Glide Test Sensitivity – How Ski Glide Performance Changes with Friction, Speed and Weight

A Basic Analysis Based on Newton’s Laws of Motion

Dan Kuylenstierna
20250501

The outcome of a glide test can be described using Newton’s laws of motion. When two skiers glide side-by-side, the difference in glide distance under given external conditions mainly depends on four parameters: the slope angle (α), skier weight (m), initial speed (v₀), and naturally the glide friction µ, which is usually the target variable of the test. One major challenge in execution is ensuring equal initial speed. Another challenge arises if the skiers have different body weights. The analysis below examines the impact of these factors.

When performing a glide test, a slope is usually chosen that is long enough for glide to be compared at a relevant skiing speed. Ideally, one finds a slope that levels out so the skiers glide onto flat terrain. Under good conditions, a glide distance of 100–200 meters on the flat can be achieved. The big question is how large the difference in glide distance can be over that distance — and what that corresponds to in glide friction. Figure 1 shows skiing speed and glide-distance difference in a case where the friction coefficient differs by 5% from µ = 0.02. Here we get a very clear result of approximately 120 cm difference in glide distance.

An interesting question is how the glide-distance difference changes if the skiers have different weights. Figure 2 shows the same test case but with a 5 kg difference in body weight. The figure shows that the glide-distance difference drops to about half when the heavier skier is on the slower skis. However, a clear difference still remains. To make the simulation even more realistic, we also test the case where the skiers have a difference in initial speed, which easily occurs in practice.

Based on experience, this difference can be on the order of 0–0.5 km/h. Figure 3 illustrates the impact of a Δv = 0.3 km/h difference. Now it becomes clear that the glide advantage shifts in the case where the heavier skier is on the slower skis and also has the higher initial speed. By averaging two attempts in which the skiers switch skis, most of the uncertainty related to weight can be removed. Therefore, going forward we only consider skiers of equal weight.

In the tests above, we have considered variations around µ = 0.02, which represents typical winter snow. The next interesting question is how this outcome changes if the snow is faster or slower. Figure 4 shows the result of a 5% variation in glide friction around µ = 0.012. Here we see that the glide-distance difference decreases, and under the given uncertainty in initial speed, we can no longer resolve a 5% difference in friction.

Another interesting question is which initial speed should be used. So far we have consistently compared tests with an initial speed of 30 km/h. One may argue whether this is fair, since the speed after 100 meters will not be the same. In faster snow, races will go quicker, so it may be reasonable to look at higher speeds. However, the resulting glide-distance difference will also be smaller, making it a trade-off.

In practical testing, one often needs more speed in slower snow, while less speed is required in faster snow. To systematically analyze outcomes in different snow conditions, we consider a thought experiment where the skiers glide on a slope just steep enough to maintain the initial speed. This allows comparison of glide difference at the same speed but in different conditions. Figure 5(a) illustrates constant speed of 25 km/h with µ = 0.02. The glide difference after 100 meters is 92 cm for a 5% variation in glide friction. Repeating the test around µ = 0.01 results in 46 cm over the same distance. Thus, the glide-distance difference decreases with lower friction.

However, the impact on race time also decreases in faster snow. For a skier at good national level (FTP = 3.5–4 W/kg), race time changes by 10–15 seconds for a 5% variation around µ = 0.02, while the impact drops to about half around µ = 0.01. To compare more fairly, it is better to consider the same absolute difference in glide friction. Then the glide-distance difference becomes identical, as seen in Fig. 6. Over 10 km, the time difference becomes smaller at lower friction because speeds are higher. In other words: larger absolute friction differences can be tolerated in faster snow.

To tie this discussion together, Figure 7 shows simulated race-time differences over 10 km corresponding to glide-test outcomes on a slope with fixed gradient and initial speed.

Note in Figure 7 that final speed varies greatly depending on conditions. To gain better sensitivity in faster snow, it is appropriate to lower the speed — for example by finding a slope with less gradient or reducing the initial speed. Figure 8 shows a similar analysis for friction coefficients in the range µ = 0.01 to 0.02.