A mathematical model for power output in rowing on an ergometer

A mathematical model relating power output of rower to stroke rate on an ergometer (the Concept II Indoor Rower TM, Model C) is studied. The model is used to analyse the ergometer performance of a particular rower. It is determined that he can be more efficient (i.e. decrease power output while maintaining fixed velocity) by decreasing stroke rate, but at the expense of increasing force during the drive. It is also shown that he can be more efficient by increasing the drag factor (using higher vent setting) without increasing force. Dependence of power output on rowing style (the shape of the force curve) is also examined. It is shown that variation of force during the drive has little effect on efficiency, but efficiency is reduced by asymmetry of the force curve that favours the legs.     

400～800 m跑运动员极量负荷后的最佳恢复强度

通过16名400～800m跑项目运动员在程控跑台上完成400m跑极量负荷使运动员机体内堆积大量的乳酸,然后分别测定各种不同强度的恢复性运动对血乳酸(HLa)清除速率的影响,观察了血乳酸清除速率与恢复性运动强度的关系,从中寻找快速清除血乳酸消除疲劳的最佳强度范围.实验结果表明清除血乳酸最快的强度为400m最大强度的50%～65%之间,心率在145～165次/min之间.研究表明,最佳恢复性运动强度是400m最大强度的60%,心率为150～160次/min,此时16名运动员的跑速为(4.21±0.67)m/s,与受试者的跑速无氧阈值(4.35±0.88)m/s无显著差异(P＞0.05).     

Changes in short-term power output in 10- to 12-year-olds

In this study, we used multi-level regression modelling to assess the influence of age, sex, body size, skinfold thicknesses, maturity, thigh muscle volume and isokinetic leg strength on the development of load- and inertia-adjusted peak (1 s) and mean power (30 s) determined using the Wingate anaerobic test. Fifteen males and 19 females were measured twice, first aged 10.0 +/- 0.3 years and then aged 11.8 +/- 0.3 years. Initial models identified body mass and height as significant explanatory variables (P < 0.05) for peak power and mean power, with an additional age effect for the former. No significant differences between the sexes or maturity effects were observed for either peak or mean power (P > 0.05). The introduction of sum of skinfolds improved the fit of the model and rendered the height term non-significant for both peak and mean power (P> 0.05). An age effect became apparent for mean power. When isokinetic leg strength and thigh muscle volume were entered into the model, the latter exerted a significant effect on both peak and mean power (P< 0.05), whereas isokinetic leg strength was not a significant explanatory variable for either (P> 0.05). In conclusion, thigh muscle volume exerts a positive influence on young people's short-term power output, which is additional to the effects of body mass, sum of skinfolds and age.     

Scaling of upper-body power output to predict time-trial roller skiing performance

Abstract

The purpose of the present study was to establish the most appropriate allometric model to predict mean skiing speed during a double-poling roller skiing time-trial using scaling of upper-body power output. Forty-five Swedish junior cross-country skiers (27 men and 18 women) of national and international standard were examined. The skiers, who had a body mass (m) of 69.3 ± 8.0 kg (mean ± s), completed a 120-s double-poling test on a ski ergometer to determine their mean upper-body power output (W). Performance data were subsequently obtained from a 2-km time-trial, using the double-poling technique, to establish mean roller skiing speed. A proportional allometric model was used to predict skiing speed. The optimal model was found to be: Skiing speed = 1.057 · W ^0.556 · m ^?0.315, which explained 58.8% of the variance in mean skiing speed (P < 0.001). The 95% confidence intervals for the scaling factors ranged from 0.391 to 0.721 for W and from ?0.626 to ?0.004 for m. The results in this study suggest that allometric scaling of upper-body power output is preferable for the prediction of performance of junior cross-country skiers rather than absolute expression or simple ratio-standard scaling of upper-body power output.     

Evaluating the contribution of lower extremity kinetics to whole body power output during the power snatch

This study evaluated the contribution of lower extremity (hip, knee and ankle) net joint torques (NJT) to whole body power (WBP) output during the power snatch (PS). Ten experienced weightlifters (five males and five females) performed five trials of the PS with 60% of one repetition maximum. Lower extremity NJT and WBP were extracted through a three-dimensional motion analyses and used for data analyses. Pearson correlation coefficients were obtained to observe the relationship between lower extremity NJT and WBP. Multiple-regression (stepwise) analyses was also conducted to evaluate the contribution of lower extremity NJT to WBP during the PS with the hip, knee and ankle NJT being the independent variables. Hip NJT was characterised as a significant positive correlation with WBP (r = 0.47, p < 0.01), while knee NJT showed a significant negative correlation with WBP (r = ?0.34, p < 0.05). A significant inter-correlation was also observed between hip NJT and knee NJT (r = ?0.66, p < 0.01). Hip NJT was identified as a significant contributor to WBP during the PS. Practically, this study suggested that training skills allowing weightlifters to utilise hip extensor muscle action would help to improve WBP during the PS.     

