Drag Forces, Equipment and Performance

Newton's laws describe the effects of forces on motion of an object. The vector sum of all forces acting on a skier determine motion changes. As shown in Figure 5 early in this chapter, reaction forces at the poles and skis are important components affecting skier motion. These reaction forces are affected by skier technique and strength and have characteristic patterns that have been illustrated above. However, the resistive forces due to air and snow also have a substantial influence on a skier's performance capabilities. These can dramatically affect skiing speed and influence technique execution and choice. While equipment in skiing is relatively simple, it's interaction with snow and air directly affect performance. Aspects of aerodynamics and snow friction will be introduced in the following sections along with discussion of equipment and technique choices to minimize drag forces acting on a skier.

Aerodynamic Drag

"Air resistance" can be thought of in terms of force acting on a body due to flow characteristics of fluids through which the body is moving. The branch of physics called fluid mechanics includes two components that contribute to development of drag force acting against a skier's motion. ("Fluid" in this context means a medium, like air, which can flow around an object.) The two components depend on an object's surface characteristics and on its shape and size and they are often referred to as skin drag and profile drag. Skin drag is a force acting against the direction of motion which derives from local characteristics of fluid flow at the surface level of an object. In some sporting situations (swimming for example) skin drag is of consequence, but in skiing it is of relatively small magnitude compared to profile drag and ski drag forces and won't be discussed further here.

Profile drag force is generated as a skier moves through air and depends on a skier's overall shape and size. With motion, air flows around the body, skis and poles and exerts varying pressure patterns on the front, back and sides of a skier. Steamlining of the body and equipment can smooth the air flow patterns and minimize pressure differences from front to back of a skier. It is air pressure difference applied across an area of the body which creates profile drag force (and explains why it is also referred to as pressure drag). If a skier can reduce pressure differences and can reduce the area upon which the pressure difference acts, drag force can be reduced.

Body shape of a skier is not easily adjusted within the constraints of techniques for propulsion. Hence relatively little is usually done to minimize air drag under normal conditions of flat and uphill skiing. However, on downhills where speed is greater and where gravity provides propulsive force, or when headwinds are encountered, ski technique is often modified to minimize air drag forces. In these circumstances, the relative velocity of air past a skier can be considerably greater than the 5 or 6 m/s average speeds in racing. Because drag force increases as the mathematical square of relative velocity, modest increases of air flow past a skier can substantially increase drag force. Figure 30 illustrates typical profile drag forces as a function of speed for upright and tucked body positions. Notice how dramatically drag force increases with speed. At 5 m/s about 10 N of drag force act against a skier; doubling speed to 10 m/s quadruples drag force to 40 N. Changing body position from upright to tucked (Figures 1 and 4, for example) is a common strategy on downhill terrain which reduces air drag by more than half. This advantage results both from streamlining of air flow around the body (reducing pressure differences) and from reducing frontal area compared to upright.

Skiers on flat terrain encountering headwinds have more difficulty in dealing with air drag force. A modest headwind of about 2 m/s will nearly double the air drag that a skier experiences; with more severe wind conditions, skiers must often adjust body positioning and/or technique to maintain performance. Despite headwinds, a skier must be able to generate propulsive force, so technique cannot be severely altered. However some lowering of the body through trunk and neck flexion is one strategy which may reduce air drag modestly. Another strategy involving drafting behind a leading skier becomes increasingly advantageous as wind speed increases. Similar to drafting in cycling or running, a skier trailing close behind another experiences reduced air drag due to a reduction in front-back pressure difference. The trailing skier, when close enough, can be skiing within a low pressure region behind the leading skier. Based on cycling experiments, drafting skiers may benefit from reductions of drag force as much as 25 to 30%.

Snow Drag

Gliding across snow is one of the joys of cross country skiing. The physics of ski-snow interaction is what makes low resistance gliding on snow possible. The physical processes involved bring together a complex interaction of liquid and solid water, ski base material, ski waxes, ski surface roughness, snow surface compaction, as well as air and snow temperature, radiant exposure, snow contaminants and probably other factors. The complexity of factors involved in studying ski glide characteristics makes determination of the relationships amongst the factors a challenging undertaking. Currently, these relationships are only partly understood. However, what is clear to any experienced skier is the wide range of ski drag forces that can be encountered during a season of skiing. Explaining the physics behind snow and ski friction is beyond the scope of this handbook. There are, however, several monographs that can be referenced if the reader wishes to delve into the details of meltwater lubrication and other esoteric topics relevant to skis and snow (for example, Colbeck, 1992, 1994 and 1997). Pragmatic details involving ski preparation and waxing are presented in a later chapter of this handbook. This section will deal with ski drag forces and performance.

