What causes a boomerang to return?
A boomerang is a rotor. The blades spin at a low linear speed compared to the transitional speed of the whole boomerang. This slow spin cannot produce a lift force strong enough to keep the boomerang in the air like helicopter blades do. The lift energy is mainly obtained from the transitional motion of boomerang. On the other hand, the spin forces the boomerang to act as a gyroscope, which is affected by forces produced by the blades. The blades’ shape and orientation make the boomerang return. Here I present a model that explains why and how boomerangs return.
How many blades does a traditional Australian Aboriginal boomerang have?
The right answer is four. According to the boomerang model (see figure above), there are two types of boomerang blades: radial and arc.
Spinning around its center of mass, a boomerang activates radial and passive blades as shown in pictures below.
Radial blades are active, arc blades are passive
Arc blades are active, radial blades are passive
The blades in active position interact with the air to produce forces whose angular momentum determines two types of boomerang gyroscopic precessions.
First type of boomerang precession
The first type of boomerang precession is well known to be responsible for the boomerang return.
When the boomerang is thrust outwardly in a vertical position, it spins with angular speed w and flies with speed v. Radial blades produce a well-known lift force, which affects the spinning boomerang when the air flow gets in front of them. The lift forces have different values for forward and backward spinning radial blades as the boomerang is moving onward. The different lift forces have angular momentum, applied to the rotation axis, which provides the first type of gyroscopic precession of the spinning boomerang around the Z-axis with angular speed Omega1. This first type of gyroscopic precession is responsible for the boomerang’s turning backwards.
Second type of boomerang precession
The second type of boomerang precession is responsible for keeping a boomerang in the air as long as possible and determines its trajectory pattern. Usually arc blades are smaller and have a little lift, which by itself cannot hold a boomerang in the air. When the boomerang is thrust outwardly almost in a vertical position, it has high speed, but a small vertical component of lift force. As the speed decreases, the vertical lift force component also decreases. This means that after some time, the boomerang begins to fall down. The main function of the arc blades is to continuously rotate the spinning plane in such a way that keeps constant the vertical component of the lift force (which is mainly produced by the radial blades). The second type of precession does the job.
The boomerang’s arc blades are perpendicularly attached to the end of the radial blades. The arc blades have either a negative dihedral and/or negative angle of attack or a positive dihedral and/or positive angle of attack. The arc blades become active when the spinning boomerang gets in a position in which the radial blades are parallel to the direction of flight. The lift force generated by said arc blades results in a second type of gyroscopic precession around axis X with angular speed Omega2. The arc blades’ angle of attack defines the precession Omega2 sign and value.
Returning boomerang relation. Joining the first and second types of precessions.
|First type of precession Omega1
|Second type of precession Omega2
|Total “8″ type precession
The flight trajectory (flight pattern) depends on a figure 8 boomerang precession, and thus, on the Omega1 to Omega2 ratio.
Both the first and second types of gyroscopic precessions direct the boomerang to return back to its launching position. The equation Omega2= K * Omega1 describes the best conditions for the boomerang to return, where the K range is about 1/3 to 1/4. The coefficient K=1/3 results in a figure 8 flight pattern. The coefficient K=1/4 results in an “O” flight pattern. If K<<1/4, the boomerang remains oriented vertically too long (lift force is oriented along a fast-spin axis) and falls down with ballistic trajectory (almost like a stone). Then it rolls on the ground making a short arc. If K>>1/3, the boomerang flies forward with a corkscrew trajectory and also does not return. When the wind speed is zero, the figure 8 (K=1/3) pattern has a landing point behind the launching point, while the “O” (K =1/4) pattern has a landing point in front of the launching point. Some in-between K values give intermediate flight patterns. The wind speed shifts the landing point. So, the boomerang has an optimum return pattern for a fixed wind speed, as the coefficient K for the particular boomerang is constant.
DESCRIPTION OF THE FLIGHT PATTERNS
“8″ type of flight pattern. Top view.
Description of the Figure 8 flight pattern.
When the boomerang is thrust outwardly in a vertical position, it will create and maintain a forward flight pattern from the point of launching; it subsequently begins an upward flight until it momentarily stalls in the air, then makes a 180° turn to the left, reverses its forward flight and simultaneously rotates 90° from vertical, taking on a horizontal, hovering type of flight pattern. It then returns closely to the point of launching, passes it and slowly flies in a second small loop to the opposite side. The total flight pattern looks like an asymmetrical “8″.
Description of the circular “O” flight pattern
When the boomerang is thrust outwardly in a vertical position, it will create and maintain a forward flight pattern from the point of launching; it subsequently begins a horizontal flight making a 270° to 360° turn to the left, reverses its forward flight and simultaneously rotates 90° from vertical, taking on a horizontal, hovering type of flight pattern. It then returns to the point of launching, passes it and slowly continues the second small loop to the same side.
The total flight pattern is a helix type and looks like an “O.” Actually, it is the same as the figure 8 pattern with a major asymmetry: a big first loop and a very delayed, small second loop of the figure 8, which in most cases is not seen, as the boomerang lands before making it. In most cases, an “O” flight pattern is preferable to a figure 8 pattern, as it features a very slow, hovering landing, making it relatively safer for the thrower.
“O″ type of flight pattern. Top view.
The full article can be found on my father’s website: http://mumris.eu/