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

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 shortcoming is that it neglects to account for a sprinter’s energy loss around a curve, a most important consideration particularly in the 200m–400m. 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 200m are discussed, and the use of the model at 300m is investigated. Some predictions are made for possible 200m outdoor and indoor times as run by Canadian 100m WR holder Donovan Bailey, based on his 100m final performance at the 1996 Olympic Games in Atlanta.