Boomerangs - The Aerodynamics
    By Martin Gardiner | December 10th 2012 11:25 AM | 3 comments | Print | E-mail | Track Comments
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    It has been said that a fully developed mathematical formula is one of the shortest possible ways to describe a physical phenomenon. Some phenomena, however, are so complex that their mathematical description can be dauntingly large. Take for example the formula to describe the aerial motion of a boomerang

    Link: Down Under Saddle Supply

    Despite its complexity, it has been single-handedly analysed by Alexander S. Kuleshov, at the Department of Mechanics and Mathematics, of  Московского государственного университета.

    “Formulation of aerodynamic forces and moments is based on the strip theory, which proved to be quite efficient in problems of dynamics of a rigid body moving in the medium. Equations of motion of the boomerang are derived and investigated numerically.“

    The mathematical formulations consider what might be called an ‘ideal boomerang’ – i.e. a completely symmetrical one traveling in still air. And the calculations appear to be firmly on-track :

    “Trajectories of the boomerang obtained in numerical experiment are very similar to the trajectories observed in reality.”

    The paper ‘A Mathematical Model of the Boomerang’ was presented at the 8th Conference of the International Sports Engineering Association (ISEA) and is published in Procedia Engineering Volume 2, Issue 2, Pages 2373-3494 (June 2010) The Engineering of Sport 8 – Engineering Emotion

    Bonus: Kuleshov is also one of the few mathematicians to have developed a Mathematical model of the skateboard


    Some years ago, I knew someone who had studied в Московском государственном университете.
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    I am no mathematician, but as an Australian, I have played with boomerangs for years and can attest to their extraordinary flight pattern. Amazing that the Aborigines devised them. I hope Alexander got away from his computer and had a throw.  
    If you cut out the aero and just go with a really simple lift as a function of forward speed of an aerofoil, you can get the maths out really easily, and 100% analytically. It's covered in year two dynamics at my old uni, and is only a little more complicated than a gyroscope.

    The final lecture was excellent - where we calculated where to tape some coins to the boomerang to change the inertia so that the curve matched the lecture hall! Live demo at the end, just skimming the walls!