# Aerodynamic drag between two cyclists: OverPressure push and effect of wheel rotation

Sébastien Terol, Antony Costes, Sébastien Ricciardi, Emmanuel Brunet, Georges Soto-Romero

► To cite this version:

Sébastien Terol, Antony Costes, Sébastien Ricciardi, Emmanuel Brunet, Georges Soto-Romero. Aerodynamic drag between two cyclists: OverPressure push and effect of wheel rotation. Results in engineering, 2025, 26, pp.105487. 10.1016/j.rineng.2025.105487. hal-05093973

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Submitted on 2 Jun 2025

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# Aerodynamic Drag Between Two Cyclists:
OverPressure Push and Effect of Wheel Rotation

Sébastien Térol<sup>ab*</sup>, Antony Costes<sup>a</sup>, Sébastien Ricciardi<sup>a</sup>, Emmanuel Brunet<sup>c</sup>, Georges Soto-Romero<sup>b</sup>

## Abstract

Based on previous scientific findings about Computational Fluid Dynamics (CFD) modeling of rotating wheels and the aerodynamic interactions between two cyclists riding one behind another, this article aims to compare and combine the effect of both parameters. The aerodynamic drag of two identical models of female track cyclists was simulated in static and with simulated wheel rotations through a validated CFD approach. Two sets of eleven simulations with and without wheel rotation at a wheel-to-wheel distance between the two bikes ranging from 5 centimeters to 5 meters were carried out. Results show that wheel rotation on an isolated cyclist model with his bike and equipment has a 3.6% larger drag than the same model without wheel rotation. Furthermore, at the usual wheel-to-wheel distance of 0.15m, two cyclists, one behind the other show a 4.3% drag reduction for the leading cyclist and 27.9% drag reduction for the trailing cyclist compared to an isolated one. The overall drag is higher with wheel rotation than without it but the gain from OverPressure Push (OPP) and drafting stays similar. These results suggest the implementation of wheel rotation and accurate 3D geometry in future CFD cycling models to make them more realistic.

## Keywords

Computational Fluid Dynamics
Wind Tunnel
Aerodynamic Drag
Track Cycling

<footnote><sup>a</sup> Direction de l'Innovation, ALTEN, Boulogne-Billancourt, France</footnote>

<footnote><sup>b</sup> LAAS-CNRS, Université de Toulouse, CNRS, INSA, Toulouse, France</footnote>

<footnote><sup>c</sup>French Cycling Federation, 78180, Saint-Quentin en Yvelines, France</footnote>

<footnote>* Corresponding author: sebastien.terol@alten.com ; sterol@laas.fr</footnote>
# 1. Introduction

Birds have learned to fly in group to reduce their aerodynamic drag [1]. Nowadays, inspired by this drafting strategy, humans are using cooperative drafting strategy in a different way to perform in cycling, marathon and other sports [2], [3]. It is well known that the greatest potential for improving a cyclist's speed lies in their aerodynamics. For professional track cyclists riding at a speed of around 18m/s (64.8km/h) in team pursuit and around 14m/s (50.4km/h) in time trial team, the aerodynamic drag force represents about 90% of total resistance [2]. Therefore, reducing the aerodynamic drag of a rider or group of riders is important for track cycling events. This reduction can be made by optimizing the cyclist's posture, the drafting tactics, and the equipment [4], [5], [6], [7], [8], [9], [10], [11], [12]. The aerodynamic drag force evaluation in cycling can be performed using wind tunnel measurements [13], [14], [15], [16], [17], [18], [19], [20], field methods [21], and digital simulations, most often referred to as Computational Fluid Dynamics (CFD) methods. CFD is a set of numerical methods allowing simulations of fluid dynamics problems. The equations involved are those of fluid mechanics, solved or approximated by numerical approaches using a finite volume decomposition. Once the model is validated, CFD becomes a reliable and relatively inexpensive tool to accurately study aerodynamic flows around cyclists [22].

Results from previous studies regarding drafting cyclists showed reductions down to 50% of drag compared to an isolated rider [10]. Moreover, Blocken et al. [21] studied the aerodynamic benefit for a leading cyclist due to the presence of a following cyclist based on static CFD simulations and wind tunnel measurements. Although the bike has not been modeled, it has been found that the trailing cyclist can provide a drag reduction of up to 2.6% for the leading cyclist because of the trailing rider's influence on the airflow. This effect was later confirmed by Defraeye et al. [23], who studied the aerodynamic drag of four cyclists in line for a team pursuit trial and showed a 3% decrease in drag force for the leader. A valid result for static cyclist model without the bike. However, a study performed by Barry et al. [10] in wind tunnel showed a significantly higher benefit of up to 5% from the presence of a trailing cyclist for the leading cyclist. This decrease of aerodynamic drag on the leading cyclist is caused by the pressure build-up on the front of the helmet of the second rider filling the low pressure behind the saddle of the leading cyclist [21], [23], [24], therefore resulting in a pushing force due to the presence of the second rider. This phenomenon is observed with either a car or a motorbike as the chasing object [13], [14]. This effect is coined as OverPressure Push (OPP) in this article.

