A review of the factors affecting cadence selection in order to optimise competitive cycling performance. Covers VO2, muscle fibre type, blood flow, perceived exertion, preferred cadence, biomechanics, muscle stress and cardiovascular system
tage could still be gained if the variance from a constant speed is minimised [3] . Swain [15] was one of the Þ rst investigators to draw attention to the mechanical performance advantage that could be obtained by varying power output (expressed as VO 2 ) in response to variances in wind and gradient. Over a theoretical 10 km course with 10 symmetrical climbs and descents of 5 -15 % gradient, Swain [15] calculated time savings of 4 -8 % were possible. Subsequently, Atkinson et al . [3] re-calculated the results of Swain [15] using a more complete model of cycling power output demands [12] . These researchers calculated that a variable power output strategy would reduce race time by 8 % . Gordon [7] modelled a 40 km course with 20 symmetrical climb / descents of 2.5 % and obtained a time saving of 1.6 % compared to an equivalent constant power output strategy. The lesser time saving of Gordon [7] reß ects the reduced gradient proÞ le and emphasises the importance of a large gradient variance if the advantage of a variable power output strategy is to be realised. Thus, whilst performance improvement has been calculated in previous studies by adopting a variable power output strategy on an undulating
Abstract. 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.Key words: Modelling, cycling, bicycle, forward dynamics Résumé. Un modèle pour l'amélioration de la performance en cyclisme de compétition.Cet article présente une model 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 autostabilisé 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.
Modelling has been utilised in competitive road cycling to identify performance optimisations that would conventionally require extensive experimental testing. However, the validity of current models is limited by incomplete representation of the cycling environment and insufficient frequency of simulation. A three dimensional road cycling model has been developed that extends existing models by combining bicycle mechanics, rider biomechanics and environmental conditions into a single dynamic system. A system of rigid bodies linked by joints and driven by actuators has been built using the MATLAB toolboxes Simulink and SimMechanics. Each body is defined in respect of mass, inertia tensor, dimension and centre of gravity. The system operates in forward dynamics mode such that a simulation inputs forces to the equations of motion which are numerically integrated at <0.1 s time steps and output system motion. Bicycle freedoms include longitudinal/lateral translation together with roll, pitch and yaw rotation. Submodels reproduce transmission, tires, wheels, frame and steering geometry. A 16 segment rider applies experimentally obtained pedal forces coordinated with upper body roll and steering input. Environmental parameters include course track and gradient obtained from digital maps together with experimentally measured wind speed/direction. The model has been validated in a trial with 20 experienced time trialists riding a 2.5 mile undulating section of the Cycling Time Trials course G10/42 at competitive pace. The course track/profile and the cyclist characteristics were loaded into the model and a simulation predicted individual completion times. Mean actual time was within 1.4 (±0.7)% of the mean predicted time. The model was then used to optimise application of a variable power pacing strategy over the same course1. A 2.9 (±0.9)% time saving was obtained which would typically represent a 40 s advantage over a full 10 mile time trial. Further model applications include investigating the mechanical performance advantages of factors that are both difficult and time consuming to examine experimentally such as saddle position, bicycle/rider weight and tire characteristics.
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