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Fighting crosswinds in cycling: A matter of aerodynamics

Published:December 10, 2022DOI:https://doi.org/10.1016/j.jsams.2022.12.003

      Abstract

      Objectives

      The main goal of this study was to compare the aerodynamic optimization level in echelon-formation strategy for riders fighting against a crosswind from the best (echelon or diagonal paceline) to the worst riders' configuration (guttered riders).

      Design

      The case reported herein concerned a group of 5 cyclists riding at 30 km/h with a 30 km/h crosswind oriented at 40° to the direction of travel. The effects of the wind, expressed in terms of aerodynamic resistance or pressure, were determined for each cyclist in the different configurations.

      Methods

      The 3D numerical simulations were performed using a calculation code based on the finite volume method and the Reynolds-averaged Navier–Stokes turbulence model k–kl–ω.

      Results

      The results showed that the lateral force savings, averaged over the whole five-riders group, ranged from 50% in the echelon-optimized configuration to 11% in the guttered straight-line one, compared to a solo rider in the same velocity and windy conditions. Individually, the rider with the best aerodynamic shelter is the 4th rider in the “4 rider echelon + 1 guttered rider” formation (− 53.6% in drag force and − 69.8% in lateral force), while the rider with the worst aerodynamic situation is the leader of the straight paceline (− 0.1% in drag force and − 0.2% in lateral force).

      Conclusions

      The analysis showed how the spatial management of riders significantly influences drag and lateral forces and supported the idea that avoiding being guttered is the best way to save energy in windy races.

      Keywords

      Practical implications

      • The management of crosswinds and deduced optimal echelon formations can help cycling teams plan race strategies so that opponents get dropped from the peloton, or in time-trial team races, share the workload between all riders.
      • Our results suggest that the greater the number of riders in the diagonal echelon formation, the higher the aerodynamic gain compared to a solo rider.
      • Findings revealed that the sheltered trailing riders spend up to 8 times less energy than the group-leading rider who produces the highest extra effort.

