Aerodynamics of Boomerang.

Construction of traditional Australian boomerang (for right hand)

Instructions how to make traditional boomerang

1. Take plywood sheet of 12mm thickness. Draw boomerang contour pattern as shown in picture above. The 107 degree angle size is not critical, just optimum. It can be more or less than 107deg. Chord length near the center of boomerang = 80 mm, and 60 mm near tips. Make wing chord length few millimeters wider as is required, because it necessarily reduces during sanding process. Also make some access length at boomerang wings tips, as it possible, that you will have to cut them during tune procedure of the boomerang.
Note:
If you make angle >>107, consider that rotation plate becomes small and it can be difficult to keep the boomerang spinning.
If you make angle of about 90 degrees, the boomerang flight trajectory circle radius is minimum. Angles <90 deg and >90 degrees increase circle radius.

2. First what you have to do is to sand dihedrals of wings. You have to make decision were is top and bottom. Put plywood boomerang on flat table and see if the tips are up or down. The traditional Australian boomerang has positive dihedral. The best choice is to find position in which the boomerang wings tips are up. (Do not care about that if your plywood is absolutely flat).
Remove some material from boomerang bottom at distance of about D=70...90 mm from both tips. It can be asymmetrical, but condition A+B = 14 mm should be satisfied.

Note:
Dihedral is the most critical part of boomerang. Boomerang model states, that dihedral determines the boomerang's trajectory. Considering D=const=70 mm, we can point out four cases:
• A+B < 14 mm gives flight trajectory pattern in which boomerang remains orientated vertically too long (lift force is orientated along spin axis) and falls down with ballistic trajectory. Then it rolls on ground making arc. Boomerang doesn't return.
• A+B = 14 mm (D=const=70 mm) gives "O" type pattern
• A+B > 14 mm gives "8" type pattern.
• A+B >> 14 mm gives cork screw pattern which goes forward. Boomerang doesn't return.

Note: other types of boomerangs different from Original Australian boomerang need other dihedral angles. For an example, threeblader or fourblader has negative angle dihedral.

3. Formation of wings profiles. Actually, boomerang is spinning rotor with blades like a helicopter or fan. The difference from fan is in angle of attack: boomerang blades should never exceed 14 degrees angle. See picture below. Take out 3...4 mm from the front edge of both boomerang's wings to get small angle of attack. This significantly increases the lift force of boomerang and prevents boomerang from bending into negative angle when plywood stress is released. Sometimes plywood bends by itself during sanding or after it.
Note:
Increasing lift force decreases the flight pattern radius. Increasing weight of boomerang (most sensitive place are tips of wing or stabilizers) increases flight pattern radius. It is easy to compensate too big lift force by increasing mass of boomerang. Just put extra varnish layer after some picture is painted. High quality varnish is recommended. It significantly increases strength and lifetime of the boomerang.

Tuning the boomerang
In most cases the only parameter you have to tune is dihedral. Before tuning it you have to throw boomerang and observe a trajectory (flight pattern).
• If boomerang makes "O" type pattern and falls down too quickly - increase dihedral. Cut of about 1 cm from both ends of boomerang and sand it (A+B should be increased).
• If boomerang makes cork screw turn - dihedral is too big. Reduce it. Step by step make few sanding procedures with throwing tests (sand A+B of about 2 mm)) until you get the type of the pattern you need.

Notes:
1. Boomerang's weight is about 0.16...0.18kg.
2. Reducing dihedral you can change boomerang pattern from "8" type to "O" type.
3. Increasing dihedral you can tune boomerang pattern from "O" type to "8" type.