Demands of the individual pursuit, part 1

(Based in part on a presentation given to the Pan American Sports Organization in 2005.)

by Andrew R. Coggan, Ph.D.

"The individual pursuit: a deceptively simple event favoring specialists who possess superior aerobic fitness coupled with a high anaerobic capacity, excellent aerodynamics, and specific technical skills.”

The individual pursuit is one of track cycling’s classic events, having been regularly contested in the early 1900s and having been included in every World Championship since their inception in 1946[1] and every Olympic Games between 1964 and 2008 inclusive. As the name implies, the event is raced pursuit-style (i.e., against an opponent starting on the opposite side of the track) over a distance of 4 km for men (5 km for professionals until 1992) and 3 km for women, and requires elite athletes approximately 3.5-4.5 min to complete. As such, it is comparable in duration to, e.g., the 1500 m in athletics (track and field) or the 400 m in swimming, and similar to these events requires extremely high levels of both aerobic and anaerobic fitness. Performance in the individual pursuit is also significantly influenced by other traits or talents of the athlete (e.g., ability to minimize aerodynamic drag while still maintaining a power output requiring ~110% of VO2max) as well as by physical factors that may or may not be within the athlete’s control (e.g., rolling resistance). In this series of articles I review these and other determinants of pursuit performance, first based on the published scientific literature and then using a conceptual model that integrates the physiological, physical, and technical aspects of this deceptively simple event. The information provided will hopefully prove to be of interest to athletes participating in the individual pursuit and/or their coaches as well as to other exercise physiologists and sports scientists. For information on the team pursuit, readers are referred to previous articles by Broker et al. (1) and Schumacher and Mueller (2).

[1]The first World Championship in track cycling was actually held in 1939, but the competition was interrupted by the outbreak of World War II and no champions were named.

Determinants of pursuit performance: physiological characteristics of elite pursuit cyclists

As might be predicted based on the event's duration, the pursuit is a predominantly aerobic competition. Specifically, it has been estimated that during a 4 km pursuit ~85% of total energy is produced via aerobic metabolism, with only ~15% coming from anaerobic sources (3,8). A slightly larger contribution from anaerobic energy supply would be expected for the shorter 3 km race contested by women (or masters riders), but the difference is unlikely to be too great, in part because of the smaller muscle mass and thus lower absolute anaerobic capacity of most women. Given the above, it is not surprising that the physiological characteristics of elite pursuiters (3,7) resemble those of elite road time-trialists (4), with both being characterized by a high VO2max and especially a high lactate threshold. On the other hand, the maximal power of elite pursuiters is quite unexceptional (3,5,7). In fact, one study (5) found that pursuiters were not different from completely untrained individuals in this regard.

Although maximal power may be unimportant to pursuit performance, anaerobic capacity clearly does play a role. Specifically, Olds et al. (7) found that variations in anaerobic capacity within the range observed in the group of athletes they studied could account for up to a 4% difference in 4k pursuit time. Similarly, a multiple regression model using the same data set (3) identified VO2max, power at LT, and anaerobic capacity as the three most important predictors of pursuit time.

Interestingly, this same regression model (3) failed to identify cycling efficiency as an independent predictor of performance, even though efficiency is widely recognized (e.g., 2) as influencing steady-state cycling power, and "first principles" modeling (7) using the same data indicated that variations in efficiency could account for even more variation in performance than variations in VO2max. This could be because efficiency is probably highly correlated with other parameters included in the model (i.e., VO2max, LT), and therefore provides no independent information. Alternatively, it is possible that the laboratory test of efficiency (in which cadence progressively increased from 85 to 120 rpm), while demonstrating differences between athletes, failed to accurately reflect differences in their on-the-bike function.

