A Mathematical Analysis of the 4 X 100 M Relay
Journal of Sports Sciences, 2002, 20, 369± 381 A mathematical analysis of the 4 ´ 100 m relay A.J. WARD-SMITH and P.F. RADFORD* Department of Sport Sciences, Brunel University, Osterley Campus, Borough Road, Isleworth, Middlesex TW7 5DU, UK Accepted 19 November 2001 In this study, we examined aspects of the 4 ´ 100 m relay that are amenable to mathematical analysis. We looked at factors that aþ ect the time required to complete the relay, focusing on the performance of elite male athletes. Factors over which the individual athletes, and the team coach, can exercise some control are: the starting positions of the runners on legs 2, 3 and 4, the positions at which baton exchanges occur, the free distances at the baton exchanges and the running order of the athletes. The lane draw is shown to have an important in¯ uence on the relay time, although it is outside the control of the team coach. Teams drawn in the outside lanes bene® t from the inverse relation between bend radius of curvature and running speed. For teams composed of athletes with diþ erent times over 100 m, we show that the fastest relay times are achieved with the fastest athlete taking the ® rst leg, with the slowest two runners allocated to the ® nal two legs. Keywords: athletics, running, sprinting. Introduction allowance is made for bend curvature in the layout of the starting lines, which are staggered across the eight The aim of this study was to examine aspects of the lanes of the track. These rules eþ ectively determine the 4 ´ 100 m relay that are amenable to mathematical distances run by the runners on each of the four legs.
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