Analysing the aerodynamics of the fastest ever marathon

In the early hours of Saturday May 6, at the Monza motor racing circuit in Italy, Eliud Kipchoge ran 26.2 miles in 2 hours and 25 seconds, beating the existing marathon world record by 2 minutes and 32 seconds. The run was the culmination of Nike’s “Breaking 2” project, a two year program aimed at demonstrating that it is physically possible for a human to run a marathon in less than two hours.

For the attempt to be successful Kipchoge would have to run about 7 seconds faster per mile than current world record holder Dennis Kimetto (who ran 2:02:57 in Berlin in 2014). Although on paper the performance increase of 2.5% required doesn’t sound too difficult, for runners operating at the very limit of human endurance, any gains would be very hard won. Many in the sports science community had predicted that the 2 hour barrier wouldn't be broken for 50 years or more in regular competition.

Although Kipchoge ran much faster than the current world record, the Breaking 2 project deliberately employed a number of tactics that meant his time is not recognised as a legitimate world record. I don’t want to go into too much detail here, but the Nike team apparently applied a “scientific” approach to optimising every part of his kit, training, nutrition, and in race tactics.

Before the run, much of the publicity had focused on Nike’s spring loaded Vaporfly Elite running shoe, which they had claimed improves running efficiency by as much as 4%. However in the days afterwards much of the conversation turned to aerodynamics, and the influence of the unfeasibly large timing board that was mounted on top of the pace car that drove in front of Kipchoge, and the “delta formation” adopted by his team of “relaying” pacers. By some calculations drafting was responsible for about 1:30 of the 2:32 that Kipchoge knocked off Kimetto’s world record.

In order to determine just how much influence "aerodynamic trickery" had in getting Kipchoge within 26 seconds of the mythical 2 hour barrier, we decided to run a series of computational fluid dynamics using STAR-CCM+, which is part of Siemens' Simcenter portfolio of simulation tools.

CFD Simulation

In order to extract the influence of both the car, and the delta formation of pacers, we performed four simulations:

The first case is a worst case scenario - an undrafted solo runner - while the fourth case simulates the actual conditions of the Breaking 2 attempt, in which our virtual Kipchoge is following the pace car (and timing board) whilst surrounded by a team of athletes in delta formation.

The simulations comprise 4 million computational cells for the solo runner, 8.5 million for the pack formation, 22.5 million for the car and virtual Kipchoge and 24 million for the whole lot with refinement around, and in the wake of, the car and runners. The k⍵-SST turbulence model was used (for those of you wondering) and we also verified the simulations using a k-ε Realizable model, which was within 2% agreement for the baseline and final cases; y+ was <20. For simplification, each of the runners is assumed to be a static mannequin frozen in a single running pose (we do not model the running movement of the arms and legs, although we have previously demonstrated that the average drag on a pedaling cyclist is well predicted using a static model).

Discussion of Results

The plots below show the velocity field around our virtual Kipchoge in each of the four scenarios. The dark blue areas show areas in which the air velocity is less than 5mph. In both the cases with pacers, Kipchoge is running into a 5 mph "wind" despite traveling at almost 13.1mph.

From the plots of velocity, you can see that the pacers do a great job of shielding Kipchoge from the wind. Our calculations suggest that the only real benefit of the car and timing combination is in preventing Kipchoge catching the wind in his face. The wake behind the timing board tends to skew upwards more because of the high speed flow beneath the car (which has a flat floor) expanding as exits the diffuser and the chasing pack has a higher pressure zone ahead of it, which then diverts the flow around it.

More usefully, we can integrate the pressure acting over the surface of our virtual Kipchoge, and calculate the drag force acting upon him in each of the four scenarios:

It is easier to interpret these results if we consider the “energy required to overcome drag”, which is the force acting on our Kipchoge, multiplied by his forward velocity (just under 13.1 mph). The energy that Kipchoge saves in not having to overcome aerodynamic drag should be available for him transfer to the road surface, and in principle run faster:

Given that Kipchoge is capable of running at roughly about 300 W, the difference between undrafted and fully drafted scenarios is around 31W, meaning that he can probably devote an extra 10% of his effort to running faster in the latter case.

Perhaps surprisingly, most of that saving is generated by the close delta formation of pacers around Kipchoge which generates a 28W saving even without the car, which only adds another 3W to the total.

Because power output varies with the cube of velocity it is possible to estimate the amount of time saved in comparison with the undrafted runner. Our calculations suggest that the pacers saved Kipchoge about 4:09 compared with a solo runner, and the pacers and car combination saved him about 4:35.

Things to note

The undrafted case is absolutely a worst case scenario (other than perhaps running into a headwind). Elite marathon runners do not set world records while running alone, typically burying themselves in a pack of runners to well beyond that halfway point. Dennis Kimetto didn’t hit the front until about 21 miles into his world record run in Berlin in 2014. We don’t think that it is unreasonable to assume that Kimetto, or Kipchoge would run several minutes slower if they were forced to run solo for 26.2 miles. The fastest female marathon runner, Paula Radcliffe, ran almost 2 minutes faster when surrounded by male runners (who were presumably drafting her) than when front running in a female only race.

The drafting cases, as simulated here, are absolutely the best case scenario (excluding a strong tailwind). As organized as the Nike pacing teams were, they weren’t the perfect static obstacles that this simulation assumes and there were times at which the runners were not running in perfect delta formation. The natural running movements of the athletes would probably also expose Kipchoge to additional drag.

There will be other limiting factors that we are not considering. Kipchoge’s ability to dissipate heat will probably have been compromised as a result of the drafting - especially when considering that any cooling air that reached him will have travelled past 6 other hot runners. This might be a second or third order effect, but worth maybe worth considering for an athlete competing at the absolute limits of human performance.

Also, the mannequin isn't a perfect representation of Kipchoge, and it looks like our "virtual Kipchoge" could usefully use some tailored nutrition to lose a few pounds of virtual fat.

Conclusions

Kipchoge is absolutely the best marathon runner in the world, probably the greatest of all time. We hope that he sets the legitimate world record that he deserves sometime soon. Whatever aids he had, legitimate or otherwise, this was still one of the greatest feats of endurance running in history.

Lots of the coverage in the days after the Breaking 2 attempt concentrated on the drafting effect caused by the ridiculously large clock that was mounted on top of the pace car. Our simulations show that the drafting caused by the clock probably did reduce the effort required to overcome drag, and therefore allowed Kipchoge and his pacers to run faster for a given level of effort. However, although significant, the drafting effect of the car was much less important (by a factor of 10) than that of the carefully orchestrated pacing formation. We think that the "large clock" took more of Kipchoge's publicity than it deserved.

Our simulations suggest that the combined influence of the car, clock, and pacers, reduced the aerodynamic drag experienced by Kipchoge by a maximum of about 83%, saving him over 30 Watts, (about 10% of his overall effort level), compared with a completely solitary runner at the same speed. This reduction in drag could be worth as much as 4.5 minutes, compared with an undrafted runner at the same speed. However, since the legitimate world record was run in partially drafted conditions, and our simulations are somewhat idealized, it is likely that the actual time saved was significantly less than 4.5 minutes, compared with a regular big-city marathon.

However, despite all of the “marginal gain” type improvements that Nike publicized in the lead up to this event, the evidence suggests that the vast majority of the performance improvement achieved was down to aerodynamic drafting.

Perhaps the most surprising conclusion is that the pace car was worth only about 30 seconds of the performance improvement, which suggests that if you could organise a group of pacemakers that were capable of running in formation for most of the distance (instead of illegally relaying as in the Nike project), then you could probably get the legitimate world record close to 2:01:00.