The Paris Olympics’ Swimming Pool
04-04-2025 | Posted by Joaquín Martí
Controversy surrounds whether the Olympic pool in the Paris La Défense Arena was not deep enough and slowed swimmers. Is this contention true?
At the Summer Olympics in Tokyo in 2021, existing world records were broken in several disciplines, six in swimming alone, mostly by a fraction of a second. Before the start of 2024 Summer Olympics in Paris, hopes for new records were high. One of the reasons for this was new training techniques using “digital twins”, a topic about which we have already published.
As it was, Léon Marchand’s world record in the men’s 400 m individual medley was the only swimming world record set during these games. Even worse, athletes seemed to fall far short of expectations. Nicolò Martinenghi, the winner of the men’s 100 m breaststroke, only managed a time of 59.03 s, 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. But 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 a complex problem in mathematics.
The Paris La Défense Arena in Nanterre is actually a rugby stadium and concert venue—Taylor Swift performed there in May—and was converted into an indoor swimming pool for the Games, to be dismantled afterward. This approach makes sense: during the 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.
But the depth of this pool is unusually shallow at 2.15 m. 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 2 m deep, but now the minimum depth is 2.5 m, and a depth of 3 m is recommended. When construction of the Olympic pool started in 2017, the 2 m rule still applied.
Pools are described as “slow” if they create currents that can slow swimmers down. As soon as swimmers jump into the water, they generate waves which are reflected at the edge of the pool and on the floor and can create currents that slow down their progress. 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. The deeper they are, the more the waves are dampened, making it less likely that their reflections will interfere with the swimmers. The impressive results of the 2008 Summer Games in Beijing seem to prove this: the swimming pool there had a depth of 3 m, and the Olympians were able to set 25 world records.
Still, it has not been proved with any certainty that the pool in Nanterre is slow—especially if the argument is based on a lack of world records. Indeed, not all results support the slow pool theory. In the women’s 400 m freestyle preliminaries, for example, the slowest time to qualify for the final in Paris was 4 min and 3.83 s, which beats the performance at the Olympic Games in Tokyo (4 min and 4.07 s).
Investigations on the topic are difficult. What happens in the water of the pool is governed by the Navier-Stokes equations, which give rise to very complex problems. These equations were developed in the 19th century to describe the relation between velocity, pressure, temperature and density of a moving fluid. One of the seven Millennium Prize Problems in mathematics, classic questions whose solutions are rewarded with $1 million, is concerned with those equations.
And it 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. There were also heated debates about the pool at the Summer Olympics in Rio de Janeiro in 2016 where, again, some of the swimmers appeared to progress faster in one direction than in the other. Statistical analyses seemed to confirm some of these observations but were not sufficiently conclusive.
At Principia we are highly experienced in solving problems governed by the Navier-Stokes equations. But we prefer it if they are simpler to analyse than the purported slowness of the Nanterre swimming pool.
This post is excerpted from “Is the Paris Olympics’ Swimming Pool ‘Slow’? Let’s Dive into the Math”, published by Scientific American on August 2, 2024.
