A Mathematical Model for the Trajectory of a Spiked Volleyball and its Coaching Application

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Shawn S. Kao
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Richard W. Sellens
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Joan M. Stevenson
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A wind tunnel test was conducted to empirically determine the relationship between the Magnus force (M), spin rate (ω), and linear velocity (V) of a spiked volleyball. This relationship was applied in a two-dimensional mathematical model for the trajectory of the spiked volleyball. After being validated mathematically and empirically, the model was used to analyze three facets of play that a coach must address: the importance of topspin, possibility of overblock spiking, and optimum spiking points. It was found that topspin can increase the spiking effectiveness dramatically in many ways. It was also found that a shot spiked from about 2 m behind the net has the least possibility of being blocked.

Shawn S. Kao and Joan M. Stevenson are with the School of Physical and Health Education, and Richard W. Sellens is with the Department of Mechanical Engineering, Queen's University, Kingston, ON, Canada K7L 3N6.

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