保齡球球體之動力學分析

本研究以牛頓第二運動定律為基礎，使用公式推導方式分析一個經過簡化的燈泡型球體，了解球體的有無對保齡球旋轉產生的影響，分析不同形狀球體對油線所造成的變化，並且得到擺放角度與內力矩的關係，進而提供選手與教練對保齡球球體有進一步之認識，研究結果顯示如下：一、球體的有無對保齡球旋轉產生的影響和沒有球體的球相比較，添加特別設計球體的保齡球因為在x方向與y方向上擁有不同的迴轉半徑值（RG值），因此會有一固z方向的內力矩產生，造成油線開展的現象，提供更多的摩擦力讓求彎曲。二、不同形狀球體對油線所造成的變化除了可以利用迴轉半徑差值（RG差值）來判斷油線開展的程度外，對一般簡單的球體設計也可以從外型上來判斷，利用球體兩個軸向尺寸上的差異程度來判定球體開展能力的強弱，差異程度越大油線開展能力越大。三、擺放角度與內力矩的關係當在球體角度與旋轉軸夾角保持為0度與90度時，不會有內力矩的產生，也不會有油線開展的現象。當球體角度與旋轉軸夾角為45度時，可以產生最大的內力矩，而得到最大的開展效果。

關鍵字

保齡球；球體力學；動力學分析

並列摘要

Using Newton's second law as a foundation, dynamic formula was derived to analyze a simplified bowling core, comprehend how the core to effect rotation of bowling ball, analyze the changing caused by different core shape in track and examine the relationship between core position and internal torque. Related results were as below. 1. How the core to effect the rotation of bowling ball Comparing with the bowling ball not containing core, the ball having specially designed core would have different radius of gyration (RG) in the x and y-dimension. Progressively, a z-dimension internal torque would be produced to cause the appearance of track flare and to offer more friction causing ball hook. 2. The changing caused by different core shape in track. Besides utilizing differential of RG to judge the extent of track flare, the discrepancy of core size in the two dimensions was another way to determine, too. 3. The relationship between core position and internal torque When the angle between core and rotation axis was 0 and 90 degrees, internal torque and track flare will not be produce. When the angle between core and rotation axis was 45 degrees, internal torque and the extent of track flare were biggest.