Estimation of CdA from anthropometric data

by Andrew R. Coggan, Ph.D.

The popularity of wind tunnel testing to determine a cyclist's aerodynamic drag characteristics (i.e., their CdA, which is the product of their frontal area, A, and a dimensionless "shape factor", Cd) has grown considerably in recent years. A number of field tests for estimating CdA have also been developed and, in at least some cases, carefully validated/evaluated (e.g., http://www.trainingandracingwithapowermeter.com/2010/10/challenge-to-cycling-aerodynamicists.html). Nonetheless, there are times when a simple, "quick-and-dirty" estimate of someone's CdA is all that is needed/desired. For example, a cyclist or triathlete lacking a powermeter on their bike may still wish to estimate how much power they need to produce to achieve a particular performance, e.g., a certain average speed in a flat TT or triathlon bike leg. A convenient way of obtaining a ballpark estimate of CdA based upon easily-obtained measurements can also be used as a "smell test" to see whether other data (e.g., CdA values presented by others) make sense, and/or to place a given athlete's CdA in better context (i.e., are they more or less aero than typically found?). In such situations, it is possible to estimate A based on various anthropometric data, which can then be combined with an estimate of Cd to arrive at a final value for CdA. While this approach is rather crude, in my experience it works well enough to occasionally still be useful.

As indicated above, the first step is to estimate an individual's projected frontal area when in the aero position on their TT or triathlon bicycle. I am aware of at least five different formulae for making this calculation, as listed below. The first was originally related to me by Sam Callan, Director of Coaching Education for USA Cycling, whereas the other four are from the listed scientific papers. In the case of Heil's equations, STA = seat tube angle, TA = torso angle, and SW = shoulder width (readers of this blog are encouraged to consult the original paper to see precisely how these were defined/determined).

1. Australian Institute of Sport

Frontal area (m^2) = 0.18964 x height (m) + 0.00215 x mass (kg) - 0.07861
n = ?; R^2 = ?.??; P = ?.??; S.E.E. = ?.??? m^2

2. Bassett et al. (Med Sci Sports Exerc 1999; 31:1665-1676):

Frontal area (m^2) = 0.0293 x height (m) x mass (kg)^0.425 + 0.0604
n=8; R^2 = 0.76; P = 0.05; S.E.E. = 0.009 m^2

3. Heil DP. (Eur J Appl Physiol 2001; 85:358-366):

Frontal area (m^2) = [0.00433 x STA (deg)^0.172 x TA (deg)^0.096 x mass (kg)^0.762] + 0.066
n=21; R^2 = 0.54; P less than 0.001; S.E.E. = 0.017 m^2

Frontal area (m^2) = [0.00653 x STA (deg)^0.183 x TA (deg)^0.099 x mass (kg)^0.493 x height (m)^1.163] + 0.066
n=21; R^2 = 0.56; P less than 0.001; S.E.E. = 0.014 m^2

Frontal area (m^2) = [0.0148 x STA (deg)^0.184 x TA (deg)^0.099 x mass (kg)^0.408 x height (m)^0.925 x SW (m)^0.426] + 0.066
n=21; R^2 = 0.69; P less than 0.001; S.E.E. = 0.013 m^2

Once a value for frontal area is obtained, this must be multiplied by an appropriate value for Cd. Contrary to the assertions of many, cyclists are not "bluff bodies", i.e., the Cd of a cyclist upon a bicycle (even sitting upright on a mountain bike) is significantly less than that of, say, a flat plate, and perhaps more importantly, can vary as a function of yaw angle. Nonetheless, reasonable estimates of CdA (at 0 deg of yaw) can still usually be obtained by multiplying the above-derived frontal area(s) by 0.707, which is the average value for n=8 cyclists of varying stature and build tested by Dr. Chet Kyle in the Texas A&M wind tunnel (cf. Cycling Science 1991; Sept/Dec: 51-56 - Cd values ranged from 0.652 to 0.793). Alternatively, Cd can be estimated from body mass using an equation derived by Heil based on a meta-analysis of the literature:

Cd (unitless) = 4.45 x mass (kg)^-0.45

Given, however, the unknown precision of this equation and the fact that Kyle found no significant relationship between Cd and mass, there seems to be little reason to recommend it over simply using a fixed value of ~0.7.

So just how precisely can CdA be estimated using the approach described above? This question can be addressed two ways, i.e., via standard propogation-of-error analysis and also by example.

1) Propogation-of-error analysis: The standard errors of the estimate (S.E.E.) provided by each equation for estimating frontal area range range from 0.009 to 0.017 m^2. Frontal area, however, only accounts for ~60% of CdA, i.e., Cd can and does vary between individuals and thus accounts for the other ~40%. The S.E.E. values listed therefore do not tell the whole story, i.e., one must also take into consideration the variability in estimating Cd. Based on the data of Kyle and using standard propogation-of-error methods, the overall imprecision in estimating CdA would be 0.016-0.019 m^2, or plus/minus somewhere between 5 and 10% of a typical value.

2) Some examples: The table below lists anthropometric data along with estimates of A, Cd, and CdA obtained using the equations discussed above for two individuals, both of whom have been tested in the Texas A&M wind tunnel. Due in part to chance alone, the values obtained by using the third equation developed by Heil combined with either method of estimating Cd agree almost exactly with those determined in wind tunnel testing. While this outcome cannot be expected in all cases, the table below does serve to illustrate the range of values the various equations provide, and in fact it is often useful to "bracket" such estimates by calculating all possible outcomes (as shown), rather than relying upon just one single estimate.

Table 1. Estimates of A, Cd, and CdA using the various equations.

Crr - roller vs. field test results, part 2

by Andrew R. Coggan, Ph.D.

In this prior blog entry:

http://www.trainingandracingwithapowermeter.com/2010/06/crr-roller-vs-field-test-results.html

I described a comparison of the Crr data I had obtained using the regression method for five pairs of tire to the Crr values Al Morrison measured for the same tires in his well-known roller tests. Since that time, I have continued to collect additional data, and so thought it might be worth updating that prior report. Thus, without further ado:

Figure 1. Crr of various tires measured on the road and on rollers.

