Mechanical Aspects of the Sprint Start in Olympic Speed Skating

Transcription

1 INTERNATIONAL JOURNAL OF SPORT BIOMECHANICS, 1989, 5, Mechanical Aspects of the Sprint Start in Olympic Speed Skating JOS J. de Koning, Gert de Groot, and Gerrit Jan van lngen Schenau Mechanical characteristics of the sprint start in speed skating were measured during the 1988 Winter Olympic Games. From three-dimensional hlm analysis of the first 4 seconds of the male and female 500-m races, biomechanical variables were determined. The first strokes during the start appeared to be performed by a running-like technique. At a forward velocity of approximately 4 mtsec, the skaters are forced to change this technique to the typical gliding technique as used during speed skating at steady speed. In explaining the time differences on the first 100 meters of the 500-m speed skating race, the effectiveness of the push-off appears to be more important than the observed high power output levels. Speed skating research has mainly focused on the biomechanics of speed skating technique as well as on exercise physiological aspects. These fields of interest were extensively reviewed by Ingen Schenau, de Boer, and de Groot (1987) and by de Groot, Hollander, Sargeant, van Ingen Schenau, and de Boer (1987). With respect to the technique, all previous studies dealt with aspects analyzed during skating at steady speed, both on the straight parts and during skating the curves. In speed skating the 500-meter race (the shortest distance in international speed skating competitions), the start is one of the most important parts of the race. From the recorded times for all participants in the 1988 Winter Olympic Games we have calculated correlation coefficients of 0.88 for the first 100- compared to the 500-meter times for both male and female speed skaters. This means that almost 80% of the variation in final times is associated with the extent to which the skater is able to accelerate during the first 100 meters. However, there has been no information about kinetics and kinematics of this part of the 500-m event. The object of this study was to analyze the mechanics of the speed skating start in world class male and female athletes. The significance of some mechani- The authors are with the Faculty of Human Movement Sciences, Vrije Universiteit, v.d. Boechorststraat 9, 1081 BT Amsterdam, The Netherlands.

2 152 DE KONING, DE GROOT, AND VAN INGEN SCHENAU cal parameters for the 100-m times is investigated. The technique during the start is compared with the previously reported technique for speed skating at steady speed. Subjects Methods Ten female and 11 male speed skaters were filmed during the 500-meter races at the 1988 Winter Olympic Games in Calgary (the analysis had to be restricted to skaters starting in the outer lane only). The final 500-m times of the filmed female speed skaters ranged from seconds (silver medalist) to seconds (19th place). The final times of the filmed male speed skaters ranged from seconds (bronze medalist) to seconds (24th place). Each skater's body mass and length were determined. Filming Procedures The speed skaters who started in the outer track were filmed with three Locam movie cameras (16 rnm, 100 frameslsec). Camera A was placed viewing into the longitudinal axis of the straight lane of the outer track, and Cameras B and C were placed along the track. Their positions are given in Figure 1. Cameras A and B combined were used for the analysis during the first 10 meters of the start, and Cameras B and C for the remaining part. The viewing field of the panning and tilting cameras was such that, apart from the skater in the middle of the frame, two markers were visible as lane separaters for the inner and outer track. The known distances between the two markers were 250 cm. The beginning of a start Figure 1 - Overview of the camera set-up. With respect to the generic reference frame (x,y,z), the camera positions are, in centimeters, A (-3071, 209.5, 730), B (974.8, , 915.7), and C (2933.8, , 912.1), obtained by extensive trigonometry. The tilt angle a! for Camera C and the pan angle P of the optical axis for Camera B are indicated. The lane indicator markers are frozen in the ice at known intervals (approx. 250 cm).

