Summary of experimental design

The study consisted of 2 test days separated by 2–7 days. Test day 1 included three individual ski-skating time trials on a roller-skiing track, while test day 2 consisted of laboratory measurements on a roller-skiing treadmill. The three time trials on test day one were conducted on the same track (length 1560 m) with 35 min recovery in-between trials. The length of the time trial was varied by completing either 1, 2, or 4 laps in a randomized order. The athletes wore a portable gas analyser and position-tracking devices with Global Navigation Satellite System (GNSS) receivers and inertial measurement units (IMU) throughout all time trials. The laboratory testing (test day 2) consisted of six different submaximal loads to establish individual models of skiing economy and a ~ 4.5 min maximal-effort test. The maximum effort test was used to measure \(\dot}\)O2max and calculate maximal accumulated oxygen deficit (MAOD). Finally, oxygen demand during the time trials of test day 1 was estimated by combining propulsive power output (calculated from the position-tracking devices) and the model of skiing economy.

Subjects

Ten competitive cross-country skiers, six males (age 21.4 ± 5.2 years, body mass 74.8 ± 4.7 kg, \(\dot}\)O2max 78.0 ± 2.2 ml∙min−1∙kg−1) and four females (age 24.6 ± 3.8 years, body mass 64.0 ± 7.0 kg, \(\dot}\)O2max 62.4 ± 3.1 ml∙min−1∙kg−1), participated in this study after giving written informed consent. Thirteen participants were initially recruited, but three were discarded due to equipment malfunction. Since we did not expect sex-related differences in the study’s outcome variables, we aggregated all participants in one group for the statistical analysis. Inclusion criteria was previous experience in cross-country skiing competitions at a national level and age > 18 years. The study was conducted in line with the rules of the Helsinki-declaration and was approved by the ethical committee of the Norwegian School of Sport Sciences (application 139) and in agreement with the Norwegian Center for Research Data (application 853,738).

Test day 1: roller-skiing time trials

The racecourse (Holmenkollen, Oslo, Norway) was 1560 m long with height difference 28 m and total climb of 65 m per lap (Fig. 1A and B). Upon arrival, the athletes were informed of the order in which to complete the time trials (1-, 2-, and 4-laps). They were instructed to complete each time trial in the shortest time possible, as if it was a cross-country skiing competition. Warm-up prior to the first time trial consisted of 10 minutes of low-intensity roller skiing, followed by a full run of the racecourse at moderate intensity (warm-up phase, Fig. 1C). After the warm-up phase, the athletes completed two progressive 30 s loads finishing at approximately the 1-lap time-trial intensity, followed by 3 minutes of light activity and 2 minutes of standing still (Prep-phase, Fig. 1C). The last 2 minutes of the Prep-phase were used by the experimenter to mount the portable gas analyzer on the athlete, which ensured a similar initial metabolic rate for the succeeding-time trial (TT-phase, Fig. 1C). The three-time trials were separated by 35 min, which consisted of 25 min of ergometer cycling at 75 W (Recovery-phase, Fig. 1C) and the 10 min Prep-phase.

Fig. 1

Racetrack topography (A) and height profile (B). Panel C illustrates the experimental protocol for the roller-skiing time trials. The protocol was divided into four phases: warm-up, preparation (Prep), time trials (TT 1, 2 or 3), and recovery. The warm-up phase was only conducted prior to the first TT. It consisted of 10 minutes roller skiing at low intensity followed by a full run of the racecourse at moderate intensity. The preparation-phase lasted 10 minutes and was conducted directly prior to the start of each TT. It consisted of two progressive 30 s loads, finishing at approximately the 1-lap test intensity, followed by 3 minutes of light activity and 3 minutes of standing still. The TT-phase consisted of the time trials, which were either 1, 2, or 4 laps of the racetrack in a randomized order. The recovery-phase consisted of 25 min of ergometer cycling at 75 W

Two position-tracking devices, consisting of a 10 Hz standalone GNSS module and 9-axis inertial measurement unit, were attached to the athlete prior to warm-up. One was positioned in a tight-fitting vest approximately at the level of the third thoracic vertebra, the other was taped laterally on the thigh approximately midway between trochanter and the distal lateral condyle of the femur.

