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Aerodynamic Characteristics as Determinants of the Drafting Effect in Cycling

EDWARDS, ANDY G.; BYRNES, WILLIAM C.

Medicine & Science in Sports & Exercise: January 2007 - Volume 39 - Issue 1 - p 170-176
doi: 10.1249/01.mss.0000239400.85955.12
APPLIED SCIENCES: Biodynamics
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Purpose: To determine whether cyclists' individual aerodynamic characteristics influence the magnitude of the drafting effect in cycling.

Methods: Thirteen competitive male cyclists performed two field protocols (individual and drafting). Hub-based power meters were used to measure power output and velocity, from which drag area (Ad) was calculated. The three subjects obtaining maximum (MAX), intermediate (INT), and minimum (MIN) values for Ad during the individual protocol acted as leaders during the drafting protocol. Measures of Ad were then made while subjects drafted each of the three leaders. The drafting effect was specifically quantified as the decrement on measured drag coefficient (Cd) and power output.

Results: The mean drafting effect increased with leader AdCd: MIN = 35.55%, INT = 41.31%, MAX = 50.47%; Δ power: MIN = 111.1 W, INT = 124.05 W, MAX = 159.23 W; P < 0.0001). Regressions between leader Ad and drafting effect for individual drafters indicated substantial interdrafter variability (slope ranged from 29.4 to 190.5%·m−2) but little intradrafter variability (mean r = 0.9689), suggesting an interaction between leader and drafter. Correlating leader:drafter ratios for Ad, Ap, and body mass to the drafting effect supported this interaction (r = 0.69-0.78, P < 0.01), but only when data for all three groups were pooled.

Conclusions: Alteration of leader Ad elicits a linear increase in the drafting effect. However, the Ad of the leader does not explain all of the interdrafter variability in the drafting effect, which is specific to the drafting subject but is minimally explained by their aerodynamic characteristics. This interdrafter variability may be attributable to the drafter's skill in obtaining maximum benefit from drafting.

Applied Exercise Science Laboratory, University of Colorado at Boulder, Boulder, CO

Address for correspondence: William C. Byrnes, Ph.D., FACSM, University of Colorado at Boulder, 354 UCB, Boulder, CO 80309-0554; E-mail: william.byrnes@colorado.edu.

Submitted for publication December 2005.

Accepted for publication July 2006.

Competitive road cycling is mechanically distinct from other endurance sports in that the resistive force experienced by the athlete is greatly dependent on the context of the race (2,10,12,18,16,19). During individual road cycling events, it is possible to very accurately predict performance given knowledge of the total mass of the system (bicycle and rider), its aerodynamic characteristics, and the athlete's physiological qualities (3,4,12,14,15,18,21). During multiple cyclist events athletes have the opportunity to draft one another. Drafting is the practice by which individuals follow closely behind one or more others to limit the aerodynamic resistive force they experience (19). Drafting affords less physiologically capable individuals the ability to maintain the pace of their more capable counterparts and, in doing so, adds complexity to the prediction of racing performance. Indeed, the respite offered by drafting is the single factor that predisposes mass-start road cycle-racing to a degree of tactical complexity not apparent in individual time-trial racing, or in other endurance sports.

The magnitude of the drafting effect in cycling can be impressive. For example, Jeukendrup et al. (6) observed an average power output of only 98 W during a stage of the Tour de France, some 152 W less than is estimated for an athlete performing alone (7). Previous attempts to describe the determinants of this magnitude have focused on the drafter's skill. Broker et al. (1) and Kyle (9) both used four-person team pursuit models to find that the drafting effect is subject to several skill-related factors-paceline position (a cyclist's position with respect to the lead of an in-series arrangement of cyclists), the drafter's left-right alignment with respect to the leader, and the distance between the leader and drafter (interwheel distance). Although these investigations provide important information about the drafting effect in cycling, both data sets also exhibit large interindividual variability that is not explained by skill-related factors. For example, Broker et al. (1) found that the drafting effect, expressed in terms of mass-normalized power output, varied by as much as 1.21 W·kg−1 (20.5% of total power), even after the removal of spurious data. To the best of our knowledge, no investigation has described how the aerodynamic and anthropometric characteristics of cyclists contribute to the drafting effect. It is possible that the additional variability observed by Kyle (9) and Broker et al. (1), can be explained by interindividual differences in these characteristics.