3 THE SPRINT START IN SKATING 153 is defined as the first observed motion of the speed skater after the starting signal has been given. On the average, 425 film frames were analyzed, a covered distance of approximately 30 meters. Internal timing lights in all three cameras coupled to a main pulse generator unit (1 Hz) provided synchronization and calibration of camera speed. For each frame, 16 segment endpoints, 2 markers, and the sprocket holes for calculating the center of the frame were digitized on a NAC motion analyzer that was coupled to an Apple microcomputer. The 16 points are rear and front ends of the skate blade, ankle, knee, hip, shoulder, elbow, and hand-right as well as left side (Figure 2a). Figure 2a - Illustration of the model of 11 linked segments with the 16 digitized points and the calculated hip (h), knee (Od, and ankle (@a) angle.

4 DE KONING, DE GROOT, AND VAN INGEN SCHENAU Figure 2b - An example of hip, knee, and ankle angles during the first 2 seconds of the race with, on the abscissa of the graph, a bar indicating the push-off, glide, and recovery phases of the skating strokes. Three-Dimensional Coordinates Since the speed skating movements during the start have significant components in three directions, a special 3-D reconstruction was necessary. Therefore a technique suitable for a large object volume with panning cameras was developed. Essentially the method is a combination of those presented by Dapena and colleagues (Dapena, 1985; Dapena & Feltner, 1987; Dapena, Harman, & Miller, 1982). It demands known locations with respect to a generic reference frame (x,y,z) of two cameras and of background markers (markers for the lane indication are used; see Figure 1). Concerning the internal camera parameters, the distance from the camera to the theoretical projection plane, as appears in the collinearity equations of photogrammetry, was obtained from film shots of the known distance between two background markers at pan angle P=O (Cameras B and C) or from film shots of the known length of the starting line (Camera A). The correction factor for vertical projected direction was disregarded. If the internal parameters of the cameras are known, the coordinates of the images of the markers in the camera's projection plane can be used to calculate the tilt angle a (vertically) and the pan angle P (horizontally) of the optical axis, that is, the z'-axis of a reference frame attached to the camera. No camera rotation about its z'-axis could be detected; the utilized values of tilt and pan angle are the averaged values obtained from two markers. The coordinatesof the image of each in the camera's projecan

5 THE SPRINT START IN SKATING 155 point. The coordinates of the image of the same point in the second camera's projection plane give the equation of the line that joins the involved object point with that camera. From the intersection of both lines the coordinates x,y,z can be derived. Actually the midpoint of the perpendicular distance between the two lines was used. With a calibration pole (175 cm), the method was evaluated on accuracy in the y,z and x,y planes, that is, the pole in the vertical position and the pole in the horizontal position in the direction of the y-axis at each location of the markers. Minimal deviations were achieved at camera orientations with a pan angle of about zero, whereas maximal deviations were reached in the most extreme camera orientations at the largest pan angle 0. For the A,B camera combination, the deviation of the calculated x,y,z coordinates from the real values of the markers and end of the pole at the different marker positions was a minimum of 1 cm. The maximal deviation was 10 cm. The error in the length of the pole was a maximum of 2.0 cm (maximal relative error of 1.1 %). The angle deviation from orthogonality was rad in the most accurate camera orientation but it increased to 0.08 if the largest pan angle was reached. The deviations as calculated for the camera combination A and B increased with 50% for camera combination B and C. Calculations Body Center of Gravity. A model of 11 linked segments is defined by the calculated three-dimensional positions of the 16 segment markers. Averaged data of relative segment mass and location of segmental centers of gravity from Dempster (1955) were used to calculate the total body center of gravity. joint Angles. The angles of ankle, knee, and hip joints were defined as the minimum angle between the lines joining the three-dimensional coordinates of the front and rear end of the blade of the skate, ankle, knee, hip, and shoulder (Figures 2a and 2b). Also the angles of the trunk, upper leg, and lower leg relative to the horizontal plane were computed. The angles were low-pass filtered with a Butterworth fourth-order zero lag filter (cutoff frequency of 13.4 Hz). First and second derivates were calculated by means of a Lanczos 5-point differentiating filter. Push-off Vector, Angle, and Velocity. The magnitude and orientation of the vector between the front end of the skate and body center of gravity is defined as the push-off vector (Figure 3). During a proper gliding technique, this vector has to be oriented perpendicular to the blade of the skate. The angle of this vector with the vertical is defined as the push-off angle p (Figure 3). The velocity difference between the front end of the skate and the body center of gravity, calculated as the first derivative of the vector length, is defined as the push-off velocity. Stroke Frequency. The time between the ends of two successive pushoffs (stroke time, tstroke) determines the stroke frequency. This time is obtained from the film rate. Displacement and Velocity. From the position of the body center of gravity, the x-coordinate of this position is used to calculate the forward displacement (sx) / time curves of the body center of gravity. These curves are low-pass filtered with a Butterworth fourth-order zero lag filter (cutoff frequency of 4 Hz). After filtering, a Lanczos 5-point differentiating filter is used for calculation of the forward velocities (vx) of the speed skaters.

