# A Novel Approach of Modelling and Predicting Track Cycling
## 1 Introduction  
In track cycling time trial events (contre la montre, against the clock), cyclists compete for the shortest run-time over a given distance, typically 500 m, 1 km or 4 km, with a standing start. Sprint time trials (200 m, 500 m, 1 km) are usually executed in an all-out fashion until complete exhaustion and are indicated by very high maximal and mean power output [1, 2]. Competition performance results from the balance of an athlete's energy supply and physical demands [3]. The propulsive power output supplied by the athlete is directly consumed to overcome physical resistance, bearing and drive-train losses, the rolling resistance of the tires and the aerodynamic drag. Power output can be measured by power meters, and data can be applied to performance models in order to analyse the contributing factors and to optimise competition results.  
A numerical simulation of human locomotion requires modelling of the supply, as well as the demand side of the energy budget [4]. Different physical and mathematical models have been published since the late 1970s to model (track) cycling performance based on physiological, anthropometric and environmental parameters, which describe the fundamentals [5, 6, 7] and details [8] of cycling performance via mathematical equations and investigate the effect of changes in modelling parameters on performance [5, 6, 7, 9, 10].  
[PERSON], [PERSON] and [PERSON] [11], [PERSON] et al. [12], [PERSON] and [PERSON] [13] and [PERSON] et al. [8] developed models specifically for track cycling, which, in contrast to themodels for road cycling, incorporate an oval track. [PERSON] additionally describes the inclined position in the curves of an indoor velodrome, and [PERSON]'s model presents a comprehensive description of all relevant physical quantities.  
The most recent contributions include measurements of power output [8; 12; 13; 14; 15; 16]. Most of these models are very complex and require either data from previous testing and a priori assumptions in order to be properly calibrated, something that renders them cumbersome for application in sports practice.  
There is no model available that can describe the energy supply component without major assumptions and limitations, as was recently also noticed by [PERSON] et al. [17]. So far, either a priori data is used as an input [12; 15], or an attempt is made to estimate fatigue-induced performance losses based on the number of revolutions at time \(t\)[14; 18]. This limits their applicability to a replication of already completed runs. A mathematical tool capable of predicting scenarios requires a generic physiological model, with its parameters fitted to the individual athlete's characteristics.  
To address this problem, we combined a physiological model with a physical model specifying the transient power required for cycling. The physiological model is based on the predictability of fatigue-induced changes in maximum possible power output and uses linear force-velocity (\(F/v\)) and parabolic power-velocity (\(P/v\)) profiles to describe these changes mathematically. We tried to increase the practicality of our method by limiting the amount of input values and reducing the complexity of the computational process. These simplifications increase the appeal of this approach for use in track cycling to optimise performance.  
This study aims to investigate the validity and predictive quality of our approach by comparing data measured by high-precision power meters during training runs of elite sprinters in the velodrome with corresponding modelled results. The verified model was applied to study the isolated effects of single parameters on the athlete's performance.