Investigation of the Most Essential Factors Influencing Ski Glide

2006:03 LICENTIATE T H E SI S

Investigation of the most essential factors influencing ski glide

Leonid Kuzmin

Luleå University of Technology Department of Applied Physics and Mechanical Engineering Division of Computer Aided Design

2006:03|: -1757|: -lic -- 06⁄03 -- 

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Paper A

CONTACT ANGLES ON THE RUNNING SURFACES OF CROSS- COUNTRY SKIS*

L. KUZMIN AND M. TINNSTEN Dept. of Engineering, Physics and Mathematics, Mid Sweden University, Teknikhuset (Q), Plan 3, Akademigatan 1, SE-831 25 Östersund, Sweden Fax:+46 (63) 16 55 00 E-mail: [email protected]

The importance of high hydrophobicity for minimising snow-ski friction has been discussed in a number of scientific papers. The chemical modification of surface forces using fluoropolymeric coatings can result in water contact angles of up to 120°, but not more. To reach extreme values of the contact angle, a second factor has to be modified, namely surface structure. In this study a number of cross-country skis were treated with a modern method of stone grinding and with old-fashioned steel scraping. The surface roughness (3D) and the surface (solid-liquid) contact angle were then measured. After this, the skis were treated with a hot glide wax and new measurements were made. This study also examines the contact angles (solid-liquid) of the flowed surface of a sample of glide wax and the surface of a sample of solid press-sintered running base (UHMWPE). Unexpectedly low hydrophobicity was observed after stone grinding.

Keywords: Hydrophobicity, skis, roughness.

1. Introduction

Skiers have always been interested in attaining a better glide on skis, but there has been considerable uncertainty about the basic model to be used. Today there is much evidence to support the idea of meltwater lubrication. Colbeck [1] considered two different mechanisms for removing water from the ski-snow contact surface. Using the squeeze mechanism, the thickness (h) of 4222 the film would be in balance: hcruL 3/2KUi where c is the ratio of area to load, r is the contact radius between the snow and the ski,Kis the viscosity of water, u is speed, L is the latent heat of fusion and Ui is the density of ice. Using 2 the shear mechanism, the thickness would be much less: hurL K S / Ui Obviously, a smooth, hydrophobic ski base would make a shear water- removal mechanism less effective. Water slides more readily on hydrophobic

* This study is partly financed by the European Union.

1 2 surfaces. In a case with excess lubrication, capillary forces would be higher on the less hydrophobic ski base. In view of this, we can see that a hydrophobic surface would be advantageous in all snow (weather) conditions [2]. All leading cross-country (X-C) ski manufacturers use an Ultra High Molecular Weight Polyethylene (UHMWPE) as the ski base. Running surface treatment consists of a mechanical base treatment and waxing. Modern glide waxes repel water very well. Nevertheless, even an extremely hydrophobic wax, such as perfluorocarbon, has a water contact angle limited to 120°. On the other hand, using the optimal mechanical running surface treatment we may attain a water contact angle of up to 180° [5]. The water contact angle is governed by the forces exerted at the three phase contact line of the drop in the plane of the solid, which is where the solid/liquid, liquid/gas and solid/gas interfaces meet. The forces acting at this line are the surface tensions, and their balance gives the Young’s equation: cosTJJJYsvsllv / where J ij denotes the surface tension (energy per unit surface) of the interface ij and where s, l and v designate the solid, liquid and vapour phases respectively. Classical studies by Wenzel [3] and Cassie and Baxter [4] established that roughness as well as surface energy are the factors that determine wettability. Wenzel proposed a model describing the contact angle on a rough surface as: cosTTWY r cos where r is the roughness factor, defined as the ratio of the actual area of a rough surface to the projected geometric area. Since r is always larger than one, the surface roughness enhances both the hydrophilicity of hydrophilic surfaces and the hydrophobicity of hydrophobic ones. Cassie and Baxter proposed an equation describing the contact angle on a surface composed of a solid and air, assuming the water contact angle for air to be 180°: cosTMCS cos TM YS 1 with MS being the area fraction of the solid-liquid interface. So, regardless of the approach, the contact angle is always larger or equal on a rough surface, so giving the running surface a structure is the most effective way to increase hydrophobicity.

2. Apparatus and procedures

2.1. General approach Our choice of tools, wax, skis and the procedure for ski preparation was based on direct application to X-C skiing. Our primary goal was to examine the relation between surface roughness and hydrophobicity. Our secondary goal was to estimate the magnitude of the water drop contact angle on the running surface of the ski. 3

2.2. Skis and their preparation We used 5 similar Karhu skis from the same batch. 4 skis were treated with 4 different patterns of stone grinding on Tazzari RP13.2. One ski was treated with an HSS scraper (Figure 1). For waxing we used Swix CH8. Paraffin was melted into the ski base 3 times, and they were then scraped with the plastic scraper. Before measurement the skis were brushed with a Red Creek steel rotary (4000 r/min) brush. A clean brush was used for the dry skis and another for the waxed skis.

Figure 1. High Speed Steel (HSS) scraper.

2.3. Contact angle measurement The running surface hydrophobicity of the ski was measured as the advanced contact angle of a water drop. The larger the angle, the higher the hydrophobicity. A goniometer FTA125 and the software Fta32_Video build 185 from “First Ten Ångstroms” were used to measure this angle. The pump on the goniometer was driven manually. 15 images with 2 f/sec were captured during each measurement. For each ski base sample we made 3 measurements at 3 different points within the marked 1,5cm2 area. An arithmetical mean value was then computed for each sample.