Cycling power output produced during flat and mountain stages in the Giro d'Italia: A case study

Abstract

Until recently, the physiological demands of cycling competitions were mostly reflected by the measurement of heart rate and the indirect estimation of exercise intensity. The purpose of this case study was to illustrate the varying power output of a professional cyclist during flat and mountain stages of a Grand Tour (Giro d'Italia). Nine stage recordings of a cyclist of the 2005 Giro d'Italia were monitored using a mobile power measurement device (SRM Trainingssystem, Julich, Germany), which recorded direct power output and heart rate. Stages were categorized into flat (n = 5) and mountain stages (n = 4). Data were processed electronically, and the overall mean power in flat and mountain stages and maximal mean power for various durations were calculated. Mean power output was 132 W ± 26 (2.0 W · kg^?1 ± 0.4) for the flat and 235 W ± 10 (3.5 W · kg^?1 ± 0.1) for the mountain stages. Mountain stages showed higher maximal mean power (367 W) for longer durations (1800 s) than flat stages (239 W). Flat stages are characterized by a large variability of power output with short bursts of high power and long periods with reduced intensity of exercise, whereas mountain stages mostly require submaximal, constant power output over longer periods.     

A comparison of methods to determine bilateral asymmetries in vertical leg stiffness

Whilst the measurement and quantification of vertical leg stiffness (K_vert) asymmetry is of important practical relevance to athletic performance, literature investigating bilateral asymmetry in K_vert is limited. Moreover, how the type of task used to assess K_vert may affect the expression of asymmetry has not been properly determined. Twelve healthy males performed three types of performance tasks on a dual force plate system to determine K_vert asymmetries; the tasks were (a) bilateral hopping, (b) bilateral drop jumping and (c) unilateral drop jumping. Across all the three methods, K_vert was significantly different between compliant and stiff limbs (P < 0.001) with a significant interaction effect between limb and method (P = 0.005). Differences in K_vert between compliant and stiff limbs were ?5.3% (P < 0.001), ?21.8% (P = 0.007) and ?15.1% (P < 0.001) for the bilateral hopping, bilateral drop jumping and unilateral drop jumping methods, respectively. All the three methods were able to detect significant differences between compliant and stiff limbs, and could be used as a diagnostic tool to assess K_vert asymmetry. Drop jumping tasks detected larger K_vert asymmetries than hopping, suggesting that asymmetries may be expressed to a greater extent in acyclic, maximal performance tasks.     

A comparison of methods to determine maximal accumulated oxygen deficit in running

Abstract

The aim of this study was to compare maximal accumulated oxygen deficit (hereafter O₂ deficit) estimated from the methods of Whipp et al. (1986 Whipp, B. J., Ward, S. A. and Wasserman, K. 1986. Respiratory markers of the anaerobic threshold. Advances in Cardiology, 35: 47–64. [Crossref], [PubMed] , [Google Scholar]), Medbo et al. (1988 Medbo, J. I., Mohn, A. C., Tabata, I., Bahr, R., Vaage, O. and Sejersted, O. M. 1988. Anaerobic capacity determined by maximal accumulated O₂ deficit. Journal of Applied Physiology, 64: 50–60. [PubMed], [Web of Science ®] , [Google Scholar]), and Hill et al. (1998 Hill, D. W., Ferguson, C. S. and Ehler, K. L. 1998. An alternative method to determine maximal accumulated O₂ deficit in runners. European Journal of Applied Physiology, 79: 114–117. [Crossref], [Web of Science ®] , [Google Scholar]) to determine whether they agree sufficiently to be used interchangeably. Nineteen moderately to highly trained endurance runners first performed an incremental test to exhaustion for the determination of maximal oxygen uptake ([Vdot]O_2max) and peak treadmill speed, followed by six randomly ordered constant-speed tests at 95, 100, 105, 110, 110, and 120% of peak treadmill speed. All tests were separated by at least 72 h and were performed within 4 weeks. The method of Whipp produced an O₂ deficit estimate that was lower than that derived from the method of Hill or Medbo (bias ± 95% limits of agreement: ?29.6 ± 36.6 and ?26.1 ± 32.8 ml · kg^?1, respectively; P < 0.001). The O₂ deficit did not differ between the methods of Hill and Medbo (bias ± 95% limits of agreement: 3.5 ± 41.6 ml · kg^?1; n.s.). However, poor correlations (0.21 < r < 0.33; n.s.) together with wide limits of agreement between O₂ deficit estimates (70 – 80% of the mean response) clearly question using these methods interchangeably.     

