ORIGINAL RESEARCH published: 20 November 2018 doi: 10.3389/fphys.2018.01631 Propulsive Power in Cross-Country Skiing: Application and Limitations of a Novel Wearable Sensor-Based Method During Roller Skiing Øyvind Gløersen 1,2*, Thomas Losnegard 2, Anders Malthe-Sørenssen 1,3, Dag Kristian Dysthe 1 and Matthias Gilgien 2,4 1 Condensed Matter Physics, Department of Physics, University of Oslo, Oslo, Norway, 2 Department of Physical Performance, Norwegian School of Sports Sciences, Oslo, Norway, 3 Department of Physics, Center for Computing in Science Education, University of Oslo, Oslo, Norway, 4 Department of Sport Science, Alpine Skiing, Norwegian Ski Federation, Oslo, Norway Cross-country skiing is an endurance sport that requires extremely high maximal aerobic power. Due to downhill sections where the athletes can recover, skiers must also have the ability to perform repeated efforts where metabolic power substantially exceeds maximal aerobic power. Since the duration of these supra-aerobic efforts is often in the order of seconds, heart rate, and pulmonary VO2 do not adequately reflect instantaneous Edited by: metabolic power. Propulsive power (Pprop) is an alternative parameter that can be used Gregoire P. Millet, to estimate metabolic power, but the validity of such calculations during cross-country Université de Lausanne, Switzerland skiing has rarely been addressed. The aim of this study was therefore twofold: to develop Reviewed by: a procedure using small non-intrusive sensors attached to the athlete for estimating H-C Holmberg, Mid Sweden University, Sweden Pprop during roller-skiing and to evaluate its limits; and (2) to utilize this procedure to William Bertucci, determine the Pprop generated by high-level skiers during a simulated distance race. Université de Reims Champagne Ardenne, France Eight elite male cross-country skiers simulated a 15 km individual distance race on roller *Correspondence: skis using ski skating techniques on a course (13.5 km) similar to World Cup skiing Øyvind Gløersen courses. Pprop was calculated using a combination of standalone and differential GNSS [email protected] measurements and inertial measurement units. The method’s measurement error was Specialty section: assessed using a Monte Carlo simulation, sampling from the most relevant sources of This article was submitted to error. Pprop decreased approximately linearly with skiing speed and acceleration, and Exercise Physiology, −1 was approximated by the equation Pprop(v, v˙) = −0.54·v −0.71·v˙ + 7.26 W·kg . Pprop a section of the journal −1 Frontiers in Physiology was typically zero for skiing speeds >9 m·s , because the athletes transitioned to the −1 Received: 29 June 2018 tuck position. Peak Pprop was 8.35 ± 0.63 W·kg and was typically attained during the Accepted: 29 October 2018 final lap in the last major ascent, while average Pprop throughout the race was 3.35 ± Published: 20 November 2018 −1 0.23 W·kg . The measurement error of Pprop increased with skiing speed, from 0.09 Citation: W·kg−1 at 2.0 m·s−1 to 0.58 W·kg−1 at 9.0 m·s−1. In summary, this study is the first Gløersen Ø, Losnegard T, Malthe-Sørenssen A, Dysthe DK and to provide continuous measurements of Pprop for distance skiing, as well as the first to Gilgien M (2018) Propulsive Power in quantify the measurement error during roller skiing using the power balance principle. Cross-Country Skiing: Application and Limitations of a Novel Wearable Therefore, these results provide novel insight into the pacing strategies employed by Sensor-Based Method During Roller high-level skiers. Skiing. Front. Physiol. 9:1631. doi: 10.3389/fphys.2018.01631 Keywords: work rate, force, energy, GNSS, GPS, validity Frontiers in Physiology | www.frontiersin.org 1 November 2018 | Volume 9 | Article 1631 Gløersen et al. Propulsive Power During Distance Skiing INTRODUCTION demands experienced by a competitive skier. Therefore, several studies have attempted to calculate Pprop during cross-country Current cross-country ski races can be categorized into two main skiing, based either on position measurements (Sandbakk et al., events; sprint skiing (<1.8km) and distance skiing (>10 and 2011; Swarén and Eriksson, 2017), or simulation of skiing 15 km, female and males respectively). Furthermore, races can performance (Moxnes and Hausken, 2008; Carlsson et al., 2011; be held using free technique, where athletes typically choose to Moxnes et al., 2013, 2014; Sundström et al., 2013). These studies use ski skating techniques, or as classic technique races, where all use the principle of power balance, as outlined by van Ingen skiers are restricted to specific sub-techniques (herringbone, Schenau and Cavanagh (1990). However, no studies are available diagonal stride, double poling, kick double poling). Due to these where Pprop has been measured continuously throughout a cross- restrictions, the average race speed in free technique events is country ski race with a duration longer than sprint skiing. typically about 10% higher than in classical technique races Furthermore, no previous studies have critically evaluated the (Bolger