# Aerodynamic challenges in running: Understanding headwind and tailwind effects

Fabien Beaumont, Guillaume Polidori

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Fabien Beaumont, Guillaume Polidori. Aerodynamic challenges in running: Understanding headwind and tailwind effects. International journal of Sports Science and Coaching, 2025, 10.1177/17479541251333944. hal-05046298

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Research note

# Aerodynamic challenges in running: Understanding headwind and tailwind effects

International Journal of Sports Science
& Coaching

2025, Vol. 20(3) 1259–1267

© The Author(s) 2025

Article reuse guidelines:

sagepub.com/journals-permissions

DOI: 10.1177/17479541251333944

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Sage

Fabien Beaumont¹ ID and Guillaume Polidori¹ ID

## Abstract

The primary objective of this study was to assess how wind affects metabolic cost of running. A numerical method was employed to investigate aerodynamic forces acting on a runner at three different running speeds (10, 15, and 20 km/h) while experiencing five headwind and tailwind speeds (ranging from 0 to 30 km/h). Additionally, a mathematical model was used to estimate aerodynamic and metabolic power based on both runner and wind speeds. Insights from the numerical investigation highlighted how wind conditions, including speed and direction, alter the turbulent wake behind the runner, ultimately affecting metabolic power requirements. While a 30 km/h tailwind leads to a modest 9% reduction in energy expenditure, a headwind of the same speed results in a substantial 37% increase. In practical terms, running at 13.7 km/h against a 20 km/h headwind imposes the same metabolic demand as running at 19.4 km/h with a 20 km/h tailwind. Furthermore, considering an out and back course, temporary tailwind advantages do not sufficiently offset headwind effects. Thus, this study underscores the critical need for runners to consider weather conditions, especially wind, to effectively manage energy expenditure and optimize performance in competitions or training sessions.

## Keywords

Computational fluid dynamics, drag, metabolic power, running, turbulence

## Introduction

Whether you're an occasional runner, an experienced amateur, or a world-class runner, wind plays an important role that cannot be ignored. It's crucial to distinguish between favourable winds, like a tailwind that propels the runner forward, and unfavourable winds, such as a headwind that directly impedes progress. Typically, in training or competition, encountering a headwind on one stretch often means benefiting from a tailwind on the return route. The fundamental question revolves around understanding how wind, whether beneficial or adverse, affects a runner's performance.

Wind directly affects performance by influencing the balance of aerodynamic forces. This effect is particularly pronounced in cycling, where aerodynamics significantly influence performance.¹⁻⁵ On a flat road, aerodynamic drag constitutes the predominant obstacle to a cyclist's speed, contributing until 90% of total resistance.⁶ In both sprint running⁷⁻⁹ and long-distance running,¹⁰ aerodynamics can play an important role though not as critical as in cycling.

Classic studies from the 1970s and 1980s provide insight into the effects of aerodynamics on long-distance running performance. Two pivotal studies provide significant clarity. In the first, Pugh¹¹ employed a treadmill within a wind tunnel

to measure a runner's oxygen consumption across different speeds and wind conditions. Pugh observed that "oxygen consumption, and thus energy expenditure, increases with the square of the airflow over the body." Simply put, running against the wind intensifies effort, with stronger winds exponentially amplifying the challenge.

In the second study performed by Davies,¹² similar methodology was applied to explore headwind and tailwind effects on three runners. Davies confirmed that running into a headwind escalates oxygen consumption, thereby diminishing performance. Conversely, a tailwind can notably enhance performance, yet this benefit fails to fully offset the headwind's adverse influence on the return. Davies

Reviewers: Rodger Kram (University of Colorado, Boulder, USA)
Prashant Pujari (University of California, Berkeley, USA)

¹Université de Reims Champagne-Ardenne, Institute of Thermal, Mechanical, and Materials Engineering ITheMM, Reims, France

**Corresponding author:**
Fabien Beaumont, Université de Reims Champagne-Ardenne, Institute of Thermal, Mechanical, and Materials Engineering ITheMM, Moulin de la Housse, CEDEX 2, 51687 Reims, France.
Email: fabien.beaumont@univ-reims.fr
estimated the energy expenditure of overcoming air resistance in calm outdoor conditions at 7.8% of total energy for sprinting (36 km/h), 4% for middle-distance running (21.6 km/h), and 2% for marathon running (18 km/h). Although aerodynamic drag in running is less than in cycling, it remains a significant performance factor. This study aims to contribute to the scientific literature by addressing the gap concerning wind effects on running.

