Mid Sweden University

INTRODUCTION:Dynamic friction is an important parameter in cross-country skate skiing. A reduction of the dynamic frictional coefficient (µ) with 47%can increase the time to exhaustion with 50% when roller-ski skating [1]. With normal ski preparation µ may vary up to 15% due to theski base texture [2]. To isolate the impact of µ on race time, numerical simulations with a power-balance model could be used aspreviously demonstrated [3],[4]. Field measurements have provided more detailed relationships for propulsive power and drag areawith the skating sub-techniques, allowing more reliable simulations [5]. Thus, the aim of this study was to examine the impact ofdifferent dynamic frictional coefficients on the required time to complete a cross-country skate skiing.METHODS:A power balance model for cross-country skate skiing was implemented and solved in Matlab for skiers with body masses of 70, 80and 90 kg respectively. Propulsive power was modelled as a function of speed, acceleration and body mass [5]. Additionally, fivevalues of µ and three wind conditions were examined, giving a total of 45 combinations. These were all simulated on two differentcourses. Total race times were taken from a 15.6 km race (5 laps of the 3 km biathlon race course in Östersund) imported fromGPS-data. Speeds at specific inclination angles were taken from a fictional course with sections of constant inclination angle (meanspeed downhill, steady state speed on the uphill and flat). In the 15.6 km race the ambient winds were aligned to give either 4 m/stailwind in the majority of downhill sections and headwind uphill (4SW), the opposite (4NE) or zero wind. In the fictional course windwas either 4 m/s tailwind, 4 m/s headwind or zero through the entire race.RESULTS:The mean total race time in the 15.6 km race was 2240.7±141.1 s, with shorter race times for the heavier skier (90 kg 19.2±1.3 s < 80kg 22.2±1.3 s < 70 kg) and for tailwind uphill (4NE 5.0±2.0 s < zero wind 5.9±2.0 < 4SW). Changing µ from 0.013 to 0.015 increasedthe total race time for the 70, 80 and 90 kg skiers with 33.6 s (1.53%), 34.0 s (1.57%) and 34.0 s (1.58%) respectively. Changing µfrom 0.025 to 0.027 gave 34.6s (1.44%), 34.2s (1.44%) and 35.1s (1.49%) increased race time for the 70, 80 and 90kg skiersrespectively. The changes in speed from the 70 to 80 to 90 kg skiers were all below 0.43% on the uphill and between 0.70 and 1.53%on the flat and downhill. Changing µ gave largest change in speed for moderate downhill (e.g. 2.15%, µ 0.015 to 0.013) followed byflat (1.29%) and moderate uphill (1.22%).CONCLUSION:An absolute change in µ of 0.002, e.g. a different preparation of the skis, have slightly larger impact on faster (µ~0.014) than slowersnow (µ~0.026) but in both cases could turn the tide in a close race. This change in race time is generated mostly in sections withmoderate or no inclination angle.

Purpose: To develop a method for individual parameter estimation of four hydraulic-analogy bioenergetic models and to assess the validity and reliability of these models’ prediction of aerobic and anaerobic metabolic utilization during sprint roller-skiing. Methods: Eleven elite cross-country skiers performed two treadmill roller-skiing time trials on a course consisting of three flat sections interspersed by two uphill sections. Aerobic and anaerobic metabolic rate contributions, external power output, and gross efficiency were determined. Two versions each (fixed or free maximal aerobic metabolic rate) of a two-tank hydraulic-analogy bioenergetic model (2TM-fixed and 2TM-free) and a more complex three-tank model (3TM-fixed and 3TM-free) were programmed into MATLAB. The aerobic metabolic rate (MRae) and the accumulated anaerobic energy expenditure (Ean,acc) from the first time trial (STT1) together with a gray-box model in MATLAB, were used to estimate the bioenergetic model parameters. Validity was assessed by simulation of each bioenergetic model using the estimated parameters from STT1 and the total metabolic rate (MRtot) in the second time trial (STT2). Results: The validity and reliability of the parameter estimation method based on STT1 revealed valid and reliable overall results for all the four models vs. measurement data with the 2TM-free model being the most valid. Mean differences in model-vs.-measured MRae ranged between -0.005 and 0.016 kW with typical errors between 0.002 and 0.009 kW. Mean differences in Ean,acc at STT termination ranged between −4.3 and 0.5 kJ and typical errors were between 0.6 and 2.1 kJ. The root mean square error (RMSE) for 2TM-free on the instantaneous STT1 data was 0.05 kW for MRae and 0.61 kJ for Ean,acc, which was lower than the other three models (all P &lt; 0.05). Compared to the results in STT1, the validity and reliability of each individually adapted bioenergetic model was worse during STT2 with models underpredicting MRae and overpredicting Ean,acc vs. measurement data (all P &lt; 0.05). Moreover, the 2TM-free had the lowest RMSEs during STT2. Conclusion: The 2TM-free provided the highest validity and reliability in MRae and Ean,acc for both the parameter estimation in STT1 and the model validity and reliability evaluation in the succeeding STT2. 

Purpose

The aim of this study was to develop and validate a bioenergetic model describing the dynamic behavior of the alactic, lactic, and aerobic metabolic energy supply systems as well as different sources of the total metabolic energy demand.

Methods

The bioenergetic supply model consisted of terms for the alactic, lactic, and aerobic system metabolic rates while the demand model consisted of terms for the corresponding metabolic rates of principal cycling work, pulmonary ventilation, and accumulated metabolites. The bioenergetic model was formulated as a system of differential equations and model parameters were estimated by a non-linear grey-box approach, utilizing power output and aerobic metabolic rate (MRae) data from fourteen cyclists performing an experimental trial (P2) on a cycle ergometer. Validity was assessed by comparing model simulation and measurements on a similar follow-up experimental trial (P3).

Results

The root mean square error between modelled and measured MRae was 61.9 ± 7.9 W and 79.2 ± 30.5 W for P2 and P3, respectively. The corresponding mean absolute percentage error was 8.6 ± 1.5% and 10.6 ± 3.3% for P2 and P3, respectively.

Conclusion

The validation of the model showed excellent overall agreement between measured and modeled MRae during intermittent cycling by well-trained male cyclist. However, the standard deviation was 38.5% of the average root mean square error for P3, indicating not as good reliability.