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A “Virtual Wind Tunnel” for Aerodynamic Assessment in Cycling

 
In track cycling, where speeds can reach up to 80 kph and margins of victory can be measured in fractions of a second, the smallest of parasitic losses can mean the difference between the podium and watching the ceremony from the stands. On flat ground, the speed of a cyclist is determined by the ratio of the power input by the athlete to the parasitic resistance forces; at racing speeds these parasitic losses are primarily due to aerodynamic drag, which increases with the square of the velocity. For a cyclist to double their speed (without altering their aerodynamic positioning) they must increase their power output by 8-fold, thus highlighting the critical importance of aerodynamic efficiency. While general rules of thumb and experience can go a long way towards good aerodynamic positioning, including bicycle component selection and configuration, relatively small alignment or positional changes can have non-negligible impacts on overall aerodynamic loading. Presently, the Canadian Olympic cycling team relies heavily on track testing, some wind tunnel testing, and considerable institutional knowledge, intuition, and trial and error in order to optimize individual athlete aerodynamics for competition. Consequently, decisions such as equipment changes or redesigns incur significant monetary and human resource costs to assess their impact on aerodynamic forces, both individually and team-wide. Wind tunnel testing, the gold standard for aerodynamic analysis, is particularly expensive and thus used sparingly.
 
Recent advances in three-dimensional scanning and numerical modeling has set the stage for computational fluid dynamics (CFD) to become a viable tool to complement track and wind tunnel testing for aerodynamic optimization of individual athletes. By offloading some of the testing to the computational domain (a “virtual wind tunnel”, if you will), the impact of equipment changes and adjustments can be explored virtually, reserving precious track and wind tunnel time for fine-scale corrections. In collaboration with Cycling Canada and 4iiii Innovations and with support from MITACs and Own The Podium, we have developed and tested the “virtual wind tunnel” (VWT) to aid Canadian Olympic and Paralympic athletes achieve success. Specifically, through this support we have (1) refined VWT methodologies and validated against experimental data; (2) performed a first-order examination of the impact of dynamic leg movement on aerodynamic loading; and (3) developed and implemented a combined CFD/component optimization strategy to configure the aerobars of a female Canadian Olympic cyclists to minimize overall drag.
 
Validation: Data from a detailed wind tunnel campaign using a realistic mannequin on a time trial bicycle (Terra et al., Exp. Fluids, 60:29; 2019) were employed as a benchmark to establish the modeling methodology, including turbulence model, meshing practices, and solver for the VWT. By adapting a low-cost turbulence model originally designed for transitional flow over airfoils to the cycling domain, and determining the requisite mesh density in various flow regions, we successfully replicated the experimental drag-area (CdA) results to within experimental uncertainty and captured well the measured wake characteristics that influence drag and drafting. By exploiting parallel processing^*, such fidelity can be obtained within 24 hours and several configurations can be tested simultaneously given sufficient access to computational resources.
 
Effect of cadence on drag: It is well-established that aerodynamic drag is a function of pedal position, with highest drag encountered when one leg is fully extended, though relatively little information is known about the effect of cadence on drag. By imposing leg motion on the cyclist model using a “moving wall”, a cost-effective first-step towards dynamic pedaling motions, the effect of cadence (60, 90, and 120 rpm) on total and individual leg component drag was investigated. We found that drag increased slightly with leg motion, though the effect was less than a 1% difference in comparison with a static leg. Furthermore, the drag increase was independent of cadence to within simulation uncertainty, suggesting that metabolic efficiency should be the driving factor in establishing cadence. Interestingly, the drag on the “down” leg did reduce by up to 2.2% (improving with increased cadence). Future work will focus on the impact on the wake dynamics and whether this could potentially be exploited by a drafting rider (e.g., in team pursuit) through appropriate setting of relatively pedaling phase.
 
Aerobar optimization: Perhaps the most exciting and immediately applicable result of this work is the development of a component configuration methodology whereby gradient-based optimization in conjunction with the VWT is used to determine a “best configuration” to minimize drag. Specifically, the aerobar of a female Canadian track cyclist was parameterized (stem height and elbow pad lateral and forward-backward position) and optimization tools were used to minimize drag force by traversing the parameter space. In the virtual space the athlete’s body position was adjusted based upon changes in aerobar configuration using the Blender software package. By decreasing stem height and moving the elbows outboard and forward the overall drag on the cyclist was reduced by 9%.
 
There remain several challenges that require further innovation. For example, true dynamic simulations with moving bodies (e.g., pedaling) remains a significant hurdle, both in terms of modeling and computational expense. In addition, the optimization tools employed herein were primitive and required a relatively large number of simulations to converge. This could be improved, particularly in the presented case of component configuration, through the use of constrained optimization, perhaps with biomechanics-based penalty functions should the optimal aerodynamic configuration diverge too much from the nominal set up.
 
Beyond cycling, aerodynamics (or hydrodynamics) is similarly the limiting factor in a variety of other Olympic and Paralympic sports, such as alpine skiing, wheelchair racing, and swimming. Building upon the VWT platform, computational modeling tools could likewise be incorporated into the aerodynamic assessment protocols for other sports. Such a cross-sport aerodynamic assessment platform with shared institutional knowledge could benefit a wide cross-section of Canadian elite sport programs.
 
^*We acknowledge the kind support of Compute Canada through the Dedicated Resources Programme, which was utilized for all simulations.