Classic boomerangs have two arms or wings normally of equal length. They are joined at the elbow, at an angle of between 105° and 110°. The reason for this angle lies in the origins of boomerang manufacture; most boomerangs were made from the junction of a tree with its lateral (sideways) root. Each arm usually has a tapered tip, which is a carry-over from the ancestor of the boomerang - the killer stick.
All boomerangs are either right or left-handed - one is an exact mirror image of the other. This is to allow right and left-handed throwers to launch their boomerangs with relative ease because it's far more comfortable to throw away from, rather than across, the body. Having said this, it is possible to throw an opposite handed boomerang, with a few adjustments to your throwing action.
During the flight of the boomerang, the effect of many different aerodynamic principles can be seen. Bernoulli's theorem, Newton's laws of motion, gyroscopic stability, gyroscopic precession and many others all have a bearing on the action of the boomerang.
When the boomerang leaves the thrower's hand, it will be spinning very fast. As each arm of the boomerang has an aerofoil shape, similar in cross-section to that of an aircraft wing, air moving over the top of each wing has to travel further, and therefore faster, than air passing beneath the wings. Bernoulli's theorem states that 'air travelling at a higher speed creates less pressure than slower moving air'. As a result, the boomerang experiences a 'lift'1 force.
Newton's second law of motion states that 'the rate of change of momentum of an object is equal to the force applied to that object'. For an object with constant mass, this reduces to the well-known formula Force applied = Mass x Acceleration. The force here is a combination of friction and other resistive forces. To reduce the acceleration (or deceleration, since the force is negative), the mass needs to be large, but not so large that the boomerang falls quickly to the ground.
The length of the boomerang's arms, and the angle at which they are joined, allow the boomerang to spin in a stable plane as a result of the spin imparted on launching. This is known as gyroscopic stability. If this were not the case, the motion of the boomerang would at best be unpredictable. At worst, the boomerang would lose its spin rapidly, and be unable to sustain flight.
We now have a stable, rapidly spinning boomerang, moving forward from the force of the throw. We now need to take a slightly closer look at the effect of Bernoulli's theorem. As each wing rotates forward, into the direction of travel, it creates more lift than the other wing because the relative air speed is higher. If you imagine the spinning boomerang as a clock face, sideways on, this leads to the maximum force being created near the 12 o'clock position.
Due to the gyroscopic stability of the spinning boomerang, the effect of this force manifests itself at 90° further round the cycle of spin - at the 9 o'clock position of our clock face. The action of this force is to change the direction of flight - to the left for a right-handed boomerang and vice versa. Compare this with a 'no hands' bicycle turn - the only difference being the magnitude of the force. A small force over most of the duration of the flight produces a large, smooth turn for the boomerang, while a sudden strong force produces an abrupt bicycle turn.
As the boomerang travels, it loses velocity2. Eventually, gyroscopic precession becomes the dominant force. Coupled with the initial 'off-vertical' tilt, the effect is to push the boomerang over on its side, so that it spins in a horizontal plane.
The effect of each of these principles varies with the way in which the boomerang is thrown. The basic flight path of a boomerang is circular, although advanced throwers can produce a virtually triangular flight path.
1 This is slightly misleading - the boomerang is thrown in a near vertical position, so the resulting 'lift' actually acts sideways.
2 As it is rare to get absolutely dead-calm conditions, the wind starts to have an effect. This means that it is necessary to launch the boomerang 50° off the wind - the flight path should curl across the wind, and end with the boomerang being almost 'blown back' to the thrower.