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.
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:
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.
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!
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