People usually laugh at me when I tell them that my athletic event of choice in school was the high jump. This is probably because I don't look very athletic and probably more so because I am rather short (five feet six and half inches - at my height every half inch counts). Anyway, If I had any success in the event, it was - shall we say - measured. But I was really enamored by the sport and followed it long after my athletic career, such as it was, came to an end.
Human Jumpers
The high jump is interesting as an athletic event as the methods used have evolved quite a bit over time. These are the techniques I am familiar with:
i) Scissors Watching it makes the name evident. This is what I used for competing back in the 1980s. I found out later that it was quite primitive even at that date.
ii) Eastern cut-off A technique that came after scissors, that some of my competitors used.
iii) Straddle Another technique, which I tried, but could never master. It was fun to clear hedges this way and roll on the grass, though. (I did not give the Western roll its own category as it seems to be related to the straddle, but no one seems to agree on precisely what form it takes).
iv) Fosbury Flop In my opinion one of the coolest and most counterintuitive - why would you jump with your back to the bar? - techniques in all of sport. Invented by Dick Fosbury - he passed away in March 2023; you can hear him talk about it in the linked video - and used by him to win the gold medal in the 1968 Mexico Olympics.
All these methods evolved basically to tackle a physics (biomechanics?) problem - how to cross the bar while keeping the center of mass of the body as low as possible. Fosbury's method, in a supremely elegant demonstration of the laws of physics, showed how to clear the bar while letting the body's center of mass pass underneath it. It accomplished this by letting all body parts that are not clearing the bar at any moment hang lower.
Javier Sotomayor's 1993 record jump of 8 feet, 1/4 inch, and Stefka Kostadinova's 1987 world record (6 feet 10 1/4 inch) are still standing today. Sotomayor is probably the greatest high jumper of all time yet. Over the years I have enjoyed watching Mutaz Essa Barshim, and Gianmarco Tamberi (you can watch them share Olympic gold in the link). On the women's side Yaroslava Mahuchikh is one of the top jumpers currently; she won at the recent World Championships in Budapest.
Non-human jumpers
How does jumping ability vary with mass of the jumper? To answer this question we can explore jumping ability in the animal and insect world. D'Arcy Wentworth Thompson was perhaps the first to give a relevant scaling argument. As a first approximation, he found that the height to which a live organism can jump is independent of its mass.
Is this contention borne out by the data? Over a survey of the insect and animal kingdoms a mass variation of eight orders of magnitude (10^8) was considered and a jumping height variation of a factor of 3 was found. This is a rough but fair confirmation of Thompson's scaling law.
The data may be tweaked to look more dramatic if we compare the height jumped to the height of the animal itself: A human being can jump roughly her/his/their own height; a flea can jump twenty times its own height.
The effects of gravity actually become less dramatic at low mass - although the acceleration of an object due to gravity is independent of its mass, see the famous experiment on the moon which showed that a feather and a hammer reach the ground at the same time. But of course, on the moon the effect of air resistance is negligible.
On earth, air resistance is not negligible. The balance of the forces of gravity and air resistance sets the terminal velocity of a falling object. This velocity is proportional to its mass. This means that for an insect with low mass the terminal velocity in a fall is small and the insect is not likely to sustain much damage to its body when it lands (does it have enough strength, one may ask, to take the fall? While mass decreases with volume, strength decreases with cross-sectional area, meaning as we lower size, strength decreases slower than mass. So the answer is yes, it does. Example: An ant can lift upto fifty times its own weight). It can basically waft down on the breeze from a large height.
It is interesting that at these scales, for small organisms, not gravity, but surface tension, becomes the killer. This force is so large, it allows insects to walk across the surface of water. By the same argument, a liquid surface can trap insects (if their legs become wet, or while they are trying to drink from it) and drown them, or not allow them to leave (until the water evaporates, by which time they may have starved).
Comments