      1. Introduction

      During cycling races, riders adopt individual and collective strategies to minimize their energy expenditure.
      • Marino F.E.
      • Kay D.
      • Cannon J.
      • et al.
      A reproducible and variable intensity cycling performance protocol for warm conditions.
      • de Koning J.J.
      • Bobbert M.F.
      • Foster C.
      Determination of optimal pacing strategy in track cycling with an energy flow model.
      • Jeukendrup A.E.
      • Craig N.P.
      • Hawley J.A.
      The bioenergetics of world class cycling.
      These strategies depend on several factors such as the number of riders, the topology of the course, or the weather conditions.
      • Atkinson G.
      • Brunskill A.
      Pacing strategies during a cycling time trial with simulated headwinds and tailwinds.
      • Sundström D.
      • Carlsson P.
      • Tinnsten M.
      On optimization of pacing strategy in road cycling.
      • Swain D.P.
      A model for optimizing cycling performance by varying power on hills and in wind.
      For example, the wind is a key factor because it requires extra effort from cyclists when it is unfavorable (headwind or crosswind).
      • Clanet C.
      • Abel H.
      • Brunet E.
      • et al.
      Cycling speeds in crosswinds.
      Riding alone and facing a strong headwind can be very difficult, while strong crosswinds can become quite dangerous as seen during the Strade Bianche 2022 (Alaphilippe crash). To limit the energy expenditure resulting from the extra aerodynamic resistance, cyclists in a peloton have developed collective strategies similar to drafting.
      • Kyle C.R.
      Reduction of wind resistance and power output of racing cyclists and runners travelling in groups.
      This aerodynamic phenomenon, well known in the sports world, involves athletes taking shelter from the wind by positioning themselves in the wake of the athlete ahead of them.
      • Beaumont F.
      • Legrand F.
      • Bogard F.
      • et al.
      Aerodynamic interaction between in-line runners: new insights on the drafting strategy in running.
      • Belloli M.
      • Giappino S.
      • Robustelli F.
      • et al.
      Drafting effect in cycling: investigation by wind tunnel tests.
      • Schickhofer L.
      • Hanson H.
      Aerodynamic effects and performance improvements of running in drafting formations.
      In the case of no wind or wind blowing in the direction of travel, riders position themselves in a single paceline.
      • Barry N.
      • Burton D.
      • Sheridan J.
      • et al.
      Aerodynamic drag interactions between cyclists in a team pursuit.
      ,
      • Blocken B.
      • Defraeye T.
      • Koninckx E.
      • et al.
      CFD simulations of the aerodynamic drag of two drafting cyclists.
      In this case, riders behind the lead runner benefit from a notable reduction in aerodynamic drag.
      • Blocken B.
      • Toparlar Y.
      • Van Druenen T.
      • et al.
      Aerodynamic drag in cycling team time trials.
      ,
      • Blocken B.
      • van Druenen T.
      • Toparlar Y.
      • et al.
      Aerodynamic drag in cyclist pelotons: new insights by CFD simulation and wind tunnel testing.
      However, when the wind is blowing across, a rider will come to be positioned, not directly, but diagonally behind the runner producing the effort.
      • Kraemer P.
      • Marro M.
      • Correia H.
      • et al.
      Preliminary study on crosswind aerodynamics for a group of road race cyclists.
      Therefore, the strategy to ride against a crosswind is to form an echelon and work in relays, thus sharing the extra effort required to fight this aerodynamic constraint. Echelon formation can significantly impact the final ranking and may also be a team strategy to get opponents into the gutter.
      • Mignot J.F.
      Strategic behaviour in road cycling competitions.
      ,
      • Phillips K.E.
      • Hopkins W.G.
      Determinants of cycling performance: a review of the dimensions and features regulating performance in elite cycling competitions.
      Cycling team strategies to counter the effects of wind have been developed empirically and few scientific studies have focused on the topic. The effects of suction and drag reduction in groups of cyclists and even in pelotons in the absence of wind are well known and have been demonstrated in several previous wind tunnel experiments
      • Belloli M.
      • Giappino S.
      • Robustelli F.
      • et al.
      Drafting effect in cycling: investigation by wind tunnel tests.
      ,
      • Barry N.
      • Burton D.
      • Sheridan J.
      • et al.
      Aerodynamic drag interactions between cyclists in a team pursuit.
      ,
      • Fitton B.
      • Caddy O.
      • Symons D.
      The impact of relative athlete characteristics on the drag reductions caused by drafting when cycling in a velodrome.
      or by numerical simulation.
      • Blocken B.
      • Defraeye T.
      • Koninckx E.
      • et al.
      CFD simulations of the aerodynamic drag of two drafting cyclists.
      ,
      • Blocken B.
      • van Druenen T.
      • Toparlar Y.
      • et al.
      Aerodynamic drag in cyclist pelotons: new insights by CFD simulation and wind tunnel testing.
      ,
      • Torre A.
      • Íñiguez J.
      Aerodynamics of a cycling team in a time trial: does the cyclist at the front benefit?.
      Although these studies provide important information about the aerodynamic performance of cyclists, they do not take into account environmental conditions such as wind.
      The few studies conducted with a crosswind have focused on the impact of wheel geometry on rider stability
      • Barry N.
      • Burton D.
      • Crouch T.N.
      • et al.
      Effect of crosswinds and wheel selection on the aerodynamic behavior of a cyclist.
      or on the aerodynamic drag of a solo rider.
      • Fintelman D.M.
      • Hemida H.
      • Sterling M.
      • et al.
      The effect of crosswinds on cyclists: an experimental study.
      ,
      • Fintelman D.M.
      • Hemida H.
      • Sterling M.
      • et al.
      CFD simulations of the flow around a cyclist subjected to crosswinds.
      Mannion et al.
      • Mannion P.
      • Toparlar Y.
      • Blocken B.
      • et al.
      Improving CFD prediction of drag on Paralympic tandem athletes: influence of grid resolution and turbulence model.
      ,
      • Mannion P.
      • Toparlar Y.
      • Clifford E.
      • et al.
      On the effects of crosswinds in tandem aerodynamics: an experimental and computational study.
      also performed CFD simulations and wind tunnel tests to analyze the effects of crosswind on the aerodynamics of a solo and tandem para-cycling competition. To the best of our knowledge, few aerodynamic studies have focused on the influence of wind on a group of cyclists. Belloli et al.
      • Belloli M.
      • Giappino S.
      • Robustelli F.
      • et al.
      Drafting effect in cycling: investigation by wind tunnel tests.
      performed wind tunnel measurements on two cyclists pedaling at different longitudinal distances, also considering slight crosswinds. Kraemer et al.
      • Kraemer P.
      • Marro M.
      • Correia H.
      • et al.
      Preliminary study on crosswind aerodynamics for a group of road race cyclists.
      performed wind tunnel measurements on a scaled-down group of cyclists to investigate crosswind effects on cyclists' echelon and gutter positioning.
      In view of the scarce literature in this sports field, a new numerical insight in the aerodynamic optimization level in echelon-formation strategy for riders fighting against a crosswind was proposed in the present study.
      To this end, the effects of a 40° crosswind on a group of 5 cyclists riding at 30 km/h were investigated. The aerodynamic forces exerted on the riders arranged in several configurations, ranging from echelon, mixed echelon–gutter to gutter arrangements were studied, and compared to the reference case of a solo rider. The 3D CFD simulations were performed with a calculation code based on the finite volume method. The results were analyzed in terms of aerodynamic drag and pressure distribution.

