A Simple Model for Predicting Sprint Race Times Accounting for Energy Loss on the Curve

Abstract
The mathematical model of J. Keller for predicting World Record race times, based on a simple differential equation of motion, predicted quite well the records of the day. One of its shortcomings is that it neglects to account for a sprinter's energy loss around a curve, a most important consideration particularly in the 200 m to 400 m range. An extension to Keller's work is considered, modeling the aforementioned energy loss as a simple function of the centrifugal force acting on the runner around the curve. Theoretical World Record performances for indoor and outdoor 200 m are discussed, and the use of the model at 300 m is investigated. Some predictions are made for possible 200 m outdoor and indoor times as run by Canadian 100 m WR holder Donovan Bailey, based on his 100 m final performance at the 1996 Olympic Games in Atlanta.