6 DE KONING, DE GROOT, AND VAN NGEN SCHENAU Figure 3 - Illustration of the push-off vector and the push-off angle (p between the push-off vector and the vertical. Kinetic Energy and Power. When the forward velocity (vx) of the body center of gravity is known, the kinetic energy Ekin = 0.5 (m vx2) (1) can be calculated. The increase in kinetic energy during one stroke (Ekin stroke) divided by stroke time (ts&oke) indicates the average net power output of the speed skater during the stroke. Pn stroke = Ekin stroke 1 hoke (2) This net power output is the power output Po delivered by the speed skater minus the power Pf to air and ice frictional forces (in a stroke). Pn stroke = Po stroke - Pf stroke (3) The net power during the stroke is positive during the accelerating push-off phase of the stroke and negative during the flight and gliding phase of the stroke. The data are presented in stroke average and push-off average values.

7 THE SPRINT START IN SKATING 157 In order to achieve measures for actual external power Po, the net values are corrected for power losses associated with frictional forces. In speed skating, the frictional force can be divided into the ice friction force and the air friction force. The ice friction force can be estimated from the relation for surface friction where p is the coefficient of ice friction and N the normal force, approximately equal to body weight (m g). Power loss to ice friction is where m is body mass, g is the gravitational acceleration, and v the velocity of the speed skater. The air friction force is described by (Tngen Schenau, 1982), with Ap the frontal projected area, Cd the drag coefficient, Q the air density, and v the velocity of the speed skater with respect to the air, that is, with respect to the ice, because the wind velocity was zero in the indoor Olympic Oval in Calgary. In speed skating, the skater's trunk position and knee angle influence the frontal projected area. The drag coefficient Cd is dependent on wind velocity and the air density Q depends on barometric pressure and altitude. Van Ingen Schenau (1982) calculated the parameter K with the equation where 1 is body length, m is body mass, 8, is angle of the trunk with the horizontal, 80 is the knee joint angle, v is the velocity of the skater with respect to the air, lnv is the natural logarithm of the velocity v, QO is the air density at sea level, and h is the altitude above sea (1,100 m in Calgary). During the Games, the barometric pressure corrected to sea level was 1015 N/mZ. Due to the absence of wind, the air frictional power loss can be calculated from The total power loss to friction is then equal to Pf = Pice + Pair (9) Prior to the Games, the ice friction coefficient was measured with special skates (de Koning, Jobse, Cserep, van Ingen Schenau, & de Groot, in press). Since these measurements were not allowed during the Games, it is assumed that the ice friction coefficient during the Games was equal to the value of previously found at an ice temperature of -4 "C. PO stroke was calculated according to Equations 2, 3, and 9, giving the mean power output during the full stroke. The corresponding value was also calculated for the accelerating push-off phase (Po acc). Statistical Methods. Pearson correlation coefficients between power and technical parameters on the one hand and 100-m times on the other hand were calculated and tested for significance w0.05). Differences in stroke parameters between male and female speed skaters were tested using a Student t test (twotailed: p<0.05).