Three characteristics are commonly used to predict individual time-trial performance (12): the projected frontal area (Ap), drag coefficient (Cd), and drag area (Ad). The Ap of any object is an index used to relate its size to its observable aerodynamic qualities, whereas the Cd relates how factors independent of size affect the aerodynamic force an object experiences. As such, the Cd is generally thought to indicate the object's "streamlining" (5). The drag area is simply the product of Ap and Cd, and, because it includes the effects of both size and streamlining, has been suggested to be the best descriptor of a cyclist's individual aerodynamic qualities (20).

We expect that all of these indices influence the drafting effect by determining the reduction in pressure drag experienced by a drafting cyclist. Pressure drag is the primary form of aerodynamic drag force experienced while cycling (3); it results from a fore-aft air-pressure differential formed during a cyclist's forward motion. The low-pressure zone (wake) trailing a leader provides a drafting cyclist with shelter from pressure drag by decreasing the differential acting across him or her (9). The size of a leading cyclist impacts the size of the wake, and the size of the drafting cyclist affects the ease with which he or she can be contained within that wake. Thus it is intuitive that projected frontal area should be an important determinant of the drafting effect. Additionally, it is likely that factors such as Cd, which is independent of size but still affects pressure drag, will also influence the drafting effect (5).

The purpose of this investigation was to quantify the individual aerodynamic and anthropometric characteristics of leading and drafting cyclists that lead to interindividual differences in the drafting effect. We hypothesized that 1) leader drag area is an important determinant of the drafting effect in cycling, 2) the ratio between the drag area of a leader and the drag area of a drafter is strongly associated with the drafting effect, and 3) leader:drafter ratios for projected frontal area and for the drag coefficient are less closely associated with the drafting effect.

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METHODS

Thirteen male subjects were recruited from the greater Boulder-Denver, CO area. All were well trained and had been regularly competitive (licensed as USCF professional, category 1 or 2 athletes) for at least 3 yr. Before involvement, all subjects were required to complete a comprehensive medical questionnaire and sign a statement of informed consent, both of which were approved by the human research committee at the University of Colorado at Boulder.

Subjects were required to perform field trials for two experimental components (individual and drafting), which were conducted on two or three different days (depending on subject availability) and spread over no more than 6 wk. Subjects were required to wear the same clothing and to use the same equipment during all testing sessions. The outer layer of this clothing was limited to a racing jersey (short- or long sleeved), arm and/or leg warmers, cycling shorts, gloves, and fabric or lycra shoe covers. Jackets, vests, and neoprene shoe covers were not allowed. Tire pressure was maintained constant at 120 psi (828 kPa) across all trials.

The individual component involved a series of field trials performed alone at five different velocities (25, 30, 35, 40, and 45 km·h−1) over the "collection trap"-a flat, 0.2-km section of public road in Boulder, CO. The grade of the collection trap was assessed via standard surveying techniques and was found to be level from start to finish, with the maximum grade over any 50-m section being 0.3%. Trials were performed in both directions (east and west) at each velocity, such that 10 trials were performed by each subject. For all trials, subjects were required to accelerate to the prescribed velocity at least 100 m before entering the collection trap, and to maintain that velocity to the end of the trap, where they ceased pedaling. Subjects were also required to maintain a constant racing posture (hands gripping the dropped section of handlebars) within and across all trials. Primary data for average power output and velocity were collected for each trial via Power Tap Pro model portable power meters (six different units were used; Graber Products, Madison, WI). These hub-mounted power meters provided visual feedback to the cyclists as discrete 1-s averages via a handlebar-mounted display and data logger. On completion of the testing session, data were downloaded to a Macintosh computer. All power meters were referenced to a first-principles external dynamometer before use, and all were found to exhibit less than 3% error in power measurement across a 100- to 500-W range. Primary data for power and velocity were then reduced to values for tractive resistance-a measure of force that includes only the effects of rolling force and aerodynamic force. These values were then further reduced to measures of cyclist drag area and rolling force (3).

The drafting component first used individual values for drag area to designate each subject as being either a leader or drafter. The three subjects obtaining the maximum, median, and minimum drag-area values during the individual component were invited to act as leaders during the drafting protocol. The median subject (subject 7, Table 1) declined and was replaced by a subject with slightly lesser value for drag area (subject 6, Table 1). The remaining 10 subjects were designated drafters and were required to perform four trials at 45 km·h−1 while drafting each of the three leaders (random order) and an additional four trials at 45 km·h−1 while cycling alone ("solo" trials). Each leader also performed four trials while drafting both of the other two leaders, and four solo trials; all of these were conducted at 45 km·h−1. See Figure 1 for a summary of the trials completed by all subjects.

