Tuesday, August 9, 2016

Some help calculating yaw-weighted CdA values

Hello everybody,

Short post but many of you will find it quite useful. As the design of bicycle components that are better tailored for the real-world conditions that the riders face has become more common, the concept of yaw-weighted CdA has gained popularity. For those that don't know about the term, yaw-weighted CdA can be understood as a mean CdA value representative of the conditions you ride in (under the assumption that Reynolds number effects are negligible) that is computed by weighting the WT/CFD yaw sweeps by the real-world yaw angle probability distribution.

Probably one of companies that has done more for the popular understanding of this metric is FLO Cycling. They wrote a first post on the topic when they launched their first generation of wheels (they employed a somewhat strange weighting function that was way off if we consider more recent real-world yaw angle probability distribution measurements) and a more mature second one where they explained a bit more in detail their methodology and employed the real-world yaw measurements that they used to drive the development of their second generation of wheels.

The method that they explain in that second post is a bit cumbersome if you want to do it yourself so I have decided to share with you a simple spreadsheet that I have been using for quite a long time. Hopefully this will simplify the task of computing yaw-weighted CdA values and make this metric even more widely used.

The spreadsheet gives the weights to be multiplied to the CdA values at the different yaw angles in order to compute the yaw-weighted CdA values. The method is based on a post that I wrote nearly four years ago. I have assumed that the component is symmetrical (if it is not you just have to use half the weight for each of the CdA values at + yaw angle and - yaw angle) and that the yaw-angle probability distribution is a null-mean Gaussian (as common sense indicates and many have found out experimentally). The procedure involves weighting the CFD/WT CdA data (assumed to be a piecewise linear fuction) by the Gaussian distribution. I have done this for a variety of values of the standard deviation/average absolute value of yaw (abs(yaw)). From this, you can modify the average abs(yaw) values, add/remove/change the yaw angles where you have data, etc. The only thing worth noting is that, as the CdA values are not measured in the full [-180º,180º] yaw range, I have assigned the remaining weight to the last considered yaw angle (20º in the original version) so you will need to move the formula in that column if the number of considered yaw angles is different.   

If you don't know what average abs(yaw) value to use, I have analysed previously published real-world measured data and these are some typical values:

FLO: 5.67º
SwissSide: 3.39º
Mavic: 8.25º

Using this and the ROT 0.005 m^2 CdA reduction=0.5 s/km time savings you can better estimate the time savings that you will observe in real-world conditions.

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