Characterisation of Alpine Skis

DEGREE PROJECT IN THE FIELD OF TECHNOLOGY VEHICLE ENGINEERING AND THE MAIN FIELD OF STUDY MATERIALS SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2016 Characterisation of alpine skis FREDRIK WIKERMAN KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES Characterization of alpine skis Fredrik Wikerman [email protected] Thesis project for the degree Master of Science School of egineering sciences, Lightweight structures Examiner & supervisors Stefan Hallström& Monica Norrby & Joakim Nord KTH, Royal Institute of Technology Sweden August 29, 2016 Acknowledgment First and foremost I would like to give a special thanks to my examiner and supervisors Stefan Hallströmand Monica Norrby at the Lightweight Structures group at KTH for believing in me and my idea to try to perform a thesis project outside of the usual thesis box. Also thanks for supporting me during the project with guidance, discussions and especially dedication of my project. Furthermore I want to show my gratitude to the Swedish Ski Team director Tommy Elias- son Winter for believing in my idea and making it possible for me to perform a thesis in an area where I have a great interest. I also want to thank Joakim Nord for supporting my idea and thank for his support and discussions during the whole project as the Swedish Ski Associations development and research responsible. Professor Jakob Kuttenkeuler at the Department SCI, Naval Architecture at KTH, Royal In- stitute of Technology has always pushed me the extra step and also shown interest in my thesis project providing with great ideas and thoughts which I am ever grateful for. I would like to thank my friend Simon Wakter for the introduction about photographing and lending me his Canon EOS550D camera and lenses during the project. I also want to acknowledge Magnus Eriksson at Alpingaraget who provided me with the test skis for the project. Finally, I must express my very profound gratitude to my parents and to my friends and girlfriend for providing me with unfailing support and continuous encouragement throughout my years of study and through the process of researching and writing this thesis. This accom- plishment would not have been possible without them. Thank you. Author Fredrik Wikerman ii Abstract Skiing is a fast and competitive sport where skiers must push their performance limit to win medals, the di↵erence can be within hundreds of a second. Therefore, technical improvements are essential for assisting in the skier’s improvement. This thesis project is a joint project between KTH and the Swedish Ski Association and Swedish Ski Team with the purpose of obtaining a better understanding of the structural properties of alpine skis, aiming to improve the individual selection process of skis for the Swedish World Cup Skiers. The goal of the project is to develop and evaluate a method to characterize alpine skis in form of two main structural properties related to the ski characteristics, bending and torsion sti↵ness. An optical measurement device and image post-processing and analysis is used to determine the deflection and twist of skis, which are used to determine the bending and torsional sti↵ness. The method provides, a structural property variation over the whole ski length compared to the existing ISO standard where only a spring coefficient of the skis main parts is determined, which is insufficient for a good over all comparison. The method could be further used in several aspects to help the Swedish World Cup skiers win more medals. It can be used to help in the selection process of new skis for the next season where an objective comparison between models can be done, as oppose to today when the selection process is highly subjective. Skiers usually vary the ski plate constellation and the method could help skiers with their race preparations, like changing the constellation of the ski plate to optimize the sti↵ness for a specific race condition with engineering knowledge rather than just trusting the feeling. The use of this method can reduce the number of ski tests performed by the skier, thus leaving more time for practice. Testing skis in a laboratory environment also increases objectivity in testing and can therefore give the Swedish Ski Association and Swedish skiers a competitive advantage in upcoming competitions. iii Contents 1 Introduction 1 1.1 Background....................................... 1 1.2 Modernskis....................................... 2 1.3 TheSwedishSkiAssociation’sskiselectionprocess . 3 1.4 LiteratureStudy .................................... 4 1.4.1 Subjective evaluation of the performance of alpine skis and correlations withmechanicalproperties . 4 1.4.2 Design of alpine skis . 4 1.4.3 Structural behavior for slalom skis in bending and torsion . 5 1.5 Scope .......................................... 