Discrepancies between results in the above publications may be due to cyclist anthropometries, bicycles settings, and the precision of their respective 3D numerical reconstruction. In addition, the 3D model of the athlete is immobile, which is not the case for a human in a wind tunnel [9]. Another source of error could also be the lack of wheel rotation and pedaling movement modeling to represent real conditions faithfully. Indeed, results show that the drag area, $C_dA$, is 2.2% higher for an isolated static wheel than the
same wheel but rotating. For a full cyclist model, the $C_dA$ value is 0.5% to 2.9% higher with wheels rotation compared to a static model at a speed of 13.41m/s [25], [26], [27]. To our knowledge, no studies have combined wheel rotation and multiple models to more realistically study a leading cyclist's aerodynamic effects over a trailing one using CFD simulations.

Therefore, results from CFD and reduced models in wind tunnels [24] differ from those carrying out wind tunnel tests with athletes [9]. Those differences, as part of our hypothesis, could be explained by the impact of wheel rotation, accuracy of models and pedaling dynamics.

In this study, we will therefore analyze the aerodynamic interactions between two identical cyclists at variable wheel-to-wheel distances with and without rotating wheels. The aim is to analyze the impact of wheel rotation on the wake interaction between two cyclists and analyze the OPP effect using a realistic model from a 3D scan to match Blocken et al., Malizia et al., and Barry et al. results.
## 2. Input Data & Wind Tunnel Measurement.

The studied geometries were obtained via a 3D scan of one female athlete from the French track cycling team and her equipment (Figure 1a). The athlete was digitalized with the Freestyle 3D scanner (Faro, Lake Mary, USA) in her racing position on a static ergometer with hands and elbows on time-trial bars (Figure 1b). Her helmet was an Aerohead (Giro, Santa Cruz, USA) retro-engineered from the 3D scan's cloud point with the Blender (Blender Foundation, Amsterdam, Netherlands) open-source software. The same process was used for retro-engineering the T20 (Look, Nevers, France) frameset and for the Lenticulaire C+ (Corima, Loriol-sur-Drome, France) disc wheels.

<figure><img src="image_2.png" /><figcaption>Figure 1 - Illustration of the French track cycling elite athlete and the geometry studied from the 3D scan</figcaption></figure>

a) Elite athlete with her equipment in the IAT S4 wind tunnel

b) Numerical model of the athlete from the 3D scan with her equipment

The wind tunnel data were obtained at the S4 wind tunnel of the Institut Aérotechnique du Conservatoire National des Arts et Métiers (CNAM, St-Cyr-l'Ecole, France) which has an experimenting chamber of 5m width, 3m height, 10m length [28]. Ten measurements with a standard deviation of 1.3% were performed with the full-scale time trial bicycle T20 and the athlete on it wearing an Aerohead helmet. Turbulence intensity measured at the inlet was 1%. The wind tunnel speed was set at 18m/s, modeling the peak speed of the studied cyclist during a team pursuit trial. The bicycle was fixed on a platform allowing or not the wheel rotation. The wind tunnel measurements with the athlete on the bicycle were sampled at 100 Hz for 30 seconds.
## 3. CFD Simulation & Validation

The CFD simulations were performed with the open-source code OpenFOAM (Open-source Field Operation And Manipulation) with the 2206 version. OpenFOAM is a C++ toolbox for developing custom numerical solvers, including computational fluid dynamics. OpenFOAM includes a meshing tool named SnappyHexMesh and a solver. According to the solver, the k-omega-Shear Stress Transport Improved Delayed Detached Eddy Simulation turbulence model (kOmegaSSTIDDES) was used [29], [30], [31], [32]. Turbulence is modeled via Reynolds-averaged Navier-Stokes (RANS) equations in the near-wall zones and solved explicitly via an Large Eddy Simulation (LES) approach in the separation and wake zones. The transition between the RANS and LES regions is dynamically managed by the IDDES formulation, which uses a switching function dependent on wall distance, local mesh size and a separation detection criterion.

In this study, the 3D Modeling Software Blender (Blender Foundation, Amsterdam, Netherlands) has been used to move geometries, OpenFOAM meshing tool, and solver have been used for the numerical part and ParaView for the visualization.

