A range of athlete torso angles were investigated for the pilot and stoker in tandem para-cycling with regards to aerodynamics. The sagittal torso angles investigated were 20°, 25°, 30°, 40° and 50° (Fig. 1), where the same athlete’s geometry was used for both the pilot and stoker in numerical simulation to remove anthropometric bias. This study found that torso angles within 20°–25° resulted in the lowest range of CDA values, with 0.322 m2 at 25°–25° and 0.308 m2 at 25°–20°, and 0.314 m2 at 20°–25° and 20°–20°. The pilot in this study could thus potentially benefit from a slightly more relaxed position at a torso angle of 25°, potentially affording greater power output, but crucially optimising the aerodynamic interaction between the pilot and stoker (if the stoker remained at 20°) to attain the lowest overall CDA. It is noted that the sagittal torso angles investigated in this study were discrete angles, and that the absolute optimum torso angle combination for the pilot and stoker may be between these discrete angles. Fintelman et al.  discussed that adopting extreme low torso angles may not benefit an athlete by compromising power output, and that a balance could be found between aerodynamics and power output. In able-bodied solo cycling, athletes are capable of attaining torso angles lower than the minimum of 20° from the horizontal plane investigated in this study, with torso angles as low as 0° [15, 31]. However, that case study was for a time-trial setup with elbow pads and aerobars, and similar low torso angles would be difficult to maintain on dropped handlebars in a road race setup. In addition, the optimal torso angle to balance power output and aerodynamics is often athlete-dependent, as demonstrated by Underwood et al. .
The proximity of the pilot and stoker can limit the torso angle range available to both athletes, with restrictions placed by the UCI on the dimensions of the tandem frame. The individual anthropometrics of the athletes also play a role in the torso angle range available. The relationship between power output and torso angle for a solo able-bodied athlete has some resemblance to the pilot of a tandem, who has a similar cockpit to that of a solo cyclist. However, the same relationship for the stoker is not well understood or investigated in the literature. The results from this research suggest that the stoker needs to maintain a torso angle equal to or less than the pilot for aerodynamic purposes, which might have a yet unknown negative impact on the power output of the stoker. Increasing torso angle for the stoker had a more detrimental effect on the CDA than increasing torso angle on the pilot (Fig. 3). A CDA of 0.329 m2 was found for the torso angle combination of 20°–30°, higher by 1.9% than 0.323 m2 found at 30°–20°, and 0.9% higher than 0.326 m2 found at 30°–25°. The 20°–25° torso angle combination resulted in the same CDA of 0.314 m2 found for 20°–20°, but was 1.9% higher than 0.308 m2 found at 25°–20°. The difference in power to maintain a velocity of 15 m/s between 25°–20° and 20°–20° was estimated at 12.4 W. Alternatively in another perspective, the 25°–20° torso angle combination could save 6.5 s over a 10 km race, compared to 20°–20°. The difference was greater between 25°–20° and 25°–25°, at 28.9 W and 15.0 s for both power and time comparisons, respectively. These calculations on time difference are conducted considering continuous power output throughout the course of the race distance. Furthermore, the clear aerodynamic advantage of lower torso angles for both the pilot and the stoker, suggests that the design of the tandem frame should accommodate the lowest possible athlete torso angles while remaining within the limits set by the UCI. A torso angle combination of 25°–20° was the optimum value found within this research for non-biased athletes; however, the result may be athlete dependant to some degree. A study that standardises athlete anthropometrics may yield further information to the preferable athlete anthropometric proportions for the pilot and stoker positioning for aerodynamics purposes. The UCI rules determine the dimensions for the tandem bicycle, which in turn, limit the positioning options for the athletes to some degree. The present study considers athletes placed on a road bicycle within the regulations; however, some athletes may prefer positions farther back or farther forwards on the saddle. Such individual and unique positioning may further expand or detract from the range of torso angles available to the stoker athlete. Furthermore, the anthropometrics of both athletes and in particular the vertical height of the stoker, have large impacts on the torso angle combinations achievable by the team. Athletes should consider where possible to adjust the tandem bicycle (saddle, seat tube, and handlebars) to allow for the lower torso angle combinations. For example, for particular tandem teams, it may be possible to achieve torso angles lower than those achieved in this study, and a new range of optimal torso angle combinations may be possible.
