Measuring Coefficient of Friction in Ski

Naoto Miyamoto, Tatsuo Morimoto, Akihiro Isomura, Yukiko Obara, Patrick Bonnaud, Ryuji Miura, Ai Suzuki, Nozomu Hatakeyama,

Akira Miyamoto, and Yusuke Yaegashi*

New Industry Creation Hatchery Center (NICHe), Tohoku University

*Gallium Co., Ltd.

Significance of Tools in Ski

1924 Paris 1924 Chamonix

2012 London 2014 Sochi

Speed up

Marathon 42.195km

2:41:22 15.7km/h

2:08:01 19.8km/h

x 1.26

XC Ski 50km

3:44:32 13.4km/h

1:46:55 28.1km/h

x 2.10

Winning record at the Olympic Games

1924 2014

Ski Plate Wood Resin＋Plywood＋Hollow Honeycomb

Ski Base Wood UHMW-Polyethylene

Poles Bamboo Carbon

Wax Pine Resin Fluorine Compound

Boots Leather Plastic＋Carbon

Wear Wool Elastic Chemical Fiber

Trail Tread down Snow Groomer＋Tracksetter

Progress of Tools in Ski

Glory shines for one who obtains and

masters excellent tools before anyone else

in the world

XC: Cross-Country UHMW: Ultra High Molecular Weight

Common Wax

Race Wax

No Wax

Requirements of Ski Wax

① Glide ② Retention

① Friction ↓ ② Water Repellency ↑ ③ Infiltration ↑

Skier Feeling test

Quantitative evaluation

θc ~ 100° θc ~ 120°

Paraffin Wax Coated Surface

Fluoro-Wax Coated Surface

Science

Paraffin Wax w/ Fluoro-Compound Fluoro-Wax

θc

Contact Angle of Water on Wax-Coated Surface

Wax Molecules Permeate UHMW-Polyethylene for 300 sec. at 120 ℃

Simulated by Computational Chemistry

50

μm

22

0μ

m

Motivation of Friction Measurement

• Factors that affect wax selection include Temperature, Snow crystals, Humidity, Wind, Course, and Sunshine.

• Currently, national team accompanies a wax expert called “Waxman” who selects race wax from several hundreds of combinations based on the factors.

• But he keeps the wax selection secret, and never leak even to ski player what kind of wax was used.

• Therefore coefficient of friction (COF) of wax has never been subject to systematic research.

• COF can be estimated using sensor fusion, though it is difficult to measure sliding friction directly.

• We have started developing a wearable COF estimator with which ski player does not feel uncomfortable during skiing.

Measurement Equipment of COF during Skiing

GPS Sensor

IMU Sensor

DGPS（～60cm 2dRMS，10Hz）

（±16G, ±1500dps, 200Hz）

Smart Phone, Tablet PC

（Logical Product）

Force Sensor

Shear & Normal stresses(2.5mm, 100N, 200Hz) USL06-H5-500N（Tech Gihan）

SX Blue II (GENEX)

2 force sensors per 1 ski plate

Temperature Sensor

(-55 to 200℃, ±1%, 4Hz)

Pressure Sensor

（13mmφ, 0.2 to 20N, 4Hz） FSR402 （Interlink Electronics）

COF: Coefficient of Friction GPS: Global Positioning System IMU: Inertial Measurement Unit B57541G1103F (TDK)

Wireless

Measurement Condition

-101234

0 10 20 30 40 50 60

START GOAL(55m)

6.0° 8.0° 5.2° 5.0° 5.0° 4.0° 3.0° 3.0° 1.5° 3.0° 2.0° 5.0° 7.0° inclination

angle

Height [m]

Length [m]

ZAO Snow Park in Yamagata

Date: 4th Apr. 2015 13:35～14:14 Weather：Fine Wind Speed：0～3m/s Air Temperature：15℃

Snow Temperature：+0.3℃@Surface， -0.2 to -0.4℃@5cm Below Surface Snow Quality：Granulated, Sintered 0.5365g/cc Skier：Junichi Sato （an expert of wax test）

