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Using mathematical analysis, we examined the three baton exchanges that occur during a 42100 m relay. Identical representative 100 m running performances were assumed for each of four elite male athletes, and the calculations were made for optimal or near-optimal positions of the baton exchanges and starting positions of the athletes running the second, third and fourth legs as determined by Ward-Smith and Radford (2002). In this paper, we focus on the calculation of the checkmark position and demonstrate the complexity of the baton exchange process. The results of the mathematical analysis show that, for optimal performance, the checkmark should be located differently for each of the three exchanges in a single race, and is further affected by lane draw and free distance (the distance between the runners at the baton exchange). For a representative free distance of 1 m at each exchange, the checkmark distance ranges from a minimum of 11.04 m at the third exchange in Lane 1 to 12.20 m for the first exchange in Lane 8. Failure by teams and their coaches to consider adequately the complexities of the baton exchanges may help explain why 25.5% of teams in recent World Championships were disqualified or did not finish. [ABSTRACT FROM AUTHOR]

In this study, we examined aspects of the 4 x 100 m relay that are amenable to mathematical analysis. We looked at factors that affect 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 influence on the relay time, although it is outside the control of the team coach. Teams drawn in the outside lanes benefit from the inverse relation between bend radius of curvature and running speed. For teams composed of athletes with different times over 100 m, we show that the fastest relay times are achieved with the fastest athlete taking the first leg, with the slowest two runners allocated to the final two legs.

Computed results from a mathematical model of the bioenergetics of sprinting, which incorporates a three-equation representation of anaerobic metabolism, were compared with measured distance-time data for female athletes from the finals of the 100-m event at the World Championships of 1987. The computed results closely model the performance of the competitors over the course of the entire race. The three main contributions to anaerobic metabolism were investigated and comparisons were made between male and female sprinters. Whereas the time constants for adenosine triphosphate (ATP) and phosphocreatine utilization for the two sexes were found to be similar, for oxygen-independent glycolysis the time constants of the female athletes were found to be higher. The maximum powers generated by female athletes during ATP conversion and glycolysis were only slightly lower than the figures found for male athletes, but the value for phosphocreatine utilization was substantially lower. The lower value for phosphocreatine utilization might explain the more pronounced fall-off in running speed over the latter stages of a race that female athletes experience in comparison with men. Although anaerobic sources dominate energy provision for both male and female sprinters, the calculations show that the latter make greater use of aerobic energy supplies.

The principal motivation for the present work was the study of the kinetics of anaerobic metabolism. A new mathematical model of the bioenergetics of sprinting, incorporating a three-equation representation of anaerobic metabolism, is developed. Results computed using the model are compared with measured data from the mens' finals of the 100m event at the 1987 World Championships. The computed results closely predict the overall average performance of the competitors over the course of the entire race. Further calculations show the three-equation model of anaerobic metabolism to be a significant improvement over the previous one-equation model. Representative values of time constants that govern the rate of anaerobic energy release have been determined for elite male athletes. For phosphocreatine utilisation, values for lambda(2)=0. 20s(-1) and psi(2)=3.0s(-1) are consistent with data previously reported in the literature. New values of lambda(3)=0.033s(-1) and psi(3)=0.34s(-1) are proposed as offering an improved representation of the kinetics of oxygen-independent glycolysis. For the first time, tentative values for the time constants of ATP utilisation, lambda(1)=0.9s(-1) and psi(1)=20s(-1), are suggested. The maximum powers developed during sprinting by oxygen-independent glycolysis, PCr utilisation and endogenous ATP utilisation were calculated as 34. 1, 30.1 and 16.6Wkg(-1), respectively, with an overall maximum anaerobic power of 51.6Wkg(-1). Sample calculations show the mathematical model can be used in principle to derive data on the kinetics of anaerobic metabolism of individual athletes.

Since September 1988 when Ben Johnson was tested positive for a banned substance at the Seoul Olympic Games, many national and international initiatives have been taken to improve the control of doping in sport. This paper summarizes the revised provisions of the International Olympic Committee list of doping classes and methods. Recent events are also reviewed, including the investigation into the use of performance-enhancing drugs by Australian sportsmen and women (the Black Enquiry), by the Canadians (the Dubin Enquiry) and by the British (the Coni Enquiry and the Jacobs Enquiry). Recent political initiatives are considered, in particular the major international agreements such as the Soviet-American Joint Commission, the International Olympic Antidoping Charter and the European Anti-Doping Convention. Sportsmen and women who, in the past, have been tested positive for banned substances have been the focus of much attention from the sporting community, the general public and the media, but others including coaches, physicians, scientists and others, must share the blame for the spread of drug abuse in sport. In the UK the new policies and programmes of the Sports Council (and the Sports Councils in Wales, Scotland and Northern Ireland) should provide a better programme for doping control than that previously used, and the new international agreements should provide a better framework for international cooperation on education, detection and research.