In the modern sporting world, not only professional, but also amateur and hobby athletes try to permanently improve their performance and results in competitions besides their main job.
In some sports the equipment choice plays a huge role in the overall performance. In cycling, particularly time trialling and triathlon competitions, the rider has to fight against the clock without outside assistance. Improving sports equipment has therefore become a big business and the number of manufacturers and their different products is almost uncountable.
As the power, needed to overcome aerodynamic drag, increases cubically with speed, good aerodynamics are essential
to competitiveness in these kind of races.
As wind tunnel testing is very expensive and almost unaffordable for small companies, these investigations should show, if a virtual wind tunnel in CFD can demonstrate the same effects as a real wind tunnel with comparable aerodynamic forces. By investigating six different wheels with varying rim profiles, depths and spoke counts, combined with upstream flow angles varying between 0° and 30°, this study should show if CFD is a valid tool to develop aerodynamic bicycle wheels.[top]
Real world race conditions never offer perfectly still air or frontal wind (0°). Bicycle wheels have therefore to be developed for upstream flow angles, which are experienced in typical weather conditions by a typical racing cyclist.
Aerodynamic drag and side forces were determined using FIRE v2008.1 and the characteristic curves compared with results from wind tunnel tests from the leading wheel manufacturers.
The time differences for the wheel sets for a given power output of a rider were calculated analytically, taking into account the before mentioned drag forces.[top]
3 MAIN SECTION
3.1 APPARENT WIND ANGLE
Figure 1: relationship between wind angle, wind speed and bicycle speed
The effective flow velocity and yaw angle can simply be determined by vector addition of the bike speed vector and
the wind speed vector (Figure 1).
These simple investigations highlight why the major wheel manufacturers optimize their aerodynamic wheels for yaw angles up to 15°.
(More details about the apparent wind angle can be found in our TechTalk area)[top]
3.2 CFD SIMULATION
3.2.1 SIMULATION MODEL
All CFD simulations were performed with FIRE v2008.1 in steady state mode using the k-e-turbulence model.
Figure 2: CFD simulation domain with dimensions
The rotating wheel is modeled with the MRF (multiple reference frame) method. Therefore the entire wheel is covered
inside the MRF volume with the arbitrary interface between MRF volume and the wind tunnel domain (see Figure 3).
Figure 3: definition of MRF volume
3.2.2 WHEEL GEOMETRIES
6 wheel geometries were investigated, which differ in rim depth, rim profile and spoke count. All investigated wheels
are thought to be aerodynamic wheels with rims built of carbon and considerably deeper than traditional aluminium rims.
|Zipp 303, rim depth 44mm, 20 spokes||Campagnolo Bora, rim depth 53mm, 18 spokes||Lightweight, rim depth 55mm, 16 spokes|
|Zipp 808, rim depth 84mm, 18 spokes||Zipp 1080, rim depth 111mm, 16 spokes||Zipp 900 Disc|
|Figure 4: Zipp 1080 real wheel||Figure 5: Zipp 1080 simulation mesh|
3.2.3 CFD RESULTS
The simulations showed a large dependency of the yaw angle on the drag force (Graph 1), as it is already known from
various wind tunnel tests by bike journals and wheel manufacturers.
The disc wheel showed decreasing drag with increasing yaw angle, up to 20° yaw, where the drag even turns negative.
Graph 1: Drag force for different yaw angle at 40 km/h air speed
The side force (Graph 2), i.e. the air forces acting perpendicular onto the wheel, depends on the projected area in y-direction (Figure 3). That means, that the side force increases with increasing rim depth. The gradient is linear over the yaw angle, except for the disc wheel.
Graph 2: Side force for different yaw angle at 40 km/h air speed
To calculate the power (chapter 3.4), which is needed to move a wheel through the air, the translational drag coefficient cw and the frontal area A of the wheel is needed. The product of cw*A, which is independent of the air speed, is plotted in Graph 3 and shows similar characteristics as the drag force.
Graph 3: cw*A for different yaw angle
One of the big advantages of CFD simulations is the possibility to visualise the streamlines, i.e. the characteristic flow around a part. In the case of a rotating wheel the air is deflected downwards by the front part of the rim (Figure 6) and forms big eddies close to the ground on both sides behind the wheel (Figures 6 & 7).
