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.
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.
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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.
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