How gate setup and turn radii influence energy dissipation in slalom ski racing

454

Journal of Applied Biomechanics, 2010, 26, 454-464© 2010 Human Kinetics, Inc.

Matej Supej is with the Faculty of Sport, University of Ljubljana, Ljubljana, Slovenia. Hans-Christer Holmberg (Corresponding Author) is with the Swedish Winter Sports Research Centre, Department of Health Sciences, Mid Sweden University, Östersund, Sweden.

How Gate Setup and Turn Radii Influence Energy Dissipation in Slalom Ski Racing

Matej Supej and Hans-Christer Holmberg

This study examined whether gate setup and turn radii influence energy dissipation in slalom skiing. 3D kinematical measurements were performed over two runs on the same slope in a WC slalom competition with two different gate setups: 1) open gates (OG) and 2) open gates with a delayed gate (DG). Using the arithmetic mean of the skis’ turn radii (RAMS) the slalom turns were divided into 1) initiation phase (RAMS > 15m) and steering phase (RAMS < 15m). The results show differences between OG and DG regarding: 1) the absolute center of gravity’s (CG) velocity, 2) absolute acceleration, 3) CG turn radii and RAMS, 4) ground reaction forces (F) and 5) energy dissipation during skiing (all p < .05). In both gate setups the highest F and the highest energy dissipation were present in the steering phase, whereas the correlation between RAMS and energy dissipation was low (OG: r = .364 and DG: r = .214, both p < .001). In summary, compared with plain open gates, an additional delayed gate prolonged the turn radii and decreased energy dissipation in the begin-ning of the initiation phase, despite the fact that the relative frequency of occurrence of the highest energy dissipation was higher in DG.

Keywords: 3D kinematical measurements, alpine skiing, forces, mechanical energy, velocity

Slalom alpine ski racing is a demanding sport in a complex outdoor environment. Elite skiers now use carv-ing skis which could be used either for carved turns, i.e., where the ski edge angle is directly related to the ski side-cut radius (Howe, 1983; Müller & Schwameder, 2003; Niessen & Müller, 1999), or side skidding turns based on other mechanical principles (Hirano & Tada, 1994, 1996; Kugovnik et al., 2000; Lieu & Mote, 1984; Renshaw & Mote, 1989; Tada & Hirano, 2002). By definition, the ski cannot carve above the ski’s sidecut radius (RS), i.e., the radial measurement of the curve that matches the inner curvature of a stretched ski. As a consequence, even at the highest racing performance level, where the skiers aim to carve as much as possible, two different mechanical modes of turning exist: 1) where the skis can carve (radii < RS) and 2) where the skis side skid or travel straight ahead (radii > RS).

Due to complexity of turning principles and chang-ing conditions in alpine skiing, it has been shown that differences among top level skiers in Word Cup (WC) races can be up to 10% over relatively short course sec-tions that are divided into slope and gate setup changes (Supej & Cernigoj, 2006). To investigate these differences in more detail, a new parameter was recently developed

for estimating the quality of alpine skiing at each point of observation, i.e., differential specific mechanical energy, diff(emech) (Supej, 2008). This is based on the following physical assumptions: there is a reason to state that the main “motor” in alpine racing ski racing is potential energy. When a skier descends a slope the difference in potential energy equals the sum of the difference in kinetic energy and the work of energy dissipation, which in alpine skiing consists of ski-snow friction and air drag. The ski-snow friction encompasses the tribological prop-erties of the skis and, most importantly, the imprecise/precise guiding of skis. A small portion of energy can also be gained by muscle work (Lind & Sanders, 1996) which depends on the skiing velocity, lateral ski-snow contact and ground reaction forces acting on the skier.

