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Mavic Engineers Talk: Yaw Angles

Inspired by an inquiry from Triathlete magazine editor Aaron Hersh, in October 2013, we decided to measure the actual apparent wind direction (yaw angle) for a rider on the entire bike course of the world championship Kona triathlon. What is the goal of this test? It’s to define where the wind comes from on various segments of the most iconic (and most windy) triathlon on the planet. Knowing perfectly the distribution of the wind yaw angle (i.e. how much time is it a direct headwind, how much time It comes from 5°, etc…), we can determine more precisely the time advantage earned by different pieces of equipment and so advise a wheel choice to athletes, based on wind tunnel measurements. Results depend of course on the weather conditions of the day, but our study gives a typical recording of the conditions on this course.

We suggest you to read (or read again) the previous article (Why weightings should be applied to wheel drag data to measure aerodynamic performance?) to be more familiar with the terms we use in describing aerodynamic drag at different yaw angles.

kona_fig-1

Fig. 1 Lava fields along Queen K Highway

1. The instrument

The instrument used for this test is a digital wind vane developed by Mavic for our R&D needs. A carbon fiber blade, perfectly balanced, is mounted on a low friction rotating axis in order to move perfectly toward the wind direction. This blade is linked to a coded disc which angular position is read by an electronic card. This device is also linked to a wheel counter to record the yaw angle for each wheel rotation, with a 2° step. At the end of the test, the entire measurement made on Kona on the course is an Excel file with 80,000 lines

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Fig. 2 Device mounted on cyclist Lars Finanger’s bike

Furthermore, it should be noticed that the wind vane is positioned upstream of the bike to limit aerodynamic disturbance due to the rider. It is located close to the front wheel, which is the most influential piece of equipment contributing to the bike’s total aerodynamic performance. Just like the arms and the head of the rider, the front wheel is the first element that the wind “sees” and it influences all the airflow around the bike and the rider.

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Fig. 3 Visual control of the windvane during the test

2. Measurements

This test was performed on October 9th 2013, 3 days before the Ironman World Championship in Kona. Wind conditions this day were similar to those usually met at that time on this race. We can note that this year, wind conditions were particularly calm on the day race (October 12th), which was very surprising for many triathletes!

The bike course was ridden by Lars Finanger, a cyclist and triathlete familiar with this race. He rode the 180 km (112 miles) at almost 40 kph. He used MAVIC CXR80 for this test (the wheel has actually no influence on the results, only on the bike speed).

This test was made on the same conditions as the race. Lars rode the official course, at the same time of day as the pros on race day. He was followed by a car with our team and journalists from Triathlete (Aaron Hersh). Lars made 3 stops to permit download of the wind vane data and to ensure the device was working properly.

After this challenging test (the wind was particularly strong and the heat is unbearable in the lava fields), raw data are not easy to read. Here’s the evolution of the yaw angle with the distance (in km):

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Fig. 4 Raw data of the yaw angle

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Fig.5 Kona Ironman bike course

We have split the course into 6 specific segments that are well-known by pros and recreational triathletes (cf. Fig 4 and Fig. 5):

Segment A: short loop around Kailua-Kona

Segment B: segment between Kailua-Kona and the airport – direction NW

Segment C: change of direction on famous Queen K highway during 40km until Kawaihae Road – direction NE

Segment D: new change of direction with the climb to reach Hawi turnaround – direction NW then N and finally NE

Segment E: Hawi turnaround until Kawaihae Road and Queen K junction – direction SW, S and SE

Segment F: go back to Kona – direction SW and SE after the airport

As we can see here, raw data give a good idea of wind direction. A yaw angle comes from high cross wind amplitude (if we consider that the forward speed of the bike is constant).

We can first note many changes in the yaw angle symbol (when a yaw angle is positive, the rider feels the wind coming from the left and vice-versa). This means that in addition to the changes of direction of the rider as he moves along the course, the wind doesn’t always come from the same direction. A local triathlete from the Big Island who knows this course by heart has explained me that in the Hapuna area, there’s a round windflow which explains why wind comes from the ocean and then from the land… In our first article, we hadn’t considered this condition in our simulation of Kona yaw angle (cf. article Why weightings should be applied to wheel drag data to measure aerodynamic performance?) because we had supposed a constant wind direction at that time.

3. Data analysis

3.1 Global course

We have made the calculation of the frequency of appearance for each yaw angle (in percentage of the complete distance).

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Fig.6 Appearance frequency of the yaw angle – 2° step

On one hand, we can observe that this law isn’t symmetrical and on the other hand, it is not centered on 0°. Another interpretation is a distribution by classes:

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Fig.7 Distribution by classes

For 30% of the total distance, the yaw angle is not very high (between -4° and 4°) but the distribution law is very spread out in comparison with a low wind law (cf. Fig.7).

For 25% of the global distance, the yaw angle is between 10° and 20° (absolute value). And we know that in this range of yaw angle, gaps between the performance of different equipment (in particular wheels) are the most import

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Fig.8 Distribution by classes on a typical low wind ride (Annecy)

In this case of low wind measurement, the yaw angle is never higher than 10° and the law is very symmetrical.