The objective of this research is to analyze how different wind conditions (headwinds and tailwinds) affect the aerodynamic forces experienced by a runner. Employing a Computational Fluid Dynamics (CFD) method, we examined three running speeds and five wind speeds from opposing directions (headwind and tailwind). The findings provide insights into how wind affects metabolic power as a function of running speed.

# Methods

## Problem definition and computational setup

Figure 1 provides a schematic representation of the problem under study and the runner's geometry, which was generated by scanning a scaled-down mannequin in a running posture.¹³ The three-dimensional model represents a static male runner (1.65 m, 56 kg) with a frontal area of 0.475 m², as reported by Polidori et al.¹⁰ The runner's body surfaces were modelled as no-slip surfaces with an equivalent sand-grain roughness height of $k_s = 0.1$ mm, based on wind tunnel roughness measurements for cycling clothing made of elastane.¹⁴ Running speeds of 10, 15, and 20 km/h were selected, representing occasional, moderately trained, and elite marathon runners, respectively.¹⁵ Wind conditions included no wind, headwinds, and tailwinds ranging from 5 to 30 km/h in 5 km/h increments.

## Boundary and turbulence modeling

For both headwind and tailwind scenarios, simulations were conducted using ANSYS Fluent 2023R2®. The Navier-Stokes equations were solved in their Reynolds-averaged (RANS) form to model momentum conservation. Turbulence was modelled using the $k-\omega$ shear-stress transport (SST) formulation,¹⁶ which has demonstrated superior performance in scenarios with adverse pressure gradients and free shear layers.¹⁷ This approach has proven effective for external aerodynamics, outperforming the Spalart-Allmaras and $k-\epsilon$ models in similar conditions. Defraeye et al.¹⁸ further validated the $k-\omega$ SST model's accuracy, showing average discrepancies of 6% and consistently below 11% when compared to wind tunnel data.

The runner model assumed a stationary posture, as Crouch et al.¹⁹ showed limb motion has negligible influence on instantaneous drag in cycling aerodynamics. A moving ground boundary was implemented to match the running

speed, preventing boundary layer formation. Dirichlet boundary conditions were applied to the velocity components at the ground, ensuring a fixed velocity profile. The surrounding walls were treated with Neumann conditions, assuming a frictionless symmetry boundary to prevent shear stress effects. The pressure outlet boundary condition was defined as ambient pressure ($p = 101325$ Pa).

To address cases where the tailwind exceeds the runner's speed, leading to negative relative velocities, the inlet and outlet boundary conditions were reversed. This approach ensures that the relative flow velocity remains positive ($U_{relative}$ between 20 and 50 km/h). The runner's position within the computational domain was adjusted accordingly. The velocity inlet, representing the combined effect of the runner's forward motion and wind speed, is calculated as follows:

$$ \text{Headwind cases: } U_{relative} = U_{runner} + U_{wind} $$

$$ \text{Tailwind cases: } U_{relative} = U_{runner} - U_{wind} $$

Turbulence intensity was set at 7%, based on average values from Watkin and Alam's study²⁰ across various headwind speeds. Its influence on the results was found to be minimal, as it characterizes the airflow in external conditions, measured at a sufficient distance upstream or downstream of the runner, where body-induced flow disturbances are negligible. Given that the inlet boundary conditions impose the relative flow velocity, ensuring a positive speed, turbulence intensity is assumed to be identical for both headwind and tailwind conditions.