A comparison of methods to determine maximal accumulated oxygen deficit in running

The aim of this study was to compare maximal accumulated oxygen deficit (hereafter O2 deficit) estimated from the methods of Whipp et al. (1986), Medbo et al. (1988), and Hill et al. (1998) to determine whether they agree sufficiently to be used interchangeably. Nineteen moderately to highly trained endurance runners first performed an incremental test to exhaustion for the determination of maximal oxygen uptake ([Vdot]O(2max)) and peak treadmill speed, followed by six randomly ordered constant-speed tests at 95, 100, 105, 110, 110, and 120% of peak treadmill speed. All tests were separated by at least 72 h and were performed within 4 weeks. The method of Whipp produced an O(2) deficit estimate that was lower than that derived from the method of Hill or Medbo (bias +/- 95% limits of agreement: -29.6 +/- 36.6 and -26.1 +/- 32.8 ml . kg(-1), respectively; P < 0.001). The O2 deficit did not differ between the methods of Hill and Medbo (bias +/- 95% limits of agreement: 3.5 +/- 41.6 ml . kg(-1); n.s.). However, poor correlations (0.21 < r < 0.33; n.s.) together with wide limits of agreement between O2 deficit estimates (70 - 80% of the mean response) clearly question using these methods interchangeably.     

Effects of external loading on power output in a squat jump on a force platform: A comparison between strength and power athletes and sedentary individuals

The aim of this study was to determine the effects of external loading on power output during a squat jump on a force platform in athletes specializing in strength and power events (6 elite weight-lifters and 16 volleyball players) and in 20 sedentary individuals. Instantaneous power was computed from time-force curves during vertical jumps with and without an external load (0, 5 or 10 kg worn in a special vest). The jumps were performed from a squat position, without lower limb counter-movement or an arm swing. Peak instantaneous power corresponded to the highest value of instantaneous power during jumping. Average power throughout the push phase of the jump was also calculated. A two‐way analysis of variance showed significant interactions between the load and group effects for peak instantaneous power ( P < 0.01) and average power ( P < 0.001). Peak instantaneous power decreased significantly in sedentary individuals when moderate external loads were added. The peak instantaneous power at 0 kg was greater than that at 5 and 10 kg in the sedentary individuals. In contrast, peak instantaneous power was independent of load in the strength and power athletes. Mean power at 0 kg was significantly lower than at 5 kg in the athletes; at 0 kg it was significantly higher than at 10 kg in the sedentary males and at 5 and 10 kg in the sedentary females. In all groups, the force corresponding to peak instantaneous power increased and the velocity corresponding to peak instantaneous power decreased with external loading. The present results suggest that the effects of external loading on peak instantaneous power are not significant in strength and power athletes provided that the loads do not prevent peak velocity from being higher than the velocity that is optimal for maximal power output.     

An accurate VO2max nonexercise regression model for 18-65-year-old adults

The purpose of this study was to develop a regression equation to predict maximal oxygen uptake (VO2max) based on nonexercise (N-EX) data. All participants (N = 100), ages 18-65 years, successfully completed a maximal graded exercise test (GXT) to assess VO2max (M = 39.96 mL x kg(-1) x min(-1), SD = 9.54). The N-EX data collected just before the maximal GXT included the participant's age; gender; body mass index (BMI); perceived functional ability (PFA) to walk, jog, or run given distances; and current physical activity (PA-R) level. Multiple linear regression generated the following N-EX prediction equation (R = .93, SEE = 3.45 mL x kg(-1) x min(-1), % SEE = 8.62): VO2max (mL x kg(-1) x min(-1)) = 48.0730 + (6.1779 x gender; women = 0, men = 1) - (0. 2463 x age) - (0.6186 x BMI) + (0.7115 x PFA) + (0.6709 x PA-R). Cross validation using PRESS (predicted residual sum of squares) statistics revealed minimal shrinkage (R(p) = .91 and SEE(p) = 3.63 mL x kg(-1) x min(-1)); thus, this model should yield acceptable accuracy when applied to an independent sample of adults (ages 18-65 years) with a similar cardiorespiratory fitness level. Based on standardized beta-weights, the PFA variable (0.41) was the most effective at predicting VO2max followed by age (-0.34), gender (0.33), BMI (-0.27), and PA-R (0.16). This study provides a N-EX regression model that yields relatively accurate results and is a convenient way to predict VO2max in adult men and women.     