8 158 DE KONiNG, DE GROOT, AND VAN lngen SCHENAU Results Reconstructions of the movements over the first 30 meters are presented in Figure 4 for the fastest male and female speed skaters studied (male bronze medalist and female silver medalist). The angles in hip, knee, and ankle joint for these subjects are presented in Figure 5. Data of the right and left legs are shown for the first 4 seconds (30 meters) of the start. To assist in data interpretation, the different phases of the strokes are indicated (see also Figure 2b). In the gliding phase (I), the hip, knee, and ankle angles are roughly constant; during the pushoff the angles increase to maximal values, after which repositioning of the leg takes place (III). It can be seen that the knee and hip angles during the gliding phases become smaller for successive strokes and that the duration of the gliding phase becomes longer. Because of the roughly constant maximal knee extension values and the decreasing gliding angle for the successive strokes, the range of extension increases and the technique changes from a running-like to a gliding technique. Figure 6 illustrates the trajectory of the body center of mass during the first 15 meters of the race (solid line) and the position of the midpoint of both skates, Figure 4 - Stick diagrams of the skaters during the f it 30 meters of the 500-m race. An image at every 10th of a second is plotted. (a) First 15 m of the female silver medalise; Oi) second 15 m of the female silver medalist; (c) first 15 m of the male bronze medalist; (d) second 15 m of the male bronze medalist.

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10 160 DE KONING, DE GROOT, AND VAN INGEN SCHENAU Figure 6 - Plot of the midpoints of left and right skate (dots) and trajectory of the center of body mass during the fist 15 meters of the race. as indicated by a dot for each successive film frame. During the first five strokes the push-off is made against a fixed point on the ice; hence the skate position in successive frames hardly changes, as reflected by the density of the dots. After these first five strokes the dots indicating skate position are clearly separated between frames, showing that the push-off was being made while the skate was gliding forward. Comparison of the mean data given in Table 1 for the stroke characteristics duringthe first 4 seconds of the &rt indicates that the females had a significantly lower stroke frequency (3.25 f 0.16 cf. 3.46f 0.26 Hz). The push-off angle cp was also significantly smaller for the females, which means they had a less horizontally directed push-off compared to the males (49.3 f 2.9 cf f2.3 "). The maximal push-off velocity (Vp-o) was 3.73 f 0.42 and 4.05 f 0.F8 mls for the females and males, respectively, and knee extension velocity (0) 639f 66 and 683f 54'1s. But these differences failed to reach conventional levels of significance. The forward displacement (sx) I time curves of all females and males are presented in Figure 7. There are already obvious differences in covered distance in 4 seconds. he forward velocities of the fastest male and female speed skaters are given in Figure 8. The kinetic energy (Ekin) of the body center of gravity for the fastest male and female speed skaters in the forward direction are given in Figure 9. In Figures 8 and 9 the major increases indicate the push-off phase and the major decreases indicate the flight and gliding phase in each stroke. Table 1 Push-off Angle, Max. Push-off Velocity, Max. Knee Extension Velocity, and Stroke Frequency; Means and Standard Deviations in First 4 Seconds of Start Push-off angle Push-off vel. Knee extn. vel. Stroke freq. (deg) (m/s) (degls) (Hz) Skaters M SD M SD M SD M SD Males (n = 10) Females (n = 11) *p<0.05 'fk0.05

