If you throw a straight piece of wood that's about the same size as a boomerang, it will simply keep going in one direction, turning end over end, until gravity pulls it to the ground. So the question is, why does changing the shape of that piece of wood make the it stay in the air longer and travel back to you?
The first thing that makes a boomerang different from a regular piece of wood is that it has at least two component parts, whereas a straight piece of wood is only one unit. This makes the boomerang spin about a central point, stabilizing its motion as it travels through the air. Non-returning boomerangs are better throwing weapons then straight sticks because of this stabilizing effect: They travel farther and you can aim them with much greater accuracy.
The returning boomerang has specialized components that make it behave a little differently than an ordinary bent stick. A classic banana-shaped boomerang is simply two wings joined together in a single unit. This is the key to its odd flight path.
The wings are set at a slight tilt and they have an airfoil design -- they are rounded on one side and flat on the other, just like an airplane wing. If you've read How Airplanes Work, then you know that this design gives a wing lift. The air particles move more quickly over the top of the wing than they do along the bottom of the wing, which creates a difference in air pressure. The wing has lift when it moves because there is greater pressure below it than above it.
As you can see in the diagram, the two wings are arranged so that the leading edges are facing in the same direction, like the blades of a propeller. At its heart, a boomerang is just a propeller that isn't attached to anything. Propellers, like the ones on the front of an airplane or the top of a helicopter, create a forward force by spinning the blades, which are just little wings, through the air. This force acts on the axis, the central point, of the propeller. To move a vehicle like a plane or helicopter, you just attach it to this axis.
The classic boomerang's propeller axis is only imaginary, so it obviously isn't attached to anything, but the propeller itself is moved by the forward 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, just as a plane with spinning propeller will move in one direction. If you held it horizontally when you threw it, as you do with a Frisbee, you would assume that the forward motion would 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 would simply fly off to the right or left. But obviously this isn't what happens.
Why Does It Come Back?
Unlike an airplane or helicopter propeller, which starts spinning while the vehicle is completely still, you throw the boomerang, so that in addition to its spinning propeller motion, it also has the motion of 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 higher rate of speed.
When a wing moves through the air more quickly, more air passes under it. This translates into more lift because the wing has to exert more force to push down the increased mass. So, it's as if somebody were constantly pushing the whole spinning propeller of the boomerang at the top of the spin.
But everybody knows that when you push something from the top, say a chair, you tip the thing over and it falls to the ground. Why doesn't this happen when you push on the top of a spinning boomerang?
If you've read How Gyroscopes Work, then you may have already guessed what's going on here. When you push on one point of a spinning object, such as a wheel, airplane propeller or boomerang, the object doesn't react in the way you might expect. When you push a spinning wheel, for example, the wheel reacts to the force as if you pushed it at a point 90 degrees off from when where you actually pushed it. To see this, roll a bicycle wheel along next to you and push on it at the top. The wheel will turn to the left or right, as if there were a force acting on the front of the wheel. This is because with a spinning object, the point you push isn't stationary, it's rotating around an axis! You applied the force to a point at the top of the wheel, but that point immediately moved around to the front of the wheel while it was still feeling the force you applied. There's a sort of delayed reaction, and the force actually has the strongest effect on the object about 90 degrees off from where it was first applied.
In this scenario, the wheel would quickly straighten out after turning slightly because as the point of force rotates around the wheel, it ends up applying force on opposite ends of the wheel, which balances out the effect of the force. But constantly pushing on the top of the wheel would keep a steady force acting on the front of the wheel. This force would be stronger than the counterbalancing forces, so the wheel would keep turning, traveling in a circle.
If you've ever steered a bicycle without using the handlebars, you've experienced this effect. You shift your weight on the bicycle so that the top of the wheel moves to the side, but every bicycle rider knows that the bike doesn't tip over as it would if it were standing still, but turns to the right or left instead.
This is the same thing that is happening in a boomerang. The uneven force caused by the difference in speed between the two wings applies a constant force at the top of the spinning boomerang, which is actually felt at the leading side of the spin. So, like a leaning bicycle wheel, the boomerang is constantly turning to the left or right, so that it travels in a circle and comes back to its starting point.
