Avaiabe onine at www.sciencedirect.com Procedia Engineering 13 (2011) 4 9 5 th Asia-Pacific Congress on Sports Technoogy (APCST) Cassica stye constructed roer skis and grip functionaity Mats Ainegren *, Peter Carsson, Mats Tinnsten Department of Engineering and Sustainabe Deveopment, Mid Sweden University, Akademigatan 1, Östersund 831 25, Sweden Received 18 March 2011; revised 30 Apri 2011; accepted 1 May 2011 Abstract Roer skis are used by cross-country skiers for snow-free training, with the aim of imitating skiing on snow. The roer skis on the market that are constructed for use in the cassica stye are equipped with a front and a back whee, one of which has a ratchet to enabe it to grip the surface when diagona striding and kick doube poing. A new type of roer ski was constructed with a function which makes it necessary to use the same kick technique as that used on snow, i.e. the ski has a camber that must be pushed down to obtain grip. Its stiffness can be adjusted based on factors that infuence grip, i.e. the skier s bodyweight and technica skiing skis. Thus, our aim was to make comparative measurements as regards grip between ratcheted roer skis and the roer ski with a camber and compare with previous pubished resuts for grip waxed skis during cross-country skiing on snow. The measurements were carried out using speciay deveoped equipment, with a bottom pate and an overying rubber mat of the same type as used on many treadmis and a function for appying different oads and generating traction on the back of the roer ski. 2011 Pubished by Esevier Ltd. Open access under CC BY-NC-ND icense. Seection and peer-review under responsibiity of RMIT University Keywords: Roer skis; cassica stye; grip; ratchet; camber; static friction coefficient 1. Introduction Cassica stye constructed cross-country skis static friction coefficients (μ S ), defined as the ratio between the tangentia and norma forces acting on the ski when it is stationary on the snow, just before it starts giding, have been studied using force pate systems attached to the skis [1] and by using a ong force patform system mounted under the snow [2-4]. As a resut, μ S of 0.04 to 0.15 have been reported, estimated from tangentia and norma forces of 0.1 to 0.2 and 1 to 3 times bodyweight, respectivey [1-4]. * Corresponding author. Te.: +46-63-165372; fax: +46-63-165740. E-mai address: Mats.Ainegren@miun.se 1877 7058 2011 Pubished by Esevier Ltd. doi:10.1016/j.proeng.2011.05.043 Open access under CC BY-NC-ND icense.
Mats Ainegren et a. / Procedia Engineering 13 (2011) 4 9 5 With the aim of imitating skiing on snow, cross-country skiers use roer skis for their snow-free training. Roer skis on the market, that are intended for use in the cassica stye, have a construction where one of the two whees (one whee at the front and one at the back) has a ratchet that aows a grip on the surface during a eg kick. Since the ratcheted mechanism is not dependent on a oad appied to the roer ski, it is ikey that this type of construction in practice provides a high μ S between the ratcheted whee and the surface, independenty of the skier s bodyweight and technica skiing ski. In such a case, this woud be in great contrast to skiing on snow on groomed trais where a proper technique is essentia to obtain a sufficient grip. Thus, the purpose of this study was to investigate μ S of ratcheted roer skis and compare the resuts to μ S reported from skiing on snow. Additionay, a different roer ski construction with a camber construction that must be pushed down to obtain grip, was evauated. Nomencature F m g N f N r S, S F F f F r F a h 1 2 3 vertica oad on roer ski tota mass from roer ski, ski binding and auminium soe acceeration of gravity norma force on the forward whee norma force on the rear whee force registered in the oad ce resisting force of the oad whee resisting force of the forward whee resisting force of the rear whee resisting force from the ratcheted spoo vertica distance between the rubber mat and the oad ce traction point distance between the axis of the forward and rear whee distance between the axis of the forward whee and the vertica oad distance between the axis of the forward whee and the centre of mass 2. Methods 2.1. Equipment The study used four cassica stye constructed roers skis (PRO-SKI C2, Sterners, Daa-Järna, Sweden), procured from the open market, described in an earier paper [5]. The roer skis were equipped with a forward and a rear whee, where the atter contained a ratchet to enabe for grip towards the surface. Aso, a different type of roer ski construction with a camber and adjustabe grip function was tested (SPORTSTECH roer ski, Mid Sweden University, Östersund, Sweden). The functionaity for this was
