Vaughan Christopher L, O'Malley Mark J
MRC/UCT Medical Imaging Research Unit, Department of Human Biology, Faculty of Health Sciences, University of Cape Town, Observatory, Western Cape 7925, South Africa.
Gait Posture. 2005 Apr;21(3):350-62. doi: 10.1016/j.gaitpost.2004.01.011.
It is fascinating to think that the ideas of two 19th century naval architects could offer useful insights for 21st century scientists contemplating the exploration of our planetary system or monitoring the long-term effects of a neurosurgical procedure on gait. The Froude number, defined as Fr = v2/gL, where v is velocity, g is gravitational acceleration and L is a characteristic linear dimension (such as leg length), has found widespread application in the biomechanics of bipedal locomotion. This review of two parameters, Fr and dimensionless velocity beta = (Fr)1/2, that have served as the criterion for dynamic similarity, has been arranged in two parts: (I) historical development, including the contributions by William Froude and his son Edmund, two ship designers who lived more than 130 years ago, the classic insights of D'Arcy Wentworth Thompson who, in his magnum opus On Growth and Form, espoused the connection between mathematics and biology, and the pioneering efforts of Robert McNeill Alexander, who popularised the application of Fr to animal locomotion; and (II) selected applications, including a comparison of walking for people of different heights, exploring the effects of different gravitational fields on human locomotion, establishing the impact of pathology and the benefits of treatment, and understanding the walking patterns of bipedal robots. Although not all applications of Fr to locomotion have been covered, the review offers an important historical context for all researchers of bipedal gait, and extends the idea of dimensionless scaling of gait parameters.
令人着迷的是，两位19世纪的海军建筑师的想法，竟能为21世纪那些思考探索我们的行星系统或监测神经外科手术对步态的长期影响的科学家提供有用的见解。弗劳德数，定义为Fr = v2/gL，其中v是速度，g是重力加速度，L是一个特征线性尺寸（如腿长），已在双足运动的生物力学中得到广泛应用。这篇对两个作为动态相似性标准的参数——弗劳德数（Fr）和无量纲速度β = (Fr)1/2——的综述分为两部分：（I）历史发展，包括130多年前的两位船舶设计师威廉·弗劳德和他的儿子埃德蒙的贡献、达西·温特沃斯·汤普森在其巨著《生长与形态》中支持数学与生物学之间联系的经典见解，以及罗伯特·麦克尼尔·亚历山大将弗劳德数应用于动物运动的开创性努力；（II）选定的应用，包括对不同身高人群行走的比较、探索不同引力场对人类运动的影响、确定病理学的影响和治疗的益处，以及理解双足机器人的行走模式。尽管并未涵盖弗劳德数在运动方面的所有应用，但这篇综述为所有双足步态研究人员提供了重要的历史背景，并扩展了步态参数无量纲缩放的概念。