To illustratively explain where the highest and the lowest energy dissipations occur, the turns can be divided into different phases. The most commonly used phases are: 1) initiation phase, 2) steering phase into the fall line and 3) steering phase out of the fall line (Müller et al., 1998). The initiation phase is mainly characterized by weight transition, the edge change period up to the point of up-loading the edge, whereas the steering phases are characterized by steering into and out of the fall line, respectively. The fall line is normally defined as a virtual line aligned with the direction of the steepest inclina-tion of the slope. Because the velocities in slalom range roughly from 10 to 15 m·s-1, the air drag’s magnitude, using the values for frontal area and coefficient of air drag (Barelle et al., 2004), is several times lower than the magnitude of the dynamic component of the force of

Gate Setup and Turn Radii Influence Energy Dissipation 455

gravity on moderate slopes. Applying Newton’s second law and the fact that the skiers, on average, maintain velocity throughout the course, friction should play the major role in slalom’s energy dissipation. Therefore, as previously shown (Reid et al., 2009; Supej, 2008), it is to be expected that the highest energy dissipation is present in the steering phases, whereas the lowest energy dissipa-tion is in the initiation phase or around weight transition.

It has also been shown that the center of gravity’s turn radius and ski attack angles, i.e., the outside ski’s degree of skidding, do not alone determine the dissipation in slalom (Reid, et al., 2009). On the other hand, the impor-tance of trajectories and the skis’ turn radii has only been demonstrated in giant slalom (Supej, 2008), but it has not been proven whether there is a relationship between the skis’ turn radii and energy dissipation. Nor has it been investigated whether different gate setups influence the skis’ turn radii and energy dissipation, despite the pos-sibility that these relationships could explain the observed high differences between skiers over short course sections (Supej & Cernigoj, 2006).

The hypotheses to be tested are (H1) that gate setup affects the turn radii and (H2) that the turn radii are related to energy dissipation in slalom ski racing. Therefore, the aims of the current study were to investigate whether 1) the gate setup affects the turn radii and 2) the turn radii are related to energy dissipation in slalom ski racing.

Methods

Subjects

The experiments were performed on 12 elite male slalom ski racers (age: 26.8 ± 2.2 years; 1.75 ± 2.1 World Cup (WC) podium places in the current season; 7.2 ± 6.5 FIS points; 7 of the racers finished in the top 10 and the other 5 were placed between the 10th and the 25th place in the current World Cup). The athletes signed informed written consent. The study was approved by the WC race director and race organizer, as well as by the Ethical Committee of the Faculty of Sport in Ljubljana.

Instruments

For three-dimensional kinematical measurements, six fixed 50 Hz gen-locked Sony DV-CAM DSR 300 PK professional camcorders and two additional Pan-Tilt-Zoom Sony MiniDV DCR-TVR 30 E camcorders (Sony Corp., Tokyo, Japan) were used (Figure 1). The space was calibrated using a tachymeter Leica TCR1102 X-Range (Leica Geosystems AG, Heerbrugg, Switzerland), and eight 1.95 m long aluminum calibration poles with special reflective markers. To estimate the error of the measured data, the outside poles of the slalom gates were used. These were first measured with the Leica tachymeter and compared with the three-dimensional kinematical

Figure 1 — The schema of the motion acquisition system placement.

456 Supej and Holmberg

measurements. The standard deviation of the differences in location was 1.6 cm. A more detailed description of the three-dimensional measurement method is described elsewhere (Supej, 2008).

Experiment Design

The three-dimensional kinematical measurements were performed at the slalom WC races held in Kranjska Gora, Slovenia. All 12 participants were recorded on the 1st and 2nd runs on the same day, using the same slope with an average slope inclination of 20°. The recording frame started at gate numbers 14 and 15 on the 1st and on the 2nd runs respectively. Thereafter, four open gates were recorded on both runs; the difference in gate setup was that on the 2nd run an additional delayed gate was set in the middle (Figure 2). All gate distances and course setting complied with the International Ski Federation (FIS) rules (http://fis-ski.com/data/document/icr2008.pdf). During both runs there were good snow conditions

with hard, groomed snow at a temperature of –1 °C with a relative humidity of 68%. In addition, gate keepers and course staff prepared the course between each racer to maintain the same conditions. The conditions were well suitable for WC race standards and the weather enabled good visibility for the skiers.