      2. Materials and methods

      The geometry of the cyclist was initially obtained by scanning a cyclist (height: 1.80 m, weight: 63 kg) in static and dropped position using a 3D structured light scanner (ARTEC® EVA, 3D reconstruction rate: 16 fps, accuracy: 0.1 mm), and assembled to that of a bicycle. Prior to the study, written consent was obtained from the athlete.
      The geometry of the cyclist–bicycle assembly and key dimensional characteristics are shown in Fig. 1(a). Furthermore, the bike geometry was simplified: it was assumed that small elements such as the chain, cables, sprockets, brakes, and spokes could be neglected as they are small enough not to influence the surrounding flow. Finally, to reduce the computational cost of the simulation, the number of geometric cells at the rider's surface was reduced (smoothing). A frontal area of 0.46 m2 was measured for the cyclist/bike assembly using the ANSYS Space Claim© CAD software.
      Fig. 1
      Fig. 1(a) Simplified geometry of the cyclist and bicycle. (b) Positioning of riders for a 40° wind blowing diagonally from the left at 30 km/h (Left). Lateral and longitudinal spacings between riders (Right). (c) Vectorial decomposition of velocity parameters.
      To protect themselves from the crosswind, the riders form an echelon, whose orientation depends on three parameters: wind angle, wind velocity and riders' velocity. In this study, the selected crosswind velocity was 30 km/h, with a 40° crosswind. Furthermore, the cyclists' velocity was considered constant at 30 km/h. Fig. 1(b) represents the different studied arrangements of the riders' group in the crosswind. Both the longitudinal distance from wheel to wheel and the lateral distance from shoulder to shoulder were set to 0.25 m (see Fig. 1(b)). Five echelon-formation configurations composed of 5 riders were studied, from the best aerodynamic management one (echelon or diagonal paceline) to the worst (guttered straight paceline).
      Six full-scale simulations were performed, one for the single cyclist and five for the echelon and guttered configurations. The corresponding computational domains were dimensioned in agreement with the CFD best practice guidelines.
      • Blocken B.
      Computational fluid dynamics for urban physics: importance, scales, possibilities, limitations, and ten tips and tricks towards accurate and reliable simulations.
      In all configurations, the domain boundaries are located 15 m downstream and 15 m to the right of the trailing rider, 6 m upstream and 6 m to the left of the leading one. The domain height is 6 m. To prevent wall effects, the maximum blockage ratio is 0.4%, which is well below the maximum recommended value of 3%.
      • Franke J.
      • Hellsten A.
      • Schlünzen H.
      • et al.
      Best practice guideline for the CFD simulation of flows in the urban environment, COST Action 732: quality assurance and improvement of microscale meteorological models Hamburg.
      Unstructured mesh of the computational domain was created based on CFD mesh generation guidelines
      • Blocken B.
      Computational fluid dynamics for urban physics: importance, scales, possibilities, limitations, and ten tips and tricks towards accurate and reliable simulations.
      • Franke J.
      • Hellsten A.
      • Schlünzen H.
      • et al.
      Best practice guideline for the CFD simulation of flows in the urban environment, COST Action 732: quality assurance and improvement of microscale meteorological models Hamburg.
      • Mannion P.
      • Toparlar Y.
      • Blocken B.
      • et al.
      Analysis of crosswind aerodynamics for competitive hand-cycling.
      and an extensive analysis of mesh size independence (Appendix A) was performed. Finally, the global mesh ranged from 19 × 106 cells for the isolated cyclist configuration to 42 × 106 cells for the other ones. Fig. 1(c) highlights the components of the cyclist and wind velocities, which enable calculation of the relative wind velocity and associated apparent wind angle. This angle corresponds to the sheltering line that the cyclist must adopt in an attempt to minimize extra energy expenditure.
      In such case, the apparent wind velocity W is defined as follows:
      W=U+Vcosα2+Vsinα2
      (1)


