400 RQES: September 2011

Supej and Holmberg

Key words: GPS, mechanics, motion analysis, performance

In numerous sports, time is one of the most crucial parameters in quantifying performance (Foster et al.,

1993; Nevill & Whyte, 2005; Nevill, Whyte, Holder, & Peyrebrune, 2007). In addition to total performance time, lap or intermediate times are often measured during com-petitions in order to provide further information about changes and improvements in performance through the different sections of a race (Robertson, Pyne, Hopkins, & Anson, 2009). In sports like running, swimming, and speed skating, these time points are standardized to cer-tain distances (each lap), whereas in other sports they are generally decided along the course of each race (e.g., in alpine and cross-country skiing).

In a recent study of alpine skiing, time was also used to evaluate the impact of the skier’s action on friction between the skis and snow (Federolf et al., 2008). An-other study in alpine skiing demonstrated that one or two intermediate times are insufficient for analyzing the

skier’s technical and tactical abilities along a course, or to demonstrate exactly where a skier loses or gains time (Supej & Cernigoj, 2006). Similarly, performance has also been studied over multiple sections in other sports such as sprint running (Smirniotou et al., 2008), orienteering (Larsson & Henriksson-Larsén, 2001), and cross-country skiing (Larsson & Henriksson-Larsén, 2005). No studies, to our knowledge, have investigated gate-to-gate times throughout the whole alpine slalom course, the benefits of which could be more detailed and precise information about where significant differences between skiers occur and for how many gates performance is affected after these differences. To measure gate-to-gate time, there is a need for a precise measurement system with high reliabil-ity. Technological methods for measuring time range from the simplest stopwatches and photocells to more advanced systems that rely on factors such as contact carpets, force plates, “clock/running chips,” and video-based systems. However, these methods have limitations regarding their accuracy and potential for use if one wants to measure multiple times over long distances in alpine skiing.

The Global Navigation Satellite System (GNSS) is a term for different satellite navigation systems that provide autonomous global geospatial positioning, among which the U.S. Global Positioning System (GPS) has been used in many different human locomotion and sport measure-ments (Larsson, 2003). GPS has been proven to be reliable

A New Time Measurement Method Using a High-End Global Navigation Satellite System to Analyze Alpine Skiing

Matej Supej and Hans-Christer Holmberg

Submitted: July 22, 2009 Accepted: August 24, 2010 Matej Supej is with the Department of Biomechanics at the University of Ljubljana. Hans-Christer Holmberg is with the Department of Health Sciences at Mid Sweden University.

Accurate time measurement is essential to temporal analysis in sport. This study aimed to (a) develop a new method for time com-putation from surveyed trajectories using a high-end global navigation satellite system (GNSS), (b) validate its precision by compar-ing GNSS with photocells, and (c) examine whether gate-to-gate times can provide more detailed information about alpine skiing performance. The results demonstrated small mean time differences with no systematic bias, with a velocity dependent scatter of time differences, which diminished at higher velocities. Furthermore, the multiple gate-to-gate and lag times demonstrated that the GNSS enabled a more detailed analysis compared to photocells. The measurements using GNSS showed high validity and potential as a tool for more specific analysis of performance in skiing.

Research Quarterly for Exercise and Sport©2011 by the American Alliance for Health,Physical Education, Recreation and DanceVol. 82, No. 3, pp. 400–411

Measurement and Evaluation

RQES: September 2011 401

Supej and Holmberg

for measuring distance and velocity in several outdoor activities (Edgecomb & Norton, 2006; Schutz & Chambaz, 1997; Schutz & Herren, 2000; Townshend, Worringham, & Stewart, 2008; Witte & Wilson, 2004, 2005). On the other hand, GNSS has never been used to accurately measure performance using intermediate times, even though the system’s internal computation of positions relies on very accurate atomic clock time measurements (Parkinson & Spilker, 1996; Terrier, Turner, & Schutz, 2005).

The aims of this study were to: (a) develop a new method and procedure for calculating times between events in different locomotor actions, using a high-end, real-time kinematics, global navigation satellite system (GNSS RTK); (b) validate its precision by comparing timings calculated from trajectories surveyed using GNSS RTK with timings based on photocell data; and (c) ex-amine whether gate-to-gate times can provide additional data to analyze competitive alpine skiing performance in more detail.

General Method

Overview

First, a new mathematical procedure was developed for time computation from GNSS RTK-recorded data. Two independent experiments were conducted, one with a specially designed trolley and one with athletes running, to validate the computation and the instruments used in more standardized conditions. Thereafter, a slalom alpine skiing experiment was conducted in open terrain and with more complex skiing movements, in order to show the functionality and advantages of the proposed system and methodology as compared to the typically limited use of photocells when analyzing alpine skiing.

