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USnavy
Nov 15, 2008, 8:45 AM
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Simple logic would tell us that the more a rope stretches the lower the impact force of the rope. Why? Because higher stretch ropes stop the load over a grater range of time and distance then lower stretch ropes.
But increasingly more often I am seeing dynamic ropes with low static and dynamic specifications with a lower impact force rating then similar higher stretch ropes. Why is this? One would think the stretch of the rope is directly proportional to the impact force of the rope but apparently this is not always true.
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JimTitt
Nov 18, 2008, 1:38 PM
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Climbing ropes don´t obey "simple logic" as the modulus of elasticity normally changes with extension. How much will depend on the weave, core twist and crimp amongst others.
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USnavy
Dec 17, 2008, 6:21 PM
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What do you mean by "the modulus of elasticity normally changes with extension"? Are you saying that the elasticity of the rope is not consistent with the load applied? UIAA tests both the dynamic elongation and the impact force of the rope on the same test so all ropes are tested in the exact same manner and the rating of one rope can be compared "apples to apples" with the rating of another rope.
(This post was edited by USnavy on Dec 17, 2008, 6:23 PM)
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JimTitt
Dec 17, 2008, 7:45 PM
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Most climbing ropes have a modulus of elasticity which increases under load. There is some info on how to calculate this in various papers by Stephen Attaway or in a simplified form and graphs in Tom Moyer´s work.
The UIAA only specify the maximum elongation (40%) allowed when drop tested, it is up the manufacturer whether he wants to give any further information.
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patto
Dec 17, 2008, 11:50 PM
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JimTitt wrote: Most climbing ropes have a modulus of elasticity which increases under load. There is some info on how to calculate this in various papers by Stephen Attaway or in a simplified form and graphs in Tom Moyer´s work. The UIAA only specify the maximum elongation (40%) allowed when drop tested, it is up the manufacturer whether he wants to give any further information.
A rope with a modulos of elasticity that increases under load gives a higher impact for a given stretch.
Thus I manufacturers decrease the rate at which the modulus increases (or even make it decrease with stretch) then the impact forces will be lower for a given stretch distance.
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villageidiot
Dec 18, 2008, 12:11 AM
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patto wrote: Thus if(sic) manufacturers decrease the rate at which the modulus increases (or even make it decrease with stretch) then the impact forces will be lower for a given stretch distance.
The modulus would decrease with increasing strain once it was past the yield point, typically what would follow would not be pleasant.
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majid_sabet
Dec 18, 2008, 1:01 AM
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JimTitt wrote: Climbing ropes don´t obey "simple logic" as the modulus of elasticity normally changes with extension. How much will depend on the weave, core twist and crimp amongst others.
Do not forget heat dissipation which converts and removes portion of the impact energy to the air.
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USnavy
Dec 18, 2008, 5:03 AM
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patto wrote: JimTitt wrote: Most climbing ropes have a modulus of elasticity which increases under load. There is some info on how to calculate this in various papers by Stephen Attaway or in a simplified form and graphs in Tom Moyer´s work. The UIAA only specify the maximum elongation (40%) allowed when drop tested, it is up the manufacturer whether he wants to give any further information. A rope with a modulos of elasticity that increases under load gives a higher impact for a given stretch. Thus I manufacturers decrease the rate at which the modulus increases (or even make it decrease with stretch) then the impact forces will be lower for a given stretch distance.
So if modulus of elasticity is not elongation, then what is it? I have looked up the definition of the term and found "the mathematical description of an object or substance's tendency to be deformed elastically (i.e., non-permanently) when a force is applied to it". But still I don’t understand what that specifically is. I have the mindset that rope elongation is the sole property that disperses a load and it’s solely responsible for force dispersion. So what is this second parameter "modulus of elongation" that defines a ropes shock absorption abilities?
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jt512
Dec 18, 2008, 5:31 AM
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USnavy wrote: I have the mindset that rope elongation is the sole property that disperses a load and it’s solely responsible for force dispersion.
Dear President Obama,
Please make it a national requirement for high school graduation that students understand the difference between energy and force.
Sincerely,
jt512
(This post was edited by jt512 on Dec 18, 2008, 5:31 AM)
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mach2
Dec 18, 2008, 6:32 AM
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JT ya better add momentum to that list if you want to go that far 
(btw this isn't meant to be rude to the OP I'm just enjoying a little engineering laugh)
To help the OP further in his pursuit to discover the all mighty E value, he might want to look into a material science textbook, or also look up phrases like Young's modulus
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JimTitt
Dec 18, 2008, 9:52 AM
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From a climbing rope point of view the simplest way to think of if is: any given force (stress) divided by the % elongation (strain) that occurs under this force.