TABLE 1

TABLE 1

FIGURE 1

FIGURE 1

In addition to carefully maintaining a racing posture throughout, drafting subjects were required to maintain an interwheel distance of less than 0.5 m (16) and to minimize lateral movement to remain in alignment with the leader.

During both the individual and drafting protocols, wind velocity was measured with a stationary hotwire anemometer (Extech Products Inc. Melrose, MA). To limit any effect of environmental wind, trials in which the mean wind velocity exceeded 1 m·s−1 were not included in further analyses. Similarly, to ensure that inertial forces would not influence our measures of aerodynamic or rolling force, trials in which a subject's velocity varied by more than 1.0 m·s−1 were either repeated or removed from further analyses. Of the 470 trials scheduled for completion, 24 were removed post hoc because of excessive acceleration within the trial, and another five were removed because the subjects were unable to maintain the 0.5-m interwheel spacing. All of these trials were eventually repeated in subsequent sessions.

Primary data for power and velocity were collected for each trial. These data were then averaged over all four trials performed in each condition. In combination with the rolling resistance measured during the individual protocol, these mean data could be reduced to values for the drafting cyclist's drag area while drafting each of the three leaders, and while cycling alone. The steps applied to arrive at these final values are described by equations 1 through 3:

where RT is the mean tractive resistance (N) acting on the cyclist across the four trials drafting any one leader, P (W) is the mean external power, and V (m·s−1) is the mean velocity;

where RA is the mean aerodynamic drag force acting across all four trials, and RR is the rolling force measured during the individual component; and

where Ad is the subject's drag area (m2) (15), ρ is the prevailing air density (kg·m−3), and, as previously V, is the mean velocity apparent across all four trials. Air density was calculated from measures of barometric pressure, temperature, and relative humidity using standard equations (8). The final reduction applied to the drafting data involved converting these measures of drag area to a related quantity: the drag coefficient (Cd dimensionless). As shown by equation 4, a cyclist's drag coefficient is simply the quotient of the projected frontal area (AP, m2) and the drag area,

Because the projected frontal area is constant for each drafter it is most precise to express any differences in terms of the drag coefficient. This was achieved by measuring projected frontal area in the laboratory using NIH image-digitizing software and procedures suggested by Olds et al. (17).

The drafting protocol used here to measure the drag area of solo subjects and subjects drafting others has not previously been validated. To provide some comparison of this protocol to the individual protocol, which involves many more trials and has received previous validation (11), a paired Student's t-test was used to search for any difference between the two. None was found (mean individual Ad = 0.3083 m2; mean drafting Ad = 0.3101 m2, P = 0.56), and results from the two protocols were well correlated (r = 0.956, P < 0.0001). With this in mind, it is still possible that differences in reliability exist between the individual and drafting protocols. To negate any effect of this possibility, we chose to include a solo condition within the drafting protocol, ensuring that the drafting effect was always calculated from two measures of drag area that were collected using the same protocol.

Previous investigations have defined the drafting effect as the difference in aerodynamic force experienced by a cyclist while drafting as compared with cycling alone (9); others have used the associated decrement in power output (1), and still others have used alterations in the drag coefficient (5). To allow both technical and applied interpretation, we present the drafting effect in terms of both the drag coefficient and the power output observed during trials.

The group mean effects were first assessed by a one-factor ANOVA for repeated measures and then post hoc via the Tukey-Kramer test. These analyses were only performed on data for subjects that followed all three leaders; that is, data for trials involving one leader drafting another were not included in these analyses. Pearson product-moment correlations and linear regression were used for all further analyses, which, unlike the group analyses, included data for all subject pairings.

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RESULTS

Table 1 shows that the 13 subjects participating in this investigation were relatively heterogeneous for the indices of body size (mass and height) and for measures of aerodynamic character (Ad, Ap, and Cd).

