# Surface Metrology of Ski Base Textures

This material is based upon worksupported under a National Science Foundation Graduate Research Fellowship.

## Project Team:

Sarah Jordan, M.S., Ohio State ’04

Prof. Christopher A. Brown, PhD

## Project Goals:

In this study, the use of surface metrology techniques such as area-scale analysis were investigated in order to determine if ground ski bases were differentiable and if properties could be correlated to the surface characteristics. It is believed that better understanding of the grinds of ski bases can improve the resulting speed during ski competitions.

## Procedures:

Five ultra-high molecular weight polyethylene ski bases that underwent different grinding preparations were examined using a surface scanning laser microscope. Measurements were made of each ski using 100 and 1 µm interval scans. In addition, scans were made of skis A, C, and D with 10 µm intervals. A representative topographic map of the texture of each ski scanned at 100 and 1 µm intervals is shown below.

## Analysis:

Area-scale analyses were conducted on the surface data according to the standard in ASME B-46.1 ch10. Results for a representative region are shown below.

## Differentiation:

The F test of significance indicates whether a surface is statistically differentiable.

The area-scale results and F test of significance at 90% confidence comparing C with D are shown below for the 100, 10, and 1 µm sampling intervals. For the 100 and 10 µm scan intervals, as the scale decreases, the Mean Square Ratio (MSR) increases to a maximum and then decreases. Textures measured on different grinds are most differentiable (i.e. the MSR is above some minimum MSR that depends the confidence interval and number of samples) when using area-scale fractal analysis at scales between 700,000 µm2 and 700 µm2. At 1 µm sampling interval, the surfaces are essentially not differentiable.

Results are also shown comparing skis A and C with a scan interval of 10 µm. Since the grinds are quite different, at almost all scales the two skis are differentiable. In addition, the MSR values are quite higher than in the case of comparing skis C and D.

Figure 5: Area-scale results and scale based F test of significance with 90% confidence comparing grinds C and D with 100 µm sampling intervals.

Figure 6: Area-scale results and scale based F test of significance with 90% confidence comparing grinds C and D with 10 µm sampling intervals.

## Functional Correlation:

A technique that can be used in conjunction with area-scale analysis is determining the functional correlation. Area-scale measurements are made of several different surfaces and another property such as wetting contact angle is measured. Functional correlation is used to relate that property to scale in order to determine the characteristic scale of interaction. It has been shown that functional correlation between surface characteristics and the particular property can be determined by linear regression as a function of scale. At large scales there is not a correlation to the property being examined. Then ideally as the scale decreases the R2 value begins to increase to some maximum before either decreasing or leveling off. This maximum in R2 is considered to be the characteristic scale of interaction for the particular property.

In this study, the wetting contact angle of DI water on the ski bases was measured (figure 9). The wetting contact angle data leads to two distinct groups that are distinguishable from each other but not differentiable within a group. The first group consists of grinds A and D; the second group consists of B, C, and E. The error associated with measuring the contact angle resulted in a lack of ability to correlate wetting contact angle with surface texture as shown in figure 10. In general the correlation is very low. Although there are some scales with a high R2 value, these occur where the scales around it have much lower correlation. It is not believed that there is some precise scale at which the ski bases are differentiable. Rather, it is believed that these points occur due to chance and that repeated measurements would reveal them as artifacts of the analysis method.

## Future Work:

Additional work using more precise contact angle measuring equipment is required to correlate the ski base texture with wetting properties that effect performance. In addition, other properties such as glide behavior should also be examined for correlation to the ski base surface texture.

## Publications

S.E. Jordan and C.A. Brown, Comparing texture characterization parameters on their ability to differentiate ground polyethylene ski bases

S. E. Jordan, T. S. Bergstrom, D. J. Geiger, C. A. Brown, Surface Metrology of Ski Base Textures, *Science and Skiing III*, (Ed. D. Bacharach and E. Mueller) Verlag Dr. Kovac, Hamburg, Germany (In Press).

S. E. Jordan and C. A. Brown, Various Methods to Study the Textures of Ground Ski Bases which has been submitted to *Wear*.

Last modified: September 13, 2007 09:17:32