Note that, except for the Continental Supersonic (SS) and Michelin Pro Race 2 SC data, where n=1, the field test results are averages based on 3-6 tests performed on separate days. The average (+/- SD) coefficient of variation across days was 7.9 +/- 2.8%.

Aero tires and wheels: skinny vs. fat?

by Andrew R. Coggan, Ph.D.

For almost 30 y, those "in the know" with respect to the aerodynamics of bicycle wheels (e.g., Chet Kyle, John Cobb) have emphasized the importance of tire width in determining overall speed. Specifically, it has long been held that it is important to closely match the width of the tire to the width of the rim to minimize aerodynamic drag, and that doing so usually outweighs any increase in rolling resistance resulting from use of a very narrow tire (e.g., 19 mm).

There are, however, some real (or at least perceived) disadvantages to using such narrow tires, such as poorer handling (especially on imperfect pavement), reduced comfort, increased susceptibility to pinch-flats, etc. Thus, during the last decade manufacturers such as Zipp have attempted to design wheels that exhibit less of an increase in aerodynamic drag when used with a slightly wider tire (e.g., 21-23 mm). In Zipp's case, this initially entailed incorporating a bulge just below the brake track, which helps smooth the turbulent flow coming off of the tire. More recently, first HED and now Zipp have introduced wheels where the brake track itself has been widened, and at least in Zipp's case the rest of the rim significantly reshaped, with one goal of these wider wheels being to permit use of wider tires while still minimizing aerodynamic drag. (Other purposes are 1) to reduce drag at higher yaw angles, i.e., beyond the point at which previous designs tended to stall, and 2) to minimize wind-induced steering torque.) Indeed, HED claims that even when using the same width tire, the wider brake track itself significantly reduces rolling resistance by allowing the tire to assume less of a "lightbulb" shape". Notably, however, this latter claim has not been supported by direct measurements.

Another factor seemingly contributing to the current trend toward use of wider tires, even by time trialists, is the more widespread availability of quantitative data for the rolling resistance of various tires. In particular, Al Morrison's well-known roller tests have enabled cyclists to choose tires based on direct measurements of their rolling resistance, and not just based upon manufacturer's claims. Apparently as a result, people are more cognizant of just how much time can be gained via judicious selection of better-rolling tires, and have tended to focus more upon this and less upon aerodynamics.

In apparent opposition to the above-described trends, however, the field testing that I have done implies that, at least at/near a yaw angle of 0 deg, narrowness is still a key element when it comes to selecting tires and wheels in an attempt to maximize speed, and that you still need to carefully consider the trade-off between aerodynamic drag and rolling resistance when selecting your tires and wheels. Since the results of such tests only reflect what is happening at very low yaw angles and the sensitivity of such "real world" bicycle-plus-rider measurements is less than what can be achieved when testing wheels in isolation in a wind tunnel, I do not profess to have the final answer to the "skinny vs. fat" debate. Nonetheless, I believe it is worth sharing the results of my experiments, if only to raise peoples' awareness regarding this issue.

Experiment #1: 1990s Campagnolo Shamal vs. 2007 Zipp 808

Based on Chung-style aerodynamic testing performed on an indoor velodrome, Alex Simmons has reported that, at least on some occasions, a tubular Campagnolo Shamal front wheel appeared to be significantly more aerodynamic than either a Zipp 808 or flat disk wheel. In other experiments, however, the results were reversed, i.e., the Shamal was measurably slower, leaving the question of which is the faster wheel unsettled, at least in my mind.

Because of the variability of Alex's results, as well as the fact that he tested the wheels using similar, although not identical, tires, I decided to try to repeat the experiment. I therefore borrowed a 12 spoke Shamal front wheel from my friend Jim Martin, and measured my CdA when using it vs. the 2007 Zipp 808 front wheel that I own when both were fitted with the same brand and model 19 mm clincher tire. As described here:

http://www.wattagetraining.com/forum/viewtopic.php?f=2&t=309#p3789

when fixing the Crr to the mean value obtained during the two back-to-back tests, my CdA when using the Shamal was only 0.001 m^2 higher than when using the 808. Given the amount of effort that has been expended in the last decade by Zipp (and others) to optimize wheel aerodynamics, these results imply that narrowness, per se, still remains a very important determinant of aerodynamic drag, at least at/near 0 deg of yaw.

Experiment #2: 2007 Zipp 808 fitted with different tires

While in the above tests the narrow Campagnolo Shamal performed quite admirably relative to the more modern Zipp 808 wheel, the latter was still slightly faster, even at/near 0 deg of yaw. In addition, it would be expected to do even better at higher yaw angles, and I already owned the wheel. For my next series of experiments, then, I set about trying to determine the optimal tire to use on it. Although Zipp has stated that the aerodynamics of the wheel are less impacted by tire width, to my knowledge at least they have never claimed that it performs better with wider tires. Based on the earlier data of Kyle, Cobb, etc., I therefore decided to compare three different 19-20 mm (nominal) tires with known, similarly-low rolling resistance but reportedly differing in aerodynamic drag. Because the results of my testing may very well be specific to my wheel and the test conditions, I will refer to them simply as tires (they were usually tested in pairs, so all data have been corrected to reflect that fact) A, B, and C, respectively.

Teasing out the precise difference between these different tires took considerable effort, especially when comparing tires B and C. Nonetheless, after multiple between-day and within-day tests, I believe that I was able to do so with reasonable confidence. Because both Crr and CdA varied between conditions, it is perhaps easiest to appreciate the results by simply examining the calculated power-vs.-speed relationship under standardized conditions (e.g., constant air density):

Figure 1. Power versus speed relationship when using tires A, B, or C (in pairs).

