# Projected frontal area during locomotion in the wind

Raphael Mesquita, Patrick Willems, Valentina Natalucci, Francesco Luciano, Gaspare Pavei, Arthur Dewolf

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Raphael Mesquita, Patrick Willems, Valentina Natalucci, Francesco Luciano, Gaspare Pavei, et al. Projected frontal area during locomotion in the wind. Multidisciplinary Biomechanics Journal, 2025, 49th congress of the Société de Biomécanique, 10.46298/mbj.14554. hal-04738043v2

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# Projected frontal area during locomotion in the wind

Raphael Mesquita<sup>a</sup>, Patrick Willems<sup>a</sup>, Valentina Natalucci<sup>b</sup>,
Francesco Luciano<sup>b</sup>, Gaspare Pavei<sup>b</sup>, Arthur Dewolf<sup>a*</sup>

<sup>a</sup> Lab. Biomechanics & Physiology of Locomotion, UCLouvain, Louvain-la-Neuve, Belgium

<sup>b</sup> Lab. Physiomechanics, Univ. Milan, Italy

* Corresponding author: arthur.dewolf@uclouvain.be

Received date: 05/04/2024

Accepted date: 28/06/2024

Publication date: 31/01/2025

**Keywords:** aerodynamics, locomotion, wind tunnel

© 2025 The Authors
Licence CC-BY 4.0
Published by Société de Biomécanique

## 1. Introduction

During terrestrial locomotion, to move across any envi-
ronment, one must expend energy to overcome the
drag ($F_d$) due to the airflow. Air resistance, at a certain
velocity, is directly proportional to an object's projected
frontal area ($A$) multiplied by the drag coefficient ($C_d$)
and by the dynamic pressure of a moving air stream,
$q$, ($F_d = q \times C_d \times A$) (Hoerner, 1965).

In still air, the speed of the relative airflow is equal to a
subject's moving speed, which during human locomo-
tion is generally low (<25km/h) equating to negligible
drag (Pugh, 1971). Indeed, as the total mechanical
work done by the body against drag is <10% of total
mechanical work during walking and running, improv-
ing aerodynamics during locomotion does not lead to
major performance improvements, contrary to other
sports such as skating or cycling (di Prampero, 1986).
However, when performance tends towards its limits,
even small changes can lead to important time gains.

Experimental data of legged locomotion in a wind tunnel
are scarce. Recently we investigated the effect of drag
on the walking and running mechanics (Mesquita et al.,
2024). $F_d$ increases with square wind speed ($U^2$) and, at
wind speeds above 12 m/s, drag differs between walking
and running due to a change in the drag area ($C_d A$) which
decreases exponentially both with $U$ and $U^2$ (Pecchiari
et al., 2023). Changes in $C_d A$ can be due to changes in
$C_d$, which is related to wind speed and airflow regime,
or a change in $A$. The latter has been previously charac-
terised by a cylinder in human locomotion (Pugh, 1971).

In our recent paper, we concluded that as $F_d$ increases, to
limit air resistance subjects adapt their $C_d A$ (Mesquita et
al., 2024), most likely by reducing their surface exposed
to the drag. However, we did not dissociate between
the two variables. The goal of the present study was
firstly to compare our present findings to previous static
measurements of projected frontal area (Davies, 1980;
Pugh, 1971). Secondly, determine how the frontal area
changes with increasing wind speeds and to what extent
the decrease in $C_d A$ is solely due to a change in $A$?

