chapter  15
20 Pages

Analysis of Spinning Ball Trajectories of Soccer Kicks and Basketball Throws

WithDhanjoo N. Ghista, Xiang Liu

CONTENTS 15.1 Scope ......................................................................................................... 425 15.2 Theory: Lateral Force on the Spinning Ball of a Soccer Kick .......... 426 15.3 Analysis of the Soccer Kick .................................................................. 429

15.3.1 Theory: Trajectory of a Spinning Soccer-Ball Kick ............. 429 15.3.2 Exemplification of the Theory: Computation

of the Spinning Ball Trajectories ............................................ 432 15.3.3 Case Study: Analysis of the Famous Ronaldinho

Goal against England in the Quarter-Final of the 2002 World Cup............................................................. 436

15.4 Basketball Foul Throw Analysis .......................................................... 439 15.5 Concluding Remarks.............................................................................. 441 Appendix............................................................................................................. 442 References ........................................................................................................... 444

It is a common observation that putting spin to a pitched baseball or to a kicked soccer-ball imparts an out-of-plane curve to the ball trajectory. This mechanism has been successfully used in soccer to deceive goalkeepers, in basketball throws to obtain a better entering angle into the net, and in baseball to induce the batter to swing and miss. So then, what is the mechanism of this curving soccer kick or a backspinning basketball throw? In addressing this issue, this chapter deals with the mechanics of a spinning ball trajectory, as to how deviations in the ball’s original trajectory are governed by different amounts of angular velocity and translational velocity. It is shown as to how the amount and direction of spin plays an important role in delineating the trajectory and the position of the ball

in its trajectory. Then, this analysis is employed to simulate a number of interesting situations in soccer and basketball, including the famous Ronaldinho’s goal against England in the 2002 World-cup semifinals.