Power laws and athletic performance

American Journal of Physics, 2010

At the 2008 Summer Olympics in Beijing, Usain Bolt broke the world record for the 100 m sprint. Just one year later, at the 2009 World Championships in Athletics in Berlin he broke it again. A few months after Beijing, Eriksen et al. [Am. J. Phys. 77, 224–228 (2009)] studied Bolt’s performance and predicted that Bolt could have run about one-tenth of a second faster, which was confirmed in Berlin. In this paper we extend the analysis of Eriksen et al. to model Bolt’s velocity time dependence for the Beijing 2008 and Berlin 2009 records. We deduce the maximum force, the maximum power, and the total mechanical energy produced by Bolt in both races. Surprisingly, we conclude that all of these values were smaller in 2009 than in 2008.

In 1906 Kennelly proposed a model for the relations between time (t lim) versus speed (S = kt lim g-1) or distance (D lim = kt lim g). In 1989, Péronnet and Thibault proposed a logarithmic model based on the decrease in the fractional use of maximal aerobic speed (MAS) for t lim beyond the exhaution time (t MAS) corresponding to MAS [S/MAS = C – EI ln(t lim /t MAS)] where C was equal to 100 and EI was an endurance index. Both models can accurately describe the relationships between S and t lim for the World records and the performances of elite endurance runners. Exponent g and EI are linearly correlated (r > 0.999) which confirms that g can be considered as an estimator of endurance ability in runners. The effect of the value of t MAS (assumed to be equal to 7 min in Péronnet-Thibault model) on EI should be more important in low-level endurance runners than in elite runners. Nevertheless, the logarithmic model is interesting because the effect of t MAS on EI is relatively small when compared with the range of EI. In theory, the best performances of low-level runners cannot be described by both models. Therefore, it would be interesting to study what is the best model.

Proceedings of the Royal Society B: Biological Sciences, 2009

Human physical performance is notably reduced with ageing. Although the effects of ageing are often compounded by disuse, the study of master athletes provides an opportunity for investigating the effects of ageing per se. It is often held that sprinting is more affected than endurance performance. However, past analyses of master athletic world record data have yielded opposite observations. We argue here that our understanding of these data improves by considering how, biomechanically, metabolic power is related to athletic performance. In line with earlier studies, our analysis showed that running speed declines with age in a more pronounced way for endurance events than for sprinting events, confirming former studies. However, when assessing the metabolic power required to achieve the running world records, sprint and endurance events show a relatively uniform decline with age across the different events. This study has reconciled formerly conflicting scientific results and improves our understanding of the ageing process. However, it is unclear as to which are the governing mechanisms that cause the different systems in our body, responsible for sprinting and for endurance performance, to be affected by ageing in a remarkably uniform way.

BMC sports science, medicine and rehabilitation, 2014

The aims of the study were (i) to investigate the relationship between elite marathon race times and age in 1-year intervals by using the world single age records in marathon running from 5 to 93 years and (ii) to evaluate the sex difference in elite marathon running performance with advancing age. World single age records in marathon running in 1-year intervals for women and men were analysed regarding changes across age for both men and women using linear and non-linear regression analyses for each age for women and men. The relationship between elite marathon race time and age was non-linear (i.e. polynomial regression 4(th) degree) for women and men. The curve was U-shaped where performance improved from 5 to ~20 years. From 5 years to ~15 years, boys and girls performed very similar. Between ~20 and ~35 years, performance was quite linear, but started to decrease at the age of ~35 years in a curvilinear manner with increasing age in both women and men. The sex difference increa...

