An empirical model for world record running speeds with distance, age, and sex: anaerobic and aerobic contributions to performance

The objective of this study is to derive mathematical equations that closely describe published data on world record running speed as a function of distance, age, and sex. Running speed declines with increasing distance and age. Over long distances, where aerobic metabolism is dominant, speed declines in proportion to the logarithm of distance. Over short distances, anaerobic metabolism contributes significantly to performance, and speed is increased relative to the trend of the long-distance data. Equations are derived that explicitly represent these effects. The decline in speed with age is represented by an age-dependent multiplicative factor, which exhibits increasing sensitivity to age as age increases. Using these equations, data are analyzed separately for males and females, and close fits to published data are demonstrated, particularly for younger age groups. These equations provide insight into the contributions of aerobic and anaerobic components of metabolism to athletic performance and a framework for comparisons of performance across wide ranges of distance and age.