# Quantitative Study of a Full-scale Pedaling Mannequin for Wind Tunnel Testing

Sébastien Térol<sup>ab*</sup>, Lucas Limousin<sup>a</sup>, Yann Nival<sup>a</sup>, Antonin Moly<sup>a</sup>, Quentin Micheletti<sup>a</sup>, Pascal Acco<sup>b</sup>, Georges Soto-Romero<sup>b</sup>, Antony Costes<sup>a</sup>

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

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

* Corresponding author: sebastien.terol@alten.com ; sterol@laas.fr

## Abstract

Human subjects introduce variability in cycling wind tunnel testing due to slight inconsistencies in position and fatigue. To address these limitations, this study introduces a dynamic, full-scale pedaling mannequin, capable of generating repeatable and controlled pedaling movements.

The study focuses on three main objectives: (1) validating the mannequin's kinematics by comparing its pedaling motion to an idealized mechanical model, (2) quantifying the dynamic forces generated by the mannequin during operation and assessing their impact on measurement stability, and (3) evaluating the variability of aerodynamic measurements across different pedaling cadences and wind speeds. Experiments were conducted in a low-turbulence wind tunnel, with kinematic analysis performed using computer vision and force measurements recorded at multiple cadences and wind speeds.

Results demonstrate that the mannequin produces highly repeatable pedaling motions with a minimal and maximal standard deviation of 0.24 % and 0.88 % across all tested conditions. The smallest detectable meaningful power change in optimal conditions was 1.61 W at 50 km/h and at a pedaling frequency of 67 rotations per minute. Pedaling-induced forces were shown to influence the aerodynamic drag measurements, highlighting the importance of distinguishing dynamic and aerodynamic components of the force signal. These findings establish the mannequin as a reliable tool for controlled aerodynamic analysis, with applications in both scientific research and performance optimization in competitive cycling.

**Keywords:** Cycling; Aerodynamics; 3D printing; Kinematics.
# 1. Introduction

Aerodynamic optimization in cycling is one of the key studies for cyclists in quest of performance. For professional cyclists who can reach average speeds above 45 km/h, aerodynamic drag accounts for almost 90 % of the resisting forces applied to the cyclist [1], [2], [3]. Cyclists' aerodynamics depend on their morphologies, positions, and equipment [4]. Wind tunnel testing is widely recognized as the gold standard for evaluating the aerodynamic performance of cyclists [5]. However, traditional testing methodologies often rely on human subjects [6] or static mannequins [7], [8]. These approaches present notable limitations: on the one hand, human subjects introduce variability due to fatigue [9], [10], slight inconsistencies in position [11], and limited availability for repeated trials. On the other hand, static mannequins cannot reproduce the dynamic pedaling motion inherent to real-world cycling but have other advantages. The use of reduced-scale static models enables complex situations to be represented, such as a group of cyclists or drafting with vehicles [12], [13]. Full-scale static models, on the other hand, offer the advantages of measurement repeatability by eliminating unwanted movements that an athlete might have, while providing an analysis of turbulence [8], [14]. In the case of mannequin studies, Crouch et al. (2012) conducted several static configurations at different crank angles to analyze the wake of the mannequin according to legs positions [15]. Seo et al. 2018 developed two simplified dynamic mannequin for tandem cycling [16]. Subsequently, Crouch et al. (2016) has developed a full-scale pedaling cyclist model with simplified joint and geometries that was able to reach elite-level pedaling cadences up to 100 rpm [17], [18]. These mannequins have one limitation in common: they are all attached to the saddle. This feature is problematic when a common goal or such mannequins is to test the effect of aerodynamic clothing [19], [20].

Building up on these previous studies about pedaling mannequins, our study introduces a dynamic, full-scale pedaling mannequin (DCM: Dynamic Cyclist Mannequin) non-fixed to the saddle, as an innovative tool for wind tunnel testing [21], [22]. Such a mannequin offers several advantages over human subjects: it is consistently available, immune to fatigue or cold testing conditions, and capable of highly repeatable and controlled movements. These properties make it an ideal platform for investigating subtle aerodynamic phenomena, such as the interaction between the cyclist's pedaling movement and airflow while respecting the pedaling dynamics of a cycling athlete.

