CD-adapco makes the Tour de France less of a Drag

Stephen Ferguson, CD-adapco, UK

As anyone who has ever ridden a bicycle on a windy day will testify, aerodynamics play a big part in cycling. Perhaps more than any other sport, top-level cycling is dominated by aerodynamics and, more specifically, the art of drafting. Drafting occurs when one cyclist rides in the wake of another, reducing their exposure to the oncoming air and ultimately the energy expended in cycling. The question of “how much energy?” is the topic of some debate. CD-adapco has recently undertaken a comprehensive CFD simulation in order to answer this question. The influence of aerodynamics is most visible in the time-trial stages of the Tour de France. Here cyclists can be seen riding special carbon-fiber bicycles on which, at a cost of tens of thousands of dollars, each component is specifically designed to minimize the aerodynamic drag. Clad in aerodynamic clothing and helmets, riders are forced to adopt uncomfortable crouched position on their bikes, minimizing their frontal area and reducing their exposure to the oncoming air.

In the Tour de France, the time-trial comes in two distinct flavors: an Individual Time Trial (ITT) and a Team Time Trial (TTT). In the Individual Time Trial, each rider competes alone. With no other riders to draft behind, the ITT is known as "the race of truth", a brutal contest of man and machine against the clock. In the Team Time Trial, riders compete as a team of (up to) nine riders. Each rider takes it in turns to ride at the front of the line, taking the full force of the oncoming air and providing a wake in which teammates can draft. As each rider tires they swing off the front of the line and drift backwards to the rear, recovering in the wake of the other riders in preparation for the next turn at the front.

Although time-trialing ability alone is not enough to win the Tour de France, each July the final recipient of the yellow jersey is almost certainly a time-trialist of supreme ability. Recent Tours have almost always been won by riders that dominate the timetrial
stages; 5 times winner Miguel Indurain and now 7 time winner Lance Armstrong typically based their victories around large time gaps opened up in the time-trial stages.

Cycling is a sport in which every second really does count , and small aerodynamic advantages can be the difference between winning and losing the Tour. In 1989, Greg Lemond trailed French rider Laurent Fignon by 50 seconds prior to the final stage, a 24.5km ITT. To most observers, this gap seemed insurmountable - requiring Lemond to ride each kilometer 2 seconds faster than Fignon, himself no mean time-trialist. On a warm Paris afternoon, Lemond, wearing an aerodynamic helmet and riding a special aerodynamic bicycle, beat Fignon, riding a normal road bike, by 58 seconds, and won the Tour by just 8 seconds. Subsequent analysis has suggested that the drag on Fignon's ponytail alone was enough to slow him down by the critical 8 seconds by which he lost the race. The TTT played a large part in deciding the winner of the 2003 Tour; of his 61 second margin Lance Armstrong won 43 seconds in the Team Time Trial.

 

By performing CFD simulations of a nine-man TTT, and a single cyclist ITT, it is possible to directly evaluate the influence of drafting. Although many individual cyclists have been subjected to windtunnel testing, the sheer size of a nine-man chain of cyclists makes physical testing impractical. In the CFD world too, entire TTT calculations were until recently, prohibitively expensive, requiring a great number of computational cells in order to sufficiently resolve the flow past the cyclists.

The CFD models were constructed and run using the STAR-CAD Series, a range of CAD-embedded CFD products. Unlike other CFD codes, which are restricted to using hexahedral or tetrahedral elements, STAR-CAD Series has the unique ability to create and solve upon meshes of arbitrary cell topology. Using specially created polyhedral elements (which typically have between 12 and 14 faces), CD-adapco's CFD technology can provide near hexahedral accuracy with at least 5 times fewer cells than a typical tetrahedral calculation. The mesh for the TTT comprised almost 7 million polyhedral cells, equivalent in accuracy to a mesh of approximately 30 million tetrahedra.

The results of the simulations were illuminating. Compared with the lead cyclist, the drag of the rider in second place is reduced by 21% - a significant saving. The third rider feels a further small decrease in drag over the second, but from the third rider back all other cyclists experience almost identical drag. As the riders are continually progressing towards the front of the chain, taking a short turn on the front, before freewheeling to the rear of the line, on average (assuming a constant rate of rider rotation and ignoring the effect of dropping back) the drag coefficient of a rider in the TTT is around 27% lower than experienced by an individual rider.

Perhaps the most surprising conclusion from the CFD simulation is that, despite feeling the full force of the oncoming air, the lead rider experiences lower drag than if he were riding an ITT at the same speed. The drag coefficient of the leading TTT rider is 0.277, while that of an individual rider is 0.285 [drag coeffient is measure of the force each rider experiences corrected for differences in size]. This rare example of "something for nothing" occurs because the second place rider reduces the influence of the lead rider's wake, increasing his base pressure and consequently reducing the drag force that he experiences.

Despite the predicted reduction in drag coefficient afforded to riders in a team time-trial, the increase in speed over an individual time trialist is not large. In the 2004 Tour, Armstrong completed the 55km individual time trial with an average speed of 49.39 km/h, while his team won the 64.5km TTT at an average speed of 53.71 km/h. This increase in average speed of just 9% seems relatively small in comparison with the effort exerted by eight extra cyclists. However, as drag increases with velocity squared, a 4 km/h increase would require a greatly increased effort for an individual rider. One would expect the difference in speed to be much greater if all nine riders were time-trialists of Armstrong's ability. In reality even the top teams consist of riders whose competence lies in areas other than time-trialing, so that the contribution of all nine riders is not equivalent. Because of this, the lead rider is also forced to temper his effort, so that the lesser time-trialist on the team can keep up, despite the reduction in drag. If gaps open up in the line, riders are liable to be left behind, cycling in the wind and unable to catch up. Although CFD calculations are so far not routinely used in perfecting time-trialing tactics for the Tour de France, CD-adapco's Dennis Nagy believes that they soon will be. "It's only a matter of time", he said, "the rewards in professional cycling are increasing all of the time, while winning margins are coming down. In the near future CFD could be the difference between winning and losing the Tour de France".