For example if a rope stretches 25% with a force of 5,000N the modulus of elasticity is 5,000/25 = 200N
(The force is in Newtons and the elongation is in % and is dimensionless, therefore the modulus is in Newtons).
This is convenient because IF the modulus was constant for the material because all you need to do for a given force is divide by this modulus and you get the elongation in %.
For example our rope above. Load of 12,000N, divide by 200 and you get a percentage elongation of 60%.
BUT climbing ropes are seldom if ever so convenient as to have a constant modulus so the result is a curve usually expressed as a mathematical formula. To get the modulus at any one point you only need to insert the appropriate stress or strain value.
Some of the energy in a fall goes into re-arranging the fibres of the rope and they slide across each other, producing heat. Some of the energy goes to alter the fibres themselves as they are not straight to start with (crimp). The rest of the energy goes ino the material of the fibres themselves and tries to straighten the molecular chains.
Some of these changes are in effect irreversible which is why ropes tend to get longer when they have been fallen on and also why the modulus of elasticity increases the more falls there have been.
This is why the UIAA/CE tests call for the maximum impact and elongation only to be measured for the first test drop. Attaway states the impact force may increase between 30% and 60% after four drops.
I work with metal which is different, I´m sure for more in-depth information the rope manufacturers will be happy to help!
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tradrenn
Dec 18, 2008, 10:06 AM
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USnavy wrote: But increasingly more often I am seeing dynamic ropes with low static and dynamic specifications with a lower impact force rating then similar higher stretch ropes.
I have a Beal Booster III Impact Force 7.2 Kn and Dynamic Elongation of 38%.
Out of curiosity, what do you have or read ?
I hope that you are not thinking that the higher the impact force the better.
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USnavy
Dec 18, 2008, 10:59 AM
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tradrenn wrote: USnavy wrote: But increasingly more often I am seeing dynamic ropes with low static and dynamic specifications with a lower impact force rating then similar higher stretch ropes. I have a Beal Booster III Impact Force 7.2 Kn and Dynamic Elongation of 38%. Out of curiosity, what do you have or read ? I hope that you are not thinking that the higher the impact force the better.
No, I don’t think that higher impact forces are better, that’s silly. My question revolves around why a rope with a low elongation can have a lower impact force then a different rope with a higher elongation. Here is an example:
Rope 1:
-10 kN impact force
-40% elongation
Rope 2:
-9 kN impact force
-34% elongation
How can rope one have a higher impact force then rope two when it stretches more and slows the load down over a greater period of time then rope two?
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USnavy
Dec 18, 2008, 11:29 AM
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JimTitt wrote: From a climbing rope point of view the simplest way to think of if is: any given force (stress) divided by the % elongation (strain) that occurs under this force. For example if a rope stretches 25% with a force of 5,000N the modulus of elasticity is 5,000/25 = 200N (The force is in Newtons and the elongation is in % and is dimensionless, therefore the modulus is in Newtons). This is convenient because IF the modulus was constant for the material because all you need to do for a given force is divide by this modulus and you get the elongation in %. For example our rope above. Load of 12,000N, divide by 200 and you get a percentage elongation of 60%. BUT climbing ropes are seldom if ever so convenient as to have a constant modulus so the result is a curve usually expressed as a mathematical formula. To get the modulus at any one point you only need to insert the appropriate stress or strain value. Some of the energy in a fall goes into re-arranging the fibres of the rope and they slide across each other, producing heat. Some of the energy goes to alter the fibres themselves as they are not straight to start with (crimp). The rest of the energy goes ino the material of the fibres themselves and tries to straighten the molecular chains. Some of these changes are in effect irreversible which is why ropes tend to get longer when they have been fallen on and also why the modulus of elasticity increases the more falls there have been. This is why the UIAA/CE tests call for the maximum impact and elongation only to be measured for the first test drop. Attaway states the impact force may increase between 30% and 60% after four drops. I work with metal which is different, I´m sure for more in-depth information the rope manufacturers will be happy to help!
Ok thanks, your post helped me to understand that parameter better. So now that I understand what you are referring to, I am not seeing how it allows one rope with a lower elongation to have a lower impact force then another rope with a higher elongation.
Ok so let me make sure I got this right. You are saying rope “a” can stretch less then rope “b” and have a lower impact force then rope “a” because the increase in the modulus of elasticity of the rope “a” is less then the increase in the modulus of elasticity of rope “b”? Well its my understanding that UIAA publishes the peek impact force sustained during the first fall as well as the maximum elongation produced in the first fall. They don’t publish the average impact force recorded along the time span of the fall.