Test day 2: laboratory tests of skiing economy

Laboratory testing was done in the biomechanics laboratory at the Norwegian School of Sport Sciences (Oslo, Norway). After 15 min of low-intensity roller skiing on the treadmill, the athletes completed six submaximal workloads of 5 min at varying speed and incline, with 2.5 min breaks in-between. During these loads, speed varied from 2.50 to 6.00 m∙s−1 for males and 2.25 to 5.40 m∙s−1 females, while incline was equal for both sexes (Table 1). This resulted in external work rates between 2.16–2.70 W∙kg−1 for males and 1.94–2.43 W∙kg−1 for females. The protocol was repeated with speed reductions on a separate day for one of the participants, since exercise intensity of the initial protocol was too high (judged by too high blood lactate and RPE values, and not attaining steady-state \(\dot}\)O2). Pulmonary \(\dot}\)O2 measurements and heart rate data were collected during the workloads, while blood lactate and rate of perceived exertion (RPE, scale from 6–20) were collected at the end of each workload. After a 15 min rest period from the submaximal loads, the participants completed a 1000 m maximal-effort test at 6.0° (males) or 4.5° (females) incline. The athletes could control their speed by moving in front of or behind two laser lines, as previously described by Losnegard et al. (Losnegard et al. 2013). Pulmonary \(\dot}\)O2 was measured throughout the test, and blood lactate and RPE were measured (or reported) at the end of the test.

Table 1 Results from submaximal loads (S1-S6) and 1000 m maximal-effort test (Max) during test day 2. All values are presented as average ± standard deviation within each sex since the protocols differed between sexes. Rating of perceived exertion (RPE) was not collected following the 1000 m maximal-effort test, while maximal accumulated oxygen deficit (MAOD) was only defined for the 1000 m maximal-effort trialInstruments and materials

The participants used the same pair of roller skis on all tests (Swenor skate long, wheel type 2), except for the 1000 m maximal-effort trial on test day 2, where they used a faster wheel type (wheel type 1) due to standardization with respect to previous testing in our laboratory. The skis’ coefficient of rolling resistance (Crr = 0.0216) was measured on a flat section of the asphalt roller-skiing track by rolling in the tucked position between four pairs of photo-cells following the method described by Sandbakk et al. (Sandbakk et al. 2011a), but also correcting for air drag using the standard drag equation with drag area 0.35 m2 and air density 1.2 kg∙m−3. Rolling resistance was measured on the treadmill using a load cell by towing the experimenter at 3 m∙s−1 and zero incline, with resulting Crr of 0.018 and 0.014 for wheel type 2 and 1, respectively.

On test day 1, the participants were equipped with two Catapult Optimeye S5 position-tracking devices, which consists of a 10 Hz standalone GNSS module and a 100 Hz inertial measurement unit (IMU), including linear accelerometers, gyroscopes and magnetic field sensors. A Cosmed K5 portable gas analyzer in dynamic mixing chamber mode was used to measure \(\dot}\)O2 in all tests, both for test day 1 (field) and test day 2 (laboratory). The gas analyzer was calibrated directly before testing of each participant using a certified calibration gas and a 3 L syringe. Blood lactate was measured using a Biosen C-line analyzer (EKF Diagnostic GmbH, Barleben, Germany).

Data analysis

Propulsive power (Pprop) was calculated as described by Gløersen et al. (2018), but with some simplifications on the air drag estimates. Specifically, frontal area in the upright position (A0) was determined using allometric scaling between body mass and frontal area using data from Gløersen et al. (2018). The allometric scaling model was A0 = k∙m2/3, where the proportionality constant k = 0.0325 m2∙kg−2/3 was determined by least squares fitting to the data from Gløersen et al. (2018).

