• Franz K. Fuss
Keywords: water-skiing, joint moments, shoulder, hip, knee, ankle


INTRODUCTION: The water-skier is a classical biomechanical example for the moment and force equilibrium of two different contact forces (water reaction force and rope force) and the gravitational force. The moment of the water reaction force is controlled by the lower limb joints, the moment of the rope force by the shoulder joints. The aim of this study was to analyze the amount of these moments exerted on these joints in juvenile water-skiers. METHODS: Ten water-skiers (7-11 years old) belonging to a local club volunteered for the experiments. Photos were taken when the skiers passed perpendicular to the axis of the camera. The speeds (10 - 20 m/s) were constant (no acceleration) at the time of the photo. The direction of the gravitational acceleration vector was defined, relative to the lake shore, by means of a plumb-line. The ski and the test persons were weighed afterwards and their segment lengths and body height were measured. Body segment parameters were also taken from the literature (Jensen, 1986). For the 2D model, the free body diagram consisted of the skier, the ski and the bar including the beginning of the rope. The x-axis of the coordinate system corresponded to the motion direction, the y-axis pointed upwards. The positions of the joint centers, center of gravity of the head, the ski, and the rope, and the direction of the gravitational acceleration were marked on the photographs. The data-sets of the marked items were brought into correct size and imported into the program developed for the mechanical calculations (quasi-static, inverse-dynamic). First, the center of gravity of the whole free body diagram was calculated from the single centers of gravity of the segments, as well as the lever arms of the rope force (rx & ry) relative to the center of gravity. The forces of the rope (Rx & Ry) and the ski (water reaction; Sx & Sy) were calculated from the gravitational force (Gy) and the inclination of the rope and the ski (relative to Gy). The friction force on the ski was considered to be zero. The lever arms (sx & sy) of the forces Sx & Sy were then calculated by means of the moment equilibrium, defining the instantaneous center of pressure on the ski. Finally, joint moments (ankle, knee, hip, shoulder) were calculated from the forces Rx, Ry, Sx, Sy, and the segment weights. The joint moments were calculated in relative values (forces per total weight, levers per body height, magnification 10000; = %TW x %BH). RESULTS: The magnitude of the joint moments depended on the skiing position. For skilled skiers, moments were half as high as for beginners. The moment values for experienced skiers were: shoulder - 20 %TW%BH tending to antevert, hip - 50 %TW%BH tending to flex; knee - 300 %TW%BH tending to flex, ankle - 250 %TW%BH tending to plantarflex. CONCLUSIONS: The reported method and results can be used for optimizing the training process in water-skiing. REFERENCES: Jensen, R.K. (1986). Body segment mass, radius and radius of gyration proportions of children. Journal of Biomechanics 19:359-368.