14 ms·

So I freely admit to not being a mathematician, however, I am a person who used to jump off swings a LOT, and indeed used to have informal contests with my frie

So I freely admit to not being a mathematician, however, I am a person who used to jump off swings a LOT, and indeed used to have informal contests with my friends about who could make the most reckless and dangerously long jumps from a swing with little thought to life or limb (we were teenage boys). So having said that, I’m not sure how the OP calculated the results but 2m is far too small for a max distance. When we used to jump from the swing our goal was to always jump so far we made it out of the “swing area” where there was wood chippings on the ground and onto the grass beyond. Making to the grass was our bare minimum for a “good jump” So I would say the minimum for a “good jump” us would be 3 meters, and anything above that would be reaching the standards of recklessness which got us a good teenage buzz going on.

blitzar 3y ago
> The original maximum distance estimation was around.... According to my numbers, you wouldn’t be able to beat the 2-meter mark. 1m is a comedy level. 2m straight up rookie numbers. Source: was a child with access to a swing.
- Someone 3y ago
  On a typical ‘real’ swing, 1m is falling of the swing backwards at its highest point.
alexmolas 3y ago
Notice that the amount of time you can spend on the swing is limited to 20 seconds. Of course with more time you can achieve much higher distances. The analysis is focused on small times/small angles approximation
Someone 3y ago
AFAICT, the model used doesn’t ever allow the jumper to push against the ground. Since it also limits the time spent getting up to speed, that limits the amount of energy one can load into the system. They also use l1 (distance between top of swing and seat) = 2m. I think that’s way too short for a swing. The modeled height of the seat from the ground is also small, at 40cm. The final expression isn’t simple, but even keeping that height the same, the first term is l1 sin Φ, and that grows with l1. I didn’t check, but suspect v also grows if l1 increases. If so, the other terms also go up if l1 increases. They also don’t model what Olympic swingers would do. I expect they would start by standing on the swing, grabbing the ropes high, and pulling hard, bringing their lower body almost horizontal, at a height at least a meter above the starting position, and then almost let go of the ropes, dropping down on the falling seat. Just before jump-off, they might even try to hang below the seat as far as possible, like they do in ring or on the horizontal bar in gymnastics.
- alexmolas 3y ago
  Notice that \phi(t) grows slower in time as l1 grows. So it's not trivial to know how the maximum distance changes as l1 grows.

blitzar 3y ago

> The original maximum distance estimation was around.... According to my numbers, you wouldn’t be able to beat the 2-meter mark. 1m is a comedy level. 2m straight up rookie numbers. Source: was a child with access to a swing.

Someone 3y ago
On a typical ‘real’ swing, 1m is falling of the swing backwards at its highest point.

alexmolas 3y ago

Notice that the amount of time you can spend on the swing is limited to 20 seconds. Of course with more time you can achieve much higher distances. The analysis is focused on small times/small angles approximation

Someone 3y ago

AFAICT, the model used doesn’t ever allow the jumper to push against the ground. Since it also limits the time spent getting up to speed, that limits the amount of energy one can load into the system. They also use l1 (distance between top of swing and seat) = 2m. I think that’s way too short for a swing. The modeled height of the seat from the ground is also small, at 40cm. The final expression isn’t simple, but even keeping that height the same, the first term is l1 sin Φ, and that grows with l1. I didn’t check, but suspect v also grows if l1 increases. If so, the other terms also go up if l1 increases. They also don’t model what Olympic swingers would do. I expect they would start by standing on the swing, grabbing the ropes high, and pulling hard, bringing their lower body almost horizontal, at a height at least a meter above the starting position, and then almost let go of the ropes, dropping down on the falling seat. Just before jump-off, they might even try to hang below the seat as far as possible, like they do in ring or on the horizontal bar in gymnastics.

alexmolas 3y ago
Notice that \phi(t) grows slower in time as l1 grows. So it's not trivial to know how the maximum distance changes as l1 grows.