The document summarizes research conducted at Worcester Polytechnic Institute's Surface Metrology Lab to develop a new method for measuring ski edge sharpness. A device was created to test edge holding and sliding performance. An Olympus confocal microscope was used to take 3D topographic measurements of edge curvature as a function of position and scale. Various edge sharpening techniques were evaluated. The research aims to understand how edge geometry relates to performance through multi-scale curvature characterization.

1. Evaluating the Sharpness of Ski Edges
with Laser Microscopy

2. “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. Brown
Professor of Mechanical Engineering
Director of the Surface Metrology Lab
Worcester Polytechnic Institute

3. Executive Summary
Ski 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.

4. Objective
To 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.

5. Methodology
With 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.

6. Methodology
The 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.

7. 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.

8. 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

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

10. 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

11. Figure 6: Profile of a used ski edge.

12. 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.

13. 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

14. 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

15. 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

16. 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.

17. Images rendered using
MountainsMap by
DigitalSurf
As honed

18. Images rendered using
MountainsMap by
DigitalSurf
Mass finished for 2.5 min.
(BelAir FMSL 8T series centrifugal disk)

19. Images rendered using
MountainsMap by
DigitalSurf
Mass finished for 7.5 min.
(BelAir FMSL 8T series centrifugal disk)

20. Concluding Remarks
The 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.

21. Summary
The 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. Brown
Professor of Mechanical Engineering
Director of the Surface Metrology Lab
Worcester Polytechnic Institute