the tail to the left and the nose to the right.

Twist the rear edges of both wings up and wind hitting the elevators pushes the rear of the wing down and the nose up.

So if your plane curves right and you want to make it go straight bend the rudder to the left.

If your plane dives into the ground nose first push the elevators up.
If the nose of your plane twists toward the sky then drops, push your elevators down.

Stalls

All of the above assumes that the air is flowing smoothly around the paper plane. But if the wings hit the air at too high an angle, the air flow will split away from the wing and tumble in vortices creating a stall. The plane will no longer be flying but falling, the nose will drop and the plane will accelerate down under gravity until the plane regains flying speed as smooth flow is re-established over the wing.

Math Root

Glide ratio.
As a paper airplane drops through the air it deflects air backwards and propels itself forward. One measure of a paper airplane is its glide ratio, the ratio of how far it goes over how far it falls.

GR = distance traveled/distance fallen

If a plane travels 30 feet while dropping 5 feet it has a glide ratio of
GR = 30/5 = 6.

The human body has a glide ratio of 1, while a high performance glider has a glide ratio of 40.

To measure the glide ratio trim a glider so that it flies straight. Throw the glider up, then as it establishes a constant descent, note the point where it passes though a height of 5 feet , then note the point where it hits the ground. Find the distance it travels from the 5 ft height to the ground, The glide ratio is this distance divided by 5 feet.

Go to a longer activity about the glide ratio.

 Scientific Explorations with Paul Doherty © 2000 27 October 2000