Original Article

Biomechanics of slalom water skiing

Proc IMechE Part P: J Sports Engineering and Technology 2015, Vol. 229(1) 47–57 Ó IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1754337114547555 pip.sagepub.com

Jordan Bray-Miners1, R John Runciman1, Gabrielle Monteith2 and Nate Groendyk1

Abstract Water skiing has received little attention in research literature and has not utilized recent advancements in analysis technology like other highly dynamic sports. In this study, six advanced slalom skiers were recruited to test four different high-performance ski designs, with the goal being to detect performance differences achieved between ski designs and between skiers during slalom turns. To aid the analysis of the resulting activity data, a series of 11 quantitative performance parameters were defined and studied. Instrumentation included a skier-mounted, wireless, Global Positioning System sensor providing instantaneous skier velocity, a uniaxial force transducer providing rope load, and a wireless, inertial measurement unit attached to the skis to provide ski roll, ski acceleration and deceleration. Statistical analysis suggested that there was a difference in the average peak roll achieved between the skis, but was unable to suggest a difference between skis in the other performance parameters. In contrast, however, statistical analysis indicated that there was a difference in the performance achieved between the skiers, which is supported by their slalom course success rates. The identified performance parameters were effective at differentiating skier ability levels with the subject with the highest success rate among the top three highest scoring for 10 of 11 parameters and the subject with the lowest success rate was among the bottom 2 in all 11 parameters.

Keywords Competitive skier, inertial measurement unit, performance parameters, coaching, water ski design

Date received: 16 September 2013; accepted: 19 June 2014

Introduction Water skiing has approximately 10 million annual North American participants and growing international participation, evident by its introduction to the Pan Am Games in 1995.1,2 Despite its growing popularity, water skiing requires equipment that is costly in terms of capital and ongoing running costs, combined with access to a suitable body of water, giving it the reputation of being a luxury sport. Slalom skiing, while an international competitive sporting event, is also considered to be an intermediate/ advanced recreational skiing activity in which the objective is to complete a course consisting of a series buoys. In this course, the skier must perform a sequence of oscillating left and right turns to travel on the outside of the buoys. The dimensions of the course are standardized but the activity can be made increasingly difficult by increasing boat speed and decreasing rope length. A basic slalom turn involves a complex sequence of motions that occur in a relatively short amount of time. Given the characteristics of the course, rope and boat, the success in performing this activity is dependent on

the available ski performance and the skill and strength of the athlete. Historically, success was based on the number of marker buoys successfully completed,3 and coaching was primarily by qualitative optical analysis.4 Within the mechanics of the activity, however, there are a number of performance parameters that may be closely tied to overall success. Ski acceleration, deceleration and orientation are a few of the important performance parameters that may be closely tied to overall success and could be used to improve product development and coaching techniques. It is important to consider parameters such as ski acceleration, deceleration and orientation independently but also how they interact. It is hypothesized

1

School of Engineering, University of Guelph, Guelph, ON, Canada Department of Clinical Studies, University of Guelph, Guelph, ON, Canada

2

Corresponding author: R John Runciman, School of Engineering, University of Guelph, Guelph, ON N1G 2W1, Canada. Email: [email protected]

48 that a higher resultant in some of the parameters will be due to a higher resultant of another. For example, higher peak roll will lead to higher deceleration, which in turn leads to higher rope load and acceleration. To help identify which of the parameters are dependent on others, it is necessary to break down the different phases of a slalom cut and what reactions are taking place in each phase. Previous research into slalom water skiing performance, ski design and skier ability level has been limited to parameters such as ski rope load,5,6 skier velocity5,6 and overall slalom course success.6 One additional study published a description of instrumentation that could be used to collect a variety of rope-based performance parameters. However, the authors were unable to support their work with any experimental data.7 It seems apparent then that the advancement of strategies for water skiing performance analysis would benefit from the development and study of instrumentation and performance measures. This article is the third in a series of papers documenting the results of a research program investigating skiing performance biomechanics. Previously we have presented the initial study results6 and instrumentation development details8 for the overall study. The goal was to provide measurement tools and analysis strategies to quantitatively analyze water skiing biomechanics and performance. This article provides details of the methodology that was used to collect and analyze ski-based experimental data and performance parameter–based results of a group of advanced slalom skiers.

Methods This study was reviewed and received ethics approval for its subject participation and written survey components by the University of Guelph Ethics Committee. Six male water skiers (Table 1) capable of making two passes of a regulation slalom course on four different slalom skis were recruited for the study. Data collection was carried out over 3 days. Each experimental trial consisted of initializing the data collection program with the ski and skier on the dock. Then, the skier was taken to one end of a regulation slalom course3 where he performed a deep water start, followed by two passes of the course (Figure 1). A pass of the course consists of a set-up cut, entrance cut where the skier enters the course through the entrance gates, followed by an oscillating sequence of six left and right turns (three of each) before exiting the course through the exit gates. To accommodate the use of unfamiliar skis, when a skier missed a marker, instead of it resulting in the entire pass being considered unsuccessful, as is the case in normal slalom competition,3 skiers were encouraged to continue through the course, after which the missed markers would be tallied for later analysis. Each subject was still required to ski the length of the course

