4.1. Measurement Values
In this study, we conducted on-slope measurements of snow tubing to analyze the effects of deceleration mats in the run-out area of a snow tubing lane. We found that deceleration mats were effective at slowing snow tubes and riders when compared to not having deceleration mats; the mats increased the peak deceleration by a factor of 5 for the flat condition and almost 8 for the folded condition compared to the no mat condition. Consistent with this, the effective (average) COF increased with deceleration mat use and was amplified when the mats were in the folded configuration. Though the deceleration increased significantly with mat use in our tests, it did not cause the riders to become unstable or fall off the snow tubes. Traversing the deceleration mats did not produce observable movement between the riders and snow tubes (from the video) and we measured less than 2.5 cm of fore-aft motion between the rider and snow tube when traversing and exiting the deceleration mats. Deceleration mats slow but do not destabilize riders.
The measurements in this study agreed well with data published on friction between other materials and snow. It was expected that the effective coefficient of friction (COF) for the snow tubes on the snow would be low in order to allow riders to accelerate downhill. The average COF for snow tubes on snow was in the range of other snow sports equipment on snow; see
Table 2. The effective COF of the snow tubes on the deceleration mats was similar to or less than ski suit fabrics on snow, footwear on snow, rubber on ice, or tires on ice.
There was improved stopping ability with the folded mats compared to the flat mats. Unlike folding the mats, there was no trend produced when changing the geometric protuberance on the mat surface (ribs vs. projections) presenting to the snow tube in our tests. Because we flipped or exchanged the mats before each test and presented a clean mat surface for the snow tube to contact, our study provided the best-case scenario for deceleration and for observing differences produced by the surface protuberances. In many tests, snow was pushed onto the deceleration mat by the snow tube and rider. Though we did not quantify the snow remaining on the mats after each test, the snow pushed onto the mat was unaffected qualitatively by the surface protuberances. Interestingly, the folded mats often shed naturally most of the snow that was pushed onto the mats in the tests. This occurred when either the mat unfolded after the snow tube moved fully past or during the decompression of the folded section. This “self-cleaning” ability of the folded mats may be useful for busy snow tubing operations or when it is actively snowing and may help produce more repeatable rider deceleration.
The kinematic data prior to the run-out area showed low frequency vibrations at the pelvis (near the COM), not unlike those found in other snow sports [
11]. In the
folded mat tests, the snow tube riders bounced slightly in the vertical direction after they passed the fold, producing a small vertical component of acceleration. This vertical component of acceleration was within the range observed prior to the run-out area during natural vibrations. The vertical component of acceleration could be attributed to the slight drop (on the order of 5 cm) from the double layer of mat at the fold. Despite this bounce, there was no significant increase in the pitch angle of the riders as they traversed the deceleration mats when compared to the
flat mat condition. We hypothesize that the pitching motions of the rider were related to the compression of the snow tube as the rider weight shifted during deceleration and that inflation pressure of the tubes could influence this motion.
In this study, we attempted to keep constant the speed of the snow tube riders entering the run-out area in order to compare the effects from the deceleration mat conditions. The results, however, exhibited a large range of speeds (5.0 to 14.1 m/s) entering the run-out area; it is unclear what caused the variation, but changes in the snow conditions on the downhill portion of the tubing run and foot drag by the riders are two likely contributing factors. The Pearson’s correlation coefficient (r) between the speed entering the run-out area and peak deceleration was 0.33; there was little relationship between speed entering the run-out area and the peak deceleration. A similar result was obtained for effective COF (r = 0.12). Because speed did not influence significantly the deceleration and effective COF across our tests, it is expected that additional, consecutive mats would further slow snow tube riders and would be recommended when shorter slowing distances are desired; additional tests at lower speed would be prudent to check this hypothesis.
4.2. Safety Considerations: Reduced Run-Out Distance Needed with Deceleration Mats
The use of multiple, consecutive deceleration mats in each snow tubing lane is not uncommon. Using a constant COF for each surface (snow or deceleration mats) and the balance of linear momentum, the run-out length and number of deceleration mats necessary to bring snow tube riders to a stop can be estimated. Care must be taken when assessing snow tube lane design in general because there are several difficult to specify factors that may influence the run-out kinematics for a given rider, such as rider mass, snow condition, temperature, variables related to air resistance, the amount of snow covering the deceleration mat surface, etc. With this caveat, the value of using deceleration mats can be shown with an example.