      The yaw angle β formed between the direction of the cyclist's motion and the direction of the apparent wind is given by the following relationship:
      β=AcosU+V×cosαWifUV,andβ=α2ifU=V.
      (2)


      The inlet velocity components used as boundary conditions in the adopted Cartesian coordinate system are U + V ×  cos α in the longitudinal direction (front face) and V sin α in the transverse direction (left face).
      The surfaces of the cyclist's body and the bicycle were considered as no-slip walls (zero roughness). A symmetry condition was imposed on the top and bottom faces of the computational domain. At the outlet (rear) and right faces, a pressure outlet boundary condition with ambient static pressure was imposed, and the law of conservation of mass (all gradients equal to zero) was applied.
      A turbulence intensity of 0.2% was applied, which corresponds to the approach-flow turbulence intensity in the test section of the wind tunnel used by Blocken et al.
      • Blocken B.
      • Toparlar Y.
      • Van Druenen T.
      • et al.
      Aerodynamic drag in cycling team time trials.
      ,
      • Blocken B.
      • van Druenen T.
      • Toparlar Y.
      • et al.
      Aerodynamic drag in cyclist pelotons: new insights by CFD simulation and wind tunnel testing.
      and Mannion et al.
      • Mannion P.
      • Toparlar Y.
      • Clifford E.
      • et al.
      On the effects of crosswinds in tandem aerodynamics: an experimental and computational study.
      In the present study, the selection of a suitable turbulence model relied on the sensitivity analysis by Mannion et al.,
      • Mannion P.
      • Toparlar Y.
      • Clifford E.
      • et al.
      On the effects of crosswinds in tandem aerodynamics: an experimental and computational study.
      who compared four different turbulence models. Their results showed that the k–kl–ω model provided more accurate predictions of the lateral and drag forces, for yaw angles between 10° and 20°. Therefore, the 3D RANS equations were solved using the three-equation k–kl–ω model. To improve the convergence criterion, the pseudo-transient approach was used with 6000 time-steps of 0.001 s. The coupled algorithm was used for pressure–velocity coupling with second-order discretization schemes and the gradients were calculated using the least square cell-based method. The simulations were performed with the commercial CFD code ANSYS® Fluent 2020R2. The drag and lateral force coefficients were monitored throughout the computational process for each rider, and stable convergence of the results was achieved when the values no longer varied over time. The drag force coefficient Cx and the lateral force coefficient Cz are defined as follows:
      Cx=Fx12ρw2AxandCz=Fz12ρw2Az
      (3)


      where Fx (N) is the drag force (acting in the direction of bike motion x) and Fz (N) the lateral force (acting in the direction perpendicular to the bike motion z). Ax is the frontal surface area (m2) and Az the projected side area of the cyclist/bike assembly (m2), ρ is the air density (kg/m3), and w (m/s) is the approach flow velocity.