As can be seen in the figure, when compared to tire A, using tire B would reduce the power requirement at my nominal TT speed by ~10 W. Stated another way, assuming the same power output the use of tire B instead of tire A should theoretically save me ~34 s in a 40 km TT. All of this estimated time savings is due to the lower CdA of tire B, as the Crr of this tire is actually slightly higher than that of tire A.

As can also been seen in the figure, the difference between tires B and C is much smaller, amounting to a power differential of only ~2 W, or a time differential of only ~10 s. In this case, however, the theoretical time-savings is due entirely to the difference in Crr between tires, as CdA did not differ.

The question then becomes, what is it about tire A that makes it aerodynamically inferior (or conversely, that makes tires B and C aerodynamically superior)? That is something that cannot be stated with certainty, but it is interesting to note that 1) although all three tires are nominally 19-20 mm in width, based on direct measurements tire A is actually ~1 mm wider, and 2) although tires B and C are significantly different in other respects, their width is nearly identical. These observations, along with other experiments that I have performed, suggest to me that the difference in CdA between tire A and tires B and C might very well be due to the subtle difference in width alone.

Conclusions

As stated before, I do not claim to have any final answers with respect to optimal wheel or tire design/width. Rather, my purpose in sharing the results of these experiments is to simply encourage people to carefully and quantitatively consider various factors when attempting to determine the wheels/tires that are best for them and the conditions under which they expect to compete.

A challenge to cycling aerodynamicists

by Andrew R. Coggan, Ph.D.

In 1950, the Nobel Prize-winning physiologist Archibald Vivian (A.V.) Hill published his famous paper, "A challenge to biochemists", in which he emphasized that up until that time no one had ever been able to demonstrate a decline in muscle ATP levels as a result of a single twitch (1). Because of this, he suggested that some new substance might still be discovered that would supplant ATP in our understanding of muscle biochemisty in precisely the same way that ATP had previously replaced phosphocreatine (PCr) and PCr had replaced lactate. To help clarify matters, he challenged biochemists to prove that ATP was indeed the molecule that directly powered muscle contraction, and outlined an experimental approach for doing so.

Approximately 50 y later, Tom Compton (developer of http://www.analyticcycling.com/) issued a comparable challenge to those performing field tests using a powermeter to determine CdA. Specifically, Tom suggested that if you wanted to test the precision of whatever approach you chose to use, you could do so by attaching an object of known aerodynamic characteristics (e.g., a flat disk) to your bicycle and see if you can detect the resulting increase in CdA and/or drag force. In this way you would have a direct indicator of the magnitude of the smallest difference you could reliably detect.

Although Tom's idea is an excellent one, I had previously never gotten around to formally acting upon it, focusing instead on experimenting with things that might make me faster, rather than slower. In preparation for a talk I recently gave at USA Cycling's biannual Coaching Summit, however, I decided to take on Tom's challenge. The purpose of this blog entry is to describe the results of these experiments, partially in hopes of motivating others to try something similar themselves.

Taking the Tom Compton challenge: equipment

As outlined above, Tom's suggestion was to attach a flat plate or disk somewhere on your bicycle (or yourself, e.g., on top of your helmet). I was concerned, however, that small variations in wind speed or direction and/or in the orientation of whatever object I chose with respect to myself/my bike could negatively impact the results. For this reason, I decided to use spheres, since their CdA would be the same regardless of the "angle of attack". The two spheres I tested were a hollow plastic ball 6.45 cm in diameter and a Styrofoam ball 10.16 cm in diameter. These were attached to the front hub via a 2 mm diameter spoke (Figs. 1 and 2):

Figure 1. Small sphere attached to front hub of bike via a spoke.

Figure 2. Large sphere attached to front hub of bike via a spoke.

At first I planned to employ some form of clamping system to attach the mounting spoke to a point very low on the fork. In playing around with various things, however, I hit upon the idea of using a rear American Classic skewer with the small nylon rod (which helps provide grip on the end-nut) removed, along with some spacers and a nut from another quick release (Fig. 3):

Figure 3. The clamping mechanism holding the spoke.

I tried other brands of skewers (e.g., Mavic, Shimano, Specialized), but only the American Classic was threaded far enough towards the lever end that I had enough rod protruding beyond the inner nut to also thread on the American Classic nut far enough to have it really clamp down on the spoke nipple.

This Golbergesque device worked quite well, holding the spoke and attached sphere securely during training rides up to 60 km in length and at speeds up to 80 km/h. (While I got rather quizzical looks from a few cyclists I encountered who noticed it, automobile drivers who apparently saw it seemed to give me extra space.) I therefore was not worried about anything coming loose and, e.g., falling into my Zipp 808 front wheel during actual testing. The sphere would periodically oscillate a bit, however, especially the smaller one/at lower speeds as shown in this video clip shot while riding at ~25 km/h (Fig. 4):

Figure 4. Motion of small sphere while riding at ~25 km/h.

This movement appeared to be due to road vibration/riding over bumps rather than variations in aerodynamic behavior, i.e., formation of vortices (which as expected could in fact be felt when placing your hand behind the sphere, at least at higher speeds).

The reason that I decided to attach the spheres lateral from the front hub rather than anywhere else is because based on, e.g., CFD analyses performed by others I felt that this would have a good chance of putting them in, or at least very near, the free air stream. In other words, I was hoping to avoid the interference/stagnation pressure effects reported by others (e.g., http://www.hupi.org/HPeJ/0008/0008.htm). To verify my assumption, I fashioned another mount to hold my Brunton ADC Pro weathermeter (http://www.brunton.com/product.php?id=262) in the same place as the spheres, and measured air speed using it while simultaneously measuring my speed over the ground using my SRM (Fig. 5):

Figure 5. Air speed vs. ground speed measurements demonstrating lack of any significant interference or stagnation effects.

The above data are averages collected over 15-100 s of riding at quasi-constant speed over a stretch of sheltered road under very low-wind conditions. As can be seen in the figure, the measured air and ground speeds agreed to within ~3%, demonstrating that the location where I mounted the spheres was free of any significant interference or stagnation effects.

