Evaluating the Sharpness of Ski Edgeswith Laser Microscopy

“A device has been designed and prototyped to measure the holding

perpendicular to an edge and sliding along an edge. A

provisional patent has been filed. Multi-scale characterization of 3D

measurements of the edge curvature versus position have

been developed.”

Dr. Christopher A. BrownProfessor of Mechanical EngineeringDirector of the Surface Metrology Lab

Worcester Polytechnic Institute

Executive SummarySki edges are studied to understand

the relation between edge sharpness, or curvature, and holding and sliding.

A method was developed at WPI’s Surface Metrology Lab to determine curvature as a function of scale and

position along a profile extracted from a 3D topographic measurement.

Correlations are sought with holding and edge curvatures over a

range of scales.

ObjectiveTo measure how sharp a ski edge

is in two fundamental ways: functional and geometric, thereby advancing the understanding of how the geometry of the edge

relates to its performance. These measures are used to evaluate

edges and preparation methods.

MethodologyWith the testing device the WPI team has constructed, an edge’s performance is analyzed by applying a predetermined load through a simulated snow material to a ski edge sample that is oriented at a certain angle. A tangential force is then applied to the edge sample, and the maximum load the edge can hold at a specific angle and at a certain normal load is recorded (Fig. 1).

Figure 1: Basic principle of device performance measurements.

MethodologyThe geometry of the ski edge is measured and its curvature is calculated as a function of scale and position over the edge.

The geometric measurements of the edge samples are made using the OLYMPUS LEXT OLS4100 laser scanning confocal microscope. This laser confocal microscope’s ability to render 3D topographies at micro-scales is necessary for calculating an edge’s curvature.

Correlations are determined by linear regression analysis of the performance data versus the calculated curvature as a function of scale. This determines the best scales for calculating the curvature for determining when a ski will carve or skid. Skidding is like machining the snow with the edge of the ski.

Skiing as Machining

When ski edge sprays snow it is essentially machining the snow surface. The ski-snow interaction can be compared to chip formation by machining. The ski edge represents the tool, the snow represents the work piece, and the spray is the chip.

The turning force on the skis is equivalent to the cutting force on the tool. The edge angle of the ski is comparable to the rake angle of the tool. The sharpness of the ski edge is similar to the sharpness of the cutting edge of a tool and can be characterized by the curvature (inverse of the radius) as a function of scale and position. Figure 2: Carving, i.e., minimizing the machining of the snow, is

facilitated by well-sharpened ski edges. Machining of the snow uses kinetic energy from the skier racers and slows them down.

Figure 3: Assembly prototype at WPI manufacturing labs.

Ski Edge Curvature

In the development of this new edge measuring and testing system, the WPI Surface Metrology Lab set out to create a new way of looking at edge curvature, which provides a means of measuring and analyzing edge sharpness.

By combining a physical assembly (Fig. 3) designed to provide performance testing with high resolution measurements made with the OLYMPUS LEXT laser scanning confocal microscope (Fig. 4), the WPI team can understand the sharpness by characterizing both ski edge curvature and measuring performance.

Normal Force Cylinder

Tangential Force Cylinder

Edge Sample

Snow Simulation Material

Figure 4: OLYMPUS LEXT OLS4100 laser scanning confocal microscope examining an edge.

Edge Images & Analysis

This new edge assessment system presents users with the means to analyze 3D topographic measurements for edge curvature. The WPI Surface Metrology Lab created and analyzed the following images with a variety of sharpening techniques. Terminology is based on a standard ski edge (Fig. 5).

Figure 5: This diagram represents the basic layout of and terminology associated with a standard ski edge which is rotated in the following images based on renderings from measurements made with the Olympus LEXT OLS4000 and 4100.

ski

Figure 6: Profile of a used ski edge.

Figure 7: The same edge after sharpening with a file. Sharpening was done in an alternating fashion (switching between base and side) to allow for the comparison of surface roughness between different sharpening instruments.

Figure 8: The same edge after additional sharpening with a coarse diamond stone, side first then base. It can be seen that after this sharpening, there is a burr on the edge extending from the base beyond the plane of the sidewall.

base sidewall

Figure 9: Edge sharpened with only a file, base first then side—there are clear irregularities on the surfaces of the edge as well as a jagged burr extending from the sidewall beyond the plane of the base.

base sidewall

Figure 10: The edge from Figure 9 after an additional sharpening with a stone. This makes the surface smoother and the burr less jagged.

base sidewall

Examples of Curvature

Calculated as a function of position and scale from a

profile perpendicular to the edge, using a method based

on Heron’s formula.

Curvature calculations, which are similar to taking a second spatial derivative, require the highest-quality topographic

measurements.

Images rendered using MountainsMap by DigitalSurf

As honed

Images rendered using MountainsMap by DigitalSurf

Mass finished for 2.5 min.(BelAir FMSL 8T series centrifugal disk)

Images rendered using MountainsMap by DigitalSurf

Mass finished for 7.5 min.(BelAir FMSL 8T series centrifugal disk)

Concluding RemarksThe OLYMPUS LEXT OLS4000 laser scanning confocal microscope reveals interesting aspects of ski edge sharpening including burrs, roundness, and curvature.•The order of sharpening determines the extent and direction of the burr on the edge. •A burr might be beneficial to a skier by providing better lateral holding perpendicular to the edge in turns; however, it could be disadvantageous by increasing friction along the edge, thus slowing the skier down.•A ski edge finished with a stone is smoother than after filing.•The curvature of the edge can be calculated as a function of scale and position from the measurement made with the LEXT OLS4000.

SummaryThe determination of curvature versus position and scale, a new calculation

method, is made possible by the direct, high-quality topographic

measurements made with Olympus confocal microscopy.

Through their work with this new edge measurement system, the WPI Surface Metrology Lab is pioneering multi-scale,

position-specific curvature characterizations for applications in

sports and industry.

Dr. Christopher A. BrownProfessor of Mechanical EngineeringDirector of the Surface Metrology Lab

Worcester Polytechnic Institute