Flight Dynamics of the Boomerang, Part 1: Fundamental Analysis

Equations of motion for boomerang flight dynamics are presented in strictly nonlinear form and solved numerically for a typical returning boomerang. The solution shows that the motion consists of both long- and short-period oscillations. The long-period oscillation originates from the exchange of potential (altitude) energy with kinetic energy mainly derived from the forward motion and the spinning motion, the latter of which is accelerated by the autorotation when the angle of attack of an apparent disk of blade rotation increases. The short-period oscillation is due to an asymmetry in the aerodynamic moment related to a large reversed-flow region and a stalled region due to high-advance-ratio flight, and a large moment of inertia or a small Lock number that is an order of magnitude smaller than that of a helicopter blade. The return flight is realized by the centripetal component of the aerodynamic force acting on the apparent disk that is tilted inwardly from the described asymmetric moment and the resulting gyro effect of the spinning motion.