### 3.1 Geometry & Domain

For CFD model validation, numerical simulations were carried out with geometries representing the cyclist and his equipment as faithfully as possible during wind tunnel tests. For practical reasons, the model's geometry has been split into several elements to allow their change or modification more easily. The geometry is broken down into four elements with a combined frontal area of 0.328m²: the front wheel, the rear wheel, the bike frame, and the body.

Two experiments have been performed. The first study is based on a grid convergence that aims to determine the size and the CFD domain's number of cells adapted to our research according to the computer resources available. According to the literature, the domain must meet some dimension requirements concerning the object [9], [33], [34]. Indeed, suppose *l*, *w*, and *h*, the characteristic lengths of our cyclist, are considered as our reference lengths for each axis. In that case, there must be 5*l* on the front, 5*w* on the left and right of our object, 6*h* over, and 15*L* downstream to eradicate edge effects which could falsify simulations (Figure 2).
<figure><img src="image_3.png" /><figcaption>**Figure 2 – Representation of the validation computational domain**
The geometry is represented by the (green) parallelepiped inside the fluid domain and facing the negative x axis</figcaption></figure>

But to compare CFD results with wind tunnel measurement, the second experiment has been realized with the same CFD domain size as the wind tunnel size (S4 dimension: 10mx5mx3m) with a blockage ratio of 0.5%. This validation study aims to validate the mathematical model used and the correct configuration of the CFD simulation. Therefore, both processes must fulfill the same conditions to compare the CFD and Wind Tunnel results. Subsequently, a last CFD analysis with the CFD dimension requirements is here to compare and discuss the model validation process.

**3.2 Computational Grid & Grid Convergence**

On OpenFOAM, the domain’s creation goes through the BlockMeshDict tool. It allows us to define the overall mesh size of the domain according to the dimensions of it (Error! Reference source not found.). The domain was therefore divided into 136 cells in length, 36 in width, and 32 in height to obtain cubic cells with a size of 0.25m. Next, the meshing step around the geometry is calculated using the SnappyHexMesh tool from OpenFOAM. It subdivides every cell according to the recommendation coming from the law of the wall.
<figure><img src="image_4.png" /><figcaption>**Figure 3 – Computational domain**

*Screenshot from Paraview Software of the computational domain with the geometries inside it*</figcaption></figure>

To validate the study's grid and verify the results consistency, it is necessary to perform a mesh grid dependence analysis to determine the ideal parameters. The objective is to perform several simulations of our model, from a coarse to a fine-resolution mesh, and compare the results. The more the mesh is refined, the lower the difference between the solutions is. This grid convergence aims to set a meshing method adapted to our model. In our study, it was decided to achieve mesh convergence with our static model and our model with wheel rotation. The wheel rotation is made by using the Multiple Reference Frame (MRF) method. The results in both cases are consistent and follow the same convergence **(Figure 4)**. It was decided to utilize a mesh of approximately 30 million cells because meshes with fewer cells cannot accurately model the narrow space between the wheels and the bike frame, which becomes problematic when the wheels are rotating.
<figure><img src="image_5.png" /><figcaption>Figure 4 – Grid convergence results</figcaption></figure>

Convergence of the MRF and static model as a function of different meshing methods. Each point corresponds to a simulation with a specific mesh.

With such complex geometry including the bike, the SnappyHexMesh tool does not manage to insert the totality of the boundary layers. The overall average thickness is 99.6% of the expected boundary layer over the model. The boundary layers have been set to have ten layers and an expansion ratio of 1.2 between each layer, which leads to a theoretical first cell size of $1.8 \times 10^{-4}m$ adjacent to walls (Figure 5). In addition, refinement boxes have been positioned around the object to better capture the flow's movements around the object and in its wake. Therefore, all these parameters constitute the mesh for a total number of cells of about 30 million.

<figure><img src="image_6.png" /><figcaption>Figure 5 – Validation Mesh</figcaption></figure>

Zoom on the validation simulation mesh created by the SnappyHexmesh tool from OpenFOAM.
### 3.3 Solver Settings & Boundary Conditions

The Semi-Implicit Method for Pressure Linked Equations (SIMPLE) FOAM algorithm from OpenFOAM has been used for the simulations. It is a steady-state solver for incompressible and turbulent flow. The strategy is to solve the equations sequentially so that the solution of the preceding equations is inserted in the following equation [35]. OpenFOAM kOmegaSSTIDDES model has been used for the turbulence model with a turbulent intensity of 1% to match the wind tunnel parameters. The simulation was fixed with a total of 2000 iterations for the solver to converge and provide accurate results. The residual relative tolerance was fixed at 0.1 for the variables, and the average value during the iterations was $4.8 * 10^{-5} \pm 4.5 * 10^{-6} m.s^{-1}$ for velocity, $6.4 * 10^{-5} \pm 1.4 * 10^{-5} Pa$ for pressure, $3.7 * 10^{-5} \pm 1.4 * 10^{-6} m^2.s^{-2}$ for turbulent kinetic energy k and $3.6 * 10^{-6} \pm 1.2 * 10^{-6} s^{-1}$ for the specific dissipation rate $\omega$.

