AUTHOR=Horvath Marton , Andersson Erik P. , Kölnas Adam , Spreitz Adam , Boström Hjalmar , Sörfeldt Arvid , Kuylenstierna Dan 

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

JOURNAL=Frontiers in Physiology

VOLUME=Volume 16 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/physiology/articles/10.3389/fphys.2025.1712475

DOI=10.3389/fphys.2025.1712475

ISSN=1664-042X

ABSTRACT=IntroductionThis 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 (CP) model parameters.MethodsTwelve 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 a modified expression of the three-parameter critical power model.ResultsThe derived power-duration relationships were significantly different between the two inclines. At an 8° incline, the estimated work capacity above CP (i.e., W′) was more than two 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.DiscussionThe 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.