I recently came across this bit of wind tunnel testing by Hunt. It led me to dig out some wind tunnel testing I did for my aerospace engineering undergraduate project 18 years ago.

Testing wheels is rather tricky! The aerodynamic drag of a rider and bike as a whole is pretty straightforward: you put the bike on a set of rollers fixed to a glorified set of scales (that measure in three directions), turn the wind tunnel on, pedal away, and get your results. Wheels are rotating though, so you need to look at the force to push them through the air (measured by the scales) and the force required to rotate the wheels (measured by some sort of torque monitoring device in the rollers). What follows is my attempt to examine the effect of wheel configuration on both these components of drag, and put it into context with the overall drag on the bike and rider (and other possible equipment variations).

The results indicate that there can, in fact, be a reduction in power required to drive the wheel for an increase in the number of spokes. It is also found that the more fashionable (18 years ago!) disc and tri-spoke wheels do not perform as well as traditional wire spoked wheels. A comparison of the power required to drive the wheels and the total power to propel the bicycle and rider show that changes in wheel configuration can be nearly as important as variations in rider position but there are much cheaper ways to get an aerodynamic advantage.

In what follows I have reduced the amount of science and maths to some extent. I am loath to do so anymore at the risk of obfuscating key findings while undermining the importance of maths. A teacher I know bemoans that it is socially more acceptable to be poor at maths compared to reading. People almost show-off by saying “I’ve never been any good at maths” but eyebrows would be raised if they said “I never really learnt to read”. I’m not speaking from any high-ground here though: at work I have to hide in the corner when people start talking about calculus of variations or eigenvector veering.

Nowadays the large wind tunnels at The University of Southampton are readily available for undergraduate projects and commercial testing of cyclists. 18 years ago it was the secret domain of F1 and Indy car teams. My testing took place in a rather modest but perfectly adequate 0.6m x 0.6m working section tunnel.

### The experiment

The force required to move a wheel forwards is split into two components which we can measure in the wind tunnel. The first component is the reaction required to hold the axle of the spinning wheel stationary in the tunnel against the force of the oncoming wind, DL, as shown in figure 1.

This this is easily measured using the wind tunnel balance (as Fbalance) and is sometimes the only force considered in wind tunnel tests (e.g. (Sayers and Stanley, 1994; Greenwell et al., 1995; Tew and Sayers, 1999)). Additionally, there is also a force required to rotate the wheel acting against the circumferential component of the drag. This drag is overcome by the road pushing backwards on the wheel with the torque DRr, with an equal and opposite forward force at the hub. Since there is no ground in our wind tunnel test, this is measured using the power, Pmotor, required to turn the wheel using an electric motor. Thus the total aerodynamic drag of the wheel, DDLDR =Fbalance + Pmotor/UB.

Experiments were carried out in a 0.61m × 0.61m tunnel using half-scale wheels with the tunnel speed and wheel rotation doubled to give Reynolds number* equivalence to full-scale wheels. In what follows we will refer to full-scale velocities, forces and powers.

*The Reynolds number effectively tells us the type of flow an object is experiencing. A ball-bearing dropped in honey is at a very low Reynolds number, where the viscosity of the fluid dominates. An aeroplane is at a much higher Reynolds number, where it is more about the aeroplane hitting the air (the inertia of the object rather than the stickiness of the air).

A solid aluminium ring represents the rim and tyre and is attached to a hub via six wire spokes with adjustable tension to allow the rim and hub centres to be aligned (‘trued’). The large momentum of this heavy rim facilitates operation at constant velocities. Further spokes are bonded to the rim and hub with cyanoacrylate adhesive. This setup allows one spoke to be added in each of the gaps between the existing spokes to give NS = 12 and 24, or two spokes to be added in each gap to give NS = 18 followed by one spoke in each gap for NS = 36. It should be noted here that only cylindrical spokes have been tested. Oval or aerofoil spokes may provide improved drag characteristics when carefully aligned to the flow to avoid stall. However, here general configurations are considered rather than a detailed examination of individual setups.

Experiments have also been conducted using ‘tri-spoke’ and disc wheel configurations. The tri-spoke was built using three extruded aluminium tubes with a thick aerofoil cross-section. These were bonded to the rim with epoxy resin and filleted with polyester filler – as seen in figure 2.

The six wire ‘trueing’ spokes were then removed and the holes plugged. The sides of the disc wheel were fabricated using tissue paper stiffened with cellulose dope (with the six truing spokes remaining inside the wheel). This construction results in the concave sides seen in figure 2. The wheel is rotated via a 30 V DC motor, controlled with a variac, with an ammeter in series and a voltmeter in parallel to allow power measurement. A commercial cycle computer is used to measure UB. The test rig is mounted on a mechanical balance located beneath the tunnel. Forces are measured via a sliding mass system to an accuracy of ±0.1 N. Tare values are taken to account for the drag of the test rig and the efficiency of the motor. The effect of the flow being constrained within the tunnel (blockage) is corrected for using empirical rules from Freeman (1980).

The tunnel used has no revolving road and so the effect of the ground cannot be taken into account. It is unlikely that the ground would have a large effect on the aerodynamic drag since the wheel is stationary where it meets the ground, with the majority of the drag coming from the fast, upper portion of the wheel.

### Detailed results

(feel free to skip forwards to ‘key results’!)

Tests were performed with the spoked wheel (for NS = 6, 12, 18, 24) and the disc and trispoke wheels at UB = 10, 20, 30, 40, 60 km/hr and UW = 0, 10, 20, 30, 40 km/hr (UW being limited by the power of the wind tunnel).

Figure 3 shows PL for varying UB and UW for each wheel configuration. The data is fitted using a statistical modelling method known as kriging (see, e.g. (Jones, 2001)), which allows us to filter experimental error, but still accommodate unusual responses by maximising the likelihood of the data. Using this method we can extract trends from the data, rather than prescribing them, e.g. by fitting a polynomial model.

For the wire-spoked wheels, the power rises from 6 to 12 to 18 spokes, as would be expected. However, for the 24 spoke wheel, the power drops back to levels similar to those for 18 spokes. The number of spokes has a significant impact on the form of the power vs. velocity surfaces in figure 3. We would normally expect to see an increase in power proportional to the velocity cubed, and this trend is indeed seen in the disc and 18 spoke plots. The tri-spoke, 6, 12 and 24 spoke plots display a more linear trend. The flow over a spinning wheel is naturally more complex than that over a solid body (where D ∝ U2 ) and it is likely that varying interaction between turbulence shed by the spinning spokes and the flow over the wheel is the reason for the differing trends. We’ll discuss this more later.

Disc wheels and tri-spokes are a popular choice amongst athletes, appearing to offer a much more streamlined profile to the wind, but the data in figure 3 does not indicate any advantage over wire spoked wheels in terms of the PL component.

The PL results must be coupled with the effort required to turn the wheel, which is measured as PR, as displayed in figure 4. More consistent trends are seen in the PR data, although this is likely to be partly due to the increased precision of measurement using a digital voltmeter and ammeter – note how close the data lies to the surface in comparison to the PL data in figure 3. We do, however, see a similar pattern in terms of wheel configuration. The power increases with spoke number from six through to 18 spokes and then drops slightly for 24. The disc and tri-spoke wheels are comparatively better, with similar PR levels to the six spoke wheel. Another difference between the PR and PL trends is that PR is more strongly related to UB than UW , with PL being affected more by UW. This follows intuition, since PL is in the direction of UW and PR is a torque multiplied by the angular velocity, ω =UBr.

We now put the two components together to give PPLPR, the result of which is shown in figure 5. These plots of the total power required to move the wheel at UB into UW accentuate the difference between the wheel configurations. DL is the overriding component contributing to P, but the inclusion of PR introduces a stronger relation between P and UB than would not be present by simply measuring DL.

It is worth noting at this point that the poor performance of the disc and tri-spoke wheels does not necessarily indicate that these configurations are inferior. One form of disc wheel with concave sides and one profile of aerofoil spokes have been tested. Different profiles will produce different results which may, of course, improve on our results. It is perhaps more interesting though to concentrate on the issue of spoke number, since this can be varied and visualised more easily than disc shape or aerofoil profile.