At the inlet, a speed of 18m/s is imposed along the increasing x-axis. The ground and the body of the cyclist and his equipment have been modeled with a non-slip condition. In other words, the speed at the wall is zero. As for the pressure, a zero-static pressure at the outlet has been imposed, and a zeroGradient condition for the rest. Regarding the quantities of k, omega, and nut (turbulent viscosity), the basic wall functions were imposed on the geometry and the ground.

Finally, to rotate the wheels, the MRF method was used to avoid mesh deformation. The parameterization of the MRF is carried out through the “MRF_Propertics” file, in which it is necessary to indicate the location of the zone and its rotation speed. The rotation speed is calculated from the reference speed of 18m/s and the exact diameter of each wheel. In contrast, the rotation area has been precisely set around each wheel by imposing a non-rotation of the bike frame. This velocity (1) will be implemented into the steady incompressible Navier-Stokes equations (2).

$$ \vec{U} = \vec{U}_r + \vec{\Omega} \cdot \vec{r} \qquad (1) $$

Where U is the global velocity, $U_r$ is the velocity relative to the wheel, r is the distance vector $r = x_{cell} - x_{center}$

$$ \left\{ \begin{array}{l} \nabla \cdot (\vec{U} \otimes \vec{U}) = -\frac{1}{\rho} \nabla p + \nu \nabla \cdot \nabla (\vec{U}) \qquad (2) \\ \\ \nabla \cdot \vec{U} = 0 \end{array} \right. $$

After some math derivation, solutions (3) and (4) can be obtained. In our case, as only the wheels are rotating, the solver will use the multiple reference frame solution. The solver will apply the source term $\Omega \cdot U$ in the rotating regions defined by the delimitation zones (Figure 6) but not in the stationary regions.
$$ \left\{ \begin{array}{l} \text{Single reference:} \\ \nabla \cdot (\vec{U}_r \otimes \vec{U}_r) = -\frac{1}{\rho}\nabla p + \nu \nabla \cdot \nabla (\vec{U}_r) - \vec{\Omega} \cdot \vec{\Omega} \cdot \vec{r} - 2\vec{\Omega} \cdot \vec{U}_r \\ \nabla \cdot \vec{U}_r = 0 \end{array} \right. \qquad (3) $$

$$ \left\{ \begin{array}{l} \text{Multiple reference:} \\ \nabla \cdot (\vec{U}_r \otimes \vec{U}) = -\frac{1}{\rho}\nabla p + \nu \nabla \cdot \nabla (\vec{U}) - \vec{\Omega} \cdot \vec{U} \\ \nabla \cdot \vec{U} = 0 \end{array} \right. \qquad (4) $$

<figure><img src="image_7.png" /><figcaption>Figure 6 – MRF zones delimitation</figcaption></figure>

The MRF zones are cylinders, a few millimeters larger by diameter than the wheels, closely positioned around the wheels to encompass them

## 3.4. Validation Result

To compare CFD result data with results from the wind tunnel test, we must first examine the effect of rotation wheels. Two CFD simulations were realized with and without the MRF method. As one can read in the literature, the wheel rotation increases the drag on the global geometry [25], [26], [27]. In the simulation carried out, this increase amounted to 4.0%, a significant result given that the uncertainty of the CFD simulation is between 0.5% and 1%. Beyond this increase, a post-processing visualization has been carried out (Figure 7 & Figure 8) showing the impact of the wheel rotation on the airflow.
Drag in the CFD simulation is 1.2% higher in static and 3.3% higher with MRF than wind tunnel values. This is considered acceptable according to previous studies [17], [25]. This confirms this study's correct choice of turbulence model and solver settings.

