## Why does a returning boomerang come back?

When most of us think of boomerangs, we imagine somebody throwing a curved stick that eventually turns around and comes right back to the thrower's hand. This device is simply amazing, and a wonderful application of some laws of physics relating to aerodynamic lift and angular momentum.

A returning boomerang is a specially crafted, lightweight piece of wood, plastic or other material. Effectively, they are two wings fashioned together into one piece, but you can find a number of different boomerang designs these days that may have three or more wings. Most returning boomerangs measure 1 to 2 feet across, but there are larger and smaller varieties. When thrown correctly, a returning boomerang flies through the air in a nearly circular path and arrives back at its starting point. Returning boomerangs are not suited for hunting, unlike the non-returning boomerangs that they evolved from.

 (Top View)

First, why does a boomerang fly?

The basic returning boomerang consists of two wings joined together to form a single unit but tilted with respect to each other. Each individual wing, or airfoil, is shaped similar to an airplane wing and produces aerodynamic lift as it moves through the air. As the Bernoulli effect tells us, there is higher air pressure along the flat surface of the airfoil than along its curved surface because the air has to move faster over the top of the wing than along the bottom of the wing. The difference in air pressure produces aerodynamic lift.

 A boomerang is two wings combined in one unit.

Or, we can think of lift as resulting directly from the impact of air molecules with the wing surface. As the tilted wing surface moves through the air, air molecules collide with it and bounce off. (Because of the effective "shadow" created by the tilt angle, fewer air molecules can reach the other side of the wing to collide with it.) The impact with the wing exerts a force on the air molecule, shoving it away from the wing surface. According to Newton's 3rd law of motion -- (for every action, there is an equal and opposite reaction) -- the air molecule exerts an equal force on the wing in the opposite direction. While the force exerted on the wing by a single air molecule is incredibly small, there are a lot of air molecules! The sum of all these small forces taken together is lift.

Like a helicopter rotor, the opposite tilt of each wing segment produces lift in the same direction as the joined wings travel in opposite directions through the air (due to the spin of the boomerang). As you can see in the diagram below, the two wings are arranged so that the leading edges are facing in the same direction. At its heart, a boomerang is just a rotor that isn't attached to anything. The lift created by a spinning rotor is a force acting along the axis, or central point, of the rotor. To move a vehicle like a helicopter, you just attach it to this axis.

 The leading edges of the two wings face in the same direction, like the blades of a helicopter rotor.

Since the boomerang's rotor axis is imaginary, it isn't actually attached to anything. But, the rotor itself is moved by the force of the wings' lift. It would be reasonable to assume, then, that a boomerang would simply fly off in one direction as it spun. If you held it horizontally when you threw it, like you do with a Frisbee, the motion arising from lift should be up because that's the direction the axis is pointing. The boomerang would fly up into the sky like a helicopter taking off, until it stopped spinning and gravity pulled it down again. If you held it vertically when you threw it, which is the proper way to throw a boomerang, it seems that it should simply fly off to the right or left. Why doesn't this happen?

Why does the boomerang come back?

Unlike an airplane or helicopter propeller, which starts spinning while the vehicle is completely still, you throw a boomerang. It does more than just spin around its axis, it also has a direct motion flying through the air.

In the diagram below, you can see that whichever wing is at the top of the spin at any one time ends up moving in the same direction as the forward motion of the throw, while whichever wing is at the bottom of the spin is moving in the opposite direction of the throw. This means that while the wing at the top is spinning at the same speed as the wing at the bottom, it is actually moving through the air at a faster speed while the wing at the bottom is moving through the air at a slower speed.

When a wing moves through the air more quickly, more air passes by it. This translates into more lift because the wing encounters more air molecules that push against it. So, it's as if somebody were constantly pushing the spinning rotor of the boomerang more strongly at the upper wing than at the lower wing. If the boomerang were not spinning, the unbalanced push at the top would make it tip. But it is torque and angular momentum that we deal with when we have a spinning object, just the way it works for a top or a gyroscope.

Since the aerodynamic lift points along the same direction as the spin axis of the boomerang, the resulting torque acts at a right angle to the boomerang's spin axis. This changes the direction of the boomerang's axis without really changing its rotation speed. As the torque turns the spin axis, the flight path of the boomerang turns along with it.

How do I throw one?

We now see the different forces that act on a boomerang and what they do. In the flight of a returning boomerang, the factors to keep in mind are:

• the force of gravity,
• the force caused by lift,
• the force of your throw,
• the torque caused by the uneven speed (top vs. bottom) of the wings, and
• the force of any wind in the area.

For the boomerang to actually travel in a circle and come back to its starting point, all of these forces have to be balanced in just the right way. Developing a good throwing technique requires a lot of practice. Right now, we'll go over the basics so you can get started on perfecting your throw.

1. You need to hold the boomerang at a slight angle off of vertical - something like 15 to 20 degrees to the right of vertical. (With experience, you will learn to adjust the tilt angle depending on your natural throw and current wind conditions.) This will aim the force of the rotor upward, just enough to balance the downward force of gravity and permit the boomerang to complete its path before hitting the ground.
2. Hold the boomerang with the V-point, called the elbow, pointing toward you and with the flat side facing out to the right. Hold it at the end of the bottom wing, with a light pinch-like grip. (Most boomerangs are designed for a right-handed person. When you hold it correctly with your right hand, the curved edge is on the left and the top wing's leading edge is facing away from you. If you try to throw it with your left hand, it probably won't come back. But there are left-handed boomerangs! If you are able to get one, just do the mirror image of everything listed here. If you are throwing with your left hand, hold the boomerang so that it is tilted to the left, with the curved side facing to the right. A right-handed boomerang will travel in a counter-clockwise circle and a left-handed boomerang will travel in a clockwise circle.)
3. To keep the wind from forcing the boomerang off course, try aiming the boomerang for a point about 45 to 50 degrees to one side of the wind direction (stand facing the wind and turn about 45 degrees clockwise or counter-clockwise). Adjust the position of the boomerang depending on how much wind there is. (You will need a bit more tilt from vertical when the wind is stronger.)
4. When you have set your grip on the boomerang and you have oriented yourself in relation to the wind, bring the boomerang back behind you and snap it forward as if you were throwing a baseball. Be careful not to pull your throw across your body. It is very important to snap your wrist as you release the boomerang so that it has a good spin to it. Spin is critical, it's what makes the boomerang curve around.
5. When you throw the boomerang vertically, the uneven force at the top of the spin tilts the axis down gradually. By the time it comes back, it should be spinning horizontally like a Frisbee. But don't try to catch it with one hand. The spinning blades are going fast enough to hurt you! The safe way to catch a returning boomerang is to clap it between your two hands.

Always be careful when throwing a boomerang. When you throw it, you need to keep track of it at all times or it could hit you on the return. If you lose track of its path, duck and cover your head rather then trying to figure out where it is. Boomerangs move quickly, with a lot of force.

Your first attempt will probably end up on the ground (or in a tree). Your second and third attempts probably will as well, so don't try to learn with an expensive hand-carved model. (The Store @ 4Physics.com offers an inexpensive but well designed wooden boomerang for practice.) Boomeranging is a difficult skill, but it can be a lot of fun to practice. You certainly get a sense of achievement when it all works!