Alpine Ski Motion Characteristics in Slalom

Abstract

Important insight into ski function, and ultimately skier technique and tactics, can be gained by studying how measured ski trajectories compare to predictions based on theoretical models of ski-snow interaction mechanics. The aim of this investigation was to use a 3D kinematic data set collected on highly-skilled skiers during slalom race simulations to quantify ski motion characteristics and to compare these measures with theoretical predictions based primarily on ski geometrical characteristics. For slalom turns on moderate steepness (19°), ski edging angles reached maximum values of 65.7 ± 1.7° and 71.0 ± 1.9° for 10 and 13 m gate spacings. Turn radii reached minimum values of 3.96 ± 0.23 and 4.94 ± 0.59 m for the 10 and 13 m courses. These values were in good agreement with theoretical predictions by Howe (2001) of turn radius based on edging angle. Other results of the study support recent developments in understanding of the role which the ski shovel plays in groove formation during carving, and also point to the need for further study of how ski geometrical and physical characteristics interact to determine the ski's trajectory, particularly at low edge angles. These results have important implications for understanding the consequences that ski design can have for skier technique and tactics in competitive slalom skiing.

Keywords: alpine ski; alpine skiing; ski characteristics; ski mechanics; ski motion; ski-snow interaction.

Figure 1

The ski edge angle (θ) and attack angle (ϕ) as defined by Lieu and Mote (1985). θ is the edge angle between the plane of the local snow surface and the running surface of the ski. The ski's angle of attack (ϕ) is the angle between the ski's longitudinal axis (E) and the center point's velocity vector (V) projected to a plane parallel to the local snow surface. The left panel presents a skidding ski with a relatively large attack angle, scraping a wide track into the snow surface. For contrast, the right panel presents a carving ski with a small angle of attack, leaving a narrow track in the snow.

Figure 2

A graphical reconstruction of the experimental set-up. Control point positions are indicated by the small points and poles. Note that camera 4 was actually placed 30 m further to the right as seen from this perspective.

Figure 3

The 15 segment ski model fitted to TIP, TAIL, and AJC. MID was defined as the point along the ski sole 16–19 cm below AJC, in the direction perpendicular to the TIP-TAIL vector.

Figure 4

Measured outside ski attack angle (A), edge angle (B), and turn radius (C) for sample turns from the 10 and 13 m courses in gray and black, respectively. Due to the different course setting, the data from the two courses are coordinated using the gate as a common point, and presenting the X axis as distance to gate. Gate passage is indicated by the vertical dashed line. It is relevant to note that turns on the 13 m course start much higher up on the slope relative to the gate than on the 10 m course.

Figure 5

Mean local ski attack angle averaged across whole ski attack angle (left panel). An example ski making the transition from skidding to carving through a turn is shown in the right panels.

Figure 6

Instantaneous measured outside ski turn radius (R_T, data points) and predicted outside ski turn radius using Equation 1 (R_HOWE, data line) for the 12 analyzed trials on the 10 m (A) and 13 m (B) courses. Data are limited to time points where the ski was carving (ϕ < 5°, n = 185 and 298 for the 10 and 13 m courses, respectively).

Figure 7

Measured (R_SKI, dark lines) and predicted (R_HOWE, gray lines) outside ski turn radius for sample turns on the 10 m (A) and 13 m (B) courses. Due to the different course setting, the data from the two courses are coordinated using the gate as a common point, and presenting the X axis as distance to gate. The vertical dashed line indicates gate passage.

Figure 8

High-speed video footage of a carving ski undergoing a disturbance possibly similar to that observed in the current investigation. This video, taken during the women's World Cup giant slalom at Åre in March, 2006, was filmed at 1,500 fps. To help the reader visualize the outside ski's motion, the solid, black line indicates the original ski orientation from Frame (A) while the dashed, white line indicates the changing ski's orientation. From Frame (A–C), the ski shovel sways toward the outside of the turn. The shovel reaches and engages the snow surface in Frame (C). Groove formation is then redirected onto a new trajectory in Frames (D, E) with the increased distance between the skier's feet indicating that the outside and inside skis have come onto diverging trajectories.