The effect of deceleration mats on the distance traveled in the run-out of a tubing hill is assessed below. To illustrate the effects of snow tube deceleration mats, we started with the balance of linear momentum for the center-of-mass of the snow tube and rider system on a horizontal (0°) run-out:
where
x is the position of the system along the run-out,
v is the velocity,
a is the acceleration of the system,
m is the mass of the snow tube and rider system,
g is the gravitational constant,
ρ is air density,
Cd is the geometric drag coefficient,
A is the cross-sectional area normal to the direction of motion, and
μx(
x) is the coefficient of friction that depends on the location of the snow tube and changes whether it is on snow, a flat mat, or a folded mat. Equation (3) can be rewritten to:
and solved numerically.
For this example, a snow tube rider enters a 50 m long, horizontal run-out at 9.5 m/s. The rider and snow tube system have a total mass (m) of 91 kg (75 kg snow tube rider with 16 kg of equipment, including clothing and a snow tube), with a total cross-sectional area (A) of 0.59 m2 projected along the downhill direction of travel. Further consider the case in which there is no wind, the temperature is 0 °C, the air density (ρ) is 1.18 kg/m3, and the Cd is 1.
Three example configurations were considered: (1)
no mats—no deceleration mats are placed in the run-out and
μX(
x) is constant at 0.08; (2)
flat mats—1.52 m long, flat mats are placed in the run-out and separated by 0.5 m, such that
μx = 0.11 while the snow tube is on a flat deceleration mat and
μx = 0.08 when the snow tube is on the snow between mats; (3)
folded mats—the mats from
flat mats (2) configuration are folded at the downhill end (the front edges of the mats remain in the same places), such that the mats are effectively 1.02 m long and
μx = 0.26 while the snow tube is on a folded mat and
μx = 0.08 when the snow tube is on the snow between mats. In this example, the number of deceleration mats was the same in the
flat mats (2) and
folded mats (3) configurations, but there is more space (tube-on-snow distance) between mats in the
folded mats configuration because of the mat folding. Equation (4) was solved numerically (using MATLAB R2021a, Mathworks, Natick, MA, USA) for the three configurations; the velocity of the snow tube system as a function of distance travelled in the run-out is shown in
Figure 4.
This example shows the value of deceleration mats for a theoretical tubing hill. In the no mats configuration, a typical snow tube and rider would require 49.1 m to stop (approximately 10.9 s), using 98% of the run-out distance and offering very little additional space in case of an unusually fast descent or a decrease in friction in the run-out; in this example, there is only a small margin to accommodate changes in environmental factors and rider characteristics that may result in faster run-out entry speeds. In the flat mats configuration, the typical snow tube and rider would require 39.4 m to stop (approximately 8.6 s), using 79% of the run-out distance. Though the friction coefficient was only slightly higher than the no mat configuration, the flat mats stop the snow tube rider in less distance and offer more space to stop in case of an unexpectedly fast descent. Finally, in the folded mats configuration, the typical snow tube and rider would require 24.8 m to stop (approximately 5.2 s), using only 49.5% of the run-out distance. Using folded mats in this example would allow for the greatest protection from a snow tube traveling too far and exiting the run-out. Because it is possible that the snow-to-snow tube friction could be lower than the values measured in our study or even decrease (during the course of a day or even more quickly), it would be advisable in this example for the run-out to be longer or for the tubing hill operator to add deceleration mats to the run-out area.
4.3. Limitations
Snow tube inflation pressure could have affected the results. In our tests, we filled the tubes until they were firm but did not measure or monitor the inflation pressure throughout testing. It is possible that the snow tube air pressure changed with ambient temperature and incident solar radiation throughout testing. This is a topic that we plan to address in future work.
Other parameters were not examined in this study and could influence the effective COF, such as rider mass, riding position, foot drag, the material and wear of the bottom of the snow tube cover, and snow properties. For example, only one riding position (chest presenting to the snow tube) was examined in the current test series, but some riders use an alternate riding position wherein the rider sits in the hole of the ring torus with his or her knees bent on top of the upper surface and feet hanging outside the torus. The interaction with the deceleration mats and the effective COF may be affected by this alternate riding position. Time and resources limited the testing and further work to assess these additional parameters is planned.