Kinematics and Kinetics of Ski Techniques

Performance in cross-country skiing is determined by the complex interaction of physiology and mechanics. The forces which drive a skier's motion come with metabolic expenses and limitations which affect the ability to generate and sustain force at ideal levels. Optimization in skiing occurs at levels ranging from waxing to equipment, technique, and race pace choices. In any optimization situation there are tradeoffs between various operational states which are balanced against each other in a manner which results in the best performance. For example, grip wax choices in classical skiing affect both the static and dynamic frictional characteristics of a ski. A "slippery" ski will have relatively low ski drag forces when gliding which is an advantage but may allow relatively little propulsive force to be generated by a diagonal stride's kick which is disadvantageous. A stickier wax will have greater ski drag forces but the kick will generate larger propulsive forces. An optimal choice of kick wax balances these characteristics to obtain the best performance. Neither maximal glide nor maximal propulsive kick force will work well. Rather, the best wax choice is probably something which allows both moderate glide and kick force. This optimization process occurs on many levels in skiing.

Preceding sections of this chapter have introduced the mechanical principles which affect a skier's motion. Force is the central physical characteristic which ultimately determines skier motion and which is involved in the optimization process. This section will discuss both classical and skating technique movement patterns and the forces involved. The reader should keep in mind that for each technique, optimization will balance the competing demands of propulsion versus drag force with physiology playing a limiting role in a skier's ability to generate force.

Classic Ski Techniques.

Diagonal Stride. Human locomotion is cyclic in nature and in the most basic patterns of walking and running the arms and legs move in opposition to each other. A full cycle in these cases involves a right and a left step combining into a full stride. The diagonal stride in skiing is closest to these fundamental movement patterns and similarly involves arms and legs working in right-left pairings (figure 9).

The movement pattern of figure 9 and the vertical and propulsive components of force shown in figure 7 represent half of a diagonal stride cycle. This classic technique involves "kicking" from a momentarily stationary ski onto the other gliding ski which in the next half cycle slows to a stop allowing the skier to kick from it. During the very brief stationary period of the ski's motion, a large vertical force compresses the mid-section of ski against the snow. With appropriate wax on the ski, the mid-section momentarily sticks to the snow due to the large normal force and high pressure in that region (figure 10). The static frictional force is large enough during the kicking phase that a brief propulsive component of force in the forward direction can be generated. The magnitude of this force depends on the frictional characteristics during kick. These can vary widely depending on snow conditions, ski stiffness, and wax properties (figure 11). While vertical forces during this kick phase may be two to three times body weight, the propulsive forces are much smaller (approximately 10-25% of body weight) and are of very short duration--about 0.1 seconds (Ekstrom, 1981; Komi, 1987). In contrast, skating forces (discussed below) are applied over a considerably longer time interval.

Generating propulsive force during the kick phase of diagonal stride requires careful timing of the vertical and horizontal forces matched to the glide speed of the ski. As the ski slows to a stop, the large vertical force must quickly compress the cambered mid-section of the ski to the snow surface which momentarily creates a static frictional force. Optimal technique directs the ski reaction force vector at an angle such that the propulsive force component matches the maximum frictional force attainable for the conditions. An early kicking motion will compress the ski mid-section while the ski is moving and tend to decrease the glide unnecessarily. A late kick will compress the ski camber after the ski has momentarily stopped and will decrease the vertical force component which will in turn decrease the static frictional force from which propulsive force is generated.

Frictional characteristics of classical skis are in large part determined by the grip wax applied in the mid-section of the ski. Coefficients of friction for grip wax (Hamalainen & Spring, 1986) depend on wax constituents, temperature and ski stiffness and range from 0.2 to 0.4 when measured statically but are considerably smaller when a ski is in motion (less than 0.1). Maximum propulsive (horizontal) force of the kick from a ski is determined by the coefficient of static friction and the vertical force generated at the same time. Combining vertical force measurements made using instrumented skis (Ekstrom, 1981; Komi, 1987) and the coefficient of static friction (Hamalainen & Spring, 1986), one can determine a theoretical maximum propulsive force for the diagonal stride kick of more than 0.4 times body weight. However, measured propulsive forces of the kick (0.1-0.25 times body weight) are considerably less than this theoretical maximum. This suggests that in typical diagonal striding skiers are unable to use the frictional characteristics of grip wax to full advantage. Whether this shortcoming is due to technique or mechanical characteristics of skis is unclear from the limited biomechanical testing currently available in the literature.