Determinants of pursuit performance: the pursuit performance "teeter totter"

As described above, one way of gaining insight into the demands of a particular athletic competition is to examine the physiological characteristics of those who excel in that event. This approach, however, does not provide truly quantitative information upon which to base decisions about, e.g., the design of an appropriate training program. Furthermore, it does not address the importance of factors other than the athlete's physiology, for example the role of physical factors such as aerodynamic drag or the individual's technical skill. Thus, to fully understand the demands of the individual pursuit, I believe that it is helpful to consider the conceptual model shown in Figure 1 below:

Figure 1. The pursuit performance "teeter totter"

In this conceptual model, physical factors acting to slow the cyclist down are shown as acting upon the left side of a child's "teeter totter" (or see-saw), whereas physiological factors contributing to their ability to generate power and hence go faster are shown as acting upon the right side. The individual's actual performance time is determined by the point at which these two "masses" act to balance each other, i.e., by the exact position of the fulcrum at the bottom representing the athlete's technical skill. The size of the font used to list the factors shown within the two masses and the fulcrum represents their relative importance, based on mathematical modeling of pursuit performance as described below.

Mathematical modeling of pursuit performance

To assess the quantitative importance of the various factors shown in Figure 1, I used a physics-based mathematical model of the power requirements of cycling (9) to model the performance of a hypothetical world class male or female pursuit cyclist. This mathematical model has previously been validated under both steady-state (9) and non-steady-state (10) conditions, and has been shown to predict power and/or speed with a high degree of accuracy. The specific characteristics of the representative athletes (see Table 1 below) were chosen such that their pursuit times would approximate those required to win at the 2005 World Championships, which were held at the ADT Event Center velodrome in Carson, CA. Performances on this track were chosen as the "benchmark" in part because of greater certainty as to the exact air density and rolling resistance of the surface versus those at other, faster velodromes. Values for height and weight were simply assumed, from which CdA was estimated using the equations of Heil (11). The power required to achieve the given performance times were then calculated from the model and cross-validated by comparison to actual data.

Table 1. Nominal characteristics of world class pursuiters used in modeling

With the above model in hand, the relative importance of the various factors shown in Figure 1 was determined by examining the change in pursuit time resulting from an equivalent change in any of the parameters listed. The results of these analyses will be described in parts 2 and 3 of this article.

References

1. Broker JP, Kyle CR, Burke ER. Racing power requirements of the 4000-m individual and team pursuits. Med Sci Sports Exerc 1999; 31:1677-1685.

2. Schumacher YO, Mueller P. The 4000-m team pursuit world record: theoretical and practical aspects. Med Sci Sports Exerc 2002; 34:1029-1036.

3. Craig NP, Norton KI, Bourdon PC, Woolford SM, Stanef T, Squires B, Olds TS, Conyers RAJ, Walsh CBV. Aerobic and anaerobic indices contributing to track endurance cycling performance. Eur J Appl Physiol 1993; 67:150-158.

4. Coyle EF, Feltner ME, Kautz SA, Hamilton MT, Montain SJ, Baylor AM, Abraham LD, Petrek GW. Physiological and biomechanical factors associated with elite endurance cycling performance. Med Sci Sports Exerc 1991; 23:93-107.

5. Davies CR, Sandstrom ER. Maximal mechanical power output and capacity of cyclists and young adults. Eur J Appl Physiol 1989; 58:838-844.

6. de Konig JJ, Bobbert MF, Foster C. Determination of the optimal pacing strategy in track cycling with an energy flow model. J Sci Med Sport 1999: 2; 266-277.

7. Olds TS, Norton KI, Craig NP. Mathematical model of cycling performance. J Appl Physiol 1993; 75:730-737.

8. van Ingen Schenau GJ, JJ de Konig, de Groot G. The distribution of anaerobic energy in 1000 and 4000 meter cycling bouts. Int J Sports Med 1992; 13:447-451.

9. Martin JC, Milliken DL, Cobb JE, McFadden KL, Coggan AR. Validation of a mathematical model for road cycling power. J Appl Biomech 1998; 14:276-291.

10. Martin JC, Gardner AS, Barras M, Martin DT. Modeling sprint cycling using field-derived parameter and forward integration. Med Sci Sports Exerc 2006; 38:592-597.

11. Heil DP. Body mass scaling of projected frontal area in competitive cyclists. Eur J Appl Physiol 2001; 85:358-366.

12. Wilberg RB, Pratt J. A survey of race profiles of cyclists in the pursuit and kilo track events. Can. J. Sports Sci. 1988; 13:208-213.

Ventoux as Stage 20...are they serious?