To calculate the mechanical parameters at each point of observation from the 3D kinematical measurements, we used custom software (KinSki 3.1, Kranjska Gora, Slovenia). This system calculated the specific mechani-cal energy emech = v2/2 + gz and differential specific mechanical energy diff(emech) = –Δ(v2/2)/Δz – g, where v represents the absolute velocity of the skier’s center of gravity, z the altitude, g the gravity and Δ the differential. Because altitude continuously decreases, the sign of diff(emech) equation is changed. Smaller (more negative) values therefore represent inefficient skiing, whereas higher values represent efficient skiing (Supej, 2008). More specifically, diff(emech) represents the rate of specific mechanical energy dissipation per altitude difference.

Figure 2 — The schema of the measured gates in the open gate (left) and the delayed gate combination (right) with absolute gate distances. Squares represent red gates and circles represent blue gates. The turn phases are shown as: I1—initiation phase 1, I2—initiation phase 2, S1—steering phase 1 and S2—steering phase 2.


Specific values are used to eliminate a skier’s mass and altitude differential, instead of time differential, to elimi-nate the factor of a skier’s exact location as explained in more detail elsewhere (Supej, 2008). The turn radii R were calculated by fitting an arc segment on each set of three neighboring points on the centers of gravity (RCG) and on the arithmetic mean of the skis’ trajectory (RAMS). The latter was derived as the arithmetic mean of the ankle joints at each point of observation. Newton’s second law was used to estimate ground reaction forces (F). These were calculated as the sum of the acceleration vector multiplied by the mass of the skier and the static component of the gravity force. The ground reaction force is presented in multiples of body weight (BW). The last parameter, the skier’s acceleration a, was calculated using linear approximation from the CG’s absolute velocity v smoothed by zero-lag 3rd order digital Butterworth filter with the cut-off frequency of 7 Hz.

Using the analogy described by Müller et al. (1998), the turns were divided into initiation and steering phases (Figure 2), but with some differences. First, the initiation phase was restricted to the area where the skiers averages were RAMS above 15 m, which is the upper limit of the used ski sidecut radius (RS). Second, the initiation phase was divided into two phases (I1 and I2) by mean weight transition point, which was defined by the mean cross section of the CG’s trajectory and the arithmetic mean of the skis’ trajectory orthogonally projected onto the snow surface of all subjects (Reid et al., 2009; Supej et al., 2003). Third, the steering phases into the turn (S1) and out of the turn (S2) were divided by the turn’s gate position.

Statistics

For all mechanical parameters, empirical cumulative distribution functions (CDF) were calculated in both gate setups and the CDFs for v, F and a. The parameters diff(emech), RCG and RAMS were compared in histograms, where bars represents the relative frequency of occur-rence. The differences between the CDF functions for the different gate setups and for all parameters were tested for suprema and medians using the Kolmogorov-Smirnov test (KS-test) and the Wilcoxon rank-sum test (WRS-test), respectively. The relationships between the parameters were estimated using scatter plots and by linear regressions. The goodness of linear regression fit was estimated by Pearson product-moment correlation coefficient. Data were expressed as means ± SD (SD).

The significance level was set at p < .05. Statistical analysis was performed in Matlab 2007a (Mathworks, Natick, MA, USA).

ResultsThe KS test demonstrated that all the investigated parameters’ CDF suprema between the two gate setups were significantly different (p < .05), whereas the WRS test showed that the median was significantly different as regards diff(emech), F and v (p < .001), with a trend (p = .059) observed for the RCG (Table 1). For both gate setups, 95% of all the measured velocities were approxi-mately 11–13 m·s–1 and the medians for the open and the delayed gate combination (abbreviated to OG and DG in the results section) were 12.41 and 12.64 m·s–1, respectively. F ranged from 0 to 4.2 BW with medians of 1.428 and 1.692 BW for the OG and DG, respectively. a ranged from approximately –8 to approximately 8 m·s–2, with similar medians for the two gate setups (OG: 0.717 m·s–2; DG: 0.551 m·s–2).

