Modeling the Relationship between Velocity and Time to Fatigue in Elite Male Long-track Speed Skaters

Several mathematical models have been used to describe the relationship between exercise intensity and time to fatigue. PURPOSE: The purpose of this study was to evaluate different methods of describing the mathematical relationship between skating velocity and time to fatigue in elite male speed skaters. METHODS: Competition results (times) for the top 11 finishers at the 2003 Men's Long-track Speed Skating All-round World Championships were used. Data for the first 100 m were excluded, due to the dissociation between metabolic demand and velocity during the acceleration phase. To determine critical velocity (CV), anaerobic work capacity (AWC), and maximal velocity (Vmax), times for the four corrected distances (400, 1400, 4900, and 9900 m) were fitted to three mathematically-equivalent 2-parameter models (1a: time = AWC · (velocity - CV)-1; 1b: distance = (time · CV) + AWC; 1c: velocity = CV + (AWC · time-1)) and two different 3-parameter models (2: time = AWC · (velocity - CV)-1 - AWC · (Vmax - CV)-1; 3: velocity = CV + AWC · (1- e- (time / tau)) · time-1). RESULTS: The 2-parameter models (1a-1c) produced significantly different values (p<0.001) for CV and AWC, and thus were deemed unacceptable for describing the velocity-time relationship. The 3-parameter models (2-3) resulted in high values for coefficients of variation (R2 > 0.999) and small values for SEE for AWC and CV (∼10% and <1% of the values for AWC and CV, respectively); however, values generated by the models differed (p<0.001): CV (10.9 ± 0.2 and 11.2 ± 0.2 m·s-1) and AWC (727 ± 179 and 404 ± 89 m) for models 2 and 3 respectively. CONCLUSION: The all-round event in competitive speed skating provides a unique and excellent source of data for use in evaluating models of the velocity - time relationship. In no other major sport does each male participant provide four timed all-out efforts with performance times ranging from <1 min to 15 min; and laboratory testing rarely elicits the level of effort achieved in competition. Only the 3-parameter models described the velocity and time to fatigue relationship well, and therefore these models might be useful in evaluating performance-related physiological characteristics (CV, AWC, and Vmax) in elite male speed skaters.