Sunday, February 19, 2006
134 Skaters Online
Report
Equation of Motion of Inline Skating

 Andre Martel, Author— Special Report, RRN    Saturday, March 19, 2005

This is an original article and report by Andre Martel.  It begins as follows:

In recent years, the growing popularity of outdoor inline skating marathons has been accompanied by the emergence of a bewildering variety of wheel and frame combinations, all meant to achieve the best possible "roll" while minimizing the skater�s energy expenditure. The general trend has steadily been towards configurations with larger wheels, from 5�80 to 5�84, and with the introduction of high-quality big wheels, to 4�100 and 5�90, as well as some intermediate combinations designed to minimize the height of the skate above the ground. Surprisingly, no concensus has yet been reached on the optimal wheel configuration for marathon skating. In principle, an understanding of the physical rules that govern the motion of a skater and of the physics of skate wheels should provide an unambiguous answer. But in practice, the problem is confounded by factors that are difficult to quantify, even subjective, such as the skater�s size, power, and ability. Moreover, no unique wheel configuration may be appropriate for all racing conditions � some wheel combinations may be superior to others depending on the topography and surface properties of the race course.

In this article, I present the equation of motion for inline skating, sometimes called the power equation, and show how it can be applied to determine the wheel configuration with the best roll independent of skater ability and technique. The power equation has been studied extensively in bicycling and in fact, some of the results presented here will be put into the context of this discipline. The equation of motion is solved with real-world measurements of the rolling resistance, the aerodynamic drag, and the moment of inertia of the wheels. To explore the differences in performance between small and big wheels, the rolling resistance of the wheels, as well as their mass and size, are varied. The following analysis will hopefully help skaters, confronted with a daunting choice of wheels and frames, make a more informed decision when selecting and purchasing their skating equipment.