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112
Oct 7, 2004, 6:07 AM
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There have been a lot of questions on the physics of climbing systems on this site. For example cam loading, forces involved in anchors with different angles, and such. I really dig these posts. Please keep them up.
I have heard arguments for the maximum loading that can occur during a climber fall. My friend even said to me “you do the math and tell me”. When I responded, “I don’t know how to model a climbing rope, do you”?
Now I like idealizations and know the “real” world has its nuances, like friction across biners in anchor analysis. I personally neglect it and say the force will be less (worst case scenario). My question is, does anyone know how I can model an idealized climbing rope, or can you point me to some literature. I really would like to do some analytical analysis of climbing systems and the rope portion of the system has got me stumped (I am board right now).
I am looking for a mathematical relation to model a climbing rope. I assume it is like a spring dampening system in car suspension (f = kx – bv, where f = rope generated force, x = rope stretch, and v = climber fall velocity). Is this correct and what would the coefficients k and b typically be (I believe k is dependent on the length of rope “paid out”). I apologize if this is too geeky for rc.com. I don’t mean to upset any of you none physics geeks, but its been bugging me for a while. Any help would be appreciated. Thanks
Ken
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eyecannon
Oct 7, 2004, 6:27 AM
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http://toad.stack.nl/~stilgar/calc.php
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overlord
Oct 7, 2004, 7:26 AM
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yes, i model it as a spring, though one with much dampening (you dont get much up/down swinging when you fall)
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tisar
Oct 7, 2004, 8:10 AM
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Have you seen the fall simulator on the petzl homepage (sport/technique/climbing/falling, I tried to get a direct link but it doesn't work out)?
Perhaps you'll be able to reprogramm it if it doesn't suit your needs.
- Daniel
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robmcc
Oct 7, 2004, 3:05 PM
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In reply to: yes, i model it as a spring, though one with much dampening (you dont get much up/down swinging when you fall)
It doesn't act precisely like one, though. If you're looking for a completely accurate answer, you need to do something different.
The spring "constant" for a rope is not constant.
Rob
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sarcat
Oct 7, 2004, 3:09 PM
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And I was hoping to see a hot babe just wearing a rope strategically placed.
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timstich
Oct 7, 2004, 3:22 PM
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I thought this thread was about how to drape a rope over a naked model. In which case I was going to suggest taking a look at that snake on Natasha Kinski circa the '80s.
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overlord
Oct 7, 2004, 3:22 PM
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In reply to: In reply to: yes, i model it as a spring, though one with much dampening (you dont get much up/down swinging when you fall) It doesn't act precisely like one, though. If you're looking for a completely accurate answer, you need to do something different. The spring "constant" for a rope is not constant. Rob
yes, im aware of that.
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thegreytradster
Oct 7, 2004, 3:25 PM
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In reply to: And I was hoping to see a hot babe just wearing a rope strategically placed.
Yo'll have to find an early 80's Mountan magazine with the Mamut add for that. There was less rope with each issue. :twisted:
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112
Oct 7, 2004, 6:45 PM
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Sorry about the misleading title. hehe too funny
Thank you all for the information. alpnclmbr1, that was exactly what I needed, www.losalamos.org/climb/xRopes.pdf, excelant site. Too bad about the climbers though. :(
Ken
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sarcat
Oct 7, 2004, 7:08 PM
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I moved to Abuqurque in the summer of '96. You even mentioned climbing to anyone and they all looked at you like deer in the headlights about your intelligence. I never really knew what happened in the Sandias. I was a n00b at the time and it all went over my head.
Now I understand.
Thanks for the link.
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eyecannon
Oct 7, 2004, 9:20 PM
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Shoot, you didn't like my link? :(
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dpurf
Oct 7, 2004, 9:27 PM
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go to this site http://www.coreyography.com/
enter into it
click on the B&W and go to the 4th picture
That is how you model a climbing rope :shock: :shock: :D
That is for you Tim :wink:
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wlderdude
Oct 7, 2004, 9:50 PM
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Are you looking to model the DYNAMICS of rope?
Wow, that's pretty tough stuff. None of that stuff will be constant.
Remeber the mechanisms for extenssion. The basic poisson effect thing you get when you pull on anything can be modeled linearly. However, modeling the twisted bundles untwisting under tenssion (the primary contributor) will be tough. A static rope would be much easier.
It may very well be that the b value is so high, the system is overdamped to the point that a simple linear model is as good as a proper one. You will need to take into account the sheath geopetry if you play with b.
On the other hand, it is pretty common to bounce on a long fall. That would be an underdamped system.
Sorry, I probably just confused you more. I know I am.
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rgold
Oct 7, 2004, 10:59 PM
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The losalmos .pdf reference gives what might be called the naive model, in which friction in the lower biners in the system is not accounted for. The model has (I am assured by people who have done or seen tests) proved to be a good approximation of what happens if the leader falls on the first piece with relatively little friction of rope against rock and a static belay. (By the way, the fact that the "spring constant isn't constant" does not seem to be a significant issue, unless you try to calculate it from body weight elongation data, in which the damping effects of the rope construction for low loads appear to produce errors.)
Although there is little difficulty in extending the naive model to account for rope slipping through the belay device, lifting of the belayer, and the effect of screamers, these extensions are not available anywhere I know of as public documents.
A more sophisticated model can be found at here (Thanks to Dirtineye to pointing this out to me.) This one gives a picture of how friction in the system can raise the "naive" fall-factor to a considerably higher value and so engender higher forces than predicted by the naive model. One thing this tells us is that the naive model provides, in many situations, a "best case scenario" if the belay is, for some reason, static. However, unlike the naive model, this one requires a lot of "real life" data in order to even get started, and so is not really the kind of thing you're likely to play around with in your spare moments. The Beal site has a particular instance of the sophisticated model that can be manipulated pretty easily.
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112
Oct 8, 2004, 5:56 AM
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yeah I guess I spoke too soon. I didn't get to read the whole thing, because I was at work. Definetly looking to model rope dynamics, and yes its tough. Was hoping for a simplfied model but not as simple as a spring.
Oh and sorry eyecannon your link was good too. thanks
This last post looks more like it, but I haven't got much time right now. Hey, I am real glad you all posted, makes me feel better about geekin out on this stuff.
Ken
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collegekid
Oct 8, 2004, 6:12 AM
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I'm not sure what sort of damping coefficient and spring constant a rope has. Those could be easily found with some (fun) experiments...
I think the most difficult part to model would be the inelastic range of loading (the most important part). Afterall, the whole point of the simulation would be to see the effects at the extremes, right?
Anyway, I've recently been learning how to program and do differential equation simulations with MATLAB. If the rope was super simple, i.e. only working in the elastic range where it could be treated as a spring/mass/damper system, it'd be pretty easy to model with matlab. You could even have animations associated with the model, so you could watch the effects of changing the mass, damping, and spring properties.
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