Variation of the drafting effect on the trailing rider for

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the race. To realize the rotation of cyclists in the team pursuit, the leading ... rider to rotate quickly to the back of the group and benefit from the strong drafting ... test with an athlete and a full-scale mannequin as two riders in a traveling ..... aerodynamic drag of the most trailing rider in 4R can be kept small to that of 2R even.
Variation of the drafting effect on the trailing rider for different numbers of riders in a cycling group Keita Shirasaki1, Kaoru Yamanobe1, Keita Akashi1, Wataru Takashima2 1,Wind

Tunnel Group, High Performance Unit, Department of Sports Sciences, Japan Institute of Sports Sciences (JISS), Tokyo,

Japan 2 Department

of Health and Medical Sciences, Hachinohe Gakuin University, Aomori, Japan

Corresponding author: Keita SHIRASAKI, Department of Sports Sciences, Japan Institute of Sports Sciences (JISS), 3-15-1 Nishigaoka, Kita-ku, Tokyo 115-0056, Japan Email: [email protected]

ABSTRACT The technique of following another rider to reduce aerodynamic drag (drafting) is a basic tactic in cycling. This study clarifies the trailing rider’s drafting effect for different numbers of riders and relative positions in the traveling group. Wind tunnel experiments were conducted with a static mannequin as the subject measured. Measurements were made with a floor-mounted six-component force balance. Athletes sat on bicycles mounted on bicycle stands and provided the drafting effect; experiments were conducted for riding groups of two riders (2R) and four riders (4R). The aerodynamic drag of the most trailing rider (i.e., mannequin) was measured for a wind speed of 16.67 m/s and different relative spatial positions (a longitudinal distance of 0– 0.75 m and lateral distance of 0–0.90 m) to the rider ahead. When the approximate tandem arrangement had a lateral distance of 0–0.25 m, the aerodynamic drag increased with the longitudinal distance in both 2R and 4R. However, the increase was much smaller in the 4R than in the 2R. In the range of lateral distance in which there is a drafting effect, the drafting effect was stronger in the 4R than in the 2R. It is thought that the fourth position without tight separation can achieve a drafting effect comparable to that of the second position with tight separation. Key Words: cycling, team pursuit, aerodynamics, drag, drafting, performance

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1 Introduction

In cycling, about 90% of total resistance experienced by the cyclist is aerodynamic drag at a racing speed of 40 km/h [1]. To reduce aerodynamic drag, multiple riders form a traveling group as a general tactic; this technique is referred to as drafting. In the process of drafting, the aerodynamic drag reduces toward the rearward position in the traveling group [2, 3, 4, 5]. An important tactic is not only to draft but also to rotate the positions of cyclists within the traveling group, such that each rider shares the burden of cycling in the front position, where he or she experiences the highest aerodynamic drag. The present study considers the team pursuit, where teams of four male or female riders cycle 4 km in a velodrome. Drafting and rotation strongly affect the outcome of the race. To realize the rotation of cyclists in the team pursuit, the leading rider moves outward on corners of the track and rejoins at the end of the traveling group by decelerating and accelerating up and down the banks of the corners. During this movement, the aerodynamic drag acting on the cyclist rotating to the back of the group, who is widely separated from the traveling group in a lateral direction, is considered to be as great as that acting on a single rider traveling alone. It is thus important for a rider to rotate quickly to the back of the group and benefit from the strong drafting effect. The spatial position (i.e., the longitudinal distance as axial displacement and traveling line as lateral displacement) is a major factor of the reduction in aerodynamic drag for drafting cyclists. The aerodynamic drag of the trailing rider has been shown in experimental and simulation studies of two riders in a tandem arrangement to be a minimum when the longitudinal distance, which is the distance in the traveling direction between the leading rider and trailing rider of a traveling group, is a minimum, and it increases as the longitudinal distance increases [6, 7, 8, 9]. Experimental studies in which two riders are in a staggered arrangement have shown that the aerodynamic drag of the trailing rider is a minimum when the traveling line, which is the lateral displacement from the centerline of the lead rider, is a minimum, and it increases as the lateral distance increases [6, 7, 9]. In particular, a wind tunnel test with an athlete and a full-scale mannequin as two riders in a traveling group has shown that the lateral distance is a major factor of aerodynamic drag reduction for drafting cyclists, more so than the longitudinal distance [9]. It is thus considered that the trailing rider needs to maintain a tandem arrangement to benefit from a stronger 2

