Is the Paris Olympics’ Swimming Pool ‘Slow’? Let’s Dive into the Math

For many athletes, it is the pinnacle of their career. They have trained hard for years to take part in the Olympic Games. Winning a medal is a childhood dream for most of them—only surpassed by setting a new world record during the competitions.

And that happens again and again. At the Summer Olympics in Tokyo in 2021, existing world records were broken in several disciplines, six in swimming alone, mostly by a difference of tenths or even hundredths of a second. As in most Olympic sports, it’s all about precision: the slightest wrong move or external disturbance can make the difference between success and failure. Nevertheless, swimming stands out in one respect: It takes place in water, or more precisely, in a pool filled with water. And the shape of the pool can have a strong influence on the performance of Olympic athletes.

Before the start of this year’s Summer Olympics in Paris, hopes for new records were high. One of the reasons for this was new training techniques using “digital twins.” These are computer models of swimmers that mathematicians use to help the athletes achieve peak performance.

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So far results for swimmers in Paris have been sobering. Only one world record had been broken as of August 1. And even worse: the Olympians seem to be falling far short of expectations. Nicolò Martinenghi, the winner of the men’s 100-meter breaststroke, only managed a time of 59.03 seconds—the slowest winning time in the event at an Olympic Game since 2004.

A cause was purportedly found: the Olympic swimming pool was not deep enough. A few days after the opening of the Games, the headlines were published: “Paris Olympics Swimmers Noticing Pool Is ‘Slow’ as Gold-Medal Times Don’t Come Near World Records,” “No World Records through Two Nights in Paris, Is the Pool in Paris ‘Slow’?,” “How Slow Paris Pool Is Thwarting Swimmers’ World Record Bids.” But can it be true? Is the pool really to blame for the lack of records? Anyone waiting for a “yes” or “no” will be disappointed. Unfortunately, there is no simple answer because the question is related to one of the most complex problems in mathematics.

The Paris La Défense Arena in Nanterre, a suburb of the city, is actually a rugby stadium and concert venue—Taylor Swift performed there in May—and has been converted into an indoor swimming pool for the Games. The huge pool will be dismantled afterward. This approach makes sense: during the summer Games, the many spectators are entitled to watch the athletes compete, but outside of these events, swimming pools with a grandstand that can accommodate 15,000 people seem completely oversize. This is why many Olympic swimming pools are designed to be temporary solutions.

What is surprising, however, is the depth of this year’s pool, which is unusually shallow at 2.15 meters. There is no standardized regulation as to what dimensions an Olympic pool should have. Until a few years ago, it had to be at least two meters deep, but now the minimum depth is 2.5 meters. A depth of three meters, however, is recommended. When construction of the Olympic pool started in 2017, the two-meter rule still applied. The pool in Nanterre is therefore permitted despite its comparatively shallow depth. And this, many are convinced, means that it is “slow.”

Pools are described as “slow” if they create currents that can slow swimmers down. Although this may sound surprising at first, it is a scientifically recognized fact. “Swimming pools can be fast or slow, and it depends on their design,” says biophysicist Joel M. Stager of Indiana University Bloomington, who studies the science of competitive swimming. “There are a number of variables to consider,” he explains. “Pool depth, channel dimensions, lane design, water return, bottom design, and so on.”

As soon as the Olympians jump into the water, they create waves. These are reflected at the edge of the pool and on the floor. This can create currents and whirlpools that slow the swimmers down. The Olympic pools and competition rules are designed to minimize these effects or, ideally, eliminate them altogether. In competitions, for example, the outermost lanes are not used. And that is also the reason for the minimum depth of the pools. The deeper they are, the more the waves are dampened. This makes it less likely that the waves will be reflected at the bottom and create braking turbulence near the athletes swimming on the surface. The impressive results of the 2008 Summer Games in Beijing seem to prove this. The swimming pool there had a depth offer three meters, and the Olympians were able to set 25 world records.

Nevertheless, there are reasons not to build a particularly deep temporary pool. In addition to budget constraints, bigger, deeper pools leave less room for spectator seats. There is also a psychological factor that limits the depth of the pools. Swimmers are often guided by markings on the pool floor, such as the distance between the tiles. If these are particularly far away, they get the feeling that they are making slow progress. This is why there seems to be a kind of optimum depth for sports pools—around three meters.