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12 162 DE KONING, DE GROOT, AND VAN lngen SCHENAU Figure 9 - Graphs of kinetic energy (Ekia) of the center of body mass against time during the first 4 seconds of the 500-m race. Solid line = female, dotted line = male. Data of the power per complete stroke (Po stroke) and the power in the accelerating push-off phase of the stroke (Po act) are presented in Table 2. Note the high mean power output during the push-off, which is more than 3 horsepower for the males. Pearson correlation coefficients between 100-m times and technique variables are given in Table 3. For the male speed skaters, significant correlations were found with power in the push-off phase of the stroke (PO ac~) and with the push-off angle p. In females, significant correlation was found only with pushoff angle q~. In the 11 male and 10 female skaters studied, the times for 100 meters and 500 meters were significantly correlated (0.87 and 0.70, respectively). These correlations are similar to those reported for all participants at the beginning (0.88). Discussion The propulsion technique of speed skating differs from other techniques used in human locomotion. In running for instance, the athlete's forward propulsion is effected by a push-off in the direction opposite the running direction. In speed skating, this technique is possible only in the first few strides. The velocity of the speed skater is low enough to allow a push-off in the backward direction.

13 THE SPRINT START IN SKATING 163 Table 2 Means and Standard Deviations of Power Output During Complete Strokes and During Acceleration Phase of Strokes in First 4 Seconds of Race (values normalized to M (Wattlkg) body weight are also given) Po stroke Po acc Skaters M (Watt) SD M (WatNkg) SD M (Watt) SD M (Wattlkg) SD Males (n = 10) Females (n = 11) Note. The four parameters are statistically different for males and females. Table 3 Pearson Correlation Coefficient for Power, Push-off Angle, and Final 500-m Times Against Times on First 100 m of the 500-m Race - - Skaters PO stroke PO acc Push-off angle 500 m Males *.87* Females '.70* *Coefficients statistically different from zero. With increasing velocity, the speed skater is forced to change the technique toward the typical gliding technique. During speed skating at relatively high speed, the speed skating push-off is only possible in a direction perpendicular to the gliding direction of the skate (Ingen Schenau, de Groot, & de Boer, 1985). The reason for this glidinglpushoff technique is that the skating velocity of speed skaters is larger than the maximal difference in velocity that can be achieved between the skate and the body center of gravity. With high skating velocities it is essentially impossible to push off against a fixed point on the ice. This is why skaters are taught to push off during gliding. This technique is henceforth referred to as the gliding technique. During the first few strokes of the speed skating start, however, the gliding technique is not necessary (Figure 6). If the maximal push-off velocity (Vp-,,) is higher than the skating velocity, the running-like technique can be used. From the values presented in Table 1, it can be concluded that the transition from the running-like technique to the gliding technique must be completed at forward velocities of 4.0 and 3.7 m/s for males and females, respectively.

14 164 DE KONING, DE GROOT, AND VAN INGEN SCHENAU The gliding technique allows the skater to achieve a higher maximal speed than does the running-like technique. When we compare the track and field 100-m sprint to the first 100 m of the race, the times over this distance are rather similar. At the 1988 Winter Olympic Games 11 male speed skaters covered the first 100 m in less than 10 seconds. The fastest speed skater covered his 100 m in 9.72 seconds, 0.12 seconds faster than the official world record in male sprint running. Ten female speed skaters were faster than 11 seconds at the 100 m. The fastest female 100-m time (10.55 see) was 0.06 seconds slower than the official world record in female sprint running. Besides propulsion techniques there is a notable difference between the way in which the 100 meters is covered. In the first seconds of the sprint, the acceleration of the sprint runners is much greater than that of the speed skaters (Cavagna, Komarek, & Mazzoleni, 1971; Ward- Smith, 1985). Due to the advantages of the gliding technique, however, the speed skaters are able to continue accelerating over a longer period and reach considerably higher maximal velocities (15 m/s vs. 11 mls). This effect is shown in Figure 10. When comparing the analyzed first 4 seconds of the speed skating start to speed skating at a steady speed, one can detect several differences. In the gliding technique the speed skater should not use the complete range of plantar flexion. In fact the gliding technique is only possible when the skate blade is in a horizontal position during the push-off. Complete plantar flexion would increase the ice friction by driving the front end of the skate into the ice. During skating at a steady speed using the normal gliding technique, maximal ankle angle values of 100" are found (de Boer et al., 1987). In the start, by comparison, ankle angle Figure 10 - Schematic graphs of the velocity during 100-m sprint running (solid line), maximal velocity 11 mls (data from Ward-Smith, 1985), and the fmst 100 m of the 500-m speed skating race, maximal velocity 15 mls.