RAMS, which defines the turn phases, and the second-order differential parameters diff(emech), F and a were plotted for both gate setups (Figure 3 & 4). The initiation phases (I1+I2) were shorter along the fall line in DG than in OG, despite longer turns. The skiers were, on average, dissipating less energy, i.e., higher diff(emech), in I1+I2, compared with the steering phases in both gate setups. The diff(emech) difference in I1+I2 between the two gate setups was highest in the middle of the measurement area, where the additional delayed gate was set (Figure 3c-d). In this area, the peak diff(emech) and a was close to the beginning of I2 in the OG (Figure 3c-d), whereas in the DG it was close to the end of I1 (Figure 4c-d). The standard deviation of diff(emech) in I2 of the 1st turn was markedly higher in the DG compared with the OG (Figure 3c-d). Relatively high diff(emech) values were measured in the I1+I2 in both gate setups, whereas the highest positive diff(emech) were observed in I2 of the 2nd turn (Figure 3c-d). F reached a minimum in I1 in all turns (Figure 4a-b).

The steering phases (S1+S2) were markedly longer along the fall line in the DG compared with the OG (Figure 3a-b). The RAMS in the OG decreased in S1 and increased in S2 (Figure 3a), whereas in the DG two RAMS minimums were observed in each turn, one in S1 and one in S2 (Figure 3b). The lowest diff(emech) in the 1st turn were observed in the middle of S1 in the OG and in the

Table 1 Statistical differences in diff(emech), RAMS, RCG, F, a and v between the open gates and the delayed gate combination

diff(emech) RAMS RCG F a v

KS-test < .0001 < .0001 < .0001 .0126 .0348 < .0001

WRS-test .0001 .379 .059 .0068 .311 < .0001

Note. Statistical differences were tested with the Kolmogorov-Smirnov test (KS-test) and Wilcoxon rank-sum test (WRS-test). Abbreviations: diff(emech), differential specific mechanical energy; RAMS, arithmetic mean of skis’ turn radii; RCG, centers of gravity’s turn radii; F, ground reaction forces; a, acceleration; v, velocity.


middle of S2 in the DG. In the 2nd turn the highest energy dissipation, i.e., the lowest diff(emech), occurred close to the open gate in both gate combinations and thereafter decreased in S2 (Figure 3c-d). A large diff(emech) standard deviation was observed in S2 of the 1st turn in the DG (Figure 3d), whereas the lowest diff(emech) were associ-ated with the 2nd turn’s RAMS minimum in both turns (Figure 3b&d). The highest F was associated with the lowest RAMS in all turns (Figure 3a-b & 4a-b). Minimum a values were observed in S1, except in the 1st turn of the DG where the a minimum occurred in S2 (Figure 3c-d).

In Figure 5a the differences in diff(emech) are divided into four intervals, where the DG had a higher frequency of diff(emech) at the values below –21.25 J·kg–1·m–1 and between –13.75 and 5 J·kg–1·m–1, whereas the OG had a

higher frequency at the values between –21.25 and –13.75 J·kg–1·m–1, as well as above 5 J·kg–1·m–1. The differences below 5 J·kg–1·m–1 were mainly the result of differences in phases S1 and S2, whereas the difference between 5 and 15 J·kg–1·m–1 was mainly the result of differences in S2 and I2 of the 1st turn (also see Figure 3c-d). In both gate setups, the RCG and RAMS differences were highest in S1 and S2 and in the OG the distributions shifted toward longer radii (Figure 5b-c). For the OG the higher frequen-cies of RCG and RAMS values were below 9.5 and 8.5 m, respectively, whereas the higher frequencies of RCG and RAMS values for the DG were between 9.5 and 15.5 m and between 8.5 and 13.5 m, respectively.

The scatter plots in Figure 6a-b show the relation-ships between F and RAMS for the two different gate

Figure 3 — The diagrams shows the arithmetic mean of skis’ turn radii RAMS for the open gates (a) and the delayed gate combina-tions (b) and the differential specific mechanical energy diff(emech) for the open gates (c) and the delayed gate combinations (d). All diagrams are plotted against fall line with marked turn phases: I1—initiation phase 1, I2—initiation phase 2, S1—steering phase 1 and S2—steering phase 2. The solid curve and the gray shade represent mean and standard deviation, respectively.