Diagonal stride in racing is primarily a technique for climbing. Uphill skiing reduces the glide phases of each stride compared to flat terrain and increases stride frequency. Temporal analysis of diagonal technique suggests that the proportion of the stride where a ski is stationary is increased as slope increases. This is associated with an increased proportion of poling during a full stride. This adjustability of diagonal stride temporal proportions is part of what makes the technique well suited for climbing. A skier can maintain some propulsive force from skis and poles throughout most of an uphill diagonal stride. Unfortunately we have little quantitative data describing the force and movement pattern changes associated with diagonal stride on varying terrain. We can only conjecture that optimizing technique on uphill terrain involves minimizing periods without propulsive force and this is best accomplished with diagonal stride rather than other classical ski techniques.

As ski tracks vary from flat to steep uphill, the distribution of propulsive force across arms and legs probably changes to larger contributions delivered through poling. Due to the relationship of ski force perpendicular to the surface affecting the horizontal frictional force and grip of a ski during kick, it becomes more difficult to generate propulsive force from the ski as slope becomes steeper. Poling in contrast simply requires firm placement of the pole basket on the surface to generate propulsive force. This remains relatively constant from flat to steep uphills. Thus the proportion of propulsive force from arms versus from legs tends to increase as slope increases. This relationship is illustrated in figure 13 for three wax conditions. It is clear that slippery grip wax increases the reliance on arm propulsion during diagonal stride.

Arm and pole movement during diagonal stride is largely in the sagittal plane. Pole angulation at pole plant is slightly inclined forward of vertical (about 10 to 15 degrees) with the amount of inclination slightly affected by skiing speed and slope. Poling forces are applied axially, that is, along the axis of the pole. Thus pole inclination angle will affect the proportion of vertical and propulsive force at any moment. At 10° of pole inclination from vertical, the propulsive component of poling force would be less than 20% of the applied force. Whereas, at 45°, the propulsive component would be greater than 70% of the applied poling force. It is clear that the effectiveness of poling force to propel a skier forward is greatly increased as the pole is inclined away from vertical (see figure 3). Likewise, it is relatively ineffective to generate large poling force early during the poling phase as most of such force would go into a vertical component which does little to propel a skier.

Fortunately, arm structure can be used to advantage to minimize the metabolic costs for generating large poling forces. The poling phase movement pattern is mainly due to elbow extension coordinated with shoulder extension. In general, the elbow is probably strongest in mid-range. Thus it would be advantageous if the arm were positioned so that the elbow is near mid-range extension when the poles are inclined substantially away from vertical. Elbow motion in poling often involves first flexion then extension of the joint (Komi and Norman, 1987). The initial phase from pole plant to nearly half way through poling involves a relatively slow flexion of the elbow (figure 14). This flexion is probably associated with eccentric stretching of the triceps muscle crossing the elbow. Later in the poling phase, the elbow rapidly extends through mid-range to near full extension with the pole inclined substantially from vertical in a relatively effective angulation for propulsive force generation. This flexion followed by extension pattern allows the skier to apply some force to the pole early in the poling phase where the pole angle is not very effective for propulsive force without "using up" any of the extension range of motion at the elbow. In addition, this pattern may pre-load the triceps, which may allow greater force generation and perhaps store some energy elastically to be returned moments later during elbow flexion. This pattern of eccentric then concentric muscle activity is often called a stretch-shortening cycle and is thought to be a common part of locomotion patterns which results in improved metabolic economy. There is some indication that muscular stretch-shortening cycles may play a role in the kick phase of diagonal stride (Komi and Norman, 1987) as well as in other ski techniques. We will observe a further example of this economizing method in the double poling technique we discuss next.

Double Pole Technique.

In contrast to the assymmetrical arm and leg motions of the diagonal stride, the double poling technique involves both arms acting in unison and minimal leg involvement. Also unlike diagonal stride, considerable trunk flexion is involved in double poling and contributes to enhanced poling forces. All propulsive force generated in this technique is via arm and trunk activity delivered axially through each pole. Double poling is typically used under fast conditions or on moderate downhills where a glide phase would occur following poling. On uphill terrain, where glide after poling would involve rapidly decreasing speed, double poling is infrequently used due to the high frequency and relatively large forces required. Several physiological tests of technique have compared double poling with diagonal stride, kick double pole and with several skating techniques (Hoffman and Clifford, 1992). These suggest that double poling on flat terrain may involve lower aerobic cost but higher lactate concentrations than other techniques. On uphill terrain, relative economy measurements have not been done comparing ski techniques.

What mechanical factors contribute to the effectiveness of double poling? Poling forces, ski reaction forces and drag forces (figure 5) are those which change with technique. Poling force effectiveness is perhaps the most complex of these relationships and we will deal with it in some detail below. Ski reaction forces in double poling involve relatively little horizontal component of force; vertical ski forces are uniformly distributed across both skis and average less than half body weight due to vertical poling force during part of a cycle. Thus the skis will be only moderately loaded during double poling and probably experience drag forces which are reduced from those of diagonal stride. Air drag force during double poling is also slightly reduced compared to diagonal stride due to the trunk flexion associated with poling. This reduces frontal area of the skier and probably drag coefficient; together these would reduce air drag acting against a double poling skier.

