Aero­dy­namic Bicycle Wheel Design Optimization

The aero­dy­namic opti­miza­tion of bicycle wheels can lead to decisive gains in running pace. Nowadays, aero­dy­namic per­for­mance is one of the key factors con­sid­ered when racing cyclists purchase new equip­ment, as the aero­dy­namic drag is known to be the main source of losses in cycling, causing between 70% to 90% of total losses in flat road races. Lateral forces felt due to a high wind yaw angles also have an impact on equip­ment selec­tion, with users opting for shallow wheel choices in these con­di­tions due to the buf­fet­ing effect deeper rims can have.

Work carried out by Green­well et.al. con­cluded that the drag con­tri­bu­tion from the wheels alone is on the order of 10% to 15% of the total drag and that by improv­ing wheel design, an overall reduc­tion in drag of more than 3% is possible. This would suggest that the outcome of races can be dra­mat­i­cally affected by equip­ment choice. Espe­cially con­sid­er­ing the extremely small margins that decide the outcomes of races. The dif­fer­ence in fin­ish­ing time for many races can be as low as a few seconds from a race spanning multiple hours.

To date, there has been a great amount of work done to test cyclists, bikes and wheels both in the wind tunnel and through CFD, although, it is dif­fi­cult to make a direct com­par­i­son between designs due to dif­fer­ent setups for both wind tunnel and CFD tests.

Far less work has been carried out regard­ing the opti­miza­tion of rim shapes for dif­fer­ent con­di­tions and yaw angles. The aim of this project was to inves­ti­gate the aero­dy­nam­ics involved in bicycle wheel design, and to optimize and design a very low drag bicycle wheel rim shape using CAESES & TCFD.

Bicycle Rim Section Optimization

The aims set for the bicycle wheel rim shape opti­miza­tion were to first deter­mine the fastest shape at an angle of attack (AOA) of 0 degrees and then review how this shape performs at higher AOA. This is due to fact that for high level cyclists, who are likely to be using per­for­mance wheels, lower AOA were deter­mined to be the most common. A section of the wheel was analyzed both facing forward and back­wards, as the airflow meets the front portion of the wheel and flows over the forward-facing section, then travels to the rear of the wheel, where it travels over the back­wards-facing section. It was impor­tant to inves­ti­gate the behavior over both portions and optimize both. This could effec­tively be done using CFD and wind tunnel testing as the sections tested could fit into the man­u­fac­tured wind tunnel. More emphasis was placed over the front rim section, espe­cially at low AOA, as the rear section will have tur­bu­lent incoming air from the front section, hub and spokes.

Opti­miza­tion Workflow

CAESES provided the CAD envi­ron­ment includ­ing robust and easy geometry vari­a­tion, effi­cient param­e­triza­tion and sim­u­la­tion-ready export. The para­me­ter­ized model was exported as surface geometry, for which a CFD sim­u­la­tion setup was created in TCFD. This setup was based on pre­vi­ously deter­mined settings for a NACA airfoil section that where val­i­dated with wind tunnel exper­i­ments (the same wind tunnel used later to test the wheel rim design). The script and input files that control the mesh gen­er­a­tion and CFD sim­u­la­tion process were inte­grated into the CAESES Software Con­nec­tor . Finally, an opti­miza­tion process could be started in CAESES, whereby each gen­er­ated geometry variant was auto­mat­i­cally meshed and sim­u­lated with TCFD.

Rim Shape Parametrization

The modeling process included a few steps. Firstly, the cross section shape was defined, includ­ing all nec­es­sary shape para­me­ters. This cross section was then revolved by 360 degrees to give the full wheel geometry. For this opti­miza­tion, a 240mm high section was cut out to simplify the problem.

A few of the avail­able para­me­ters were selected for the opti­miza­tion of the rim shape and their ranges defined. These para­me­ters were:

• Weight – This para­me­ter is used to describe the shape of the curve. A higher value defines a more blunt curve, while lower values yield a sharper profile.
• Width – This deter­mines the width of the rim (the tire is fixed at 25 mm).
• Straight Length – This length is the portion of the rim which is straight before the curve begins.

Opti­miza­tion Process and Results

The opti­miza­tion was per­formed on an Intel Xeon E5-2680 v2 CPU with 20 cores. One design loop, includ­ing mesh gen­er­a­tion and the TCFD sim­u­la­tion, took about 60 minutes. All sim­u­la­tions were run sequen­tially on the described hardware. For the 3 selected design vari­ables, an initial set of 40 design variants was eval­u­ated, which took about 2 days to simulate. This explo­ration of the complete design space was per­formed by a DoE using a Sobol sequence. The results from this step already gave a very good indi­ca­tion regard­ing cor­re­la­tions and trends. Then, a further 20 designs were auto­mat­i­cally eval­u­ated using a local opti­miza­tion starting from the lowest drag design from the initial set of designs.

In this opti­miza­tion, the rim drag obtained from the TCFD sim­u­la­tion was deter­mined to be the objec­tive function. Both the front and rear portions of the rim were opti­mized inde­pen­dently and then combined to find a suitable compromise.

Before the actual opti­miza­tion process, the baseline design was sim­u­lated for both the front and rear portions.

After 40 sim­u­la­tions we get the best designs listed in the table below.

The reason for the dif­fi­culty in reducing the drag on the rear part of the wheel is that the tire is on the aft of the model. Further work into surface features on the tire, such as dimples, may reduce the drag further.

From the results, a variant with the best balance between the opti­miza­tions from the front and the rear was chosen. The opti­miza­tion process reduced the drag value by 13% on the front portion of the rim and 2% on the rear portion of the rim when compared to the baseline design. The final outcome of this study is sum­ma­rized in the table below:

Wind Tunnel Testing

Several selected design variants were tested in the wind tunnel to verify the CFD results The model was capable of being attached both facing forwards and back­wards to allow the front and rear sections to be tested, as well as being rotated in pre­scribed incre­ments to test dif­fer­ent angles of attack. All models were tested from ‑16 degrees to 22 degrees. This allowed inves­ti­ga­tion into not only the models at low yaw AOA but also stall angles. The drag values cal­cu­lated from the CFD solver matched the wind tunnel values closely, which gives addi­tional con­fi­dence for using this opti­miza­tion process to develop fast bicycle rim shapes.

About the Author

Thanks a lot to Daniel Cain from Stream­line Cycling, for pro­vid­ing these inter­est­ing details and images for this blog post.

Daniel Cain is the founder and CFD spe­cial­ist at Stream­line Cycling, a company that develops aero­dy­namic bicycle wheels and equip­ment. He grad­u­ated with a MEng in Aero-Mechan­i­cal Engi­neer­ing from Strath­clyde Uni­ver­sity in Glasgow, before spe­cial­iz­ing in product design and CFD. He is cur­rently working towards the launch of his product range of bicycle wheels.

“CAESES has been an integral part of the product design process, allowing us to easily optimize many para­me­ters that affect the aero­dy­namic per­for­mance of bike wheels. CAESES is extremely impor­tant in allowing us to explore the design space intel­li­gently and refine designs. Many hundreds of designs can be auto­mat­i­cally eval­u­ated, and complete Pareto fronts generated.”

– Daniel Cain, founder and CFD spe­cial­ist at Stream­line Cycling

More Infor­ma­tion

You can find more infor­ma­tion about the bicycle wheel opti­miza­tion case by down­load­ing the full report. Further general infor­ma­tion about the Stream­line Cycling can be found on their website.

Feel free to contact us if you have any ques­tions about this or other applications.