That waxing is a crucial and often decisive factor in skiing is something no follower of the sport can have missed. But how significant is it? Can we quantify the impact of waxing in measurable terms, and how does it compare to other factors, such as the skier’s physical capacity? – It’s not a trivial question, but with a few simple assumptions, we can actually make significant progress in understanding the magnitude of this difficult-to-control factor, which both elite skiers and recreational athletes invest considerable resources in.
To quantify this issue in the simplest possible way, we start by considering only glide waxing—that is, a race in free technique or double poling on classic skis without grip wax. Under this very basic assumption, we can set up a force balance for the skier. The braking forces acting on the skier while skiing at a constant speed are:
(1)
Where m is the skier’s weight, α is the terrain slope, A is the skier’s cross-sectional area, ρ is the air density, Cd is the drag coefficient (a constant describing how aerodynamic the skier is), v is the speed in meters per second, and µ is the friction coefficient—a dimensionless constant that measures how well the skis glide.
As we have written multiple times in this discussion, a skier’s speed is not limited by the amount of force they can generate at low speed but rather by the maximum power they can sustain at top speed. The challenge lies in maintaining high force output as speed increases, which translates into a limiting power capacity.
(2)
In a more detailed analysis, we would also need to include acceleration and deceleration in equation (1) using Newton’s second law, as well as consider a specific course profile with slopes, curves, tailwinds, and headwinds. However, for a first approximation aimed at understanding the magnitude of friction’s impact, we disregard these factors. We assume the skier is moving in a straight line on a completely flat course with no wind. By combining equations (1) and (2), we obtain a cubic equation where the skier’s velocity can be solved as a function of body weight, power output, aerodynamics (CdA), and the friction coefficient µ.
The results of the calculations are summarized in Table 1, which presents 10 km times for male and female skiers with different physical capacities under varying glide friction conditions. The skiers’ capacities are expressed as average power per kg of body weight over the race distance, with values chosen to represent skiers ranging from strong national-level competitors to world-class athletes capable of winning Olympic and World Championship medals.
For those interested, average power output can be converted to oxygen uptake based on assumptions about efficiency and utilization rates. Assuming an efficiency of 17% and a utilization rate of 90%, the corresponding values are:
- 4.5 watts/kg → 84 ml/kg/min
- 4.1 watts/kg → 76 ml/kg/min
- 3.8 watts/kg → 72 ml/kg/min
- 3.5 watts/kg → 65 ml/kg/min
- 3.1 watts/kg → 58 ml/kg/min
Table 1: Time in a 10 km flat race as a function of glide friction for male and female skiers with different physical capacities expressed in watts/kg.
Table 1 presents several interesting conclusions.
At first glance, we see that a world-class male skier with a glide friction of 0.02 (corresponding to excellent glide in firm tracks) reaches a speed of nearly 30 km/h, which is reasonable on a flat course without curves. Looking further down the table, we observe that a 10% deterioration in glide friction for this skier results in approximately 20 seconds of additional skiing time. When examining the female skier, we notice the same trends, but glide plays an even greater relative role since air resistance has a smaller effect on a shorter skier who moves at a slightly lower speed. Additionally, by looking further to the right in the table, we see that a 10% improvement in glide can compensate for a 3.5% lower physical capacity.
One conclusion from this discussion is that a 10% decrease in glide has a decisive impact on the outcome of elite-level ski races. A 20-second loss over 10 km is significant, and a 3.5% difference in capacity is substantial among world-class skiers. A natural follow-up question is whether it is reasonable to expect a 10% variation in ski glide friction among skiers at the elite level, where we can assume that all have waxing teams working meticulously to provide the best possible skis.
Without deeper insight into waxing teams’ methods, our assessment is that differences as large as 10% in glide friction are quite rare when only glide (and not grip) is involved. We make this claim based on measurements we have conducted using Skisens handles. For example, we have measured a nearly 20% difference in rolling friction between #2 and #3 wheels on roller skis. We have also measured about 25% variation in glide friction between old wooden skis and modern plastic skis in dry, cold snow. In both cases, skiers clearly perceive the slower pair as significantly inferior in terms of rolling or gliding. Given this background, it is very difficult to believe that a well-organized waxing team comparing materials would fail to detect a 10% difference.
Our estimate is that glide differences between skis at the world-class level are rarely greater than 5% when only glide is considered. This would correspond to time differences on the order of 10 seconds, which could certainly decide a race on the margins but would not drastically alter the rankings to the extent that a top skier drops out of the top 10 due to a waxing failure. If grip were involved, the uncertainties would be much greater. Grip affects glide, and it is also very difficult to quantify the time loss caused by poor grip.
During the winter, Skisens will conduct a series of tests using handle measurement data to determine the impact of different waxing methods. For example, we will study how glide is affected by ski structure or the application of grip wax on classic skis.
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