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Least squares model for the running curve.

Abstract This study investigated the utilization of the Henry model with the method of least squares to describe the average velocity versus distance running curve. A historical review of previous attempts to derive a model for the running curve is presented. It is concluded that the formulation with five exponential terms derived by Henry can adequately describe the running curve. The five linear and five exponential model parameters can be determined by the method of least squares on a computer using a homogeneous set of velocity and distance data points. With this technique the original solution obtained by Henry is optimized to produce an average relative deviation of .9%, and a solution obtained with the running world records for men on December 31, 1970, shows an average relative deviation of 1.35%. In addition, this study indicates how the running curve may be employed to aid in the generation of scoring tables for any running distance.