How far can you jump from a swing?
alexmolas.com
alexmolas.com
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.
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.
It’s entirely incorrect but it keeps life fun!
Fortunately the breath eventually comes back…
Thanks for reminding me of this memory :)
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).)
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
So no, it was a hill, not a cliff. Not being a native English speaker bites me again XD
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.
This does look pretty close to 3 meters doesn't it? https://www.youtube.com/shorts/KOaT850cArE
Now who can jump the furthest head first over that line onto the concrete.
* back in my day we didnt have gravel or mulch under or around the swing, just concrete / ashphalt
Stiff legged.
On asphalt.
How we didn't die, I'll never know.
Again. Death and dismemberment should've been the thing.
https://www.wallacecollection.org/explore/collection/search-...
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.
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.
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.
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 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.
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.
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.
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.
I doubt this is better under most conditions, but it might win for some set of constraints.
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.)
tldw: it is.
You can also jump arbitrarily far by jumping off the swing at its lowest point.
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)
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. :)
> 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)
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’d never let my kids do that though.
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.
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.
Someone can correct me if I've misunderstood.