Participants

The participants consisted of 8 top-level alpine ski racers, 4 women (M age = 22.8 years, SD = 4.9; M height = 1.67 m, SD = .03; M weight = 57 kg, SD = 3.5) and 4 men (M age = 21.8 years, SD = 4.1; M weight = 1.78 m, SD = .08; M weight = 78 kg, SD = 4.3). Procedures were explained in detail before participants signed a written informed consent. The Ethical Committee of the Faculty of Sport in Ljubljana, Slovenia, approved all procedures for this study, which was conducted according to the Declaration of Helsinki.

Time Computation

All GNSS systems can capture a single point in space or track a single three-dimensional (3D) trajectory, r, in time sequences, ti, denoted as r(ti). Despite the fact that

GNSS systems retrieve geodetic latitude, longitude and height, the trajectory r(ti) can be expressed with two per-pendicular planar coordinates and height, using Universal Transverse Mercator zone projections. When GNSS is used on athletes, the r(ti) represents the survey of the locomo-tion. Because measuring time on certain sections of the trajectory is of interest, it is necessary to construct j refer-ence planes, Pj, along the trajectory, which represents the boundaries of those sections. If the trajectory r(ti) passes boundary planes Pj, intersection points can be found (see Figure 1), representing the events of entering and exiting a certain section along the movement.

To calculate the times of intersections, it is only when r(ti) passes Pj, not where that is of interest. For that purpose, a special routine was created in Matlab R2007a (Math-works, Natick, MA, USA). A two-way Kalman filter is used on the surveyed trajectory r(ti) with boundary conditions, so that each filtered position on the r(ti) will be within the known error for each position point provided by the GNSS. After that, the time calculation process continues and uses the following assumptions. By mathematical definition, one point, pj, located on Pj and a normal vector, nj, declares [AQ: Unless this is jargon, “defines” would be better.] the plane Pj. In this case, pj represents the location of the boundary plane Pj, and the normal vector nj gives the orientation of the plane, which should be approximately aligned with the athlete’s movement when passing this plane. If the product nj · (r(ti) - pj) > 0, then the point r(ti) has a time sequence location after the plane Pj and vice versa. This principle is used to find an approximate time, tj’. If the product in this region equals zero, the r(ti) is located on the plane, and ti is the time of cross-section tj. If the r(ti) is not located on the plane, to

1

2

3

4

Figure 1. Drawing of the trajectory r(ti) passing the reference plane Pj defined with a reference point pj and normal vector n. The arrow points to the intersection between the surface Pj and trajectory r(ti).

402 RQES: September 2011

Supej and Holmberg

calculate a more accurate time or the final time tj, cubic spline interpolation has been used on r(ti) and a minimi-zation process with the condition nj · (r(tj) - pj) ≤ .001 m.

Normal vectors that define the orientation of the reference planes, Pj, also need to be derived in the calcula-tion process. For this purpose, besides measuring a single point, pj, for each Pj, an auxiliary point, pj’, also needs to be defined or measured to calculate nj = (pj’ - pj)/pj’ - pj. This point pj’ is established so that nj is approximately aligned with the athlete’s trajectory at point pj. Furthermore, ath-letes’ trajectories in outdoor sports may have various con-figurations, resulting in several crossings of r(ti) through the same Pj. Therefore, boundary conditions were set for each Pj where it should be crossed by r(ti). All time calcu-lations were executed in a custom-built application after the GNSS data were transferred to a portable computer.

Instruments

A high-end GNSS RTK system with 99.99% position survey reliability, according to the manufacturer (Leica Geosystems AG, Heerbrugg, Switzerland), was used to measure athletes’ trajectories, r(ti). A rover and a refer-ence station were built from equal hardware components: a dual-frequency L1/L2, geodetic, GNSS RTK receiver (Leica GX1230GG); Leica GLONASS/GPS AX1202 GG survey antenna; and Leica Satelline 3AS radio modems for real-time corrections. The system works in RTK mode at a maximum 20 Hz sampling rate, with horizontal and vertical accuracy, respectively, of SD = 10 mm + 1 ppm (parts per million) and SD = 20 mm + 1 ppm, according to the manufacturer.

During all data collection, the reference station stood on a fixed tripod less than 350 m away from all the sur-veyed points in order to transmit real-time corrections. To capture the athletes’ trajectories r(ti) the rover’s receiver, modem, and antenna were placed in a small backpack worn by the athlete (see Figure 2c), with the antenna at the level of the upper thoracic spine (T2–T4). Despite the size (.212 x .166 x .079 m) and weight (1.64 kg), the athletes did not complain of performance-related discom-fort and/or disturbance, nor were any such disruptions observable by researchers during the experiments. For survey reference points pj and pj’, the antenna was attached to a 2-m high carbon geodetic pole and the rover was set to a static measurement mode, with horizontal and vertical accuracy, respectively, of SD = 5 mm + .5 ppm and SD = 10 mm + .5 ppm, according to the manufacturer. A local geodetic coordinate system was used; an elevation cut-off angle was set to 15° for all measurements, and the measurements were planned according to a satellite availability prediction using Leica Geo Office Combined software (Leica Geosystems AG, Heerbrugg, Switzerland), in order to provide accuracy (Parkinson & Spilker, 1996). For validation purposes, six sets of Microgate Polyfemo

