[HN Gopher] How far can you jump from a swing?
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How far can you jump from a swing?
Author : alexmolas
Score : 90 points
Date : 2023-08-29 20:26 UTC (2 hours ago)
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| amluto wrote:
| > The paper proceeds by assuming the swinger pumps the swing by
| forcing [sinusoidal pumping].
|
| I doubt that's particularly close to optimal. I've generally
| assumed, without proof, that the optimal pumping strategy is to
| change one's position abruptly at the highest point. The
| intuition is that this delivers all of the fixed amount of
| available angular displacement at the position in which it adds
| the most energy to the system.
| version_five wrote:
| There could be some dynamics I'm overlooking that make your
| theory work. Normally with a resonant system, energy
| essentially gets added near the resonant frequency and it acts
| as a bandpass filter for everything else, so my guess is it's
| only the first harmonic of whatever jerking motion you try
| that's actually contributing energy.
|
| As I say, that's really for a simple oscillator, there may be
| something about the swing system that gives it an impulse
| response that matches what you are describing.
|
| Edit: I wonder if the abrupt change is better simply because it
| lets a person maximize the amplitude of the push they give, so
| more energy goes in at the first harmonic anyway. That's
| probably the explanation.
| amluto wrote:
| But the process isn't energy-limited -- it's displacement
| limited. Your arms have a certain length, your body has a
| certain mass distribution, and you can force the _angle_ by a
| certain amount.
|
| So, if you want a heuristic, integrate pumping displacement
| times swing position, where the pumping displacement has a
| fixed maximum. The result is maximized by a square wave.
| helf wrote:
| [dead]
| thedanbob wrote:
| As an avid swing jumper in my youth I can say with some certainty
| that 3m is closer to the mark than 2. Also, my brother and I
| devised a variant that would work for the winter Olympics: jump
| at the lowest point of the swing for maximum velocity and slide
| over the snow.
| dgfitz wrote:
| I agree, and in my experience the taller the swing in terms of
| rope/chain length, the further I could jump.
| estebarb wrote:
| I came to say too that 3m is more realistic, from what I did in
| school. Also, around 1-2m is possible if you jump backwards,
| but you may end up visiting the hospital as well.
|
| At my school the swing was near a clift, so sometimes you were
| able to combine swing jump, ski jump and hospital visit with a
| single jump. Good times XD
| amelius wrote:
| Arbitrarily far if you jump if the swing is furthest back.
| amluto wrote:
| That's a good point. I assume the author meant jumping by
| ejecting oneself with no momentum transfer. But winning a
| competition by following the unstated rules isn't always the
| right choice :)
|
| You can also jump arbitrarily far by jumping off the swing at
| its lowest point.
| checkyoursudo wrote:
| Alternatively, infinitely far (into stable orbit) if the swing
| is tall enough and you have enough momentum.
| _fs wrote:
| I was curious, so chat GPT to the rescue:
|
| you would need a swing that is bigger than the Earth itself.
| The reason is that the gravitational force of the Earth
| decreases with distance, so as you go higher, the force
| pulling you back becomes weaker. This means that your
| potential energy increases as you go higher. To reach a
| certain height, you need to have enough kinetic energy to
| overcome the potential energy at that height. The kinetic
| energy depends on your mass and your speed squared, while the
| potential energy depends on your mass and the gravitational
| constant and the mass and radius of the Earth. If we assume
| that your mass is 70 kg and your speed is 3.07 km/s (the
| orbital speed at geostationary orbit), then we can calculate
| how high you can go by equating your kinetic energy and
| potential energy
|
| Therefore, to reach geostationary orbit by jumping off a
| swing, you would need a swing that is longer than 32.63
| million meters (the difference between geostationary orbit
| altitude and your maximum height). This is more than five
| times longer than the diameter of the Earth (12.74 million
| meters). Such a swing would not be possible to build or use.
|
| > If it was possible to build, how long would you have to
| pump the swing before you could jump off into orbit
|
| That is a very hypothetical question, since it is impossible
| to build such a long swing or pump it fast enough to reach
| orbital speed. However, for the sake of curiosity, let us
| assume that you have a swing that is 32.63 million meters
| long, and you can pump it with the same frequency and phase
| as the natural frequency of the swing. In other words, you
| can apply the maximum possible force to the swing at every
| turn.
