Modelling and Three-Dimensional Flight Dynamics Simulation of the ‘V’ Shape Boomerang

Abstract

A boomerang generally refers to a simple aerodynamically designed object that makes quasi-circular flight and roughly returns to its starting point when thrown correctly. Aerodynamic characteristics and motion of boomerangs have been investigated in the past. There are only a few mathematical models developed and simulated numerically for V-shaped boomerangs. In this study, the dynamics of boomerangs were investigated using theoretical equations and verified using numerical simulation. We intend to overcome the deficiencies of previous mathematical models and provide a new mathematical model which can predict the actual 3-dimensional flight trajectory of the boomerang. A detailed literature review was performed on the mathematical modeling of boomerang dynamics and critically analysed. Though there are a few models developed in the past, most of the mathematical models are based on assumptions such as steady flow, uniform cross-section, and the level circular flight path. The research includes the development of a 3-dimensional flight trajectory using numerical simulations for a newly designed non-flat V-shaped boomerang. A V-shaped non-flat boomerang was designed using CATIAV5 and numerically simulated for the 3-dimensional flight trajectory of the 0.308m radius V-shaped boomerang. The improvement of our model is that a level circular flight path was not assumed in the new mathematical model. Unlike the previous models, our model will have a resultant acceleration in the Z direction during the flight. The simulation results show a significant difference in the displacement in the 3-dimensional trajectory. During the flight, the inclination angle decays faster at the rate of 1.5rad/s than the previous models, also the spinning frequency decays faster at the rate of 9Hz/s. Hence, a level circular flight path cannot be assumed in the mathematical model of a boomerang. The new mathematical model leads to some significant findings regarding the 3-dimensional trajectory and the nutation of the boomerang.