Taking the Tom Compton challenge: experimental approach

Having put together my equipment and having verified its safety and function, I picked a calm day and headed out to the road that I normally use for aerodynamic testing (see http://www.trainingandracingwithapowermeter.com/2010/04/which-is-faster-cervelo-p2t-or-javelin.html for details). I then proceeded to do 12 runs (6 in each direction) without anything extra attached to my bike, followed by 12 runs using the large sphere (going for the big effect first, in case I wasn't able to finish making all the measurements I wanted to make), followed by 12 runs using the small sphere. I then used the CdA determined during the 1st set of control trials along with the Crr, the air density, my ground speed, etc., to predict how much of an increase in drag force should result during the runs with the small and large spheres. I then compared this measured increase in drag force to that expected based on the measured frontal areas of the spheres, spokes, and mounting device, using Cd values derived from the literature (i..e, 1.2 for cylinders, 0.45-0.50 varying with speed for the spheres) based on the Reynolds number.

Taking the Tom Compton challenge: the results

Figure 6 shows the results of these experiments. As can be seen in the figure, on average the measured increase in aerodynamic drag closely paralleled the expected increase, but was 0.07-0.08 N higher in both cases. The reason for this discrepancy is not clear, but it could be due to error in either value. For example, it is possible that modeling the "air brake" as a simple combination of a sphere and two cylinders (i.e., spoke plus clamp) underestimated the true increase in drag that should result. Alternatively, it is possible that vibration/oscillation of the sphere resulted in a greater-than-expected drag due to non-ideal aerodynamic behavior.

Regardless, the important findings here are that it was possible to detect not only the increase in drag resulting from the small sphere (i.e., 0.18 vs. 0 N), but also the difference in the increase in drag between the small and large spheres (i.e., 0.30 vs. 0.18 N). The limit of detection would therefore appear to be less than ~0.15 N (~15 g) in drag force, which at typical racing speeds/air densities translates to a difference in CdA of less than ~0.0015 m^2, a difference in power requirement of less than ~1.5 W, and/or a difference in 40 km TT time of less than ~6 s.

Figure 6. Measured vs. expected increase in drag force due to small and large spheres.

Taking the Tom Compton challenge: conclusions

With careful attention to detail, it is possible to use a powermeter to measure aerodynamic drag with a degree of sensitivity that rivals that of a wind tunnel. Nonetheless, wind tunnel testing remains the method of choice for those who can afford it, due to the speed/convenience of such measurements as well as the ability to make measurements at multiple yaw angles.

Acknowledgements

I would like to thank Tom Compton for suggesting these experiments on various online forums roughly one decade ago. My apologies for taking so long to getting around to taking up your challenge!

References

1. Hill AV. A challenge to biochemists. Biochim Biophys Acta 4:4-11, 1950.

Crr - roller vs. field test results

by Andrew R. Coggan, Ph.D.

One of the "perks" that comes with owning a power meter is the ability to quantify two of the most important physical factors determining our speed at a given power, i.e., our aerodynamic drag characteristics (i.e., CdA) and our coefficient of rolling resistance (i.e., Crr). (Our "all up" mass, of course, is also an important factor, especially when climbing or accelerating, but obviously you don't need a power meter to know how much you and your bicycle weigh.) Various methods for estimating these parameters are outlined on pages 249-252 of our book, and I have provided more detail about my specific approach in prior posts, e.g.:

http://www.trainingandracingwithapowermeter.com/2010/04/which-is-faster-cervelo-p2t-or-javelin.html

Here, I would like to share the results of a compilation of such tests that I have done over the last 7 y, in particular focussing on how well the Crr values that I have obtained for various tires compare to the well-known roller tests performed by Al Morrison. The results of this comparison are shown in the figure below:

Figure 1. Comparison of field vs. roller data for Crr for five pairs of tires.

The data shown in the figure represent the average values (n=3-5 per pair of tires) of a subset of all such experiments I have performed, including only those where the temperature was between 15 and 25 deg C (ambient temperature for the experiments shown was 19.9 +/- 2.1 deg C). When mismatched pairs of tires were tested, I used the average value obtained during Al's roller tests, i.e., I assumed that my weight was equally distributed on the front and rear wheels of my TT bike. Finally, since I tested the Continental Ultra 2000 clincher tires using butyl tubes, whereas Al tested these (my) tires using latex tubes, I have adjusted the value he obtained upward by 0.00038, i.e., the average difference he has obtained in his roller tests when comparing butyl vs. latex tubes.

As can be seen in the figure, the roller and field test data agree quite closely, even though they have been performed by different individuals using different equipment and procedures. As might be expected, however, the Crr values I have obtained on an asphalt road are higher than what Al has measured using plastic rollers. Part of this difference, of course, is almost certainly due to differences in the two surfaces, and in fact when testing on aluminum rollers I have consistently obtained Crr values that are 18% lower than those found by Al, even when using identical procedures. It is also possible, however, that other factors contribute to the difference between the field-test and roller data, e.g., differences in the calibrations of our power meters (or scales), small biases in the values assumed for chain friction (field tests) or bearing friction (roller tests), etc.

The most important "take home" message, however, is the high correlation found between the roller and field test data (over a wide range of Crr values), which strongly supports the validity of the former as an approach for differentiating between the Crr of different tires. Indeed, the precision of roller testing is so much greater (i.e., by a factor of ~10x, in my experience) that it should be considered the method of choice for anyone who owns a power meter (and rollers).

(Note: I have previously posted the above plot to various web fora. If it differs from such prior versions, it is the result of more meticulously examining the data to spot errors, make certain that the brand, model, and width of tire that I tested was exactly the same as that tested by Al, etc.)

Which is faster: the Cervelo P3C or the Cervelo P2T?

by Andrew R. Coggan, Ph.D.