Ski races often are decided by small time differences of a few seconds which seem almost insignificant across the span of a one or two hour or longer race. Small differences in snow drag force can easily result in minute differences in performance. For example, imagine a 10 kilometer skating race in which a certain skier can maintain a 5 m/s average speed, finishing the race in 2000 seconds. With a typical coefficient of friction for skis of 0.05 the skier would experience a snow drag force of about 35 N; air drag would be somewhat less, about 10 N. Thus, the skier would be working against 45 N of combined drag force throughout the race. At the average speed of 5 m/s, this would require mechanical power of about 225 watts and this would in large part determine the skier's metabolic rate. Now consider the effect of a 5% increase in the coefficient of friction for the skis. Snow drag would increase proportionally and total drag force would increase as well. Skiing at the same intensity (225 watts), speed would have to be reduced to about 4.86 m/s which would increase the skier's race time to about 2058 seconds--almost a minute slower!

The 5% change in coefficient of friction suggested in the example above is not large and probably would not be detectable by most skiers were they to ski two pairs of otherwise identical skis which differed only in this small amount. But the effect on performance is substantial. To assess how influential snow drag force may be during ski competitions, data were collected on glide speed of Olympic skiers in the men's 50 km race at the Les Saisies venue near Albertville, France in 1992. Figure 31 illustrates the terrain in the race where speed measurements were made. Skiers came over the crest of a hill, skated several times and then settled into a tight tuck position in straight, well set tracks. They glided across a flat section at the bottom of the downhill and maintained a tuck position until well past the measurement zone. Video was used to record skier movement through the zone. Subsequent analysis determined skier time to traverse the 20 meter zone from which glide speed was calculated. Average glide speed across the flat was about 15 m/s. As can be seen in Figure 32, glide speed was negatively related to finish time in the race. That is, faster skiers overall in the race were also faster in downhill ski glide.

Ski Pressure Distribution

Newton's third law deals with "action-reaction". A force applied through the ski to snow is paired with a reaction force of equal magnitude of snow on ski transmitted to the skier. While it may be convenient mathematically to think about such forces as having a single point of application (to the foot of the skier, for example), such simplification would ignore an aspect of ski design which has important implications for skier performance. Skiers generate external force through muscle activity and body motions which are transmitted to skis and poles which in turn transmit the reaction forces to the skier. Force applied to a ski is transmitted to snow across the large bottom surface area. Pressure is a measure of how force is spread out over a surface and is described in units of force per area. A force applied to the top surface of a ski at the binding is transmitted to snow all across the bottom surface but in characteristic non-uniform patterns. Small areas near the tip or tail of a ski may carry considerably more force than do other regions. Because snow is a deformable material which responds in a manner which depends in part on the pressure applied to it, regions of high pressure under a ski are likely to penetrate more deeply into a snow surface than do low pressure regions. Snow deforms inelastically and returns little energy to a ski. Such deformation heats up snow through energy loss to the ski which ultimately decreases glide. Therefore, attention to pressure distribution patterns of skis is of interest for purposes of improving performance.

Skating skis involve complex designs which must not only glide well but must have sufficient torsional stiffness to resist twisting about the ski's longitudinal axis during edging under load. In addition, stiffness of a skating ski's camber must be sufficient to enable straight tracking in the forward direction. These sometimes competing demands are what manufacturers grapple with in each new design. Typical pressure distribution patterns for skating and classic skis are shown in Figure 33. The patterns clearly change with magnitude of loading. It is these rather large scale overall patterns which determine a ski's tracking, edging and stability characteristics.

The classical ski has an additional challenge required for good performance. The mid-region must be sufficiently stiff that under moderate loading very low pressure is observed in the region. This allows kick wax in the mid-region to remain unloaded and not dragging along the snow surface when a skier is gliding on both skis. But with larger forces above body weight magnitudes, the classic ski mid-region is compressed against the snow allowing good adherence of grip wax with surface snow. During this compression when static frictional force is greatest, a kick from the momentarily static ski is made. Thus appropriate matching of skier weight with ski stiffness is crucial for optimal generation of propulsive force.

