Optimal Pacing in a Time Trial
(overview adapted from my thesis proposal, linked below)
Many different sports have events which involve “racing against the clock” - running, swimming, rowing, and cycling are examples. Some competitions might involve other athletes but not direct competition; swimming competitions, regattas, and some running events involve different lanes, and cycling time trials do not permit drafting which removes the influence of other competitors.
In these types of events victory is determined by an individual’s athletic abilities and pacing strategy, not by interactions with other competitors. This leaves limited options to improve performance: equipment selection, training/conditioning, and pacing strategy. While these factors are all controllable to some degree, this research only considers the pacing strategy.
The goal of this research is to expand upon previous work in multiple fields and applying all of it to pacing strategies for cycling. Cycling time trials have been chosen due to the ease of modeling the physical system and measuring actual riders. Time trials are ideal because they remove the other riders from the problem, and thus remove the issue of drafting (and optimal positioning within the peloton). By formulating a more realistic model of human bioenergetics and creating optimization and optimal control tools, it is hoped that new insights into the minimum time problem for cyclists can be found.
While a number of other authors have studied human pacing strategies for sporting events, the models used all leave something to be desired. Part of my work has been examining the currently available models, and examining if they are adaptable or extendable to my applications. The work of [Xia2008] proved to be a good starting point. A paper on the developed model has been submitted to a journal - more information will be made available soon.
Many optimal control problems are solved by discretizing and transforming them into numerical optimization problems, where a variety of well-developed tools can be used. Part of this work was creating an open-source non-linear programming (NLP) solver; a local solver capable of handling general constraints (equality and inequality) and nonlinear objective and constraint functions. You can follow this work here: https://github.com/gilbertgede/PyIntropt .
This section will soon be updated.
The Optimal Strategy
To be calculated, hopefully soon.