photocells and Racetime 2 chronometers (Microgate S.r.l., Bolzano, Italy) were used, with a resolution of 3.47·10-5 and 1.25·10-4 s, respectively. The photocells were set approxi-mately at hip height according to the recommendations of Yeadon, Kato, and Kerwin (1999) for a single beam system. At the beginning of the experiments, the rover’s survey antenna was fixed to a geodetic pole, and a minimum of 1,000 positions were surveyed while standing still in RTK mode. This enabled inspection of the “static” accuracy of the GNSS RTK system using the following parameters: (a) the number of visible satellites, which should be ≥ 5 for the system to work, (b) geometric dilution of precision (GDOP) below 6 to assure high precision, and (c) latitude, longitude, and altitude position error below the values specified by the manufacturer, as previously presented.

Experiment 1: Validation with the Trolley

The initial experiment aimed to validate the GNSS system and time computation procedure with a high level of standardization. The GNSS system and photocells both rely on the body’s posture while crossing the refer-ence plane and crossing the optical beam, respectively. Therefore, a special trolley with a vertical straight-edged platform on front was constructed (see Figure 2). This enabled the front edge of the trolley to break the pho-tocell beam at the same time as the antenna passed the reference plane.

Method

Two photocells were placed 10 m apart on a straight and level sprint track. The positions of photocells p1 and p2 were surveyed by the GNSS system. In this case n1 = n2 = (p2 - p1)/p2 - p1. The center of the GNSS antenna, where the midpoint of the surveying sensor is located, was set exactly above the edge of the specially built trolley (see Figure 2a). Three sets of 10 trials were performed, in which the trolley was pushed along the track and trajectories r(ti) were surveyed. Each set of trials had a different velocity: running, fast walking, and slow walking. The start of move-ment was 30 m away from the first photocell.

For the static accuracy test, empirical cumulative dis-tribution functions (CDF) and 95% confidence intervals were calculated for the GDOP values and position error. Statistical significance was set at p < .05 for all analyses. The times that were measured with photocells and calculated from GNSS RTK-surveyed trajectories were compared using Bland and Altman analysis (1986, 1995). The Bland-Altman plots show the time differences on the y-axis. The bias is shown by mean differences. The upper and lower limits are defined with a double standard deviation range (± 2SD), within which 95% of differences should occur if

RQES: September 2011 403

Supej and Holmberg

they are normally distributed. Additionally, linear regres-sion analysis (y = k·x + n) was used to estimate the change in the 2SD of time differences, y, with velocity of move-ment, x. The goodness of the linear regression fit was vali-dated statistically with the coefficient of correlation. The mean times and mean velocities with the corresponding standard deviations for traveling the distance of the 10-m interval photocells were calculated.

Results

The static GNSS accuracy test demonstrated that 95% of all the position errors were less than .007 and .013 m for the latitude/longitude and altitude coordinates, re-spectively. GDOPs were below 2.9 with 10 visible satellites. The Bland-Altman plot in Figure 3a shows the differences in time between the photocell and GNSS measurements.

1

2

3

4

Figure 2. Schema of a rigid trolley’s movement (a), a human body’s changing posture when sprinting (b) past a photocell beam and a reference plane, and (c) an athlete skiing down the course wearing a small backpack equipped with the global navigation satellite system and passing the reference planes Pj-1 and Pj.

404 RQES: September 2011

Supej and Holmberg

The mean differences were small, with no observed sys-tematic bias: -.00008 s (2SD = .006), .0015 s (2SD = .011), and .00004 s (2SD = .018) for the three different transport times for the trolley on the 10-m distance (2.38 ± .4 s, 4.86 ± .65 s, and 9.87 ± .98 s). These times correspond to mean velocities of 4.33 m·s-1 (SD = .8), 2.09 m·s-1 (SD = .28), and 1.02 m·s-1 (SD = .1). The time difference scatter increases with 10-m times. The shorter times correspond to higher velocities, demonstrating a linear relationship between the scatter and velocity, as estimated using linear regression parameters k and n (-.00341 m-1·s2 and .0201 s; r2 = .926, p = .176).

Discussion

The scatter of time differences decreased with velocity (Fig. 3a). The velocity relationship and small mean differ-ences can also be mechanically explained by a relatively constant and small position error in the surveyed data compared to the velocities. The linear regression of the scatter velocity relationship in the validation experiment with the trolley provided two boundary results: (a) the scatter would be zero at velocities higher than 5.89 m·s-1 and (b) at zero velocity, where the highest error would be present, 95% of the differences would be lower than .02 s. Obviously, the times at zero velocities cannot be measured with GNSS or with photocells. However, even at relatively low velocities (4.33 m·s-1), 95% of all the differences will be lower than .01 s. This satisfies the needs for analyzing sport performance, for example in alpine ski racing, where the velocities are more than twice as high.

