How far is 1500 metres?

 

It's time for the Olympics. Which means it's time for your Maths Masters to get nitpicking.

Not that we won't also enjoy some late night cheering and suffer some bleary mornings. In particular we'll be barracking for Nauruan weightlifter Itte Detenamo. (There'll be plenty of people to cheer on the Aussies, and our heart is with Itte, the sole representative of a beleaguered nation of 10,000 people.)

In 2010 we happily nitpicked the Vancouver Winter Olympics. We had good fun with the ridiculous scoring system for long jump skiing, and we calculated how far the skaters in the 10,000 metres event actually skated. Now it's swimming's turn.

In our skating column we suggested an amusing (for us) solution to the problem of the competitors skating too far: mimic swimming competitions, use a straight 50-metre track, and have the skaters slam into the wall at the end of each lap. But, slapstick aside, the distances may still not add up.

When measuring the distance traveled by a bulky object we usually focus upon the object's centre of mass. In this case, our "bulky object" is swimmer Jarrod Poort, Australia's representative in the 1500 metres.

A person's centre of mass is located slightly below their belly button. So, as Jarrod does his turn his centre of mass will remain some distance from the pool wall. That means the actual distance traveled by Jarrod in the 1500m will be less than 1500 metres. How much less?

We can get a rough idea from a video of a swimmer doing his turn. The following screenshot shows a swimmer at the moment when his center of mass is closest to the wall.

 

The exact value of this minimal distance will vary but is about 50 cm for an Olympic swimmer. So, over the 30 laps of the 1500m (and ignoring the start and the finish), that amounts to something like a 30 metres reduction in distance swum.

Of course if Jarrod can talk the organisers into using a short course (25 metre) pool then he and his fellow swimmers will save about twice that distance, something like 60 metres. And why stop there? Why not compete in a 3 metre long "pool" and then the "swimmers" can bounce back and forth between their fingers and toes? Hmm.

Are we being too nitpicky? Probably. But we don't see why the whole issue couldn't simply be avoided by competing in a 1500 metre long pool. And at the Olympics at least, such a pool is readily available: we just have to ask the rowers to move aside for a few days.

Nitpicky or not, the above discussion raises interesting questions about long course versus short course swimming. It is well-known that short course swimming is quicker. Is this then simply because of the swimmer's centre of mass having to cover less distance?

We had a chat with biomechanist and coach, Dr. Nat Benjanuvatra. As well as pointing out the centre of mass issue, Nat discussed his and others' extensive research. It turns out that there are many factors at play.

An obvious drawback of the greater number of turns in short course swimming is that the swimmer must momentarily stop at each turn. However, it turns out that the extra turns also benefit the swimmers' performance in a number of ways: the short but effective rest for the arms during the turn; the push-off at the turn; the efficient underwater dolphin-swimming after the turn; and, yes, the shorter distances.

Essentially, swimming is a triathlon consisting of the three disciplines of starting, turning and (truly ruly) swimming. Distances aside, long courses and short courses give different weight to the three disciplines. So, if the point is to have a competition in (truly ruly) swimming then throwing the swimmers in with the rowers is probably the way to go.

(While we're here, we may as well pick a rather large nit with the actual triathlon. The cycling component of the triathlon has so much greater weight than the running and swimming, it is better regarded as an enhanced cycling event).

In any case, we're looking forward to cheering for Jarrod and the other Aussie swimmers (and turners). Oh, and for Itte Detenamo.

 

Burkard Polster teaches mathematics at Monash and is the university's resident mathemagician, mathematical juggler, origami expert, bubble-master, shoelace charmer, and Count von Count impersonator.

Marty Ross is a mathematical nomad. His hobby is smashing calculators with a hammer.

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