## Domain and mesh configuration

The computational domain (Figure 1(b)) extended 6 m upstream, 18 m downstream, and 6 m above and on either side of the runner. The computational domain was subsequently discretized using the ANSYS meshing software. The mesh was refined near the runner, with the cell size progressively increasing towards the domain boundaries. To ensure accurate boundary layer resolution, 20 prism layers (inflation layers) were applied along the runner's surfaces, with a growth factor of 1.2 for layer thickness, maintaining a dimensionless wall distance ($y^+$) of approximately 1 throughout. The grid consisted of $10.9 \times 10^6$ cells, comprising tetrahedral and hexahedral elements with prism layers near the runner's surfaces. The mean cell size near the surface was $5 \times 10^{-3}$ m, while the maximum size at the domain boundaries was 0.5 m.

To evaluate the influence of mesh size on the simulation results, a grid dependency study was performed. The aerodynamic forces acting on a runner moving at 20 km/h were computed using four different grid resolutions (see Figure 2). The total drag force was tracked throughout the simulations, with values averaged over the final 100 time steps. The three-dimensional
<figure><img src="image_4.png" /><figcaption>**Figure 1.** (a) Illustration of the problem studied. The runner runs at a speed of 10, 15 or 20 km/h with either no wind, a headwind (5 to 30 km/h in 5 km/h increments) or a tailwind (5 to 30 km/h in 5 km/h increments). (b) Computational domain and description of boundary conditions.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Evolution of the drag force exerted on the runner according to the grid size.</figcaption></figure>

computational domain was meshed using ANSYS Workbench Meshing®, employing an unstructured tetrahedral grid, in accordance with the dynamic meshing method. The grid convergence test was conducted for a reference case (no wind, running speed of 20 km/h)

using successively finer grids with cell counts of 7×10⁶, 8.6×10⁶, 10.9×10⁶, and 12.9×10⁶. The results, presented in Figure 2, demonstrate that the drag force varies with the number of cells, while computational cost increases accordingly.
A converged solution with residuals of $10^{-3}$ was obtained using a grid with 7 million cells, serving as the baseline for comparison. Refining the mesh to 8.6 and subsequently 10.9 million cells led to a notable increase in the computed drag force. However, further increasing the resolution to 12.9 million cells yielded a result nearly identical to that obtained with the 10.9 million-cell grid. This suggests that beyond this threshold, the solution becomes independent of mesh refinement.

For an optimal balance between accuracy and computational efficiency, the 10.9 million-cell grid was selected for this study.

## Numerical methods and fluid properties

Spatial discretization was performed using a second-order scheme, and pressure and velocity were computed through a coupled approach. In this study, air was modelled with a density of 1.25 kg/m³, a temperature of 20°C (293.15 K), and a kinematic viscosity $\nu = 1.516 \times 10^{-5}$ m². Drag coefficients were monitored until stable convergence was achieved, typically after approximately 1000 pseudo time steps of 0.001 s. The solution converged, and iterations ceased when the residual values fell below the maximum allowed threshold, usually around $10^{-4}$.

## Methods for estimating mechanical power in running

To convert the aerodynamic drag forces experienced during running into the corresponding metabolic power, researchers have employed various methods, including the theoretical model developed by Cavagna and Kaneko.²¹ However, there is considerable debate surrounding the concept of efficiency and the appropriate values used in these methodologies*.

To address this issue, we adopted an alternative approach to convert drag force values into changes in metabolic power. A particularly relevant method involves empirical measurements of the metabolic cost associated with horizontal impeding forces, which serve as a proxy for aerodynamic drag.

da Silva et al.²² conducted physiological measurements on indoor treadmill runners to quantify the effect of small horizontal resistance forces (0, 4, and 8 N) applied at the athletes' waist on gross metabolic power at different speeds (12, 14, and 16 km/h) in competitive runners. Their study established linear regression equations linking gross metabolic power (W/kg) to horizontal resistance force (expressed as a percentage of body weight). The empirical results indicate that metabolic power increases by approximately 6% per unit of body weight applied as a resistance force.