effect of drafting. Therefore, it is important that the relative spatial positions of all riders forming a traveling group are noted. However, it is considered that the drafting effects of the relative spatial positions are not necessarily equivalent for the second and fourth riders in the team pursuit because of the different magnitudes of drag reduction. Previous studies on drafting in cycling have compared the drafting effects on the second and fourth of four riders in close proximity and a tandem arrangement, but there has been no study on the effect of the spatial position of the fourth rider on the drafting effect. Therefore, the difference in drafting effects between the second and fourth riders is not obvious and is affected by the relative spatial positions of riders in a traveling group. The present study investigates how the position of the trailing rider in traveling groups composed of two and four riders affects the drafting effect, and clarifies the benefits of rotation and drafting in the team pursuit.

2 Methodology

The present study conducts wind tunnel tests for two riders traveling in a group (2R) and four riders traveling in a group (4R). All tests were conducted in the wind tunnel of the Japan Institute of Sports Sciences. This facility has an open jet test section with height of 3 m, width of 2.5 m, and length of 8 m.

2.1 Subject measured (most trailing rider)

As the most trailing rider, the 2R and 4R use a static mannequin as the subject measured. The mannequin and its track bicycle were installed using a bicycle jig and a six-component floor-mounted force balance. The front wheel of the bicycle was set about 6 m downstream from the nozzle exit of the wind tunnel. The mannequin was positioned in a time trial posture on the bicycle.

2.2 Subject not measured (leading rider) 3

In the 2R, as the leading rider, an athlete mounted a track bicycle on a stand (MINOURA, SS-700) in front of the mannequin and disrupted the airflow. The lead bicycle was installed on a bicycle stand, which was approximately 0.03 m higher than the bicycle jig. The athlete adopted a time trial posture. The 4R involved three athletes in a similar manner. The pairing of the mannequin and athlete was the same in 4R and 2R (i.e., the pair of third and fourth riders in the 4R was the same as the pair of first and second riders in the 2R). Each athlete maintained the same posture as long as possible. Table 1 shows the physical parameters of each subject (characteristic body size and height of helmet top in the riding position). However, circumference of athlete 1 was not measured.

Table 1 Physical parameters of each subject (characteristic body size and height of helmet top in the riding position)

2.3 Relative position of the rider in a traveling group

The longitudinal distance between the front end of the front tire of the most trailing rider and the rear end of the rear wheel of the rider in front (either the lead or third rider in 2R and 4R respectively) is denoted X [m], while the lateral distance is similarly denoted Y [m]. Test ranges of X and Y are described in Figure 1. As mentioned section 2.1, the mannequin was always fixed on the same position of the test section thorough out the experiments, while the leading athlete(s) repositioned. In addition, between the third and fourth riders in the 4R, the longitudinal distance was kept constant at 0.15 4

m and the lateral distance was 0 m (for a tandem arrangement). When X = 0 m, to prevent contact, X was, strictly speaking, 0.01 m. In addition, the aerodynamic drag was measured for the mannequin in isolation for reference.

Figure 1 Grid of the relative spatial position, longitudinal distance X [m] and lateral distance Y [m].