Despite the promise of DCM, several open questions remain about their behavior and suitability for aerodynamic testing. Specifically, it is unclear how well the kinematics of a DCM replicate the idealized “perfect” motion necessary for controlled aerodynamic studies. Additionally, the mechanical forces introduced by the DCM during operation and how these forces influence its stability and the accuracy of wind tunnel measurements are not well understood. Furthermore, it is uncertain whether the use of such DCM can reduce measurement variability and provide reliable results across a range of pedaling cadences and wind speeds.
Our hypotheses are as follows: The DCM generates highly repeatable pedaling motions, with deviations within acceptable limits for aerodynamic studies. The forces generated by the DCM during pedaling have a minimal and quantifiable impact on both pedaling stability and wind tunnel measurements. Finally, the use of the DCM enables precise analysis of aerodynamic effects across different pedaling cadences and wind speeds.

The goals of the present study are to validate the kinematic performance of the DCM by comparing its motion to an idealized model, quantify the dynamic behavior of the DCM, including the forces it generates and their influence on stability and aerodynamic measurements to assess the variability of aerodynamic measurements obtained under varying cadences and wind speeds.

By addressing these objectives, this study seeks to establish the DCM as a reliable and effective tool for aerodynamic analysis, advancing the precision and repeatability of wind tunnel testing in cycling. This contribution is expected to benefit both scientific research and practical applications in the optimization of athletic performance.

## 2. Materials and Methods

### 2.1. Design and Fabrication of the Dynamic Cyclist Mannequin

The DCM was designed from the 3D scan, specially done for this study, of a professional athlete belonging to category 1 in Ansley and Cangley (2009) classification [23]. From the cleaned 3D model, cut-outs were made for each joint. Each joint was designed on a case-by-case basis, with the objective of preserving the degrees of freedom of human joints to the greatest extent possible. The detailed design of the DCM is available in supplementary materials [22], [24]. A flowchart for the whole DCM design process is presented in Fig. 1, illustrating the iterative steps from 3D scanning to final assembly.

<figure><img src="image_1.png" /><figcaption>**Fig. 1** Evolution of the dynamic mannequin design</figcaption></figure>

I. 3D scan of the athlete and recovery of a digital point cloud

II. Creation of a digital model from the point cloud

III. Cut out limbs before joint designs

IV. Kinematic validation on Blender

V. Final assembly & wind tunnel tests
## 2.2. Kinematic Validation of the Dynamic Cyclist Mannequin

Validation of the pedaling kinematics was necessary to ensure the subsequent printing and assembly of the DCM. This validation was conducted using the OpenModelica software, an open-source environment for modeling and analyzing complex dynamics systems. This software was employed to design a digital model of an idealized mechanical system composed of armatures and links representing the DCM lower limbs (Fig. 2). The model is considered to be “idealized” in the sense that it represents a theoretical DCM characterized by perfectly balanced segment lengths, masses, inertia moments and no joint frictions.

<figure><img src="image_2.png" /><figcaption>**Fig. 2** OpenModelica idealized model. Geometrical representation</figcaption></figure>

Inertial properties of each segment were incorporated to enable calculation of joint and whole system forces. The objective of this modelling was twofold: firstly, to identify the stresses applied to the joints so that they can be properly designed, and secondly, to enable kinematic comparison between the idealized model and the final DCM. The detailed model is represented in Supplementary Materials (Fig. 2 (Supplementary Materials)). The study focused on the forces applied to the pelvis to facilitate a comprehensive analysis of the DCM's overall movements [25], [26].
## 2.3. Experimental Setup in the Wind Tunnel

Experiments were carried out in the S4 wind tunnel at the Institut Aérotechnique of the Conservatoire National des Arts et Métiers (IAT CNAM, St-Cyr-l'Ecole, France). The 1:1 scale DCM was mounted on a track racing bike (L96, Look, Nevers, France) and two disc-wheels (Lenticulaire C+, Corima, Loriol-sur-Drome, France) that were attached to the structure of the IAT CNAM force platform whose characteristics are specified by Clanet et al. (2021) [27]. The DCM was equipped with an Aerohead MIPS helmet (Giro, Irvine, USA) and Lycra skinsuit. Test section dimensions are 3m high and 5m wide, introducing a 1.9 % blockage ratio [28]. The target turbulent intensity in the test section was set at 1 %. The system {Bike + DCM} was positioned on a force platform to measure the overall forces exerted by the system during pedaling. Measurements were conducted at free-stream test velocities ranging from 40km/h to 80km/h, corresponding to Reynolds numbers ranging from $6.7 \times 10^6$ to $13.8 \times 10^6$ based on the full bicycle length (1.64 m) and a kinematic air viscosity of $1.56 \times 10^{-5}$ m²/s.