Proc IMechE Part P: J Sports Engineering and Technology 229(1) and complete as many ‘‘good’’ slalom cuts as possible. The number of completed turns around the buoys was recorded as a performance parameter. After completing each of their trials, skiers were asked to complete the corresponding section of a written survey subjectively ranking the performance of the skis. Skis were instrumented with an inertial measurement unit (IMU; 3DM-GX2; Microstrain, Inc., Williston, VT, USA) weighing 16.7 N (dry weight including mounting hardware) mounted directly in front of the front binding. A custom fabricated plate was fastened to the ski, using the same bolt footprint as the front binding, and extended out towards the ski tip. The IMU housing was wrapped in plastic and strapped to the plate. Data from the sensor were transmitted, via custom radio frequency (RF) transmission system, to a computer (Acer Aspire One ZG5; Acer America Corporation, Mississauga, ON, Canada) located in the toe boat. The RF transmission system consisted of two custom-designed RF units, one located on the ski and the other was connected to the computer via universal serial bus (USB) port. Each unit had two RF transceiver modules (nRF2401; Nordic Semiconductor ASA, Tiller, Norway) that were operated by a microcontroller. The data were parsed by the computer using a custom data collection program (LabVIEW 8.2; National Instruments Corporation, Austin, TX, USA). Rope load was measured using a load cell placed in series with the tow rope, skier speed was measured using a helmet-mounted 5-Hz Global Positioning System (GPS) unit and boat speed was measured using a 1-Hz GPS unit. Full details of the ski, skier and boat instrumentation have been published previously.8 Each subject was required to perform one test run on each of the four skis. The skis varied in classification from ‘‘performance’’ to ‘‘tournament,’’ and all skis were commonly associated with advanced amateur and competitive level use. A brief summary of the skis can be found in Table 2 and ski profiles can be seen in Figure 2. A number of methods were incorporated to attempt to minimize unwanted data artifacts. A randomized testing order based on a Latin square design9 was used to help minimize the effects of fatigue and changing weather throughout the day. To further minimize the factors that would influence the results, all of the ski runs were done on the same slalom course with a 17.9 m rope length. This rope when combined with the load cell instrumentation yielded an overall functional length of 18.25 m, equivalent to the international standard slalom competition rope length.3 In addition, all of the ski runs were done with the same boat (1996, 5.7 l, MasterCraft Prostar 190; MasterCraft Boat Company, Cove Vonore, TN, USA) operating at 51.5 km/h (approximately equivalent to international competition standard boat speed for difficult conditions3) for all experimental test runs (DigitalPro, PerfectPass; PerfectPass Control Systems Inc., Dartmouth, NS, Canada). Additionally,

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Table 1. Summary of personal data for the participants (top) and skier turn success data (middle) and ski roll and ski deceleration/ acceleration results for both dominant and nondominant turns (bottom) listed as a function of the skiers included in the study. Skiers Personal data Age Mass (kg) Height (m) Foot forward Years skiing at current level Turn success data No. of turns No. of successful buoys Buoy Success Rate (%) Ski roll a Integral dominant (°s) a Integral nondominant (°s) b Peak dominant (°) b Peak nondominant (°) Ski deceleration b Integral dominant (m/s2
s) b Integral nondominant b(m/s2
s) 2 Peak dominant (m/s ) b Peak nondominant (m/s2) Ski acceleration a Integral dominant (m/s2
s) a Integral nondominanta (m/s2
s) 2 Peak dominant (m/s ) a Peak nondominant (m/s2)