<figure><img src="image_8.png" /><figcaption>Figure 7 – Speed Streamlines comparison with and without MRF from above</figcaption></figure>

In this figure, streamlines come from a vertical zone with -0.001m < y < 0.001m.

a) Top view streamlines visualization of CFD results with static model

b) Top view streamlines visualization of CFD results with rotating wheels method (MRF)

<figure><img src="image_9.png" /><figcaption>Figure 8 – Speed Streamlines comparison with and without MRF</figcaption></figure>

In both cases, the streamlines come from a vertical line at y=-0.001m.

c) Streamlines visualization of CFD results with static model

d) Streamlines visualization of CFD results with rotating wheels method (MRF)
# 4. CFD Simulations – part II: Parametric Analysis

## 4.1. Strategy & Computational geometry

Eleven simulations were carried out with the same geometry model for each. The resulting geometry from the validation stage was used to study the aerodynamic interactions between two cyclists, one behind the other. The first geometry has been positioned similarly to the previous study and will remain stationary for all simulations. The second geometry, identical to the first, will be translated in the flow direction at each simulation. Thus, the 11 simulations correspond to a spacing variation between the two cyclists from 5cm to 5m for a distance d of 0.05, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.75, 1, 2, and 5m (Figure 9).

<figure><img src="image_10.png" /><figcaption>Figure 9 – Wheel-to-wheel distance illustration</figcaption></figure>

It is important to know that the minimum distance of 0.05 m corresponds to a very difficult distance to achieve in race conditions because the slightest error can be dramatic at this distance and speed. The usual wheel-to-wheel distance can go up to 1m in field conditions. Therefore, most spacing values are in this range. While for values greater than 0.5 m, the aim was to study how far the drafting and OPP effects remain prevalent.
## 4.2. Computational Settings & Parameters

The eleven simulations were carried out with an identical domain size with an inlet area of 12m² for a total length of 20m. Geometry number one was placed in the same position as for the validation study, which is two times its length from the inlet. In the presence of both geometries, the total number of cells varies around 60 million cells. The blockage ratio is 0.5%, which is well below the recommended value of 3% [36], [37].

The boundary conditions are the same as for the validation study. A speed of 18m/s is imposed at the inlet along the increasing x-axis with a turbulent intensity of 1%. A non-slip condition has modeled the ground and geometries. A zero-static pressure at the outlet has been imposed, and a zero Gradient condition for the rest. The complete set of simulations has been realized with and without the MRF method with a rotational speed based on the 18m/s flow speed and a non-rotation condition on the bike.

For all simulations, solver configuration parameters are identical to those used during the grid convergence study in Section 3.3. Results visualizations are displayed in **Figure 10**.

<figure><img src="image_11.png" /><figcaption>**Figure 10 – Speed streamlines visualization from two points of view**</figcaption></figure>

a) Streamlines are applied on a surface corresponding to the frontal area of the cyclist with a 40% opacity

b) Top view: Streamlines are applied on a 0.2m diameter semi-circle starting from the ground to capture wheel rotation effects.
4.3. Results: Drag of Two Cyclists with rotating wheels

Once the eleven simulations with rotating wheels were completed and the data analyzed, several
observations were retained:

(1) By comparing the drag value of the two cyclists with rotating wheels, for a spacing distance of 5m, the first cyclist has a drag value similar to the study with a single isolated cyclist. In contrast, the second cyclist sees its drag value reduced by 16.8%. This drag difference between the two cyclists is due to the drafting effect. So even with a spacing distance of 5m, the Drag reduction on the second cyclist is not negligible. It corresponds to 112W of savings compared to the case where it would be isolated. Indeed, for an input speed of 18m/s with a density of 1.225, the power developed by the isolated cyclist amounts to 670W.

(2) By listing all the drag values of the trailing cyclist, according to the different simulations, it becomes possible to see that the drag reduction is related to the spacing between the two cyclists. **Figure 11a** highlights this evolution. The first drag value for a spacing of 5m amounting to 31.1 N, and the last drag value for a spacing of 0.05m amounting to 26.4 N. Between these two spacings 5m and 0.05m, the drag value decreases by 15.2%.

(3) This observation is based on the drag results listed in the diagram of **Figure 11b**. Although the drag reduction curve is not as evident as the previous observation, the same reduction phenomenon is still observed. Indeed, for the leading cyclist, despite the lack of solid moving in front of her, thus the lack of drafting effect, we find a decrease of 5.4% between the cases of spacing 5m and 0.05m. Knowing that the standard deviation on the drag value is about 1% of the value, it is undeniable that the presence of a second cyclist benefits the first one as well.
<figure><img src="image_12.png" /><figcaption>Figure 11 – Drag evolution according to wheel-to-wheel distance between both cyclists</figcaption></figure>

a) Second cyclist drag evolution

b) First cyclist drag evolution

**4.4. Results: Comparison of the static and rotating wheel models**

According to the previous results, the eleven static simulations were analyzed and compared to the eleven MRF simulations to test the wheel rotation hypotheses (Figure 12). This set of simulations aims to determine the impact of the wheel rotation according to the wheel-to-wheel distance. On an isolated cyclist, the MRF model's drag increase compared to the static model is about 3.6% ± 0.8%. With two cyclists, one behind the other, this drag increase for the leading cyclist is 4.4% ± 0.9%, and for the trailing cyclist 3.6 ± 2.1%.
<figure><img src="image_13.png" /><figcaption>**Figure 12 – Drag difference between rotating wheel model and static model**</figcaption></figure>