|
| This means that one complete cycle of the swing takes about
| 3.17 hours. Therefore, to increase your speed by 3.07 km/s
| (the orbital speed at geostationary orbit), you would need to
| pump the swing for half a cycle, or about 1.59 hours.
|
| However, this is a very optimistic estimate, because it
| ignores several factors that would make it harder to pump the
| swing, such as air resistance, friction, and the fact that
| you cannot apply a constant force throughout the swing. In
| reality, you would need much more time and energy to pump the
| swing to such a high speed.
| bhaney wrote:
| > 32.63 million meters [...] is more than five times longer
| than the diameter of the Earth (12.74 million meters)
|
| These walls of generated bullshit should just be considered
| spam at this point.
| amluto wrote:
| Even ignoring the egregiously nonsensical numbers:
|
| > The reason is that the gravitational force of the Earth
| decreases with distance, so as you go higher, the force
| pulling you back becomes weaker. This means that your
| potential energy increases as you go higher.
|
| Saying "this means that" does not make it in any respect
| correct.
| brianpan wrote:
| Not yet!
|
| https://www.youtube.com/watch?v=M_50TM3OeEw
| vvpan wrote:
| [flagged]
| micw wrote:
| Empirical determined short answer: way too far. I tried this
| years ago when I was with my kids on a playground and broke me a
| toe that way.
| avar wrote:
| The proposed Olympic sport seems like an elaborate reinvention of
| the standing long jump [1], just executed at an angle, and
| standing on a moving, unstable and elevated platform.
|
| Clearly the author expects (and the interesting mathematical
| problem is) that the athletes would restrict themselves to the
| swing itself to gain momentum.
|
| But nothing about the proposed rules prevents one from standing
| on the swing, and jumping forward at an angle on the backwards
| swing.
|
| 1. https://en.wikipedia.org/wiki/Standing_long_jump
| amluto wrote:
| > But nothing about the proposed rules prevents one from
| standing on the swing, and jumping forward at an angle on the
| backwards swing.
|
| That doesn't sound like a very good strategy. The athlete is
| likely much heavier than the swing, and applying a backwards
| force to the swing will mostly just push the swing back.
|
| As mentioned elsewhere in the comments, one strategy is to jump
| off the swing at the farthest back point (so the jumping force
| is mostly balanced by the chain). Another is to jump _up_ while
| the swing is moving forward. Some combination should work too.
| seventytwo wrote:
| Killjoy
| [deleted]
| dang wrote:
| Recent and related:
|
| _How far can you jump from a swing?_ -
| https://news.ycombinator.com/item?id=37255330 - Aug 2023 (28
| comments)
|
| (I invited the author to repost it because while that thread got
| some comments, it never made the front page, and it seemed like a
| good candidate for the SCP
| (https://news.ycombinator.com/item?id=26998308).)
| kirse wrote:
| I had a friend in 2nd or 3rd grade who would stand on the swing
| seat to use his legs to assist with gaining height and then
| eventually do a backflip with the chains near parallel.
|
| Of course we always begged him to show off this trick every
| recess. Looking back now I have no idea where he got the idea or
| how he practiced his way into it, but he was always a playground
| daredevil who routinely made teachers come sprinting over the
| tarmac.
|
| I will say you knew you jumped far when that playground mulch
| embedded itself in your hands and knees.
| chowells wrote:
| When I was a kid, lots of us learned to do a backflip off the
| swing without even bothering to stand up. It isn't that hard to
| just lean back at the apex, roll out of the seat, and land on
| your feet. I mean... It's not that hard when you're small,
| light weight, and heal quickly.
| lampshades wrote:
| [dead]
| pak9rabid wrote:
| Heh, I remember a group of us doing that as well. Also "penny
| drops" off the monkey bars, where you'd hang upside-down with
| your legs, swing back and forth, release and essentially do a
| flip and land on your feet. God we were fearless back in the
| day.
| Fricken wrote:
| We called those "baby drops", and flipping back off the swing
| seat as it comes forward we called "cherry pickers". I'm 46
| now, I can still do both. Once you've learned them, they're
| easy.
| dylan604 wrote:
| can and do are two different things. things heal a lot
| faster when the landings are wrong in playground days than
| they do at 46. i have personal experience with the healing
| slower bit if not from a cherry picker move.
| lampshades wrote:
| [dead]
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