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

Journal article, 2025

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 critical power ( C P ) model parameters.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 degrees and 8 degrees inclines in a randomized order. The testing protocol also included maximum speed tests performed at both inclines. Power-duration relationships were modeled using a modified expression of the three-parameter critical power model.Results The derived power-duration relationships were significantly different between the two inclines. At an 8 degrees incline, the estimated work capacity above C P (i.e., W ' ) was more than two times higher than at a 2 degrees incline ( 24.87 +/- 8.75 kJ vs. 7.07 +/- 1.61 kJ, respectively; Z = 3.06 , P = 0.002 , r r b = 0.88 ), which was partly explained by an increased anaerobic power capacity (i.e., P a n = 4.82 +/- 0.64 W & sdot; kg-1 vs. 1.67 +/- 0.34 W & sdot; kg-1, respectively; Z = 3.06 , P = 0.002 , r r b = 0.88 ). Although C P estimates differed by approximately 16 % between the two inclines on a group level ( 2.78 +/- 0.22 W & sdot; kg-1 vs. 2.39 +/- 0.74 W & sdot; kg-1 at a 2 degrees and at an 8 degrees incline, respectively), a moderate non-significant effect of incline was observed with large individual variances ( Z = 1.88 , P = 0.06 , r r b = 0.54 ). The incline had a non-significant effect on the time constant parameter estimates ( Z = 1.57 , P = 0.12 , r r b = 0.45 ), yet inter-individual variation remained considerable.Discussion The findings demonstrate that in cross-country skiing, both W ' and P a n are highly incline-dependent, showing markedly higher values at steeper gradients. Moreover, the variability observed in C P 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.