### 2.3.1. Kinematic Analysis Experiment

A validated kinematic analysis of the DCM was conducted using computer vision techniques [29], [30]. The objective of this analysis was to track the motion of a fixed red point on the DCM, located at the midpoint of the hips. Movements were analyzed in a two-dimensional plane, constructed from the lateral Y-axis and the vertical Z-axis. The lateral Y-axis evolves positively to the right of the cyclist, the vertical Z-axis evolves positively upwards of the cyclist. A camera allowed the capture of images at several pedaling cadences, expressed in rotations per minute (rpm). The camera was placed 3.3m behind the target point of the DCM and outside the force platform of the wind tunnel on a small rigid structure to limit aerodynamic impact. The schematic representation of the wind tunnel setup is represented in supplementary materials Fig. 3 (Supplementary Materials). A point detection algorithm developed using the OpenCV Python library was used to retrieve the pixel coordinates corresponding to the red dot, then, the point displacement in pixels, which was converted into millimeters via a known characteristic distance (1 pixel = $6.7 \times 10^{-2}$ mm). This technique allowed the extraction of a peak-to-peak amplitude of the fixed point's movement, with a 1-pixel accuracy, and therefore the DCM's movement, for each cadence.

### 2.3.2. Cadence Variation Wind Tunnel Test

The preliminary stage of the wind tunnel experiment process consisted in analyzing the impact of the DCM's pedaling on the longitudinal force values collected by the wind tunnel. To this end, an initial test was conducted with a variable cadence and no wind speed, yielding data on the forces induced by only pedaling with wind effect. Then, the speed of the wind tunnel was set at 65 km/h, while pedaling cadence was servo-controlled, varying from 25 rpm to 82 rpm with an accuracy of $\pm$1 rpm. The measured cadences from the cadence sensor were: {25 rpm; 32 rpm; 40 rpm; 54 rpm; 61 rpm; 68 rpm; 82 rpm}.
Measurements at a cadence of 0 rpm in the same condition were also done to compare dynamic data with static ones. The aim of this analysis was to identify the impact of the DCM's cadence on its aerodynamic drag.

### 2.3.3. Wind Speed Variation Wind Tunnel Test

In a second step, the DCM's cadence was set at 68rpm, and the wind tunnel's airflow speed was controlled, varying from 40 km/h to 80 km/h in 10 km/h steps. The measured wind speeds were: {40 km/h; 50 km/h; 60 km/h; 70 km/h}. The aim of this analysis was to identify the impact of wind speed on the DCM aerodynamic coefficient. No gear changes were made, so there is no direct link between pedaling cadence and wind speed.

### 2.3.4. Wind Tunnel Data Processing

For each configuration of cadence and wind speed, ten force measurements were performed. The force measurement was a time-averaged result of a 20 second sample recorded at 1000 Hz. A system offset was performed between each configuration. The analysis focuses on forces measured along the longitudinal X-axis which evolves positively in the flow direction. The raw wind tunnel acquisition data contains noise inherent to the measurement process. The employed filter performs two distinct operations on the raw signal. Initially, a second-order IIR notch filter from the python-scipy library was employed to remove a high amplitude frequency that was found to be distorting the measurements at exactly 4.7 Hz present even without wind and without cadence from the DCM. Secondly, a low-frequency filter using a 4^th^ order with a 25 Hz cutoff frequency was applied to retain only the low frequencies, including the pedaling frequency and its harmonics [31]. The effective signal of the measurement obtained appeared periodic after being filtered. This signal was subsequently broken down into full periods so that they could be stacked on top of each other, allowing for the observation of the DCM's pedaling repeatability. These filtered results, based on the mean period of the 20 sec-signal, which always start when crossing the global mean value of each measurement, allow comparison between multiple tests with and without wind at different cadences. In addition, given the slight difference in time between wind and windless recordings, a linear interpolation was performed to present both on a similar total timeframe.

