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.
Probably my worst memory of around 3rd grade was when I left the swing in such a high and terrifying arc, that I shat myself when I landed. Also my first introduction to Mother's Logic after I explained why I propelled myself into the air: "If the other boys jump off a cliff, are you going to do that too?"
As a kid I once tried to jump off a swing that was much taller than I was used to and instead of landing on my feet I hit flat on my back. Thankfully the ground was relatively soft. That was the day I learned that the phrase "knocked the wind out of me" can be literal: I couldn't breathe right for a few minutes after.
I also did that and had never heard of getting the wind knocked out of you. I thought I had collapsed my lungs and was going to die. I tried to tell a friend but couldn’t talk obviously. So I just sat on a bench to accept my fate. “Mom will be very sad” I remember thinking.
That is very interesting. I had a similar experience when I was I child. I had a toy electronics set and thought of using an outlet instead of the weak battery. Of course I got a nasty shock. I was sure I would die know. I wasn't really scared or upset about that. More about how my parents would feel. It wouldn't be fair that my father had to carry his dead son out of the house so I sat outside against the wall of the house waiting to die. Reading your report makes me wonder if this is just the state of mind of a child.
If one of the snow-buried sidewalk tiles is raised higher than the others; don't push a snow shovel with your hands against your chest, when you pickup speed and then slam to a stop on the raised bit...
I had a similar experience walking over a set of bars (on a hog feeder, not a playground), slipping, and landing right on my diaphragm on top of a bar. It was a small eternity before I could take a breath.
Icy playground. I managed to skid, trip, fly, and then land on the upturned hard-shoe of another kid. He ran off laughing oblivious, I could stand but was unable to breathe properly for a few breaths
When I was 6 or so I did the same off a rope swing hanging from a tree. I guess I was lucky because another kid broke their arm off the same swing not too long afterwards.
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.
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.
I have a rule on myself to stay young. Every time I see a swing rope into water I must do a back flip, and every time I see a 1m diving board, I must do a gainer (run forward, back flip).
I'm 41 now, I'm really curious how old I'll be when I can't do them anymore.
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.
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.
I tore a rotator cuff when convinced that riding a long board down the street while not in a sober state would be easy. Going downhill of not an impressive hill, and the speed wobble on a board I had been on for 3 minutes suggested time to bail. I didn't roll nearly as well as a younger me would have. Nearly a year sounds about right.
Yeah, You're way off your game when you're drunk. I learned that lesson the hard way a few times over in my early 20s (though not so hard that I needed a trip to the hospital).
My friends and I used to do the same thing. Even without drawing your body in while spinning the momentum and height make it possible to pretty easily flip off the swing.
(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).)
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.
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
LOL, by bad, I wanted to say hill instead. For reference, here is a recent photo: https://mcs.ed.cr/wp-content/uploads/2023/03/WhatsApp-Image-... . They had the swing in the hill (yes, now I know the difference) where now there is the second floor of the 3 stories building in the center. So if we jumped too far we end up more or less near the small yellow roofs that I think are a playground.
So no, it was a hill, not a cliff. Not being a native English speaker bites me again XD
I think it was clear that the author wasn't finding the maximum possible distance, only the maximum achievable in a short amount of time.
I say this because his graph of distance only went up with time, whereas we know that eventually it will have to level off as a larger angle won't translate into more distance.
Personally for swing jumps I would only start counting the distance at the furthest point of the swing when it is fully perpendicular, and not from the point of the jump.
Our variation was to jump out at the exact moment the swing started to return at the top of the motion. That way you just stepped out into space in a leisurely manner, and immediately fell straight down into a standing position.
As a swing builder for my kids, I can say that it depends on the rope length... Their swing had 10 meters of rope and you could have easily jumped 10 meters and hurt yourself
Fragonard is knocking on the door (It's in the Wallace Collection in London. Colloquially me and my friends call it "the up-skirter of the 18th century")
> 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.
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.
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.
Isn't the flaw that the posted model assumes that you're essentially bolted to the swing by your ass, and only able to move your legs and upper body, excluding the arms?
