Incline-dependency of the power-duration relationship in cross-country skiing

Marton Horvath¹Erik Petrus Andersson^1*Adam Kölnas²Adam Spreitz²Hjalmar Boström²Arvid Sörfeldt²Dan Kuylenstierna²

• ¹Mittuniversitetet Nationellt vintersportcentrum, Östersund, Sweden
• ²Chalmers University of Technology, Gothenburg, Sweden

Introduction: This study aimed to develop a methodology for establishing the power–duration relationship in cross-country skiers and to investigate the influence of incline on the parameters of the critical power (CP) model. Methods: Twelve trained male cross-country skiers performed four constant work-rate predictive trials on a motor-driven treadmill, using the double poling sub-technique, to determine their power–duration relationships at 2° and 8° inclines in a randomized order. The testing protocol also included maximum speed tests performed at both inclines. Power-duration relationships were modeled using the modified three-parameter critical power model. Results: The derived power-duration relationships were significantly different between the two inclines. At an 8° incline, the estimated work capacity above CP (W′) was more than three times higher than at a 2° incline (24.87±8.75 kJ vs. 7.07±1.61 kJ, respectively; Z=3.06, P=0.002, rrb=0.88), which was partly explained by an increased anaerobic power capacity (i.e., Pan=4.82±0.64 W·kg−1 vs. 1.67±0.34 W·kg−1, respectively; Z=3.06, P=0.002, rrb=0.88). Although CP estimates differed by approximately 16% between the two inclines on a group level (2.78±0.22 W·kg−1 vs. 2.39±0.74 W·kg−1 at a 2° and at an 8° incline, respectively), a moderate non-significant effect of incline was observed with large individual variances (Z=1.88, P=0.06, rrb=0.54). The incline had a non-significant effect on the time constant parameter estimates (Z=1.57, P=0.12, rrb=0.45), yet inter-individual variation remained considerable. Discussion: The findings demonstrate that in cross-country skiing, both W ′ and Pan are highly incline-dependent, showing markedly higher values at steeper gradients. Moreover, the variability observed in CP and W′ across inclines exceeded the typical sensitivity of these parameters to external factors reported in cycling. A large proportion of the incline-related changes in model parameters could be explained by accounting for the estimated variations in gross efficiency across speeds and inclines. However, the persistence of a significant difference in W' even when expressed in terms of estimated metabolic power at steeper inclines suggests the involvement of additional physiological mechanisms, potentially a larger amount of recruited muscle mass due to differences in muscle fiber recruitment between conditions.