3.2 Application to aerodynamic performance

As we have explained in the previous article, those measurements allow us to define a specific law to adjust our calculation on the performance of wheel-tyre systems.

By convention, in the wind tunnel, we test the systems (bikes, wheels, etc…) from -20° to 20° with a specific sequence (for organization and cost reasons, and also because yaw angles higher than 20° are extremely rare). Therefore, we have to adjust mathematically this empiric law with the wind tunnel sequence:

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Fig. 9 Law measured in Hawaï adjusted with angular sequence in the wind tunnel*

The law we get will be used to give a “weight” to each yaw angle value measured in the wind tunnel (cf. Why weightings should be applied to wheel drag data to measure aerodynamic performance?). We can apply this law to all the data we get from our numerous tests in the HEPIA wind tunnel in Geneva, Switzerland.

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Fig. 10 Mounting of a bike before a wind tunnel test in Geneva, Switzerland

Here are the drag values of MAVIC CXR and the most high performing competitors with Kona specific wind conditions[1]:

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Fig. 11 Extrapolation of wind tunnel data with empirical measurements in Kona

[1] Gaps are based on front wheel wind tunnel measurements in steady and repeatable conditions. MAVIC wheels are tested with their corresponding tyre; competitive wheels are also tested with corresponding tyre (ZIPP, BONTRAGER) or with VITTORIA Corsa Evo CX.

Power gaps are calculated at 40 kph with a system {rider; bike} of 87 kg, a power of 280 W, a Cd.A of 0,3 m² and a rolling resistance coefficient of 0,003. For a slower rider, drag gaps would be lower but the time spent on the bike would be higher and thus, the time saved with the fastest wheel would increase!

3.3 Application to wheel choice

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Fig. 12 Real-time measurement of yaw angle

This empirical data allows us to advise the rider regarding specific wheel models.

In light of the extreme changes of yaw angle and higher value measured (higher than 30° in segment E), the choice of a 80mm height wheel such as CXR80 is not easy for everybody. Our professional triathletes (Fred Van Lierde, Tim O’Donnell, Andrew Starykovicz, Leanda Cave…) are accustomed to riding with CXR80 wheels, so it’s not really a problem for them. Furthermore, CXR80 is incredibly steady in those conditions. But for recreational riders, a CXR60 could be the best choice (cf. Fig. 11).

3.4 Segments split

The split of the course (cf. Fig. 5 and Fig. 6) can give fascinating observations:

Segment A (km 0 to 12)

segmentA

 

segmentA_graph

 

This is the segment where the wind was the lowest, especially at 7:15 a.m.

Segment B (km 12 to 23)

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The law is most spread, which shows that the segment is more exposed to the wind.

Segment C (km 23 to 63)

segmentC
segmentC_graph

The distribution is more and more spread. Before the junction with Kawaihae Road, the yaw angle amplitude is increasing.

Segment D (km 63 to 96)

segmentD_graph

On the last segment before Hawi turnaround, the yaw angle is increasing again, especially on the climb section (speed is decreasing and thus the yaw angle is increasing with lateral wind).

Segment E (km 96 to 125)

segmentE_graph

That segment is completely chaotic, especially in the downhill to Queen K where the speed was higher than 50 kph and the yaw angle close to 30°. The distribution is totally spread out.

After kilometer 205, we have observed that the blade of the wind vane was at its maximum position (limit), which means that periodically, the yaw angle in this section would probably be around 35°.

Segment F (km 125 to 180)

segmentF_graph

The return on Queen K Highway was very difficult with a significant headwind. To make things worse, around 12:00 p.m. the heat became a real enemy!

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Fig. 13 Going back to Kailua-Kona around 12:00 p.m.

4. Conclusions and follow-up

72 hours before the Ironman World Championship in Kona, this test confirms and proves what we have expected according to our first simulations. Of course, to be completely accurate, we would have to conduct additional tests on 3 or 4 different days and make an average. But in any case, these data confirm what we expected and show that during a race such as Kona Ironman, a significant part of the bike ride is made with high yaw angle. In these conditions, gaps between the equipment (time and power saved) are the most important (20W gaps just on front wheel at 15° for example).

This is proof and confirmation that equipment choice is decisive on this race and it is validated by the great performances of Andrew Starykowicz (fastest bike split), Tim O’Donnell (5th place) and of course of the Ironman World Champion Frederick Van Lierde (1st place) who all raced with CXR 80 wheels.

kona_conclusion

With more than 80,000 lines in a spreadsheet of recorded data, we still have many analyses to make in order to progress our study. In the future, we could also improve or upgrade the device itself… But at the core of all this effort, the main goal is still the same: to grow our knowledge of aerodynamics because every rider, every triathlete, pro or recreational, is exposed daily to aerodynamic phenomena. Of course, for us, the aim is always to produce the best innovations and products to improve all cyclists’ daily experience.

Brieuc Cretoux
Mavic research engineer

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