A mathematical model for simulating cycling: applied to track cycling

A review of existing mathematical models for velodrome cycling suggests that cyclists and cycling coaches could benefit from an improved simulation tool. A continuous mathematical model for cycling has been developed that includes calculated slip and steering angles and, therefore, allows for resulting variation in rolling resistance. The model focuses on aspects that are particular, but not unique, to velodrome cycling but could be used for any cycling event. Validation of the model is provided by power meter, wheel speed and timing data obtained from two different studies and eight different athletes. The model is shown to predict the lap by lap performance of six elite female athletes to an average accuracy of 0.36% and the finishing times of two elite athletes competing in a 3-km individual pursuit track cycling event to an average accuracy of 0.20%. Possible reasons for these errors are presented. The impact of speed on steering input is discussed as an example application of the model.     

A modified TRIMP to quantify the in-season training load of team sport players

The aims of the study were to modify the training impulse (TRIMP) method of quantifying training load for use with intermittent team sports, and to examine the relationship between this modified TRIMP (TRIMP(MOD)) and changes in the physiological profile of team sport players during a competitive season. Eight male field hockey players, participating in the English Premier Division, took part in the study (mean+/-s: age 26+/-4 years, body mass 80.8+/-5.2 kg, stature 1.82+/-0.04 m). Participants performed three treadmill exercise tests at the start of the competitive season and mid-season: a submaximal test to establish the treadmill speed at a blood lactate concentration of 4 mmol . l(-1); a maximal incremental test to determine maximal oxygen uptake ([V]O(2max)) and peak running speed; and an all-out constant-load test to determine time to exhaustion. Heart rate was recorded during all training sessions and match-play, from which TRIMP(MOD) was calculated. Mean weekly TRIMP(MOD) was correlated with the change in [V]O(2max) and treadmill speed at a blood lactate concentration of 4 mmol x l(-1) from the start of to mid-season (P<0.05). The results suggest that TRIMP(MOD) is a means of quantifying training load in team sports and can be used to prescribe training for the maintenance or improvement of aerobic fitness during the competitive season.     

Simulation of puck flight to determine spectator safety for various ice hockey board heights

The boards of ice hockey rinks are equipped with protective glass to prevent the spectators from being hit by the puck. According to international rules, the minimum height of the board with protective glass is 197 cm. This is not high enough to protect the spectators from puck-related injuries, and severe accidents have occurred in the past. This study investigates what increase in the height of the safety glass is necessary to reduce the risk of severe puck-related injuries to spectators. Puck flights towards the safety board are simulated, based on initial take-off conditions of the puck, by top-level players. The simulations show that increasing the security glass from a board height without any protective glass of 117 cm to a total band height of 380 cm will lower the relative frequency of shots with a potential to hit a spectator by 80%. The maximum velocity of such dangerous shots was only slightly decreased from 28.4 m s⁻¹ to 25.2 m s⁻¹ for the same difference in band height. However, the reduced number of dangerous shots does not protect the spectators completely from injuries. The simulation model suggests that a safety wall height of 10.8 m leads to a 100% reduction in all outgoing shots.     

A modified TRIMP to quantify the in-season training load of team sport players

Abstract

The aims of the study were to modify the training impulse (TRIMP) method of quantifying training load for use with intermittent team sports, and to examine the relationship between this modified TRIMP (TRIMP_MOD) and changes in the physiological profile of team sport players during a competitive season. Eight male field hockey players, participating in the English Premier Division, took part in the study (mean±s: age 26±4 years, body mass 80.8±5.2 kg, stature 1.82±0.04 m). Participants performed three treadmill exercise tests at the start of the competitive season and mid-season: a submaximal test to establish the treadmill speed at a blood lactate concentration of 4 mmol · l^?1; a maximal incremental test to determine maximal oxygen uptake ([Vdot]O_2max) and peak running speed; and an all-out constant-load test to determine time to exhaustion. Heart rate was recorded during all training sessions and match-play, from which TRIMP_MOD was calculated. Mean weekly TRIMP_MOD was correlated with the change in [Vdot]O_2max and treadmill speed at a blood lactate concentration of 4 mmol · l^?1 from the start of to mid-season (P<0.05). The results suggest that TRIMP_MOD is a means of quantifying training load in team sports and can be used to prescribe training for the maintenance or improvement of aerobic fitness during the competitive season.