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Sports engineering can be considered as the bridge between the knowledge of sports science and the principles of engineering and has an important role not only in improving the athletic performance, but also in increasing the safety of the athletes. Testing and optimization of sports equipment and athletic performance are essential for supporting athletes in their quest to reach the podium. However, most of the equipment used by world-class athletes is chosen based only on subjective tests and the athletes’ feelings. Consequently, one of the aims of this thesis was to combine mechanics and mathematics to develop new objective test methods for sports equipment. Another objective was to investigate the possibility to accurately track and analyse cross-country skiing performance by using a real-time locating system. A long term aim is the contribution to increased knowledge about objective test and analysis methods in sports. The main methodological advancements are the modification of established test methods for sports equipment and the implementation of spline-interpolated measured positioning data to evaluate cross-country skiing performance. The first two papers show that it is possible to design objective yet sport specific test methods for different sports equipment. New test devices and methodologies are proposed for alpine ski helmets and cross-country ski poles. The third paper gives suggestions for improved test setups and theoretical simulations are introduced for glide tests of skis. It is shown, it the fourth paper, that data from a real-time locating system in combination with a spline model offers considerable potential for performance analysis in cross-country sprint skiing. In the last paper, for the first time, propulsive power during a cross-country sprint skiing race is estimated by applying a power balance model to spline-interpolated measured positioning data, enabling in-depth analyses of power output and pacing strategies in cross-country skiing. Even though it has not been a first priority aim in this work, the results from the first two papers have been used by manufacturers to design new helmets with increased safety properties and cross-country ski poles with increased force transfer properties. In summary, the results of this thesis demonstrate the feasibility of using mechanics and mathematics to increase the objectiveness and relevance when analysing sports equipment and athletic performance.