## 4 Discussion  
The primary objective of this study was to identify the key biomechanical and physiological factors that most significantly impact XCS performance among elite athletes. By integrating both biomechanical and physiological data, we aimed to develop a neural network model capable of accurately predicting skiing speeds. This study highlighted a key insight within the domain of gross cycle kinematics: cycle length emerges as a critical determinant of skiing speed, with cycle rate having less effect. This result is consistent with previous reports [9; 33], which have indicated that faster skiers tend to have longer cycle lengths, but no marked difference in cycle rates when compared to slower skiers. Moreover, an analysis conducted on the 15 km classical race at the Norwegian XC skiing championships for men in 2016 revealed a significant correlation between cycle length and average skiing speed across flat, medium, and steep uphill terrains. Conversely, cycle rate was only positively correlated with speed on steep uphill sections during the final lap [34]. We also observed a greater influence of cycle length on skiing speed on uphill than flat terrain, an important consideration when designing training programs. In addition, this study found that the vertical displacement of the CoM on uphill terrain significantly affected skiing speed. This displacement, indicative of motion stability and energy economy, can precipitate excessive energy expenditure if overly pronounced. For instance, when skiers were monitored while performing 5 min of submaximal speed skiing on a running platform with a slope of 2\({}^{\circ}\), the better skiers exhibited lower energy expenditure, better economy of movement, and a smaller range of vertical displacement of the CoM [35]. Moreover, the current study indicates that the vertical displacement of the CoM on uphill terrain had a more significant effect on average skiing speed than on  
Figure 3: Bland–Altman analysis of the speeds predicted by the model established and the actual values measured. flat terrain, suggesting that energy expenditure on uphill terrain may be more critical to overall performance. Physiological parameters, such as VO2 max and 30 s anaerobic capacity, have also been affirmed as key determinants of skiing performance, findings that are consistent with those reported earlier. For example, [PERSON] and colleagues [36] reported that higher VO2 max was associated with better performance, with gross efficiency being the strongest determinant of performance. Although considerable aerobic capacity has always been recognized as essential for effective XCS, the current investigation indicates that high anaerobic capacity is also crucial. This endurance sport is both physiologically and technically demanding, with the involvement of many muscles, as well as exceptionally high rates of work on uphill terrain [37]. In this connection, [PERSON] and co-workers [1] found that cross-country skiers repeatedly exceed their maximal aerobic power, accumulating more pronounced oxygen deficits on uphill than flat terrain. Since performance on uphill terrain is a major determinant of overall performance in XCS [9], it is hardly surprising that high anaerobic capacity is also essential. Clearly, for physiological factors, cross-country skiers should focus on improving both their aerobic and anaerobic capacities in their training programs. The integration of appropriate independent variables into our neural network model yielded accurate predictions of skiing speed, with a minimal mean error margin between the predicted and actual values. Furthermore, this close agreement suggests that the reliable modeling of a skier's movement should be non-linear. A non-linear perspective on dynamic systems is rapidly becoming one of the dominant paradigms in the natural sciences and offers promising possibilities in analyzing the performance of competitive athletes, e.g., by providing a more integrated understanding of training [38].