Tuesday, October 12, 2010

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.

video

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.

6 comments:

  1. Really interesting and very clearly explained. Thanks!

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  2. Wow -- what a treat!

    Characterizing the measurement errors in aero testing can be quite a daunting task. Your careful approach to a very difficult problem is something I can use for my own testing.

    Thanks for posting this article!

    Andy Froncioni
    http://andyfroncioni.com

    ReplyDelete
  3. I don't know much about biochemistry, Andy. What was the outcome of the A.V. Hill challenge, if any?

    AndyF
    http://andyfroncioni.com

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  4. Andy,

    Hill's challenge stimulated a number of experiments, but it wasn't until 1962 that Dennis F. Cain (1930-) and Robert E. Davies (1919-1993) were able to definitively demonstrate a change in ATP concentration during a single muscle contraction (1). What made this possible was the use of 1-fluoro-2,4-dinitrobenzene to irreversibly inhibit the Lohman reaction (i.e., rephosphorylation of ADP by PCr via creatine kinase). While this study really just confirmed what was already believed to be true, it (and Hill's challenge that stimulated it) was nonetheless important in pushing the field forward.

    1. Cain DF, Davies RE. Breakdown of adenosine triphosphate during a single contraction of working muscle. Biochem Biophys Res Commun 8:361–366, 1962.

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  5. Dr. Coggan,

    I'd like to know if I correctly understand the process. Forgive my question here, but I'm stuck with the first edition, so I don't quite get how you initially derive CdA from measurements.

    I'm assuming you measure the power and velocity from the SRM and then calculate from that the drag force due to wind by

    Pd = Dw*v

    where Pd is the Power required to overcome drag, Dw is the drag due to wind, and v is the velocity.

    From there you get

    Cd = [2Dw] / [pAv^2]

    where p is the air density, A is the frontal area, and v is velocity. Am I correct in this? If so, my follow-on question is whether you arrived at A by some type of direct measurement or by approximation.

    I assume that, regardless of the answer, the point is moot in this experiment because the CdA of the rider and bike remain constant and the effect of the ball is the experimental focus.

    For that, I assume that you begin with:
    Ptotal = Pdrag + Prr

    Where Ptotal is the total power generated, Pdrag is the power required to overcome drag and Prr is the power required to overcome rolling resistance. The experiment then was to measure the change in power required to maintain a set speed, and then compare the measured change to that which was expected in calculations.

    The only thing you have to do is compare the change in Pdrag, as Prr is assumed constant. However, I've seen a couple of papers proposing that Crr is dependent on velocity. They focused on automotive applications, but could that have been the small factor that was still large enough to create the error discussed here?

    I also did not see you specify whether you maintained speed or power as the constant in your trial runs. Since you indicate the use of only one Reynolds number, I'm assuming you kept speed constant and used the increase in power to gauge the correlating increase in resistance. What is your opinion of how the experiment would have run if you'd maintained constant power?

    Thanks for the clarification. This was a fascinating read.

    Regards,
    Jim Gourley

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  6. Hello Jim,

    The approach that I used is described in greater detail in this blog entry, to which I linked from the present one:

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

    As for changes in Crr with velocity, some experiments indicate that this may also occur with bicycle tires, but others do not support this conclusion. In any case, such non-linearities would appear to be quite small, and hence I have ignored them.

    Although I tested over a range of velocities, wind tunnel experiments have indicated that cyclists do not undergo any significant transition effects, i.e., as a whole our Cd (and hence CdA) is velocity-independent.

    OTOH, the Cd of a sphere would change very slightly (i.e., 5-10%) over the range of velocities and hence Reynolds numbers that I tested, so I took this into account when calculating the expected increase in drag.

    Hope this helps,

    Andy

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