# A COMPOSITE MODEL FOR THE SIMULATION OF SKIING TECHNIQUES

### Abstract

INTRODUCTION In this work we present a model for skiing technique analysis and simulation: it consists of a man model, an equipment model and a contact (ski-snow) model. Such a model is the basis for a deeper understanding of the interaction between skier and equipment and its use will be profitable in various applications such as: equipment optimisation and technique improvement. Moreover this simulation technique can be profitably used for teaching the basic principles of skiing. MATERIAL AND METHODS To build our model we combined the methods used for multibody systems dynamic analysis (man model with finite element techniques (ski model). The human body model consists of 3D chains of rigid bodies: according to the "sophistication" of the simulation we use 16 segments, with 39'internal d.0.f (full man model), or 7 segments, with 6 internal d.0.f . To describe rigid body dynamics and kinematics (man model) we adopt a method based on homogeneous matrices (Casolo 1995): both the absolute and the relative position, velocity and acceleration are described by 4x4 matrices, as well as the inertial properties and the external loads. This approach allows to embed both the linear and angular terms in the same formalism. To derive the equation of motion a Lagrangian approach was adopted, leading to this expression: Mq+C(cf.q.t) = Fl(q.q,t) +Ft(q,q) where M is the mass matrix, C contain the weight, the centrifugal and Coriolis effect, Ft contains joint torques, F2 represent the action exchanged with ski through the bindings and the vector q contains joints laws of motion. The model can be used to perform direct and inverse dynamics analysis of skiing, since it allows the input of joint torques and/or joint relative movements, that can be experimental data or can be generated by scratch, by a law of motion preprocessor. Skis are modelled with Finite Element techniques. The internal structure of a ski is quite complex: different material, with complex arrangement, are employed giving rise to properties (stiffness, damping and mass) which can be determined by experimental measures or by complex FE analysis. These properties can be quite well reproduced by means of a simplified model consisting of 3D beam elements . Some geometrical features, such as camber and sidecut, can be easily reproduced. Ski equations of motion, in matrix form, are: M9+ q v r e l + Kq&f = F,,I +Fnlon-ski f F.+.ki - cn,,wn where M, C, K are, respectively, the ski mass, damping and stiffness matrices. The ski load consists of three terms: weight, action exerted by the skier through the bindings and the contact action exerted by the snow. A simple contact model has been also developed, based on the assumption that the snow reacts both to ski deepening, sliding and skidding. This simple model can take into account, for example, the effect of ski vibration on the ski-snow interaction. RESULTS Some simulations have been performed to test model capabilities: we analysed the effect of ski torsional stiffness, as well as the amount of sidecut, on skier trajectory during traverse and turns. The model is also used to simulate the aerial phase of a free-style jump and the following landing phase. In all of these cases simulation can be an useful tool for predicting the effect of changing joint movements (i.e varying skiing technique) and equipment characteristics. A sensitivity analysis can be a first step toward a technique and equipment optimisation. References Casolo F., Legnani G., Righettini P., Zappa B. "A homogeneous matrix approach to 3D kinematics and dynamics", TMM (in press).
Section

Modelling / Simulation

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