Mathematical modeling of the velocity-time relationship in rowing - Franchini, E.; Mello, F. C.; Kennedy, M.; Hill, D. W. (Book of Abstracts - 9th Annual Congress European College of Sport Science, July 3-6, 2004, Clermont-Ferrand, France, 2004)
Introduction The hyperbolic relationship between power and time to fatigue is defined by two parameters, critical power (Pcritical) and anaerobic work capacity (AWC). For rowing, power is replaced by velocity and Pcritical is replaced by Vcritical. Bishop et al. (1998) have shown that this critical power model adequately describes the power-time or velocity-time relationship over a range of exercise durations of ~3 to >10 min, and they suggested that that shorter durations should be avoided because of the confounding effect of VO2 kinetics and incomplete use of anaerobic reserves in short exercise bouts. Despite their directive, when the concept was first applied to rowing, durations were as short as ~30 s and no longer than ~6.5 min, i.e., for the 2000-m distance (Kennedy and Bell, 2000). The purpose of this study was to evaluate modeling applied to durations that were advocated by Bishop et al. (1998). Methods Eight men performed exhaustive rowing ergometer tests over distances of 1000 m (mean ± SD time = 193 ± 7 s), 1500 m (306 ± 7 s), 2000 m (411 ± 13 s), and an individually-determined distance (3231 ± 804 m; 679 ± 168 s), referred to herein as 3000 m. Data from the 1000-1500-2000-3000 distances or only the 1000-1500-2000 distances were fit to three mathematically-equivalent equations: (1) hyperbolic, velocity-time: time to fatigue = AWC / (velocity - Vcritical) (2) linear, distance-time: distance = (time to fatigue · Vcritical) + AWC (3) linear, velocity-(1/time): velocity = Vcritical + (AWC / time to fatigue). The values for Vcritical and AWC were compared using a two-way (equation x distances) repeated measures ANOVA. In addition, equation 2 was used to describe the velocity-time relationship using data from only the 1000 and 1500 trials (the three equations give identical values when only two data points are used). The values for Vcritical and AWC were compared using a one-way ANOVA, with repeated measures across distances. Results of the two-way ANOVA revealed that, when the 3000 m distance was excluded from the modeling process, values for Vcritical and AWC generated by the three equations tended to differ (P = 0.06 and P = 0.08, respectively). In addition, the SEE associated with Vcritical and AWC were consistently greater (both P < 0.01) when the 3000 m was not used. However, values of the parameters from each equation were not significantly affected by exclusion of the 3000 m. Results of the one-way ANOVA revealed that restricting modeling to only the 1000 m and 1500 m distances resulted in lower (P < 0.01) estimates of Vcritical and higher (P < 0.01) estimates of AWC. Discussion / Conclusions It has been reported that, in order to accurately describe the velocity-time relationship for competitive rowers, it is necessary to include distances up to and including race distance, i.e., 2000 m (Hill et al., 2003). In the present study, based on the similarity of estimates from the three equations and smaller SEE for each estimate when the 3000 m distance was included, it is concluded that using this longer distance enhances the precision and validity of the parameter estimates. Consistent with our earlier results, not including the 2000 m distance dramatically affected the values of the parameters. If a rowing Vcritical is to have the same physiological significance as a running Vcritical or a cycle ergometer Pcritical, it must be calculated with the inclusion of a 2000 m (or longer) trial and with the exclusion of very short trials. However, from a practical standpoint, limiting testing to only 1000-1500-2000 produces acceptable parameter estimates from each equation, although choice of equation becomes an issue.