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.

Playing with the limits of UCI rules

Hello everybody,

Long time without posting (18 months), I lost a bit of motivation but happy to see that people still come here quite regularly looking for updates. Many things have passed since then: finished my undergraduate studies in France and Spain, went to Brazil for my final year internship and currently pursuing a MSc in CFD at Cranfield University, UK.

This post is related to the UCI rules on equipment and how subtle they can be. What happened a few years ago in F1 with front wings that employed aeroelastic phenomena in order to improve performance is a good example of what happens when rulebooks are too detailed and does not give room for too much improvement using "traditional" methods. Engineers always find ways to improve performance and the governing body introduce more complex rules (deflection tests for front wings) that benefit nobody. Hopefully the same will not happen for bikes.

With this I don't want to be critical with the current version of the UCI rules in any way. I think that it is good to have a document that defines the rules of the game. Just noting how open to subjectivity are some of these rules and the problems that may arise if more manufacturers try to play with the limits that they set. Latest version of UCI's clarification to the rules can be found here.

The latest road "super" bikes, the Specialized Venge VIAS and the Trek Madone 2016, are a good example of pushing the boundaries of what the UCI rules allow.

First example, the front brake of the Venge VIAS. First, let's see what the UCI rules say about brake-fork integration.

Now take a look to the front end of the Venge VIAS and determine the width of the bounding box that contains the fork and brake.

Ok, it is clear that the fork and brake does not fit within a 8cm box. From the UCI rules, a brake is considered to be standard if "their shape and system of attachment allow them to be used on all types of frames and forks." That is clearly not the case for that front brake. By elimination the brake should be cosidered "integrated", shouldn't it? And this means that the brake "...whether a cover is fitted or not,... must in all cases be contained within the corresponding 8cm box". Let's read the interpretation of an "integrated" brake and imagine how it could be legal: "...which are designed for a specific model of frame/fork and which can only be used with this frame/fork due to their shape or attachment system". So if you build two minimally different models of fork and frame that use the same integrated brake, you are free to go because your integrated brake does not fit within their definition of an "integrated" brake and the dimension limits do not apply. This has not happened yet but it may have been taken into account when considering if the bike is legal.

So, if this brake is legal by not being compatible with UCI's definition of "integrated", why the typical brakes integrated in the fork (e.g. BMC TMR01) cannot use the same argument and go beyond the 8cm box? The reason is that in the UCI rules there is a specific paragraph limiting the dimensions of brakes with covers: "The combination of the frame tube (or fork tube) + brake + cover must respect the 1:3 rule, as well as the minimum and maximum dimension rules and must be contained completely within the corresponding 8 cm box.".

So, Specialized basically found a loophole in the rules by playing with the definition of an "integrated" brake and not using a cover. Hats off.

Second example, the seat tube of the Madone 2016. First, let's read the UCI rules about fairings:

"Any device, added or blended into the structure, that is destined to decrease, or which has the effect of decreasing, resistance to air penetration or artificially to accelerate propulsion, such as a protective screen, fuselage form fairing or the like, shall be prohibited."

Now, let's take a look to the internal structure of the frame.

From Madone's white paper.

Inner seat tube. From this video. Note the stepped joints (patent).

Outer seat tube.

The whole system.

The seat tube structure is basically the same as their comfort-oriented Domane except that the Madone has an aerodynamic outer tube from the BB to the seat stays-TT junction. Now remember the UCI rules about fairings. Is the outer tube really necessary or is it just a fairing for the inner one? You can argue that the inner one is not enough to give enough torsional stiffness at the BB. But, is it really the case if you are already producing the Domane and it is stiff enough? I suppose that Trek has given convincing answers to these questions when passing the approval procedure.

Some interesting questions arise: will the UCI need to use the famous motor-detecting scanners to study the internal structure of the frames when conducting the approval procedure to know if a tube is structural or just a fairing? will the approval procedure include deflection tests in the future (like for the F1 wings) in order to check this?

A very interesting topic. I would love to hear your opinions.

Eduardo Bueno