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jt512
Mar 24, 2010, 3:18 AM
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bhp wrote: He's saying that climbing ropes don't behave like ideal springs.
Yeah, suuure he is.
In reply to: In an elementary theoretical basis, the force exerted by/on a rope should be proportional to the percentage of stretch. In climbing ropes, and most other systems, really, this isn't exactly true. The stress/strain function is not linear.
However, that's not the claim he made. He said, "The coefficient of elasticity changes as the weight on the rope changes."
Jay
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USnavy
Mar 24, 2010, 6:34 AM
Post #27 of 45
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jt512 wrote: USnavy wrote: The coefficient of elasticity changes as the weight on the rope changes. Huh?
(This post was edited by USnavy on Mar 24, 2010, 6:36 AM)
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ptlong
Mar 24, 2010, 5:48 PM
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USnavy wrote: Modulus of elasticity, sorry. I have no idea where I got coefficient, its been a long day. Anyway I was saying that the elongation properties of a rope are not linear. Say placing 50 kg on a rope yields a stretch of 5%. Doubling that number to 100 kg will not yield a stretch of 10%. When you add a second identical rope the force created by the climber is shared between each rope. However the impact force is not doubled and the dynamic elongation is not halved because the elongation properties of the rope are not linear and adding a second rope to the system changes the properties.
Huh? Even if the stress/strain curves were perfectly linear the impact force would not be doubled and the elongation would not be halved. Nice try.
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USnavy
Mar 24, 2010, 5:54 PM
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ptlong wrote: USnavy wrote: Modulus of elasticity, sorry. I have no idea where I got coefficient, its been a long day. Anyway I was saying that the elongation properties of a rope are not linear. Say placing 50 kg on a rope yields a stretch of 5%. Doubling that number to 100 kg will not yield a stretch of 10%. When you add a second identical rope the force created by the climber is shared between each rope. However the impact force is not doubled and the dynamic elongation is not halved because the elongation properties of the rope are not linear and adding a second rope to the system changes the properties. Huh? Even if the stress/strain curves were perfectly linear the impact force would not be doubled and the elongation would not be halved. Nice try.
(This post was edited by USnavy on Mar 24, 2010, 5:56 PM)
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jt512
Mar 24, 2010, 5:58 PM
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USnavy wrote: ptlong wrote: USnavy wrote: Modulus of elasticity, sorry. I have no idea where I got coefficient, its been a long day. Anyway I was saying that the elongation properties of a rope are not linear. Say placing 50 kg on a rope yields a stretch of 5%. Doubling that number to 100 kg will not yield a stretch of 10%. When you add a second identical rope the force created by the climber is shared between each rope. However the impact force is not doubled and the dynamic elongation is not halved because the elongation properties of the rope are not linear and adding a second rope to the system changes the properties. Huh? Even if the stress/strain curves were perfectly linear the impact force would not be doubled and the elongation would not be halved. Nice try. Please carefully reread what you quoted then slap yourself in the face. I said it would NOT be doubled or halved. Nice try.
Apparently you have trouble understanding conditional statements.
Jay
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adatesman
Mar 24, 2010, 6:06 PM
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ptlong
Mar 24, 2010, 6:10 PM
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USnavy wrote: ptlong wrote: USnavy wrote: Modulus of elasticity, sorry. I have no idea where I got coefficient, its been a long day. Anyway I was saying that the elongation properties of a rope are not linear. Say placing 50 kg on a rope yields a stretch of 5%. Doubling that number to 100 kg will not yield a stretch of 10%. When you add a second identical rope the force created by the climber is shared between each rope. However the impact force is not doubled and the dynamic elongation is not halved because the elongation properties of the rope are not linear and adding a second rope to the system changes the properties. Huh? Even if the stress/strain curves were perfectly linear the impact force would not be doubled and the elongation would not be halved. Nice try. Please carefully reread what you quoted then slap yourself in the face. I said it would NOT be doubled or halved. Nice try.
The REASON they are NOT doubled/halved is what I'm saying you have wrong.
Take the simplest case, two identical ideal springs in parallel. Now do a UIAA drop test. The increase in maximum impact force is what? (Hint: it isn't double).
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trenchdigger
Mar 24, 2010, 6:26 PM
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jt512 wrote: northcave wrote: USnavy wrote: Lets look at the Beal Joker. When that rope is used as a single it has an impact force of 8.2 kN. When used as a twin it has an impact force of 9.5 kN, an increase of only 14%. True but the stress on the rope is halved even if the impact force on the person is more. Apparently, the tension in the rope isn't quite halved, since 9.5 / 2 > 8.2 / 2 . Jay
This is a big oversimplified since (roughly) T = w + sqrt(w^2 + 2*k*w*FF).
where:
T=impact force
w=weight of climber
k=spring constant
FF=fall factor
The point, however, is valid. The spring constant of a rope does increase with rope stretch. I would venture to guess that the increase in the spring constant with stretch is also non-linear.