The absolute power output required while drafting was 131 (33.25%) W less than while cycling alone (P < 0.05). This was also true when the data were expressed in terms of the drag coefficient, which decreased by 0.335 ± 0.071 (42.44%). Whether expressed in terms of power output or drag coefficient, the drafting effect was least while drafting the minimum drag-area leader (Δpower = 111.1 ± 25.71 W, ΔCd = 0.28 ± 0.07), intermediate while drafting the intermediate drag-area leader (Δpower = 124.05 ± 19.78 W, ΔCd = 0.33 ± 0.05), and most while drafting the maximum drag-area leader (Δpower = 159.23 ± 16.21 W, ΔCd = 0.39 ± 0.03). These results are expressed in relative terms in Figure 2.

FIGURE 2-De

FIGURE 2-De

Table 2 and Figure 3 show the pronounced variability of these data. Not only are the data varied within the three lead groups, but the slopes of the individual relationships indicate that the effect of changing leader drag area was also quite variable (Fig. 3). The range of slopes apparent for these regressions is large (29.41-190.15%·m−2), but the relationships are also strong (mean correlation coefficient = 0.969), suggesting that this large range is not attributable to random errors in the data.

TABLE 2

TABLE 2

FIGURE 3

FIGURE 3

To describe how the characteristics of the leader and drafter may have interacted, we correlated leader:drafter ratios for drag area, projected frontal area, drag coefficient, and system mass, to the drafting effects observed for the various drafting pairs. These analyses were performed within each of the three leader groups and across all three groups (pooled data). Table 2 indicates that although these correlations were significant among the pooled data, they were not when performed within each of the three leader groups.

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DISCUSSION

Our first hypothesis was that leader drag area is an important determinant of the drafting effect in cycling. Our data support this by indicating a strong mean effect of leader drag area, whether that effect is expressed in terms of the drag coefficient or power output. Also of interest is that across the three groups, our results show a greater mean drafting effect than was found by either Kyle (9,10) or Broker et al. (1). Kyle's 38% reduction in aerodynamic drag force is approximately 4% less than our 42.44% reduction in the drag coefficient. The difference between our power-based estimate of the drafting effect (33.25%) and that of Broker et al. (26.9% when corrected to a 45-km·h−1 velocity) is greater again at 6.35%. There are several possible explanations for these differences, but the most likely is that the current investigation involved a greater mean leader drag area than did either of the previous two. To illustrate this, it is possible to estimate the average drag area of the subjects from Broker et al. (1) by applying the mean regression found here (Fig. 2) to their power-output data. Such estimation provides a value of 0.212 m2, which, although extremely low, is not dissimilar to a value (0.22 m2) that has been suggested as the limit of aerodynamic refinement for cyclists of similar size. Certainly, it is reasonable to expect that the specialized aerodynamic positions and equipment used by those subjects (as part of the United States' preparation for the 1996 Atlanta Olympics) could reach such a limit. It should also be noted that the above analysis of Broker's data would underestimate the true leader drag area if the drafting cyclists had a reverse or "pushing" effect on the leader. Our data indicate that any such effect was minimal (1.63% across the three leaders; Table 4) and also inconsistent (17 of the 36 pairings revealed a slight pushing effect; 19 were either neutral or indicated a slight pulling effect). However, our experiment was not designed to address this question, and formal statistical analysis of these data is not possible.

Although it is clear from our data that leader drag area is an important determinant of the drafting effect, it is also clear that it is not the only determinant. Large interindividual variability is apparent within each of the three leader groups and in the slopes of the individual regressions (Fig. 3). Interestingly, this variability does not seem to be random. The mean correlation coefficient (r = 0.969) obtained for the individual regressions presented in Table 2 indicates that the effect of leader drag area was relatively consistent on an intradrafter basis. The fact that the regression slopes were highly variable, yet formed by strong individual relationships, suggests an interaction between the leader and drafter. This can be seen in Figure 3, which shows several subjects benefiting very little while drafting the minimum leader, but approaching the average while drafting the maximum leader. Other subjects seem to experience little more benefit while drafting the most aerodynamic leader than they do while drafting the least aerodynamic leader.