“Even if there was a technical reason it needed to be 2.15 [meters], they should have found a way to address it and pay the money/engineer to make it 3 [meters]” wrote Reddit user FreestyleRobinson, who claimed to work regularly with Myrtha Pools, the manufacturer of the temporary Olympic pool in Nanterre. German national swimming coach Bernd Berkhahn has agreed: “It creates a lot of turbulence,” he explained to the German outlet Swimsportnews. “That … doesn’t produce good times.”

Stager points out another problem. “Our studies have shown that temporary swimming pools can be problematic,” he says. In a 2015 study, he and his colleagues examined 16 professional swimming competitions and concluded through statistical analysis that 70 percent of the lanes in temporary pools have disruptive currents compared with only 35 percent of the lanes in permanent pools.

Still, it has not yet been possible to prove with certainty that the pool in Nanterre is slow—especially if the argument is based on a lack of world records. “World records are, by definition, ‘outliers’ and don’t say much about the pool design itself,” Stager explains. Additionally, not all results support the slow pool theory. If you look at the times the swimmers achieved in the women’s 400-meter freestyle preliminaries, for example, the slowest time to qualify for the Olympic final in Paris was four minutes and 3.83 seconds, which beats the performance at the Olympic Games in Tokyo (four minutes and 4.07 seconds). “I know that people talk about the fact that performances are better when the pool is deeper,” Roberto Colletto, CEO of Myrtha Pools, told French outlet RMC Sport. “But from a technical point of view, there is no problem with the pool.” The company has built the pools for the last six Summer Olympics and uses technologies such as computational fluid dynamics simulations to create the best possible competition conditions.

Such investigations are difficult. The reason for this is that the construction of an ideal pool is linked to one of the most complex problems in mathematics: the Navier-Stokes equations. For about two centuries, experts have been trying to solve it without success: it seems impossible to calculate an exact solution. In practice, this means that if you want to model the flow of water—for example, in a pool—you have to rely on complex computer simulations. And these may be very inaccurate, because even the smallest deviations can have a major impact in such models—recall the famous butterfly effect, originally termed to explain the difficulties and uncertainties in weather forecasting.

The Navier-Stokes equations were developed in the 19th century to describe how the velocity, pressure, temperature and density of a moving fluid are related. The equation doesn’t just look complicated; it is one of seven Millennium Prize Problems in mathematics, classic questions in the field whose solutions are rewarded with $1 million. In this case, however, it is not about solving the equations—the prize money is awarded if you manage to show that the formula always has a solution.

This is not the first time that a swimming pool has come under criticism. At the 2013 FINA World Swimming Championships in Barcelona, for example, spectators raised concerns that currents in the pool were affecting the swimmers unevenly. Stager and his team tried to study the problem. The researchers were unable to investigate the pool directly, however, because it had been dismantled immediately after the competition. Instead, they examined the times of all swimmers, compared them with previous performances and carried out a statistical analysis. To do this, they evaluated the average time difference between the outward and return journey for each lane and found evidence that swimmers were advantaged or disadvantaged depending on the direction and lane in which they swam. The researchers wrote that a current was the only known cause that could explain their results.

There were also heated debates about the pool at the Summer Olympics in Rio de Janeiro in 2016. Again, some of the swimmers seemed to progress faster in one direction than in the other. And once again, through statistical analysis, Stager and his colleagues were able to identify a lane-dependent difference in performance. They pointed out in their paper, however, that “since we did not measure the physical properties of the swimming pools in any of these cases, we cannot say for sure if the lane biases were caused by water currents or other factors. What we can say, however, is that our results have been consistent with water currents in the competition pools.”

Whether there are disturbing currents in the pool in the Paris La Défense Arena cannot yet be determined. It would be necessary to take measurements in the pool or—as with previous sporting events—carry out statistical analysis afterward. “When the Games are over, the results can be examined, and perhaps we will know more then,” Stager says. In the meantime, only one thing will help: “we have to let the swimmers swim!”

This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission.