Aerodynamics has become a real buzz word in the cycling world, and we are increasingly seeing dramatic disparities in the advertised wattages for different pieces of equipment. But how are these figures calculated, and are they realistic?
First, we need to define the term “drag”. An object moving in a fluid (say a wheel in motion in the air) is subject to pressure forces and friction forces (because air is a viscous fluid). The combination of these two forces is called aerodynamic drag. This drag is the aerodynamic resistance counteracting the forward movement of the object in the fluid. The drag is proportional to the velocity squared – in other words if a cyclist moves at twice the speed (from 20 km/h to 40 km/h for example), the aerodynamic drag will be four times as high. Therefore, at high speeds (usually above 30 km/h) and on flat roads, aerodynamic drag is the main form of resistance acting against a cyclist (far exceeding rolling resistance, the resistive force caused by the tyres rolling on the ground).
To assess the aerodynamic performance of a wheel, a force balance is used to measure the aerodynamic drag in a wind tunnel. In the real world, however, the air does not always come towards the wheel from straight ahead – it can also arrive at an angle known as the yaw angle. For a more realistic assessment of a wheel’s aerodynamic efficiency, measurements must therefore be made with several yaw angles. Afterwards, the results are “weighted” in order to obtain a single and more realistic drag value for the wheel.
1. Apparent wind
At a speed of 40 km/h, the movement generates a perceived headwind of 40 km/h. In reality, however, there is always a certain amount of “weather wind” coming from any direction and at any speed.
In the example above, the weather wind has a speed of 13 km/h and is coming from the right in relation to the direction of travel. This means that the perceived wind on the bicycle is the combination of the two “winds” (green arrow) and is called the apparent wind. In this scenario the apparent wind speed is 42 km/h and is perceived to be arriving at an angle of 18° (called the yaw angle) in relation to the direction of travel. This is straightforward trigonometry.
2. Measuring the apparent wind
On a ride, the apparent wind is never constant either in terms of direction or speed. In fact the forward speed varies, and the weather wind fluctuates and changes direction as the route twists and turns.
We have developed a tool – a kind of weather vane with instruments – to measure the yaw angle. It indicates the apparent wind during a ride, recording the angle of incidence on every wheel rotation.
After carrying out a number of trials in different locations we have been able to formulate a general law describing the frequency of each yaw angle as follows:
The law indicates that on average more time is spent with an apparent wind from straight ahead or with quite a low yaw angle than with a high yaw angle. Of course, this is a general law and is subject to alteration by the weather conditions and the location. Yet is can be used as a basis for weighting wind tunnel results as described below.
3. Wind tunnel tests
In the wind tunnel, wheel drag is measured for yaw angles between -20° and +20°, those most likely to be encountered on the road. The resulting data comparing two wheels is as follows (in this example the CXR80 is contrasted with the best 80 mm competitor):
The data shows that the CXR80 has lower drag at 0° (when the wind is coming from straight ahead) and there is a very substantial disparity between the two wheels after 10°. This indicates that the drag of the CXR80 is lower than its competitor, making it is less of a struggle for the cyclist to maintain speed. The disparity between the two wheels is greater as the yaw angle increases (in very windy conditions in the real world).
There are several ways in which the disparities between the two wheels can be interpreted in terms of performance
- Frontal drag
Limiting the calculation to the drag at 0°. In this case the values are as follows:
However, it is not sufficient to consider the frontal drag in isolation if there is a weather wind.
- Average drag
Calculating the average of all the values for every yaw angle. In other words, equal importance is given to a yaw angle of 0° and a yaw angle of 20°:
- Weighted average drag
In the third solution, an average is calculated on the basis of the law formulated using the weather vane, which places more importance on the angles that occur frequently in the real world and less on the more extreme values (which nevertheless do occur from time to time):
As shown here, aerodynamic curves are highly susceptible to interpretation and can produce sometimes large disparities: we could have chosen to calculate a simple average and advertise a difference of 16.8 W between the CXR80 and its competitor. Instead, we prefer to calculate an average that is as accurate and realistic as possible, taking account of our road trials. We call this method of calculation the weighted average.
5. Application for our profesional riders
It is also possible to take the weighting law further and apply it to a specific route. We supply the technical data to our professional teams and triathletes, for example to help them choose the right equipment.
We carried out the following simulation for the latest Ironman Triathlon in 2012 in Hawaii:
The bike course is known.
Using weather data (National Climate Data Center for example), the average wind speed and, importantly, direction can be estimated for the date of the event. Even better, the model can be refined on the basis of forecasts several days before the race.
Armed with the weather data, the race is divided into a number of segments in which the apparent wind speed and direction are calculated. A highly accurate theoretical disparity can be calculated on the basis of the disparities between the two wheels as shown above.
In the very specific case of Hawaii, this simulation showed that the total disparity between the CXR80 and its competitor was around 2:30 minutes over the 180 km cycling leg of the Ironman. This is about the same as the difference between Open category finishing times, so the choice of material is crucial for events like this.
Fred Van Lierde, 3rd in the 2012 Hawaii Ironman