Synchronous measurement of applied force and key kinematic variables as linear and angular velocities and accelerations are obtained in flatwater kayaking. The specific equipment needed includes an instrumented paddle, on board sensor and data acquisition system, all of them electronically synchronized at 100Hz frequency [1, 2]. This equipment provides high quality experimental data which are used to feed a recently developed physical a propulsion model for kayaking[3]. By modeling the paddler stroke using mathematical tools and introducing a few physical parameters, mean force, steady average velocity and mass, the model is not only able to approximate the experimental velocity-time curves but also to extract meaningful physical magnitudes that characterize the paddler performance. Two national level paddlers participate in this study. Experimental data were recorded for two distances (200m and 500m) and paces (medium and high), and provide the set of experimental data to analyze. For each series, recorded paddler stroke was modelled using Fourier series (Figure 1) and introduced in the model with the mentioned parameters. Starting from rest, the resulting velocity function has the following expression: (see source). With f the average force, d the drag coefficient, m the mass and an and bn coefficients to be obtained. The first terms represents the transition from rest to the steady velocity reached after acceleration is completed and the seconds the oscillatory contribution due to propulsion. Although fatigue is not modeled, this expression approximates well the correspondent experimental velocity curve and provides many physically meaningful of its performance. Figure 2 shows a fit from our data. Some interesting physical magnitudes could be extracted from our model. Table 1 shows some of them for the different trials. Among them of special interest is the impulse, defined by: (see source). Where freq = 1/T is the stroke frequency and T its correspondent period, f(t) is the time dependent applied force. It was observed [5, 4, 6], impulse is conserved over a paddler frequency range. Obtained impulses are shown in figure 3, a fairly conservation is found although a sensible difference between distances are shown for the paddler2. This magnitude could be an interesting metrics to evaluate paddler fitness and technical stability as well.
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