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bill413
Feb 2, 2010, 8:58 PM
Post #101 of 107
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ptlong wrote: kennoyce wrote: I'm not reading all of this, but I just wanted to let you know that it is incredibly easy to get an infinite fall factor in normal climbing situations. Lets just say you fall, the rope contacts a sharp part of the rock and is severed. At this point you have zero rope to absorb the impact of the fall, so no matter how far you fall, the fall length divided by zero is infinity. There you go, infinite fall factor. Clever, Ken. But it doesn't work. In the limit as the fall factor becomes infinite the tension in the rope also is infinite. But that won't happen in your example. How far above your last piece of pro (numerator of the fall factor ratio) are you when you have no protection? It's undefined, as is the fall factor.
False. FF = distance fallen / (effective) rope out.
distance above your last piece of pro contributes to the distance fallen, but is not the sole determinant (5 feet above pro with rope taut yields 10foot fall, 5 feet above pro with 5 feet of slack = 15 foot fall).
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ptlong
Feb 2, 2010, 9:24 PM
Post #102 of 107
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bill413 wrote: ptlong wrote: kennoyce wrote: I'm not reading all of this, but I just wanted to let you know that it is incredibly easy to get an infinite fall factor in normal climbing situations. Lets just say you fall, the rope contacts a sharp part of the rock and is severed. At this point you have zero rope to absorb the impact of the fall, so no matter how far you fall, the fall length divided by zero is infinity. There you go, infinite fall factor. Clever, Ken. But it doesn't work. In the limit as the fall factor becomes infinite the tension in the rope also is infinite. But that won't happen in your example. How far above your last piece of pro (numerator of the fall factor ratio) are you when you have no protection? It's undefined, as is the fall factor. False. FF = distance fallen / (effective) rope out. distance above your last piece of pro contributes to the distance fallen, but is not the sole determinant (5 feet above pro with rope taut yields 10foot fall, 5 feet above pro with 5 feet of slack = 15 foot fall).
Oops, you're right, I did get it wrong. But now so have you. It isn't the distance fallen, it's the distance fallen before the rope begins to stretch. Otherwise you'd have to know the rope characteristics in order to calculate the fall factor.
The rope never stretches in Ken's example. So the fall factor is undefined.
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kennoyce
Feb 2, 2010, 10:27 PM
Post #103 of 107
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okay, maybe my example doesn't give an infinite fall factor, but here is an example that does. All you have to do is climb with a rope made from a material with a negative youngs modulus, any fall on this rope would give you an infinite fall factor.
edit to add: even a rope with a youngs modulus of zero would give you an infinite fall factor regardless of fall length.
(This post was edited by kennoyce on Feb 2, 2010, 11:08 PM)
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ptlong
Feb 3, 2010, 12:00 AM
Post #104 of 107
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kennoyce wrote: okay, maybe my example doesn't give an infinite fall factor, but here is an example that does. All you have to do is climb with a rope made from a material with a negative youngs modulus, any fall on this rope would give you an infinite fall factor. edit to add: even a rope with a youngs modulus of zero would give you an infinite fall factor regardless of fall length.
Ken, I like your "thinking outside the box" style. But the usual definition of fall factor does not include the distance fallen after the rope begins to stretch.
The discussion about actual infinity was a lot more interesting.
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knudenoggin
Feb 4, 2010, 12:04 AM
Post #105 of 107
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rgold wrote: guangzhou wrote: A well crafted answer until your last paragraph. Last couple sentences really. Yes, I do start heading down the road to incoherence at the end, although I thank Jay for standing up for me.
do w/o the gratuitous full-post copy. And which goes against your
own advice to put aside "degrees or not, we all make mistakes,
so I'd hold on to your scepticism and judge what you read by how
much sense it makes rather than who said it, no matter how
purportedly qualified they may be."
I see a question in it at least that has bothered me, in that
FF has been touted as THE determining factor in impact force
to the exclusion of fallen-upon material. E.g., that a big
whipper on low-elongation rope would be no worse than some
shorter fall of the same FF (though worse than on climbing rope,
for sure). Now, RGold's above assertion
contradicts that; and I think then that he should throw in some
significant discount towards the FF calculation for the rather static
webbing (dogbone duobled/trebled material, even?), as is implied
for the pair of (not perfectly static) 'biners.
*kN*
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rgold
Feb 4, 2010, 2:22 AM
Post #106 of 107
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*KN* wrote: I see a question in it at least that has bothered me, in that FF has been touted as THE determining factor in impact force to the exclusion of fallen-upon material.
The fall factor is obtained by assuming that the material behaves, during extension like an ideal elastic material, meaning that it obeys Hooke's Law. This approximation isn't too bad for nylon climbing ropes. It is worse for other materials (unless, somewhat paradoxically, they stretch so little that Hooke's Law is a good first-order approximation).
More accurate models assume the presence of viscous damping, although there is, as far as I know no theoretical basis for these assumptions. The "right" configuration of springs and dashpots appears to behave in the same way as actual ropes.
*KN* wrote: ... E.g., that a big whipper on low-elongation rope would be no worse than some shorter fall of the same FF (though worse than on climbing rope, for sure).
To the extent that internal frictional forces and/or frictional forces between the rope, the rock, and the protections system serve to dissipate fall energy, the actual height of the fall will matter in the final determination of maximum impact load, even if the rope is perfectly elastic. The model leading to the fall factor concept is the simplest in a chain of approximations.
*KN* wrote: I think then that he should throw in some significant discount towards the FF calculation for the rather static webbing (dogbone duobled/trebled material, even?), as is implied for the pair of (not perfectly static) 'biners.
Congratulations: I think you managed to surpass my not inconsiderable level of incoherence with this last remark. In any case, the original subject was about how fall factors greater than two can occur. You are complaining that my response doesn't address issues that were never part of the discussion, which could have gone on more or less as it did even if the fall factor had nothing to do with maximum impact.
In response to another question, I posted some references about rope behavior on Super Topo, which may relieve some of your discomfort with the simple model.
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jt512
Feb 4, 2010, 3:41 AM
Post #107 of 107
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rgold wrote: *KN* wrote: I think then that he should throw in some significant discount towards the FF calculation for the rather static webbing (dogbone duobled/trebled material, even?), as is implied for the pair of (not perfectly static) 'biners. Congratulations: I think you managed to surpass my not inconsiderable level of incoherence with this last remark.
He has, indeed, but even his last remark failed to attain complete incomprehensibility; although, to understand it, it helps to have read hundreds of posts by David Kastrup on rec.climbing. They're still accessible via groups.google.com, if you need a refresher.
Jay
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