Effects of material properties of cue on impact behaviour in follow and draw shots in billiards

The effective numerical method proposed by Shimamuraet al. (2007) is extended to predict the ball motion in a draw shot as well as a follow shot in billiards. The extended method is verified experimentally using a high speed camera. It is observed in the experiment that a ball rotates backwards with a lot of slip (between ball and table) at first and then rotates forwards in a draw shot. Such a ball motion is predicted quantitatively with the numerical method. Numerical simulations are performed to investigate the effects of material properties of a cue on ball behaviour in follow and draw shots and it is found that the impact force increases with increasing stiffness of the shaft in both follow and draw shots, while its duration time is shortened with increasing wave velocity in the shaft for both shots. It is also found that there is a certain shaft stiffness that gives the minimum ball centre velocity, the minimum angular velocity, the minimum slip velocity between ball and table and also the minimum time when the backward rotation changes to a forward one in a draw shot, while the ball centre velocity and the angular velocity increase with increasing shaft stiffness in a follow shot.