Over on another forum, I mentioned in passing that I had previously field-tested both a Cervelo P2T (Cervelo's track version of their original P2k) and Cervelo P3C (also the track version), and found that the latter was measurably faster. Another poster expressed a bit of surprise at this result, so I thought I would share the data here.

To compare the two frames, I used exactly the same procedures as described in this prior article:

http://www.trainingandracingwithapowermeter.com/2010/04/which-is-faster-cervelo-p2t-or-javelin.html

except that I used a different saddle, front brake, helmet, wheels, and tires in this more recent round of experiments. The P2T and P3C were, however, fitted with the same components, i.e., the only thing that differed was the frameset. Furthermore, my position on the two bikes was identical (facilitated, again, by their equivalent geometries).

The results of this testing are shown in Figure 1 below, which illustrates my power vs. speed relationship (corrected for slight differences in air density) when riding the two bikes. (Note that for the sake of clarity, I have chosen to start both the X and the Y axis at a positive value, and not at zero.)

Figure 1. Power versus speed when riding a Cervelo P2T vs. a Cervelo P3C.

As can be seen in the figure, I required slightly, but nonetheless measurably, less power when riding the P3C, especially at higher speeds where wind resistance becomes progressively more important. For example, to ride at 13.89 m/s (50 km/h) on the P3C I would need to produce "only" 395 W, versus 402 W when riding the P2T, corresponding to a reduction in my CdA from 0.220 to 0.212 m^2. While this 7 W (1.7%) difference in power requirement/0.008 m^2 difference in CdA may seem small, anyone who has trained/raced with a power meter and/or done any field testing using one will realize that it is not. In terms of a time differential, using the P3C instead of a P2T would save me 0.85 s/km, or 2.55 s in a 3 km pursuit or 34 s in a 40 km TT.

Note that the above measurements were made under very low wind conditions, i.e., at/near 0 deg of yaw. Since modern aero frames are designed to especially effective at the yaw angles typically encountered in competition, the above is likely an underestimate of the difference that would be observed under non-calm conditions. Indeed, Tom Anhalt has previously reported a slightly larger difference than the above when comparing identically-equipped Cervelo P2k and P3C time trial bikes in mildy breezy weather.

Demands of the individual pursuit, part 3

by Andrew R. Coggan, Ph.D.

In this series of articles I have combined the use of a conceptual model of pursuit performance (i.e., the pursuit performance "teeter totter") with a mathematical model of the physics of cycling (7) to assess the relative importance of various factors in determining success in this particular event. The overall approach was described in part 1 (http://www.trainingandracingwithapowermeter.com/2010/04/demands-of-individual-pursuit-part-1.html), whereas the physical and physiological determinants of pursuit performance were discussed in part 2 (http://www.trainingandracingwithapowermeter.com/2010/05/demands-of-individual-pursuit-part-2.html). The role played by various technical factors is considered below.

Determinants of pursuit performance: technical factors

Unlike the physical and physiological factors discussed previously, it is more difficult to determine the precise impact of variations in technical factors, i.e., an individual's technique or skill, in determining pursuit performance. This is because it is much more difficult (if not impossible) objectively quantify such factors versus the physical and physiological determinants of performance. Nonetheless, it should be apparent from the previous discussion that, e.g., a pursuiter's starting technique, per se, plays a very small role in their final overall time (Table 4). By starting technique, I am referring to precisely how an individual achieves a particular power output while accelerating up to speed, their coincidence anticipation timing (i.e., their ability to synchronize their movements with the count-down clock/starting gate), when they choose to sit down during the first lap, etc. Of course, this is not to say that pursuiters should not practice their start with regularity, as such races are not infrequently decided by 0.1 s or less. Clearly, however, a high degree of skill in starting is far less important to a pursuiter than, e.g., a kilometer or 500 m specialist (or even a team pursuiter), and this fact should be reflected in the relative emphasis placed upon start practice in a pursuit cyclist's training program.

Table 4. Time changes resulting from variations in technical determinants of pursuit performance.

In comparison to the individual's starting technique, their skill at riding as low as possible on the track can have a large impact upon their performance. For example, riding just 20 cm (~8 in) up from the measurement line will cost a pursuiter almost 0.1 s per lap on a 250 m track, or 1.1-1.3 s (0.5%) overall. Thus, riders should (and of course do) strive to ride as low on the track as possible when in the turns, especially when competing against a closely-matched opponent or when it is important to achieve the lowest possible time (e.g., qualifying, record attempt). On the other hand, knowing precisely how much time is gained/lost based on the line taken in the turns may provide the rider with the confidence needed to wisely "play it safe" in other situations, to avoid hitting a sponge and potentially crashing. Similarly, understanding the quantitative effect of other possible lines on the track (e.g., swinging wide in the straights) can help an athlete and/or coach choose an optimal path for a given track (and rider).

The third, and probably most important, aspect of skill or technique that influences a rider's pursuit time in the context of the physical and physiological factors previously discussed is pacing strategy. Contrary to what is believed by some, perfectly constant split times do not appear to be ideal (although such a pacing strategy is not far from optimal). Rather, modeling of pursuit performance based on physical and physiological information (6,8) suggests that a slightly faster overall time results when a peak velocity greater than the average steady-state velocity is achieved during the 2nd lap[2], with a very slight slowing (i.e., less than 1 s/km; corresponding to a gradual decline in power of ~15%) occurring thereafter. This conclusion is consistent with actual practice (9). I suspect that this somewhat counterintuitive strategy is the result of two factors: 1) by starting at a pace or effort slightly greater than that which can be sustained, utilization of your full anaerobic capacity is assured, and 2) any kinetic energy you have when you cross the finish line is "wasted", in the sense that it can no longer be used to improve performance (8). This latter concept seems to be especially important in the kilometer (and probably even more so in the 500 m), but apparently also applies to the pursuit.