11

12

16

14

13

15

41 79.5 1.78 L 20 +

51 86.4 1.78 R 11–15

38 74.5 1.75 R 16–20

30 81.8 1.78 L 52

28 90.9 1.91 R 11–15

30 75.5 1.88 L 11–15

106 94 88.7

90 73 81.1

46 32 69.6

45 26 57.8

75 17 22.7

64 0 0

96.4 6 3.3 104.7 6 4.6 54.2 6 0.8 56.8 6 0.8

104.4 6 4.4 85.0 6 3.0 59.4 6 0.8 53.4 6 0.8

109.4 6 6.8 92.6 6 4.6 59.3 6 1.1 54.9 6 1.1

84.7 6 3.9 99.1 6 5.4 51.5 6 1.0 51.1 6 1.1

103.4 6 4.5 79.0 6 3.2 52.2 6 0.9 44.5 6 0.9

68.8 6 3.1 67.3 6 3.7 47.0 6 0.9 46.1 6 1.0

29.2 6 0.2 29.3 6 0.3 212.6 6 0.4 211.3 6 0.4

28.2 6 0.3 29.0 6 0.2 211.5 6 0.4 213.1 6 0.4

28.4 6 0.4 28.8 6 0.4 212.1 6 0.6 212.8 6 0.5

27.7 6 0.3 27.9 6 0.4 211.2 6 0.5 210.4 6 0.5

25.5 6 0.3 27.1 6 0.3 27.5 6 0.5 28.6 6 0.4

24.3 6 0.3 24.4 6 0.4 28.7 6 0.5 28.7 6 0.5

5.6 6 0.4 5.5 6 0.4 13.6 6 0.9 11.4 6 0.7

5.9 6 0.4 4.7 6 0.4 12.4 6 0.8 10.9 6 0.4

6.2 6 0.7 4.8 6 0.5 12.1 6 1.2 11.6 6 1.1

4.4 6 0.4 5.0 6 0.5 11.4 6 1.0 9.5 6 0.8

4.1 6 0.3 3.7 6 0.3 8.1 6 0.6 7.7 6 0.6

2.1 6 0.2 2.1 6 0.2 6.1 6 0.5 5.2 6 0.4

Data are organized with the most successful skier to the left and least successful to the right. The maximum and minimum values in each category (row) are given in boldface. aError values are upper and lower 95% confidence interval as calculated from the statistical analysis. bError values are pooled standard error calculated from the statistical analysis.

turn data were normalized for each skier’s forward foot. This resulted in the definition of dominant and nondominant turns where left foot forward skiers performed their dominant turns while on the port side of the slalom course (right turns), while right footed skiers performed their dominant turns while on the starboard side (left turns). Wind was monitored using a temporary weather station. Data were collected by a data logger (SynphoniePLUS; NRG Systems Inc., Hinesburg, VT, USA) from an anemometer (#40C, NRG Systems Inc.), located such that it was exposed to similar wind conditions as the slalom course. Data files were processed using Microsft Excel (Microsoft Canada Co., Mississauga, ON, Canada) after each of the test days. The orientation generated by the IMU was used to calculate pitch, roll and heading, which were then used to identify the left and right turns within each file. The quantitative threshold for a turn was defined as when ski roll passed through 0° of roll. For a left turn, the roll values were positive, and for a right turn, the values were negative. Individual turns were subdivided into five distinct phases: turn initiation, approach, apex, exit and wake crossing. A series of 11 performance parameters were identified and used for data analysis. The first of these was

the Buoy Success Rate. Six performance parameters were determined as simple peak values, which included Rope Load, Maximum Skier Velocity, Minimum Skier Velocity, Ski Acceleration, Ski Deceleration and Ski Roll. While each of these latter six performance parameters will have their respective peaks, they do not all occur during the same phase of the turn. A skier slows through both the approach and apex phases of a turn, and Peak Ski Deceleration was calculated using the largest negative ski acceleration occurring during this period (Figure 3). Peak Ski Acceleration was calculated using maximum ski acceleration during the exit phase. A further three performance parameters were determined by integrating results with time; these included Integrated Roll, Integrated Ski Acceleration and Integrated Ski Deceleration. These integrated performance parameters were implemented to include time as a factor in these specific performance measures. The concept in this approach being that overall skier performance may not be only related to discrete peak values but the result of a given parameter as a function of time. All of the integrations were calculated as the area under the respective data curve with respect to time. Integrated Roll was calculated across the entire turn, whereas Integrated Ski Deceleration was calculated from ski acceleration data during the approach and

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Proc IMechE Part P: J Sports Engineering and Technology 229(1) were plotted against predicted values and explanatory variables. If there was a need for data transformation or data were presented as a percent, analyses were done on a logit or log scale. Finally, if the overall F-test was significant, a Tukey test was applied to determine the adjusted p value; otherwise, we did not proceed with paired comparisons (SAS Institute Inc., 2004; SAS OnlineDOC (R) 9.1.3; SAS Institute Inc., Cary, NC, USA).

Results

Figure 1. Diagram of slalom course including entrance gates (x), skier path and buoys 1–6 (o) and sample dimensions.3

apex phases, and Integrated Ski Acceleration was calculated using ski acceleration data from the exit phase of the turn. Performance parameters were analyzed using a generalized linear mixed-model for statistical significance. When testing the performance of the skis, factors included in the model were ski (fixed effect), turn (fixed effect) and skier (random effect) as well as their interactions. When testing the performance of the skiers, factors included in the model were skier (fixed effect), turn (fixed effect) and ski (random effect) as well as their interactions. A comprehensive residual analysis was used to access the assumptions of the analysis of variance (ANOVA). Overall normality was assessed by a Shapiro–Wilk test, a Kolmogorov–Smirnov test, a Cramer–von Mises test and an Anderson–Darling test. In order to look for patterns in the data that suggest outliers, unequal variance or other problems, residuals