Our second hypothesis was that the ratio between the drag area of a leader and the drag area of a drafter is strongly associated with the drafting effect. This hypothesis is supported by correlation between the leader:drafter Ad ratio and the drafting effect among the pooled data, but not within each of the three leader's groups (Table 3). The pooled correlations indicate that some 61% of the drafting effect variance can be accounted for by variation in the leader:drafter drag-area ratio. To limit the variation to include only the drafter's characteristics, we performed similar correlations within each leader group and expected to find them significant. To our surprise, significance was only achieved for the maximum leader (R2 = 0.46), suggesting that the drafter's characteristics were of greater importance when drafting a less aerodynamic leader. However, if the drafter's characteristics had a predictable influence on the drafting effect, significant correlations should be apparent within each of the leader groups as well as across them. This was clearly not the case. It is possible that the within-groups analyses failed to achieve significance because they involved fewer observations and inherently less statistical power, but the accompanying correlation coefficients were also substantially lower than those for the pooled analyses. Thus, the likely explanation for the relatively weak within-groups relationship for leader:drafter Ad is that the leader's Ad has a more powerful and predictable influence on the drafting effect than does the drafter's.

TABLE 3

TABLE 3

TABLE 4

TABLE 4

Our third and final hypothesis was that leader:drafter ratios for projected frontal area, and the drag coefficient, are less closely associated with the drafting effect. The pooled analyses are supportive of this hypothesis, with both Ap and Cd ratios being less closely associated with the drafting effect than was the leader:drafter ratio for Ad. The within-groups analyses are less supportive and offer little additional information. Perhaps the most important interpretation of the within-groups analyses comes in comparing their weakness with the relative strength of the pooled analyses, which serves to reinforce the importance of the leader's characteristics in determining the drafting effect. Also important is that the ratio of leader Cd to drafter Cd is not related to the drafting effect, either for the pooled or within-groups analyses. This suggests that the drag coefficient is a less important determinant of the drafting effect than either Ap or Ad.

Finally, multiple correlations involving leader:drafter ratios for Ad, Ap, Cd, and body mass did not improve the strength of the relationship. Thus, these indices share a large proportion of their variance, and body size is likely to be a reasonable indicator of the benefit to be gained when drafting an unknown leader.

It seems from these data that the drafter's aerodynamic and anthropometric characteristics have little influence on the measured drafting effect. Yet, it is clear from the individual regressions that the effect of changing leader Ad is specific to the drafter. It is possible that this specificity is attributable to differences in the drafter's skill rather than their aerodynamic characteristics. Certainly, we attempted to limit variation in known skill-related determinants such as interwheel distance and left-right alignment, but we did not quantify such variation. In a retrospective attempt to assess these possible differences, we used the variability of power output and velocity while drafting as a putative measure of the drafter's skill. The basis of this analysis is the assumption that less skilled drafters had greater difficulty being contained within the leader's wake. This difficulty can be exhibited in two ways: 1) difficulty in maintaining a constant interwheel distance (and, hence, a constant velocity) or 2) difficulty in maintaining left-right alignment with the leader (and, hence, a constant power output, given the aerodynamic cost of cycling outside the wake). We hypothesized that variability in power and velocity while drafting (as indicated by the grand standard deviation for each drafter's 12 trials) would be positively related to the slopes of the drafters' individual regressions. Unfortunately, these analyses did not explain the drafter specificity of the individual regressions. The relationship between velocity variation and regression slope was modest (r = 0.29) but was stronger than that for power-output variation (r = −0.08). A likely reason for this is that there was transfer between kinetic energy and aerodynamic work during the trials. This would occur if the drafter moved from within the wake to either side of it to avoid getting too close to the leader. In this event, the kinetic energy carried by the drafter would be transferred into work done in overcoming an elevated level of aerodynamic force, which would then be reflected by an increased average power output for the trial but not an increased variation in power or velocity. With this noted, it is not possible to quantify such transfer without a measure of the drafters' lateral displacement, and we are unable to offer a strong explanation for the drafter specificity apparent in the individual regressions.

In summary, we found that during paired cycling, 1) the drafting effect increases in proportion to the drag area of the leading cyclist, 2) the magnitude of this response demonstrates significant interindividual variability, and 3) this interindividual variability is not explained by the drafter's aerodynamic or anthropometric characteristics and may, therefore, be dependent on the drafter's skill in positioning him- or herself within the leader's wake.

We believe there are two novel applications of these findings for racing cyclists:

  1. Because leader drag area strongly determines the magnitude of the drafting effect, it would be desirable for the fastest member of a team time trial or team pursuit to also have the largest drag area. This would allow the remaining members to gain maximal respite while drafting and would allow for a more even distribution of effort across all members.
  2. Because much of the drafting affect is attributable to projected frontal area, and very little is attributable to the drag coefficient, it would be advantageous for a leader to have a relatively high projected frontal area (providing shelter for the drafter) but a low drag coefficient (allowing the leader to maintain a high speed). This is likely to be important for the team time trial and pursuit, and perhaps even more so for group sprinting, where one team member is able to "lead out" a designated sprinter.

