Volume 7, Issue 9 (October 2010)
Reaction Forces and Moments in Carved Turns
We computed reaction forces and moments acting on a skier during a carved turn. We performed an inverse and a forward dynamic analysis. For a run of an elite skier, marker positions on skier and skis were obtained as functions of time from a video analysis and smoothed by splines. Linear velocities and accelerations were computed by differentiating the splines, angular velocities, and accelerations via rotation matrices. The forces acting at the right ski were measured with two Kistler force plates. For the inverse dynamics, we used an adapted Hanavan model for a skier consisting of upper body, left and right thighs, shanks, and skis. Applied forces considered were weight and ski-snow friction. Drag was neglected. By prescribing a lateral weight distribution from the outer to the inner ski during the turn, reaction forces and moments at the left and right ankle, knee and hip joints were computed from the Newton–Euler equations of motion for constrained rigid multibody systems. The forward dynamics was performed with a three-segment model of a mono-skier consisting of trunk, thigh, and shank. Rotational joints were assumed in knee and hip. The track and the joint angles were prescribed. The inward lean angle was determined by a balance condition that led to nonholonomic constraints. After formulating the equations of motion in descriptor form, the resulting differential-algebraic system was solved with the numerical code RADAU5. Computed and measured reaction forces and moments agreed well within the accuracy of the measurements. The calculated joint loads are consistent with results from the literature. The forward dynamics model can be used to simulate consecutive ski turns. With parameter studies, the effects of slope, tracks, segment properties, ski-snow friction, and velocity of the skier on joint loads and performance of a run can be investigated. Further, injury mechanisms can be analyzed.