著者

島村 真介 須賀 一博 江澤 良孝 青木 繁

出版者

一般社団法人日本機械学会

雑誌

日本機械学會論文集. C編 (ISSN:03875024)

巻号頁・発行日

vol.73, no.729, pp.1480-1485, 2007-05-25

被引用文献数

1

---

Impact characteristics of a cue in billiards are evaluated numerically by developing a simple method. It is assumed that the cue and ball are elastic and rigid, respectively. The displacement of the cue is evaluated by the finite element method and that of the ball is calculated by solving the equation of motion. The time variation of impact force is estimated by equating these displacements at contact point. The accuracy of the analysis is checked by performing a detailed finite element analysis and an experiment, in which a freely supported cue is hit with a swinging ball. It is shown that (1) the impact force and the ball velocity increase with increase in the stiffness of the shaft, (2) the contact period decreases with increase in the stress wave velocity in the cue, (3) with increase in the stiffness of the tap, the impact force rises rapidly, reaches a large maximum value and falls in a short time (4) the ratio of slip to rotation of a ball during the contact period increases with increase in the stiffness of the shaft and the tap and (5) a peak appears in the time variation of impact force for a soft shaft due to the metal screw in the middle of the shaft.

著者

島村 真介 須賀 一博 江澤 良孝 青木 繁

出版者

公益社団法人 日本材料学会

雑誌

材料 (ISSN:05145163)

巻号頁・発行日

vol.57, no.10, pp.1043-1048, 2008-10-15 (Released:2008-10-18)

参考文献数

6

被引用文献数

1 1

---

The impact characteristics of a cue in billiards are investigated for the case where a ball is hit on the right or the left part to give a spin. The efficient computational method developed in the previous paper is extended for this investigation. The extended method is verified with an experiment using a high speed camera, i,e., the ball trajectory calculated with the extended method is shown to agree well with that measured using a high speed camera. It is shown from a numerical simulation that the impact force, the ball velocity, the spinning velocity and the deviation of the ball trajectory from the hitting direction increase with increase in the Young's modulus and density of a shaft. Because the proposed analytical method can predict quantitatively these impact characteristics of a cue, it is useful for designing an easy-to-use cue.