Tour de France pimples, dimples, trips and chevrons: are vortex generators in cycling worth the effort?

Tour de France time-trial stages are often decisive in confirming a rider’s general classification ranking. Riders battle against the clock to win, or lose time against their competitors. The two time-trail stages of the 2017 Tour de France are notable for being relatively short in distance thereby limiting the possible time gains or losses. Stage 20 is a 22.5 km jaunt around the locality of Marseille, whilst the first stage was a 14 km course around Dusseldorf.

Team Sky dominated the Dusseldorf time trail by placing four riders in the top 10. This was quickly followed by inevitable questions of ‘how did they do it’? Many quickly pointed to the incorporation of pimples, a form of vortex generator upon the Team Sky skinsuits, located on the outer arms and running from elbow to shoulder. They were not alone in the use of such features, Movistar incorporated chevron shaped features in similar locations. The use of surface textures, and features such as seams to manipulate aerodynamics is also nothing new in cycling and has been apparent in elite and national teams for years. The features are clearly incorporated to benefit aerodynamics, but the extent of the actual benefit is perhaps less clear. Fred Grappe a coach for Tour de France team FDJ, was vocal about the suits claiming a possible drag reduction of as much as 25%. However he appeared to have based this statement on a paper authored by Len Brownlie who investigated the incorporation of vortex generators in athletic sprint or marathon apparel. Brownlie had estimated a drag reduction of 3.7% and 6.8% for suits that contained vortex generators, but these suits may incorporate features on arms, legs and torso. So, if we were to consider a cyclist just using vortex generators on the arms, as per Team Sky, what sort of aerodynamic time savings might we expect? And how do these features actually work?

Drag on a cyclist

jh1The extent to which different parts of the body contribute to aerodynamic drag force.

A few years ago now I was working with a local cycle manufacturer investigating the aerodynamic performance of their triathlon bike offering using Computational Fluid Dynamics (CFD) ANSYS Fluent software. This is a technique that allows us to create a simulated wind tunnel on a computer and visualise and measure the aerodynamic phenomena associated with cycling. The cyclist was positioned on aerobars in a time trial position, and a force breakdown by body part can be seen in the image above. Unsurprisingly, the cyclist accounts for up to 70% of the aerodynamic drag, with the legs producing the majority of this. What we also see is the significant contribution of the upper arms and shoulders to the aerodynamic drag (18%). This is location where the teams have been placing these vortex generators. So why do the upper arms produce such a high contribution?

jh2The oil flow over the arms.

If we again look to our simulation, we can use a visualisation method called oil-flow. This allows us to understand how air flow moves over an object and importantly whether it stays attached to that objects surface. In the image we can see that air moves smoothly over the cyclist’s arms but then abruptly separates, a separation line being visible running from elbow to shoulder. The location of this separation is important, as once the flow is separated a wake forms which leads to drag force, and the earlier the separation position the higher the drag force will be. What the teams are doing with the incorporation of vortex generators on the arms is attempting to control the position of this separation. But it’s not quite as straightforward as just sticking on a few pimples, dimples, trips or chevrons. If they are to be of benefit, you need to understand the behaviour of airflow around the arm, and at its most basic this is dependent upon air velocity, and diameter.

The basic physics

jh3The basic physics of drag.

An arm is essentially cylindrical in shape, and if we look at air movement over cylinders, the position that the flow separates from and the associated drag force will depend on whether we are operating in the subcritical (laminar boundary layer separation) or supercritical (turbulent boundary layer separation). Subcritical laminar boundary layer flows are characterised by early separation leading to large wakes and high drag. Whereas with a supercritical turbulent boundary layer, separation occurs later resulting in a smaller wake and thus lower drag. This is because the turbulent boundary layer contains more energy and is able to cling to the surface for longer. To determine the type of flow we have around our arm we can calculate the Reynolds Number (a dimensionless parameter, that helps us predict flow structures) for the cylinder:

Re = ρud/μ

where Re = Reynolds Number, ρ = density, u = velocity, d = diameter, and μ = viscosity.