6 2 Method 7 2.1 Codeoverview ..................................... 7 2.2 Bending sti↵ness .................................... 7 2.2.1 Euler-Bernoulli beam theory and finite element theory . 8 2.3 Torsional sti↵ness . 9 2.3.1 Saint Venant torsion theory . 9 3 Experiment 11 3.1 Bending sti↵ness .................................... 11 3.1.1 Experimentalprocedure . 12 3.1.2 Bendingmomentrig .............................. 12 3.1.3 Image acquisition . 13 3.1.4 Image Post-processing . 13 3.1.5 Image Analysis . 14 3.1.6 Determination of the Bending sti↵ness . 14 3.2 Torsional sti↵ness . 15 3.2.1 Experimentalprocedure . 16 3.2.2 Torsion moment rig . 16 3.2.3 Laser setup . 16 3.2.4 Image acquisition . 17 3.2.5 Image post-processing . 17 3.2.6 Image analysis . 17 3.2.7 Determination of torsional sti↵ness . 17 3.3 Repeatability verification . 18 3.4 Experimental limitations and errors . 19 4 Test cases and Results 21 4.1 Bending sti↵ness .................................... 22 4.2 Torsional sti↵ness . 23 4.3 Skicrosssection .................................... 24 iv 5 Discussion 25 5.1 Results.......................................... 25 5.2 Improvements...................................... 25 5.3 Useofmethod ..................................... 26 5.4 Furtherdevelopment .................................. 26 6 Conclusion 28 v vi Chapter 1 Introduction This thesis is a joint project with the Swedish Ski Association to gain a better understanding of the structural properties of alpine skis, thus improving the selection process for the Swedish World Cup Skiers. The thesis covers an analysis of a systematic and objectified way of selecting skis, in terms of developing a method to determine the bending and torsion sti↵ness profile along the ski length. 1.1 Background For 2500 years people have used skis as a means of transportation over snow covered landscapes. At the beginning the skis were a carved piece of wood with leather straps as bindings. During the 18 century skiing evolved as a sport and the equipment improved to follow the athletes progression. Today the ski industry is a rapidly developing industry where ski brands strive to develop the most innovative and highest performing pair of skis. Due to the competitive market there is little exchange between ski companies and users regarding a ski’s characteristics, even with top level World Cup skiers. The information and knowledge regarding skis at the Swedish Ski Association is high, however, the knowledge of why a ski is performing in a certain way is largely unknown and the knowledge of di↵erences in comparable terms is non-existing. Overall one could say that the sport rely on the feeling of the equipment which is an important aspect for the performance of the rider. If a rider is not confident with the equipment he or she will not win medals. However, a feeling of hardware is difficult to quantify and compare as it is on a subjective measurement scale. In addition to the feeling of a ski the conditions the ski is used in also varies. This e↵ects the behavior of a ski and the skier drastically. For example, skiing on a hard-packed groomed slope compared with skiing on a soft slushy slope or skiing in clear blue sky compared with skiing in fog and so on the skier will not perform equally, see an illustration in Figure 1.1 and 1.2. 1 Figure 1.1: Slope in sunny weather[7] Figure 1.2: Slope in foggy weather [8] 1.2 Modern skis The most common skis that are seen in sporting goods stores or at ski resorts are so called carving skis, where the tip and tail of the skis are wider than the waist. This provides an easier edging and a shorter turning radius. Turning radius or sidecut radius is a global name for the radius of the part of a ”circle” the skier makes in a theoretical optimal turn for that specific ski, see Figure 1.4. In Figure 1.4 ”Tip” and ”Tail” contact points are also indicated. These are specified points according to ISO standard 6289:2003(en) Skis-Vocabulary [1] and the length in between these two contact points is referred to as the skis contact length or e↵ective length in the report. A typical modern ski is made of several di↵erent materials both along the ski length and thick- ness. The bottom-, or base-layer which is the surface closest to the snow is a polyethyl-plastic material with high absorption capabilities for wax. The bottom layer is wrapped in by an outer steel edge. The next layer is usually a layer of fiber reinforced plastic and/or metal sheet fol- lowed by a thicker core of a variety of wood or foam. Above the core a fiber reinforced plastic and/or metal is applied to increase the ski’s sti↵ness. Some skis also have a rubber material on top to improve the damping characteristics and finally a surface layer or topsheet is added to improve the esthetics’s of the ski as Figure 1.3 illustrates.

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