## 3. Results

A standard deviation of the drag coefficient from the mean of the measurements has been calculated and displayed in the Fig. 3 (a). Over all measurements, except for the 40 km/h measurement, this standard deviation did not exceed 0.51 % of the mean, reflecting the excellent repeatability of the DCM. In addition, according to the Fig. 3 (b), the DCM is capable of detecting a minimum power change of 1.61 W at 50 km/h and a 67 rpm pedaling frequency.
<figure><img src="image_3.png" /><figcaption>Fig. 3 Heatmap representation of the mannequin repeatability according to wind speed and cadence:</figcaption></figure>

(a) Standard Deviation presented as a percentage of total drag force

(b) Standard Deviation presented as a power in Watts
## 3.1. Simulated Kinematics

The kinematic model of the idealized DCM allows us to visualize forces at each point on the lower limbs. In addition to joint forces, it is possible to understand DCM kinematics by looking at the resultant forces at the crank axis. Experimental data from the red point at pelvic level and data from the wind tunnel force platform were also compared. In a simulation with idealized leg pivot joints, the lateral forces along the Y-axis were zero in all conditions. Since the analysis focuses on the vertical displacements of the pelvis and the longitudinal forces of the entire system, only results along the vertical Z-axis for the pelvis and the longitudinal X-axis for the attachment point are analyzed.

An analysis of the results shown in Fig. 4 for vertical forces on the pelvis shows that there are indeed forces associated with the pedaling motion as a result of crankset rotation. Outside of the bottom dead center of each leg, these forces tend to lift the pelvis off the saddle with a magnitude between 30 N and 43 N. At the bottom dead center, at 90° crank angle for the right leg and 270° for the left leg, a force pulling the pelvis downward was measured.

<figure><img src="image_4.png" /><figcaption>**Fig. 4** Maximum and minimum pelvis efforts along the vertical Z-axis as a function of right crank angle according to different cadences</figcaption></figure>

For forces comparable to those obtained on the wind tunnel force platform, Fig. 5 shows the longitudinal forces at the bottom bracket axle of the idealized DCM model. This shows that forces are not zero even on an idealized model. In addition, there are two peaks at the top and bottom dead center of both legs.
<figure><img src="image_5.png" /><figcaption>**Fig. 5** Longitudinal efforts applied on the idealized model attachment point as a function of right crank angle according to different cadences. The right crankshaft is rotating clockwise, and the 0-degree angle corresponds to a horizontal crankshaft with the left leg in the downstream location. Drawings allow the legs position as a function of right crank angle. The right leg (R) is represented in green; the left leg (L) is represented in red.</figcaption></figure>
## 3.2. Effect of Cadence on Kinematics

Using computer vision analysis, the lateral and vertical displacements of the DCM show a maximum value which evolves with the different cadences. As illustrated in Fig. 6, the maximum peak-to-peak amplitudes of the pelvis displacements during a fixed cadence measurement vary between 0.6 mm and 4.1 mm laterally and between 0.1 mm and 1.5 mm vertically. As the effort required to pedal increases, the vertical peak-to-peak amplitude increases accordingly. However, a contrasting trend is observed in the lateral peak-to-peak amplitude, which exhibits a decrease at 82 rpm compared to 61 rpm and 69 rpm.

<figure><img src="image_6.png" /><figcaption>Fig. 6 Mannequin Pelvis Displacement according to different cadences:</figcaption></figure>

(a) Lateral Displacement in millimeters (Y-axis)

(b) Vertical Displacement in millimeters (Z-axis)
### 3.3. Force Measurements

Fig. 7 shows the result of the filtering step in both the time and frequency domain, allowing to see the impact of the 4.7 Hz filter. This figure also shows the first and last cut boundaries and the frequencies used in the filters. More details can be seen on the zoomed-in version (Fig. 4 (Supplementary Materials)). The filtered signal is cut at the lower and upper boundaries to obtain a signal with 19 full periods as shown in Fig. 8 (a). Fig. 8 (b) illustrates the stacked periods and standard deviation of a canonical recording. In this example, the instantaneous maximum standard deviation between pedaling cycles over the 20-second measurement was not greater than 1.67 N at 60 rpm. The results of the cadence variation tests yielded analogous outcomes for all cadences ranging from 25 to 82 rpm, with a standard deviation that ranged from 2.3 % to 9.3 %, showing an increase with cadence.

In the absence of cadence, the DCM is considered static, with an aerodynamic drag coefficient standard deviation of 0.34%. This value is comparable to those in the dynamic case, with an average for all cadences of 0.37%. However, it is noteworthy that in the static case, the drag coefficient is on average 4.9% lower than in the dynamic cases.