### Key results

To examine the behaviour of NS more closely, P for varying UB and NS at UW = 0 is plotted in figure 6. Further experiments have been conducted with NS = 36 to confirm that there is, as expected, a rise in P beyond the drop for NS = 24. The number of spokes is largely immaterial below 20 km/hr, e.g. for uphill races, but above this point, NS significantly affects P. Also note that each set of data for a given NS exhibits the type of trend we would expect of P ∝ UB3.

It is clear that for this wheel there is an optimum number of spokes somewhere between 18 and 36. Only NS = 24 has been tested in this range, and NS = 28 is the only other number of spokes for which hubs and rims are readily available, due to commonly used spoke ‘lacing’ patterns. However, a radially spoked wheel (for front wheel use only, due to the torque transmitted from the hub in the rear wheel) with any even number of spokes may be produced and such a wheel may, of course, perform better than our 24 spoke example.

The apparent ‘critical spoke number’ where this drag reduction paradox is seen for our wheel may not occur on all wheels and, if it does, will not necessarily be at the same NS. The explanation for the drag reduction is likely to be analogous to active flow control methods in aerodynamic design where the flow is modified by the introduction of jets, or by suction. For the bicycle wheel, flow shed by the passing spokes is interacting with the axial flow over the wheel. At the critical spoke number, it is likely that this interaction reduces the drag associated with the longitudinal flow.

A visualisation of the unsteady, vortex shedding flow over a wheel is shown below. This is the result of a computational fluid dynamics simulation from a more recent University of Southampton undergraduate project. As well as the flow over the spokes, an interesting feature of this simulation is the ‘Kármán vortex street’ behind the hub. High drag and unpredictable behaviour are associated with this phenomenon when it occurs on flying objects. Dimples on golf balls and seems on footballs ‘trip’ the flow into a smaller and more stable turbulent wake. It looks like a few dimples on bicycle hubs might not be a bad idea!

### In the context of the whole bike and rider

To put the above results in context, we must compare them to the total power required to overcome the resistive force acting on the bicycle and rider. The power required to ride at 25 mph (40km/hr) for varying position and clothing are shown in table 1 (see All you need to know about bicycle aerodynamics: part I for information about the tests to produce these data, and Aerodynamics: the Sagan position for lower drag positions).

Let’s assume we are only looking at the effect of changes to the front wheel (we can’t simply multiply our results by two, since the flow over the rear wheel will be far more complex), the difference between six and 36 spokes is approximately 12 watts (see figure 6). The difference between riding on the drops and on the hoods is 20 watts (table 1). So, with such a large position change not making much more of a difference, it looks like wheels are a good place to look for aerodynamics gains?

Most riders will be considering wheels in the NS = 18 to 28 range. We can see from figure 6 that this choice could make a difference of around 5 watts. Unfortunately, we cannot be confident in what is the best choice. We can, however, see from table 1 that the potential benefits are only around half that which can be had with an aeroshell helmet cover. An aeroshell costs around £10 and a new set of wheels can cost thousands. £100 or so on a skinsuit offers four times the possible gains from a new set of wheels.

This isn’t to say that you shouldn’t go and get yourself a nice, new, good quality set of wheels. Improved stiffness, plus better cornering from the new breed of wider rim profiles are good reasons to upgrade. With some manufacturers offering returns policies, armed with a few wheels and a power meter, you could even try a bit of aerodynamic testing yourself to see if you’re in the right place on figure 6 before you make your final choice (if indeed that sweet spot exists for other wheels!).