et al., 2015). Regardless of events, the race course accuracy achieved when applying the power balance principle to regulations specify that courses should contain approximately cross-country skiing. The aims of this study were (1) to develop a equal parts of uphill, downhill, and flat terrain, to “test the skier procedure for estimating the propulsive power generated during in a technical, tactical and physical manner” (FIS Cross-Country roller-skiing using small non-intrusive sensors (GNSS and IMUs) Homologation Manual, June 2017). attached to the athlete and evaluate its limitations; and (2) Regardless of race distance, cross-country skiing is an to utilize this procedure to determine the propulsive power endurance sport that demands an exceptionally high aerobic generated by high-level skiers during a simulated distance race. energy turnover, in addition to high movement efficacy. This is underlined by the fact that elite cross-country skiers have Theoretical Background among the highest maximal oxygen consumptions of any sports As stated by van Ingen Schenau and Cavanagh (1990), the Pprop (Sandbakk and Holmberg, 2014; Haugen et al., 2017), typically is equal to the rate of change in mechanical energy (Emech) of −1 −1 ranging from 80 to 90 and 70 to 80 mL·kg ·min for world the system and the work done on the environment (Wenv). In class males and females, respectively (Ingjer, 1991; Losnegard cross-country skiing Pprop is customarily estimated by modeling and Hallén, 2014; Sandbakk et al., 2016a). In addition, several the skier and his/her equipment as a point mass (Moxnes and studies also indicate substantial anaerobic turnover rates during Hausken, 2008; Carlsson et al., 2011; Moxnes et al., 2013, 2014; a race, a phenomenon attributed to the large variations in course Sundström et al., 2013; Swarén and Eriksson, 2017). Under this inclination. Moreover, skiers typically choose to increase their assumption, the mechanical energy is the sum of translational metabolic power in uphill terrain (Karlsson et al., 2018), often kinetic energy and the gravitational potential energy. Work done attaining a metabolic power that substantially exceeds their peak on the environment is primarily due to ski/snow-friction forces aerobic power (estimated at 110–160% of VO2peak Norman and (or rolling resistance, denoted Ff) and the aerodynamic drag force Komi, 1987; Sandbakk et al., 2011; Karlsson et al., 2018). These (Fd). This is summarized in Equation 1: repeated supra-aerobic efforts vary in duration from seconds to ˙ ˙ minutes, and incur an oxygen debt that must be recovered in Pprop = Emech + Wenv (1) the downhill or flat sections (Sandbakk and Holmberg, 2014; mv˙ − F − F − F · v. = g d f Karlsson et al., 2018). Such transient changes in energetic demand Point mass assumption are not well reflected by measurements of pulmonary VO2 or heart rate, because both have a blunted response due to the use of In Equation 1 m refers to the total mass of the system (the local oxygen stores and anaerobic energy pathways. Hence, both sum of body mass and equipment), v is the velocity of the parameters behave as if they passed through a lagged low pass center of mass (COM), v˙ is the COM acceleration, and Fg is the filter and remain high (85–95% of their peak values) throughout gravitational force. Furthermore, the magnitude of the propulsive the race (Welde et al., 2003; Bolger et al., 2015; Karlsson et al., force (Fprop), i.e., the force in the skiing direction that is not 2018). due to gravity or frictional forces (air drag, ski/snow-friction or −1 The combination of high and sustained aerobic energy rolling friction) is calculated using Fprop = Pprop · |v| (Carlsson turnover with repeated supra-aerobic efforts distinguishes cross- et al., 2011). country skiing from many other endurance racing sports, where For skiing and roller skiing applications Ff has commonly the work rate is relatively constant and requires measurement been modeled using the Amonton-Coulomb equations (Carlsson of parameters that reflect the instantaneous energy demands in et al., 2011; Moxnes et al., 2013, 2014; Sundström et al., 2013; a competition setting. A frequently used parameter that often Swarén and Eriksson, 2017). This friction model is attractive corresponds well with instantaneous energy requirement is the because of its simplicity, but it is unable to capture complex propulsive power (Pprop) generated by the athlete. For some ski-snow interactions (Bowden and Hughes, 1939; Buhl et al., endurance sports, like cycling, Pprop can be measured directly, 2001; Theile et al., 2009), and Ff may change considerably over and metabolic energy requirements are approximately linearly the course due to changing snow conditions. This challenge related to Pprop (Ettema and Lorås, 2009). Hence, if Pprop can be can be partially overcome using roller skis, which have a more linked to metabolic power in skiing (Millet et al., 2003; Sandbakk constant coefficient of rolling resistance, except during the warm- et al., 2011; Karlsson et al., 2018), in-field measurements of Pprop up period (Ainegren et al., 2008).