Whereas an actual person on a swing has two points of contact along the pendulum: where they sit, but also the point at where their arms are grabbing the rope (or "rod", in this model).
I think what the GP is talking about is a technique where you essentially perform a partial pull-up near the top of the arch.
I think m_1 is roughly your butt, and m_3 is roughly your shoulders. Phi is the angle your body makes wrt the chain. So pulling on the chain changes phi.
I think the idea is that three masses can model a center of mass that may not coincide with the butt as well as moment of inertia — mass, moment of inertia and CM displacement is three parameters, and three point masses gives enough degrees of freedom.
But three point masses cannot model non-rigid-body effects. The offset of CM from butt can vary (by bending one’s knees if nothing else), the CM offset from the swing can vary in two dimensions. I don’t know how much this matters.
A swing (pendulum generally) isn't a harmonic oscillator, except in the limit of small angle. But to your point, that just means the user (subconsciously) adjusts the frequency.
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.
> 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.
An athlete’s maximum forward velocity is when the swing is closest to the ground. If you executed a standing jump at that moment your horizontal velocity remains the same and your vertical velocity comes from your jump height.
I doubt this is better under most conditions, but it might win for some set of constraints.
If you think you can jump up, then you can also jump forward by jumping "up". it's just a matter of what angle the swing is at when you execute the jump.
It's clearly trickier than a standing long jump, but mostly the same.
One way to think about it is that it's similar to jumping from a stationary platform situated on the ground that's continually tilting between 45° backwards and forwards.
The major difference is that even if the stationary platform is at 0° you can still get traction, but a swing will just be pushed back unless you're at the optimal angle, as you correctly point out.
But if you time that jump exactly right the swing will behave like a rigid platform tilted 45° forward.
At which point the proposed Olympic sport is just a standing long jump on a 45° elevated platform, with the added requirement of exquisite timing.
> 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.
I assume this is why GP specified "on the backwards swing." That is (as I understand it) when the swing is behind the crossbar, say at 45⁰ backwards. Then any pushing motion to propel the jumper forward would transfer through the chains to the bar, which is presumably stable.
That said, I'm not sure if this is a good strategy, since you're starting further back. Yes, the world record for a standing jump is over 3 meters, but if you're starting 3 meters back it's not very good.
(I'm assuming the measurement is from the crossbar, not from the origin of the jump, which would be very hard to measure.)
A swing with rigid rods (as opposed to ropes or chains) can potentially spin all the way around its hinges. If you ignore friction and keep adding energy at the right frequency (once it becomes a rotary system instead of a pendulum, it will increase as speed picks up) and jump off at a good ballistic angle, is there really any reason why you can't reach the cold dark voids of outer space?
That has the be the most disappointing rocket launch video ever. Could they really not put a camera on it or show the launch itself for longer than 1.5 seconds? It almost feels like they're hiding something.
You wouldn't be able to get into orbit with a single launch. You could reach escape velocity (assuming you didn't burn up leaving the atmosphere), or a balistic trajectory.
In theory on a perfectly uniform sphere in a vacuum if you stood on a ladder, launched parallel to the ground, and knocked the ladder over on launch, you'd be in a pretty stable orbit with a periapsis of the height of the ladder.
If you didn't knock the ladder, even with a rotating sphere, eventually your orbit would coincide with the ladder again.
(I'm not sure how much frame dragging would cause your orbit to decay and there may be some other issues, like solar pressure)
To get into "stable" orbit (what does stable mean) in the real world you'd need to change your direction once you reached a certain height (typically above the majority of air). A single launch would form an orbit which intersect with your starting point (which even if you started on top of Chimborazo would still have plenty of air resistance)
I think we are just making some different assumptions. TFA also made a whole bunch of unreasonable assumptions, such as maximum time allowed on the swing, a certain height for the beam, no mention of rocket-assist at all...
When you were a kid, did you ever make the swing complete a full revolution? Not while you were sitting on it, pumping it yourself of course. But the headline and proposed question of TFA was simply "How far can you jump from a swing?" So I just made some different assumptions.
