1. Introduction
Numerous tools are available to researchers for the measurement of ground reaction forces (GRFs). In cross-country (XC) skiing, one approach to measuring the GRFs between skis and snow in early studies was by using the force measurement systems buried under snow [
1,
2,
3,
4]. These systems allow skiers to ski freely on snow while recording the force data. However, only two or three ski contacts could be measured for one trial with classic-style XC skiing due to the length and construction of the force plate [
1,
2,
3]. The system introduced by Leppävuori [
4] could be used to measure the GRFs with the skating technique. This system was able to measure three-dimensional (3D) GRFs, which means the force generated by medio-lateral movement was included as well, but skiers had to position the ski directly over the force plate. Moreover, only one ski contact for one trial could be recorded. Although the force measurement systems buried under snow did not influence the skiing technique, the movements were restricted to limited space. Therefore, more flexible ski force measurement equipment has emerged.
Several studies started to implement force transducers to the ski or roller ski bindings and measure the forces between ski boots and skis (or roller skis). Small force plates were implemented in the bindings introduced by Komi [
1]. The vertical and anterior–posterior forces could be measured while skiing on snow, but they could not be used in the skate skiing technique which contains medio-lateral movements. Similarly, small force plates have also been implemented to roller ski bindings [
5]. The vertical and medio-lateral forces were measured, but one equipped roller ski was about 50% heavier than a normal roller ski. In some studies, strain gauges have been installed on the bindings and measured the forces in several dimensions [
6,
7,
8]. The force measurement bindings developed by Ohtonen et al. [
8] have been used with both skis on snow [
9,
10,
11,
12] and roller skis on a treadmill [
13]. The extra weight and height added by these bindings may, however, affect the skier’s performance on the treadmill using a roller ski [
13]. The pressure insoles have also been used in several studies [
14,
15,
16,
17], but only vertical forces could be obtained.
For most skiers, roller skiing is one primary form of training method during the dry land training season [
5] and is a ski-specific laboratory testing model that could reveal skiing technique in more detail [
18]. Therefore, instrumented roller skis have also been investigated in previous studies [
19,
20]. The strain gauges were installed on the roller skis directly to measure the vertical [
19,
20] and horizontal [
19] forces. However, there is also movement in the medio-lateral direction in skate skiing techniques. Thus, instrumented force measurement roller skis which could measure medio-lateral forces may be of good help for investigating the relevant skating techniques in cross-country skiing.
Consequently, the main aim of this present study was to validate a pair of newly designed two-dimensional (2D) force measurement roller skis. This pair of roller skis were first calibrated by the Technical Research Center of Finland (VTT MIKES, Kajaani, Finland). Then, forces measured by the roller skis were resolved in the global coordinate system (GCS) [
20], and the accuracy of the force measurement roller ski would be checked by comparing forces measured by the roller skis and forces measured by a 3D force plate with a static and a simulated skating push-off test. To demonstrate whether the force measurement roller ski would affect roller skiing performance on a treadmill, a maximum speed test with the V2 technique would be performed by using both normal and force measurement roller skis.
3. Results
In the static test, the relative difference in resultant forces between the force measurement roller ski and the AMTI force plate was lower than 2.0% (0.11~1.92%). The maximum relative difference in resultant forces was 1.92% when the additional weight was 10 kg (
Figure 6).
In the simulated skating push-off test, the CMC values for force-time curves obtained from the force measurement roller ski and the force plate were generally above 0.940 (
Figure 7). The average absolute differences for the forces in the X direction over one push-off cycle at different push-off loads were 8.5–33.3 N (
Table 2). The average absolute differences for the forces in the Z direction at different push-off loads were 3.9–23.4 N (
Table 3). The maximum absolute difference was 20.1–101.2 N in the X direction and was 21.0–66.6 N in the Z direction (
Figure 8 and
Figure 9).
When skiing on the treadmill, the durations for the tests did not have any major differences with different roller skis. Male skiers even had longer duration and better performance by using the force measurement roller ski (
Table 4). The cycle characteristics, while using both roller skis at different speeds, are shown in
Figure 10 and
Figure 11. For the female skier, lower cycle rate, longer cycle length, and longer ski contact time were discovered by using the normal roller ski but for the male skier, the effects of the roller ski on cycle characteristics were not obvious (
Figure 11).
4. Discussion
The force measurement roller ski used in this study was not the first one used in scientific studies. However, compared with the force measurement roller ski introduced in a previous study [
20], these new roller skis can measure both vertical and medio-lateral forces which are more appropriate for the relevant skating techniques in cross-country skiing. The idea of this force measurement roller ski was from the force measurement bindings developed by Ohtonen et al. [
8]. The binding was used in roller skiing on the treadmill [
13] and the weight of one equipped roller ski was 1650 g, which is 27.6% heavier than the force measurement roller ski used in this current study. The Coachtech nodes placed between the binding and the front wheel of both roller skis were used for power supply and data transmission. This means that the data measured by the force measurement roller ski could be transported wirelessly via the Coachtech system. Therefore, from a construction point of view, this force measurement roller ski has the benefit of being lightweight and can wirelessly measure forces in more dimensions without any interfering cables and transmitters need to carry but subject. In addition, no extra height was added to the roller ski in the current study, which was reported as a problem in earlier studies [
8]. The calibration factors used in this study were obtained in the calibration test carried out in June 2022. Another calibration test was in December 2020, and the calibration factors from this previous test can be found in the appendix (
Appendix A). During these 18 months, the force measurement roller skis were used intensively by skiers to check the signal collection via the Coachtech system. The calibration factors used in this study did not change obviously when compared to the factors from the earlier calibration test, which indicated that the measurements could remain reliable and stable over several months. However, periodic calibration is recommended.
