# A Novel Approach of Modelling and Predicting Track Cycling
###### Abstract  
In cycling, performance models are used to investigate factors that determine performance and to optimise competition results. We present an innovative and easily applicable mathematical model describing time-resolved approaches for both the physical aspects of fractional resistance and the physiological side of propelling force generated by muscular activity and test its validity to reproduce and forecast time trials in track cycling. Six elite track cyclists completed a special preparation and two sprint time trials in an official velodrome under continuous measurement of crank force and cadence. Fatigue-free force-velocity profiles were calculated, and their fatigue-induced changes were determined by non-linear regression analysis using a monoexponential equation at a constant slope. Model parameters were calibrated based on pre-exercise performance testing and the first of the two time-trials and then used to predict the performance of the second sprint. Measured values for power output and cycling velocity were compared to the modelled data. The modelled results were highly correlated to the measured values (\(R^{2}>0.99\)) without any difference between runs (\(p>0.05\); \(d<0.1\)). Our mathematical model can accurately describe sprint track cycling time trial performance. It is simple enough to be used in practice yet sufficiently accurate to predict highly dynamic maximal sprint performances. It can be employed for the evaluation of completed runs, to forecast expected results with different setups, and to study various contributing factors and quantify their effect on sprint cycling performance.  
force-velocity profile; fatigue characteristics; performance modelling; track cycling; performance optimisation 2021  
15 November 2021  
16 December 2021  
19 December 2021  
###### Abstract  
In cycling, performance models are used to investigate factors that determine performance and to optimise competition results. We present an innovative and easily applicable mathematical model describing time-resolved approaches for both the physical aspects of fractional resistance and the physiological side of propelling force generated by muscular activity and test its validity to reproduce and forecast time trials in track cycling. Six elite track cyclists completed a special preparation and two sprint time trials in an official velodrome under continuous measurement of crank force and cadence. Fatigue-free force-velocity profiles were calculated, and their fatigue-induced changes were determined by non-linear regression analysis using a monoexponential equation at a constant slope. Model parameters were calibrated based on pre-exercise performance testing and the first of the two time-trials and then used to predict the performance of the second sprint. Measured values for power output and cycling velocity were compared to the modelled data. The modelled results were highly correlated to the measured values (\(R^{2}>0.99\)) without any difference between runs (\(p>0.05\); \(d<0.1\)). Our mathematical model can accurately describe sprint track cycling time trial performance. It is simple enough to be used in practice yet sufficiently accurate to predict highly dynamic maximal sprint performances. It can be employed for the evaluation of completed runs, to forecast expected results with different setups, and to study various contributing factors and quantify their effect on sprint cycling performance.  
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