<figure><img src="image_7.png" /><figcaption>**Fig. 7** Comparison between a signal with its filtered version: Time and frequency analysis of efforts recorded by the wind tunnel force platform along the X longitudinal axis at 60 rpm and fixed wind speed of 65 km/h</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 8** Example of efforts recorded by the wind tunnel force platform along the X longitudinal axis at 60 rpm and fixed wind speed of 65 km/h:</figcaption></figure>

(a) Cutting of 19 full periods from the filtered signal with start/end of each period (correspond to the filtered signal of Fig. 7)

(b) Average efforts over a period. The average period and standard deviation are obtained from the superposition of 19 entire periods

For a fixed cadence and a variable wind speed, the results show a standard deviation ranging from 3.8 % to 10 % with the minimum reached at 70 km/h wind speed. So, pedaling precision appears to be enhanced at 70 km/h compared to other wind speeds, including 40, 50, 60, and 80 km/h. In addition, Fig. 9 reveals that an increase in wind speed exerts a significant influence on the drag value, that is, the continuous component of the pedaling signal. The mean Pearson correlation coefficient between all five curves was 0.996 with a minimum value of 0.988 and a maximum of 0.998. This result shows that for a given cadence of 68 rpm, the variations in longitudinal force stay similar and their magnitude is modified by an offset depending on the wind speed.
<figure><img src="image_9.png" /><figcaption>**Fig. 9** Total longitudinal forces recorded by the wind tunnel force platform as a function of wind speed at a fixed cadence of 68 rpm</figcaption></figure>

To verify that the pedaling pattern is independent of wind speed, a comparison was made between the case with 65 km/h wind and the case without wind for a given cadence. The results of this comparison are shown in Fig. 10. It can be seen that the pedaling pattern is remarkably similar in the windy and windless cases for all cadences, with an average Pearson correlation coefficient for all the six configurations of 0.971 between the windy and windless periods. Finally, the difference between signals with and without wind represents the aerodynamic effects that were not filtered beforehand.
<figure><img src="image_10.png" /><figcaption>**Fig. 10** Average pedaling period difference with and without wind speed according to different cadences at a fixed wind speed of 65 km/h</figcaption></figure>

For windless measurements, a mean resultant force emerges as the cadence increases. Specifically, at low cadence, the average of the windless signal was close to null, while at high cadence, the average increases up to a maximum test cadence of 82.3 rpm during which the resultant magnitude reaches 0.24 N resulting in an additional force representing a systematical bias on the longitudinal axis.

<table><caption>**Table 1** Average resultant longitudinal force as a function of cadence in windless conditions</caption><thead><tr><th>Cadence (rpm)</th><th>25.1</th><th>32.6</th><th>39.8</th><th>54.3</th><th>61.0</th><th>69.1</th><th>82.3</th></tr></thead><tbody><tr><th>Effort Deviation (N)</th><td>0.01</td><td>0.03</td><td>0.02</td><td>0.07</td><td>0.07</td><td>0.05</td><td>0.24</td></tr></tbody></table>
## 4. Discussion

The DCM developed in this study represents a significant advancement in the aerodynamic testing of cycling performance. Unlike static mannequins or human test subjects, this tool offers a unique capability to mimic realistic pedaling motion while ensuring consistency and repeatability. The findings of this study highlight key aspects of its performance and raise important considerations for its application in wind tunnel testing.

The DCM brings technologies from previous mannequin studies together, providing the ability to pedal at real athlete cadences up to 80 rpm while maintaining good repeatability and an accurate representation of the athlete's morphology thanks to 3D scanning. According to Fig. 3, the DCM achieves very good repeatability in all tested conditions with a minimum standard deviation of 0.24 % and a maximum of 0.88 %. In the literature for such wind tunnel tests on human athletes, this standard deviation has been shown to be higher with 2.2 % in Martin et al. (1998) [32] and 1.6 % in Barry et al. (2015) [6]. If the DCM's pedaling motion is blocked, the aerodynamic drag coefficient standard deviation remains in the same order of magnitude while the aerodynamic coefficient decreases by an average of 4.9 %. A reduction that makes sense in view of Malizia et al.'s work on the impact of wheel rotation [33]. While heel rotation induces a higher drag coefficient compared with a fully static cyclist, the results of the present study show that wheel rotation combined with pedaling movements induces a higher drag coefficient as well. When considered as a whole, these results indicate that the DCM tested in the present study is more appropriate than humans as a tool to discern smaller meaningful aerodynamic effects.