Well although I see how a higher modulus of elasticity value would translate to a higher average impact force that’s recorded along the time span of the fall, I don’t see how it would translate to a higher peek value, which is what UIAA publishes. The only way I could see a higher modulus of elasticity could be the cause of rope “a” to hold a lower impact force and elongation rating then rope “b” is if UIAA records the elongation of the rope at the point where the impact force of the system is at its peek value and not when the rope elongation is at its peek value (assuming they are not both at their peek value at the same time which I suspect they are). However I find that unlikely for it would be hard to record such and it kind of skews the whole point of the dynamic elongation specification. So what am I still missing because it’s a matter of fact that it is possible for one rope with a lower elongation to have a lower impact force then a different rope with a higher elongation?
(This post was edited by USnavy on Dec 18, 2008, 11:30 AM)
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JimTitt
Dec 18, 2008, 1:09 PM
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Rope a) could be constructed so that the modulus rises very rapidly to give say a force of 5kN, the rope is also constructed so that the modulus than stays constant so the force then continues to remain at 5kN.
Rope b) could be constructed to have a constant modulus giving a force of say 0,1kN and then rises very rapidly.
Rope a) never produces a higher force (impact) than 5kN but has worked at stopping the fall all the time so the elongation will be relatively low.
Rope b) has not done any work to stop the fall until the last moment when it then has to apply a much higher force.
A good way to think about this is to consider driving a car. A smooth driver applies the brakes consistently until the car come to a halt, a poor driver brakes too gently at first so at the last moment they have to stand on the pedal, throwing you into the windscreen.
Both have braked from the same speed and for the same distance but the peak forces are wildly different.
I would just look at the areas under the force/time graphs which represent the work done by the rope stopping the fall and then see where the elongation or max force lies but these graphs are not normally available.
Personally I just buy a strong, cheap rope and don´t fall off too often!
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adatesman
Dec 18, 2008, 2:53 PM
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USnavy
Dec 18, 2008, 3:38 PM
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JimTitt wrote: Rope a) could be constructed so that the modulus rises very rapidly to give say a force of 5kN, the rope is also constructed so that the modulus than stays constant so the force then continues to remain at 5kN. Rope b) could be constructed to have a constant modulus giving a force of say 0,1kN and then rises very rapidly. Rope a) never produces a higher force (impact) than 5kN but has worked at stopping the fall all the time so the elongation will be relatively low. Rope b) has not done any work to stop the fall until the last moment when it then has to apply a much higher force. A good way to think about this is to consider driving a car. A smooth driver applies the brakes consistently until the car come to a halt, a poor driver brakes too gently at first so at the last moment they have to stand on the pedal, throwing you into the windscreen. Both have braked from the same speed and for the same distance but the peak forces are wildly different. I would just look at the areas under the force/time graphs which represent the work done by the rope stopping the fall and then see where the elongation or max force lies but these graphs are not normally available. Personally I just buy a strong, cheap rope and don´t fall off too often!
Ok, that makes sense. I now understand where your coming from and finally understand the answer to my question.
But that leads to another question. Say you have two ropes:
Rope A:
Impact force: 8 kN
Dynamic Elongation: 35%
Rope B:
Impact force: 8 kN
Dynamic Elongation: 30%
Which rope will provide a softer catch? Will rope “a” provide a softer catch because it slows the load down over more time or will it provide a harder catch because the first few percent of the rope stretch will not be doing any load dispersion work ultimately leavening a lower percentile of rope stretch then rope “b” in which to disperse the load?
So then is the ultimate goal to choose a rope that has both the lowest impact force and the lowest dynamic elongation? Because after all there is no reason to buy a rope the stretches more and has the same impact force because you just increase the chance of falling on an object. Right?
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brenta
Dec 18, 2008, 3:42 PM
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JimTitt wrote: A good way to think about this is to consider driving a car. A smooth driver applies the brakes consistently until the car come to a halt, a poor driver brakes too gently at first so at the last moment they have to stand on the pedal, throwing you into the windscreen.
If ropes were ideal springs, a falling climber would bob up and down for quite a while. Our experience, however, is that the oscillation dies soon. If the climber is free-hanging, almost all the damping comes from the rope.
The interesting thing is that the force exerted by an ideal damper is proportional to the speed of the climber. Hence, it is maximum when the rope comes taut and then tapers off while the climber decelerates. The force of the spring depends on the stretch, and therefore grows from null at the beginning to maximum when the climber stops.
So, one sees that by "tuning the suspensions," by changing, that is, the relative contribution of damper and spring, one can indeed achieve the different braking behaviors JimTitt refers to.
So far, I have talked of linear (ideal) spring and damper. In reality, springs and the dampers are nonlinear, which adds some complexity to the analysis.
I'll finish with a suggestion. Take the specs of any single rope on the market and compute the following two ratios: 800N/(static elongation) and (impact force)/(dynamic elongation). If the rope behaved like an ideal spring, you'd get the same value. However...