6 Mats Ainegren et a. / Procedia Engineering 13 (2011) 4 9 appied to the forward whee of the roer ski, see Fig 1. When sufficient oad was exerted to press down the camber, the forward whee estabished contact with a ratcheted spoo (F a, Ø 20 mm, auminium, cross ettering size 1.6) situated above the forward whee. The degree of grip was therefore depending on the stiffness of the roer ski s camber, which was simpy adjusted via a spring-oaded screw (SF-TFX 2691, Lesjöfors Stockoms Fjäder AB), and the amount of oad put on top of the roer ski (norma force on the forward whee). This construction used whees of the same type as the non ratcheted (forward) whee of PRO-SKI C2. The roer skis were equipped with ski bindings (Saomon Equipe or Rottefea R3 Cassic) mounted with the ski boot fix point at the roer ski centre of mass. The tota weight of a roer ski with ski binding and a fat auminium soe, mounted at the ski boot fix point, was 1.5 kg (PRO-SKI) and 1.8 kg (SPORTSTECH) and the ength between the axes of the forward and rear whee was 722 mm for both types of roer skis. The μ S was measured with the roer skis mounted in a fixture speciay produced to measure ski characteristics on ordinary cross-country skis [6]. The fixture was suppemented with an appicabe bottom pate with an overying rubber mat of the same type as used on treadmis of a known manufacturer (Rodby Innovation AB, Vänge, Sweden) and a function for appying different oads norma to the surface (F) and generating tangentia traction of the roer ski (S ), see Figure 1. To minimize the infuence of resisting force from the vertica oad (F ), the bar was equipped with a stainess stee ba bearing whee which was abe to ro on the fat soe. Further, the soe was verticay adjustabe at the rear part, as we as the tangentia traction point, to aow for eve adjustments due to different oads and constructions of the tested roer skis (h). 2.2. Mechanics of the roer skis There is a schematic sketch of the experimenta setup in the free-body diagram in Figure 1. F 2 Fa F h S Load ce F f 3 F r N f 1 mg N r Fig. 1 Free body diagram of the experimenta setup. Horizonta equiibrium, when measured without any contact between the ratcheted spoo (F a ) and the forward whee, shows that: S F F F = 0 (1) f r
Mats Ainegren et a. / Procedia Engineering 13 (2011) 4 9 7 In the situation when the ratcheted spoo (F a ) is pushed against the forward whee the force registered in the oad ce (S ) gives the equation: S = F + F + F + F f r a With the static friction coefficient (μ S ) defined as the ratio of the resisting force to the norma force (N) on the whee with the grip function (N f or N r ), the foowing reationship was estabished: S S μs = N The individua norma forces of the forward (N f ) and rear (N r ) whee were cacuated as: And N f N r mg( = mg = 2.3. Experiments + 1 3) F( 1 2) S 1 1 3 + F 2 + S h h The roer skis static friction coefficients (μ S ) was studied as a function of different vertica oads and norma forces acting on the whee with the grip functionaity. Masses within the range of 60 to 100 kg, in a 10 kg interva, was put on top of the soe on the roer ski, 100 mm behind the ski boot fix point. Together with the mass of the tested roer ski, this corresponded to the tota norma forces of 603.3 to 995.7 (PRO-SKI) and 606.3 to 998.7 Newton [N] (SPORTSTECH). The ength ( 2 ) between the axis of the forward whee and the vertica oad put on top of the roer ski was 480 mm (PRO-SKI) and 410 mm (SPORTSTECH). Before starting the measurements with the SPORTSTECH roer ski, the camber was adjusted so that the ratcheted spoo (F a ) and the forward whee merey estabished contact on the initia measuring oad (606.3 [N]), after which the camber was no more adjusted. Further, the tangentia forces derived from the sum of the resisting forces (S) of the vertica stainess stee ba bearing whee and the forward and rear whee of the roer skis was measured using the same oads as above and finay subtracted from the resuts on μ s, see equations (1-3). For the PRO-SKI roer skis the measurements of S was executed by turning the ratcheted (rear) whee to grip and ro, respectivey, the opposite way and for the SPORTSTECH roer ski without any contact between the ratcheted spoo (F a ) and the forward whee. 3. Resuts and Discussion The resuts of the measurements on μ s for the two types of cassica stye constructed roer skis are presented in Tabe 1 and Figure 2. (2) (3) (4) (5)