The linear regression equations are as follows:

The gross metabolic power (W/kg) is defined as follows:²²

$$ \text{For a running velocity of 12 km / h:}0.6977 \times F(N) \\ + 11.996 \qquad (1) $$

$$ \text{For a running velocity of 14 km / h:}0.8386 \times F(N) \\ + 14.594 \qquad (2) $$

$$ \text{For a running velocity of 16 km / h:}1.1048 \times F(N) \\ + 16.993 \qquad (3) $$

In the study by da Silva et al.,²² F(N) represents the horizontal impeding force (N), whereas in the present study, we specifically consider the drag force. Gross metabolic power refers to the total energy expenditure rate (expressed in watts or W/kg) during physical activity. This includes both net metabolic power, the energy used specifically for movement, and basal metabolic rate, which accounts for essential physiological functions such as breathing, circulation, and thermoregulation.

By applying this empirical relationship, one can estimate the increase in metabolic power due to aerodynamic drag. It is important to note that these empirical laws were derived from experiments using small impeding forces (0, 4, and 8 N), corresponding to the aerodynamic drag experienced by runners without additional wind.

A similar approach was used by Chang and Kram,²³ who estimated the metabolic cost of generating horizontal forces while subjects ran at approximately 12 km/h. Their study found that a 3% body weight aiding force (simulating a tailwind) reduced metabolic power (oxygen consumption) by 13.3%, corresponding to a 4.5% decrease per unit of body weight in aiding force. Unlike da Silva et al.,²² Chang and Kram²³ examined both positive and negative horizontal forces, which can be interpreted as the effects of additional forces induced by headwinds or tailwinds. Despite this difference, both studies demonstrated that an impeding force, similar to headwinds, increases oxygen consumption ($\dot{VO}_2$), while an aiding force, akin to tailwinds, reduces it.

*Remark:* While efficiency is well-defined for machines, it is more complex in human locomotion, where muscles generate force and tendons store and return elastic energy. Cavagna was among the first to show that external mechanical power measurements tend to overestimate actual muscular work due to tendon elasticity, leading many researchers to describe these estimates as “apparent” efficiencies. Given the ongoing debate, establishing a consensus on running efficiency would enhance both scientific understanding and practical applications.

## Results and discussion

Figure 3(a) illustrates the variation of aerodynamic force on the runner in respect to the running-to-wind relative speed. To validate our model, we compared our results with data from Pecchiari et al.,²⁴ Mesquita et al.,²⁵ and Schickhofer and Hanson.²⁶ On average, our findings are 6% higher than those reported by Schickhofer and Hanson²⁶ but approximately 15% and 13% lower than those of
<figure><img src="image_6.png" /><figcaption>**Figure 3.** (a) Evolution of aerodynamic force as a function of the relative flow velocity calculated as the combination of runner speed and wind speed. For headwind: $U_{relative} = U_{runner} + U_{wind}$ whereas for the tailwind, $U_{relative} = U_{runner} - U_{wind}$. Comparison with results from Pecchiari et al.,²⁴ Mesquita et al.,²⁵ and Schickhofer and Hanson.²⁶ (b) Aerodynamic power, determined as the product of aerodynamic drag and running velocity, was calculated for three running speeds (10, 15, and 20 km/h) under varying wind conditions, including headwind and tailwind.</figcaption></figure>

Pecchiari et al.²⁴ and Mesquita et al.,²⁵ respectively, for comparable speeds in the 10–30 km/h range. Furthermore, across the broader speed range of –20 to 50 km/h, the variation in drag with respect to relative speed follows a trend consistent with Mesquita et al.’s observations. A comparison with the literature reveals slight deviations, likely attributable to methodological differences outlined in the study’s limitations. Nevertheless, our results closely align with the experimental data from Mesquita et al.²⁵ and Pecchiari et al.,²⁴ underscoring the robustness and reliability of our methodology.