The average wind speeds recorded by the anemometer for the 3 days were 2.37, 3.03 and 0.87 m/s. Wind direction was approximated to be consistently 5°–10° off the centerline of the slalom course. This level of wind allowed each subject to complete one pass with the wind and another into the wind. The number of completed turns and completed turns where the skier was successful in negotiating the buoy can be seen at the top of Table 1. A pair of single-turn data sets is shown in Figure 4 to illustrate the typical turn dynamics observed in the study. Figure 4(a) is for a left foot forward skier, Subject 11, performing a left turn, which occurs when the skier is on the starboard side of the boat, making it a nondominant turn. The horizontal axis is plotted in terms of percent of turn completed where the 0° ski roll orientation that occurs with turn initiation demarcates the start and end of each turn cycle. In the approach phase, the ski has transitioned from negative roll values from the previous right turn, starts at 0° and increases, and deceleration occurs and skier velocity decreases, thus causing the rope load to decrease. This portion of the turn occurs when skiers adjust their deceleration to have the right timing for completing their turn around the buoy (Figure 4(a), from 0%–30%). As the skier enters the turn apex, direction of travel changes, roll reaches its peak value, 55°, while rope load and velocity reach their minimum values, approximately 0 N and 41 km/h, respectively. During this portion of the turn, the skier physically travels around the buoy, and by the end of this phase, the ski is pointed back across the wake and has fully changed direction (Figure 4(a), from 30% to 65%). As the skier exits the turn, roll decreases but at a slower rate than in the approach phase, rope load begins to increase again and the skier generates acceleration. Velocity increases as acceleration continues and rope load reaches its peak value of approximately 2100 N (2.7 3 body weight) before beginning to decrease (Figure 4(a), from 65% to 85%). When the skier crosses the wake, roll and rope load continue to decrease as the skier reaches peak velocity of 72 km/h. There are two identifiable bumps in the load and roll profiles as the skier absorbs the wakes (Figure 4(a), from 85% to 95%).

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Table 2. Ski data including a summary of the four ski models used in this study, survey results for each of the skis (values are the totals from all six skiers, with each skier using the scale of 1 being poor to 5 excellent) and the ski roll and ski deceleration and acceleration results for both dominant and nondominant turns are listed as a function of the ski models. Skis Ski data Length (cm) Width at widest point (cm) Mass (kg) Classification Survey results: performance Acceleration Deceleration Responsiveness Smooth Turn initiation Cut through wake Performance total Survey results: nonperformance Rope load during run Rope load during water start Overall effort Nonperformance total Ski roll a Integral dominant (°s) a Integral nondominant (°s) b Peak dominant (°) b Peak nondominant (°) Ski deceleration b Integral dominant (m/s2
s) b Integral nondominant b(m/s2
s) 2 Peak dominant (m/s ) b Peak nondominant (m/s2) Ski acceleration b Integral dominant (m/s2
s) b Integral nondominant b(m/s2
s) 2 Peak dominant (m/s ) b Peak nondominant (m/s2)

A

B

C

D

170 17.28 2.81 Tournament

170 18.53 2.81 Tournament

170 20.34 2.75 Performance

170 17.26 2.00 Tournament

20 19 19 20 18 20 116

26 26 24 24 25 25 150

20 18 22 23 20 19 122

27 26 27 22 25 26 153

23 17 20 60

25 25 24 74

27 29 22 78

26 17 24 67

87.8 6 10.0 88.5 6 10.2 54.2 6 1.9 52.5 6 1.9

93.7 6 10.6 84.7 6 9.6 53.0 6 1.9 48.9 6 1.9

92.6 6 10.6 83.4 6 9.5 54.1 6 1.9 50.8 6 1.9

96.4 6 11.2 86.6 6 10.1 53.8 6 2.0 52.1 6 2.0

27.4 6 0.8 28.0 6 0.8 211.1 6 0.9 210.6 6 0.9

26.8 6 0.8 27.6 6 0.8 210.0 6 0.8 210.8 6 0.8

27.3 6 0.8 27.7 6 0.8 210.2 6 0.9 210.9 6 0.9

27.5 6 0.8 27.8 6 0.8 211.3 6 0.9 211.1 6 0.9

4.7 6 0.6 4.5 6 0.6 10.9 6 1.2 9.4 6 1.1

4.8 6 0.6 4.5 6 0.6 11.0 6 1.1 9.9 6 1.1

4.9 6 0.6 4.2 6 0.6 10.7 6 1.2 9.1 6 1.2

4.8 6 0.6 4.3 6 0.6 11.2 6 1.2 9.4 6 1.2

The maximum and minimum values in each category (row) are given in boldface. aError values are upper and lower 95% confidence interval as calculated from the statistical analysis. bError values are pooled standard error calculated from the statistical analysis.

As the skier initiates his next turn, velocity begins to decrease as rope load and roll continue to decrease until roll reaches 0° again. During this portion of the turn, the skier has already crossed the wake but is often required to absorb continued oscillations from the impact after the second wake (Figure 4(a), from 95% to 100%). The results shown in Figure 4(a) are a generalization of what was found in the large majority of the turns from the skiers. However, the timing of each phase and the resultant performance parameters can change slightly from one turn to the next. The most obvious example of this occurred with Subject 15. A comparable data sample (left, nondominant turn) from one of his left turns can be found (Figure 4(b)). Similar turn phases can be identified; however, the peak parameters are smaller in magnitude and occurring at different times. For example, the maximum ski roll was 52° versus 55°, maximum skier velocity 62 versus 71 km/h, minimum skier velocity 45 versus 41 km/h and

maximum rope load was 1500 versus 2100 N (2.0 vs 2.7 3 body weight) for the less versus more successful skier. Timing was also different between the skiers with maximum ski roll and maximum rope loads occurring earlier in the turn cycle for the less successful skier (20% vs 35% for roll and 58% vs 70% for rope load). Tabulated results for ski roll, ski deceleration during turn approach and ski acceleration for turn exits are listed for skiers and skis in Tables 1 and 2, respectively. The columns of skier data in Table 1 have been ordered by Buoy Success Rate, with the most successful skier’s data on the left to the weakest on the right. Maximum and minimum values for each row are given in boldface. The ranges of parameter values obtained for the skiers were 44.5°–59.4° for peak roll, 67.3°–109.4°
s for integral of roll, 5.2–13.6 m/s2 for peak acceleration, 28.1 to 12.5 m/s2 for peak deceleration, 2.1–6.2 m/s2
s for integral of acceleration and 24.3 to 29.3 m/s2
s for integral of deceleration.

