Theoretical justification for distal foot power equation
Introduction
Rigid-body, link-segment models are commonly used in experimental studies of human movement. The rigid-body assumption should be better for some segments with a primary long bone, such as the shank and thigh, than others with many articulating bones, such as the foot and trunk. Over two decades ago, Siegel et al. (1996) introduced an equation for approximating the power due to the non-rigid nature of the foot that has come to be known as “distal foot power.” In recent years, numerous studies have used and expanded upon this concept of distal foot power (Farinelli et al., 2019, McGibbon and Krebs, 1998, Takahashi et al., 2012, Takahashi and Stanhope, 2013, Zelik et al., 2015, Zelik and Honert, 2018, Zhao et al., 2020). Despite the increasing use of this approach for estimating foot power, no rigorous derivation of distal foot power has been provided in the literature. Siegel et al. (1996) briefly described how to calculate distal foot power, but their justification for the formulation is insufficient and perhaps problematic, as is discussed later. The purpose of this communication is to provide a more thorough justification for the distal foot power equation. A proper understanding of the theoretical basis of the distal foot power equation, as well as its underlying assumptions, should help researchers as they interpret results obtained using this formula.
Section snippets
Equation derivation
Fig. 1 is used as an aid for the derivations of distal foot power provided in this communication. The “foot” in this figure includes the foot along with any footwear. Point represents the mass center of the foot, point represents the location of the center of pressure on the foot, point represents the point on the ground touching at a given instant, and represents the position vector on the foot from to . The resultant ground reaction force vector is assumed to act on the
Discussion
In classrooms across the world, innumerable students have endured long derivations as each silently wonders, “Why do I care how this equation is derived? Just tell me how to use it.” The answer to that question is simply, “You can’t truly know how to use an equation if you don’t know where it comes from.” The same is true for the distal foot power equation. Without a clear and proper description of how this equation is derived along with what assumptions were made along the way, it is
Declaration of Competing Interest
There are no conflicts of interests to disclose.
Acknowledgments
Special thanks are given to Karl Zelik, Gordon Alderink, and Kundan Joshi for challenging, thought-provoking, and illuminating conversations on this topic.
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