Modeling the Relationship between Velocity and Time to Fatigue in Speed Skating

Abstract

Several mathematical models have been used to describe the relationship between running velocity and time to fatigue. PURPOSE: The purpose of this study was to compare physiological characteristics of elite speed skaters obtained using different mathematical models of the relationship between skating velocity and time to fatigue. METHODS: Times for the top 15 male (mean ± SD: 21–35 yr, 27 ± 4 yr, 183 ± 5 cm, and 82 ± 6 kg) finishers at the 2003 All-round European 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 two-parameter models (1a: time to fatigue = AWC · (velocity - CV)-1; 1b: distance = (time to fatigue · CV) + AWC; 1c: velocity = CV + (AWC · time-1)) and three different three-parameter models (2: time = AWC · (velocity - CV)-1 - AWC · (Vmax - CV)-1; 3: velocity = CV + (Vmax - CV) · (e - (time / tau)); 4: velocity = CV + (tau · (Vmax - CV) · (time)-1 · (1 - e- (time/tau))). In addition, corrected times for the three longest trials (3L) were fitted to the two-parameter models. RESULTS: Exclusion of data from the shortest (400 m) trial resulted in significantly (p < 0.05) higher R2 for 1a-c. For 1c, 3L produced lower (p < 0.001) CV (11.9 ± 0.3 vs. 12.5 ± 0.2 m· s-1) and higher AWC (223 ± 34 vs. 68 ± 12 m) and R2 (0.957 ± 0.028 vs. 0.645 ± 0.072) compared to using all 4 distances. Models 2–4 all produced similar (p > 0.05) coefficient of variation (R2 = 0.999), however, there where small but significant differences (p < 0.01) in CV (2: 11.2 ± 0.4 < 4: 11.4 ± 0.3 < 3: 11.8 ± 0.3 m· s-1) and Vmax (3: 15.1 ± 0.4 < 4: 15.2 ± 0.4 < 2: 15.6 ± 0.7 m· s-1). CONCLUSION: When all 4 distances in the all-round speed skating event are included (including very short trials ∼27 s), models 2–4 but not models 1a-1c appear to describe the velocity and time to fatigue relationship in elite speed skating well. When only the 3L are included, models 1a-c also appear to describe the velocity-time relationship well. This study confirms the use of elite speed skating in the investigation of CV models and suggests that CV models may be useful in evaluating CV, AWC, and Vmax in elite speed skaters.