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Proc IMechE Part P: J Sports Engineering and Technology 229(1)

Figure 2. Top and side profiles of the tested skis. Binding mounting points are shown by white circles. Front binding and testing instrumentation was mounted using the forward six mounting points. The rear binding was secured using the rearmost four mounting points.

Each skier’s overall average integral of roll and peak roll for dominant and nondominant turns is listed in Table 1. Statistical analysis suggests that at least one of the subjects had a significantly different result than another subject (p \ 0.0001 for both integral and peak resultant). The skier with the highest integral average on all of the skis was Subject 16 for dominant turns and Subject 11 for nondominant turns, 109.4°
s and 104.7°
s, respectively. The skier with the lowest integral average on all of the skis was Subject 15 for both dominant and nondominant turns, 68.8 and 67.3°
s, respectively. The skier with the highest peak average on all of the skis was Subject 12 for dominant turns and Subject 11 for nondominant turns, 59.4° and 56.8°, respectively. The skier with the lowest peak average on all of the skis was Subject 15 for dominant turns and Subject 13 for nondominant turns, 47.0° and 44.5°, respectively. The overall average integral of deceleration for each skier including both dominant and nondominant turns is listed in Table 1. Statistical analysis suggests that at least one of the subjects had a significantly different result than another subject (p \ 0.0001). The skier with the highest average on all of the skis was Subject

11 for both dominant and nondominant turns, 29.2 and 29.3 m/s2
s, respectively. The skier with the lowest average on all of the skis was Subject 15 for both dominant and nondominant turns, 24.3 and 24.4 m/s2
s, respectively. The overall average peak decelerations for the skiers are listed in Table 1. The statistical analysis suggests that at least one of the subjects had a statistically significant, different result than another (p \ 0.0001), but there was no statistical difference between dominant and nondominant turn results. The skiers with the highest peak averages were Subject 11 for dominant turns, Subject 12 for nondominant turns and Subject 16 at 212.5 m/s2 (average) for both dominant and nondominant turns. Subject 13 attained the lowest magnitude dominant and nondominant decelerations. Skier overall average integral of acceleration and peak acceleration for dominant and nondominant turns is listed in Table 1. Statistical analysis led to the conclusion that one of the subjects had a statistically significant, different result in both parameters than another (p \ 0.0001 for both integral and peak resultant). The skier with the highest integral average on all of the skis

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Figure 3. The five distinct phases of a slalom turn as seen from the tow boat. This series of images shows a nondominant turn.

was Subject 16 for dominant turns and Subject 11 for nondominant turns, 6.2 and 5.5 m/s2
s, respectively. The skier with the lowest integral average on all of the skis was Subject 15 for both dominant and nondominant turns, 2.1 and 2.1 m/s2
s, respectively. The skier with the highest peak average on all of the skis was Subject 11 for dominant turns and Subject 16 for nondominant turns, 13.6 and 11.6 m/s2, respectively. The skier with the lowest peak average on all of the skis was Subject 15 for both dominant and nondominant turns, 6.1 and 5.2 m/s2, respectively. Table 2 lists the overall average integral of roll and peak roll for each ski for dominant and nondominant turns. Statistical analysis suggests that there was no

significant difference in the integral of roll produced from the different skis (p = 0.3464). However, it does suggest that there is a significant difference in the peak roll produced from the different skis (p = 0.0014). The ski with the highest integral average was Ski D for dominant turns and Ski A for nondominant turns, 96.4 and 88.5°
s, respectively. The ski with the lowest integral average was Ski A for dominant turns and Ski C for nondominant turns, 87.8 and 83.4°
s, respectively. The ski with the highest peak average was Ski A for both dominant and nondominant turns, 54.2° and 52.5°, respectively. The ski with the lowest peak average was Ski B for both dominant and nondominant turns, 53.0° and 48.9°, respectively. Ski B had a

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Proc IMechE Part P: J Sports Engineering and Technology 229(1)

Figure 4. Typical left turn ski roll, ski acceleration, skier velocity and rope load for (a) Subject 11 who had an overall success rate of 88.7% and (b) Subject 15 who had an overall success rate of 0%. The five phases of a slalom cut can be identified: approach, apex, exit, WC and NTI. WC: wake crossing; NTI: next turn initiation. Acceleration data were smoothed for clarity using a moving average approach, n = 4.