The individual drag trends of the pilot and stoker increased and decreased as the other athlete adopted smaller or larger torso angles, respectively (Fig. 3b, c), excluding the torso angle combination of 25°–20°. The drag experienced by the stoker followed the same trend for each fixed pilot torso angle and resulting variations in stoker’s torso angle (Fig. 3c). Higher drag forces were found on the stoker for increasing torso angle. As the pilot’s torso angle increased for fixed stokers’ torso angles, the typical trend across all fixed stoker torso angles was for the drag to decrease (Fig. 3c). However, the drag experienced by the stoker increased by 1.9% from 20°–30° to 25°–30°, and by 1.4% from 20°–40° to 25°–40°. The drag on the pilot increased with his increasing torso angle (Fig. 3b). The typical trend with increasing stoker’s torso angle was for the drag on the pilot to decrease. However, at fixed pilots’ torso angles of 20° and 40° there were variations to this trend, with the drag of the pilot increasing between torso angle combinations of 30°–30° to 30°–40°, and between 40°–30° and 40°–40°. These outliers from the general trends are associated with subtle aerodynamic interactions between the pilot and stoker. The CDA (Fig. 3a) broke from its typical trend of increasing with larger pilot torso angles when the torso angle of the stoker was fixed at 50°. Maximum CDA values of 0.399 m2 were measured for 20°–50°, 25°–50° and 50°–50°, with the minimum CDA value of 0.383 m2 at this fixed stoker torso angle occurring at 40°–50°.
Tandem cyclists are exposed to atmospheric wind conditions in outdoor events. The properties of the atmospheric wind conditions may impact the aerodynamics of the tandem cyclists and the optimal torso angle combination may not be applicable to all wind conditions. Mannion et al.  demonstrated that crosswinds can impact the drag distribution of the pilot and stoker. It was found that the drag of the pilot reduced from a 0° yaw angle to 15° yaw. In contrast, the drag of the stoker increased between the same yaw angles. This infers that a singular torso angle combination optimised for 0° yaw conditions, may not be the optimum choice in crosswind conditions. This holds greater significance in outdoor competitive events than indoor velodrome events, as crosswinds may be more prevalent in the former. Moreover, this study considered still air with a low turbulence intensity with no headwind, tailwind or crosswind. It is likely that in reality, turbulence intensity may be higher due to wind conditions which may impact the flow separation locations on the athletes, further impacting their aerodynamic drag.
There were several limitations and simplifications with this study. First, the study considered static geometries with no leg or wheel rotation. It is possible that the movement of the athletes’ legs may transfer some movement to the torso of the athlete. This may impact the aerodynamics, and thus the optimum torso angle combination. Second, all surfaces of the athletes and bicycle geometries were considered as smooth, with zero roughness. The roughness would vary from the skin to the skin suits, bicycle frame, tyres and other components in actual cycling conditions. The roughness of the athletes’ skinsuits coupled with the torso angle adopted by the athletes could impact the locations of flow separation on the torso surfaces of the athletes. This in turn could positively or negatively impact the drag of the athletes. Third, the head angle relative to the torso angle was not changed between torso angle variations. The head and helmet of the athlete were rotated with the torso for each increment. Athletes typically adjust their head angle to maintain forward visibility and for relaxation/comfort. The head angle would impact the orientation of the helmet which, typically, has aerodynamic considerations in its design. There may be an optimum head angle to minimise aerodynamic drag and this angle may be specific to unique helmet designs. Thus, further torso angle combination optimisation for tandem athletes should consider this variable within their analyses.
Future research could couple CFD and wind tunnel experiments, by utilising articulated mannequins in the wind tunnel to allow for precise adjustments of torso angles, while maintaining repeatability and preventing a bias between the anthropometrics of the pilot and the stoker. However, the effect of differing anthropometrics between the pilot and stoker is also of interest for future research. A pilot that is larger than the stoker may provide good aerodynamic shielding at a greater range of torso angles, allowing for more relaxed positions for the stoker to increase power output without negatively impacting the overall aerodynamics. Furthermore, the optimal choice of helmets and skin suits for tandem athletes may have a dependency on the postures adopted by the athletes. Finally, an investigation should be conducted to optimise the balance between power output and aerodynamics for the pilot and stoker in tandem para-cycling, with additional focus on the stoker.