Figure 3(a) indicates that the force can be modelled using a second-order polynomial law, separating it into two distinct components. Firstly, drag, a hindering force

opposing the runner’s motion, evident at positive relative speeds; secondly, thrust, a force aiding the runner’s motion, apparent at negative relative speeds. The figure shows that wind direction significantly influence a runner’s performance, even at the same wind speed. For example, a runner moving at 20 km/h with a 30 km/h tailwind experiences a 1.89 N push, while facing a 30 km/h headwind causes a impeding force of 43.4 N.

Figure 3(b) illustrates how aerodynamic power varies with wind speed and direction across three different running speeds. The figure clearly shows the transition between “negative” powers, which contribute to propulsion, and positive powers, which impose a braking force. It also highlights the significant effect of headwinds on
<table><caption>**Table 1.** Metabolic power, extrapolated from da Silva et al.'s study²² for 3 running speeds (10, 15 and 20 km/h) and different wind speeds (headwind and tailwind). ΔP<sub>meta</sub>/Ref corresponds to the percentage difference between the reference case, with no wind, and the case with wind.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">U<sub>Wind</sub> (km/h)</th><th colspan="2">U<sub>running</sub> 20 km/h</th><th colspan="2">U<sub>running</sub> 15 km/h</th><th colspan="2">U<sub>running</sub> 10 km/h</th></tr><tr><th>P<sub>meta</sub> (W/Kg)</th><th>ΔP<sub>meta</sub> / Ref</th><th>P<sub>meta</sub> (W/Kg)</th><th>ΔP<sub>meta</sub> / Ref</th><th>P<sub>meta</sub> (W/Kg)</th><th>ΔP<sub>meta</sub> / Ref</th></tr></thead><tbody><tr><td rowspan="4">Tailwind (km/h)</td><td>30</td><td>21.5</td><td>-9.0</td><td>15.1</td><td>-7.8</td><td>9.0</td><td>-7.0</td></tr><tr><td>20</td><td>22.0</td><td>-7.1</td><td>15.7</td><td>-4.2</td><td>9.4</td><td>-2.7</td></tr><tr><td>15</td><td>22.1</td><td>-6.6</td><td>15.7</td><td>-3.8</td><td>9.5</td><td>-1.7</td></tr><tr><td>10</td><td>22.4</td><td>-5.3</td><td>15.8</td><td>-3.3</td><td>9.5</td><td>-1.3</td></tr><tr><td rowspan="2">Ref.</td><td>5</td><td>22.9</td><td>-3.1</td><td>16.0</td><td>-2.1</td><td>9.5</td><td>-1.0</td></tr><tr><td>0</td><td>23.6</td><td>0.0</td><td>16.3</td><td>0.0</td><td>9.6</td><td>0.0</td></tr><tr><td rowspan="4">Headwind (km/h)</td><td>5</td><td>24.5</td><td>+3.8</td><td>16.8</td><td>+2.9</td><td>9.8</td><td>+1.7</td></tr><tr><td>10</td><td>25.7</td><td>+8.7</td><td>17.4</td><td>+6.6</td><td>10.0</td><td>+4.0</td></tr><tr><td>15</td><td>27.0</td><td>+14.4</td><td>18.2</td><td>+11.2</td><td>10.3</td><td>+6.8</td></tr><tr><td>20</td><td>28.6</td><td>+21.0</td><td>19.1</td><td>+16.6</td><td>10.6</td><td>+10.4</td></tr><tr><td>30</td><td>32.3</td><td>+36.8</td><td>21.2</td><td>+29.8</td><td>11.5</td><td>+19.6</td></tr></tbody></table>

power output, regardless of running speed. For instance, at 20 km/h in still air, the estimated aerodynamic power is approximately 39 W. However, with a 30 km/h headwind at the same speed, aerodynamic power surges to 602 W, nearly 15 times higher. In contrast, tailwinds provide only a modest reduction in the aerodynamic power demand. A 30 km/h tailwind lowers aerodynamic power by about 47 W, whereas a headwind of the same magnitude increases it by 564 W.