statistically lower average peak roll than Ski A and Ski D (p = 0.0013 and 0.0178, respectively). Each ski’s overall average integral of deceleration for dominant and nondominant turns is listed in Table 2. Statistical analysis suggests that there was no significant difference between the skis (p = 0.1341). The ski with the highest average was Ski D for dominant turns and Ski A for nondominant turns, 27.5 and 28.0 m/ s2
s, respectively. The ski with the lowest average deceleration was Ski B for both dominant and nondominant turns, 26.8 and 27.6 m/s2
s. The average peak deceleration for each of the skis is listed in Table 2. Statistical analysis suggests that there was no statistical difference in the peak deceleration produced from the different skis (p = 0.1134) or between dominant and nondominant turn results. The ski with the greatest average deceleration was Ski D, for both dominant and nondominant turns, 211.3 and 211.1 m/s2, respectively. The skis with the lowest average deceleration magnitudes were Ski B, at 210.0 m/s2 for dominant turns, and Ski A, at 210.6 m/s2 for nondominant turns. The overall average integral of acceleration and peak acceleration during dominant and nondominant turns is listed in Table 2. Statistical analysis led to the

conclusion that there was no statistical difference in both parameters produced from the different skis (p = 0.9314 and 0.9326 for integral and peak, respectively). The ski with the highest integral average was Ski C for dominant turns and Ski A for nondominant turns, 4.9 and 4.5 m/s2
s, respectively. The ski with the lowest integral average was Ski A for dominant turns and Ski C for nondominant turns, 4.8 and 4.2 m/s2
s, respectively. The ski with the highest peak average was Ski D for dominant turns and Ski B for nondominant turns, 11.2 and 9.9 m/s2, respectively. The ski with the lowest peak average was Ski C for both dominant and nondominant turns, 10.7 and 9.1 m/s2, respectively. Table 2 also contains the results of the qualitative ski survey. Of note is the contrast between the perceived and the actual ski performance. Ski D scored highest in perceived performance with a total of 153 points and was rated as the best ski in five of the six performance questions. In contrast, however, actual performance achieved with this ski was not universally the highest, with Skis A, B and C outperforming it in several of the performance measures. In contrast, Ski A scored lowest in the performance questions with 116 points and scored lowest in all of the nonperformance questions too.

Bray-Miners et al.

Discussion Wherever possible all efforts were made to ensure that skiing conditions would remain consistent with typical competition conditions as outlined by the International Waterski & Wakeboard Federation.3 To this end, the boat, boat speed, functional rope length, course and skis were all chosen to comply with this requirement. Where options were available, such as in rope length and boat speed, actual testing parameters were chosen to provide the skier with the least difficult skiing scenario. For example, the combination of the rope and instrumentation used in the testing provided the functional equivalent of a full regulation rope length, recognizing that in competition, rope lengths are often shortened from this to increase the overall difficulty of the course. This decision was based on the realization that the skiers were all going to be skiing on unfamiliar equipment, and it was expected that this would potentially reduce their overall success rate. The four skis chosen for the study were selected to provide a reasonable representation of skis currently available to the advanced amateur and competitive water skier. Each is unique in terms of the combination of their overall top and side profiles, binding positions, fin design and mass. Preference of one ski design over another is personal and highly subjective, with little objective data available to support the decision. It was felt that by including this range of designs in the testing, a representative overview of the behavior of current tournament and performance level ski designs might be achieved. The recorded wind speed and direction were relatively similar for all three test days and wave action due to wind was also minimal due to the small size of the lake (150 m 3 1.2 km). It should be noted that subjects did not all ski on the same test days and in some cases subjects completed their runs in more than 1 day. Due to this, if one day affected performance significantly more than another, it might affect the ability to compare between the skiers. An investigation into the subjects who skied over multiple test days concluded that there was no noticeable impact of the different skiing conditions on Buoy Success Rate results. Therefore, it was assumed that differing weather conditions encountered during the testing had a negligible impact on the results. Skis were all used equally over the three test days, so the effect on the analysis between the skis was also negligible. Typical data profiles as shown in Figure 4(a) demonstrate how it is possible to identify the different phases of a slalom cut and the interaction between performance parameters. The timing of when a specific peak performance parameter occurs in one of the phases has a cascading effect on the result in the subsequent phases and overall success of the turn. One key example of this is in the exit phase, when the skier is generating acceleration. The skier must first reach a high peak roll in the turn apex in order to build enough

