This is going to be a bit of a departure for me, since I have practically no interest in sport. I run, more in the breach than the observance there, enjoyed (field) hockey at school, and was actually good at it, but my involvement in sport is exceedingly limited. Maybe you have to be born into a sporting family or something, as nobody in my nuclear or extended family was remotely into it. However, today I’ve decided to write something on the question of the high jump, as it happens to be relevant to a physical phenomenon.
Earth is of course round, but it isn’t spherical. That is, not only does it have an irregular surface, with valleys and mountains, continents and abyssal plains, but even considered in a “smoothed out” kind of way it is not spherical. Its diameter is forty-three kilometres greater at the Equator than between the poles. There are also some smaller deviations. The Equator itself is slightly elliptical and one pole, I think the North, is further away from the centre than the other. Then there are some even more minor deviations which have led to it being described as “lumpy shaped”. Another description is “pear-shaped”, but both of these can give the impression that it deviates radically from the spherical, which it really doesn’t.
Measuring Earth’s dimensions in terms of the metric system reveals a slightly unusual relationship between the planet and its units, because a metre was initially defined as a ten millionth of the distance between the North Pole and the Equator on a quadrant passing through Calais, if I recall correctly. In any case, this means that a spherical Earth would be exactly forty million metres in circumference, or more sensibly expressed, 40 000 kilometres, and that there are also a mathematically derivable diameter and radius for this ideal shape – Earth “should” be 12 732 kilometres and 395 metres, forty-five centimetres in diameter and 6 366.197724 kilometres in radius. However, this is not the case. It wasn’t, as far as I know, possible to survey that meridian with that accuracy along the whole of its length and in any case land expands and contracts seasonally. The metre is no longer defined in this way but by the distance travelled in vacuo by light in 1/299 792 458 of a second.
In fact, the diameter at the Equator is 12 742 kilometres and between the poles 12 713.6 kilometres. I learnt the first figure as 12 756, so I wonder what’s happened there. Therefore the question arises of how much difference this makes to gravity, to which the answer is quite easy to calculate. Simply divide 12 742 by 12 713.6 and square it. This yields 0.447%, rounded down. It also means that a cubic decimetre of distilled water at 4°C will weigh a kilogramme at the Equator and a little over 1 004 grammes at the poles. Both of these are assumed to be at sea level, and this raises a further complication.
The heights of mountains can be measured in a number of ways, one of which is to measure how high above sea level the peaks are, but another is distance from the centre of the planet, and in this case that second number is more relevant. Although Mount Everest is the highest point on land above sea level, the highest point from Earth’s centre is actually Mount Chimborazo in the Andes, even though it’s only the thirty-ninth highest peak in the Andes. This is, I’m guessing, because Chimborazo is close to the Equator. It’s 6 384.4 kilometres from Earth’s centre, and if you halve our equatorial diameter you get 6 371 kilometres. This suggests that South America straddles a bulge in the Equator, suggesting there’s another one off the east coast of Asia, and this is important because another location, quite a long way off the east coast of Asia is the deepest point on Earth’s solid surface, the Challenger Deep in the Marianas Trench. Hence the Challenger Deep is potentially not the closest location to the centre, and in fact it isn’t. The closest point to Earth’s centre is unsurprisingly in the Arctic Ocean at the Litke Deep, which is 6 351.61 kilometres from it. Taking these two together leads to a difference in gravity, all other things being equal, of one percent. The actual height difference is thirty-two and three-quarters kilometres.
However, all other things are not equal. There are gravitational anomalies. Hudson Bay in Canada has unusually low gravity, for example, because geologically speaking it was recently covered in a thick and heavy ice sheet. Once this melted, just as in Europe, the rocks of the crust beneath began to spring upwards and are therefore less dense than they would be in a tropical area. Parts of the crust have also been squeezed out sideways. This has led to the gravity there being lower, but it isn’t the only factor. Convection currents in the magma mantle underneath the crust also pull the rocks downward in the area. The greatest gravitational anomaly on the planet is in the Indian Ocean south of Sri Lanka, which may be due to the plate carrying the Subcontinent moving particularly fast. There will also inevitably be slight variations in gravity all over the planet due to the
The reason Earth bulges slightly around the Equator is that it’s spinning, which pulls the substance outwards. This rotation also influences how heavy things are, although gravity is not different because of that alone, because of the centrifugal effect. This leads to something called the Eötvös Effect, where objects weigh slightly less if they’re moving east at a constant velocity relative to Earth’s surface than they are if they’re moving west. However, even a stationary object feels the centrifugal effect, which is unsurprisingly most pronounced at the Equator. A line graph for this effect on a ten kilogramme mass looks like this:
This is at the Equator. A newton amounts to about a hundred grammes if it’s thought of as a unit of weight. Added to the effect of gravity, it means that gravity combined with rotation will reduce the weight of an object by 0.9% at the Equator at sea level assuming no gravitational anomaly compared to the North Pole at sea level.
Now I’ve done all that, I’m finally ready to consider the male high jump record. A few preliminary remarks are in order here. One is that I’m aware that both the land and water speed records went from dramatic improvements to increasingly small incremental improvements as they approached the sound barrier, but this can be put down to technological progress. It isn’t so clear that this would, at least legally, be the case with human athletic records, although it’s conceivable that training or selection of athletes might improve. I’ve chosen the male high jump records because they’re higher than the female ones, which would magnify any observed difference. My question, then, is this: is there any discernible difference between high jump records achieved at high and low latitudes? That is, is it easier to jump near the Equator because of being assisted by the lower gravity and the rotation of the planet? Another question, which I think is probably exceedingly hard to answer, is: is it easier to jump if one does so to the east? In order to answer that, I’d need to know the minutiæ of the sites where the records were made. There is another factor which acts against the altitude issue – there is less oxygen higher up. This will be further confounded by oxygen doping, and would also be by the presumably illegal practice of using drugs to promote the production of red blood corpuscles or receiving a self transfusion of banked blood.
Anyway, here is a map of Olympic sites since 1896:
(Unfortunately this is Mercator but I have shifted it to put the Pacific in the middle). It’s interesting to note how uneven the distribution is. They had apparently never been held in the Middle East, South America or Afrika up to whenever this was compiled, but they took place in Rio de Janeiro in 2016. The closest to the Equator they’ve ever been held is Mexico City in 1968, and the furthest seems to be Helsinki. Then there’s the list of progressive men’s high jump records, in teeny-tiny writing:
This is from here.
What one could expect would be that the same person could jump two metres at the North Pole but 2.02 metres at sea level at the Equator. Another problem is that the above list doesn’t seem to correspond to Olympic high jump records. Interestingly, though, all of these records are sufficiently close to each other to be influenced by such a change in gravitational strength in the limiting cases. The biggest difference between latitudes of successive records is Malmö and Los Angeles, which is twenty-one and a half degrees. The difference in those results is 0.9%, and since the difference is smaller than the extremes, it wouldn’t’ve meant the record would not have been broken if the two were swapped, all other things being equal.
Unfortunately, therefore, this is inconclusive because it isn’t possible to isolate the factors involved sufficiently, but if it ever happens that there is a less than one percent difference in records, gravity and the centrifugal effect will be at least approaching significance. The question arises of how close or far from the Equator it’s sensible to hold the Summer Olympics or high jump competitions. There seems to be a series of sports zones determined partly by latitude, so it’s impossible to compare like with like, and altitude could be expected to make a bigger difference.
A Box Of Chocolates 