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Mathematica Puts New "Spin" on Cricket Bowling Action

December 11, 2001--Mathematica user and New Zealand physicist Rene Ferdinands from the University of Waikato has been using Mathematica to investigate the dynamics of the bowling action in the game of cricket, thereby providing a mechanical basis for evaluating player technique. Cricket is among the oldest and most popular sports worldwide, particularly in the United Kingdom where it originated, and is as popular as baseball in the United States.

Ferdinands and his colleagues have access to the excellent research facilities at the University of Auckland, and this helped them attract one of the top-three spin bowlers in world cricket today to serve as a subject for their analysis. Using an array of high-resolution cameras, retroflective markers, and an EVa 3D motion analysis system, they were able to define and calculate the center of joint rotation for all the major body segments: head and neck, thorax, lower trunk, thighs, shanks, feet, upper arms, forearms, and hands. The subject performed two sets of trials, and the collected data were analyzed using Mathematica.

The Mathematica standard add-on package NumericalMath`SplineFit and the fourth-order recursive Butterworth filtering routine written in Mathematica were used to smooth, interpolate, and convert the data into a form suitable for use in an inverse solution model. To develop the dynamic model, Ferdinands relied on the Mechanical Systems application package for Mathematica. This package of functions enabled Ferdinands to create a 3D representation of the human body as a system of 15 rigid-body segments with mass and inertia properties and also to calculate the external joint torques and forces on the body during the motion of bowling a cricket ball. It also enabled him to run a forward solution model to check the inverse dynamic solutions.

Ferdinands presented his findings this summer at the XVIII Congress of the International Society of Biomechanics in Zürich, Switzerland, and at the VIII International Symposium on Computer Simulation in Biomechanics in Milan, Italy. Conference attendees were impressed to see how mechanically complex the cricket bowling action is and to see that Mathematica is such a powerful and flexible tool for biomechanical analysis and simulation.

This study is of broad interest to the cricket community for several reasons. It marks the first time that a 3D full-body dynamic analysis of bowling has been carried out. Also, the studies that do exist have centered mainly on "fast" bowlers, and the subject has been a "spin" bowler, using a different style. The results of this study are quite significant because cricketers will be surprised to learn that the subject--a top-notch cricket player--did not conform to established technical principles of bowling.

For example, it is generally considered that the non-bowling arm should accelerate clockwise during the bowling motion to help propel the bowling arm forward. Instead, the subject's non-bowling arm was found to be subject to a counterclockwise torque. Other differences in expected acceleration and positioning in body segments were also found contrary to fundamental assumptions about bowling techniques.

Ferdinands and his colleagues now plan to investigate a larger sample of bowlers to see whether these unexpected results are in fact characteristic of elite bowlers--or are perhaps indicative of differences in dynamics between the fast and spin styles of bowling. They say that Mathematica is helping to unravel the biomechanical principles of elite bowlers, both fast and spin, so that coaches have an enhanced ability to improve the performance of bowlers throughout the cricketing world.