The kinematic analysis revealed that the DCM exhibits lateral and vertical displacements of the pelvis, which aligns with observations in human pedaling biomechanics. These displacements stem from forces generated during pedaling that are not absorbed by the DCM's simplified joints and soft tissues, as highlighted in prior literature [25], [26], [34]. While the simplification of the hip and knee joints was necessary to reduce mechanical complexity, it does introduce limitations. The absence of lateral flexibility in these joints results in movements concentrated at the pelvis, potentially amplifying displacements that would otherwise be distributed throughout a human cyclist's body. However, it is striking that even a theoretically perfectly balanced (in segment weights, lengths and moments of inertia) DCM produces significant resultant forces at the pelvis (Fig. 4). These forces are induced by crank rotation and inertial effect even in the absence of muscular leg forces. Such forces are normally balanced vertically by arm and leg pulling, synchronized torso accelerations and body weight actions in a human cyclist [25]. In the DCM's case, only its weight and a magnetic saddle system can provide this stabilization [22]. Moreover, Fig. 6 show that lateral movement does not increase as linearly as vertical movement. On the other hand, the ideal pedaling model does not induce any movement or lateral forces in the joints, but this claim is limited by the choice of simplified pivot joints for the hip and knee joints.
In fact, the literature shows that there are lateral movements during pedaling [24]. In Fig. 6, an increase can be seen at 61 rpm and 69 rpm, even exceeding the maximum lateral movement reached at 82 rpm. It is important to note that the observed lateral movements include contributions from the deformation of the bicycle and the wind tunnel attachment structure. In addition, the measured overall variability could also be influenced by the accuracy of wind tunnel measurements. This variability can be attributed to several factors, including the precision of the force balance and the ability of the wind tunnel to deliver a highly repeatable wind speed. Consequently, the repeatability of the measurements obtained is also affected by the wind tunnel itself. A comparative study of wind tunnels could provide further insights into this matter. Another bias could also lie in the exact positioning of the DCM on the bicycle. This interplay between DCM dynamics and external factors underscores the complexity of replicating human-like movement in controlled testing environments. Future designs might benefit from incorporating advanced joint mechanisms or materials that better replicate human biomechanical behavior to reduce discrepancies and enhance biomechanical fidelity and measurement repeatability.

The method of analyzing the raw wind tunnel results makes it possible to identify the pedaling dynamics of the DCM and verify its repeatability. However, this method involves the filtration of raw data, which may result in a slight loss of information at the initiation of the analysis. In some cases, the frequency at 4.7 Hz filtered by the notch filter may correspond to a pedaling harmonic frequency but this 4.7 Hz frequency is present even without wind and without cadence of the DCM and has to be filtered. A hypothesis for the origin of this frequency could involve the wind tunnel frequency of machinery operation. The impact on the pedaling signal is not significant (see Fig. 7 for a comparison between raw and filtered signals). The pedaling pattern obtained from this signal analysis at different cadences shows similarities with the theoretical ideal pattern presented in Fig. 5. The analysis reveals two pronounced peaks in effort magnitude, accompanied by smaller oscillations, as illustrated in Fig. 10. According to the crank angle, these two peaks correspond to the right leg at the top and bottom dead center. These findings are consistent with those reported by Crouch et al. (2016) [17]. Furthermore, the study's findings indicate that a change in wind speed has little or no effect on the mannequin's pedaling dynamics, while the wind theoretically hits the DCM's lower limbs, creating a force along the longitudinal X-axis. These drag forces are therefore expected to be much smaller than the forces acting on the DCM as it pedals. It is common practice to change wind speeds to compare the effect of a device at different Reynolds numbers. Ideally, a change in wind speed should be accompanied by a change in gear ratio to match cadence, wheel speed and wind speed. For simplicity's sake, no gear changes were made, adding a bias to the wind variation measurements. On the other hand, changes in cadence play a key role in the force output patterns. It is therefore essential to maintain the same cadence throughout the measurement process, whether testing a DCM or a human in a wind tunnel. In addition, it should be noted that in windless conditions, the mean longitudinal X efforts from the wind tunnel force platform should be null. However, as illustrated in Table 1, residual efforts are observed. This result tells that
higher cadences produce an increasingly higher measurement bias to consider. The Modelica analysis demonstrates that these forces are inherently associated with pedaling and are impossible to suppress. Furthermore, these values increase at high cadence, thus necessitating their consideration when assessing the overall condition. This finding underscores the necessity for consideration of measurement bias, which is known to amplify with increasing cadence.

