A MEASURING INSTRUMENT FOR THE HARDNESS AND THE ROUGHNESS OFTHE SKI SLOPE - CORRELATlON TO THE GLIDING PROPERTIES OF SKIS

PENETROMETER AND PROFILOMETER

Daniel BUhI 1, Mathieu Fauve, Martin Schneebeli, Hansueli Rhyner, Walter AmmannSwiss Federallnsitute for Snow and Avalanche Research

ABSTRACT: The analysis of the ski slope is crucial for understanding the gliding of skis. Especially in skiracing a detailed knowledge of the parameters of the snow influencing the gliding properties helps tooptimize the skis. Unfortunately, the analysis of the slope surface is limited to only a few parameters like.snoW temperature, air humidity and air temperature, so far. We proved that there is a large number ofparameters concerning directly the snow surface like snow humidity, hardness, roughness, grain size,thermal conductivity and more that are strongly influencing the gliding properties. This paper presents atool developed at the Swiss Federal Institute for Snow and Avalanche Research for measuring thehardness and the roughness of ski slopes. Results of gliding tests prove the correlation of these twoparameters to better gliding.

KEYWORDS: ski slope, hardness, roughness, gliding, skiing.

1. INTRODUCTION

The gliding properties of polyethylen onsnow depend on a large number of parameters ofthe weather conditions and the snow conditionsbesides the characteristics of the ski itself [Buhl,Colbeck]. Especially the characterization of thesnow surface is crucial for the understanding ofthe tribological effects describing the frictionbetween ski and snow.

Unfortunately, this analysation has beenrestricted to only a few parameters like density,temperature and grain size, so far. Others likethermal conductivity or wetness are hardly knownand difficult to measure. From the tribological pointof view the knowledge of the hardness and theroughness of the snow surface is important inorder to estimate the friction between ski andsnow.

The purpose of the present work wasthe development of a tool measuring both, thehardness and the roughness of the snow surface[Schneebeli]. Therefore, the snow profile of theslope has to be measured with a high resolutionespecially for the first millimetres and the profile ofthe surface has to be recorded. It turned out thatthe combination of these two features enables toestimate the contact area between ski and snow,as well.

. During gliding tests of skis on snowthe hardness and the roughness of the slope wereconstantly measured. It is shown that there existsa strong correlation between both parameters andthe gliding properties. The numerical quantity ofthe parameters is compared with the coefficient offriction. In addition, an estimation of the contactarea shows its influence on the gliding properties,as well.

2. EXPERIMENTAL

A penetrometer was fixed on a sledge inorder to be able to perform field measurementswith this mobile measuring instrument. The mainparts of the penetrometer are the engine unit as aprime mover, the sensor measuring the resistanceand the electronic unit recording the signals of thesensor and transforming them into practicablevalues. The hardness value indicates theresistance offered by the snow surface and thelayers beneath to the vertical penetration of ametal cone of given dimensions. The cone isconnected to the sensor and driven into theground by the engine unit. Different shapes of themetal were used for investigations of the surface(stamp) and the depth profile (standard 30° cone).

1 Corresponding author address: Daniel Buhl, Swiss Federal Institute for Snow and Avalanche Research,Fluelastrasse 11, 7260 Davos Dorf, Suisse; tel: 0041814170103; fax: 0041814170110; email:bUhl@slf.ch

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3. RESULTS

In figure 3 the snow profile of a raejslope is shown, measured on the same spot at~different times. Two hard layers are visible at thefirst measurement. One is on the sUrface, theother one is at 15 cm depth. It is suggested, thatthis second layer once was the surface of theslope before it was covered by fresh snow. TWOhours later this second layer remains unchanQedwhereas the surface has significantly weakenedby about 50%. The surface has split into threedifferent layers which is a result of the repeatedpassing of skis.

Depth profile Jakobshorn (Usser Isch), 1. April '98

Figure 3: Penetration of a ski slope, penetrationforce as a function of depth at two different times

200100 150

Distance I mm

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Figure 4 shows the Abbott curve of the snowsurface. From the profile, the amount of snow asafunction of the depth is determined (on top of thesurface, the amount is 0%, in a depth of 2.2 mmthe amount is 100%). Measuring the penetrationdepth for a load of 2.5 MPa (performed by astamp, corresponding to the average pressuredistribution of a skier) gives 0.28 mm (Xl) and thusa contact area of 8% (Ml ). The penetration depthtwo hours later has increased to 0.56 mm (X2lwhich results in a contact area of 37% (M2).

Figure 1: Penetrometer for measuring thehardness of the ski slope.

On the same sledge, there wasmounted a profilometer for measuring the profile ofthe snow surface. The main parts of theprofilometer are the engine unit as a prime mover,a laser measuring the distance to the snowsurface and the electronic unit recording thesignals of the sensor and transforming them intodistance values. The laser is moved at a constantrate horizontally above the snow surface. Thesnow surface is dusted with black powder in orderto enable maximum reflection of the laser beam.Thus, the distance between the laser and thesnow surface is recorded as a function of theposition of the laser and the data enables to drawthe profile of the surface. The profile is furtheranalysed by standard methods and a largenumber of roughness values are determined.

Figure 2: Profilometer for measuring theroughness of the ski slope.

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Abbott Curve of snow surface profile Influence of the surface roughness on the gliding properties

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roughness value I mm

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Figure 4: Abbott curve of the snow surface givingthe amount of snow at a defined depth.

Figure 6: Gliding time versus surface roughness.The skis are faster with increasing roughness.

4. DISCUSSION AND CONCLUSIONS 5. ACKNOWLEDGEMENTS

The influence of the hardness and the roughnesson the gliding properties are investigated.Therefore, the force for the penetration into adepth of 5 mm from the snow surface wasmeasured and the roughness extracted from theprofile of the snow surface during several dayswhile gliding tests where performed on the slope.Figure 3 shows that the gliding performance of theskis strongly decreases with decreasing hardnessof the slope.

Influence of the surface hardness on the gliding properties

This project, is supported by the KTI(Kommission fUr Technologie und Innovation, CH)and several industrial partners (Stockli AG, TokoAG, Fritschi AG, Nidecker SA, IMS KunststoffeAG).

6. REFERENCES

Buhl D., Bruderer C., Fauve M., Rhyner H.,Schlussbericht KTI-Projekt 3781.1. Internalreport (2000).

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Buhl D., Rhyner H., Amman W., this issue.

Colbeck S.C., The kinetic friction of snow. J. ofGlaciology, Vol 34, NO.116 (1988), pp. 78-86.

Schneebeli M., Pielmeier C., Johnson J.B., ColdRegions Science and Technology 30 (1999)101-114.

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penetration force I 5N/mmA4,A7-5erie winter 98199

Figure 5: Gliding time versus surface hardness.The skis are faster with increasing hardness up toabout 2.5 N/mm.

Figure 6 shows that the gliding performance of theskis is increased with increasing roughness of thesnow surface.

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