2.4 Wind tunnel tests for the traveling group

The athletes in the group were male cyclists shown in Table 1. It has been shown that the leg position generating the most symmetric wake (i.e., the right foot was at 105 degrees from top dead center while the left foot was at 285 degrees) [10]. In this study, the horizontal position (90 and 180 degrees) was chosen that is close to this and easy to fix. The pedals of all bicycle were thus set by fixing the crank arm and chain stay on the non-drive side. All tests were conducted at a wind speed of 16.67 m/s, which was measured using a Pitot tube at the nozzle exit of the wind tunnel and Pitot coefficients for the location of the front end of the front tire of the leading rider. The speed is approximately the average speed of a team competing at a world-class level. The aerodynamic drag of the mannequin as the most trailing rider was measured. The measurement resolution was 20 bits and the sampling rate was 1000 Hz. The aerodynamic drag (D [N]) was the average value taken over 5 s. The Reynolds number was approximately Re = 5.7 × 105, taking the torso chord of the mannequin as the characteristic length. The aerodynamic drag of the bicycle jig was deducted from the measured aerodynamic drag. Figure 2 shows the situation of the tests. Drag area 𝐶𝐷 𝐴 [m2 ] is calculated from D [N] according to

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𝐶𝐷 𝐴 = 1

𝐷

𝜌𝑈 2 2

(1)

where ρ is the air density [N/m2] and U is the mainstream speed of the wind tunnel [m/s]. The drag area of the mannequin, when tested in isolation, was 0.190 m2 .

Figure 2 Situations of 2R tests (X = 0 m, Y = 0 m) and 4R tests (X = 0.75 m, Y = 0.9 m).

2.5 Bicycle jig drag tests

As explained in section 2.4, the aerodynamic drag of the bicycle jig only must be deducted from the aerodynamic drag of the most trailing rider. However, this value depends on placing of the leading rider(s). Therefore, the interference of the bicycle jig was measured with the leading rider(s) in place for each test run and the most trailing rider removed. The leading rider(s) comprised a mannequin for the 2R and two mannequins and a cyclist for the 4R; all sat on bicycles mounted on stands. The aerodynamic drag of only the bicycle jig was 0.0277 m2 in wind tunnel tests, and 6

0.0220 m2 in Bicycle jig drag tests. The difference of about 0.0057 m2 is considered to be due to different conditions of the test sections under the floor. The difference was added to the interference drag of each bicycle jig as an offset value, and deducted from the results of wind tunnel tests conducted for the traveling group. Table 2 gives the deducted amounts in each test run as percentages of the aerodynamic drag of the bicycle jig only for the wind tunnel tests conducted on the traveling group. It is a specific characterization test in the wind tunnel to determine appropriate strut tares to subtract from measured drag on the mannequin during 2R and 4R.

Table 2 Drag deducted depending on the placement of the leading riders on each run. Values were calculated from the offset due to the difference in the experimentation environment and the resistance measured in each run.

2.6 Comparison with previous studies in the tandem arrangement

The percentage of the required power output at each position of the traveling group has been investigated in an actual riding experiment for the team pursuit; the second rider needed to generate 68.0% of the power output of the lead rider and the fourth rider needed to generate 61.0% [2]. In the wind tunnel experiment that measured the tandem trailing group of four riders, it is shown that the second rider is 55% and the fourth rider is 43% compared with the single state [5] In order to compare the aerodynamic drag of present study with the previous studies, the power of each position based on the lead rider rather than the single state was estimated. The power calculation method used the following equation, Barry et al. [5] was referenced. The used constants are shown in Table 3.

𝑃 = [𝐶𝑟𝑟 (𝑚1 + 𝑚2 )𝑔 + 𝐹𝑏 + 𝐷]𝑉

(2)

The aerodynamic drag for the lead rider was not measured in this study. So on the 7

interference effect of the lead rider received from the follow rider, Barry et al. [5] (95% compared with the single state) was referenced to present study. Because it is the experiment environment (for 4 riders and bicycles) similar to this study.

Table 3 The constants used in the power calculation.

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3 Results

The results of this study are shown in this chapter that tandem drag was compared with previous studies, and the tendency of aerodynamic drag by the relative spatial position.

3.1 Comparison with previous studies in the tandem arrangement

The power as a percentage of the leader, at each position, is shown in Figure 3. The percentage for the present study was calculated by the minimum aerodynamic drag, that was 46.9% (Y = 0 m, X = 0 m) in the 2R and 35.1% (Y = 0 m, X = 0.25 m) in the 4R as shown in Figure 4(a). The results of present study showed lower values than the track test (the differences are 14.1% at the position 2 and 16.7% at the position 4) and other wind tunnel experiments (7.0~9.3% and 5.5~8.9%).

