The Quest for Speed: An Optimal Control Framework for optimizing Speed Skating Technique for Efficiency and Speed across Diverse Conditions
F. van der Veen (TU Delft - Mechanical Engineering)
E. van der Kruk (TU Delft - Biomechatronics & Human-Machine Control)
T. Van Wouwe (TU Delft - Biomechatronics & Human-Machine Control)
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Abstract
The optimal technique for individual speed skaters remains poorly understood, due to the complex interplay of technique variables (like stroke frequency, skate trajectory and push-off mechanics). Optimization with a biomechanical model can help to identify the most efficient techniques for individual skaters. This research aimed to use a validated model of a speed skater (van der Kruk et al. 2017) within an optimization framework to investigate how the optimal speed skating techniques on the straightaways are influenced by individual characteristics and environmental conditions.
Finding the optimal technique that either minimizes effort at a target velocity or maximizes velocity, was formulated as an optimal control problem and solved using direct collocation. Across different optimizations, stroke frequency, mass, leg length, air and ice friction and limits on average and maximal power were incrementally varied.
Variations in velocity and stroke frequency most clearly influenced the optimal technique. Conditions requiring less energy (optimizations for low velocity, low ice or air friction), optimized towards energy-efficient strokes with longer gliding phases and minimal lateral forces. Conditions with higher speeds and frequencies converged to longer, forceful push-offs. These push-offs maximized leg extension by descending into a deep crouched position to emphasize a sideways push-off. Generally, optimized techniques adapted a small steer angle during the gliding phase to prioritize forward gain, and larger steering angles during the push-off to direct push-off forces forward. Optimizations for higher frequencies adopted more narrow strokes, and reached higher maximized speeds. Regarding personal characteristics, increasing the model's average and maximal power limits most significantly increased maximal velocity.