Numerical Evaluation of Impact Characteristics of Cue in Billiards: Case Where Ball Trajectory is Curved

The numerical evaluation of impact characteristics of a cue in billiards is performed for the case where the ball trajectory is curved by hitting a ball on its upper left or right part with an inclined cue. The effective numerical method developed in the previous papers, in which a cue and a ball are assumed to be isotropically elastic and rigid, respectively, is extended for this case. The extended method is verified with an experiment using a high speed camera. The result obtained with the extended method also shows that the curvature of the ball trajectory is large for the impact on its almost exactly left part with a slightly inclined cue, and this result agrees with an empirical one. It is found from a numerical simulation that if the Young's modulus or mass density of a shaft of a cue is large, the ball trajectory immediately after the impact is deviated largely and then is curved with a large curvature. Because the extended method can evaluate quantitatively this kind of effects of material properties, it is useful for a design of a cue.