On the other hand, it is far more common for pursuiters to start out too rapidly than too slowly, even at the elite level. This was evident in, e.g., the recent 2010 World Championships, in which the highly anticipated showdown between Jack Bobridge of Australia and Taylor Phinney of the United States for the gold medal failed to materialize after Bobridge qualified in 3rd place. Based on the official kilometer split times, it is clear that Bobridge started out consideraly faster than Phinney or the eventual silver medalist, Jesse Sergent of New Zealand, then slowed down far more than is ideal during the latter stages of the race (Figure 5). In contrast, the 4th place qualifer, Alexander Serov of Russia, started out more conservatively than the other three, but then accelerated too much during his 2nd kilometer in an apparent attempt to make up time.

Figure 5. Kilometer split times for the top four men during qualifying at the 2010 World Championships.

While in many cases riders must aim for a particular time that they believe is necessary to win even if this means risking "blowing up", it is nonetheless natural to wonder how the results of this recent competition might have been altered overall if Bobridge (or Serov) had paced himself differently in qualifying.

The negative consequences of starting too rapidly during a pursuit are largely due to the impact that this has upon the rider's physiology, i.e., the reduction in power that results from premature fatigue. However, even if a rider is sufficiently well-trained so as to largely withstand these negative physiological consequences, they may still go slower as result of a differences in the physics, i.e., an increase in aerodynamic drag resulting from the higher peak speed. This is illustrated in Figure 6 below, which shows the speed and power of a female track cyclist during the qualifying round and during the final round of a recent U.S. national championships.

Figure 6. Effect of pacing on 3 km pursuit performance when overall average power is equivalent.

The rider whose data are shown was considered an inside favorite to win the jersey, having shattered their personal best 3 km time in training just a few weeks beforehand. Nerves got the better of them in qualifying, however, and they started out too fast and then "died a thousand deaths" during the final kilometer (to the point that they could not dismount from their bicycle, but had to be lifted off by their handlers). Had the competition been run under current rules, this mistake may not have proved too costly, as they still posted the 2nd fastest time in qualifying. At the time, however, the 2nd and 3rd (and 1st and 4th) fastest riders still met in a semi-final round, meaning that they had to face another athlete who at the time was ranked #1 in the pursuit by the UCI and who just a few weeks later placed 7th at the World Championships. Fortunately for the rider in question, they were able to adjust their pacing strategy and went on to win nationals in a time 2 s faster than they recorded in qualifying, despite the fact that their average power differed by only 3 W, i.e., by less than 1%.

Determinants of pursuit performance: role of individual differences

To illustrate the various points made in this series of articles, I have assumed nominal values for parameters used to perform the modeling. It is unlikely, however, that the characteristics of any given individual will perfectly match these assumed values, i.e., the room for individual differences exists even if performance itself is equivalent. In particular, although the relative distribution of power is unlikely to vary significantly between athletes (as evidenced by the similar relative distributions shown in Figure 1 for 4 km and 3 km events), the absolute power required to achieve a certain time can vary. Likewise, athletes may differ in terms of the exact combination of aerobic and anaerobic energy production yielding a particular power output. An example of the latter is discussed on pages 247-248 of Training and Racing with a Power Meter. The point that I would like to emphasize here is that the systematic approach to analyzing pursuit performance that I have described can be used to identify and then capitalize upon such individual differences to optimize a given rider's preparation and training. In other words, it is the process that I have presented, rather than the exact outcome, that is most important.

Summary and conclusions

To summarize this series of articles, I believe that it most appropriate to simply repeat the synopsis that I provided at the outset:

"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.”

[2]In my experience, it is actually the 2nd half of the 1st lap that is most important, as it is during this part of the race that riders are most likely to "overcook it", i.e., to continue to accelerate beyond their goal pace. Because half-lap splits are not recorded as often as full laps splits, however, most coaches and athletes believe that it is the 2nd lap that is critical.

Demands of the individual pursuit, part 2

by Andrew R. Coggan, Ph.D.

In part 1 of this article:

http://www.trainingandracingwithapowermeter.com/2010/04/demands-of-individual-pursuit-part-1.html

I presented a conceptual model that I refer to as the pursuit performance "teeter totter", and described how it could be used in conjunction with a mathematical model of the physics of cycling to assess the relative importance of various physical, physiological, and technical factors in pursuiting. Before describing the results of these analyses, however, I believe it is worth providing additional detail re. the mathematical model of Martin et al. (7):

Figure 2. Mathematical model of the physics of cycling of Martin et al. (7) .

As described previously, this model has been shown to accurately and precisely describe the physics of cycling under both steady-state and highly non-steady state conditions (e.g., maximal one lap effort on a velodrome from a standing start). This is illustrated in Figure 3 below, which compares the modeled versus directly-measured speed of an elite female cyclist performing a 3 km pursuit:

Figure 3. Model-predicted vs. directly-measured speed of a cyclist performing a 3 km pursuit.

As can be seen in the figure, there is a very close correspondence between the speed at any moment as calculated from the model and that actually measured during the race. This makes it possible to accurately and quantitatively predict the effect of changes in the physical and physiological determinants of pursuit performance shown in Figure 1. The results of analyses are presented below.

Determinants of pursuit performance: physical factors

By "physical factors" I refer to the sources of resistance to forward motion that a pursuit cyclist must overcome, which include drivetrain (and bearing) friction, rolling resistance, inertia (changes in kinetic energy), and aerodynamic drag. Using the model of Martin et al. (7) and the nominal athlete/equipment data and competition conditions presented in the previous article, it is possible to calculate the absolute and relative power requirements of world class pursuit performance, as shown in Figure 3 below:

Figure 3. Power requirements of world class pursuit performance.

As can be seen in the figure, overcoming aerodynamic drag requires by far the most power, with the other factors being much less important. This, of course, is not all that surprising, and explains the widespread use by pursuiters of positions and equipment chosen with aerodynamics in mind. What such an analysis permits, however, is the ability to make such decisions in a quantitatively-informed manner. This is perhaps best illustrated by considering the absolute and relative time savings during a pursuit that would result from an equivalent (e.g., 5%) change (reduction) in any of these factors, as shown in Table 2 below:

Table 2. Time saved as a result of 5% changes in physical determinants of pursuit performance.