Medicine & Science in Sports & Exercise, 2001

Purpose: The typical variation in an athlete's performance from race to race sets a benchmark for assessing the utility of performance tests and the magnitude of factors affecting medal prospects. We report here the typical variation in competitive performance of endurance runners. Methods: Repeated-measures analysis of log-transformed official race times provided the typical within-athlete variation in performance as coefficients of variation (CV). The types of race were crosscountry runs (4 races over 9 wk), summer road runs (5 races over 4 wk), winter road runs (4 races over 9 wk), half marathons (3 races over 13 wk and 2 races over 22 wk), and marathons (2 races over 22 wk). Results: Typical variation of times for the fastest quartile of male runners was 1.2-1.9% in the crosscountry and road runs, 2.7% and 4.2% in half marathons, and 2.6% in marathons. Times for the slower half of runners in most events were more variable than those of the faster half (ratio of slower/faster CV, 1.0-2.3). Times of younger adult runners were more variable than times of older runners (ratio of younger/older CV, 1.1-1.8). Times of male runners were generally more variable than those of female runners (ratio of male/female CV, 0.9-1.7). Conclusion: Tests of endurance power suitable for assessing the smallest worthwhile changes in running performance for top runners need CV Յ 2.5% and Յ 1.5% for tests simulating half or full marathons and shorter running races, respectively. Most of the differences in variability of race times between types of race, ability groups, age groups, and sexes probably arise from differences in competitive experience and attitude toward competing.

Journal of Theoretical Biology, 2012

In the twentieth century, scientists have examined running speed over various distances, analyzing world records and studying the ability of an athlete to sustain a given speed. Assuming that running speed expresses the response of a non-linear multisystemic behavior, the relationship between these two variables (distance vs. velocity) can therefore be evaluated by applying scaling laws that fulfill the key principles of specificity and individuality of each athlete, yet responding to bioenergetic and functional patterns that are well-known to sports physiology. Since speed loss as distance increases exhibits fractal behavior, with small changes in the speed-reduction curve due to the effect of fatigue, it must be recognized that no universal scaling law can account, with acceptable precision, for the effect exerted by fatigue on potential speed at any given moment in a race. Power laws using a range of scaling exponents provide technical staff and athletes with a reliable, non-invasive tool for planning of training schedules, predicting athletes' performances over various distances and comparing the performance of specialists in different track events. The equations for the scaling laws for the distances investigated here were: V 1500 ¼ 15.00 Â D À 0.10 (R 2 ¼0.99); V 3000 ¼ 12.76 Â D À 0.08 (R 2 ¼0.99); V 5000 ¼11.55 Â D À 0.07 (R 2 ¼ 0.99); V 10,000 ¼ 11.59 Â D À 0.07 (R 2 ¼0.99); V 21,095 ¼10.78 Â D À 0.06 (R 2 ¼ 0.97); V 42,175 ¼ 10.27 Â D À 0.057 (R 2 ¼ 0.99).

British Medical Bulletin, 2008

Introduction: Progression of world records (WRs) in athletics is a reliable mean to assess the potentiality of the human body, which also reflects how society has evolved over time and will continue to evolve. We conducted a quantitative analysis of WRs in measurable Olympic events from nine representative disciplines (100, 400, 1500, 10 000 m, marathon, long jump, high jump, shot put and javelin throw) in order to identify progression and trends.

British Journal of Sports Medicine, 1972

Open access journal of sports medicine, 2018

The age of peak performance (APP) has been studied extensively in various endurance and ultra-endurance sports; however, less information exists in regard to duathlon (ie, Run1, Bike, and Run2). The aim of the present study was to assess the APP of duathletes competing either in a short (ie, 10 km Run1, 50 km Bike, and 5 km Run2) or a long distance (ie, 10 km Run1, 150 km Bike, and 30 km Run2) race. We analyzed 6,671 participants (women, n=1,037, age 36.6±9.1 years; men, n=5,634, 40.0±10.0 years) in "Powerman Zofingen" from 2003 to 2017. Considering the finishers in 5-year age groups, in the short distance, a small main effect of sex on race time was observed (<0.001, η =0.052) with men (171.7±20.9 min) being faster than women (186.0±21.5 min) by -7.7%. A small main effect of age group on race was shown (<0.001, η =0.049) with 20-24 years being the fastest and 70-74 years the slowest. No sex × age group interaction was found (=0.314, η =0.003). In the long distance, ...

In the present study, we show that the fastest runners and swimmers are becoming not only faster but also heavier, taller and more slender. During the past century, the world record speeds for 100 m-freestyle and 100 m-dash have increased with body mass (M) raised to the power 1/6, in accordance with the constructal scaling of animal locomotion. The world records also show that the speeds have increased in proportion with body heights (H) raised to the power 1/2, in accordance with animal locomotion scaling. If the athlete's body is modeled with two length scales (H, body width L), the (M, H) data can be used to calculate the slenderness of the body, H/L. The world records show that the body slenderness is increasing very slowly over time.