(Reprinted with permission from the October 2009 issue of ROAD magazine: http://bluetoad.com/publication/?i=21569)

by Hunter Allen - I am sure that when the race director of the Tour de France, Christian Prudhomme proposed that the next to last day of Le Tour finish on the summit of Mt. Ventoux, he got some quizzical looks, opposition and downright questions of his sanity. From a logistical standpoint alone, the stage would be tough for the riders, with a big transfer afterward to Paris and the fact that it would be going against the normal time trial which usually makes up the penultimate stage, I am sure that Monsieur Prudhomme received quite the opposition to this idea. However much it was, he got it passed through the committee and the race route was announced to even more disbelief from the riders and the team directors. Mt. Ventoux? On the penultimate day? Are they serious? Finally that day came for the riders, and it was Stage 20. Yes, Stage 20 and still hard to believe. Most of us have no idea what it takes to do a 21 day stage race, the level of soreness in the legs or mental effort needed to keep on pushing each day to get to the front, or how tired you get of eating, much less doing a massive mountain top finish on the 20th stage! Chris Anker Sorenson does though, and as a domestic on the Saxo Bank team, he had some serious responsibilities in getting the Schleck brothers to the front, setting tempo on the lower slopes of important climbs and helping bring bottles to his teammates throughout the race. Chris used his SRM power meter for each of the stages and shared those files with us on http://www.trainingpeaks.com/. A big thanks goes out to SRM, Team Saxo Bank and all the people involved in bringing those files to us to review and examine. Let’s take an in depth look at that infamous Mt. Ventoux stage and see what Chris had to do for his team and for himself to just finish the stage.

Figure 1. Chris Anker Sorenson's power data from stage 20 of the 2009 Tour de France.

With just over 100 miles to race, four categorized climbs on the profile BEFORE Mt. Ventoux, and over 11,000 feet of climbing, Chris burned over 4600 calories for the day and averaged 21.1 mph for the stage! (See Figure 1 above). His normalized power (power he would do if he pedaled smoothly and steadily for the whole stage) was 309 watts for nearly 5 hours of racing, and his best 20 minute average power was 398 watts as he set tempo at the base of Mt. Ventoux. This pace setting effort in the beginning of the climb was not only an incredible effort at 398 watts, but it also was his BEST 20 minute effort for the entire Tour! When I see that an athlete does his very best effort at the end of a long stage race, then that tells me that he has improved his ability to recover over the duration of the stage race, he has taken good care of his body during the race, he has the ability to ‘rise’ up to the demands and needs of the team and lastly….he underperformed at the beginning of the race. In this case, Chris most likely underperformed at the beginning of the Tour because he knew that he was going to have to work for the team in the latter parts of the race, (however remember that Saxo bank had the yellow jersey (Cancellara) in the early stages of the race as well) so Chris really had to meter out his efforts without overdoing it and therefore just didn’t get the chance early in the race to show us what he could do if he went all out for a stage victory.

When we examine the power file for Stage 20 further, one important thing becomes clear as well and this might provide a clue to why Chris was able to put out his very best 20 minute power on this penultimate stage. As I have stated in the past, the road racers that win the most pedal only about 83% or less of the time of the race. The best road racers have learned how to pace their energy expenditures throughout the stage and put out effort only when absolutely necessary. In other words, the best road racers are lazy and the best stage racers…even lazier! In Stage 20, Chris only pedals 80% of the time (see Figure 2 below), and that means nearly an hour of the stage he spent coasting and not pedaling, which is the mark of a good road racer and also gives us some insight in why he could do a huge effort on that stage. With the cumulative effects of resting more than most other riders in each stage, one can see that just by resting more in the peloton over a 21 day race can give you a huge advantage near the end of the race.

Figure 2. Distribution of cadence for the entire stage.

The next most interesting thing about Chris’ power file is the Mt. Ventoux climb itself. First off, at the beginning of the climb, you can see his power fluctuating highly in the first nine minutes (see Figure 3 below) and this was because he was sitting on his teammate’s wheel- Nicki Sorenson- as Nicki was the first one on the team to set the pace. After Nicki was done with his turn at the front, it’s up to Chris, so he nails it at his limit and pushes the pace harder than he has done in ALL the previous stages for over 5minutes at 418 watts! This was Chris’ 2nd best 5 minute effort of the entire tour with his absolute best 5 minute effort happening just before...at the base of Mt. Ventoux! So within the span of about 20 minutes, Chris had done his best 5 minute wattage, his 2nd best 5 minute wattage AND his best 20 minute wattage for the entire 21 stages!!!! Clearly, an amazing effort for Chris and this really shows his potential for stage racing and for future success.