Experiment 2: Validation with Running

The second experiment was performed to investigate the influence of the human factor when breaking the pho-tocell beam with different body parts, with the antenna crossing the reference beam stationed on the body. To do so, this experiment was performed using the same setup as the validation with the trolley but in more standardized terrain conditions and with linear movement compared to alpine skiing, where more complex conditions occur.

Method

Using the same setup as in Experiment 1, 3 par-ticipants performed 10 runs each. Morphological and anthropometrical characteristics do not influence the accuracy of the GNSS survey. Thus, for validation studies related to GPS the number of participants is not critical (see Townshend et al., 2008). The athletes wore the back-pack with the GNSS system during all runs. The accuracy tests at the beginning of Experiment 1 and both validation

experiments (1 and 2) were conducted over 3 hr on the same day. The statistical procedures used in Experiment 1 were repeated, except for the linear regression analysis.

Results

The Bland-Altman plot in Figure 3b also shows small time differences between the photocell and GNSS mea-surements (.0005 s, 2SD = .0068), with no systematic bias. The athletes ran the 10-m distance in 1.042 (SD = .0046), 1.24 (SD = .01), and 1.48 s (SD = .014), respectively, with corresponding mean velocities of 9.6 (SD = .042), 8.06 (SD = .068), and 6.75 m·s-1 (SD = .064).

Discussion

Based on the velocity-time relationship observed in Experiment 1, it was expected that there would be no scatter, because the velocities were above 5.89 m·s-1. Nevertheless, only a small scatter was present (see Figure 3b), which could be due to one of the problems of using photocells (i.e., that the athletes break the photocell beams randomly with different body parts; Yeadon et al., 1999). This is less apparent when using the GNSS system, because the antenna that triggers the time is fixed to the torso, which is likely to be more stationary than the moving extremities in relation to the center of mass. As a consequence of breaking the photocell beams randomly with different body parts, and due to higher and more similar velocities than those in Experiment 1, the small scatter was velocity independent.

Experiment 3: Slalom Alpine Skiing

The slalom alpine skiing experiment was conducted to validate the GNSS system in open terrain with various configurations, curvilinear motion, and alpine skiing body movements, as well as to demonstrate the functionality and advantages of the GNSS over photocells in alpine skiing conditions.

Method

The alpine skiing experiment took place on open terrain, which was reserved, fenced, and prepared for alpine skiing training so as to minimize risk to the athletes. The terrain began with a steep slope in the first half, with a relatively gentle transition phase, and a flatter slope in the second half. Thirty slalom gates were set, with a gate distance of 12–13 m in the first half and 10–11 m in the second half of the course, where two hairpins with gate dis-tances of 5–6 m were set. All gate distances and course set-tings were according to the International Ski Federation

RQES: September 2011 405

Supej and Holmberg

(FIS) rules (http://www.fis-ski.com/data/document/icr2008.pdf) [AQ: This should be cited as a reference]. The snow was hard and groomed; the skiers had good visibility with an air temperature of -5 °C. Three sets of photocells were used to measure time and were installed below knee height, in accordance with the FIS rules. The first photocell was set one meter below the starting gate, the second at gate 15, and the third at the last gate. The first photocell position, p0, and all gate positions, p1 to p30, were surveyed with the GNSS device. Thus, times at gates p15 to p30 were also recorded using photocells. An addi-tional point, p31, facing the finish line, was also surveyed, enabling the calculation of all nj = (pj+1 – pj)/pj+1 – pj for j = 1, 2…30. The 8 participants performed one run each. An intermediate, an intermediate-to-final, and a final time were measured with the photocells. Gate times from the

GNSS measurements were derived by time computation. In order to examine the GNSS and photocell time dif-ferences, the same sections were derived from the GNSS system as with the photocells. Four female skiers were selected for additional time analysis. The shortest times for these skiers from the start to each of the gates were se-lected. Thereafter the cumulative lags, or time differences to the fastest time up to a certain gate, were calculated.

For the static accuracy test and for the positions sur-veyed during alpine skiing, the statistical analysis used was equivalent to that of Experiment 1. The differences in sec-tion times obtained from the photocells and GNSS were tested with a two-sample t test. The differences between skiers were compared using a range of lags, mean lags, and their 95% confidence intervals. Furthermore, the absolute and relative differences in gate-to-gate times, according

1

2

3

4

Figure 3. A Bland Altman plot shows the differences in time measurements (y-axis) using the GNSS RTK system and pho-tocells in Experiment 1 with the specially built trolley (a) and three different athletes in Experiment 2 (b). The x-axis is the time required to cover a distance of 10 m. Dashed lines correspond to mean differences in time and dash-dot lines to the upper and lower limits within which 95% of differences should occur (M ± 2·SD) in a normal distribution. The oblique arrows (a) indicate the velocity dependency of the scatter. Note that for each test in Experiment 1 (a) mean values and the 95 % interval are shown. The vertical arrows denote the mean velocities vmean.