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cracklover
Mar 24, 2010, 7:02 PM
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ptlong wrote: USnavy wrote: ptlong wrote: USnavy wrote: Modulus of elasticity, sorry. I have no idea where I got coefficient, its been a long day. Anyway I was saying that the elongation properties of a rope are not linear. Say placing 50 kg on a rope yields a stretch of 5%. Doubling that number to 100 kg will not yield a stretch of 10%. When you add a second identical rope the force created by the climber is shared between each rope. However the impact force is not doubled and the dynamic elongation is not halved because the elongation properties of the rope are not linear and adding a second rope to the system changes the properties. Huh? Even if the stress/strain curves were perfectly linear the impact force would not be doubled and the elongation would not be halved. Nice try. Please carefully reread what you quoted then slap yourself in the face. I said it would NOT be doubled or halved. Nice try. The REASON they are NOT doubled/halved is what I'm saying you have wrong. Take the simplest case, two identical ideal springs in parallel. Now do a UIAA drop test. The increase in maximum impact force is what? (Hint: it isn't double).
I can't tell if USNavy doesn't understand what he's talking about or not. He's just not speaking (typing) very clearly.
Anyway, to answer your question - you'd have to solve for the new modulus given by the two springs working in parallel, and then plug that into the standard equations, with each spring getting half the load.
I'll leave solving the problem itself as an exercise for the reader.
GO
(edited typo)
(This post was edited by cracklover on Mar 24, 2010, 7:03 PM)
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ptlong
Mar 24, 2010, 7:37 PM
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cracklover wrote: I can't tell if USNavy doesn't understand what he's talking about or not. He's just not speaking (typing) very clearly.
That's always a possibility. But I'd put my money on the former.
In reply to: Anyway, to answer your question - you'd have to solve for the new modulus given by the two springs working in parallel, and then plug that into the standard equations, with each spring getting half the load.
Two identical springs in parallel have twice the stiffness (modulus). Using the Wexler equation posted by trenchdigger for a UIAA drop (about 1.8 factor) you get an increase in max impact of about 40%.
Now the reason that real ropes (e.g. those Beal numbers posted above) don't jive with the 40% number is partly due to what USnavy is talking about. But only partly.
(edit:grammar)
(This post was edited by ptlong on Mar 24, 2010, 7:40 PM)
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Rudmin
Mar 24, 2010, 7:40 PM
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USnavy wrote: That's not true. Yes adding a second rope will increase the impact factor but it wont be double. The coefficient of elasticity changes as the weight on the rope changes. Generally adding a second rope will increase the impact factor by about 20%. But that number can very quite a bit. Lets look at the Beal Joker. When that rope is used as a single it has an impact force of 8.2 kN. When used as a twin it has an impact force of 9.5 kN, an increase of only 14%.
Actually that's %16%
(This post was edited by Rudmin on Mar 24, 2010, 7:46 PM)
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jt512
Mar 24, 2010, 7:45 PM
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Rudmin wrote: USnavy wrote: That's not true. Yes adding a second rope will increase the impact factor but it wont be double. The coefficient of elasticity changes as the weight on the rope changes. Generally adding a second rope will increase the impact factor by about 20%. But that number can very quite a bit. Lets look at the Beal Joker. When that rope is used as a single it has an impact force of 8.2 kN. When used as a twin it has an impact force of 9.5 kN, an increase of only 14%. Actually that's %16
Maybe edit it again, and put the percent sign after the number.
Jay
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cracklover
Mar 24, 2010, 8:06 PM
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ptlong wrote: cracklover wrote: I can't tell if USNavy doesn't understand what he's talking about or not. He's just not speaking (typing) very clearly. That's always a possibility. But I'd put my money on the former. In reply to: Anyway, to answer your question - you'd have to solve for the new modulus given by the two springs working in parallel, and then plug that into the standard equations, with each spring getting half the load. Two identical springs in parallel have twice the stiffness (modulus). Using the Wexler equation posted by trenchdigger for a UIAA drop (about 1.8 factor) you get an increase in max impact of about 40%.
Actually, an easier way to solve it than what I posted above is simply to think of the two ropes independently, with each holding half the force. Then the modulus doesn't need to be changed - you just add up the force on the two ropes, each with half the weight of the climber.
