JOURNAL OF APPLIED BIOMECHANICS, 1994,10, 393-399 O 1994 by Human Kinetics Publishers, Inc. Relationship Between Glide Speed and Olympic Cross-Country Ski Performance Glenn M. Street and Robert W. Gregory While the scientific literature has confirmed the importance of high maximal aerobic power to successful cross-country skiing performance, the same cannot be said of skiing technique or gliding characteristics of skis. The purpose of this study was to determine whether glide speed was related to Olympic race performance. Male competitors in the 50-km freestyle event were videotaped during the 1992 Winter Olympic Games. Glide speeds of the entire field were measured through a 20-m flat section at the bottom of a 150-m, 12" downhill. A significant correlation (r = -.73) was found between finish time and glide speed, showing that the more successful competitors tended to have faster glide speeds through this section of the course. A predictive model of glide speed suggested that the faster glide speeds were due primarily to differences in friction. There was little evidence to suggest that differences in air drag, body mass, or initial speed accounted for the major differences in glide speeds. Scientists who regularly test ski equipment and evaluate the physiological characteristics of elite Nordic skiers often identify high maximal aerobic power, good skiing technique, and skis with good glide characteristics as being necessary for excelling in World Cup and Olympic cross-country skiing competitions. The first of these has been examined extensively by several independent researchers (Bergh, 1982; Ingjer, 1991; Rusko, 1987). These researchers' data indicate that the world's best skiers have exceptionally high maximal aerobic powers, averaging 275.and 355 ml. mid. kg-2" for women and men, respectively. Aerobic power (V02max) is reported relative to body mass to the 213 power to account for the theoretical advantage that heavier racers have in cross country skiing (Bergh, 1992). Ingjer (1991), who studied 5 1 Norwegian National Team members over a 10-year period, showed that the skiers who. consistently won Olympic medals and World Cup points had 69% higher VOlmax than did their less successful teammates. Olympic skiers believe that glide characteristics of their skating skis can affect the outcome of a freestyle race. Coaches and athletes generally agree that the top-place finishers in freestyle races have skis with better glide characteristics, yet this belief remains undocumented. In two classic races at the 1978 World Glenn M. Street and Robert W. Gregory are with the Human Performance Lab, HaH S102, St. Cloud State University, St. Cloud, MN 56301.
394 Street and Gregory Championships, Rusko and Kantola (1978) showed that the leaders lost the most time on uphills, with less time lost on flat and rolling terrain and on downhills. While Rusko and Kantola's analysis showed where individual skiers lost time on the course to the top place finishers, it did not examine the importance of glide characteristics of skis to time lost. Because good glide is thought to be important to the outcome of freestyle races, the purpose of the current study is to determine if glide speed is related to finish time during Olympic competition in a freestyle event. We examine the relationship between finish time and glide speed at the bottom of a 150-m downhill section in the men's 50-km freestyle event at the 1992 Winter Olympic Games. A model is used to predict glide speed through this section of the course and to assess the factors that govern glide speed. Methods Cross-country ski races at the 1992 Albertville Winter Olympics took place in Les Saisies, France. The men's 50-km freestyle race was selected for analysis because it provided multiple opportunities to measure glide speed for each competitor. The race course consisted of three laps of the same loop that was approximately 16.7 km in length. Glide speed data were successfully collected on all competitors during the first two laps at approximately 1.5 km from the end of each loop, so videotaping took place at approximately the 15.2- and 31.9-km points of the race. To determine the relationship between glide speed and race performance, glide time through a 20-m zone at the bottom of a 150-m downhill was measured with video. Skier speeds were measured at the bottom of a steep (12") downhill to ensure that all competitors would be in similar tuck positions. Each competitor ascended a challenging uphill before descending the downhill. They typically took 2-3 skating steps at the top of the hill