Figure 6: Streamlines around rotating Zipp 1080 wheel at 40 km/h
Figure 7: Streamlines around and velocity plot behind rotating Zipp 1080 wheel at 40 km/h
For more detailed result plots click here[top]
3.3 COMPARISON WITH MEASUREMENTS
As we do not have the facilities to do our own wind tunnel tests to compare with our CFD results, we have to rely on
tests done by bike journals or the leading wheel manufacturers. The problem with these external tests is, that they mostly
are carried out under different conditions and these conditions are not well documented.
Graph 4 shows the power, which is needed to move a wheel through the air at 45 km/h bike speed, i.e. the frontal air speed was kept const. at 45 km/h for the different yaw angles, which means that the wind tunnel speed had to be increased for increasing yaw angles. In our simulations in contrast the wind tunnel speed was held const. This leads to the fact, that in this wind tunnel test of the German journal Velomotion, the drag (power) is higher than in our simulations, the larger the yaw angle.
From our investigations, the Zipp 808 (green), Lightweight (red) and a disc wheel (orange) was measured.
Graph 4: Wind tunnel test of german bike journal Velomotion: power needed to move the wheel through the air at 45 km/h bike speed for varying yaw angles
Graph 5 shows the drag forces measured in wind tunnel tests from HED Cycling.
Graph 5: Wind tunnel test of wheel manufacturer HED: drag force at 30mph for varying yaw angles, Campagnolo Bora (red), Zipp 808 (green), Zipp 1080 (blue)
The manufacturer Zipp measured the side forces on the wheels, which are plotted in graph 6.
Graph 6: Wind tunnel test of wheel manufacturer Zipp: side force at 30mph for varying yaw angles
3.4 TIME GAINS
It may be nice to know, that one wheel performs better than another. But when it comes to racing, it is the time
differences that count.
Total Power = Pd (Power drag) + Pr (Power rolling resistance) + Pf (Power friction) + Ps (Power slope) + Pa (Power acceleration)
air velocity of the bicycle tangent to the direction of travel of the bike and rider
(which depends on wind velocity and the ground velocity of the bicycle - chapter 3.1)
|cw||overall drag coefficient of bike (including frame, fork, wheels, ...) and rider|
|A||frontal area of bike and rider|
|crr||coefficient of rolling resistance|
|mt||total mass of bike and rider|
|g||acceleration due to gravity|
|Gr||gradient of the road surface|
With this equation it is easily possible to calculate the average velocity for different bike & rider combinations on a given course.
|professional rider||amateur rider||hobby triathlet|
|avg. Power [W]||450||350||250|
|total mass [kg]||77||77||77|
|cw*A rider [m²]||0.225||0.225||0.268|
|cw*A frame [m²]||0.045||0.045||0.045|
|crr (high performance tubular)||0.0027||0.0027||0.0027|
|front wheel||Campa Bora||Zipp 1080||Campa Bora||Zipp 1080||Campa Bora||Zipp 1080|
|rear wheel||Campa Bora||Zipp Disc||Campa Bora||Zipp Disc||Campa Bora||Zipp Disc|
|v avg. [km/h]||47.97||49.27||43.93||45.11||37.43||38.30|
|time for 40 km||50min 1.76sec||48min 42.63sec||54min 37.5sec||53min 11.51sec||64min 6.9sec||62min 39sec|
|time gain [sec]||79||86||88|
On a flat 40km time trial a professional rider can gain 79sec with the fastest wheel set (Zipp 1080 & Disc) compared to
a Campa Bora wheel set.
The results of the CFD simulations, and the subsequent comparisons with the wind tunnel test results, proves that CFD is a valid tool to investigate the aerodynamic behaviour of bicycle wheels. It is not only possible to determine aerodynamic drag values, but one can also visualise the airflow around the wheel and detect areas of flow separation, resulting in increased drag. Therefore CFD with the applied method is thought to be the perfect, time and money saving tool to help to design improved wheel geometries.[top]
As the spokes did not show the biggest effect on the overall drag of a wheel, in further investigations only the rim
and hub will be meshed and simulated. This gives a large benefit in model size (reduced cell quantity) with the additional
advantage that we can surrender the MRF method and instead mesh rim and hub as a "moving rotating wall". First tests
showed a reduction in simulation time of appr. 30-40%.