A model for performance enhancement in competitive cycling

A 3D cycling model is presented that combines bicycle dynamics, a tyre model, rider biomechanics and environmental factors into a single dynamic system. The system is constructed using Matlab toolboxes (SimMechanics/Simulink) with the aim of identifying mechanical mechanisms that can influence performance in a road cycling time trial. Initial conditions are specified and a variable step ODE solver numerically integrates solutions to the equations of motion. Initial validation compared rider-less self-stability presented in a published “benchmark” with model simulation and found an error of <1.5%. Model results included the weave eigenvalue becoming negative at 4.2 m/s and the capsize eigenvalue approaching a positive value at 6.1 m/s. The tyre model predicted peak front tyre slip and camber forces of 130 N and 17 N respectively which were within 0.9% of values reported in the literature. Experimental field validation compared actual and model predicted time taken by 14 experienced cyclists to complete a time trial over an undulating 2.5 mile road course. An error level of 1.4% (±1.5%) was found between actual and predicted time. This compares well with the average 1.32% error reported by existing road cycling models over simpler courses

Determinants of “optimal” cadence during cycling

Cadence is one of the only variables cyclists can adjust to manage their performance and fatigue during an event. Not surprisingly, cadence has received a great deal of attention from the scientific community in an effort to identify the cadence that optimizes power output while minimizing the fatigue that is incurred. The literature appears to present conflicting results with little consensus as regards the optimal pedalling cadence. This is in large part due to the inconsistent definition of the term “optimal” cadence, which has been used to describe energetic cost, muscular stress, and perception of effort. The issue is further confounded by the workload-dependent nature of the “optimal” cadence - that is, at higher power outputs, the optimized cadence is different from that at lower power outputs. Although the optimal cadence is different for energetic, muscular, and perceptual definitions, the curves that describe the effect of changes in cadence on these variables consistently exhibit a J-shaped response. This suggests that there is an underlying principle that is common to each of the definitions. Indeed, it would appear that the response of both the cardio-respiratory system (energetic cost) and the muscular system (muscular stress) is determined by the types of muscle motor units that are recruited during the exercise. Furthermore, although part of the response may be due to the inherent differences in the characteristics between the different motor units, the absolute contraction velocity relative to fibre type optimum may be of greater significance. Even when the power output is increased, the shape of the response curves to changes in cadence remains constant, although the nadir of the curve does shift to the right for increasing power outputs. We propose that the point at which the energetic vs. power and the muscular stress vs. power curves intercept is defined by the cadence at which the perceived effort is minimized (i.e. the preferred cadence). However, cadence fluctuations occur under field conditions that are unrelated to physiological factors and, therefore, the ability to identify an “optimal” cadence is limited to the laboratory environment and specific field conditions

A model for performance enhancement in competitive cycling

Cet article présente un modèle dynamique 3D de l’activité cyclisme qui comprend la dynamique de la bicyclette, un modèle de pneumatique, la biomécanique du cycliste et des facteurs environnementaux. Le système est construit en utilisant des boîtes à outils Matlab (SimMechanics/Simulink) dans le but d’identifier les mécanismes mécaniques qui peuvent influencer la performance dans un contre la montre en cyclisme sur route. Les conditions initiales sont spécifiées et un solveur ODE à pas variable intègre numériquement les solutions aux équations du mouvement. Une validation initiale présentée dans une publication benchmark a comparée des résultats obtenus sans cycliste et auto-stabilisé avec le modèle de simulation. Cette comparaison a montré une erreur inférieure à 1,5 %. Les résultats obtenus par ce modèle donnent, en particulier, une valeur propre du lacet devenant négative à 4,2 m/s et une valeur propre du tangage approchant une valeur positive à 6,1 m/s. Le modèle de pneumatique prédit des forces maximales de glissement et de « camber » respectivement, de 130 N et 17 N. Ces valeurs sont proches (moins de 0,9 %) de celles rapportées dans la littérature. Afin de valider le modèle, le temps prédit a été comparé à celui réalisé par 14 cyclistes expérimentés lors d une épreuve chronométrée sur un circuit routier vallonné d’une longueur de 4 km. Une erreur de l’ordre de 1,4 % (±1,5 %) a été trouvée entre le temps réel et le temps prédit. Ce résultat est en adéquation avec l’erreur moyenne de 1,32 % rapportée par les différents modèles existants en cyclisme sur route pour des parcours plus simples. Mots clés : Modélisation / cyclisme / bicyclette / dynamique directe