to increase speed before stepping into the prepared tracks and descending the hill in a tight tuck position. At the bottom of the hill the skiers stayed in the tuck position through a relatively flat 40-m section. Glide speeds of all competitors were measured through the center 20 m of the flat section on the first two laps of the race. The camera was positioned approximately 75 m from the side of the track to minimize parallax error. Its optical axis was oriented perpendicular to the track. Two markers spaced 20 m apart and placed above the track were videotaped prior to competition for calibration purposes. The resolution of time measurement through the 20-m zone with the 30-Hz camera was 2.4% (0.4 m. s-') of the average glide speed. The weather conditions were stable throughout the race with clear skies and negligible winds. The official race results reported a wind speed of 0.0 km hr-i. The radiant air temperature measured in full sunlight and snow temperature measured at a depth of 4 cm averaged 12 and -7 "C, respectively. Relationships between glide speeds and finish times for the first two laps were evaluated with a Pearson product moment correlation coefficient (r) using a second-order polynomial. Level of significance was set at a =.01. The lastplace skier (67th place) was excluded from all statistical analyses since he finished over 30 minutes behind his nearest competitor. A model was developed to estimate skier speed through the 20-m zone
Glide Speed and Ski Performance 395 (Street, 1990). The model incorporated the hill angle profile which was obtained from a topographical map of the course. Newton's law of acceleration was used to compute a skier's speed profile from estimates of drag forces acting on the skis (F,), component of body weight acting parallel to the trail (W,,), air resistance (D), skier mass (M), and initial (v,) and final (vp) speeds updated each.2 s (At). The drag forces acting on the skis (F,), which will subsequently be referred to as kinetic friction, were determined with where 8 is the hill angle, W is skier weight and p., is the coefficient of kinetic friction. The component of weight acting parallel to the trail (W,) was calculated with where 8 is the hill angle and W is skier weight. Air resistance (D) was determined with where p is air density, A is projected frontal area of the skier, C, is the coefficient of drag and v is skier speed. The model was first used to estimate a "reference" skier's speed profile. Numerical estimates used for the reference skier were carefully selected to reflect realistic values for the conditions present during the race. A coefficient of kinetic friction (pk) of.07, which is typical for skating skis on warm snow, was used to calculate kinetic friction (Colbeck, 1992; Spring, 1988). A body mass of 71 kg was used, which was the average for data that were available on the Olympians (52 out of the field of 67). Air resistance was calculated using air density of 1.25 kg. mj, drag area (CdA = coefficient of drag x projected frontal area) of.3 m2, and speeds that were updated every.2 s (Spring, Savolainen, Erkkila, Hamalainen, & Pihkala, 1988; Watanabe & Ohtsuki, 1978). The speed at the top of the hill (vi) was estimated to be 6.0 m. s-i from previous timing studies (Street, 1990). To evaluate the relative importance of the four variables (friction, body weight, air resistance, and initial speed) that determine glide speed in the 20-m zone, one variable was manipulated while the other three were kept constant at their reference values. Glide speeds for the 20-m zone were recalculated using minimum and maximum values for each variable. The minimum and maximum values for body mass were obtained from available skier masses (n = 52), and the literature provided reasonable ranges for pk, CdA and vi. The mass range used was 58-85 kg. Coefficients of friction for warm snow conditions have been shown to vary by at least 5.01, which provided a range of.06-.08 (Colbeck, 1992; Spring, 1988). The range of drag areas used in the calculation of air resistance (CdA =.27-.33) was obtained from published results on skiers of widely different body sizes while they were in tuck positions (Spring et al., 1988;