Poling force effectiveness depends on positioning of the trunk, shoulder, elbow, hand and pole (see figure 3). Axial force is transmitted through each pole and has force components in the vertical and horizontal (propulsive) directions. As a pole is inclined away from vertical, the propulsive component increases, for a given applied force. In double poling, pole inclination is affected by the complex interaction of trunk flexion, shoulder and elbow positioning. Pole positions with the greatest horizontal, propulsive force components will be quite inclined forward of vertical. To get into such positioning requires trunk flexion combined with elbow extension. If these joint motions are coordinated, a skier's hands and pole handles can pass below knee level during poling with corresponding pole angles of more than 65Á from vertical (figure 16). In diagonal stride during the latter part of poling, propulsive force is about 70% of poling force. In double poling, the more effective positioning of the poles allows as much as 90% of poling force to be propulsive.

But in addition to larger pole inclination, arm positioning of shoulder and elbow may allow for generation of greater poling forces during later portions of poling phase where the pole is most effectively inclined. This advantage of double poling is due to trunk flexion which not only lowers the arm and pole but allows the shoulder and elbow to remain in mid-range positions where greater joint torque resulting in greater poling force can be generated compared with diagonal stride. In high speed double poling, at pole plant the shoulder is flexed slightly beyond mid-range and then extends throughout poling. The elbow in contrast is often somewhat extended at pole plant and initially flexes to 80 or 90Á before extending late in poling (figure 17). This pattern is a more dramatic example of a muscle stretch-shortening cycle which was discussed above with respect to diagonal stride poling. Elbow flexion followed by extension likely is associated with triceps eccentric activity which may enhance force development followed by triceps concentric activity during elbow extension in later poling phase. This combination allows for greatest force development when the pole is inclined at large angles and propulsive force generation can be maximized. Whether a similar stretch-shortening cycle occurs across the shoulder is uncertain. In some skiers, a small amount of shoulder flexion follows pole plant (for example, skier number 49 in figure 17). Whether shoulder extensor musculature (largely latissimus dorsi in this case) is stretched after pole plant in double poling, is unknown. Muscle activation patterns during double poling have not been measured; the kinematic characteristics of the elbow and shoulder reported here (from Smith, Fewster and Braudt, 1996) suggest the possibility of muscle stretch-shortening but do not confirm such patterns. In addition, poling force relationships to various arm-trunk positionings have not been systematically researched. Our conjectures are based on observed movement patterns and anatomical principles but have not been directly measured.

Trunk motion during double poling is a central feature of the technique and may involve more than 45 degrees of flexion during poling phase. Due to the large mass of the head and trunk and the considerable flexion that occurs, total body center of mass oscillates vertically some 25 to 30 cm during a double poling cycle (figure 18). Coaching descriptions of double poling often highlight the importance of abdominal muscles to effective force generation. While both the abdominal and back extensor muscle groups are recognized as important contributors to dynamic trunk responses in skiing, it is not clear that the abdominal group is more important in double poling than it is in other techniques. In particular, poling forces are what propel a skier in double poling. The reaction forces acting on the poles and skis reflect the acceleration of the body's center of mass. It is upward acceleration of the center of mass which enhances pole reaction forces. Downward acceleration of a skier's body would serve to diminish the poling forces, thus forceful abdominal action to increase trunk acceleration downward would be counterproductive for poling force generation. Instead, trunk flexion during poling is probably controlled largely through the back extensor musculature which allows gravity to flex the trunk. The trunk's weight contributes to poling forces as it is partially supported through the arms and poles, but probably the most important role that trunk flexion plays in double poling is to put the arms into an advantageous position for generating propulsive force during poling.

Kick Double Pole Technique.

The double poling technique is very effective under fast conditions where a glide phase between poling actions does not involve substantial slowing. But when good glide is not available due to snow conditions or slight uphill, an additional propulsive phase can be inserted between poling actions to maintain momentum. The kick phase of this technique is similar to that of diagonal stride. It depends on a momentarily stationary ski gripping the surface and a careful balance of vertical, propulsive and frictional forces. Right and left leg kicks are often alternatively used in straight tracks while the technique is easily adapted to skiing corners with repeated kicks on one side.

Skiing speed in all ski techniques is determined by basic cycle characteristics of stride length and stride frequency (number cycles per second). Theoretically, speed can be increased by increasing stride length or frequency. However in practice, skiers control speed at any moment largely by adjusting the frequency of striding while changing stride length relatively little. This is clearly seen in figures 21 and 22 where kick double pole technique on flat terrain was observed to increase frequency by about 20% as skier speed increase by 10% and while stride length decreased by about 4%. Other ski techniques also control speed in a similar manner, however it should be noted that beyond normal race speeds either slower or at maximum, more dramatic decreases of stride length are observed.