Figure 4 — The diagrams shows the ground reaction forces F for the open gates (a) and the delayed gate combinations (b) and the acceleration a for the open gates (c) and the delayed gate combinations (d). All diagrams are plotted against the fall line with marked turn phases: I1—initiation phase 1, I2—initiation phase 2, S1—steering phase 1 and S2—steering phase 2. The solid curve and the gray shade represent mean and standard deviation, respectively.

setups. Two distinct phases aligned with the turn phases were observed. For the S1+S2, the relationships were estimated using linear regression functions. The correla-tion coefficient was lower in the DG (Figure 6b). In both cases the p-values were below .001. The linear relation-ships demonstrate that the ground reaction forces at lower radii were higher in the DG, when compared with the OG.

The scatter plots in Figure 6c-d show the difference between the RAMS and RCG (diff R) in relation to RAMS. The linear relationships have a high correlation coefficient (OG, r = .988; DG, r = .911) with a small p-value (< .001), a steeper slope (k) and a lower y-intercept (n) compared with the OG. For the S1+S2 the relation between RAMS and diff(emech) was estimated with linear regression. In both cases the p-values were small (< .001), but the correlation

coefficients were low (OG, r = .365; DG, r = .214). A markedly higher difference in the slope (k) was observed, 0.141 vs. 0.042 kg·m2/J for the OG and DG, respectively.

DiscussionThe main findings of the study were as follows: 1) the gate setup directly influenced and changed the following mechanical parameters: a) center of gravity’s turn radii, b) arithmetic mean of the skis’ turn radii (RAMS), c) veloc-ity, d) acceleration e) ground reaction forces (F), and f) differential specific mechanical energy (diff(emech)) and 2) the highest F and the highest energy dissipation were present in the steering phases, whereas the correlation between RAMS and diff(emech) was low.

460

Figure 5 — Histograms comparing the open gate and the delayed gate combination’s distribution for the differential specific mechanical energy diff(emech) (a), centers of gravity’s turn radii RCG (b) and the arithmetic mean of skis’ turn radii RAMS (c). The intervals with higher relative frequency of occurrence in the presented parameter of the open gates (OG) and the delayed gate combination (DG) are illustrated with arrows. aI1, initiation phase 1; I2, initiation phase 2; S1, steering phase 1 and S2, steering phase 2.

461

Figure 6 — Scatter plots showing 1) the relationship between the ground reaction forces F and the arithmetic mean of skis’ turn radii RAMS for the open gate combination (a) and for the closed gate combination (b), the relationship between diff R (=RCG—RAMS) and the centers of gravity’s turn radii RCG for the open gate combination (c) and for the closed gate combination (d) and 3) the relations between the arithmetic mean of skis’ turn radii RAMS and the differential specific mechanical energy diff(emech) for the open gate combination (e) and for the closed gate combination (f). In diagrams (a & b) the phase transition between initiation and steering phase is indicated by arrows and in diagrams (a), (b), (e) and (f) the initiation (RAMS >15 m) and steering (RAMS <15 m) phase is plotted by diamonds and dots by, respectively. The line in all diagrams represents the linear regression for the initiation phase in diagrams (a), (b), (e) and (f) and for all data in diagrams (c) and (d). The slope (k), y-intercept (n) and correlation coefficient (r) and p-value are also shown. aI1, initiation phase 1; I2, initiation phase 2; S1, steering phase 1 and S2, steering phase 2.


In the current study, alpine slalom ski racing was specifically compared over four open gates, with and without an additional delayed gate. The results show that the turn radii distributions, RCG and RAMS, were strongly dependent on the course setup (Table 1 and Figure 5b-c), even though the median in RCG showed only a trend (p = .06). More specifically, the gate combination with the delayed gate increased both the RCG and the RAMS. The gate setup also influenced the distribution of energy dis-sipation (Table 1), which was apparently higher in the delayed gate combination (Figure 5a). Furthermore, the median F increased markedly, despite the fact that the median v was only slightly increased in the delayed gate combination (0.24 m·s–1). This was mainly due to a longer period in the steering phases, when compared with the initiation phases, in the delayed gate combination.