*A positive value means that the rotating wheel model has a higher drag than the static model.*

By confronting the static and rotating wheels model, drag results show that the two models follow the same trend for the leading cyclist (Figure 13) as well as the trailing cyclist (Figure 14). Therefore, the difference between the static and dynamic models is approximately the same. However, we note that the drag gain for the second cyclist (Figure 14) is about 16.8% with wheel rotation and 19.9% without wheel rotation at a wheel distance of 5m. As the wheel-to-wheel distance becomes smaller, the drag reduction increases for both models and at a wheel-to-wheel distances of 10cm and 5cm, the gain with MRF is around 29.3%, while that for the static case is 26.9%. For the leading cyclist, the gain is not as pronounced but at certain wheel-to-wheel distances, results show that the gain is greater with MRF model than with the static one.

<figure><img src="image_14.png" /><figcaption>**Figure 13 – Percentage gain of the leading cyclist's drag with a trailing cyclist**</figcaption></figure>

*This graphic represents the gain in % of the first cyclist compared to an isolated cyclist with and without rotating wheels.*
<figure><img src="image_15.png" /><figcaption>Figure 14 – Percentage gain of the trailing cyclist's drag with a leading cyclist</figcaption></figure>

*This graphic represents the gain in % of the second cyclist compared to an isolated cyclist with and without rotating wheels*
## 4.5. Results: Pressure distribution

From the results of the simulations, other elements can be analyzed. This is the case of the pressure coefficient found in **Figure 15** on a cut plane in the lateral and top views. The static pressure coefficient Cp is defined by:

$$C_p = \frac{p - p_\infty}{\frac{1}{2} \rho_\infty V_\infty^2}$$

Where p is the static pressure, $p_\infty$ is the static pressure in the freestream, $\rho_\infty$ is the freestream fluid density and $V_\infty$ is the freestream velocity of the fluid.

In the simulations carried out, $p_\infty$, $V_\infty$ and $\rho_\infty$ are fixed imposed values, it is then possible to determine $C_p$ knowing p using the CFD calculation. While the pressure coefficient $C_p$ allows for a normalized comparison of pressure effects on the surface, a direct visualization of the pressure field provides essential insight into the absolute pressure levels and gradients that drive the aerodynamic forces. Thus, the Figure 15 and Figure 16 were obtained, and the following observations were made:

(1) When comparing the different spacing configurations, the low-pressure region in the wake of the leading cyclist evolves significantly with the distance to the trailing cyclist. As the second cyclist moves closer, this wake depression tends to decrease in both size and intensity due to frontal overpressure zone of the trailing cyclist. The most decisive change in aerodynamic behavior is not only due to the upstream pressure disturbance. Instead, it is the viscous interaction between the turbulent wakes and the modification of the pressure field within the wake that predominantly governs the evolution of the wake drag. In particular, the leading cyclist benefits from a compression of their wake caused by the presence of the trailing cyclist, which results in an increase in base pressure and consequently a reduction in drag.

(2) For the second cyclist, a reduction in the size and magnitude of the frontal overpressure zone is observed. This phenomenon arises from the interaction between the wake depression of the leading cyclist and the frontal overpressure of the trailing cyclist. These two regions overlap and partially cancel each other, leading to a more favorable pressure distribution. In addition to the wake shielding effect, the trailing cyclist benefits from a locally slowed and less energetic flow, resulting in a reduced pressure gradient and hence lower aerodynamic drag.
<figure><img src="image_16.png" /><figcaption>Figure 15 – Results visualization of pressure coefficient applied on the two-cyclist based on their wheel-to-wheel distance</figcaption></figure>

The drafting effect has an impact on the pressure coefficient. On this figure, this impact is compared according to
the wheel-to-wheel distance varying from d=0.05m to d=5m

$(d \in [0.05, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.75, 1, 2, 5])$

This Figure shows a zoom of a slice along the y normal axis on the left and along the z normal axis on the right
<figure><img src="image_17.png" /><figcaption>Figure 16 – Results visualization of pressure field slice at y=0 for two different wheel-to-wheel distance</figcaption></figure>

a) CFD simulation at 1 m wheel-to-wheel distance

b) CFD simulation at 0.2 m wheel-to-wheel distance
**5. Discussion**

The impact of rotating wheels on drafting gains or OPP had not been previously investigated simultaneously. The results from these CFD simulations allow us to analyze the interaction between two cyclists. The addition of wheel rotation provides a drag modification for the trailing cyclist as well as the leading cyclist.

