Experimental validation of the 3-parameter critical power model in cycling

The three-parameter model of critical power (3-p) implies that in the severe exercise intensity domain time to exhaustion (T_lim) decreases hyperbolically with power output starting from the power asymptote (critical power, ẇ_cr) and reaching 0 s at a finite power limit (ẇ₀) thanks to a negative time asymptote (k). We aimed to validate 3-p for short T_lim and to test the hypothesis that ẇ₀ represents the maximal instantaneous muscular power.

Ten subjects performed an incremental test and nine constant-power trials to exhaustion on an electronically braked cycle ergometer. All trials were fitted to 3-p by means of non-linear regression, and those with T_lim greater than 2 min also to the 2-parameter model (2-p), obtained constraining k to 0 s. Five vertical squat jumps on a force platform were also performed to determine the single-leg (i.e., halved) maximal instantaneous power.

T_lim ranged from 26 ± 4 s to 15.7 ± 4.9 min. In 3-p, with respect to 2-p, ẇ_cr was identical (177 ± 26 W), while curvature constant W' was higher (17.0 ± 4.3 vs 15.9 ± 4.2 kJ, p < 0.01). 3-p-derived ẇ₀ was lower than single-leg maximal instantaneous power (1184 ± 265 vs 1554 ± 235 W, p < 0.01).

3-p is a good descriptor of the work capacity above ẇ_cr up to T_lim as short as 20 s. However, since there is a discrepancy between estimated ẇ₀ and measured maximal instantaneous power, a modification of the model has been proposed.