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A PHYSICIST WRITES . . .
Are you still glowing from memories of watching the Rio Olympic Games (and likewise the Paralympics which, as I write, haven’t yet begun)? If not, well, forgive me if I look back with a physicist’s curiosity at some aspects of that fabulous fortnight. I’ve uncovered a few surprising facts! Here first is a simple question (the answer is below): how long around is a 400 metre running track?
You might reasonably want to dismiss this puzzle, pointing out that what matters more (in the final race of a competition) is who finishes first, second and third – collecting a gold, silver and bronze medal respectively. All right then, let’s think about these three prizes: which of the medals (or metals) is not what it seems? The answer is the gold one, which is actually gold-plated silver. If the medal was all gold, it would be valued well into four figures!
Next question: which of the silver and bronze medals is worth more? It’s the silver naturally, in monetary terms. But what about as a reward? Twenty years ago in the US, a survey revealed that athletes who had gained an Olympic bronze medal were distinctly happier with their prize than those had won silver.
The reason seemed to be a combination of frustration among the second-placers at not coming first, and delight among the third-placers at getting a medal at all. This difference in attitude was even more detectable in knockout competitions, in which you get the bronze medal for winning the play-off match (between the two losing semifinalists), whereas the silver is effectively a reward for not winning the final – more of a booby prize, in other words.
Now for an intriguing question regarding any knockout tournament: will the silver and bronze medals be won by the second-best and third-best players respectively? Not necessarily (especially as they may not have played each other)! Take the men’s tennis competition in Rio as an example: in the semifinals, Andy Murray beat Nishikori and Del Potro won against Nadal. Then in the final, Murray was victorious over Del Potro who therefore took silver, while in the play-off Nadal succumbed to Nishikori, who gained bronze.
But Juan Martin Del Potro is far below Kei Nishikori in the world rankings, and might well have lost if they had faced each other at some stage of the competition. So you could argue that the silver and bronze medals were wrongly awarded. No wonder Del Potro bucked the trend I described above, and was happy with his silver one: “...it means as much as a gold for me.”
Thinking still about knockout matches, how absurd it was that in two events at Rio (men’s football and women’s hockey) the gold medal had to be decided by a penalty shoot-out: why has my proposal for avoiding such situations – offered six years ago in this column – never been adopted? (Not anywhere, as far as I know!) My idea was to hold the shoot-out at the start of the game and count the outcome as half a goal. It would thus avert a draw, just as it does now, but the end result would be reached by proper team-play, instead of unsatisfyingly by individual responsibility for contrived goal-kicks. OK, every knockout match would have to begin with the shoot-out but, against that, ‘extra time’ would never be needed. What could be more logical?
Next, let’s consider the physics of field sports in which things are thrown. It’s well known (to physicists) that in theory, and for any given launch speed, the maximum range of a projectile is achieved when its angle of launch is 45°. Certainly this should apply to weighty items like the shot. Hence a question that used to puzzle me: why do shot-putters seem to throw at a significantly lower angle than 45°?
The answer, I later realized, is that if they did aim at 45° they wouldn’t be able to achieve the same launch speed, because of having to work harder against gravity. Hence they are better off throwing at a rather lower angle (which I haven’t time now to calculate for you, sorry). It’s a case of a valid theory not applying in practice!
As for the other Olympic projectiles, the hammer (what a strange name for a ball on a wire) weighs the same as the shot, but throwing it is a test of arm’s length more than strength – and makes shot-putting itself look rather feeble, to my eyes. The javelin has certain aerodynamic properties which, 30 years ago, had to be ‘improved’ to encourage the point to turn down (during flight) and stick in the ground! The discus, I would say, is merely a poorly designed frisbee...
And now back to the standard 400 metre oval track and my opening question: the answer to it is that the distance around the inside edge is barely 398 m. The explanation for this is that runners aren’t expected to stick to the edge (and risk disqualification for stepping on it) but instead are assumed, though not obliged, to follow a path 30 cm out from it, which will be 400 m long. We’re talking about the innermost lane, of course, but the other lanes similarly offer short measure, taking into account their larger radiuses and staggered starts.
This was news to me, when I was exploring the topic after Rio. It rather suggests that whenever records are broken, the distances run (other than in the straight 100 m) may have been slightly curtailed! Actually, what I was hoping to find out in my research was why some runners stay right in the middle of their lanes on the bend. They could easily run 40 cm closer to the inner line: don’t they realize this would save them 2.5 m, in a full circuit? I can only assume that they are being over-cautious, with their eyes on the distant finish rather than on the track immediately in front of them.
There’s even more at stake in races beyond 400 metres, in which everyone is aiming to stay close to the inner edge of the track, because you might find that to overtake the others you need to go as much as two lane-widths out, all round a bend – but this would add 7 m to your path. What a dilemma, if a gold (plated) medal hangs on the result! Anyway, here’s my summing up of the whole Olympic Games: advanced striving...
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