15 THE SPRINT START IN SKATING 165 values of 140" are not unusual (Figure 5). This means that during the first few strokes of the start, the speed skaters plantar-flex their ankle joint and continue the push-off by using the front end of their skate. Thus more work per stroke can be achieved than during the normal gliding technique, which does not allow continuation of the push-off with a strong plantar flexion. Differences in kinematics of the knee between the start and skating at a steady speed were found in preextension knee angle and knee angular velocity. In this study, preextension knee angles of - 130" for females and - 120" for males were found in the first few steps. Ingen Schenau, de Groot, and Hollander (1983) reported preextension knee angles of 117" and 105" for females and males, respectively, during the full lap of the 500-m race. Similar smaller values are also found in this study after the completion of six strokes. This indicates the transition from a running-like technique to the gliding technique necessary at higher speeds. The maximum knee angular velocities during the first 4 seconds of the start are larger than those reported by Ingen Schenau et al. (1985) for steadystate speed skating. We found maximum extension velocities for males and females of and 639.4"/sec, respectively, while Ingen Schenau et al. (1985) found values of 591 "Isec during female 500-m speed skating races. This is directly related to the higher push-off velocities (4 rnlsec) during the start in comparison to steady speed skating (1.5 m/sec, de Koning, de Groot, & Ingen Schenau, 1988). Effectiveness of speed skating strokes can be expressed by the angle between the vertical and the vector from the ankle of the push-off leg to the body center of gravity (Figure 3) (Ingen Schenau et al., 1985). This angle (p), measured at the end of the push-off, indicates the direction of the push-off. Clearly the more horizontal the direction of push-off (a large angle p), the greater the contribution to horizontal rather than vertical velocity. At the beginning of the start, the horizontal velocity is generated in the direction of the straight. After a few strokes the skater is forced to push off during gliding, and the direction of the push-off must then always be perpendicular to the gliding direction of the skate. De Boer, Schermerhorn, Gademan, de Groot, and van Ingen Schenau (1986) found a significant difference in push-off angle between elite and trained speed skaters. The elite speed skaters show a larger angle cp at the end of their pushoff. Ingen Schenau et al. (1985) reported push-off angles of 39" for world class female 500-m speed skaters, measured in the straight during the last full lap of 500-m races. For male and female speed skaters, we found mean values over the first 4 seconds of the start of 53.9 and 49.3", respectively. This indicates that the start strokes are more effective in terms of the push-off angle (p) than the strokes during the last lap. The fact that this effectiveness during the start correlates with speed (100-m time, Table 3) underlines the importance of this technical aspect in speed skating. Next to the mechanical aspects of the start technique, there is also an important physiological aspect: the availhility of energy rich phosphates in the muscles. Performance in endurance sports is largely limited by the production rate of those energy rich phosphates. Considerably more power output is possible during the first seconds of an exercise than later on. This high power is reflected by the high mean power output per stroke values as presented in Table 2. This power output is calculated from the sum of the power necessary to accelerate the body center of gravity forward and the power lost to air and ice frictional forces during the first 4 seconds of the start. In the start, the largest destination