## 2. Methods

Based on a power analysis, eight male endurance athletes (age: 32±6 y, mass: 63.2±6.6 kg; height: 1.77±0.05 m, PB 10000 m: 31:20±01:12 min:s) walked and ran at 1.5 and 4 m/s respectively, on an instrumented treadmill in a wind tunnel. Wind speeds ($U$) ranged from -15 to 15 m/s, where the negative and positive signs indicate tailwind and headwind, respectively. $U$ deviated from the nominal wind speed on average by 2 ± 0.4% over all trials. Informed written consent was obtained and the study followed the guidelines of the Declaration of Helsinki. All procedures were accepted by the local ethics committee (Politecnico di Milano, n°16/2022). Bilateral, full-body 3D kinematics were captured at 250 Hz with an 8-camera (6 MX-13 and 2 T20-S) VICON system (Oxford, UK) placed around the treadmill. Participants were equipped with 18 retro-reflective markers glued onto the skin. Data were oversampled at 1kHz and lowpass filtered (Bessel, cut-off frequency:
30Hz). The frontal area was estimated using a polygon surface function (LABVIEW) from the instantaneous bilateral frontal plane coordinates of the Vth metatarsal, external malleolus, external femoral condyle, greater trochanter, shoulder, and temple markers and averaged per stride. The error in A by excluding the arms was expected to be offset by considering the lower limbs as a single block. To observe the difference in strategy between locomotion without wind and against wind, a ratio between the subject's frontal area over the subject's frontal area without added wind, A/A₀, was measured. Between 13-84 strides were analysed per condition, and for all subjects a total of 8850 strides were analysed (5443 in running, 3307 in walking). A mixed-effect model regressed the A and A/A₀ over U and U² to assess which had the lowest Akaike Information Criterion. The fixed effect of wind (F) and significance (p-value, α = 0.05) were reported. Differences between walking and running were assessed by pooling data together and analysing wind, speed, and the interaction effect for A/A₀.

### 3. Results and discussion

Frontal area decreases with increasing nominal wind speed in walking (F = 1622.8 p < 0.001) and running (F = 1812.7 p < 0.001). A/A₀ decreases with stronger headwinds (F = 20.1 p < 0.001) and increases with increasing tailwinds, rising more in running than in walking (F = 10.81 p < 0.001).

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Panel A: Frontal area (A) model of one subject walking with a 15 m/s headwind. Panel B: A as a function of U in walking (red) and running (blue). Panel C: ratio A/A₀. Symbols represent the grand mean ± SD of all subjects. Lines are 3rd knot spline fits.</figcaption></figure>

Frontal area has previously been calculated in standing by photographic measurements in studies with smaller sample sizes (Davies, 1980; Pugh, 1971). Here, based on kinematic data recorded over multiple strides, we obtain an average value of 0.139 x subject height² in locomotion without wind. This slightly lower value compared to Davies (1980) of 0.142 x subject height² can be partly explained by our subjects being in motion (Pugh, 1971).