The full ski pressure patterns of Figure 33 certainly have some influence on pure glide characteristics. One would expect that extremely stiff skis with very high pressure at tip and tail of the ski would cause more deformation of snow, plowing it in front of the ski, than would softer designs which might allow the ski tip to ride up and over softer snow. While these relationships have perhaps been studied by manufacturers, the details are confidential and not available to the public.

Moving from the large scale pressure patterns which affect ski handling, a more localized pressure distribution could in principle be measured as well. On a scale of several centimeters, it is likely that pressure differences also affect localized drag forces acting on the ski. A small localized high pressure region will also deform the snow surface and increase ski drag. Flattening a ski to minimize localized fluctuations of pressure in the longitudinal direction is an arduous task with hand tools. However, stone grinding instrumentation and experienced technicians to run it have become more widely available in recent years. These can reduce centimeter scale irregularities of a ski's pressure distribution while introducing millimeter scale roughness ("structure"). This is thought to enhance glide through better matching of snow crystals, surface asperities, and water droplet adhesion which result in drag force acting on a ski surface at the microscopic level. Practical details on ski structure and glide are provided in a succeeding chapter of this handbook.

Economy and Technique Optimization

Human locomotion mechanics and physiology have been of interest to scientists from the beginnings of science. A question that has attracted attention in recent decades is relevant to our discussion of ski biomechanics. Humans naturally walk at slow speeds and run at faster speeds. When asked to move through a range of speeds from slow to fast, humans transition from walking to running at about 2 m/s. What mechanical and/or physiological factors explain this human walk-run transition point? At first look, the answer seems intuitively obvious: the walk-run transition point must be the speed where the metabolic cost of walking exceeds the cost of running. However, measurement of this "cross over point" of walking and running metabolic costs is somewhat lower than is actually observed. Other factors might also be involved. Various researchers have found evidence for kinematic, muscular, and force "triggers" of the walk-run transition or perhaps a more global dynamic system response using many input factors. A comprehensive explanation of the human walk-run transition point has not currently been formulated.

In skiing, various locomotion patterns are used by skiers as they encounter terrain and environmental conditions that affect the speed and metabolic demands of moving over snow. In racing where competitors operate at relatively constant metabolic rates throughout a race, terrain largely determines a skier's choice of technique. As terrain varies, skiers transition from double pole with kick to diagonal stride or from open field skate to V1 and back again in a rather unconscious manner not unlike the walk-run transition over ground. What factors trigger these transitions? Are there clearly advantageous techniques to be used on the flats? on moderate uphills or downhills? These questions are probably no easier to answer for researchers than that dealing with the walk-run transition and unfortunately we have less evidence with which to work.

Skating Technique and Terrain. A study comparing skiing speed with V1, V2, and Open Field skate with elite skiers on varied terrain of a 3 km course (Bilodeau et al., 1991) found that race pace skiing had similar metabolic demands (based on heart rate) for each technique. Further, similar speeds were observed for the techniques with a trend in the data suggesting that V1 was slightly faster uphill and Open Field slightly faster downhill. A follow up study (Boulay et al., 1994) had skiers skate at maximal effort on various slopes using the three skating techniques. Little difference in skating speed was observed for moderate terrain up through 6% uphill. However on steeper uphills, V1 skating was clearly faster. Figure 34 shows the speed, cycle length and rate relationships for the varying slopes.

These responses shed light on the distinct differences of the three skating techniques. Across quite varied terrain, very similar skating frequencies were used for a given technique and these were dramatically different amongst the three techniques. V1 skate is consistently much higher frequency than Open Field and V2 skating. Do these results match with typical technique choices made by racers in varied terrain? Yes, V1 skating is usually the technique of choice on uphills. But on easy rolling terrain, skiers are more likely to ski with Open Field or with V2 techniques. The research findings suggest that V1 may well be as fast; why is it not the technique of choice on flat terrain? The full answer is unknown, but like the walk-run transition, metabolic comparisons of the techniques do not provide an explanation. Perhaps the distribution of effort from arms to legs is sufficiently different in the V1 and Open Field, for example, that alternating technique where possible becomes advantageous. Optimizing performance in a race involves not only momentary choices of technique, but longer duration choices of effort in uphill and downhill terrain and on overall race pacing. Mechanical characteristics of techniques, a skier's physiological attributes and even ski equipment responses combine in a complex manner that is rapidly assessed by skiers as they smoothly transition between techniques going uphill to downhill and back up. But we have rather limited understanding of the nature of that internal calculus.