At 65 km/h, validation results show a drag increases by around 3.6% when wheels are rotating for a cyclist alone, which matches the results obtained by Malizia [25], [26], [27]. This increase in drag force corresponds to an increase in local turbulence. In the case of disc wheels, rotation locally increases surface velocities, resulting in greater skin friction drag. Furthermore, the proximity of the wheels to the frame at the rear and the fork at the front suggests that the introduction of radial velocity may cause disruption to the flow in these sensitive areas. As for a group of two cyclists one behind the other, as demonstrated in Figures 13 and 14, wheel rotation also exerts an influence on drafting. For the leading cyclist, the results demonstrate that wheel rotation facilitates a greater reduction in overall drag than in the static case for wheel-to-wheel distance of less than 20cm. In the case of the trailing cyclist, it is observed that the aerodynamic gain is less significant in the dynamic case than in the static case when the two cyclists are at a wheel-to-wheel distance of 2m or 5m. It is hypothesized that the turbulence engendered by the leader may disrupt the aerodynamics of the following cyclist. In contrast, Figure 14 demonstrates that for a wheel-to-wheel distance of less than 20 cm, the opposite is true: the following cyclist experiences a superior aerodynamic gain with wheel rotation in comparison to the absence of rotation. As demonstrated by streamline visualizations, wheel rotation generates a moment in the air, thereby creating a circular velocity zone around the wheel which potentially stabilizes the wake behind locally, allowing the following cyclist to benefit from it and reduce his drag [38].

Independently of the wheel rotation, results show that the leading cyclist's drag decreases as the second one gets closer, with a maximal gain for static simulation of around 4.2% when a trailing cyclist is 5cm behind. These numbers are similar to Blocken et al. (2013) [21], who showed a gain of drag of around 2.6%. The higher results from our study may be explained by a greater air speed (15 m/s in Blocken study, against 18 m/s here), the presence of the bike and the precise geometry from the 3D scan. With the wheel rotation, the simulation shows a maximum value of 5.2% drag reduction for the leading cyclist with a trailing cyclist 5cm behind. The results are also close to Barry et al. (2015) [9] wind tunnel testing values, which were around 5% of drag reduction for the leading cyclist. Besides, gains are higher in MRF simulations than in static ones. It seems that certain wheel-to-wheel distance configurations allow the MRF model to provide better drag gain. It is therefore possible that, depending on the turbulence generated by wheel rotation of the leading cyclist, there may be an ideal distance or position for the trailing cyclist to reduce drag. It would
be interesting to carry out a similar study by moving one of the two cyclists on the lateral axis in order to
add another parameter and obtain results that could lead to the ideal positioning of one cyclist in relation to
the other in order to benefit from better drafting or better OPP effect.

In aerodynamics, the position and morphology of the cyclist play a crucial role, which is why it would
have been interesting to rely on different geometries based on the morphology of other athletes to determine
if it impacts the OPP. The frontal area and $C_dA$ of different cyclists should be measured in a wind tunnel,
then compared to the projected frontal area of the 3D models numerically measured. Is there a correlation
between the frontal area of the downstream cyclist and the OPP gains for the leading one? We can
reasonably assume that the taller and more prominent the trailing cyclist is, the bigger the pressure build-
up at the front will be and, therefore, the greater the OPP will be. This will be the subject of future research.

This study analyzed the aerodynamic evolution of two cyclists using different methods. The current
team pursuit consists of four cyclists from the same team behind each other. It is possible to extend this
study to four cyclists with different morphologies to go further in the analysis. Such a study would allow
teams to optimize their starting arrangement, considering the OPP of each possible pair of {1st+2nd rider}.
It will then be possible to define an optimized relay order for the entire race based on the $C_dA$ of each
athlete. A method that can also be used in team time trials.