An analysis of metabolic power (estimated using da Silva et al.'s results²²) reveals that wind has a greater percent effect at higher running speeds. For instance, at 10 km/h, metabolic power increases by 19.6%, from 9.6 W/kg to 11.5 W/kg, as headwind speed rises from 0 to 30 km/h. The effect is even more pronounced at 20 km/h, where metabolic power increases by nearly 37%. Tailwinds exhibit similar trends: for a running velocity of 10 km/h, a 30 km/h tailwind reduces metabolic power by 7%, while at 15 km/h, the reduction is 7.8%, and at 20 km/h, it reaches 9%. For a metabolic power of 1209 W (21.6 W/Kg), running at 19.7 km/h with a 20 km/h tailwind is equivalent to running at 16.2 km/h with a 20 km/h headwind. In all cases, relative speed is the main factor affecting these outcomes.

Consider a scenario where a runner aims to regulate energy expenditure by maintaining a consistent metabolic power throughout a race. To do so, the runner must adjust their speed according to wind conditions. Specifically, runners must slow down when facing a headwind and speed up with a tailwind to maintain a constant metabolic power output. In a 10 km out-and-back course, where a runner maintains a speed of 14 km/h in still air (P<sub>meta</sub> = 850 W or 15.2 W/kg), the total time is just under 43 min. However, introducing a 30 km/h wind, headwind in the first half and tailwind in the second, alters the pacing dynamics. To sustain 850 W against the headwind over

the first 5 km, the runner slows to approximately 11.9 km/h, covering this section in 25 min and 12 s, compared to 21 min and 24 s in still air. With the tailwind on the return leg, the runner accelerates to 15 km/h, completing the second half in 20 min. Consequently, while the total time in still air remains around 43 min, with wind, it increases to just over 45 min. This highlights that in an out-and-back course, the tailwind does not fully compensate for the performance loss caused by the headwind.

To further illustrate the data presented in Table 1, Figure 4 shows the evolution of metabolic power as a function of %BW (percentage of body weight). It includes the experimental results from da Silva et al.²² at running speeds of 12, 14, and 16 km/h, alongside our study's results at 10, 15, and 20 km/h.

While da Silva et al.²² constrained the %BW range to 0-1.5%, we expanded it from -1.4% to 7.9% to account for the effects of headwinds and tailwinds. However, for direct comparison with their findings, we present our results only within the -0.5% to 2% range.

Additionally, Figure 4 highlights the %BW ranges corresponding to aiding aerodynamic forces (negative %BW) and braking aerodynamic forces (positive %BW). The results clearly demonstrate that metabolic power increases proportionally with force, expressed in %BW.

Our findings align with previous research. For instance, at a running speed of 20 km/h in still air, the drag force acting on a 56 kg runner (K. Bekele) is 7N, equivalent to 1.3% of body weight. This is consistent with the results of Mesquita et al.,²⁵ who reported a drag force of 8.1N (1.4% of body weight) for E. Kipchoge (58 kg). Chang and Kram²³ estimated the metabolic cost of generating horizontal forces in runners at approximately 12 km/h. Their study found that a propulsive force of 3% of body weight (simulating a tailwind) reduced metabolic power (oxygen consumption) by 13.3%. In comparison, our results at a running speed of 10 km/h show that
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Gross metabolic power (W/kg) as a function of the force acting on the runner (N). Experimental data from da Silva et al.²² at 12, 14, and 16 km/h are compared with the results of the present CFD study at 10, 15, and 20 km/h. Results from da Silva et al.'s study,²² which covered the range of 0 to 1.5% BW, were extrapolated in our study to extend from -0.5% to 2% BW.</figcaption></figure>

a 3% propulsive force leads to a 12.6% reduction in metabolic power, a value of the same order of magnitude as reported by Chang and Kram.²³

To deepen our analysis, we have also expressed our results in terms of oxygen consumption and compared them with existing literature data. The effects of running against the wind were studied by Pugh²⁷ and Davies,¹² who measured oxygen uptake to quantify wind resistance. To compare their results with ours, we estimated oxygen consumption ($\dot{VO}_2$) by converting metabolic power to energy expenditure, then to $\dot{VO}_2$. Figure 5 illustrates that $\dot{VO}_2$ increases proportionally to the square of relative speed. Our estimates yield a linear trend curve with slightly higher values than those reported by Pugh and Davies, while maintaining proportional increases with speed. Since our estimates are based on a speed of 20 km/h, whereas Pugh and Davies reported values at 16 km/h and 14.5 km/h, respectively, our results align well with previous findings. Regardless of the study, the data consistently confirm that oxygen consumption rises with headwind speed.