The results demonstrated that in the initiation phases 1) the energy dissipation estimated by diff(emech) was normally lower (Figure 3c-d), 2) the skiers were pre-dominantly accelerating (positive a) (Figure 4c-d) and 3) the ground reaction forces (F) were lower (Figure 4a-b) compared with those in the steering phases. Nevertheless, different gate combinations resulted in different energy behavior. For example, in the first initiation phase (I1) of the 1st turn in the open gates combination (Figure 3c and 4c), high energy dissipation and consequently deceleration was observed. Combining these results with the range of diff(emech) for the I1+I2 phases (Figure 6e-f), it can be concluded that these phases were also of great importance, because the skiers skied either with high or low energy dissipation. Finally, the initiation phases in the open gates combination, compared with the delayed gate combination, played an even greater role because they lasted longer along the fall line (Figure 3a-b) and in relative time, i.e., the relative frequency of occurrence (Figure 5c).

In the steering phases (S1+S2) the highest F, the lowest a, as well as in most cases the lowest diff(emech), were observed (Figure 3c-d & 4a-d). Therefore, diff(emech) was related to turn radii, even though that the linear rela-tionship was rather weak (Figure 6e-f). In the open gates combination it can be concluded that, depending on the turn, the skiers have the highest energy dissipation in S1, which is similar to previous findings by Reid et al. (2009), or in S2. In either case, the highest energy dissipation was always close to the lowest RAMS (Figure 3a & c). In the delayed gate combination, the skiers showed a different pattern, in which both turns had two RAMS minimums, and the highest energy dissipation occurred very close to the 2nd minimum and always in S2 (Figure 3b & d). Similarly to the open gates combination, this was related to the low or lowest RAMS, which is analogous to a previ-ous study in giant slalom (Supej, 2008).

Nevertheless, our data shows that the energy dissipa-tion is not only related to turn radii and has previously been shown not to be directly related to the attack angle, i.e., the angle difference between the ski’s direction of movement and the orientation of the ski (Reid, et al., 2009). We suggest that energy dissipation is most likely

to be related to a combination of low RAMS, high F (Figure 3a-d & 4a-b) and, importantly, nonsmooth running of the skis. The latter could be a consequence of racing tactics, e.g., controlling velocity, or poor guiding of the skis. Furthermore, from the velocities and altitude dif-ferences used for calculating energy dissipation in the current study, together with experimental values for the skier’s frontal area and drag coefficient from a previous study (Barelle, et al., 2004), it can be estimated that the air drag’s contribution to diff(emech) was approximately 1.5 J·kg–1·m–1, with a variation that is less than ±0.35 J·kg–1·m–1. Therefore, energy dissipation in slalom is mainly due to ski-snow friction and, to much lesser extent, air drag.

Positive diff(emech) values were also present, indi-cating that the skiers should have gained some energy during skiing. It is noteworthy that these values were always present around the phase transitions from I1 to S1 or from S2 to I2 (Figure 3c-d). In both these transitions the skiers could have performed extensions i.e., positive muscle work, depending on whether they used single (one extension-flexion cycle per turn) or double motion technique (two extension-flexion cycles per turn (Supej et al., 2002, 2004). However, in the current study the energy contribution from muscle work, as regards an increase in kinetic and potential energy, can be estimated as less than 1.5 J·kg–1·m–1 and 0.25 J·kg–1·m–1, respectively. For this estimation, beside mean skiing velocity and mean altitude difference, previous findings of 1) peak extension velocity around 1 m·s–1 in heavy-load squat-jumps (Harris et al., 2007; McBride et al., 2002) perpendicular to the skiing velocity (a skier can mainly push/extend perpendicular to the skis, due to low longitudinal ski-snow friction) and 2) 0.3 m amplitude of CG movement have been used. Taking into consideration the estimation of the energy dissipation due to air drag demonstrates that the measured positive values cannot only be a conse-quence of muscle work but are/most likely also due to another mechanical principle and not to measurement error, because positive values have also been consis-tently reported in previous studies (Reid, et al., 2009; Supej, 2008). According to the place of occurrence, the positive values might be related to high eccentric forces acting on the body producing rotational kinetic energies which could be transformed to skier’s center-of-gravity translational-kinetic energy. However, this topic needs to be further investigated.