### Apendix

#### Original abstract

Cyclists routinely vary the configuration of the wheels on their bicycles in order to change the weight, stiffness, strength and drag. However, while weight, stiffness and durability can be easily assessed, wheel selection for low drag tends to be based on gut feeling and, more often than not, wheel manufacturers’ publicity. Here, a set of generic bicycle wheels have been tested in a wind tunnel in order to assess which general configurations work best and to quantify the differences in drag between various wheels. Results indicate that there can in fact be a reduction in power required to drive the wheel for an increase in number of spokes. It is also found that the more fashionable disc and tri-spoke wheels do not perform as well as traditional wire spoked wheels. A comparison of the power required to drive the wheels and the total power to propel the bicycle and rider shows that changes in wheel configuration can be as important as variations in rider position.

#### Original introduction

The importance of aerodynamics first hit professional cycling when Greg Lemond won the 1989 Tour de France from Laurent Fignon by taking the last stage on the Champs Elyses with a new handlebar setup and streamlined helmet. Since then, the Scottish underdog Graham Obree broke the cycling status quo with his novel aerodynamic riding positions, breaking the hour record twice and winning two world titles. After Chris Boardman smashed the world hour record using Obree’s ‘Superman position’, cycling’s governing body (the UCI) brought in rules to restrict the positions riders can use. There are also rules regulating the use of aerodynamic monocoque frames, such as the Lotus frame used by Chris Boardman in the 1992 Barcelona Olympics. There is now a new ‘best human effort’ record where riders must use more primitive equipment, similar to that used by Eddy Merckx in 1972.

So far, however, there have been no severe limitations on the type of wheel that is used (outside of the hour record). Competitors are free to choose rim profile, spoke numbers and profiles, and even use a solid wheel in many races. The restrictions on wheel configuration is dependent on the type of race, with three categories: 1) hour record, with 16 to 32 spokes and a rim with width and depth no greater than 22 mm; 2) massed start races, with greater than 12 spokes; and 3) individual and track races, no restrictions (UCI, 2005).

There is an obvious tradeoff between using fewer spokes for weight saving and more for durability, and this is likely to be decided by the type of rider and the course. However, the relationship between wheel configuration and aerodynamic drag is less obvious. While there have been startling displays of how position and helmet (or head fairing) shape can turn the tide in races, there is little evidence as to which wheel configuration is optimal and how much impact the wheel has on the performance of the rider. This paper presents an experimental investigation into the effect of various wheel configurations. Data is available on the performance of various commercially available wheels (Greenwell et al., 1995; Tew and Sayers, 1999), but here a generic wheel is used throughout in order that configuration changes can be quantified – e.g. the number of spokes can be changed while using the same rim and hub.

### References

Freeman, B. C. (1980). Blockage corrections for bluff bodies in confined flows. Technical Report 80024, ESDU. Ammended 1998.

Grappe, F., Candau, R., Belli, A.,Rouillon, J. D. (1997). Aerodynamic drag in field cycling with special reference to the Obree’s position. Ergonomics, 40,1299–1311.

Greenwell, D. I., Wood, N. J., Bridge, E. K. L.,Addy, R. J. (1995). Aerodynamic charac- teristics of low drag bicycle wheels. Aeronautical Journal, 99,109–120.

Jones, D. R. (2001). A taxonomy of global optimization methods based on response surfaces. Journal of Global Optimization, 21,345–383.

Sayers, A. T.Stanley, P. (1994). Drag force on rotating cycle wheels. J. Wind Eng. Ind. Aerodynamics, 53,431–440.

Tew, G. S.Sayers, A. T. (1999). Aerodynamics of yawed racing cycle wheels. J. Wind Eng. Ind. Aerodynamics, 82,209–222.

UCI (2005). UCI cycling regulations. Union Cycliste Internationale, http://www.uci.ch.

## 4 thoughts on “Wheel aerodynamics”

1. This is very interesting Alex, thank you for publishing! It seems that my old large flange Campag Record hubs with PX50 rims may be ok at least!!

2. IRIS Bicycles says:

I’m looking forward to sitting down with a cup of coffee and settling into this!

3. Duncan Martin says:

This is really interesting, thanks for sharing it. If I’m understanding it right, the results are for wind with 0 degrees of yaw. Did you collect any data where the wind is not head on? I don’t think I’ve seen anything to back it up, but the benefits of discs and trispokes are said to become manifest when there is a sidewind and they can act as sails.