406 RQES: September 2011

Supej and Holmberg

to their mean values, were calculated for each skier. They were divided into four groups: G1 = the first two gates’ time differences, G2 = the 14th and the 16th gates’ time differences, G3 = the 26th, 27th, 29th, and the 30th gates’ time differences, and G4 = all the remaining gates’ time differences, where G1 is aligned with the starting phase and G2–3 represent special gate combinations and/or ter-rain changes. The Ansari-Bradley test was used to test the dispersion differences between the groups distributions (Ansari & Bradley, 1960).

Results

The static GNSS accuracy test demonstrates that 95% of all the position errors were below .007 and .012 m for the latitude/longitude and altitude coordinates, respec-tively. GDOPs were below 2.6 with 11 satellites visible. During the alpine skiing measurements the number of visible satellites amounted to between 7 and 11. Ninety-five percent of all GDOPs, latitude/longitude, and altitude position errors showed higher values than in the static test: 5.7, .013, and .032 m respectively (see Figure 4). As a result, 83% and 62% of the horizontal and vertical coordinate position errors, respectively, were within the

range specified by the manufacturer. The times provided by the photocells and the GNSS

for the same time sections for the skiers (A–H), and the differences in time between the systems, are presented in Table 1. The mean intermediate time for all skiers was 17.05 s (SD = .07), the mean intermediate-to-final time was 10.75 s (SD =.26), and the mean final time was 27.8 s (SD =.28), with no statistical differences in time between the two measurement systems (p = .998).

Gate-to-gate times for all skiers, as measured by the GNSS, are presented in Figure 5a. The data from GNSS enabled the division of the course into a start phase and three terrain phases: a steep slope phase with relatively long gate-to-gate mean times; a transition phase, where the gate-to-gate mean times decreased; and a flat slope phase with the shortest gate-to-gate mean times. In these phases, four special groups of gates were analyzed in more detail: G1, two gates in the starting phase; G2, two gates in the transition phase, where the change in distance between the gates occurred; G3, four gates after the first hairpin and before the finish line; and G4, all remaining gates set in more constant slope inclination and gate distances. Analysis of these groups of gates demonstrated that the largest absolute time differences between the skiers were (a) in the start phase (G1), (b) during the transition phase

1

2

3

4

5

Figure 4. For the surveyed data in the alpine skiing experiment, the empirical cumulative distribution function (CDF) is shown for geometric dilution of precision (GDOP) values (a) and latitude/longitude and altitude position error (b). The vertical arrows point to the 95% confidence interval.

RQES: September 2011 407

Supej and Holmberg

in G2, and (c) in the flat slope phase after the first hairpin (G3), compared to the differences in gate-to-gate times in G4 (p < .001). The relative gate-to-gate time differences were significantly higher in G2 and G3 compared to G4 (p < .001). The p value for comparison G1–G4 was .11.

All skiers were also analyzed with regard to their cumulative lag times along the course. The results from GNSS and photocells for 4 skiers (A–D; all women) are presented as an example in Figure 5b. The photocells (P1, P2, and P3) demonstrate (a) only a slight difference between the skiers’ intermediate lag times (P2; < .085 s), (b) a large difference in final lag times (range .1–.57 s), and (c) more specifically, that the skiers C and D were faster in the intermediate time (P2) whereas A and B, in contrast, were faster from the intermediate to the final time (P2–P3). The multiple data from the GNSS system provided a comprehensive time profile along the course, where the highest GNSS lag times were always higher than the differences in intermediate lag times obtained with the photocells, except at Gates 1, 16, and 17. Notably, the lag times measured over all gates with the GNSS were smaller than the highest lag times at the end of the course (P3). Analyzing the lag times from the GNSS according to the defined course phases reveals that the skiers performed considerably differently in the various sections of the course and that this information would be missed with typical photocell timing. [AQ: The photocell designations previously were lower case italic with subscripts. Why are they different in this paragraph?]

Discussion

The results demonstrate that the latitude/longitude, as well as altitude, position errors were almost twice and almost three times as high, respectively, during the alpine skiing measurements as in the static tests. In the latter the

position error was markedly lower, but during skiing it was considerably higher than the manufacturer’s specifica-tions. It should be pointed out that the higher position errors predominantly corresponded to a larger GDOP value and a lower number of visible satellites. Therefore, when performing measurements of more complex and curvilinear motion in various terrain configurations, more attention should be paid to monitoring accuracy. Despite the larger GDOP value and lower number of visible satel-lites, the comparison between the section times derived from photocells and GNSS in alpine skiing demonstrated only negligible differences (see Table 1), smaller than those for running in Experiment 2. Smaller differences could be due to a slightly higher velocity and lesser sagittal-plane body movements in alpine skiing than in running.