(This post was edited by brenta on Dec 18, 2008, 3:47 PM)
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USnavy
Dec 18, 2008, 3:51 PM
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brenta wrote: JimTitt wrote: A good way to think about this is to consider driving a car. A smooth driver applies the brakes consistently until the car come to a halt, a poor driver brakes too gently at first so at the last moment they have to stand on the pedal, throwing you into the windscreen. 800N/(static elongation) and (impact force)/(dynamic elongation). If the rope behaved like an ideal spring, you'd get the same value. However...
So what specifically does that formula calculate?
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brenta
Dec 18, 2008, 3:56 PM
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USnavy wrote: So what specifically does that formula calculate?
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rgold
Dec 18, 2008, 4:21 PM
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Edit: Brenta posted pretty much the same thing while I was typing this.
I'm not an engineer and I don't know the first thing about materials science, but I know a little (just a little, really) about mathematical modeling.
The standard model for a climbing rope assumes a constant "modulus" (this term is used in many different and not always equivalent ways). This means that the graph of tension vs. elongation (or % elongation) is a straight line through the origin. In reality, the tension-elongation curves are S-shaped, like an integral sign. Presumably, the manufacturer has some ability to "tune" this curve, I'd be surprised to learn they have the level of control suggested by JT. Just from the perspective of modeling, without any reference to the realities of rope manufacture, the discrepancies in UIAA impact data have a very plausible explanation that does not rely on such tuning at all.
If one assumes constant modulus, then the associated differential equation that describes how the rope behaves is the standard equation for simple harmonic motion.
A real rope is not, of course, exactly like a spring, and this isn't simply because the tension-elongation curve isn't a straight line. We don't see a fallen leader bouncing up and down (forever), for example. The motion observed in real ropes is closer to what would be called critically damped simple harmonic motion, in which a resisting force suppresses the oscillations. There is also a standard differential equation for this, in which the resisting force is assumed to be proportional to velocity (called viscous damping because it models the effect of a fluid-filled shock absorber).
The CMT section of the Italian Alpine Club has created a mathematical model that relies on the viscous-damping differential equation, or rather on a system of such equations, that is claimed to agree well with experimental data.
The reason for mentioning this here is that the viscosity term introduces a second parameter into the model which describes how much resistance to motion is built into the rope. Results on such things as elongation and impact force thus depend on two parameters, so all observations are not consequences of the rope modulus alone. Since the energy absorbed by the rope is now the sum of energy absorbed by stretching and work done agains the damping force, there is no contradiction the kinds of examples USN cites, even under the assumption of constant rope modulus.
In other words, you don't necessarily need to greatly alter the tension-elongation curve at all to obtain differing results such as USN mentions. As I said, I'm not an engineer and have no idea what happens in reality, but in theory there are more parameters to work with than just the rope modulus.
By the way, and this heads in a very different direction, I'd be interested to hear an explanation, from some appropriate set of first principles, for why damping in ropes should be viscous, namely, proportional to velocity. The attraction of viscous damping is that the associated differential equations are linear and so easy to solve, but that is an accomodation to the convenience of the model-maker, not necessarily a reflection of what goes on inside a rope.
(This post was edited by rgold on Dec 18, 2008, 4:22 PM)
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el_layclimber
Dec 18, 2008, 4:40 PM
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USnavy wrote: ... Here is an example: Rope 1: -10 kN impact force -40% elongation Rope 2: -9 kN impact force -34% elongation How can rope one have a higher impact force then rope two when it stretches more and slows the load down over a greater period of time then rope two?
There must be other variables here that help to determine those numbers. Rope diameter must be important, and I would hazard that the way the rope is constructed is relevant as well.
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ptlong
Dec 18, 2008, 5:28 PM
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USnavy wrote: So then is the ultimate goal to choose a rope that has both the lowest impact force and the lowest dynamic elongation? Because after all there is no reason to buy a rope the stretches more and has the same impact force because you just increase the chance of falling on an object. Right?
Remember that these numbers are for a UIAA drop test (the first one).
It isn't intuitively obvious that a rope that minimizes impact force and elongation for a statically belayed 1.78 factor fall on a brand new rope will do the same for the types of falls you might actually take.
"Personally I just buy a strong, cheap rope and don´t fall off too often!" - JimTitt
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moose_droppings
Dec 18, 2008, 6:08 PM
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ptlong wrote: USnavy wrote: So then is the ultimate goal to choose a rope that has both the lowest impact force and the lowest dynamic elongation? Because after all there is no reason to buy a rope the stretches more and has the same impact force because you just increase the chance of falling on an object. Right? Remember that these numbers are for a UIAA drop test (the first one).
And I'm guessing the these numbers diminish at different rates (given equal falls) depending on materials and construction of individual ropes.
???
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