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10:20   Race prediction and pacing Chair: Heather Driscoll 10:20 20 mins TOUR DE FRANCE MODELING: 2015 RESULTS AND COMPARISONS WITH ELITE CYCLIST POWER DATA Chad Hobson, John Goff Abstract: For the past dozen years, our research group has been refining a physical model used to predict the winning times for each stage of the Tour de France. Our model is based upon a series of incline planes and incorporates real stage data and cyclist power output, as well as air and rolling resistances. We report on our most recent model modification in which we utilized allometric scaling to adjust our model cyclist's power output based upon varied rider masses for different stage types. We also provide a comparison between our model and published power data for top level cyclists and recent Tour de France winners such as Chris Froome and Vincenzo Nibali. This juxtaposition showcases not only how well our model predicts stage-winning times, but also the extent to which our model matches reality. We finally report on how our model performed in predicting the winning times for each stage in the 2015 Tour de France. 10:40 20 mins THE OPTIMAL POWER DISTRIBUTION FOR CYCLING IN A TIME TRIAL Robbert Fokkink, Jenny de Jong, Geert Jan Olsder, Arend Schwab Abstract: The optimal pacing strategy of a cyclist in an individual time-trial depends on terrain, weather conditions and the cyclist’s endurance capacity. Previous experimental and theoretical studies [2,5] have shown that a suboptimal pacing strategy may have a substantial negative effect. In this paper we express the optimal pacing problem as a mathematical optimal control problem that can be solved using Pontryagin’s maximum principle [1]. The control variable is the cyclist’s endurance capacity (power) which we model according to a hyperbolic power-time relationship [6]. The Hamiltonian is linear with respect to this control variable. We redefine the minimum time problem as a maximum excursion problem, which is related to Goddard’s problem of a rocket’s ascent through the atmosphere. Our analysis of the optimal pacing strategy borrows ideas of Dmitruk and Samylovksiy’s work on the simplified Goddard problem [3]. It turns out that the optimal pacing problem is a singular control problem. Such problems are difficult to solve, numerically and analytically, and they only occur sporadically in control theory [1, p 246]. Intricate mathematical arguments are required to prove that the singular control times form a single interval: optimal pacing starts with maximum power and decays through a singular control to minimum power. The singular arc may be degenerate, it may be a bang-bang control. Our solution of the pacing problem is partly numerical and partly analytical. It applies to a straight course without bends, but it can be extended to an arbitrary course by dividing it into straight segments between bends and solving a linear optimization problem. The analysis is not yet complete. A more intricate study of the optimal trajectory through a bend is required and we still need to compare our results to experimental studies. We include some initial results in this direction, which appear in [4]. 11:00 20 mins DEVELOPMENT OF A KAYAK RACE PREDICTION INCLUDING ENVIRONMENTAL AND ATHLETE EFFECTS Adam Higgens, Lauren Conway, Joe Banks, Dominic Taunton, Dominic Hudson, Stephen Turnock Abstract: Sprint Kayak and Canoe events take place on a straight course on typically a wide expanse of water. The events are usually for a set of boats that commence from a standing start within their own delineated lanes. Victory goes to the boat and crew that traverse the course in the shortest time. The purpose of the crew is to ensure that at any time during the race they are propelling the craft with the maximum effort such that they rapidly accelerate the craft to an appropriate speed, modify their stroke rate during the race and if deemed necessary respond to the efforts of the other crews such that at the finish they finish first. What is not clear is what is the most appropriate race strategy for a particular combination of crew and boat type for a given set of environmental conditions? One of the dangers is that the crew overexerts itself too early in the race such that later on they have insufficient reserves to respond to the efforts of other crews. Similarly that the perceived psychological benefit of being in front outweighs a more cautious strategy that attempts to manage crew workrate. The performance of the boat and crew will depend on a wide variety of factors. For instance the design of the equipment used, boats and paddles primarily, are governed by the individual event/sports’ rules and regulations whereas, within certain constraints, the environmental effects of the wind’s strength, direction and variability, and resultant wind generated waves will all have an influence on the actual speed obtained by the participants. In this work a visual Matlab-Simulink based environment has been developed that allows a whole race to be simulated. Appropriate Naval Architecture tools (Molland et al, 2011) for the prediction of the performance of the boat in terms of its displacement, surface area, form and wave drag have been used for the resistance model with additional modelling applied for the influence of wind and waves on speed loss. The crew members themselves are represented in terms of their mass, a model for the developed thrust of their individual stroke (Banks et al 2014) alongside a simple model for the maximum total and sustained effort. The paper itself will present the basis of the three degree-of-freedom manouevring model (surge,yaw and sway) which will then be evaluated using a series of case studies based on data from appropriate world championship events. One key comparator has been the relative differences in race times for K1, K2, and K4 which helps demonstrate the correct assessment of the fundamental boat performance itself. Molland et al, 2011, Ship Resistance and Propulsion, Cambridge University Press. Banks et al, 2014, Kayak blade-hull interactions: a body-force approach for self-propelled simulations. Proceedings of the Institution of Mechanical Engineers Part P Journal of Sports Engineering and Technology, 228, (1), 49-60.