Measurement Results

1029

1030

1031

1032

1033

1034

245 247 249 251 253 255

標高

0.0

2.0

4.0

6.0

8.0

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速度

1029

1030

1031

1032

1033

1034

895 897 899 901 903 905

標高

0.0

2.0

4.0

6.0

8.0

895 897 899 901 903 905

速度

Hei

ght[

m]

Vel

oci

ty[m

/s]

Hei

ght[

m]

Vel

oci

ty[m

/s]

-1.0

-0.5

0.0

0.5

1.0

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摩擦係数CO

F

Time [s]

-1.0

-0.5

0.0

0.5

1.0

895 897 899 901 903 905

摩擦係数CO

F

Time [s]

Before Waxing After Waxing* * Gallium Co., Ltd. MaxFluor Wet

μ=0.046586, σ=0.185554 μ=0.069922, σ=0.193538

Before Waxing* After Waxing**

Test No. COF σ Top Speed

[km/h] COF σ

Top Speed [km/h]

1st 0.06992 0.19354 7.3620 0.04659 0.18555 8.8200

2nd 0.06768 0.21690 7.8552 0.04766 0.15475 8.9496

3rd 0.06810 0.19163 7.5780 0.04701 0.16135 8.8560

4th 0.06830 0.16676 7.9236 0.04616 0.19038 8.6472

Average 0.06850 0.19221 7.6797 0.04686 0.17301 8.8182

COF is effective because it is more sensitive than speed.

Measurement Results (Cont’d) * Stored in warehouse for several years ** MaxFluor Wet (Gallium Co., Ltd.)

However standard deviation (σ) is not small enough.

33%↓ 15%↑

Discussion

-1.0

-0.5

0.0

0.5

1.0

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摩擦係数

-1.0

-0.5

0.0

0.5

1.0

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第1項

第2項-1.0

-0.5

0.0

0.5

1.0

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第1項

第2項-1.0

-0.5

0.0

0.5

1.0

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第1項

第2項

CO

F

∆𝑑

∆ℎ

𝒗𝟏

∆𝑙 𝒗𝟐

𝑡 + ∆𝑡

𝑚𝑔∆ℎ =1

2𝑚∆𝑣2 + 𝐹𝑓𝑟𝑖𝑐∆𝑙

𝐹𝑓𝑟𝑖𝑐

𝜇 = 𝜇𝑘 + 𝜇𝑝

𝜃

𝜇𝑘 = −1

2𝑔∆𝑑∙ 𝑣1

2 − 𝑣22

𝜇𝑝 = tan𝜃

𝑣1 + 𝑣2 𝑣1 − 𝑣2 𝜇𝑘 = −1

2𝑔∆𝑑∙

𝜇𝑘 𝜇𝑝

𝜇

CO

F 𝜇

𝐹𝑓𝑟𝑖𝑐 : Friction force

𝑡

𝜇𝑘 : COF from kinetic energy

𝜇𝑝 : COF from potential energy

where

𝝁𝒌 is more variable than 𝝁𝒑

Discussion (Cont’d)

Variability of COF is due to speed difference ∆𝒗 = 𝒗𝟏 − 𝒗𝟐 We have developed more accurate GPS with accelerometer in order to reduce the variability

-0.4

-0.2

0.0

0.2

0.4

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系…

0.0

2.0

4.0

6.0

8.0

10.0

12.0

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系…

-4.0

-2.0

0.0

2.0

4.0

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v2^…

𝒗𝟏𝟐−𝒗𝟐𝟐

𝒗𝟏+𝒗𝟐

𝒗𝟏−𝒗𝟐

𝜇𝑘 = −1

2𝑔∆𝑑∙ 𝒗𝟏

𝟐 − 𝒗𝟐𝟐 = −

1

2𝑔∆𝑑∙ 𝒗𝟏 + 𝒗𝟐 𝒗𝟏 − 𝒗𝟐

Conclusion

This research is supported by SIP (Cross-ministerial Strategic Innovation Promotion Program）

Innovative Design/Manufacturing Technologies

• Coefficient of friction (COF) is very important in ski

• We have successfully measured and estimated COF during skiing

• Results show that COF is more than twice as effective as conventional speed test.

• Variability in COF estimation is the issue, but we have already developed a solution which we plan to evaluate in this season.