The static test was conducted to quantify the accuracy of the resultant forces obtained by the force measurement roller ski. The forces measured by the force plate also contained the weight of the roller ski and the custom-made frame; however, these weights were subtracted while doing the comparison. Although differences in relative resultant force difference were found between left and right force measurement roller skis at lower additional weights (10–30 kg), we are not focusing on the accuracy difference between left and right force measurement roller skis. In addition, the static test results are within measurement uncertainty for the vertical direction defined in the calibration process (
Appendix B). The relative difference in resultant forces ranged from 0.11%~1.92% in this study. In a previous study, the difference of vertical resultant forces measured by the force plate and the instrumented one-dimensional roller ski ranged from 5.40% to 10.59% [
20], which is greater than what we found in the present study. Possible reasons for improved accuracy may be due to the different construction of the force measurement roller skis.
The simulated skating push-off jump test was conducted to validate the force measurement roller ski in an applied dynamic situation. The CMC depicting the similarity between waveforms and the value of the CMC close to one implies that the curves involved were similar [
13,
22,
23,
24]. The CMC values in this study were generally above 0.940, which indicated that at each push-off load, the force-time curves obtained by the force plate and the force measurement roller ski after being transformed into the GCS were similar in each direction. Similar to the static test, the forces measured by the force plate contained the weight of the roller ski. However, the weight of the roller ski could not be subtracted during the dynamic test when comparing the force component in the GCS. Therefore, there must be some difference between the forces measured by the force plate and the forces measured by the roller ski. The average absolute difference for the forces in the Z direction at different push-off loads was 3.9–23.4 N (
Table 3) and the maximum absolute difference was 21.0–66.6 N in the Z direction (
Figure 8 and
Figure 9). The result from a previous study shows that the leg vertical force change among one skate skiing cycle from sub-maximum speed up to maximum speed was about 60–1415 N [
11]. Since the differences between the forces measured by the force measurement roller ski and the reference force plate in the present study are smaller than observed during different-intensity skiing, the accuracy of the forces measured by the force measurement roller ski can be considered to be high enough to be used in practice e.g., for skiing technique observations. Although it is impossible to have the forces measured by the force measurement roller ski in full accord with forces measured by the force plate, the differences can be considered promising and acceptable.
Figure 8 and
Figure 9 presented the absolute differences over time. The absolute differences were constant before the maximum push-off forces appeared. Moreover, the maximum absolute differences generally appeared around the maximum push-off force or at the end of the push-off. This may be due to the inconsistency of the force change from these two different force measurement systems. In cross-country skiing, the heel of the ski boot is not fixed on the roller ski. When the heel of the ski boot is about to go off the roller ski, the resistance of the strain gauge on the force measurement roller ski may change, thereafter leading to the change in forces. Since the full weight of the subject and the roller ski were still on the force plate, the forces measured by the force plate may not change. This inconsistency may lead to a change in the absolute difference over time. In addition, force transmission parts typically in calibrations are made from steel but, in this case, the force transmission parts are the rubber wheels which may also affect the difference in forces measured by the force measurement roller ski and the force plate. The absolute differences between these two force measurement systems in this dynamic test were greater than that in the static test. This is possibly caused by the direction of the applied force. The force measurement roller ski measured the forces between the foot and the roller ski, and the force plate measured the forces between the roller ski and the force plate. When the subject was performing the push-off jump, the roller ski was edged. The applied force on the roller ski and the force plate may not be parallel to each other. The crosstalk from the vertical force channel into the medio-lateral channel may also be an effect that may influence the amplitude of the measured force in the medio-lateral channel. These may cause some errors when comparing the force component converted to the GCS.
The extra weight of the force measurement roller ski did not affect the performance of the skiers. The duration skiers stayed on the treadmill and the final speed skiers could reach were not affected much by the roller skis they use. Although there was a 333 g difference between the roller skis, the balance point of the roller ski changed as well. This led to the torque difference around the ski boot attach point on the roller ski being 0.01 N·m, which could be considered negligible. Therefore, the extra weight of the force measurement roller ski appears to be acceptable to the athletes. However, the extra weight may still affect the cycle characteristics while roller skiing, especially for female athletes. This may be due to the lighter body weight and relatively lower muscle strength when comparing the female athletes with the male athletes. The male athlete even seem to have a better performance by using the force measurement roller ski. This may be because the stiffness of the force measurement roller ski suited her better. The body of the force measurement roller ski is made of aluminum and the body of the reference roller ski is a honeycomb wooden structure. The stiffness of the two bodies may have some difference and, thereafter, affect the performance.