Related papers: Testing the Sprint Curve Model using the 150m Bail…
Using the model framework for curve running as described in physics/9704022, the possible outcome of the 150m "One to One" showdown between sprinters Donovan Bailey and Michael Johnson are discussed (to be run 01 Jun 1997 at Skydome in…
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…
In order to describe the velocity and the anaerobic energy of two runners competing against each other for middle-distance races, we present a mathematical model relying on an optimal control problem for a system of ordinary differential…
A quasi-physical model (having both physical and mathematical roots) of sprint performances is presented, accounting for the influence of drag modification via wind and altitude variations. The race time corrections for both men and women…
This study analysed sprint kayak pacing profiles in order to categorise and compare an athlete's race profile throughout their career. We used functional principal component analysis of normalised velocity data for 500m and 1000m races to…
Our aim is to present a new model which encompasses pace optimization and motor control effort for a runner on a fixed distance. We see that for long races, the long term behaviour is well approximated by a turnpike problem. We provide…
Many university texts on Mechanics deal with the problem of the effect of the air drag force, using as example the slowing down of a parachute. Hardly no one discuss what happens when the drag force is proportional to both $u$ and $u^2$. In…
This work proposes to use evolutionary computation as a pathway to allow a new perspective on the modeling of energy expenditure and recovery of an individual athlete during exercise. We revisit a theoretical concept called the "three…
The Olympic 500 meter sprint competition is the `Formula One event' of speed skating, and is watched by millions of television viewers. A draw decides who should start in inner lane and who in outer lane. Many skaters dread the last inner…
We present a mathematical model for optimizing breakaway strategies in competitive cycling, balancing power expenditure, aerodynamic drag, and crashing. Our framework incorporates probabilistic crash dynamics, allowing a cyclist's risk…
Traffic flow of athletes in classic-style cross-country ski marathons, with the Swedish Vasaloppet as prominent example, represents a non-vehicular system of driven particles with many properties of vehicular traffic flow such as…
The aim of this paper is to bring a mathematical justification to the optimal way of organizing one's effort when running. It is well known from physiologists that all running exercises of duration less than 3mn are run with a strong…
Sample splitting is widely used in statistical applications, including classically in classification and more recently for inference post model selection. Motivating by problems in the study of diet, physical activity, and health, we…
In some athletic races, such as cycling and types of speed skating races, athletes have to complete a relatively long distance at a high speed in the presence of direct opponents. To win such a race, athletes are motivated to hide behind…
We propose a macroscopic model in form of a dispersion-transport equation for non-congested flow of the athletes which is coupled to a kinematic-wave model for congested flow. The model takes into account the performance (i.e., free-flow…
Models for human running performances of various complexities and underlying principles have been proposed, often combining data from world record performances and bio-energetic facts of human physiology. Here we present a novel, minimal…
Because the decathlon tests many facets of athleticism, including sprinting, throwing, jumping, and endurance, many consider it to be the ultimate test of athletic ability. On this view, estimating the maximal decathlon score and…
This paper formulates optimal pacing of a cyclist on hilly terrain time-trials as a minimum-time optimal control problem. Maximal power of a cyclist serves as a time-varying constraint and depends on fatigue and recovery which are captured…
We present a new rigorous method for estimating statistical quantities in fluid dynamics such as the (average) energy dissipation rate directly from the equations of motion. The method is tested on shear flow, channel flow,…
Physicists seeking to understand complex biological systems often find it rewarding to create simple "toy models" that reproduce system behavior. Here a toy model is used to understand a puzzling phenomenon from the sport of track and…