Figure 3 Percentage of the power of each position relative to the lead rider power.

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3.2 Lateral distance

The drag area of the most trailing rider is given as a percentage of the aerodynamic drag when a cyclist rides alone in Figure 4(a)–(e). In 2R, all values of aerodynamic drag were lower than those for the single rider (riding alone) for Y = 0–0.25 m and almost equivalent to those for the single rider when Y = 0.50–0.90 m, as shown in Figure 4(a)–(d). In 4R, all values of aerodynamic drag were lower than those for the single rider when Y = 0–0.50 m. Thus, at Y = 0.50 m, the aerodynamic drag reduction was observed only in 4R. In both 2R and 4R, the aerodynamic drag of the most trailing rider tended towards that of the single rider as Y increased. At the same scale of 0–0.75 m, Y had a greater effect than X on the aerodynamic drag of the most trailing rider. In addition, Y >= 0.5 m in 2R and Y >= 0.75 m in 4R showed equal or greater drag than the single rider.

Figure 4 Most trailing rider’s aerodynamic drag basis of the aerodynamic drag of the single state consider compared to the aerodynamic drag of the single state by the relative spatial position. 10

3.3 Longitudinal distance

3.3.1 Within small lateral distance (Y=0.50 m)

The aerodynamic drag was a maximum (106.5%) at X = 0 m and Y = 0.90 m in the 4R, as shown in Figure 4(e); this drag was larger than that of the single rider. For Y = 0.50– 0.90 m in 4R, Figure 4(c)–4(e) show the trend that the aerodynamic drag reduced as X increased. On the other hand, the tendency between aerodynamic drag and X in 4R was not shown in 2R (Figure 4(c)-(e)).

4 Discussion

4.1 Comparison with previous studies in the tandem arrangement

The results of this study found lower required power values compared to track tests[2] (the differences are 14.1% at the position 2 and 16.7% at the position 4) in tandem arrangements (Figure 3). Barry et al.[5] suggested that the lower drag for wind tunnel tests may be due to rider difficulty to maintain tandem formation in the actual riding. This study on the lateral distance in section 3.2 seems to support that 11

suggestion. Our results also showed the lower required power values than other wind tunnel experiments by the previous studies [2,5] (the differences are 7.0~9.3% at the position 2 and 5.5~8.9% at the position 4) in tandem arrangements of 2R (positon 2) and 4R (position 4). The authors suggest that the main reason why the result of present study had been smaller than other wind tunnel experiments is the difference between the rider’s size. The details of the physical characteristics of the subject were as shown in Table 1, the circumferences of the mannequin were smaller than athletes participating in this study. Also the height of the helmet top in riding posture of the mannequin was the lowest in the group. In addition, the athletes for leading riders were installed about 0.03 m higher than the mannequin as shown in section 2.2. Edwards and Byrnes [11] shows that when the leading rider has a greater drag area and frontal area than the trailing rider (the drag area ratio between the leading rider and the trailing rider is 125% on average, the frontal area ratio is 126% on average), the aerodynamic drag of the trailing rider compared with the single state was 50% on average. In particular the subject of the greatest drafting effect was 43.3%. Thus, the rider’s size in the drafting effect is already known. However, it is difficult for present study to be compared with Edwards and Byrnes' research since the drag area and the frontal area of the leading riders was not measured in this study. Nevertheless we could show the most trailing rider was very small compared to the leading rider as mentioned above. And it is inferred that the leading riders had an extremely large drag area and frontal area than the trailing rider. Therefore it is considered that there is due to the rider’s size in this study and the reduction in aerodynamic drag was larger than that reported in the other studies. In the data measured by the wind tunnel performance test, the thickness of boundary layer (less than 95% of the mainstream velocity) was about 0.10 m at the 7 m point of the test section area. It is considered that no influence for the measurement of bicycle in the situation there is anything on near the floor. However, when the bicycle stand was installed in the test section area, the thickness of low speed range near the floor increased to about 0.4 m (for one bicycle stand) and about 0.45 m (for three bicycle stands). This is equivalent to about half of the height of the wheel. Therefore, it is considered to the feet and the lower half of the wheel of the subject measured were received excessive interference effect by the bicycle stand. Other due to be considered, it is conceivable that the growth wake of the bicycle stand which fixed the lead rider.