      3. Results

      During a race, air resistance acts as a force acting against the cyclist's movement, i.e. the rider is slowed by the force due to air resistance.
      The aerodynamic coefficients Cx and Cz are summarized in Table 1 for the six studied configurations and were obtained after averaging over the last 2000 iterations. The results of the present study obtained for a yaw angle of 20° were previously compared with the literature data
      • Clanet C.
      • Abel H.
      • Brunet E.
      • et al.
      Cycling speeds in crosswinds.
      ,
      • Kraemer P.
      • Marro M.
      • Correia H.
      • et al.
      Preliminary study on crosswind aerodynamics for a group of road race cyclists.
      ,
      • Fintelman D.M.
      • Hemida H.
      • Sterling M.
      • et al.
      CFD simulations of the flow around a cyclist subjected to crosswinds.
      to assess the validity of the numerical method (see Appendix A). Results show that the lateral force is predominant compared to the drag force in the present study conditions (due to the relative sizes of the frontal and lateral area of the cyclists). The lateral to drag force ratio averaged over the whole group varies according to the number of guttered riders and ranges from 1.18 ± 0.17 to 1.46 ± 0.06. In tunnel experiments, Barry et al.
      • Barry N.
      • Burton D.
      • Crouch T.N.
      • et al.
      Effect of crosswinds and wheel selection on the aerodynamic behavior of a cyclist.
      deduced that the lateral force was approximately twice the drag force for a yaw angle of 15° and a 50 km/h apparent wind velocity.
      The histogram in Fig. 2(a) represents the aerodynamic benefit (% reduction in drag and lateral forces) for each position in the group compared to the reference case (cyclist alone), as well as the average gain per group of 5 cyclists (red number next to the dashed line).
      Fig. 2
      Fig. 2(a) Relative aerodynamic gain (%) for each cyclist and configuration compared to the reference case of a solo rider. The corresponding dotted line represents the gain averaged over the whole group of 5 riders. (b) Dynamic pressure isosurfaces for P = 55 Pa for each configuration. (c) Focus on the pressure coefficients on the bodies of riders 1 and 4 in the group of 5 riders in echelon configuration.
      This figure clearly highlights the aerodynamic benefit that the echelon formation provides for all cyclists in the group compared to the other configurations studied (echelon + gutter or gutter alone). It is also remarkable that all cyclists in the echelon group but also in groups in which cyclists are both in the echelon and the gutter benefit from reduced aerodynamic forces. The results showed that the drag force savings, averaged over the whole five-riders group, ranged from 39.0±15.3% in the echelon-optimized configuration to 9.0±6.2% in the guttered straight-line one, compared to a solo rider in the same velocity and windy conditions. The estimated gains for lateral force are even higher with values ranging from 50±18.7% to 11±8.3%. It should be noted that the estimated savings could depend largely on the distance between riders and of the yaw angle, this latter acting on various flow phenomena contributed to the trends in aerodynamic forces.
      • Mannion P.
      • Toparlar Y.
      • Clifford E.
      • et al.
      On the effects of crosswinds in tandem aerodynamics: an experimental and computational study.
      For example, Kraemer et al.
      • Kraemer P.
      • Marro M.
      • Correia H.
      • et al.
      Preliminary study on crosswind aerodynamics for a group of road race cyclists.
      estimated that it was more interesting to ride in the gutter, behind the runners in echelon (4 runners in echelon + 1 in gutter) than to ride within the echelon in last position. This finding, although opposite to our results, is valid for small wheel spacings and small yaw angles.
      • Kraemer P.
      • Marro M.
      • Correia H.
      • et al.
      Preliminary study on crosswind aerodynamics for a group of road race cyclists.
      When cyclists are in motion, the mass of air that they are moving exerts pressure on their bodies and their bikes. For the sake of clarity, Fig. 2(b) qualitatively shows the unfavorable pressure bulks (P > 55 Pa) that riders have to experience in crosswind positions. The larger the volume of the isosurfaces, the higher the total aerodynamic force on the rider, in agreement with Table 1. It is clear from Fig. 2(b) that the leading riders are those who undergo the highest overpressures. To complete this analysis, a focus is conducted on the static pressure, which is known to be a fundamental parameter in competitive cycling. The pressure coefficient is defined as follows:
      Cp=2PP0ρu2
      (4)


      where P is the static pressure, P0 is the reference static pressure (i.e. atmospheric pressure), ρ the air density, and u, the speed of the body through the fluid (m/s).
      To further the analysis and to provide a better understanding of the aerodynamic gain from drafting, Fig. 2(c) exhibits the extreme Cp values for cyclists 1 and 4 of the echelon group. To better highlight the slightest change in the pressure field, the pressure range is arbitrarily limited, even though the maximum and minimum absolute Cp values are much larger. This figure shows us, for example, that compared to rider 1, the value of the coefficient on the top of the left foot of rider 4 is reduced by 78%, this reduction even reaching 82% at the bottom of the bike frame. What can also be seen is that the low-pressure zone, which extends on the side of the leg up to the rider's arm, is less extensive on the rider 4 who is in a sheltered position. The trend is the same for the overpressure zones, which are less extensive on cyclist 4 compared to cyclist 1, who is subjected to larger pressure gradients.

