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

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 ( $CP$ ) model parameters.

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 a modified expression of the three-parameter critical power model.

The derived power-duration relationships were significantly different between the two inclines. At an 8° incline, the estimated work capacity above $CP$ (i.e., $W^{\text{'}}$ ) was more than two times higher than at a 2° incline ( $24.87\pm 8.75$ kJ vs. $7.07\pm 1.61$ kJ, respectively; $Z=3.06$ , $P=0.002$ , $r_{rb}=0.88$ ), which was partly explained by an increased anaerobic power capacity (i.e., $P_{an}$ = $4.82\pm 0.64$ W $\cdot$ kg^-1 vs. $1.67\pm 0.34$ W $\cdot$ kg^-1, respectively; $Z=3.06$ , $P=0.002$ , $r_{rb}=0.88$ ). Although $CP$ estimates differed by approximately $16\%$ between the two inclines on a group level ( $2.78\pm 0.22$ W $\cdot$ kg^-1 vs. $2.39\pm 0.74$ W $\cdot$ kg^-1 at a 2° and at an 8° incline, respectively), a moderate non-significant effect of incline was observed with large individual variances ( $Z=1.88$ , $P=0.06$ , $r_{rb}=0.54$ ). The incline had a non-significant effect on the time constant parameter estimates ( $Z=1.57$ , $P=0.12$ , $r_{rb}=0.45$ ), yet inter-individual variation remained considerable.

The findings demonstrate that in cross-country skiing, both $W^{\text{'}}$ and $P_{an}$ are highly incline-dependent, showing markedly higher values at steeper gradients. Moreover, the variability observed in $CP$ and $W^{\text{'}}$ 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 $W^{\text{'}}$ 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.