مدل شبیه سازی تقریبی برای طراحی اولیه مسیر لوژسواری

Competitive and recreational sport on artificial ice tracks has grown in popularity. For track design one needs knowledge of the expected speed and acceleration of the luge on the ice track. The purpose of this study was to develop an approximate simulation model for luge in order to support the initial design of new ice tracks. Forces considered were weight, drag, friction, and surface reaction force. The trajectory of the luge on the ice track was estimated using a quasi-static force balance and a 1d equation of motion was solved along that trajectory. The drag area and the coefficient of friction for two runs were determined by parameter identification using split times of five sections of the Whistler Olympic ice track. The values obtained agreed with experimental data from ice friction and wind tunnel measurements. To validate the ability of the model to predict speed and accelerations normal to the track surface, a luge was equipped with an accelerometer to record the normal acceleration during the entire run. Simulated and measured normal accelerations agreed well. In a parameter study the vertical drop and the individual turn radii turned out to be the main variables that determine speed and acceleration. Thus the safety of a new ice track is mainly ensured in the planning phase, in which the use of a simulation model similar to this is essential.

Bobsled, luge, and skeleton are considerable fast winter sports, for example at the Whistler Sliding Centre a speed of 41 m/s (148 km/h)1 and a normal acceleration of 5g were measured in luge. Even for elite runners such high speeds and accelerations are difficult to handle. Because of safety issues, ice tracks have to be restricted in maximum speed and maximum normal acceleration. For the initial design of new tracks one needs a knowledge of the expected running dynamics of the bobsled, luge, or skeleton. Misjudgment in the development may lead to inadmissible high speeds and, consequently, to accident prone accelerations acting on the athlete. To simulate sport on artificial ice tracks one needs data of the track course as well as of drag and friction. General construction principles for bobsled tracks were given in Stoye (1990). Data for a particular track can be obtained from construction plans. For example the bobsled track for the 1964 Winter Olympics in Innsbruck had already an elliptic cross section and clothoids for the transition of straight to turn sections. New tracks still use these elements and usually are built as combined tracks for bobsled, luge, and skeleton. Drag and friction have been described by several authors. Walpert and Kyle (1989) reported values for the drag coefficient in sport including luge. Brownlie (1992) investigated the effect of body segments and apparel on the drag resistance in the case of running, cycling and skiing. In many cases drag resistance data are classified by the national federations (e.g. Meile, 2006). Comprehensive descriptions of friction on snow and ice were given by Colbeck (1992) and Petrenko and Whitworth (2002). Friction of steel on ice was investigated for skating by Evans et al. (1976) and de Koning et al. (1992), for bobsled by Hainzlmaier (2005) and Itagaki et al. (1987), and for luge by Fauve and Rhyner (2008). To our knowledge, no results are available for the shearing force in the transverse direction for a runner on ice.

Running safety is one of the main concerns when designing a new ice track. High accelerations and a large amount of vibrations are reported by coaches to be the origin of driving faults and thus are accident prone. In case of accidents, a high speed causes a severe impact load. Since kinetic energy depends quadratically on speed, any speed reduction considerably reduces the impact energy in accidents and therefore efficiently increases safety. So, maximum speed and normal acceleration were used as a measure for running safety. Run-time, speed, and acceleration were simulated for a competitive run in single and double luge at the Whistler Sliding Centre. Run-time and maximum speed compared well with the official results. Measured and calculated acceleration agreed for the entire run. Since the simulation model accurately predicted the speed and the acceleration of the luge, the model is adequate to initially evaluate the safety of proposed layouts of new luge tracks. Parameter studies show that changes in drag area, coefficient of friction, or luge mass were of minor importance as long as variations, relevant for elite luge, were considered. Moderate changes in the vertical drop or the turn radii caused significant changes in the maximum speed and normal acceleration (Table 2). In early planning stages of new tracks turn radii and vertical drop are adapted to a given terrain. For the detailed specification of the course a simulation model has to be applied. In the design phase, speed can most effectively be restricted by choosing a smaller vertical drop and normal acceleration by a larger turn radius. After construction, the only option to reduce speed and acceleration is to start at a lower point. Thus, running safety can effectively be influenced in the planning phase. The presented model was used to predict the driving dynamics of two recently designed but not yet built luge tracks in Bludenz, AT and Schliersee, DE (CTSAS, 2009).