Because the RAMS and RCG distributions were differ-ent in the two gate combinations, with a small difference in velocity (0.24 m·s–1), it can be suggested that skis with different sidecuts would be better for different gate setups. This is based on the following assumptions: 1) carving skis turn more when they are inclined more (Howe, 1983; Niessen & Müller, 1999) and 2) the skier needs to maintain balance, which is, according to quasi-static approximation, when the total ground reaction force is centric to the CoM, i.e., the vector of the ground reaction force passes through the CoM. Further evidence that dif-ferent sidecuts should be used for different gate setups is


demonstrated by the different relationships between diff R (= RCG – RAMS) and RCG (Figure 6c-d), due to the skiers needing to turn the skis differently (RAMS) for the same RCG in the two gate setups, i.e., having the skis inclined differently. Skis with an inappropriate sidecut might also have been the reason for the two RAMS minimums per turn in the delayed gate combination (Figure 3b). It is probable that a skier with an inappropriate sidecut had to release the edge set and prolong the RAMS in the middle of the steering phase, to be able to perform a long enough turn. The conclusion that is beneficial to use different sidecuts for different turning demands had already been suggested by computer simulation in side-skidding turns (Nordt et al., 1999), but never in alpine skiing on snow.

The F vs. RAMS results, with the phase transition at RAMS = approximately15 m (Figure 6a-b), demonstrated that the skiers’ skiing radii below 15 m (steering phases) worked using a different ground reaction forces’ regimen than for the radii above this (initiation phases). This supports the importance of the turning principle using carving skis (Howe, 1983; Niessen & Müller, 1999) and using the skis’ sidecut RS for the boundary condition to differentiate between turn phases.

Calculating ground reaction forces F from cam-corder-based 3D kinematical measurements, as in the current study, could be regarded as rather ambitious, due to double differentiation. However, comparing this method to 1) pressure insoles and 2) special-build force plates mounted between the skis and the ski bindings, has proven that it is adequate for estimating the behavior of F, but not vibrations (Lüthi et al., 2005). From our measurement error (see Methods) and the findings by Lüthi et al. (2005) it can be estimated that the accuracy of F calculation was approximately ±0.25 BW, which was considered to be adequate for the demands of the current study.

From the application point of view, the result that the lowest turn radii in combination with high ground reaction forces may increase energy dissipation, due to the skis running less smoothly, is important in under-standing how to provide adequate feedback to athletes to help them ski fast and achieve top level results. This relationship together with the attack angle (Reid, et al., 2009) should be further investigated, as it may serve as the basis for optimizing the turn radii along the trajec-tory. Because the trajectories are the consequence of how the skiers guide their skis, i.e., skiing technique, the optimization of turn radii is directly related to different ski techniques and racing tactics, as suggested by other studies (Supej & Cernigoj, 2006; Supej, et al., 2002). Another important perspective deduced from the results is the suggestion that skiers would have an advantage in using skis with different sidecuts in different gate setups, but this has two major limitations: 1) the skiers have to be able to rapidly adapt to skis with different sidecuts, e.g., between the racing runs, and 2) using more pairs of skis per race would result in a more complex sport regarding equipment requirements.

Acknowledgments

This study was supported in part by a grant from the Foundation for Financing Sport Organizations in Slovenia and the Slovenian Research Agency. We are thankful to Günter Hujara, chief WC race director, and ASK Kranjska Gora, organizer of the racing event, and especially Sre ̆ ko Medven for the approval of the study and help in measurement preparation.

ReferencesBarelle, C., Ruby, A., & Tavernier, M. (2004). Experimental

model of the aerodynamic drag coefficient in alpine skiing. Journal of Applied Biomechanics, 20(2), 167–176.