Traditional wind tunnel measurements typically assume that the total measured force directly reflects aerodynamic drag alone. However, this assumption is overly simplistic and prone to errors, especially due to dynamic contributions associated with the cyclist's movement.

In this study, the overall force signal measured along the X-axis (aerodynamic drag) was decomposed into two primary components:

1. An oscillatory component arising from the pedaling motion and the associated dynamics of limb movement.

2. A component representing pure aerodynamic drag due to airflow around the cyclist.

The findings revealed that the oscillatory component can represent a significant proportion of the total signal, particularly at high cadences. Failing to account for this can result in an overestimation of aerodynamic drag, as the pedaling-induced oscillations may obscure subtle differences in actual aerodynamic performance. This methodological distinction is particularly important in comparative testing, where the search for marginal gains demands high precision. Incorrectly attributing variations solely to aerodynamic drag could lead to inappropriate decisions during the optimization of positions or equipment. In consideration of the elevated demand for precision in these optimization procedures, this method can also be employed to enhance wind tunnel testing protocols. A judicious combination of wind speed and cadence has to be chosen for precise drag measurement. Another application of this method lies in numerical attempts to model pedaling movement aerodynamics [15], [17], [35], [36]. In such computational fluid dynamics approaches, instantaneous wind tunnel measurements are seen as references to calibrate accurate numerical models. However, the present study shows that without pedaling dynamics removal from the wind tunnel force platform signal, a significant bias exists in force measurements usually and wrongly interpreted as caused by aerodynamics phenomena.

Beyond the results of this study, the method used to analyze wind tunnel data could be used to locally monitor aerodynamic changes during a measurement. This would make it possible to identify a change in an athlete's position during a measurement and easily correlate it with a synchronized video of the measurement. It would also be interesting to be able to compare these results with the athlete who served as the physical model for the creation of the DCM, allowing for a human-DCM comparison. This comparison will be the subject of a future study. Future work will also focus on multidisciplinary optimization of cycling objects where the DCM will be used as a precise tool to discern small aerodynamic drag differences.
The results of this study demonstrate that accounting for dynamic forces induced by pedaling not only enables more accurate evaluations of aerodynamic performance but also improves the understanding of interactions between the cyclists and their environment. These advances pave the way for more robust wind tunnel testing protocols, allowing for the detection of subtle adjustments in position or variations due to specific equipment. From a practical perspective, the DCM offers a versatile and reliable platform for aerodynamic testing in cycling. Its ability to maintain highly repeatable pedaling motions, even under varying wind speeds and cadences, makes it an invaluable tool for both research and equipment optimization. However, users must carefully consider test conditions—particularly cadence—to ensure that results align with the objectives of the study.
## 5. Conclusion

In conclusion, this article underscores both the strengths and limitations of the 3D printed DCM. The DCM integrates technologies from previous studies, enabling pedaling at cadences up to 80 rpm with high repeatability and accurate athlete morphology representation through 3D scanning. The DCM shows excellent drag repeatability with a standard deviation between 0.24% and 0.88%, outperforming human athletes in wind tunnel tests. As the DCM is not attached to the saddle, kinematic analysis reveals lateral and vertical pelvis displacements similar to human biomechanics, but simplified joints limit lateral flexibility, concentrating movements at the pelvis. The DCM's forces, induced by crank rotation and inertial effects, are balanced by its weight and a magnetic saddle system.

Wind tunnel data analysis identifies DCM pedaling dynamics and verifies repeatability through force signals. Wind speed changes have an insignificant impact on pedaling dynamics, but cadence changes significantly affect force output patterns. Higher cadences increase measurement bias due to unwanted DCM pelvis movements.

The DCM's ability to maintain repeatable pedaling motions under varying conditions makes it a valuable tool for aerodynamic testing and equipment optimization, though test conditions, especially cadence, must be carefully considered. These advancements would not only improve the reliability of aerodynamic testing but also contribute to the broader understanding of cycling performance optimization.
## 6. 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 and replicated as a mannequin for this study. The Wind Tunnel team of the Institut AéroTechnique (IAT, Le CNAM, 15 rue Marat 78210, Saint Cyr-l'Ecole, FRANCE) for the wind-tunnel measurements are gratefully acknowledged.

## 7. 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 Agence 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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