The alpine skiing experiment demonstrated the importance of having gate-to-gate time analysis, which enables the division of the course into multiple terrain sec-tions and/or rhythm phases (see Figure 5). The present study shows that the start phase is very important in slalom. Similarly, the phase transition and the regions around and after the hairpin bends also show great time differences between the racers. Specific information identifying the gate or turn where the skier started to lose or gain time can be obtained from the cumulative lag times. The new methodology for computing time from high-end GNSS RTK-surveyed trajectories enables precise analysis of the athletes’ performance. Comparing the gate-to-gate times and cumulative lag times to times provided from a limited number of photocells, as is common in alpine skiing, demonstrates how little information is provided by only one intermediate and one final time. Additionally, the study shows that after the two-gate start phase, where the differences between the racers were high, the lag time can start to decrease quickly, because the following gates were on a steep slope (see Figure 5b). On the contrary,

Table 1. GNSS and photocell times(s): intermediate, intermediate to final, and final time differences for all skiers

Intermediate time Intermediate to final time Final time Photocell GNSS Difference Photocell GNSS Difference Photocell GNSS Difference

Skier A 17.072 17.071 0.0008 10.633 10.635 -0.0017 27.705 27.706 -0.0009Skier B 17.104 17.104 0.0001 10.700 10.701 -0.0008 27.804 27.805 -0.0007Skier C 17.045 17.047 -0.0014 11.228 11.226 0.0021 28.273 28.273 0.0007Skier D 17.020 17.018 0.0022 10.984 10.981 0.0023 28.003 27.999 0.0045Skier E 16.920 16.924 -0.0041 10.441 10.439 0.0020 27.361 27.363 -0.0021Skier F 17.088 17.085 0.0031 10.653 10.657 -0.0040 27.741 27.742 -0.0009Skier G 17.140 17.144 -0.0041 10.807 10.803 0.0048 27.947 27.946 0.0007Skier H 17.016 17.012 0.0046 10.536 10.540 -0.0031 27.553 27.551 0.0015M 17.051 17.050 0.00015 10.748 10.748 0.00020 27.798 27.798 0.00035SD 0.068 0.068 0.00320 0.254 0.253 0.00306 0.281 0.280 0.00204

Note. GNSS = global navigation satellite system; M = mean; SD = standard deviation. [AQ: What is the significance of num-bers in bold type?]

408 RQES: September 2011

Supej and Holmberg

when the skiers started to lose time on the flat slope, thus increasing the time lag, many gates were required before they were able to regain gate-to-gate times comparable

to the fastest skier again. Performance behavior on the steep and flat slopes is directly related to regaining the dis-sipated mechanical energy, as discussed by Supej (2008).

1

2

3

4

5 Figure 5. (a) Gate-to-gate times for all 30 recorded gates. Error bars present the 95% confidence interval. Vertical dash-dot lines represent the boundaries of phases along the course, and the horizontal dashed line indicates the 1-s time. Ellipses mark G1–G3 where the highest differences in time between the racers were observed. (b) Cumulative time lags (y-axis) at each gate (x-axis) for four top-level slalom athletes (A–D). Note that the skier with the shortest time to a certain gate has zero cumulative lag (i.e., the fastest time up to that gate). The two rectangles indicate where the intermediate time (P2) and final time (P3) were measured with photocells (P1–P3).

RQES: September 2011 409

Supej and Holmberg

General Discussion

This study produced three main results: (a) a new method and procedure to compute time was developed; (b) validation experiments in more standardized condi-tions showed small differences compared to photocells at low velocities and no difference at velocities higher than 5.89 m·s-1; and (c) compared to photocells, the GNSS pro-vides a more comprehensive analysis of performance, with only negligible differences in time for the more complex curvilinear movement of alpine ski racing.

The time computation method provided times from high-end GNSS RTK-surveyed trajectories in all the se-lected sections, which confirms the method’s robustness regarding errors during the measurements. The results from all three experiments indicate that the derived times are valid. Furthermore, the derived times have small mean differences, no systematic bias, and a narrow scatter compared to the photocell measurements, even though the GNSS system itself works at a 20 Hz sampling rate (see Figure 3).

Some important conclusions can be drawn from the differences in GNSS accuracy measured in the initial static accuracy tests and when monitoring accuracy during al-pine skiing measurements. When high-position precision is needed, the GDOP, the number of satellites, and the position error have to be monitored for each surveyed position during measurements, because the error when using GNSS technology may change rapidly during the measurement period. A static accuracy test alone is not suf-ficient to validate the position error of the system in sports that need precision in centimeters, such as alpine skiing. However, it may be sufficient in other activities such as walking (Townshend, et al., 2008). Furthermore, other fac-tors may affect accuracy. For example, in alpine skiing, the antenna with the inbuilt sensor receiving signals from the satellites is inclined in several directions, or even hidden behind body parts. This decreases the satellites’ visibility and increases the GDOP, thereby negatively influencing the accuracy of the position. Moreover, measurements are affected by the constantly changing constellation of the satellites during the day (Parkinson & Spilker, 1996). Therefore, to ensure the highest number of satellites and the lowest GDOP, planning the time for taking measure-ments according to satellite availability is vital, as previously discussed by Terrier and Schutz (2003); such planning was done in the present study, where 95% of the positions remained below .013 and .032 m in longitude/latitude and altitude, respectively. However, it can be expected that GNSS technology will become even more accurate with the upcoming second generation of European GNSS, called Galileo, and that satellite availability will further increase with Galileo and the increasing number of GPS and GLONASS satellites (Takac & Walford, 2006).