<table><caption>**Table 1.** Average C₉ and C₉A as a function of U in both head, (H) and tailwind (T) for walking (W) and running (R).</caption><thead><tr><th>U (m/s)</th><th>Walk Run</th><th>Wind direction</th><th>C<sub>d</sub></th><th>C<sub>d</sub>A (m<sup>2</sup>)</th></tr></thead><tbody><tr><td rowspan="2">0</td><td rowspan="2">W/R</td><td rowspan="2">/</td><td rowspan="2">/</td><td rowspan="2">/</td></tr><tr><td>W</td><td>1.08±0.04</td><td>0.51±0.04</td></tr><tr><td rowspan="4">5</td><td rowspan="2">R</td><td rowspan="2">T</td><td rowspan="2">1.11±0.04</td><td rowspan="2">0.48±0.03</td></tr><tr><td>W</td><td>1.15±0.05</td><td>0.54±0.05</td></tr><tr><td>R</td><td>1.07±0.06</td><td>0.46±0.05</td></tr><tr><td rowspan="4">7.5</td><td rowspan="2">R</td><td rowspan="2">T</td><td rowspan="2">1.01±0.04</td><td rowspan="2">0.48±0.04</td></tr><tr><td>W</td><td>1.06±0.04</td><td>0.46±0.04</td></tr><tr><td rowspan="2">R</td><td rowspan="2">H</td><td rowspan="2">1.08±0.04</td><td rowspan="2">0.50±0.05</td></tr><tr><td>W</td><td>1.03±0.05</td><td>0.44±0.04</td></tr><tr><td rowspan="4">10</td><td rowspan="2">R</td><td rowspan="2">T</td><td rowspan="2">1.00±0.04</td><td rowspan="2">0.47±0.04</td></tr><tr><td>W</td><td>1.05±0.04</td><td>0.45±0.03</td></tr><tr><td rowspan="2">R</td><td rowspan="2">H</td><td rowspan="2">1.07±0.03</td><td rowspan="2">0.49±0.05</td></tr><tr><td>W</td><td>1.00±0.04</td><td>0.42±0.03</td></tr><tr><td rowspan="4">12.5</td><td rowspan="2">R</td><td rowspan="2">T</td><td rowspan="2">1.00±0.04</td><td rowspan="2">0.47±0.04</td></tr><tr><td>W</td><td>1.03±0.04</td><td>0.45±0.03</td></tr><tr><td rowspan="2">R</td><td rowspan="2">H</td><td rowspan="2">1.07±0.04</td><td rowspan="2">0.49±0.03</td></tr><tr><td>W</td><td>1.00±0.04</td><td>0.42±0.03</td></tr><tr><td rowspan="4">15</td><td rowspan="2">R</td><td rowspan="2">T</td><td rowspan="2">0.99±0.03</td><td rowspan="2">0.46±0.04</td></tr><tr><td>W</td><td>1.01±0.04</td><td>0.44±0.03</td></tr><tr><td rowspan="2">R</td><td rowspan="2">H</td><td rowspan="2">1.05±0.04</td><td rowspan="2">0.48±0.03</td></tr><tr><td>W</td><td>0.99±0.04</td><td>0.41±0.03</td></tr></tbody></table>

A is slightly larger in walking than in running, likely due the double stance phase and more erect posture in walking. As headwind increases, subjects tuck their
head in and tilt forwards to reduce their frontal area exposed to drag (Davies, 1980, Mesquita et al., 2024). Against tailwinds, particularly in running, subjects slightly increase frontal area, mostly done by leaning backwards into the wind. This gives the wind a larger projected area to exert force on, decreasing the power done during running propulsion (Mesquita et al., 2024). Contrarily, $C_dA$ decreases against tailwinds despite an increase in A (Mesquita et al., 2024). This indicates a decrease in $C_d$, possibly due to changes in the airflow regime which tends towards turbulence beyond the speeds studied presently (Davies, 1980; Pugh, 1971).

## 4. Conclusion

Our study confirms and updates the relationship of frontal area and body height which is constantly used in computational fluid dynamics (CFD) simulations (Fernandes et al., 2023). This investigation is particularly relevant in the field of sports science where the marathon world record approaches the 2-hour mark.

## Conflict of interest

The authors have no conflict of interests to report.

## References

* Davies, C. T. (1980). Effects of wind assistance and resistance on the forward motion of a runner. *Journal of Applied Physiology, 48*(4), 702-709. https://doi.org/10.1152/jappl.1980.48.4.702

* di Prampero, P. (1986). The Energy Cost of Human Locomotion on Land and in Water. *International Journal of Sports Medicine, 07*(02), 55-72. https://doi.org/10.1055/s-2008-1025736

* Fernandes, G., Gandur, N. L., Santos, D., & Maldonado, V. (2023). *The sub 2-hour official marathon is possible: Developing a drafting strategy for a historic breakthrough in sports* [Preprint]. In Review. https://doi.org/10.21203/rs.3.rs-3390553/v1

* Hoerner, S. (1965). *Fluid Dynamic Drag*. Wiley.

* Pecchiari, M. M., Legramandi, M. A., Gibertini, G., & Cavagna, G. A. (2023). Still air resistance during walking and running. *Proceedings of the Royal Society B: Biological Sciences, 290*(2013), 20231763. https://doi.org/10.1098/rspb.2023.1763

* Pugh, L. (1971). The influence of wind resistance in running and walking and the mechanical efficiency of work against horizontal or vertical forces. *The Journal of Physiology, 213*(2), 255-276. https://doi.org/10.1113/jphysiol.1971.sp009381