396 Street and Gregory Watanabe & Ohtsuki, 1978). Speeds entering downhills can be expected to vary by as much as +_1 m. s-', providing a range of 5-7 m. s-' (Street, 1990; Street, McNitt-Gray, & Nelson, 1985). Results and Discussion Significant correlations were found for Laps 1 (r = -.73) and 2 (r = -.73) between glide speed in the 20-m zone and finish time. The higher placing finishers tended to have faster glide speeds on both laps, as shown in Figure 1. The field's average speeds through the glide zone were not different between laps: 14.8 and 14.7 m. s-i for Laps 1 and 2, respectively. As shown in Figure 1, there was no discernible pattern in the data to suggest that glide speed changed between laps. An unpaired t test comparing the glide speeds of the top-10 and bottom-10 finishers on Lap 1 revealed that the top-10 skiers had a 13% faster (p <.01) glide speed: 15.4 versus 13.6 m. s-'. This discrepancy in glide speed could be attributed to differences in kinetic friction, body weight, air resistance, or initial speed at the top of the hill. For the reference skier and conditions, the model estimated a glide speed through the 20-m zone of 14.78 m. s-', which compares favorably with the field's average speeds for Laps 1 and 2 of 14.8 and 14.7 m. s-i, respectively. These reference conditions and the resulting 20-m speed are summarized in Column 2 of Table 1. To evaluate the relative importance of the four variables to glide speed in the 20-m zone, one variable was manipulated while the other three were kept constant at their reference values. Glide speeds for the 20-m zone were recalculated using minimum and maximum values for each variable. The estimated speeds for the 20-m zone for each of the sets of conditions are shown in Table 1. In comparing the glide speeds, it is evident that friction and skier mass have the greatest potential for influencing glide speed, followed by air resistance and. I I I I I 7000 7500 8000 8500 9000 9500 FINISH TIME (s) Figure 1 - Relationships @ <.01) between finish time in the race and speed through the 20-m glide zone for Laps 1 (n = 66) and 2 (n = 66).
Glide Speed and Ski Performance Table 1 Estimated 20-m Glide Zone Speeds for Reference Values and Variations From the Reference Values Reference Friction Mass Drag area Initial speed Variable values High Low Low High High Low Low High Est. speed (m. s-i) 14.8 13.9 15.5 13.8 15.5 14.4 15.1 14.6 14.9 A speed (m. s-i)" 1.6 1.7 0.7 0.3 "A speed indicates the effect that the variables could have on glide speed. initial speed. The changes in p, and skier mass caused the largest fluctuations in glide speed: 1.6 and 1.7 m - s-', respectively. Changes in air resistance and initial speed caused smaller fluctuations in glide speed:.7 and.3 m. s-l, respectively. If the ranges defined are reasonable, friction and skier mass potentially have approximately 2.4 and 5.5 times greater influence on glide speed than drag area or initial speed, respectively. Though this theoretical analysis illustrates the relative importance of the four factors in determining glide speed, other considerations must be weighed. Bergh and Forsberg (1992) studied a group of elite cross-country skiers and reported that large and small skiers were nearly evenly distributed across the performance spectrum. His data showed that there was no significant relationship between race performance and mass, although he suggested there may have been a tendency for the faster skiers to be heavier. Similar results were found in the current study. No significant relationships were found between skier mass and finish time (r =.12, n = 52), skier mass and glide speed during Lap 1 (r =.24), and skier mass and glide speed during Lap 2 (r =.16). These findings indicate that one of the other factors (friction or air resistance) probably accounts for the relationship between finish time and glide speed (see Figure 1). Air resistance data from experiments on cross-country and alpine skiers indicate that air resistance is affected mostly by posture and, to a lesser extent, by size of the skier and type of clothing (Spring et al., 1988; Watanabe & Ohtsuki, 1978). Skier posture can have a sizable effect on air resistance because of the influence of posture on projected frontal area and on the body's aerodynamic characteristics. Standing in only a partial tuck position can elevate the drag area by 10-15% (Spring et al., 1988). The video records showed no noticeable differences between skiers in their tuck postures through the 20-m zone, and all the skiers tended to hold tight tucks because of the steep hill angle. The skiers stood in tight tuck positions with slight knee flexion, torso parallel to the track, elbows resting on the knees, and hands pressed to the face. To evaluate the possibility that the slower skiers had slower speeds through the 20-m zone because they were slower getting into a tuck position, the reference skier was placed in