The small error in time derived from the GNSS system is partially due to the orientation of the reference planes and not only the system’s position error. The problem of orientation is similar when using photocells; it depends on where and which part of the body breaks the photocell beam or where the antenna passes the reference plane. When the photocells or the reference planes are set along a linear movement, as in sprint running, they need to be perpendicular to the running direction in order to minimize error. In alpine skiing, where more complex curvilinear motion is present, the “left-right” orientation of the reference planes and photocells should be approxi-mately aligned with the ski direction in order to trigger times, but this alignment can be intentionally altered for different research questions. On the other hand, the forward-backward inclination of the reference planes may introduce errors, which were minimized in the current study by aligning planes with the slope inclination (gate positions were used to calculate normal vectors). The reason for these alignments being advantageous is the skiers’ precise longitudinal balance around the gates due to high ground-reaction forces. The precise longitudinal balance, as a consequence of various trunk inclinations, leads to differences of a few centimeters in the antenna’s position relative to the center of mass. Therefore, an ex-pected difference of 3 cm at 10 ms-1 skiing velocity would introduce a time error of 0.003 s.

The present study shows that GNSS RTK provides reliable and accurate data and can be used both for scientific purposes and for training in sports with high technical demands, which benefit from detailed infor-mation. At present, use is reserved to sport scientists and more technically skilled coaches. However, in the future we believe that it might become more widely used among coaches if the methodology were to be integrated with the system. The GNSS system, compared to photocells, enables a large number of section times that can be added or shifted after the measurements without any additional costs. Moreover, the system was proven to be functional in the demanding sport of alpine skiing, where turns can have a duration of much less than one second (see Fig-ure 5a) and the surveyed trajectories are predominantly curvilinear, which has proven to be problematic in less complex human locomotion, such as walking and cycling, using a ordinary handheld GPS with 20 times lower GPS-position sampling rate (Duncan, Badland, & Mummery, 2009; Townshend, et al., 2008). The introduced computa-tion method can also be used in combination with other measuring technology, such as a local positioning system, laser guns, three-dimensional kinematics or other sensor-based systems that capture full body movement. One prerequisite is that they should provide adequate accuracy and sampling rate for the representative trajectory when compared to the required time resolution, as well as the type of locomotion.

410 RQES: September 2011

Supej and Holmberg

In theory, using photocells and a GNSS system would provide the same time information, if the photocells were placed at every gate. However, in practice it is nearly impossible to set a photocell system in a reasonable time on a slalom course, which typically exceeds 50 gates. Furthermore, accidents have also been reported when using multiple photocells in skiing. At present, there are no commercially available photocell sets that can control more than 10 wireless photocells with identification (i.e., the stopwatch receives time and identification from each photocell). This is essential for measurements where a large number of photocells are used and the times are as short as those in alpine skiing. Therefore, only a custom-built system is currently applicable, and it has a price comparable to a high-end GNSS. As with other technolo-gies, GNSS technology is in the process of miniaturization, which will most likely further improve its applicability. An obvious limitation is that a GNSS system can only be used outdoors, whereas in sports with a permanent measure-ment site, such as in running, or when a lower number of intermediate times is needed, photocells could be the preferred alternative.

The method of computing time from a high-end GNSS RTK-surveyed trajectory provides reliable and ac-curate results for measurements in outdoor sports. GNSS RTK also enables the measurement of a large number of times, which is of great importance for more detailed performance analysis of demanding human locomo-tion. When multiple section times and high accuracy are required, time measurements using GNSS are a potential alternative to the commonly used photocells. Although the GNSS RTK is expensive and heavy for use during com-petitions, it is the only global navigation satellite system that currently provides a low enough position error and high enough sampling rate to adequately calculate time in demanding elite sports.

References

Ansari, A. R., & Bradley, R. A. (1960). Rank sum tests for disper-sions. Annals of Mathematical Statistics, 31, 1174–1184.

Bland, J. M., & Altman, D. G. (1986). Statistical methods for assessing agreement between two methods of clinical measurement. Lancet, 327, 307–310.

Bland, J. M., & Altman, D. G. (1995). Comparing methods of measurement: Why plotting difference against standard method is misleading. Lancet, 346, 1085–1087.