55 rope load, which they can use to generate high accelerations. Furthermore, they need to ensure that they have created enough acceleration before the wake crossing phase to generate a sufficiently high peak velocity because it is difficult to continue to accelerate once they have started to cross the wake. In fact, it is a challenge not to lose momentum during the complex kinematics that occur during the wake crossing phase. This is often one of the most difficult things for an amateur skier to master. If a skier has not accomplished all of this and reached a high peak velocity, it is less likely that they will be able to successfully complete their next turn around the next buoy. The scenario previously described can also be seen in Figure 4(b), which shows the same parameter profiles as Figure 4(a), this time for Subject 15. As seen by the Buoy Success Rate results in Table 1, Subject 15 was not able to successfully complete any of his turns around the buoys. In Figure 4(b), it can be seen that Subject 15 was reaching peak roll earlier in the turn cycle and reaching a lower overall peak magnitude. As expected, this correlates with the skier not being able to produce the same deceleration magnitude or generate as high a subsequent rope load. With a lower peak rope load that also is occurring earlier in the turn, the skier is unable to generate the same type of acceleration or peak velocity. The peak velocity is also occurring at the very end of the turn, which indicates that after they cross the wake, they are still trying to accelerate the ski to allow them to get out far enough to the side of the boat. This in turn would affect the timing of next turn initiation. Even though all the subjects were advanced slalom skiers, the analysis procedure developed in this study was successful in detecting differences in skier performance. Furthermore, the results were in agreement with what was expected based on Buoy Success Rates. The skier with the highest Buoy Success Rate did not always achieve the highest resultant performance parameter; however, they were always in the top grouping. For example, Subject 11 achieved the highest Buoy Success Rate but only had the highest resultant in 6 of the 11 performance parameters. They were however among the top three highest in 10 of the 11 parameters. Similarly, the two subjects with the lowest Buoy Success Rates were always in the lower grouping with respect to performance. Subject 15 achieved the lowest Buoy Success Rate and had the lowest resultant in 10 of the 11 performance parameters and was in the bottom two lowest in all 11 parameters. These results indicate that our analysis procedures could be used for the quantitative assessment of a skier’s performance and ultimately could be employed as an advanced coaching tool. The results shown in Table 1 indicate that the highest peak values were not always consistent with the highest integral values. This was expected since the profile shape plays a large role in the calculated integral. For example, if a skier is able to hold a slightly smaller

56 peak roll for longer, they will produce a larger integral of roll. However, it would be expected that those skiers capable of producing high peaks will also generally produce higher integral values. This assumption is supported by the results for Subjects 11, 12 and 16 who had the highest peak roll averages for both dominant and nondominant turns, and 12 and 16 produced the highest integral roll values for dominant turns and Subject 11 generated the highest integral roll values for his nondominant turns. In the same regard, Subject 15 had the lowest integral for every parameter and also produced the lowest peaks in every parameter except for deceleration. These findings are supported by the Buoy Success Rate results found in Table 1 where Subjects 11, 12 and 16 had the highest Buoy Success Rates and Subject 15 the lowest. Examining dominant versus nondominant results shows an interesting differentiation between the strong and weaker skiers. Two of the successful skiers, Subjects 11 and 14, were able to generate higher overall average integral of roll on their nondominant side as opposed to their dominant side. For the dominant side, they ranked 4th and 5th out of the six subjects, and on their nondominant side, they were the 1st and 2nd. Of the remaining skiers, all achieved equal or lower values on their nondominant sides. These results would seem to indicate that at least some of the stronger skiers were able to perform at a very high level on both dominant and nondominant sides, whereas other skiers showed a bias towards their dominant side. The ski results did not show the same trend. In some cases, the highest peak average for a parameter corresponded to the lowest integral average of that parameter (i.e. integral versus peak roll, dominant side, Ski A and integral versus peak acceleration, Ski C). In another case, Ski A provided the highest integral ski acceleration for nondominant turns but the lowest for dominant turns. This is not what would be expected but can be explained by the fact that there is no statistically significant difference between the skis for any of the parameters except peak roll. Thus, the results are similar enough that it is harder to make conclusions based on the trend found among the skis. It should be noted that peak roll is the only parameter where a ski was highest for both dominant and nondominant turns and another ski was lowest for both dominant and nondominant turns. This is what was expected because skis are symmetrical and therefore one ski would not have an advantage based on what edge is being used. Another point of interest for all the results is that there was no common trend within each parameter of highest-to-lowest between dominant and nondominant turns. This would be expected when analyzing the skis due to the fact that there was not a significant difference between them for any of the parameters except peak roll. However, in the case of the skiers, one would expect to see more situations where a skier was able to achieve the highest result for both dominant and nondominant turns. Without a more detailed investigation,

Proc IMechE Part P: J Sports Engineering and Technology 229(1) it is hard to determine why this was the case, but it might be due to an individual skier being more proficient with both types of turns than another. For example, a skier who achieved a higher result during dominant turns might have been lower for nondominant turns simply because his or her ability in dominant turns is greater than in the nondominant turns. As previously discussed, it is expected that to a certain extent, the performance parameters are dependent on each other, and a skier who is capable of achieving high peak and integration of roll will be able to produce more deceleration and acceleration. This was seen in the results in the nondominant case with Subject 11, where he had the highest peak and integration of roll as well as integration of acceleration and deceleration. These performance results were expected because Subject 11 had the highest Buoy Success Rate. It is interesting to note that even though this subject was able to achieve the highest integration of acceleration and deceleration for nondominant turns, he did not have the highest peaks in either parameter for his nondominant turns. The dependence between parameters was also seen in the average results from each of the skis. For example, in the nondominant case, Ski A had the highest peak and integration of roll as well as integration of acceleration and deceleration. However, the trend might be considered more of a coincidence in this case since the statistical analysis of the data indicated that there was not a statistically significant difference between the skis, except for peak roll. The only parameter that had no significant difference between dominant and nondominant turns was peak deceleration. This is not what was expected because peak deceleration occurs during the turn approach and apex phases which is also when peak roll occurs, and this is typically when you would expect to see a difference between dominant and nondominant turns. It is unclear why peak roll is the only parameter that was found to have a significant difference between the skis. It is hypothesized that under the test conditions, the subjects were able to generate similar accelerations from all the ski designs. If the difficulty of the slalom course was increased, by increasing boat speed and decreasing rope length, it is expected that differences in performance would be more identifiable. This would make it subsequently more difficult for the subjects to adjust to using new equipment and it might be required to allow the subjects to practice before test days. Furthermore, it was not expected that Ski A would result in the highest average peak roll because it was not the most aggressive ski design. The fact that Ski B had a statistically significant lower average than Ski A and Ski D also does not correspond to the qualitative survey, in which Ski A ranked lowest in the performance questions, Ski D had the highest point total with 153 points, Ski B was second highest with 150 points and Ski A was lowest with 116 points.

