# A Novel Approach of Modelling and Predicting Track Cycling
## 4 Discussion
For short races, the importance of the time constant, or endurance, is much lower than for longer distances. Figure 10: Change in the calculated run-time \(T\) of the generic athlete as a function of change in aerodynamic drag area \(c_{D}\cdot A\) for distances from 250 m to 1000 m.  
A congruent observation is found for the sensitivity of the run-time for changes in the residual value \(c\), to which the pedal force drops when fatigue is \"fully\" developed and which, according to [PERSON]'s critical power concept [34], may be related to an athlete's aerobic power. After a 250 m run, this situation is not yet reached, but it is realised in longer efforts of up to 1000 m. Consequently, in Figure 13, the graph for 250 m shows a negligible impact, while at 1000 m, a linear correlation is present. Figure 11: Change in the calculated run-time \(\Delta T\) of the generic athlete as a function of development for distances from 250 m to 1000 m.  
Figure 12: Change in the calculated run-time of the generic athlete as a function of change in the time constant \(\tau\) for distances from 250 m to 1000 m.  
In Figure 14, the effect of maximum power attainable for the non-fattigued athlete on run-time is studied. It is important to note that all curves collapse on the same line, rendering this correlation independent from a distance. The gradient slightly decreases with increasing level of \(P_{max}\), indicating that for every step gained in maximum power by, e.g., training, an ever-smaller benefit in run-time will be achieved. This is mainly caused by the aerodynamic drag being proportional to \(v^{2}\), the power required to maintain a given velocity increasing rapidly with \(v^{5}\). Nevertheless, changes in \(P_{max}\) show nominally the largest impact on run-time. Our physical model describing the demand side of the energy budget is based on fundamental engineering and physical principles and is similar to various models proposed by previous investigators [5; 6; 7; 8; 9; 10; 11; 12; 13]. The innovative element in our contribution is the combination of a physical model describing the instantaneous energy demand in time-trial track cycling with a description of maximal fatigue-free power output and fatigue characteristics as current maximal cadence-independent biomechanical performance. This enables the computing of (future) time-dependent power output for any setup or ambient conditions. This aspect has recently  
Figure 14: Change in the calculated run-time of the generic athlete as a function of change in the fatigue-free maximum power output \(P_{max}\) for distances from 250 to 1000 m.  
Figure 13: Change in the calculated run-time of the generic athlete as a function of change in the residual value c for distances from 250 m to 1000 m.  
been re-identified as one of the most important topics for research in track cycling by [PERSON] et al. [17]. The physiological model is reliable and reproduces the athlete's current performance potential with reasonable accuracy, provided that the athlete performs in an all-out fashion and, in the case of multiple runs, that fatigue is controlled by an appropriate recovery protocol during the rest phase. Our results suggest that power development potentiation effects after activation can increase power output in cycling [35], while fatigue can decrease it [36; 37]. The fatigue-free power output had to be slightly adjusted for the accurate reconstruction of the second run for one athlete. To avoid a misjudgement due to an unaddressed change in fatigue-free power output, the fatigue-free \(F/v\) profile should be retested shortly before the start of each run. Physical performance is also subject to daily fluctuations [38], so a regular, preferably daily adjustment of the personal model parameters would be beneficial to ensure a sufficiently good prediction quality. Expanding this idea, the physiological model parameters also offer the possibility to document and analyse individual biomechanical performance in a more generalised way on a long-term basis.