Despite consistent results, this study encounters several limitations ranging from the geometry used to
the computing power. The geometry used, although faithful to reality, was scanned in 3D and then
reconstructed under 3D modeling software. This reconstruction may have led to minimal differences
between the real athlete and his equipment. In addition, the two cyclists are identical and motionless in this
study. Only wheel rotation has been implemented. We can also assume that wheel rotation with a different
bike or wheels would affect the aerodynamic wake of the cyclist. Moreover, with wheel rotation, pedaling
movements are the main movements a cyclist generates that can affect the aerodynamic flow. Therefore,
the lack of pedaling movement can be discussed and future study could be carried out implementing a
numerical pedaling cyclist to the CFD simulation [39], [40]. Future studies could also investigate the effects
of yaw angle on the drafting and the OPP effect to represent as faithfully as possible velodrome conditions.
As far as the configuration of the simulation is concerned, such geometries combining precision and
complexity make the meshing task complicated. It was, therefore, necessary to set up a suitable mesh while
considering the computational power limits. With the approximations and model choices made for this
study, the results obtained are utterly consistent with those from wind tunnel and other studies [17], [24],
[25]. The drag results obtained during the validation stage have a variation rate compared to wind tunnel
values of less than 5%. As for the drafting study, with two identical copies of one real athlete, it cannot be
tested. Hence, it is based on the validation of the model of an isolated cyclist and uses the same simulation
settings. Regarding wind tunnel measurements, it is noteworthy that only measurements at 65 km/h were
conducted. However, in a drafting configuration, the trailing cyclist perceives a decrease in the velocity of
the flow due to the presence of the leading cyclist. To validate the results, it would have been interesting to
study local flow velocity variations, to carry out wind tunnel measurements at different speeds to match the
flow speeds encountered by the second cyclist. In addition, the wind tunnel supports for the bike was not
modelled in CFD.

The CFD simulation of two identical cyclist models following each other provides additional
information about aerodynamic interaction between them such as drafting and OPP. Wheel rotation
modeling affects the aerodynamics interactions between the leading and the trailing cyclist.
## 6. Conclusion

This article presents a complete analysis of the drag of two simulated cyclists, one behind the other with and without wheel rotation and a wheel spacing ranging from 0.05cm to 5m, for eleven different spacings. A total of 2x11 CFD simulations were performed with the 3D kOmegaSSTIDDES equation model. The simulation model was validated by comparing the CFD drag results with those obtained in wind tunnels. Concerning the wheel rotation, the MRF method generates a drag increase of up to 3.6% compared to the static one. Compared with a static case, wheel rotation has a significant impact on the aerodynamic interaction between two cyclists. When the two cyclists are less than 20cm wheel-to-wheel, wheel rotation brings a greater draft benefit of 1.4% to the second cyclist than in the static case. Conversely, beyond 1m, wheel rotation decreases this aerodynamic gain by 3.2%.

Two beneficial aerodynamic effects govern a cycling configuration paceline of two riders: first, the well-known drafting effect, whereby a trailing rider experiences less drag due to its presence in the wake of the leading cyclist. Then, the lesser-known subsonic upstream disturbance on the second cyclist generates an OverPressure Push on the downstream part of the leading rider.

The modification in the wheel-to-wheel distance results in a meaningful change in the drag value of the trailing cyclist. The results of this study highlight the presence of a drafting effect of up to 5m spacing between two cyclists. At 5m distance, a 16.8% reduction in the drag value was noted. At a spacing distance of 0.05m, this reduction amounts to 29.3%. For a wheel-to-wheel distance of 0.15m, which corresponds to an average trailing distance in racing, the drag reduction is 27.9%, which is a loss of 1.4% compared with a 0.05m spacing.

As for the leading cyclist, the study confirms a drag reduction due to the presence of a trailing cyclist. At a spacing distance of 5m, the effect is not identifiable and remains insignificant; at 0.05m, the drag reduction is 5.2%. For a more common distance of 0.15m, this reduction is still 4.3%. This demonstrates the significant benefit of a close formation of cyclists, one behind the other, for the whole group to save energy. Results recommend implementing wheel rotation in CFD simulation if there is aerodynamic interaction between at least two cyclists to have a better representation of drafting and OPP effect. The closer the cyclists are to each other, the greater the OPP effect.

The results of previous static simulations, therefore, underestimate the gain in drag that the rotation of the wheels generates on the drafting and OPP. This study highlights that the addition of the rotational movement on the wheels significantly impacts the drafting studies' results.
## 7. Acknowledgements

The authors would like to thank the French Cycling Federation for its cooperation in the present work.
The authors would also like to express a special thanks to the athlete who was digitalized.
The Wind Tunnel team of the Institut AéroTechnique (IAT, Le Cnam, 15 rue Marat 78210, Saint Cyr-l'école) for the wind-tunnel measurements are gratefully acknowledged.

## 8. Statements and Declarations

**Conflict of interest:** The authors declare that they have no conflict of interest.

**Funding:** First author received a CIFRE thesis funding (N. 2022/1391) by the ALTEN SA company and the Association Nationale de la Recherche et de la Technologie (ANRT).

**Ethic Statement:** This study was conducted in accordance with the principles outlined in the Declaration of Helsinki. Written informed consent was obtained from the athlete for the publication of anonymized information related to their participation in this research. No personally identifiable data are disclosed in this article.
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