Of course, an equivalent change in any of these variables may not always be readily achievable, and pursuit performance will be reduced to some degree by any and all improvements that can be made. Nonetheless, this information can be quite useful when considering situations where a trade-off does exist, e.g., when deciding whether to use wider, better rolling, but less aerodynamic tires versus narrower, poorer rolling, but more aerodynamic tires, or when deciding to invest money into specially-treated chains and chainrings that are designed to reduce drivetrain friction versus on a trip to a wind tunnel. Such information can also be very helpful when making decisions re. the preparation of athletes themselves - for example, although changes in stored kinetic energy represent the second-most important energy "sink" during a pursuit, any time savings resulting from having the athlete attempt to reduce body mass may be easily outweighed by a reduction in their absolute power output, as even relatively large changes in total mass have very little impact on pursuit time. While clearly such decisions can only be made on an individual, i.e., case-by-case, basis, the approach described here can be used to do so in a cogent fashion, instead of basing such decisions on tradition, intuition, etc.

Determinants of pursuit performance: physiological factors

As described in part 1 of this article, scientific research into the physiological characterstics of successful pursuit cyclists indicates that both aerobic power and anaerobic power, but not neuromuscular power, are important determinants of success in the pursuit. Consistent with these conclusions, the modeling approach I have used predicts that a 5% improvement in aerobic power output would reduce a rider's time by 1.4%, whereas a comparable increase in neuromuscular power would reduce their time by only 0.1% (Table 3). On the other hand, a similar increase in anaerobic capacity would improve their performance by 0.3%.

Table 3. Time saved as a result of 5% changes in physiological determinants of pursuit performance.

In this analysis, the cyclist is essentially being viewed as simply a motor, with no consideration given to the actual metabolic requirement of generating the required power output. This, of course, is determined by the individual's thermodynamic efficiency, i.e., the ratio between the rate of energy production and utilization in the form of ATP and the rate of external work production while cycling. Since an improvement in gross cycling efficiency would enhance a rider's power output regardless of the energy system supplying the ATP, an equivalent improvement in efficiency would have a cumlative impact upon an athlete's pursuit time. Specifically, a 5% improvement in gross efficiency would reduce the 4 km time of a world class male pursuit cyclist by 4.6 s (1.7%) and the 3 km time of a world class female pursuit cyclist by 3.7 s (1.7%). While an improvement in cycling efficiency of this magnitude is much greater than is realistically achievable, this observation may help explain the tendency of elite pursuit cyclists to perform very high volumes of training, despite the short duration of their event. This is because the skeletal muscle characterstic most closely associated with cycling efficiency, i.e., fiber type/myosin expression, likely only significantly changes in response to a very high training load (and/or maturation of the individual).

In part 3 of this series of articles, I will discuss the effects of changes in the technical determinants of pursuit performance (i.e., the fulcrum of the pursuit performance "teeter totter"), as well as the role of individual differences in how a given individual achieves a particular level of performance.

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.

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.

Which is faster: the Cervelo P2T or the Javelin Arcole?

(First posted to the internet in 2005.)

by Andrew R. Coggan, Ph.D. - Faced with the question of which of these two frames to use for the pursuit at master track nationals in 2004, I opted for the Cervelo. I did so because 1) unlike the Javelin, it is a true track frame with horizontal fork ends, thus making gear selection much easier, and 2) this particular P2T had a winning “pedigree”. However, after an unexpectedly poor performance at nationals due in part to higher-than-expected aerodynamic drag, I began to wonder if perhaps I had made the wrong choice. In the fall of that year I therefore conducted a series of field experiments using my powermeter to see if I could discern any difference in aerodynamic drag characteristics between the two frames. The results of this study are described in this report.

Methods

Data collection

To compare the two frames, I used an SRM Professional track crank to measure the power required to propel them at steady speeds ranging from ~20 to ~50 km/h. I used these data, along with measurements of barometric pressure and air temperature (to calculate air density), to determine my effective frontal area (i.e., CdA in m^2; product of coefficient of drag, Cd, and frontal area, A) on each bicycle (see Data Analysis). These tests were performed on a ~1 km segment of a very flat, smooth, asphalt road (i.e., Centaur Road in Wildwood, MO). The influence of wind was minimized by 1) using the westernmost portion of this road, which is sheltered by dense woods, 2) collecting data immediately after sunrise and only on days when wind speeds were minimal (i.e., less than 0.5 m/s), and 3) performing 6-9 “runs” in both the easterly and westerly directions and in a random order. With this approach, I was able to estimate my CdA to within ±2%, or with approximately the same degree of precision as can be achieved when testing a pedaling rider in a wind tunnel.

I tested both the Cervelo and the Javelin using two different positions, i.e., once with a 17 cm drop from the saddle to the elbow pads of the aerobars, and once with a 20 cm drop. These distances, along with saddle height, saddle setback, distance from saddle to end of elbow bars, etc., were all confirmed by careful measurement. Fortunately, the two frames had essentially the same “reach” and “stack” (i.e., length of top tube forward of, and height of the top of the headset above, the bottom bracket, respectively). Thus, after positioning my saddle in the same location relative to the bottom bracket on each, all that I needed to do to ensure that my position was the same on both of them was to simply transfer the same handlebars and stem from one to the other.

