ABSTRACT
The results clearly show that the Hausdorff dimension is a suitable replacement for the smoothness factor previously applied for performance analysis (Fuss et al., 2003ab, 2004; Fuss & Niegl, 2006a). It has to be tested extensively, however, as to general application for performance analysis and route grading. Nevertheless, this study presents preliminary results and suggests a specific procedure. The necessary tool for advanced performance analysis in sport climbing is the fully instrumented climbing wall. The wall developed for this project consists of eight holds, which is sufficient enough for a circular boulder and within budgetary limits. A further advantage of an instrumented wall is the visualization of forces with 3D vector diagrams, which become 4D vectors, if the time is colour-coded. These diagrams help to understand the dynamics of climbing by means of a single picture (Figure 3), whereas parameter – movement or parameter – hold diagrams (Figure 2) are difficult to read. In the latter diagrams, the Hausdorff dimension has to be normalised to the force, as the Hausdorff dimension increases with the amplitude. The normalisation to the force depends on whether a single hold or the entire route is of interest. In the former case, the Hausdorff dimension is divided by the mean force at the hold of interest (Figure 2a). As the force applied to foot holds is usually higher then the one at handholds, it is logical that footholds have a smaller normalized Hausdorff dimension. Apart from that, the performance of hands and upper limbs is more crucial in climbing. If the entire route has to be graded, or the performance throughout the route to be quantified, then the Hausdorff dimensions of the individual loads has to be divided by the average of all mean forces at the individual holds (Figure 2a). In this diagram, the Hausdorff dimension of the individual hold becomes unimportant with respect to the overall trend. Thus, a single value, namely the mean of the Hausdorff dimensions at all holds suffices to express the performance of a climber or the difficulty of a route.
