铅球运动最佳抛射角和最大射程的理论研究

THEORETICAL STUDY ON OPTIMAL THROW ANGLE AND MAXIMUM RANGE OF PROJECTILE MOTION

从力学运动公式出发,假设运动员抛出物体时输出能量固定,应用能量守恒定律研究以一定高度和角度抛出物体的运动规律,详细定量分析运动员输出能量、肩膀高度和手臂长度对抛射速度、最佳抛射角和最大射程的影响。研究表明,对铅球成绩影响最大的是抛射速度和抛射角,而50厘米的肩膀高度或手臂长度差别对铅球成绩的影响分别为分米和厘米量级。另外,理论计算结果与三名铅球运动员实际投掷数据的比较说明理论计算结果的可靠性高,研究结果对投掷类运动具有一定指导和借鉴意义。

Starting from the mechanical motion formula and assuming that the athlete’s output energy is fixed when throwing an object,we study the movement law of projectile with the consideration of the law of energy conservation.The effects of athlete’s output energy,shoulder height,and arm length on the initial velocity,optimal throw angle,and maximum range of the projectile motion are quantitatively discussed in detail.It is found that various factors that influence the shot put are dominated in turn by the initial velocity and projecting angle,while 50 cm differences in shoulder height and arm length will result in the change of results in order of decimeters and centimeters,respectively.In addition,the comparison between theoretical calculations and actual throwing data of the shot putter shows that the results are in good agreement with each other,and the obtained results are expected to provide useful advice and guidance to the training of the sports like shot put.