Future directions for research of the drafting effect in cycling should specifically focus on separating the effects of a cyclist's skill and aerodynamic characteristics. This may be achieved via unique mechanical coupling of the leader and drafter or by specialized techniques to quantify the left-right alignment and interwheel distance while drafting.

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REFERENCES

1. Broker, J., C. R. Kyle, and E. R. Burke. Racing cyclist requirements in the 4000-m individual and teams pursuit. Med. Sci. Sport Exerc. 31:1677-1681, 1999.
2. Craig, N. P., and K. I. Norton. Characteristics of track cycling. Sports Med. 31:457-466, 2001.
3. di Prampero, P. Cycling on earth, in space, on the moon. Eur. J. Appl. Physiol. 82:345-360, 2000.
4. Heil, D., O. F. Murphy, A. R. Mattingly, and B. K. Higginson. Prediction of uphill time-trial bicycling performance in humans with a scaling-derived protocol. Eur. J. Appl. Physiol. 85: 374-382, 2001.
5. Hoerner, S. F. Fluid Dynamic Drag. Brick Town, NJ: Hoerner Fluid Dynamics, 1965.
6. Jeukendrup, A., N. Craig, and J. A. Hawley. The bioenergetics of world class cycling. J. Sci. Med. Sport. 4:414-433, 2000.
7. Jeukendrup, A., and J. Martin. Improving cycling performance: how should we spend our time and money? Sports Med. 31: 559-569, 2001.
8. Jones, F. E., and R. M. Schoonover. Handbook of Mass Measurement XXV. Boca Raton, FL: CRC Press, 2002.
9. Kyle, C. R. Reduction of wind resistance and power output of racing cyclists and runners traveling in groups. Ergonomics 22: 387-397, 1979.
10. Kyle, C. R. The mechanics and aerodynamics of cycling. In:Medical and Scientific Aspects of Cycling, E. Burke and M.M. Newsom (Eds.). Champaign, IL: Human Kinetics, pp. 235-251, 1988.
11. Lim, A. C., A. G. Edwards, T. C. Carver, R. Kram, and W. C. Byrnes. The use of a portable power meter to estimate aerodynamic and rolling resistance in road cycling. Med. Sci. Sports Exerc. 35:78, 2003.
12. Martin, J., D. G. Milliken, J. E. Cobb, and K. L. McFadden. Validation of a mathematical model for road cycling power. J. Appl. Biomech. 14:276-291, 1998.
13. Milliken, W. F., and D. L. Milliken. Race Car Vehicle Dynamics. Warrendale, PA: SAE International, 1995.
    14. Olds, T., K. I. Norton, and N. P. Craig. Mathematical model of cycling performance. J. Appl. Physiol. 78:1596-1611, 1993.
    15. Olds, T., K. I. Norton, E. L. A. Lowe, S. Olive, F. Reay, and S. Ly. Modelling road-cycling performance. J. Appl. Physiol. 78: 1596-1611, 1995.
    16. Olds, T. The mathematics of breaking away and chasing in cycling. Eur. J. Appl. Physiol. 77:492-497, 1998.
    17. Olds, T., and S. Olive. Methodological considerations in the determination of projected frontal area in cyclists. J. Sport Sci. 17:335-345, 1999.
    18. Olds, T. Modelling human locomotion: applications to cycling. Sports Med. 31:497-509, 2001.
    19. Padilla, S., I. Mujika, G. Cuesta, and J. J. Gioriena. Level ground and uphill cycling ability in professional road cycling. Med. Sci. Sport Exerc. 31:878-885, 1999.
    20. Padilla, S., I. Mujika, F. Angulo, and J. J. Gioriena. Scientific approach to the 1-h cycling world record. J. Appl. Physiol. 89: 1522-1527, 2000.
    21. Schumacher, Y. O., and P. Mueller. The 4000-m team pursuit cycling world record: theoretical and practical aspects. Med. Sci. Sport Exerc. 34:1029-1036, 2002.
    Keywords:

    CYCLING TACTICS; FORMATION AERODYNAMICS; PELOTON; GROUP AERODYNAMICS

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