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Field CdA Testing

I am not an especially powerful cyclist. In order to improve my time trialling (and the cycling leg of duathlon) I have tried to improve my aerodynamics, and maximise my potential. Of course, I am not alone in this ambition, but rather than relying purely on marketing claims and hearsay I have recruited a bit of empiricism to support my approach. With a bit of care, and some understanding of the principles, it is easy enough to perform meaningful testing of position and kit. I have essentially followed the classic method for estimating CdA with a power meter, presented below in my own words.

I'd strongly recommend reading more about the Chung Method to understand how this approach is commonly extrapolated in various widely available software platforms.

The cat we like to call Dr Robert Chung - seen here in the dishwasher.




It's really helpful to understand the basic principles. Speed correlates mathematically to power, taking into account a number of other variables:

  • Grade & weight (which combine to define the gravitational force that needs to be overcome)
  • Rolling resistance
  • Temperature & air pressure (from which you can calculate an estimate of air density)

  • and...

  • CdA (drag coefficient x frontal area, the measure of 'aero-ness')



The outcome is readily observed; that applying more power will increase ride speed (and therefore reduce ride time over a fixed distance). If you could measure all of the variables 'accurately', you would be able to calculate 'accurately' the impact.

With this mathematical relationship determined, you can use it in reverse - that is, you can measure the speed and power (and the other variables) to calculate CdA.

That is exactly what the calculations built into GoldenCheetah and software like MyWindsock / BestBikeSplit and others do. The data collected for the duration of your ride, with a few assumptions for values that can't be measured 'accurately', are run through the equation on a point-by-point basis, as described by Dr Chung (not the cat). I have no reason to doubt their maths, and so I'm sure the results are very 'precise'.

 

Aside: Why do I keep putting quotes around 'accurate' and 'precise'? These words have very specific scientific meanings, in short: 'Accurate' means the result is close to the absolute true value. 'Precise' means the result is repeatable. A result can be one, both, or neither of these things. Ideally we'd be able to measure 'accurately' and 'precisely', in order to calculate results as close to the true absolute value as possible with a high degree of repeatability.


Often, in field aero testing, the best we can achieve is 'precision'. Unfortunately in the real world there are a variety of other factors: wind speed & direction, passing vehicles, and even the variation of molecules making up the air (a gas coefficient, taking into account the relative humidity of the air, is used in the calculation of density from pressure and temperature). Plus you also have to consider the effect of accelerating and decelerating on the equation.

If you account for all the variations, and minimise them accordingly, I believe you can obtain repeatable ('precise') results with the tools available. That also means you can generate meaningful results to compare the impact of different kit or position. Whilst in theory it is possible, I would not try to use ride data to calculate an 'accurate' absolute CdA number. That is something you are going to need a wind tunnel for. I think the margin for error in the assumptions you are inevitably going to make with field testing will reduce the 'accuracy'. I am only ever looking to compare results to gauge the relative effect of whatever position or kit change I am looking at. I only look at like-for-like data, i.e. collected from runs performed on the same route, on the same day, in the same conditions.

The reason why I think novel equipment like the Notio & Body Rocket are especially exciting is that they also aim to collect additional live measurements to reduce the number of assumptions and estimates made in the calculations. The 'accuracy' and 'precision' of the calculated result will be improved, perhaps even to the point of being able to compare calculated CdA between rides (or a least different sections of the same ride). As such they open the door to the possibility of displaying a live CdA feedback on your headunit which could be invaluable in a long time trial.



How I would go about testing:

  • Decide what I want to test. Pick one thing at a time, say helmet A vs helmet B, or hand position A vs hand position B. Just like you would do in a good tunnel testing protocol, always testing against a benchmark (the difference being that in field testing, you will re-calibrate your benchmark every testing session)
  • Pick a perfect course. Ideally a short loop of a few miles, quiet and with no junctions (or only left turns). The flatter the better - it means you can pretty much ignore rider / bike weight. Obviously a velodrome is excellent for this reason. I have an out-and-back test course. It's on a old straight stretch of dual carriageway which has recently been bypassed, so traffic is exceptionally light. I use two flat segments created on Strava, one in each direction, avoiding the turnaround at either end
  • Ideally I will do my testing on a still day, unless I want to evaluate the effect of different conditions (say a crosswind)
  • Pick a time when conditions / traffic aren't going to vary significantly i.e. avoid morning or evening when temperature changes rapidly, and rush hour etc
  • I record temperature and air pressure (using a phone app) at the start and end of my testing. I'm not too worried about the absolute number, but I am hoping it doesn't vary wildly
  • Ride each variation a few times. I'll aim for three times each, in order that I can take an average (and also hopefully spot any obvious outliers). To accommodate any changes in conditions, I'll try to run tests as A,B,B,A,A,B (which can be a bit of a nuisance if you are switching kit or spannering)
  • When riding, I try to hit and hold the same constant target speed everytime I ride through the segments for the whole testing session. I try to deliver the power needed to hold that speed as uniformly as possibly. It takes a bit of practice, and I find it easier with a fairly solid effort... you can therefore make this into a nice sweetspot or tempo session. My tests usually work out at around 12 * 3mins (accounting for 6 out-and-back runs).

 

Aside: Why ride to a target speed and not a target power? Well, drag (Cd) is proportional to speed squared... so drag itself actually increases as you ride faster. Likewise, at different speeds the yaw angle (your effective angle of attack through the air) defined by any degree of cross wind will change. A constant speed helps to reduce variations in drag and yaw angle between test runs. Also you won't have to calculate for any acceleration.


Once I'm done I'll use all the data from each test run (mostly plucked off Strava for the segments I have previously created along my course) to calculate a relative CdA. I actually wrote my own calculator to do this www.bikeaerodata.com (because I'm really quite dull, and I wanted to understand the maths), but this is where those other online tools can be of use (and will likely be more 'accurate' unless your data collection is very good, but I'm more interested in 'precision' than 'accuracy'...). I usually average the out-and-back elements across all runs for each test scenario and then examine whether there is a difference. Sometimes for a special treat I'll check if the difference is statistically significant.

 

Aside: Measuring power introduces another couple of variables: Firstly, the 'accuracy' and 'precision' of the power meter from run to run. Secondly, the type of power meter and drive train efficiency. If you have a pedal based meter you can anticipate a percentage loss as those forces work their way to the rear wheel. The loss could be measured with a second ('accurate' and 'precise') wheel based power meter; for a more practical approach just keep your machine and chain well maintained in order to keep this factor constant.


I haven't really mentioned rolling resistance at all, but that's because I generally stick with the same tyres and pressure... and typically you can look up accurate values for most tyres. Plus I'm riding the same surface for each test run. I guess you could actually use the method described above to perform a relative analysis of rolling resistance between two different tyre combos by running tests with all other variables kept constant. I haven't bothered - I just buy the most expensive ones!

Hope that gives you some ideas and basis for trying a few tests of your own.



Thanks for reading! Sorry this was a particularly niche blog, even by my own high standards of niche ;)

Nic