Figure 2. Ski under FTA125 goniometer. 4

2.4. 3D ski running surface measurement Surface measurements were taken using a Wyko NT1100 Optical Profiler and the software Vision32 for NT-1100 (version 2.303 SMU4 build 5). Standard indexes such as Ra, Rq, Rt and Rz were recorded. For each new ski base sample we made 2 measurements at 2 different points within the marked 1,5cm2 area. An arithmetical mean value was then computed for each sample.

3. Results

3.1. Relation between running surface roughness and hydrophobicity We did not find any significant relation between the roughness of the samples and hydrophobicity. Pearson's correlation between each of the indexes and the contact angle lies in the range: -0,07 y 0,19.

Table 1. Contact angle and surface standard indexes.

Contact Ski and kind of treatment Ra Rq Rz Rt Angle

Nr. 3 Stone grinding - pattern 1A. Dry. 104,83 3,66 4,52 31,69 41,33 Nr. 3 Stone grinding - pattern 1A, CH8. 113,14 3,19 4,13 28,79 33,80 Nr. 4 Stone grinding - pattern 1B. Dry. 110,48 4,75 5,72 31,46 35,26 Nr. 4 Stone grinding - pattern 1B, CH8. 113,14 4,78 6,08 35,08 36,84 Nr. 5 Stone grinding - pattern 2A. Dry. 107,18 2,76 3,51 26,10 31,62 Nr. 5 Stone grinding - pattern 2A, CH8. 115,88 2,73 3,49 23,94 26,50 Nr. 6 Stone grinding - pattern 2B. Dry. 111,92 3,12 4,02 27,48 30,14 Nr. 6 Stone grinding - pattern 2B CH8. 112,15 3,07 3,89 24,78 29,63 Nr. 7 Treated with HSS scraper. Dry. 117,26 4,60 5,71 32,11 34,69 Nr. 7 Treated with HSS scraper, CH8. 115,17 3,75 4,64 28,91 33,03

Where Ra is the average roughness, Rq is the root-mean-squared roughness, Rt is the peak-to-valley difference, and Rz is the average of the ten greatest peak- to-valley separations on the sample. For more details see ISO and DIN standards. 5

3.2. The magnitude of the water drop contact angle

Advanced Contact Angle Waxed - Dry

Waxed Dry Cut UHMWPE

12 0 , 0 0 118 , 0 0 116 , 0 0 114 , 0 0 112 , 0 0 110 , 0 0 10 8 , 0 0 10 6 , 0 0 10 4 , 0 0 10 2 , 0 0 10 0 , 0 0 98,00 Nr. 3 - stone Nr. 4 - stone Nr. 5 - stone Nr. 6 - stone Nr. 7 - HSS scraper grinding grinding grinding grinding

Figure 3. Contact angle comparison for differently treated surfaces. In addition, we measured the contact angle of the flowed surface of a sample of glide wax Swix CH8 – 108,01°, and on a solid sample of graphite UHMWPE – 104,67°. This solid sample represents similar material to the ski base.

4. Discussion and conclusions

4.1. Roughness and hydrophobicity From our results we can draw the conclusion that the above-mentioned surface standard indexes are unsuitable for measuring hydrophobicity. These indexes do not help us to estimate the fractal structure of the surface [5]. We have to find other methods to measure the fractality of the surface.

4.2. Running surface hydrophobicity Figure 3 (or Table 1) shows a quite unexpected phenomenon: dry stone ground surfaces have a low contact angle, much lower than the scraped surface (104,83° compared with 117,26°). After applying hot wax to the skis with a stone ground base, the contact angle increased dramatically. We can assume that stone grinding reduced the hydrophobicity of UHMWPE as a material (by 6 temperature, by interaction with coolant fluid, etc.), but scraping did not. And we may suppose that the manual scraping resulted in some kind of randomly rough surface [5], with quite high hydrophobicity. However, stone grinding increases the contact angle, because both the flowed surface of the sample of glide wax and the solid sample have lower contact angles. The disadvantage of the stone grinding procedure is that wax has to be applied to the surface, which increases the attraction of polluting substances to the ski base. The degree of pollution adhesion depends on the hardness of the ski running surface.

Acknowledgments

The authors are grateful to their colleagues at the Tribology Laboratory at Luleå University of Technology for help with the 3D measurement of the ski running surfaces, to Klaus Krenn at ISOSPORT GmbH for the samples of running base and the fruitful discussions, and to Lars Svensson for the professional stone grinding of our samples.

References

1. S.C. Colbeck, “Kinetic friction of snow”, Journal of Glaciology, 34, 78-86 (1988). 2. S.C. Colbeck, “A Review of the Processes that Control Snow Friction”, CRREL Monograph 92-2. Hanover, NH: US Army Cold Regions Research and Engineering Laboratory (1992). 3. R.N. Wenzel, “Surface roughness and contact angle”, Ind. Eng. Chem. 28, 988–994 (1936). 4. A. B. D. Cassie, S. Baxter, “Wettability of porous surfaces”, Trans. Faraday Soc. 40, 546–551 (1944). 5. R. Blossey, “Self-cleaning surfaces-virtual realities” Nature Mater., Vol. 2, pp. 301-306 (2003). Paper B

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