8 Mats Ainegren et a. / Procedia Engineering 13 (2011) 4 9 Tabe 1. Resuts of static friction coefficients (μ s) for the PRO-SKI and SPORTSTECH roer ski. N r and N f are vaues for the norma forces acting on the whee with the grip functionaity. Vertica oad (F) 588.6 686.7 784.8 882.9 981.0 PRO-SKI N r 426.3 492.7 560.4 627.4 693.9 μ s 0.93 0.86 0.84 0.81 0.78 SPORTSTECH N f 192.0 218.0 242.9 269.3 295.6 μ s 0.042 0.293 0.548 0.698 0.829 Fig. 2. The figure iustrates the static friction coefficients (μ s) for the two types of cassica stye constructed roer skis (PRO-SKI, mean + SD, and SPORTSTECH roer ski). The resuts in this study shows that ratcheted whee constructed PRO-SKI roer skis, within the vertica oads 600 to 1000 [N], have μ s around 0.8, which is more than 5 times the vaues reported from on-snow skiing with grip waxed cross-country skis [1-4]. The resuts for the tested SPORTSTECH camber roer ski showed that μ s changed from merey nothing up to the eve of the tested PRO-SKI. Thus, one probem with ratcheted whee constructed roer skis is that this mechanism provides a secure grip even when skiing with a poory performed technique. This is in great contrast to skiing on snow on groomed trais, where proper technique is essentia for good grip. Training with the roer skis that are currenty on the market can thus entai that the wrong kick technique is earned, and that there is no opportunity to earn the correct kick during snow-free training. Additionay, much of the current sports research into the physioogy and biomechanics of cross-country skiing is conducted on treadmis using ratcheted roer skis, which woud not appear to be optima.
Mats Ainegren et a. / Procedia Engineering 13 (2011) 4 9 9 The measurements in this study were made on a rubber mat of the same type as used on many treadmis, whie most of the training sessions, performed by cross-country skiers, probaby are carried out on asphat surfaces. Thus, how outdoor environment and surfaces affect μ s of ratcheted whee constructed roer skis is not investigated in this study. However, during norma weather conditions, it is not ikey that μ s on asphat surfaces strongy deviate from the resuts in this study. Different manufacturers use different types of materia for the roer ski whees (rubber, thermopastic poyurethane) and, aso, choose to mount the ratcheted whee either in the rear or in the front position. Depending on the position, this wi affect the norma force of the ratcheted whee and may thus have some infuence on μ s. Thus, an enarged study of μs is needed, invoving different roer ski manufacturers with aternative positions for the ratcheted whee. Aso, more of the SPORTSTECH roer skis need to be measured in order to estabish mean and SD vaues for this type of construction. Foowing this, an integrated biomechanica and physioogica study for comparisons between roer skiing, invoving both types of cassica stye constructed roer skis, and cross-country skiing on snow. 4. Concusion The resuts of this study showed that ratcheted whee constructed roer skis reached vaues of μ s which were five times more than the vaues reported from on-snow skiing with grip waxed cross-country skis, whie μ s of the tested camber roer ski varied from zero up to the eve of the tested ratcheted roer skis. Acknowedgements Thanks are due to the European Union s regiona deveopment fund, which provided financia support for the study. References [1] Ekstrom H. Force interpay in cross-country skiing. Scand J Sports Sci 1981; 3 (2):69-76. [2] Komi PV. Ground reaction forces in cross-country skiing. In: Winter D, Norman R, Wes R, Hayes K, Pata A, editors. Biomechanics ix-b. Human Kinetics, Champaign, 1985; p. 185-190 [3] Komi PV, Norman RW. Preoading of the thrust phase in cross-country skiing. Int J Sports Med 1987; 8 (SUPPL. 1):48-54. [4] Vahasoyrinki P, Komi PV, Seppaa S, Ishikawa M, Koehmainen V, Sami JA, Linnamo V. Effect of skiing speed on ski and poe forces in cross-country skiing. Med Sci Sports Exerc 2008; 40 (6):1111-1116. [5] Ainegren M, Carsson P, Tinnsten M. Roing resistance for treadmi roer skiing. Sports Eng 2008; 11:23-29. [6] Backstrom M, Dahen L, Tinnsten M. Essentia ski characteristics for cross-country skis performance. The Engineering of Sport 7. Internationa sports engineering association, Biarritz, 2008; p. 543-549