398 Street and Gregory a standing position (projected frontal area was doubled,.45 to.9 m2) for the first 15 m of the downhill. Standing the first 15 m reduced the estimated glide speed by only.8%, from 14.78 to 14.66 m. s-'. The reason standing had minimal effect on glide speed was because air resistance was relatively small at the top of the hill when velocities were still quite slow. Average air resistance in this 15-m section was only 18 N, compared with 48 N of friction and 145 N of propulsive force from the skier's weight. Size of the skier can also affect air resistance since larger skiers tend to have greater projected frontal areas. Because no relationship existed between mass and finish time, projected frontal area does not explain the reason top-place finishers tended to have faster glide speeds. Even if the more successful skiers had been heavier, this potential advantage would have been counterbalanced to some extent by increased air drag. Finally, because all Olympic competitors wore similar skin-tight suits, it is unlikely that differences in glide speed were attributable to clothing. In light of these considerations, it seems unlikely that the more successful skiers had lower air resistance. Therefore, it appears that the more successful skiers had skis with better glide characteristics, which allowed them to attain higher speeds through the 20-m zone. At minimum, these results suggest that the top-place finishers had a frictional advantage on downhills. Based on the profile map of the course and timing study data (Street et al., 1985), we estimated that the competitors spent 10-20% of the race on downhills. This is in agreement with Rusko and Kantola (1978), who showed that the first place finisher in the men's 15-km classic race at the 1978 World Championships spent 12% of total race time on downhills. More realistically, this frictional advantage probably assisted the top finishers throughout the race. Although glide speeds were only measured at high speeds, published data on snow kinetic friction indicate that frictional differences remain evident across the full range of cross-country skiing speeds, 2-18 m. s-' (Colbeck, 1992; Spring, 1988). This is particularly relevant to skating since the ski is seldom stationary, even on steep uphill terrain. The findings of the current study suggest that the glide characteristics of cross-country skating skis can influence the outcome of a freestyle event during Olympic competition. This illustrates the need for further research on friction in Nordic skiing. References Bergh, U. (1982). Physiology of cross-countty ski racing. Champaign, IL: Human Kinetics. Bergh, U., & Forsberg, A. (1992). Influence of body mass on cross-country ski racing performance. Medicine and Science in Sports and Exercise, 24, 1033-1039. Colbeck, S.C. (1992). A review of the processes that control snow friction (U.S. Army Cold Regions Research and Engineering Laboratory, Monograph 92-2). Office of the Chief of Engineers, U.S. Army. Ingjer, F. (1991). Maximal oxygen uptake as a predictor of performance ability in women and men elite cross-country skiers. Scandinavian Journal of Medicine and Science in Sports, 1, 25-30. Rusko, H. (1987). The effect of training on aerobic power characteristics of young crosscountry skiers. Journal of Sports Sciences, 5, 273-286.
Glide Speed and Ski Performance 399 Rusko, H., & Kantola, H. (1978). Time-interval study at the World Championship Games. Journal of the United States Ski Coaches Association, 2(4), 85-88. Spring, E. (1988). A method for testing the gliding quality of skis. Tribologia, 7(1), 9-14. Spring, E., Savolainen, S., Erkkila, J., Hamalainen, T., & Pihkala, P. (1988). Drag area of a cross-country skier. International Journal of Sport Biomechanics, 4, 103-1 13. Street, G.M. (1990). Biomechanics of cross-country skiing. In: J. Casey, C. Foster, & E. Hixson (Eds.), Winter sports medicine (pp. 284-301). Philadelphia: Davis. Street, G.M., McNitt-Gray, J., & Nelson, R.C. (1985). Timing study: World Cup crosscountry ski race. Unpublished manuscript, Penn State University, Biomechanics Laboratory. Watanabe, K., & Ohtsuki, T. (1978). The effect of posture on the running speed of skiing. Ergonomics, 21, 987-998. Acknowledgments Support for this project was provided by the Medical Subcommission of the International Olympic Committee. In addition, support from Peak Performance Technologies (Englewood, Colorado, USA) and T m (Munich, Germany) made data collection possible. We also wish to recognize David Bacharach, Steve Gaskill, Sean Humphreys, and John Kelly for their contributions to the study.