Duncan, M. J., Badland, H. M., & Mummery, W. K. (2009). Ap-plying GPS to enhance understanding of transport-related physical activity. Journal of Science and Medicine in Sport, 12, 549–56.

Edgecomb, S. J., & Norton, K. I. (2006). Comparison of global positioning and computer-based tracking systems for meas-uring player movement distance during Australian football. Journal of Science and Medicine in Sport, 9, 25–32.

Federolf, P., Scheiber, P., Rauscher, E., Schwameder, H., Luthi, A., Rhyner, H. U., & Müller, E. (2008). Impact of skier actions on the gliding times in alpine skiing. Scandinavian Journal of Medicine and Science in Sports, 18, 790–797.

Foster, C., Snyder, A. C., Thompson, N. N., Green, M. A., Foley, M., & Schrager, M. (1993). Effect of pacing strategy on cycle time trial performance. Medicine & Science in Sports & Exercise, 25, 383–388.

Larsson, P. (2003). Global positioning system and sport-specific testing. Sports Medicine, 33, 1093–1101.

Larsson, P., & Henriksson-Larsén, K. (2001). The use of dGPS and simultaneous metabolic measurements during orienteering. Medicine & Science in Sports & Exercise, 33, 1919–1924.

Larsson, P., & Henriksson-Larsén, K. (2005). Combined meta-bolic gas analyser and dGPS analysis of performance in cross-country skiing. Journal of Sports Sciences, 23, 861–870.

Nevill, A. M., & Whyte, G. (2005). Are there limits to running world records? Medicine & Science in Sports & Exercise, 37, 1785–1788.

Nevill, A. M., Whyte, G. P., Holder, R. L., & Peyrebrune, M. (2007). Are there limits to swimming world records? [Arti-cle]. International Journal of Sports Medicine, 28, 1012–1017.

Parkinson, B. W., & Spilker, J. J. (1996). Global positioning system: Theory and application. Vol.1. Washington, DC: American Institute of Aeronautics and Astronautics.

Robertson, E., Pyne, D., Hopkins, W., & Anson, J. (2009). Analy-sis of lap times in international swimming competitions. Journal of Sports Sciences, 27, 387–395.

Schutz, Y., & Chambaz, A. (1997). Could a satellite-based naviga-tion system (GPS) be used to assess the physical activity of individuals on earth? European Journal of Clinical Nutrition, 51, 338–339.

Schutz, Y., & Herren, R. (2000). Assessment of speed of human locomotion using a differential satellite global positioning system. Medicine & Science in Sports & Exercise, 32, 642– 646.

Smirniotou, A., Katsikas, C., Paradisis, G., Argeitaki, P., Zacharogi-annis, E., & Tziortzis, S. (2008). Strength-power parameters as predictors of sprinting performance. The Journal of Sports Medicine and Physical Fitness, 48, 447–454.

Supej, M. (2008). Differential specific mechanical energy as a quality parameter in racing alpine skiing. Journal of Applied Biomechanics, 24, 121–129.

Supej, M., & Cernigoj, M. (2006). Relations between different technical and tactical approaches and overall time at men’s world cup giant slalom races. Kinesiologia Slovenica, 12(1), 63–69.

Takac, F., & Walford, J. (2006, September 26–29). Leica system 1200—High performance GNSS technology for RTK applications. Paper presented at the 19th International Technical Meet-ing of the Satellite Division of the Institute of Navigation (ION GNSS 2006), Fort Worth, TX.

Terrier, P., & Schutz, Y. (2003). Variability of gait patterns dur-ing unconstrained walking assessed by satellite positioning (GPS). European Journal of Applied Physiology, 90, 554–561.

Terrier, P., Turner, V., & Schutz, Y. (2005). GPS analysis of human locomotion: Further evidence for long-range correlations in stride-to-stride fluctuations of gait parameters. Human Movement Science, 24, 97–115.

RQES: September 2011 411

Supej and Holmberg

Townshend, A. D., Worringham, C. J., & Stewart, I. B. (2008). Assessment of speed and position during human locomo-tion using nondifferential GPS. Medicine & Science in Sports & Exercise, 40, 124–132.

Witte, T. H., & Wilson, A. M. (2004). Accuracy of non-differential GPS for the determination of speed over ground. Journal of Biomechanics, 37, 1891–1898.

Witte, T. H., & Wilson, A. M. (2005). Accuracy of WAAS-enabled GPS for the determination of position and speed over ground. Journal of Biomechanics, 38, 1717–1722.

Yeadon, M. R., Kato, T., & Kerwin, D. G. (1999). Measuring running speed using photocells. Journal of Sports Sciences, 17, 249–257.

Authors’ Notes

A grant from the Foundation for Financing Sport Orga-nizations in Slovenia and the Slovenian Research Agency provided support for this study. Please address correspon-dence concerning this article to Hans-Christer Holmberg, Swedish Winter Sports Research Centre, Department of Health Sciences, Mid Sweden University, Östersund, Sweden.

E-mail: hc.holmberg@miun.se