Timing of a cycle in double poling is largely determined by the extent of glide following poling. This can be very brief when a skier is sprinting or can be relatively long when on downhill terrain. In contrast, when a kick is included with double poling, stride times cannot be as short as high frequency double poling. A skier must judge the relative advantages of additional propulsive force during a longer stride versus high stride frequency when deciding between double poling with or without a kick. Optimization of technique depends on snow conditions, skiing speed, wax grip and glide characteristics and a skier's physiological attributes at any given moment. Unfortunately, much of the mechanical data about the force-time characteristics of double poling with or without a kick are simply unknown at present. This shortcoming makes discussions of ski technique optimization more conjecture based on intuition and physical principles than on kinetic data.

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Figure Captions for this section:

Figure 9: Diagonal stride involves poling and kicking phases. The half cycle illustrated includes a left arm poling phase in the interval between positions 1 and 4 and the brief right leg kick phase between positions 3 and 4. Glide phase on the left ski occurs after position 4 and continues until the next kick phase. The relative proportions of poling, kick and glide phases are adjusted in going from flat to steep uphills.

Figure 10. Pressure distribution pattern under a ski depends on the applied force. Under a classic ski, a region of low pressure exists in the middle with moderate vertical forces. However with greater loading, this mid-region of the ski experiences high pressure. Grip wax placed in this zone has little effect on glide when a ski is weighted moderately but when kicked the wax is pressed firmly into the snow. Figure reproduced with permission (Ekstrom, 1981).

Figure 11. Direction of the reaction force applied to a ski must be carefully matched against the static frictional characteristics of the grip wax during kick. This graph plots horizontal versus vertical component of the ski reaction force during the kick phase and shows how good kick wax allows an advantageous orientation of the force vector. Figure reproduced with permission (Komi, 1987).

Figure 12. Distribution of effort between arms and legs in the diagonal stride changes with slope and with kick wax characteristics. With moderate to good wax, about 15 to 30% of propulsive force comes from poling. Figure reproduced with permission (Komi, 1987).

Figure 13. Elbow angular velocity and poling force components during diagonal stride. Pole plant occurred where forces became non-zero on the graph. The shaded region of the angular velocity graph is where the elbow is being flexed while force is applied through the poles. This probably involves eccentric activity of the triceps muscle crossing the elbow and suggests that a stretch-shortening cycle is an important aspect of poling. Figure reproduced with permission (Komi & Norman, 1987).

Figure 14. Double poling technique involves a poling phase (positions 2 through 5) followed by a recovery phase simply gliding. The length of the recovery phase is adjustable to meet the demands of high frequency sprinting or less intense double poling.

Figure 15. Elbow angle versus pole angle during the poling phase of double poling. Pole plant is at the left of each curve with the pole angled about 10 to 15 degrees from vertical. Immediately following pole plant, elbow flexion (decreasing elbow angle) occurs for most skiers. This phase stretches the triceps muscles crossing the elbow prior to vigorous elbow extension later in poling phase. Graphs are for three skiers in the women's 30 km race of the Lillehammer Winter Olympics. Figure reproduced with permission (Smith et al., 1996).

Figure 16. Elbow angle versus shoulder angle during poling phase of double poling. Pole plant is at the right of each curve. Differences of technique can be observed here. Most skiers plant the pole with the elbow extended in a position of 100 degrees or more and then allow the elbow to flex through 20 to 30 degrees. Other skiers choose to plant the poles with relatively flexed elbow and extended shoulder positions (skiers 39 and 40 for example). While this allowed greater elbow range of motion through out poling it greatly diminished shoulder range. This pattern is probably disadvantageous though no poling force measurements comparing the patterns have been made to definitively determine effectiveness. Graphs are for skiers in the women's 30 km race of the Lillehammer Winter Olympics. Figure reproduced with permission (Smith et al., 1996).

Figure 17. Trunk angle and center of mass vertical motion during a double poling cycle. A vertical oscillation of center of mass occurs during poling phase of double poling. This is a result of the large trunk flexion preceding and during poling. Figure reproduced with permission (Smith et al., 1996).

Figure 18. Double pole with kick technique involves a brief kick (positions 1 to 3) and a poling phase (positions 4 to 7). Not shown is a recovery phase of gliding on the skis until the next stride begins.

Figure 19. Stride frequency and Stride length versus skiing speed for double poling with kick. Skiers control speed largely through adjustment of stride frequency while stride length changes much less. Data from Smith (1985).

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