This paper presents empirically-based simulation results of descent time to completion in road cycling. A mathematical model is formulated to predict time saved on road cycling descents where a cyclist's position is static through manipulation of aerodynamic drag area, system parameters and initial conditions. Road cyclists often adopt drastic static riding positions on long descents in order to minimize aerodynamic drag and optimize performance, measured as race time to completion. In those riding positions bicycle control is compromised and the risk of fall and injury increases.The aims of this study were to empirically determine whether there is a difference in aerodynamic drag area associated with the 'Top-Tube' descending riding position compared to 'Normal' descending riding position, and to investigate the effect of the difference on time to completion of road descents.Two elite male Australian time-trial cyclists were tested in an open jet wind tunnel. Drag force was measured using a force platform and a custom air bearing drag measurement system at 50 Hz at wind velocity of 15.6 m/s. Athletes were tested in their 'Normal' descending position and in the 'Top-Tube' position. Based on Newtonian-Lagrangian equations of motion of the cyclist-bicycle system, an analogue mathematical model as a non-linear Riccati ordinary differential equation was developed to enable prediction of velocity and time to completion of a road cycling course descent of known length and gradient as measures of performance for an athlete of known mass and empirically determined drag area in a descending position. Previously, proposed models of cycling performance have been based on physiological, anthropometric, and mechanical power output. No general closed-form time-to-completion mathematical model for cycling was found in the literature. Analytical solutions allow for a concise investigation of a dynamical system model behaviour that is not as readily available with a numerical solution.Wind tunnel testing showed up to 25% reduction in drag area for changes to cyclists riding position from their 'Normal' to the 'Top-Tube' dropped descending position. The analytical solution to the nonlinear Riccati differential equation showed that large time savings as a result of reduction of drag area can be made on road cycling race descents. In the example scenario simulated here, 29.2 s may be saved on a 5 km descent of 10% gradient with 25% reduction in aerodynamic drag area (CdA).The 'Top-Tube' riding position is associated with a large reduction in aerodynamic drag area in road descents compared to conventional descending riding position. Our model enables the prediction of time to completion on descents. This may assist cyclists to assess the trade-off between undertaking increased risk associated with drastic rider descending position and the potential for improved performance in the context of race tactics and strategy.

We present a supervised machine learning approach for markerless estimation of human full-body kinematics for a cyclist from an unconstrained colour image. This approach is motivated by the limitations of existing marker-based approaches restricted by infrastructure, environmental conditions, and obtrusive markers. By using a discriminatively learned mixture-of-parts model, we construct a probabilistic tree representation to model the configuration and appearance of human body joints. During the learning stage, a Structured Support Vector Machine (SSVM) learns body parts appearance and spatial relations. In the testing stage, the learned models are employed to recover body pose via searching in a test image over a pyramid structure. We focus on the movement modality of cycling to demonstrate the efficacy of our approach. In natura estimation of cycling kinematics using images is challenging because of human interaction with a bicycle causing frequent occlusions. We make no assumptions in relation to the kinematic constraints of the model, nor the appearance of the scene. Our technique finds multiple quality hypotheses for the pose. We evaluate the precision of our method on two new datasets using loss functions. Our method achieves a score of 91.1 and 69.3 on mean Probability of Correct Keypoint (PCK) measure and 88.7 and 66.1 on the Average Precision of Keypoints (APK) measure for the frontal and sagittal datasets respectively. We conclude that our method opens new vistas to robust user-interaction free estimation of full body kinematics, a prerequisite to motion analysis.

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