Build a swing such that the beam is about 75km off the ground or maybe just a bit more to be safe, with about 75km long suspension tethers for the seat to hang on. Get your rocket-boosted seat going at whatever velocity you need to make a full revolution plus inserting yourself into orbit at around 150km. Once your seat reaches right about the zenith of the swing's circular path, along the line running from you through the beam perpendicular to the tangent of the earth's surface below, you jump. Or "jump", since you'll mostly be upside down and puking into your fantasy tech space suit or whatever you need to get this done.
Since the seat, no longer rocket boosted, will experience a nice amount of drag once it re-enters the atmosphere, you don't even have to worry about colliding with it anymore either.
I don't see what the problem is.
By stable orbit I just mean one that does not suffer atmospheric drag, since you won't have any extra propulsion once you jump. Probably. Who knows. Do whatever you want. Reckoning with other possible sources of orbital decay is too far outside of this nonsense to bother with. :)
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.
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.
My daughter (nine years old at the time) was wearing shorts and went to jump from our backyard swing. She let go of the chain at a good time, but her slightly sweating leg skin stuck to the flexible plastic/rubber swing. She ended up swinging back and fell forward on the backward upswing and would have landed straight on her head ... but she broke her fall with her right arm. She broke both bones in her forearm and had some metal support rods in them for six months while they healed. My wife and I were sitting right by the swing when it happened and could do nothing about it. My daughter quite possibly saved herself from a broken neck.
> There are several papers about the pumping of a swing ³, ⁴, and ⁵ and much more. In this section, I’ll focus in particular on ⁴.
Either those little numbers are references to footnotes, and so are outside of the text flow, either they are part of it. Here the text explicitely use them ("I’ll focus in particular on ⁴") but still put them in superscript with role=doc-noteref, meaning screen readers will skip them.
(I simulated <sup> with unicode chars because HN doesn’t support HTML)
My elementary school responded to the swing jumping threat by putting a fence in the way. But they put it just close enough that you could jump over it if you were really ambitious and get hurt pretty bad if you hesitated.
I still wonder if the move was 100% oversight or if somebody on staff recognized the lesson in it: be good or be good at it.
I was recently on a good empty playground with my kids, and the major factors limiting my swing jump distance were the width of my shoulders and hips! They limit your ability to slip out, especially your shoulders, which you want behind the chains to pump but in front to jump. It's a youngster's game!
I did a lot of stupid things as a child. 80s were definitely different times. Sometimes, I think I am lucky to be alive.
Life is about knowing when and how to take risks. I took unnecessary risks as a child. Plus even if I let my kids go free, I know there will be eager parents willing to call the CPS for the slightest oversight. For better or worse, we live in a very different world.
I have fond memories of having swing jumping competitions as a kid. No major injuries. My parents definitely wouldn't approve, but they also would never know. Your kids will probably still do it given the chance. It's too much fun. From what I remember reading, playgrounds are kind of engineered in a way for encourage kids to take potentially painful risks without severely injuring themselves.
There was a park near my aunt that had a decommissioned delta wing Korean War jet in the sand pit and a caged steel sculpture that doubled as a maze for kids. Nothing of the sort can be found today because of the cultural shift to helicopter parenting and placing zero risk above all else. I'm wondering if kids today grow up without as much of an understanding of their physical boundaries as a result.
Having skimmed the paper...Can you all help me interpret the findings? It appears that the longer you ride the swing, the farther you can jump tending toward infinity? I was looking for some kind of min/max for optimization. What am I missing?
I think that the author felt that question had already been answered sufficiently by other papers -- his citations 1 and 2.
The author was interested in adding pumping to the model, but as far as I can understand the pumping equations only work for low angles, so he restricted his work to those low angles. Within that range, the distance only increases as the angle increases.
Important point I discovered when doing this for years growing up: You need swings with wooden seats. Jumping out of swings with the rubber-sling seats SUCKS. I stopped bothering.
A lot of parks in the city I grew up in replaced wooden structures in parks with steel and rubber. I think the rationale was that wood was hard to maintain and also super dangerous when it turned into a splinter. We're too squishy for wood.
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.