Either way, the answer (roughly 40% increase) is the same.
In reply to: Now the reason that real ropes (e.g. those Beal numbers posted above) don't jive with the 40% number is partly due to what USnavy is talking about. But only partly.
What exactly are you referring to?
GO
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jt512
Mar 24, 2010, 8:14 PM
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cracklover wrote: ptlong wrote: Now the reason that real ropes (e.g. those Beal numbers posted above) don't jive with the 40% number is partly due to what USnavy is talking about. But only partly. What exactly are you referring to? GO
He's referring to the UIAA ratings, posted by USNavy, of the Joker used singly and as twins. Take a look at my post right above yours.
Jay
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cracklover
Mar 24, 2010, 8:28 PM
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jt512 wrote: cracklover wrote: ptlong wrote: Now the reason that real ropes (e.g. those Beal numbers posted above) don't jive with the 40% number is partly due to what USnavy is talking about. But only partly. What exactly are you referring to? GO He's referring to the UIAA ratings, posted by USNavy, of the Joker used singly and as twins. Take a look at my post right above yours. Jay
That much I got. But in relation to that discrepancy (between the predicted 40% and the measured 16%), he states that it is explained "partly due to what USnavy is talking about. But only partly." What is it that USNavy said that explains that discrepancy? And what is the "rest" of the explanation?
GO
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dugl33
Mar 24, 2010, 8:46 PM
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Come on guys. You are all making this way more complicated than it is.
Its a rope swing for f sake! With two ropes no less. Even if the ropes were static the forces on our test dummy wouldn't ever amount to much. He will harmlessly accelerate through the bottom of the arc.
Ya'll ever played on a swing set? How's this any different? Throwing around equations, fall factor, impact forces, modulus of elasticity, non-existent "impact factors" ... all to solve the wrong fricken problem.
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fxgranite
Mar 24, 2010, 9:00 PM
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adatesman wrote: [image]http://www.freesmileys.org/smileys/smiley-basic/popcorn.gif[/image]
It's a rope swing! Lets get torque involved!
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redlude97
Mar 24, 2010, 9:03 PM
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cracklover wrote: jt512 wrote: cracklover wrote: ptlong wrote: Now the reason that real ropes (e.g. those Beal numbers posted above) don't jive with the 40% number is partly due to what USnavy is talking about. But only partly. What exactly are you referring to? GO He's referring to the UIAA ratings, posted by USNavy, of the Joker used singly and as twins. Take a look at my post right above yours. Jay That much I got. But in relation to that discrepancy (between the predicted 40% and the measured 16%), he states that it is explained "partly due to what USnavy is talking about. But only partly." What is it that USNavy said that explains that discrepancy? And what is the "rest" of the explanation? GO
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ptlong
Mar 24, 2010, 9:57 PM
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Cracklover, I'm not exactly sure why you prefer to halve the mass instead of double the modulus. Either way it's a doubling of the term under the radical in the Wexler equation and so (for large fall factors at least) an increase in max impact force of roughly the square root of two. But perhaps you're doing something else?
As to why real ropes don't behave like ideal springs there are a couple of important reasons I am aware of. The first is what USnavy is talking about, namely that the static pull stress/strain relationship is not perfectly linear. The second is that ropes convert a significant fraction of the fall energy into heat through internal friction of some sort. If you first assume that the stress/strain is linear you can get a rough idea of how much of the energy goes to heat this way by using Hooke's Law and the max impact force and dynamic elongation specs for a rope. But of course things aren't linear so this approach likely underestimates the heat lost due to damping.
In any case, with two ropes you are not only doubling the stiffness of the system but also increasing the amount of damping. This extra damping, in addition to the increase in stiffness with elongation, means that you get less impact from two ropes than Wexler predicts.
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dugl33
Mar 24, 2010, 10:07 PM
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Maximum Tension (in Newtons) = M * g * (1 + 2*h/L)
M = mass of swing-bob-square pants
g = acceleration of gravity
h = height above bottom of swing from start
L = length of rope strand
So, for a 100kg dude, 15 meter height diff, 100*9.8*(1+(2*15/15)) = 100*9.8*3 = 2940 N = 2.940 KN
or more simply put, you are pulling 3 Gs, so forces of three times your weight spread over two ropes and two anchor points. How will it evar hold you? 
Of course, all this assumes you actually swing. Taking a factor 1 straight drop will feel much different, and result in much more force. And with two ropes instead of 1 it may well injure you, and will put much more force on the attachment points.
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