# A Novel Approach of Modelling and Predicting Track Cycling
## 4 Discussion  
We experimentally demonstrated, in test runs with six athletes, that using our combined physio-physical model, time trial track cycling performed in an all-out fashion can be modelled, and the results can be predicted with reasonable precision. This enables the evaluation of each individual factor's contribution to the overall performance. A generic rider was created as proposed in [24], with its physiological parameters derived from the arithmetic mean of the respective parameters found on our six individual athletes. Figure 9 depicts the sensitivity of the run-time for a change in the system's mass for distances of 250 to 1000 m. For each distance, a monotonous linear correlation was observed. The slope of these curves decreases with the increasing length of the run, indicating that the effect of a change in the system's mass is more prominent in short-distance races. This is plausible, as an increase in mass is particularly detrimental during the acceleration phase. Once accelerated, mass only affects the rolling resistance, which is orders of magnitude smaller than the inertia force. In Figure 10, the effect of a change in aerodynamic drag area on run-time is shown for four different distances. This result is particularly useful as it helps to translate an improvement found by wind-tunnel measurements into run-time savings on the track. Figure 8: Dispersion of the modelled from measured velocity \(v_{w}\) vs. the distance travelled for both runs of all six athletes. Black lines indicate upper and lower limits of the 95%-confidence interval. Figure 9: Change in the calculated run-time \(T\) of the generic athlete as a function of change in system mass \(m\) for distances from 250 to 1000 m.  
In contrast to the effect of a change in mass, the importance of a change in aerodynamic drag increases with increasing run distance, as is apparent by the slope of the curves becoming steeper. As aerodynamic resistance is proportional to \(v^{2}\), its impact increases at higher speeds and accumulates over time. Perhaps the most relevant setup parameter is the gear-ratio, physically coupling power available and power required. It cannot be changed during the effort but has to be chosen carefully in advance. A relatively low gear ratio will augment the acceleration of the system at the expense of premature fatigue of the cyclist, while too high a gear ratio will keep the athlete from reaching top speed in a reasonable time. Our model can be used to create individual gear ratio profiles and determine an athlete's optimal gear for different race distances. Figure 11 exhibits the expected change in run-time of the generic athlete, normalised to the minimum run-time found, for four race distances at different developments, i.e., the distance travelled per one crank revolution. A distinct optimum development, resulting in the shortest possible run-time under given circumstances and training level, can be observed at 0%. This optimum is shifted towards higher gearing with increasing race distance. This observation is supported by practical experience: short-distance events are dominated by start performance, which is improved with lower gearing, while longer distances emphasise maintaining a high speed for a prolonged time, where a higher gearing is advantageous. Comparing the gradient of the curves left and right of the apex, it becomes evident that too high a gear ratio is less detrimental on the run-time than a gear ratio too low by the same amount. In practice, this implies that if there is uncertainty about the individual optimum, it is advisable to select a gear that is slightly too large rather than one that is slightly too small. To our knowledge, this observation is in contradiction to the recent common practice on the track. Similar studies can be conducted with regard to the athlete's physiological parameters. In Figure 12, the time constant \(\tau\) of the generic rider, which is a measure linked to its individual resistance to fatigue, was varied.