During all trials, I wore the same technical fabric T-shirt, skinsuit, socks, shoes, shoe covers, and Troxel Radius II helmet. Furthermore, in addition to using the same handlebars (Oval Concept A700) and stem on each bike, the following components were also kept the same:

Fork: Cervelo Chord

Front brake/brake lever: Shimano Ultegra/Tektro 4.0

Front wheel: Zipp 404 with Veloflex Record tubular inflated to 125 psi

Rear wheel: Hed track disk with Tufo S3 tubular inflated to 135 psi

Crank/bottom bracket: SRM Professional track model/generic square taper sealed bearing

Pedals: Speedplay X-2Saddle: Avocet O2 Air

Thus, the only things that differed between tests were 1) the frame, 2) the seatpost, and 3) the chainring and cog used (i.e., 53x13 on Cervelo, 50x14 on Javelin). Different seatposts had to be used because of the Cervelo’s proprietary aerodynamic design, whereas different gearing was used to keep the distance between the trailing edge of the seat tube cut-out and the rear tire the same (i.e., 1.0 cm) on both bikes. Although in theory this could have resulted in a difference between the two bicycles in drivetrain efficiency, any such difference was considered likely to be insignificant and less important than standardizing the frame-tire gap. Finally, to make the comparison the two bikes as easy to interpret as possible, I used electrician’s tape to seal over openings in the Javelin frame normally used for internal routing of brake and shift cables (however, I chose not to saw off the front derailleur hanger!).

Data analysis

Following completion of each set of trials, data were downloaded from the SRM handlebar computer into TrainingPeaks WKO+ (http://home.trainingpeaks.com/wko-desktop-software/analysis-software-for-training-files.aspx) for subsequent analysis. The average speed and power during each run was first determined, taking care to ensure that the speed was identical at the starting and ending points of each run (to eliminate variations in stored kinetic energy). These directly-measured power data were then adjusted downward by 2.5% to account for frictional losses in the drivetrain. This value was assumed based on the results of published scientific studies as well as extensive comparisons of this specific SRM crank to other power-measuring devices that sense power at the rear wheel (i.e., PowerTap, Velodyne). The power and speed data were then analyzed by fitting them to a curvilinear regression of the form:

Y = aX + bX^3

where Y is the power (in W) and X is the speed (in m/s). As such, the constants a and b represent rolling resistance (in N) and the product of one-half times the air density (in g/mL) times CdA (in m^2), respectively. Air density was calculated based on air temperature and barometric pressure at the time of each trial as reported online from the nearby (~2 km) Spirit of St. Louis Airport in Chesterfield, MO. Furthermore, the absence of any significant local variations in temperature was confirmed by comparing those reported from the airport to those measured on-site using the SRM handlebar computer. To check for possible gradient- or wind-effects, data from easterly and westerly trials were first analyzed separately; however, no significant trends in the data were apparent. Data from both easterly and westerly trials were therefore pooled for further analysis, yielding a single estimate of CdA per day/condition (bicycle set-up).

Results

Data from a representative series of runs are shown in Figure 1, whereas the overall results are shown in Table 1, both of which are shown below.

Figure 1. Power vs. speed relationship from a representative series of measurements.

Table 1. Complete results.

As displayed graphically in the figure and as demonstrated by the low standard errors of the estimate shown in the table, the model provided a very close fit to the experimental results. Furthermore, in both positions my CdA was lower when riding the Cervelo than when riding the Javelin, although the magnitude of this difference was only slightly greater than the uncertainty of the measurement.

Discussion

It must be emphasized from the outset that the difference in CdA between the Javelin and Cervelo was so small that it could have been entirely due to chance alone. On the other hand, the fact that the magnitude of the difference was consistent across the two positions, as well as the fact that it was apparently possible to detect a difference between the two positions in the first place, suggests that the difference in CdA between the two bikes may in fact be real. Although small, a difference of the magnitude observed (i.e., ~0.005 m^2) is potentially quite significant in competition, as at normal racing speeds it would result in a time differential of ~0.5 s/km, e.g., ~1.5 s in a 3 km pursuit or ~20 s in a 40k TT.

While the data suggest (but do not prove) that the Cervelo has less drag than the Javelin, the reason why there might be such a difference is not immediately clear. Obviously, however, the difference must lie in the frame (and/or seatpost) itself, since all of the other components were the same. It is therefore interesting to compare and contrast the specific design features of the two frames, even though it is impossible to draw any definitive conclusions.

The P2T is the track version of Cervelo’s ubiquitous P2k time trial/triathlon frame, which in turn is the successor to their original P2. As such, it features down and seat tubes with Cervelo’s now-familiar NACA (or NACA-derived/inspired) profiles, i.e., tubes with a relatively high aspect (i.e., chord-to-thickness, or depth-to-width) ratios, rounded leading edges, and sharp trailing edges. The down and seat tubes of the Javelin Arcole, on the other hand, are not only slightly wider, but are blunter on their leading and especially their trailing edges. According to the designer, John Cobb, these tube profiles were specifically chosen to minimize drag at typical yaw angles encountered during “real world” cycling (and in fact the tube profiles resemble those found on other aerodynamic frames designed by Cobb, e.g., the Trek TTT). Thus, one possible explanation for the present results is simply that the test conditions favored the Cervelo over the Javelin because they were, of necessity, conducted when there was minimal wind. Alternatively, it is also possible that the Javelin’s wider tubes themselves accounted for the apparent difference in CdA between the two frames. This interpretation is consistent with the fact that, based on the results of competitive time trials using a powermeter, my CdA appears higher when riding either the Cervelo or the Javelin compared to the Hooker Cat. 1 frame that I used previously. The down and seat tubes on the non-UCI-legal Hooker were even narrower than those found on the Cervelo, although other features of the Hooker (especially their proprietary handlebars) could also explain this apparent difference.

Finally, it also possible that some other difference between the Cervelo and Javelin explains the apparent difference in CdA that was observed. For example, as previously mentioned the Cervelo was tested using their proprietary aerodynamic seatpost, whereas the Javelin was tested using a narrow (25.0 mm) but round Selcof Bi-Position seatpost. On the other hand, the Cervelo P2T (and its road counterpart, the P2k) has round seatstays, whereas the seat stays of the Javelin Arcole have a flat/oval profile for most of their length (changing to round near the drop-outs). Again, whether these or other less-obvious differences between the two frames account for the apparent difference in CdA – assuming, again, that it is real – cannot be determined from the present results.