Assuming that our cyclist is travelling at an average 50 kph, and the width of the arm is less than 105 mm, this results in Re < 100,000, so we are in the subcritical region. To reduce the wake and drag we need to get the flow into the supercritical region. To do this we can introduce a feature (a vortex generator) to energise the flow on the arm and cause an early transition from subcritical to supercritical flow. But what might the drag reduction be when incorporating these features?

A simple test

jh4Five different surface textures.

To estimate the effect of vortex generators we ran a series of simple simulations using Computational Fluid Dynamics. We use software called ANSYS Fluent which incorporates many models that help us to understand laminar, transitional, and turbulent flows. We’ve taken a cylinder of representative arm diameter, and incorporated a series of features upon the surface, pimples, dimples, chevrons, and trips (representing a seam). These have all been approximated; the pimple design for example is based on photographs of Team Sky suits and estimating the diameter height and positioning of the feature. The same method was used for creating the Chevrons based on the Movistar suit. The trip seam, was placed where you may expect a flow separation to occur. None of these vortex generators have been optimised, although we can assume that the teams will have done so. So, how much drag did we save with our approximate vortex generator features?

Drag reduction results

jh5Drag vs time for each vortex generator.

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We can see the results in the chart of normalised drag force vs. time history, and tabulated below. Pimples and dimples both perform comparably, producing a 16~17% drag reduction, chevrons slightly less so at 13%, and a carefully positioned trip producing the best result of 26.3%. So why do the teams use pimples/chevrons instead of a trip? The simple answer is a trip only works well if the direction of airflow is consistent, if you have wind movement in an external environment it is better to use a patterned vortex generator to account for this directional variation. This is why you are more likely to see carefully positioned seams in a velodrome and patterned features out on the road.

Visualising how they work

jh6The wake structures for each vortex generator.

By looking at flow visualisation around these cylinders we can begin to understand how these vortex generators work. Visualisation of instantaneous wake structure reveals how the flow sheds alternately from one side of the cylinder and then the other, producing the oscillatory force histories (shown earlier). For the smooth cylinder, the wake structures can be seen to separate early producing a wider wake (and thus higher drag) than when vortex generators are introduced.

jh7The flow lines over each vortex generator.

Using flowlines released in front of the vortex generators we can see how they stir up the flow. The vortices generated then delay the separation. With the dimples it can be seen that the swirling flow resides within, rather than behind the generator as seen with the pimple and chevron. As flow moves across the dimple it separates at the leading edge of the dimple, before subsequently reattaching at the rear stirring the flow up. The trip is the most effective device of them all, with a full width circulating flow. However, it is also clear that the effectiveness of a trip is highly dependent on its location.

Predicting the savings

So what does this all actually mean? We’ve seen that the upper arms and shoulders might account for 18% of the 70% of drag attributable to the cyclist, the remainder being the bike itself. We’ve also seen that a dimple feature on a cylinder will reduce measured drag by 16%. Does this really equate to a 25 second time saving as reported in the media? To determine possible savings, we’ve performed a calculation based on the equation below;

ma=(ηstηbηdt(Pcyc/v)) – (CdA(1/2)ρv2)-(mgμr)

where m = mass, a = acceleration, ηst= bike stiffness (99%), ηb= bearing efficiency (99.64%), ηdt= drive train efficiency (95%), Pcyc = cyclist power, v = velocity, CdA = drag area, ρ = density, g = gravity, and μr = frictional rolling coefficient.

Now if we were to assume that the cyclist could average 450 W power output, and that the drag area CdA = 0.25 m2, which would be a typical value for a cyclist in time trial position, then using this model the cyclist could cover 14 km in around 17 minutes. This is comparable with an average time of what we saw achieved in the 14 km stage one time trial. Let’s now reduce CdA to account for the possible reductions from the introduction of vortex generators, the time savings are in the table below.

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What we can see is that through the incorporation of pimples on to the upper arms of a cyclist we may achieve a time reduction of 7 seconds over 14 km (stage 1), and 11.3 seconds over 22.5 km (stage 20). Whilst these time savings are important and possibly influential in the final general classification ranking, they are much lower than figures being widely discussed by commentators in the media.

So, are vortex generators worth it? Considering that Geraint Thomas won the stage one time trial by just 5 seconds from second placed Stefan Kung, I’d say they’re worth a go…

John Hart

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