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4.2 Lateral distance

A wind tunnel experiment conducted for two riders in a traveling group [9] found that the lateral distance has a stronger effect than the longitudinal distance on aerodynamic drag reduction for drafting cyclists. The same trend was found in the present study. However, in the present study, as previously described, because of the larger reduction in aerodynamic drag for close proximity and a tandem arrangement, this trend was more pronounced. An experiment for two riders as a traveling group [9] confirmed an aerodynamic drag reduction for a lateral distance of up to 0.275 m. By contrast, the aerodynamic drag reduction was up to 0.25 m in the 2R and up to 0.50 m in the 4R of the present study. The results of the present study suggest that the drafting effect at X = 0–0.90 m is attenuated at Y = 0.25–0.50 m in the case of two riders and Y = 0.50–0.75 m in the case of four riders. The greater drag than the single state was shown at large Y. This trend has been shown in the wind tunnel experiment of the two riders [7, 9]. It is estimated that the relationship between aerodynamic drag and relative spatial position for the most trailing rider is driven by the separated shear layer generated by leading riders and the flow aspect of wake.

4.3 Longitudinal distance

4.3.1 Within small lateral distance (Y=0.50 m)

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At Y = 0.50–0.90 m in the 4R of the present study, the aerodynamic drag decreased as X increased. A previous study found for the downstream cylinder of a staggered arrangement of two cylinders, when the lateral (center-to-center) distance was about 0.5–1.5 times the cylinder diameter, the drag coefficient decreased as the distance in the airflow direction increased [12, 13]. The study of two race car showed the same tendency as present study, when the lateral (center-to-center) distance was about 0.5 times the width of the car and the longitudinal distance (between car and car) was about 1 times the length of the car [14]. As a more practical example, a similar trend is shown in the wind tunnel experiment of the overtaking situation for two riders [9]. As mentioned in Section 4.2 about the greater drag than the single rider, it is considered that the influence of shear layer generated by leading riders and the flow aspect of wake.

5.

Conclusion

This study conducted the wind tunnel experiment to verify the drafting effect of the most trailing rider in the riding groups of two riders (2R) and four riders (4R). The results of this study suggested that the drag force of the most trailing rider would decrease with decreasing lateral and longitudinal distance between the most trailing rider and a rider ahead in 2R and 4R. Furthermore, it was shown that a reduction in aerodynamic drag within a larger range of the lateral distance in the 4R than in the 2R. On the other hand, the drag reduction of the most trailing rider in 4R was less sensitive to longitudinal distance than those of 2R over the distances tested. It suggests that aerodynamic drag of the most trailing rider in 4R can be kept small to that of 2R even if he/she does not get close to a rider ahead to the same extent in 2R. To strengthen the drafting effect on the trailing rider, it is important that all riders in the traveling group note the travel line of the front rider and follow in series. The second rider needs to more closely maintain the longitudinal distance than the forth rider, and both is sensitive the lateral distance. However, if there are multiple lead riders (such as a team pursuit) the trailing rider may still experience a drag reduction with small lateral offset. In the rotation of cyclists in the team pursuit, because the fourth rider can receive a strong drafting effect without a small longitudinal distance, the rotating rider should minimize the time that he or she is away from the traveling group and immediately 14

follow as the fourth rider. The rider should seek to reduce his or her longitudinal distance during the rotation, being ready to take the forward position of the traveling group. This is because the relationship between the drafting effect and the relative spatial position is considered to be stronger for the forward position than for the rearward position and the traveling group can remain more forward on the track by remaining compact.

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