Dec. 14, 2024
The goal of this CFD (Computational Fluid Dynamics) investigation is to assses whether the BOA closure mechanism, utilized for tightening and loosening laces in cycling shoes, may increase the drag force.
Two simulations were carried out: in the first one we used a high-end Specialized shoe (a S-Works Torch) with two BOA dials, and in the second one we used the identical shoe from which we removed the BOA dials.
The simulations include the shoe and the ankle to accurately replicate the interferences that the BOA dials may exert on adjacent elements. Adding other parts of the leg or the body or the bicycle or inserting the ground would not have substantially modified the surrounding environment, while it would introduced additional elements that could potentially amplify diffusion errors.
The shoe has been studied in a position parallel to the ground, a condition that occurs when the crank reaches approximately 110 degrees, considering the TDC (Top Dead Center) as the 0 position, in the pedalling cycle.
In the first simulation including the BOA dials, we obtained a drag force of 0.4505 N while in the second one, without the BOA dials, the drag force was 0.4011 N. The addition of two BOA dials to the shoe+ankle system resulted in a 0.05 N increase in drag force, a difference of 12% between the two scenarios. Since the environment we studied can be considered exhaustive of the influence of the BOA dials on the whole cyclist, we can generalize the influence of two shoes with 2 BOA dials each as an increase of 0.1N on the total drag force of a cyclist. Finally, we can consider the impact of the 4 BOA dials to be 0.33% of the total drag force, given that a medium cyclist riding at the simulation speed of 50.4 km/h in a standard position (not a time trial posture) experiences a drag force of approximately 30 N.
This research is based on some simplified assumptions, such as using a frontal wind, a single position of the shoe, and not considering the velocity of the shoe as it rotates around the bottom bracket, creating a relative wind. A lateral wind would probably influence the results by increasing the difference in drag of the shoes on the wind-facing side and reducing the drag on the opposite side. The influence of the slight inclination of the shoe in other positions along the pedaling cycle is, in our opinion, less significant. Finally, the relative wind of the pedaling rotation, supposing a cadence of 100 rpm, will generate a tangential velocity of 1.8 m/s with only minor and anyway opposite influences at 0 and 180 degrees. Nevertheless, we consider that the results we obtained have a general meaning, showing the aerodynamic disturbance created by the BOA dials is not negligible, as it approximately increases the total drag of a cyclist by 0.33%.
A workflow simulation requires a geometry that includes only essential sharp angles to provide an optimal mesh. Therefore, a 3D scanner that would have indiscriminately duplicated the shoe without discerning critical components from those that may be simplified or omitted to enhance the simulation has not been utilized. For this reason we choose to reproduce the shoe using Blender 3D computer graphics software.
The mesh has been constructed by seeking minimal values for skewness, orthogonality, aspect ratio, and growth rat e. To model the region close to the wall where the friction of the wall affects the flow of the fluid, 12 boundary layers are introduced, and we have placed the first cell center at a small distance from the wall (Y+ < 1), the so-called Low-Reynolds number modeling.
OpenFoam, a CFD opensource code, has been used for the simulation. It is assumed that there is no crosswind and that the cyclist is moving at a speed of 14 m/s (50.4 km/h). An unsteady simulation and a k-ω SST turbulence model have been employed, applying a turbulence intensity of 1%. We initially used the potentialFoam solver, assuming the flow to be incompressible, irrotational, and inviscid and with vorticity uniformly zero, to obtain an initial solution. Since the initial transient is of no interest, a steady simulation has been used to initialize the flow. Before switching to a second-order discretization scheme, a first-order discretization scheme was used. Subsequently, we proceeded to the PISO (Pressure-Implicit with Splitting of Operators) solver, a pressure-based algorithm designed for transient simulations of incompressible flows, utilizing a second-order discretization scheme. We have constrained our time-step to a maximum CFL number of 0.9. During the simulation we constantly sdf checked that the minimum and maximum values of the field variables don`t oscillate or diverge to unrealistic values and that the continuity errors are decreasing. We assessed the steps continuity errors and the minimum and maximum values of the field variables throughout the simulation. In order to assess convergence we monitor residuals, flow field and scalar fields, keeping in mind that we are analyzing an unsteady flow.
Streamlines colored by their velocity magnitude depict the generation of vortices behind both BOA dials.
Side view of the shoe with streamlines passing over and around the BOA dials and generating vortices.
From this pressure rapresentation we can detect a high pressure zone in the frontal side of the two BOA dials and a low pressure zone on the rear side of the BOA dials.
Unear, defined as the flow velocity at 1mm from the surface of the shoe, results close to zero in the frontal area, where the pressure on the BOA dials is maximal. Laterally, the velocity grows rapidilly and then slows down posteriorly, as it is even more evident in the next image.
In the BOA dial closer to the ankle, the low velocity area behind the dial is very large and extends in its length toward the posterior end of the shoe.
An image with a lic representation with the velocity magnitude color-code. Line integral convolution (LIC) is a method to visualize a vector field, in our image it shows the movement of the fluid 1mm from the surface of the shoe.
A close-up of a lic image showing a planar slice of the frontal BOA dial. The vortices on the rear side of the dial are clearly visible.
The following image shows a lic representation with the velocity magnitude color-code from the two simulations. The left image represents the side view of the shoe with the BOA dials. The right one shows the shoe without the BOA dials where the flow is not disturbed by the two dials.
The vortical flow structures around the two types of shoe are visualized by the iso-surface of the Q-criterion and colored by the velocity magnitude. Vortices located posterior to both BOA dials are evident in the left image.