Figure 3. The start of the Ventoux climb.

The next thing that I find highly fascinating in the climb up Mt. Ventoux is Chris’ cadence on the climb. When he was following Nicki and then when he took a pull at the front, which was a total of 17 minutes of effort at over 400 watts and an average heart rate of 181 bpm, his cadence was relatively high. During these 17 minutes, Chris’ cadence was right at 100 rpm and clearly when Chris has to go ‘full gas’, then he needs to keep his cadence right near that 100 rpm mark to produce the most amount of watts. After these first 17 minutes (when teammate Andy Schleck started to attack!), then Chris’ job was over and he immediately dialed back the intensity to a more do-able wattage of 345 watts (roughly 90% of his FTP) and dropped his cadence to 80 rpm (see Figure 4 below). Initially you might think, well…it got steeper so he could only do 80 rpm, but in reality the steepness of the climb didn’t change at all when we examine the elevation data from his downloaded power file. This really highlights the roll that cadence plays in the production of power at your absolute limit. In the case of Chris Sorenson, there is a 20% difference in cadence (from 100 rpm to 80 rpm) which causes a 15% difference in wattage that he can produce. That 15% wattage difference isn’t just any 15% difference, but it’s THE uppermost watts that he can produce, which counts as a very significant amount of effort and the difference between being able to do your job for the team or not.

Figure 4. Power and cadence during the first 17 minutes of the climb vs. the last 45 minutes.

Clearly, this is just a snapshot of the toughest 21 day stage race in the world, but it also goes to show just how hard these riders can continue to ride day after day. One begins to wonder at what point (how many days?) would all the riders begin to slow down significantly and eventually ride at a speed of 14mph for the entire stage? Making the hardest mountain top finish on the penultimate stage made for an exciting stage, huge spectacle and great battle, even if in the end the general classification didn’t change turned out to be a great idea for this year’s Tour. Congrats to Chris and all the riders on the Saxo bank for a very impressive Tour! I am sure I won’t get any thanks from the riders in this years’ TDF, but I commend Monsieur Prudhomme for taking such a bold step and making this stage such a memorable one. I hope he will continue with other surprises for 2010!

Does drafting benefit the leading rider?

by Andrew R. Coggan, Ph.D. - Based on aerodynamic theory, the power that a cyclist needs to produce to ride at any particular speed should be lower when one or more additional riders are drafting closely behind. This is because the “bow wave” of air in front of the trailing rider(s) helps to fill in the zone of reduced pressure that normally exists in the leading rider’s wake, thus reducing the leader’s aerodynamic drag. While this effect is widely recognized in auto racing circles (especially NASCAR), it has long been held that cyclists do not travel fast enough and/or in close enough proximity to each other for the effect to be measurable. Purely by chance, however, in 2007 I happened to collect some powermeter data on an indoor track that suggest that this may not be true. Despite considerable searching I have not encountered similar findings discussed or presented elsewhere, and so I would like to share them here.

Figure 1 below shows, in blue, the power-vs.-speed relationship for an elite female pursuit cyclist when riding on the ADT Event Center velodrome in Carson, CA. These data were collected using an SRM Professional track crank during 12 x 1 km flying efforts performed at varying speeds to determine Crr and CdA on the track, and hence aid in equipment selection and pacing strategy. The results have been corrected for 1) minor variations in starting and ending speeds and thus in stored kinetic energy and 2) frictional power losses in the drive train (assuming an efficiency of 97.5%). The cyclist was in full race kit (i.e., race wheels, skinsuit, shoe covers, aerodynamic helmet), and the velodrome was empty except for one other cyclist who was performing identical efforts on the opposite side of the track (more on this below).

Figure 1. Power vs. speed relationship when riding solo.