These findings clearly indicate that an increase in relative speed leads to higher oxygen consumption. Applied to our study, this means that running against a headwind increases relative speed, defined as the sum of the runner's speed and the wind speed, thereby elevating $\dot{VO}_2$. Conversely, running with a tailwind reduces relative speed, leading to lower oxygen consumption. For instance, running at 20 km/h in still air results in an oxygen consumption of 3.8 L/min. However, with a 30 km/h headwind, this value increases to 5.18 L/min, an increase of 37%. In contrast, a 30 km/h tailwind reduces $\dot{VO}_2$ by only about 9%.

Figure 6 visually depicts the effect of wind on the runner through wake regions represented by total pressure

isosurfaces. These surfaces delineate the boundary between regions of negative and positive pressure resulting from flow recovery. Wind direction plays a crucial role in wake formation. In headwind conditions, the wake trails behind the runner, whereas when the tailwind surpasses the runner's speed, the wake shifts forward. Additionally, a headwind generates a more elongated wake than in calm air, corresponding to the increased relative airflow velocity.

## Study limitations, directions for further research, and practical applications

The results presented here should be interpreted in light of several limitations. Firstly, the runner's geometry utilized in this numerical study has been simplified, omitting factors such as the influence of clothing. Additionally, the CFD calculations were performed under the assumption of a static position, which does not account for the dynamic movements of the body during running. Wind velocity and direction are assumed to be constant and fixed, whereas, in reality, atmospheric conditions are continuously changing. Furthermore, while the runner's frontal area is treated as constant, the trunk's posture, which affects this area, actually varies with wind direction (Mesquita et al.²⁵).

Further experimental research is needed to validate the conclusions of this study. Nonetheless, this study contributes to a deeper understanding of how wind affects running performance, emphasizing its benefits as a tailwind and challenges as a headwind. The findings offer practical applications of aerodynamic principles to running dynamics. Moreover, the power estimations presented here could
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Variation of VO₂ with the square of relative speed, as reported by Pugh²⁷ for a running speed of 16 km/h, Davies¹² for 14.5 km/h, and estimated in the present study for 20 km/h under headwind conditions.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Wake region behind the runner visualized by isosurfaces of total pressure at $p=0$ Pa.</figcaption></figure>

prove to be a valuable resource for runners and their coaches, supporting effective preparation and performance optimization and racing tactics.

## Conclusion

The analysis of aerodynamic forces clearly demonstrates that wind can significantly influence a runner's performance, either positively or negatively, depending on its direction and speed. The findings highlight that the effect of wind on metabolic cost of running is significantly influenced by headwinds. The presence of wind greatly affects the metabolic cost of running. While a 30 km/h tailwind provides only a slight 9% reduction in energy use, a 30 km/h headwind dramatically increases it by 37%. To put this into perspective, running at 13.7 km/h against a 20 km/h headwind feels as demanding as running at 19.4 km/h with a 20 km/h tailwind. Moreover, on a 10 km out-and-back course, the contrasting running times between headwind and tailwind sections underscore the importance of adjusting speed to maintain consistent

effort. Our findings demonstrate that headwinds and tailwinds on an out-and-back course lead to a slower average running speed than running the same distance in still air conditions. Therefore, this study underscores the critical necessity for runners to consider weather conditions, particularly wind, to effectively manage energy expenditure and optimize performance in competitions or training sessions.

## Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

## Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

## ORCID iDs

Fabien Beaumont ID https://orcid.org/0000-0002-2895-5795

Guillaume Polidori ID https://orcid.org/0000-0002-6078-6397
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