16 166 DE KONINC, DE CROOT, AND VAN INCEN SCHENAU of the produced power is the rate of change of kinetic energy (acceleration) of the body center of gravity (Figure 9). The power output found during the first 4 seconds of the speed skating start have the same magnitude as the mean power output produced during the first 4 seconds of a 30-sec sprint test on an electrically braked cycle ergometer. Ingen Schenau, de Boer, Geysel, and de Groot (1988) reported power output values on the cycle ergometer for elite male and female speed skaters of 17.3 and 14.8 Wattlkg, respectively (17.1 and 12.7 in speed skating). Due to the difference in power output pattern, the work output during speed skating is mainly achieved in the short push-off phase whereas during cycling the power can be produced over a larger period-at the same mean power outputyet larger peak power output values are expected in speed skating (de Groot, de Boer, & van Ingen Schenau, 1985). A speed skating stroke can be divided into a gliding phase, or in the start a flight phase, a push-off phase and a repositioning phase. Effective power can only be produced in the push-off phase of the stroke. In the plots of the velocity and kinetic energy of the body center of gravity (Figures 8 and 9), this phenomenon can be seen as acceleration and deceleration, respectively, during the pushoff and gliding phases of the speed skating strokes. Stroke values of power are values averaged over the push-off phase and the nonproductive deceleration phase. The values for average effective power during the push-off phase (Po acc) are 2,688 Watt for males and 1,848 Watt for females. There are still differences between males and females for power output values normalized to body weight (Po acjkg): 35.4 Wlkg for males and 28.4 Wlkg for females. These differences can in part be explained by differences in effectiveness of the push-off as measured by push-off angle p (Table 1). When the pushoff angle is larger and thus more effective, more of the produced power can be used for propulsion in the forward direction. Times for the 100 and 500 meters are significantly correlated with push-off angle; the significance of the power output is shown by the correlation between power during the push-off phase and 100-m time as found for males (Table 3). It should be noted that the power values (Po act) are averaged over the complete push-off times. oreo over,-the power is calculated from the rate of change of kinetic energy of the body center of gravity based on the velocity in the forward direction only. This means that the actual mean power production must be considerably higher, including power associated with sideward and vertical movements and power lost in accelerating and decelerating of body segments relative to the body center of gravity (Aleshinsky, 1986a, 1986b). The powers calculated in this study are therefore underestimations of the actual muscular power output. These considerations emphasize the explosion of power output during the start of these sprinters. In conclusion, the first strokes during the start are performed by a runninglike technique. At a forward velocity of approximately 4 rnlsec, the skaters are forced to change this technique to the typical gliding technique as used during speed skating at steady speed. The effectiveness of the push-off appears to be an important parameter. At the observed high power output levels, the individual values of the power output are of minor importance in explaining the time differences on the first 100 meters of the 500-m speed skating race.

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18 168 DE KONING, DE GROOT, AND VAN INGEN SCHENAU Koning, J.J. de, de Groot, G., & van Ingen Schenau, G.J. (1988). Muscle coordination in elite and trained speed skaters. In W. Wallinga, H.B.K. Boom, & J. de Vries (Eds), Electrophysiological ). Amsterdam: Elsevier Science Publ. Koning, J.J. de, Jobse, H., Cserep, F., van Ingen Schenau, G.J., & de Groot, G. (in press). Push-off force and ice friction during speed skating [Abstract ESB, Bristol]. Journal of Biomechanics. Ward-Smith, A.J. (1985). A mathematical theory of running, based on the first law of thermodynamics, and its application to the performance of world-class athletes. Jouml of Biomechanics, 18, Acknowledgments This study was made possible through the IOC Medical Commission's Subcommittee on Biomechanics and Sport Physiology, Red Lake Corporation, XV Olympic Winter Games Organizing Committee (OCO '88), and The University of Calgary. The authors gratefully acknowledge the cooperation of the Olympic speed skating research group--ruud de Boer, Kim Nilsen, Maarten Bobbert, Marge Hartfel, Yasuo Yoshihuku, and Todd Allinger; Christa Bakker and Christine Aaftink for their skillful assistance, and Tony Sargeant for his comments on the manuscript.