      4. Discussion

      In windy cycling races, strategies to fight against aerodynamic constraints often induce sheltering race patterns, ranging from straight-in-line to echelon organizations, to cover longer distances at higher velocities. In a race and according to the wind direction, cyclists who are not included in an echelon and do not benefit from aerodynamic shelter, called guttered cyclists, must therefore produce a much greater effort to ride at the same velocity as the echelon in order to keep up with the pace. Consequently, the management of crosswinds and deduced optimal echelon formations can help cycling teams plan race strategies so that opponents get dropped from the peloton, or in time-trial team races, share the workload between all riders.
      By analyzing different possible echelon configurations in crosswind, from the best diagonal echelon to the worst guttered straight line, the results of the present study show that the optimization of echelon-formations is key in minimizing the overall energy expenditure of a 5-rider group to fight against wind.
      As a matter of fact, aerodynamic drag resistance is known to represent about 90% of the overall resistance in road cycling.
      • Barry N.
      • Burton D.
      • Sheridan J.
      • et al.
      Aerodynamic drag interactions between cyclists in a team pursuit.
      ,
      • Blocken B.
      • Toparlar Y.
      • Van Druenen T.
      • et al.
      Aerodynamic drag in cycling team time trials.
      In the conditions selected for the present study (U = 30 km/h, V = 30 km/h, α = 40°), results show for example that all echelon configurations are beneficial to the leader compared to a solo cyclist: gains in aerodynamic drags range from 0.1% to 4.8% depending on the number of riders in the echelon. A same trend is observed for the lateral forces, with estimated gains between 0.2 and 10% compared to a solo cyclist. What should be a counter-intuitive finding can be explained by the presence of the following rider which decreases the absolute value of the underpressure behind the lead rider, resulting in a reduction of the lead rider's drag.
      • Blocken B.
      • Defraeye T.
      • Koninckx E.
      • et al.
      CFD simulations of the aerodynamic drag of two drafting cyclists.
      Considering the collective strategy, the results suggest that the larger the number of riders in echelon, the higher the aerodynamic gains for each rider in the group (compared to the solo rider). Averaging the gain over the entire group, the 5 echelon runners benefit from a 50% reduction in lateral force (compared to the single rider) versus only 11% for the 5 gutter runners (number in red, Fig. 2(a)). From an aerodynamic viewpoint, every cyclist causes disturbances in the flow both upstream and downstream. When riding, the lead cyclist creates a low-pressure wake in which the following cyclist must position himself to minimize his energy expenditure. Finally, since the highest pressures are located in the areas perpendicular to the flow, riding in the wake of another rider is the best way to reduce both the pressures and the aerodynamic forces that increase the effort to maintain the race pace. For example, the drag reduction (compared to a solo rider) is 53.6% for the second to last of the 5 riders in the echelon while it is only 16% for the second of the group of 2 riders in the echelon + 3 guttered riders. Finally, the findings of this study must be viewed in the context of a number of limitations that are listed in Appendix B.

      5. Conclusion

      The purpose of this study was to investigate the effects of a 40° crosswind on a group of 5 cyclists riding at 30 km/h. The aerodynamic forces exerted on the riders arranged in several configurations, ranging from echelon, and mixed echelon–gutter to gutter arrangements were studied, and compared to the reference case of a solo rider. The results revealed that all echelon configurations are favorable for the group leader compared to a solo rider: the drag force is reduced by up to 4.8% while the lateral force is reduced by up to 10%, the benefit depending on the number and position of the rider in the echelon. It is worth noting that the sheltered trailing riders spend less energy (by reducing aerodynamic resistance) than the group-leading rider who produces the highest extra effort (except for the configuration featuring 5 guttered riders). For example, the lateral force exerted on the second to last of the 5 runners in the echelon is only one-third of the force exerted on the group leader (relative to a solo runner). Our results also suggest that the greater the number of riders in the diagonal echelon formation, the higher the aerodynamic gain of the group compared to a solo rider. Averaging the benefit over the whole group, the 5 echelon riders benefit from a 50% reduction in lateral force versus 11% for the 5 gutter riders (compared to the single rider).
      The following are the supplementary data related to this article.

      Funding information

      There are no financial conflicts of interest related to the research that require reporting in the manuscript. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

      Confirmation of ethical compliance

      Not applicable: this research does not involve human participants and/or animals.

      CRediT authorship contribution statement

      Fabien Beaumont: Methodology, Investigation, Writing – original draft. Fabien Bogard: Conceptualization, Validation, Formal analysis. Sébastien Murer: Validation, Data curation. Guillaume Polidori: Conceptualization, Validation, Writing – review & editing, Project administration.

      Declaration of interest statement

      All authors declare that they don't have any financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work.

      Acknowledgments

      Not applicable.

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