![]() ![]() They proposed that, to be elastically similar, running animals must undergo equal relative peak virtual leg compressions. (1993) added an elastic similarity requirement to the original set of dynamic similarity criteria. In this sense, elastic similarity is a requirement for dynamic similarity ( Alexander, 1989).įollowing Alexander’s (1989) synthesis of dynamic and elastic similarity theory, Farley et al. Elastic similarity requires geometrically similar length changes. Similar changes in joint angles equate to geometrically similar changes in leg length. To be dynamically similar, the joints of running animals must move through equal angles. While recognizing the morphological inconsistencies between elastic and geometric similarity, Alexander (1989) revised the original dynamic similarity requirements to include aspects of elastic similarity. McMahon (1975) demonstrated that the concept of elastic similarity not only describes relationships between size and structure, but also accurately predicts how measures of locomotion such as stride frequency and gait transition velocities scale with body size. For example, elastic similarity requires larger animals to have relatively thicker bones than smaller animals in order to have comparable deformations. Structures, including those of animals, are considered elastically similar if they deform under gravity in a geometrically similar manner ( McMahon, 1973). To be dynamically similar, running animals must be elastically similar. The success of their dynamic similarity hypothesis has led investigators in fields ranging from anthropology to zoology to use the Froude number for analyzing both walking and running gaits (examples are, for walking, Alexander, 1984 Alexander and Jayes, 1980 Cavagna et al., 1983 McGeer, 1990, 1992 Minetti et al., 1994 Moretto et al., 1996 Wagenaar and Beek, 1992 Zani and Claussen, 1994 Zijlstra et al., 1996 for running, Alexander, 1991 Alexander and Maloiy, 1984 Bennett, 1987 Blickhan and Full, 1993 Cavanagh and Kram, 1989 Farley et al., 1993 Full and Tu, 1990 Gatesy and Biewener, 1991 Muir et al., 1996 Newman, 1996). They found that, despite very large differences in sizes and velocities, animals move with remarkably similar mechanics at equal values of the Froude number. Alexander and Jayes (1983) tested their hypothesis by comparing the locomotion mechanics of small and very large animal species (from rodents to rhinoceroses) walking, running, trotting and galloping over a wide velocity range. ![]() Where u is forward velocity, g is gravitational acceleration and L leg is the animal’s leg length (usually measured as height to hip). This suggests that a single unifying hypothesis for the effects of size, velocity and gravity on both walking and running gaits will not be successful. A comparison of walking and running results demonstrated that reduced gravity had different effects on the mechanics of each gait. The effects of velocity and gravity on the requirements of dynamic similarity differed in both magnitude and direction, indicating that there are no two velocity and gravity combinations at which humans will prefer to run in a dynamically similar manner. To better understand the separate effects of velocity and gravity, we also studied running mechanics at fixed absolute velocities under different levels of gravity. Further, two dimensionless numbers that incorporate elastic forces, the Groucho number and the vertical Strouhal number, also failed to predict dynamic similarity in reduced-gravity running. Thus, the inertial and gravitational forces that comprise the Froude number were not sufficient to characterize running in reduced gravity. ![]() We found that at equal Froude numbers, achieved through different combinations of velocity and levels of gravity, our subjects did not run in a dynamically similar manner. We simulated reduced gravity by applying a nearly constant upward force to the torsos of our subjects while they ran on a treadmill. We used simulated reduced gravity as a tool for exploring dynamic similarity in human running. This is puzzling because the Froude number ignores elastic forces that are crucial for understanding running gaits. The Froude number (a ratio of inertial to gravitational forces) predicts the occurrence of dynamic similarity in legged animals over a wide range of sizes and velocities for both walking and running gaits at Earth gravity. ![]()
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