Oxygen demand (\(\dot}\)O2dem) was predicted based on the approach presented in Gløersen et al. (2020), which is based on an athlete-specific linear relationship between the cost of transport (C, measured in milliliters of oxygen above baseline per meter travelled) and propulsive force (Fprop = Pprop/v):

$$\frac_^-V_^}}}}}=_\cdot _}+_$$

(1)

Here \(\dot}\)O2rest represents baseline metabolic rate, which was set to 5.1 mL∙kg−1∙min−1, as in (Gløersen et al. 2020). To determine the regression coefficients (βi), the left-hand side in Eq. 1 was evaluated by setting \(\dot}\)O2dem equal to steady-state \(\dot}\)O2 during the submaximal trials and v equal to treadmill speed in meters per second. Propulsive power (Fprop) in the right hand side was defined as m∙g∙(sin θ + Crr∙cos θ). The coefficients β1 and β0 were determined individually for each athlete by ordinary least squares linear regression. Predictions of \(\dot}\)O2dem during the time trials (test day 1) and 1000 m maximal-effort test (test day 2) was achieved by solving Eq. 1 for \(\dot}\)O2dem. Oxygen demand during periods where participants were in the tucked position (i.e., not generating propulsion) was set equal to 20 mL∙kg−1∙min−1. Accumulated oxygen deficit (∑O2def) was defined as the difference between accumulated oxygen demand and accumulated oxygen uptake during a given time interval. Accumulated oxygen deficit during the 1000 m maximal-effort test was termed “maximal accumulated oxygen deficit” (MAOD).

Oxygen uptake measured by the portable gas analyzer included a time delay, since it was used in dynamic mixing chamber mode. To correct for the delay, we detected when measured \(\dot}\)O2 exceeded initial \(\dot}\)O2 by more than 2.5 mL∙kg−1∙min−1 during the time trials, which was on average 26 ± 4 s after the start. The \(\dot}\)O2 measurements were shifted in time with this delay for all tests, on both test days.

During the time trials, fractional utilization of VO2max was defined as average \(\dot}\)O2 divided by \(\dot}\)O2max, excluding the first 40 s of each trial from the average to minimize the effect of \(\dot}\)O2 measurement delays. VO2max was defined as the highest 1 min average from the 1000 m maximal-effort test.

Evaluation of average oxygen demand and skiing speed vs duration

Following the “critical \(\dot}\)O2”-model, individual relationships between time-trial duration and average oxygen demand were established by least squares fitting of average oxygen demand to the inverse of duration, i.e., \(\dot}\)O2dem = a1∙t−1 + b1, where a1 and b1 are model coefficients and t is duration. The same relationships were also established for average oxygen demand excluding tucked position (i.e., \(\dot}\)O2dem, excl. tuck = a2∙t−1 + b2), and average speed (i.e., v = a3∙t−1 + b3). Agreement between modelled and measured oxygen demand was assessed graphically (Fig. 3).

Statistical analysis

Effects of time-trial length on speed, oxygen demand, oxygen uptake, percentage aerobic contribution, accumulated oxygen deficit, and average accumulated oxygen deficit per work bout (separated by at least 5 s of tucked position) was assessed using repeated measures ANOVA with time-trial length as a categorical within-subject factor. Differences between MAOD and accumulated oxygen deficit at the end of each time trial, and between \(\dot}\)O2max (test day 2) and \(\dot}\)O2peak from test day 1, was assessed using repeated measures ANOVA with time-trial length and 1000 m performance trial as categorical within-subject factors.

Post-hoc comparisons were conducted using Bonferroni’s correction. Normality was assessed using Kolmogorov–Smirnov’s test, sphericity was assessed using Mauchly’s test, and Greenhouse–Geisser’s correction was used if sphericity was violated. Differences in instantaneous oxygen demand throughout the race course was evaluated using one-way repeated measures ANOVA with 1D statistical parametric mapping (Pataky et al. 2015) using the SPM1D Matlab toolbox, version M.0.4.10. Post-hoc testing on the SPM1D results was not conducted since methods for this are still under development. Level of significance was set to α = 0.05 for all tests. All analysis were performed in Matlab R2022b (The MathWorks, Natick, USA). Data from three of the participants were discarded due to erratic measurements from the portable gas analyzer (most likely caused by saliva affecting the flow turbine) or missing GNSS measurements (receiver out of battery). Hence, the analyses were performed on six males and four females. Results are presented as mean ± standard deviation (SD).