Cycle Characteristics and Performance. Stride length and frequency are kinematic variables that together determine skiing speed. Interaction of these characteristics depends on terrain, intensity (metabolic cost), snow conditions and, as we've seen above, on technique choice. Under most conditions, control of skiing speed is determined by a skier's stride frequency while stride length remains relatively constant (Figure 19). Each technique seems to have its own frequency at maximal speed which also remains relatively constant across terrain (Figure 34). How does a skier's self determined stride length and frequency relate to race performance?

If instead of looking at an individual skier's speed-frequency-stride length relationship, we look across skiers and compare cycle characteristics, a quite different picture emerges. Figure 35 shows cycle length of Olympic skiers in the women's 30 km race (1994) while double poling on a moderate downhill. Faster skiers through the measurement site were generally those with greater cycle lengths. Double poling frequencies of these skiers were not significantly related to skiing speed. This pattern of skier speed related to stride length has been observed with both skating and classic techniques and on a uphill, flat and this moderate downhill terrain. In general, the fastest skiers as well as slower racers stride with rather similar frequencies for a given condition, but the fastest skiers consistently have greater stride lengths than slower skiers. Putting these relationships together: skiers control speed at any point primarily by adjusting stride frequency but faster skiers obtain their speed advantage by greater stride length. At any point in a race, a skier should focus on stride frequency as the mechanism of speed control. But in training, it is stride length which must be increased through technique, strength and other preparation focussed on this key characteristic.

What factors enable the fastest skiers to generate longer strides than slower skiers? That is a central question to which biomechanics can contribute at least part of the answer. Clearly the forces acting on a skier determine motion characteristics. As we have seen in our discussion of snow drag forces, the fastest skiers may often have skis with less snow drag. This advantage may come from the ski's overall pressure distribution, from its surface preparation and from its waxing. The fastest skiers probably have the fastest skis. This partly accounts for the greater stride lengths fast skiers exhibit.

But technique also affects forces acting on a skier. Effective technique generates propulsive force without increasing drag forces, without increasing side to side motion in skating, and without increasing metabolic demands. Effective technique requires equipment well matched to a skier's height and weight so that optimal body positioning can be obtained in poling and so that effective thrust can be obtained from the skis. Determining equipment characteristics which optimally match a skier's characteristics is a challenge to which biomechanics can contribute relevant data but which ultimately requires the insights that coaches and athletes bring together.

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Figure Captions for this section:

Figure 30. Air drag force versus speed for upright and tucked positions. Data from Svensson (1995).

Figure 31. Glide testing of Olympic skiers was carried out during the men's 50 km race at the Albertville Winter Olympics. The section of the race course involved a steep, straight downhill of about 150 meter length. At the bottom as skiers glided across a flat, speed was determined using video motion analysis.

Figure 32. Glide speed and race finish time were recorded for participants in the men's 50 km race at the Albertville Winter Olympics. Glide speed was strongly related to finish time for each lap of the race. Faster skiers in the race also were faster through the glide test. Subsequent modeling analysis of skier downhill glide found little relationship of glide speed to skier mass. Glide speed was most strongly influenced by ski drag force. Graph adapted from Street and Gregory, 1994.

Figure 33. Pressure distribution for a skating and a classic ski. Note that pressure distributions change under each ski as loading changes from half to full body weight. The skating ski remains lightly loaded in the mid-region at body weight while the classic ski compresses the mid-region so that wax can grip the snow during kick to the ski. Illustrations adapted from Eagle River Nordic, 1999.

Figure 34. Comparison of V1, V2 and Open Field Skating characteristics on varying slopes. On each slope skiers skated at maximal effort. Video was used to determine velocity, cycle length and rate. The skating techniques were equally effective on -1, 0 and 6 % slopes but V1 was faster on steeper uphills. Note that cycle rate (frequency) stayed nearly constant for each technique across the range of slopes. Adapted from Boulay et al., 1994.

Figure 35. Cycle length versus cycle velocity in double poling. Data were obtained during the women's 30 km race of the 1994 Winter Olympics in Lillehammer. Faster skiers had greater cycle lengths than slower skiers. Similar patterns have been observed for skiers using other techniques and on other terrain.

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