Boomerang
Flight path

The projection of the flight path of long-distance boomerang on the ground resembles a water drop. For older types of long-distance boomerangs (all types of so-called big hooks), the first and last third of the flight path are very low, while the middle third is a fast climb followed by a fast descent. Nowadays, boomerangs are made in a way that their whole flight path is almost planar with a constant climb during the first half of the trajectory and then a rather constant descent during the second half.

From theoretical point of view, distance boomerangs are interesting also for the following reason: for achieving a different behaviour during different flight phases, the ratio of the rotation frequency to the forward velocity has a U-shaped function, i.e., its derivative crosses 0. Practically, it means that the boomerang being at the furthest point has a very low forward velocity. The kinetic energy of the forward component is then stored in the potential energy. This is not true for other types of boomerangs, where the loss of kinetic energy is non-reversible (the MTAs also store kinetic energy in potential energy during the first half of the flight, but then the potential energy is lost directly by the drag).
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