A Simple Model for Predicting Sprint Race Times Accounting for Energy Loss on the Curve --- J. R. Mureika

1. Introduction

In 1973, mathematician J. Keller [1] proposed a model for predicting World Record (WR) race times based on a simple least-square fit of the records of the day. The fit was quite good, and provided a simple tool for gauging possible optimal performances in races, based on results from others. Keller's model was limiting in the sense that it could only "in reality" predict possible records of linear races, with no consideration for those run on curves. For distance races (over 400 m), the impact of running the curve is negligible. When the race speeds are much higher, though, the curve contributions cannot be left out.

Recent WR performances in athletics have prompted various new studies based on Keller's work. Tibshirani [2] introduces a more realistic energy loss model for sprinting, accounting for the sprinter's actual velocity curve. Still, though, the curve of the track is not considered; this is mentioned in [2], but no solution is offered. The following work will formulate a simple model to account for energy loss around the curve, and predict possible WR performances accordingly, using data obtained from a least-square fit of contemporary short sprint records. Both outdoor races, as well as indoor competitions, are discussed. As a practical example, the 100 m WR sprint race of Donovan Bailey (Canada) is used as empirical data to further determine the validity of the model for predicting 200 m sprint times. A brief discussion of indoor 300 m records is offered. The possibility of using such a model as a training tool for athletes and coaches in considered.

Section index
2. The Keller Model
Curve Model
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