Bray-Miners et al. An overriding limitation of this study is the number of skiers used and the breadth of their skill levels. It was the intent of this study to examine the performance of advanced slalom skiers on a range of performance skis. The use of a greater number of test subjects could have helped increase the overall strength of the analysis. In the end, only two of the six skiers were able to perform with a better than 80% Buoy Success Rate, while one of the six achieved a 0% success rate. This breadth of performance while not unexpected would have the result of lessening the strength of the subsequent analysis with respect to differentiating small differences in ski performance. Our statistical results did show, however, that our sample size and breadth was sufficient for detecting differences between skiers, as indicated by the small standard error values and detected statistical differences between skiers. From another perspective, our test group was somewhat more representative of a typical buyer demographic for the tested skis than a specially selected, more homogeneous test group might be.

Conclusion A versatile quantitative data set was produced from the designed instrumentation system and methodology. The uncontrollable factors that present themselves in the natural environment of slalom water skiing were effectively minimized. The data streams produced from the IMU on the water ski, rope-mounted transducer, and skier- and boat-mounted GPS sensors allowed the reliable differentiation between left and right turns, the subsequent subdivision of slalom turn biomechanics into five distinct phases and the quantification of 11 performance parameters. The maximum and minimum values for each parameter were determined from the overall data set. The range of values obtained for each parameter was 44.5°– 59.4° for peak roll, 67.3–109.4°
s for integral of roll, 5.2–13.6 m/s2 for peak acceleration, 28.1 to 12.5 m/s2 for peak deceleration, 2.1–6.2 m/s2
s for integral of acceleration and 24.3 to 29.3 m/s2
s for integral of deceleration. A statistical analysis was only able to identify a difference between the ski designs for one of the performance parameters, peak roll. Statistical analysis was also able to identify the expected difference between skiers for all of the performance parameters. In addition, based on the Buoy Success Rate versus performance parameter results, each subject achieved their expected level of performance. The subject with the highest Buoy Success Rate was among the top three highest for 10 of the 11 performance parameters, and the subject with the lowest

57 success rate was among the bottom two in all the 11 parameters. The expectation that performance parameters are not independent was supported by the quantitative results. The skiers included in this study, those that were able to produce higher peak roll and integration of roll, were able to produce more ski acceleration and deceleration. These same skiers also had greater success in completing the slalom course. Acknowledgements The authors would like to thank Connelly Skis for donating equipment to this study and Leo and Deb Cormier for the use of their water ski facility, Lighthouse Lake Water Sports Centre. Declaration of conflicting interests The authors declare that there is no conflict of interest. Funding This work was supported in part by the Natural Science and Engineering Research Council of Canada (grant no. 218075). References 1. SGMA International. Sports participation in America 2003, http://www.sfia.org/reports/145_Sports-Participation-in-America-2003 (2003). 2. Pan American Games Records, http://www.iwsf.com/ panamnews/?page_id=27 (accessed April 2011). 3. International Waterski & Wakeboard Federation. International Waterski & Wakeboard Federation 2011 tournament water ski rules, http://www.iwsf.com/rules/2011/ 2011WaterskiRulebook.pdf (accessed April 2011). 4. Water Ski and Wakeboard Canada. Build the skills water ski technical manual. Ottawa, ON, Canada: Water Ski and Wakeboard Canada, 2011. 5. Runciman RJ. Water skiing biomechanics: a study of intermediate skiers. Proc IMechE, Part P: J Sports Engineering and Technology 2011; 225(4): 231–240. 6. Bray-Miners J, Runciman RJ and Monteith G. Water skiing biomechanics: a study of advanced skiers. Proc IMechE, Part P: J Sports Engineering and Technology 2013; 227(2): 137–146. 7. Macken JA. Water ski performance analysis method and apparatus. Patent 5694337, USA, 1997. 8. Bray-Miners J, Runciman RJ and Groendyk N. Methods and instrumentation for the biomechanical analysis of slalom water skiing. Proc IMechE, Part P: J Sports Engineering and Technology 2014; 228: 75–85. 9. Snedecor GW and Cochran WG. Statistical methods. 7th ed. Ames, IA: Iowa State University Press, 1980.