As expected/as can be seen in the figure, the power-vs.-speed relationship was well-fitted (i.e., R^2 = 0.9998) by an equation of the form:

Y = 3.22X + 0.1146X^3

which corresponds to an apparent (i.e., uncorrected for increased normal force in the turns) Crr of 0.0043 and a CdA of 0.198 m^2. Taking into consideration the increase in normal force, the former would equate to an actual Crr of ~0.003, which is consistent with the results of subsequent straight-line tests conducted on smooth asphalt using identical procedures, which yielded a Crr of 0.0032±0.0003 for these tires (i.e., VeloFlex Record clinchers with Michelin latex tubes) when inflated to the same pressure as used on the track (i.e., 115 psi). On the other hand, the value for CdA obtained during the field tests agrees exactly with that measured (over 0 to 10 deg of yaw) in the Oran W. Nicks Low Speed Wind Tunnel at Texas A&M University just two weeks previously. As such, these data are in keeping with the results of Martin et al. (Med Sci Sports Exerc 2006; 20:592-597), who reported excellent congruence (average difference = -0.001±0.002 m^2) between field test- and wind tunnel-derived measurements of CdA in five out of six subjects. (CdA in their other subject inexplicably differed by almost 10%, strongly suggesting, e.g., an inadvertent difference in clothing.)

The formal testing described above was conducted on the second day of a multi-day training camp. On the third day, the cyclist in question performed a workout that included 4 x 3 km flying efforts with a goal pace of 13.5 m/s (i.e., 3:42 for 3 km). They followed the same warm-up and used precisely the same equipment, position, and tire pressure as the previous day; air density (measured trackside using a Brunton ADC Pro) was also identical. Unlike the previous day, however, throughout these efforts the second rider mentioned above drafted very closely behind the “test subject”, as shown in Figure 2 below.

Figure 2. Second rider drafting closely behind pursuit cyclist whose power data form the basis of this report.

This was not a planned experiment, but simply reflected the desire of the drafting rider for an easier, but still high speed/high cadence, workout. Interestingly, however, the presence of this second rider seemingly reduced the pursuiter’s power requirement, as shown in Figure 3 below.

Figure 3. Power vs. speed relationship when being drafted.

Specifically, their power during the 4 x 3 km flying efforts was, on average, 9 (range 3 to 15) W lower (P=0.024 by one-tailed t test) than expected based on their power-vs.-speed relationship established the day before. To put it another way, having a rider drafting closely behind them apparently lowered their CdA by 3.2%, i.e., from 0.198 to 0.192 m^2. In terms of time saved, this would permit them to cover 3 km (e.g., in a team pursuit) ~1.5 s faster than riding alone, even if the following rider(s) never even “pulled through”.

As stated at the outset and as reiterated in the paragraph above, this was not an intentional experiment, and so it is possible that other factors explain the small, but nonetheless apparently measurable, reduction in the leading rider’s power when another rider was drafting. For example, it is possible that the presence of another rider on the track during the formal testing disturbed the air sufficiently to influence the power-vs.-speed relationship shown in Figure 1. Care was taken, however, to synchronize the two riders’ efforts so as to maintain approximately one-half lap (i.e., ~125 m) separation between them at all times. Furthermore, based on the reports of others if anything the presence of another rider on the opposite side of the track should have reduced, not increased, the power that the pursuit rider had to generate. Finally, as mentioned previously the CdA calculated from these data agrees exactly with that determined via wind tunnel testing. Thus, this explanation seems unlikely.

Possibly a more plausible scenario would be that having the two cyclists riding together at high speed created more of a counterclockwise rotation of air than when the riders were on opposite sides of the track, i.e., on the second occasion the two riders were effectively drafting 250 m behind themselves (vs. 125 m behind each other). Indeed, it would only require a self-generated “tailwind” of 0.15 m/s to explain the observed difference in power, and standing in the infield at ADT I have measured wind speeds of >2 m/s when many riders are on the track simultaneously, e.g., during pre-event warmup. Arguing against this possibility, however, is the lack of any perceptible flow of air when the two cyclists were riding together (except immediately following their passing), as well as the fact that close inspection of the powermeter data failed to reveal any trends over time as one might expect if the riders were truly causing the air to start to swirl inside the building. In any case, I believe that these observations are intriguing, and I encourage anyone who agrees to undertake more formal theoretical or experimental studies of the phenomenon on their own.