Harris, N.K., Cronin, J.B., & Hopkins, W.G. (2007). Power outputs of a machine squat-jump across a spectrum of loads. Journal of Strength and Conditioning Research, 21(4), 1260–1264.

Hirano, Y., & Tada, N. (1994). Mechanics of a turning snow ski. International Journal of Mechanical Sciences, 36(5), 421–429.

Hirano, Y., & Tada, N. (1996). Numerical simulation of a turning alpine ski during recreational skiing. Medicine and Science in Sports and Exercise, 28(9), 1209–1213.

Howe, J. (1983). Skiing Mechanics. Laporte: Poudre Press.Kugovnik, O., Nemec, B., & Supej, M. (2000). A skidding

model for carving skis. Kinesiology, 32(2), 42–50.Lieu, D.K., & Mote, C.D. (1984). Experiments in the machin-

ing of ice at negative rake angles. Journal of Glaciology, 30(104), 77–81.

Lind, D., & Sanders, S.P. (1996). Pumping to increase veloc-ity The Physics of Skiing: Skiing at the triple point (pp. 233–235). New York: Springer-Verlag.

Lüthi, A., Federolf, M., Fauve, M., Oberhofer, K., Rhyner, H., Ammann, W., et al. (2005). Determination of forces in carving using three independent methods. Paper pre-sented at the Science and skiing III Aspen Snowmass, CO, USA.

McBride, J.M., Triplett-McBride, T., Davie, A., & Newton, R.U. (2002). The effect of heavy- vs. light-load jump squats on the development of strength, power, and speed. Journal of Strength and Conditioning Research, 16(1), 75–82.

Müller, E., Bartlett, R., Raschner, C., Schwameder, H., Benko-Bernwick, U., & Lindinger, S. (1998). Comparisons of the ski turn techniques of experienced and intermediate skiers. Journal of Sports Sciences, 16(6), 545–559.

Müller, E., & Schwameder, H. (2003). Biomechanical aspects of new techniques in alpine skiing and ski-jumping. Journal of Sports Sciences, 21(9), 679–692.

Niessen, W., & Müller, E. (1999). Carving - biomechanische Aspekte zur Verwendung stark taillierter Skier und erhoehter Standflachen im alpinen Skisport. / Carving - biomechanical aspects of using strongly waisted skis and higher standing areas in alpine skiing. Leistungssport, 29(1), 39–44.

Nordt, A.A., Springer, G.S., & Kollar, L.P. (1999). Simulation of a turn on alpine skis. Sports Engineering, 2(3), 181–199.

Reid, R., Gilgien, M., Moger, T., Tjørhom, H., Haugen, P., Kipp, R., et al. (2009). Turn characteristics and energy dissipation in slalom. Paper presented at the Science and skiing IV, St. Cristoph am Arlberg, Austria.

Renshaw, A.A., & Mote, C.D. (1989). Model for the turning snow ski. International Journal of Mechanical Sciences, 31(10), 721–736.

c


Supej, M. (2008). Differential specific mechanical energy as a quality parameter in racing alpine skiing. Journal of Applied Biomechanics, 24(2), 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.

Supej, M., Kugovnik, O., & Nemec, B. (2002). New advances in racing slalom technique. Kinesiologia Slovenica, 8(1), 25–29.

Supej, M., Kugovnik, O., & Nemec, B. (2003). Kinematic determination of the beginning of a ski turn. Kinesiologia Slovenica, 9(1), 5–11.

Supej, M., Kugovnik, O., & Nemec, B. (2004). Modelling and simulation of two competition slalom techniques. Kinesiol-ogy, 36(2), 206–212.

Tada, N., & Hirano, Y. (2002). In search of the mechanics of a turning alpine ski using snow cutting force measurements. Sports Engineering, 5(1), 15–22.

How gate setup and turn radii influence energy dissipation in slalom ski racing

Documents

Transcript of How gate setup and turn radii influence energy dissipation in slalom ski racing