A theoretical question of common sense.

OK, so take a dynamic piece of cord (perhaps such as the BD tether for leashless tools)-it is "dynamic", to a degree. You clip it to your ice tools, and it is still dynamic. If you add a loop of 5mm tech cord to the bottom of your tool, then clip the tether to it-is it still dynamic? or does adding thos three inch loop of static cord effectively ruin the dynamic qualities of the system?

Please educate me, oh wise masses

yes, it's still at least as dynamic (as absorbent/elastic/resilient??) as it would be without the tech-cord.

i know, this was settling an argument material

no different then extending the tether at the bottom by using say two locking biners to give you 5 inches of extension.

alexanderblum wrote:OK, so take a dynamic piece of cord (perhaps such as the BD tether for leashless tools)-it is "dynamic", to a degree. You clip it to your ice tools, and it is still dynamic. If you add a loop of 5mm tech cord to the bottom of your tool, then clip the tether to it-is it still dynamic? or does adding those three inch loop of static cord effectively ruin the dynamic qualities of the system?

According Einstein, "common sense is the collection of prejudices acquired by age thirteen," so best perhaps to leave common sense out of it.

The question lacks enough specifics to give any kind of "theoretical" answer. Moreover, it isn't clear what "dynamic qualities of the system" is supposed to mean. But it is worth noting that (1) if the system is supposed to stop falls, and (2) if a relatively rigid link is added, then it is possible at higher peak loads will occur.

For an extreme example unlikely to occur with axe leashes, fall factors greater than 2 become possible. How much effect the rigid material has will depend on the ratio of its length to the length of the dynamic material, so a loop that is small compared to the length of the leash is unlikely to have much effect.

Whether the potential for increased loads is viewed as a change in "the dynamic qualities of the system" or rather as some sort of new outcome that couldn't have occurred previously depends on a level of precision that hasn't been achieved with the question.

interesting (ie pretty sharp) that you bring the length of the fall into it rgold. for the typical leash scenario, adding pretty much anything in series will decrease the overall stiffness of the system. however, like rgold said, if you are looking at a FF2 situation, you would probably have to calculate the impact speed, and basically the distance or time of deceleration (ie the system stretching). most likely, you would need something long and stiff (relatively) to actually increase the peak loads, but it is possible.

1. you're not really creating enough distance to realistically see that
2. people aren't made of steel
3. any moron that leads above tools to such an extreme FF like that is a tool to be removed from the gene pool anyway.
4. omg wtf, are you guys serious? -- both of you, condense that bullshit down to one sentence each.
5. good morning, gents! I'm feeling salty today

slim wrote:...for the typical leash scenario, adding pretty much anything in series will decrease the overall stiffness of the system.

More undefined terms? As it is usually used, the stiffness of the system would be unchanged by adding completely rigid material, since the energy-absorbing properties would be the same.

slim wrote:however...if you are looking at a FF2 situation, you would probably have to calculate the impact speed, and basically the distance or time of deceleration (ie the system stretching).

Not really. The essential ingredient is the fall factor, which as I mentioned will now be greater than 2 if essentially rigid material is added.

slim wrote:...most likely, you would need something long and stiff (relatively) to actually increase the peak loads, but it is possible.

Agreed.

rich,

1) i didn't say adding a RIGID element would decrease the stiffness. first, there isn't such thing as a completely rigid element. second, if you add an element in series, you are going to increase the amount of elongation for a given force (ie decrease stiffness).

2) not sure what you are getting at by undefined terms. just bickering?

3) fall factor the essential ingredient? ummm, no stiffness is going to be more important. an FF2 on a bungy cord isn't shit compared to an ff 0.2 on 3/8 inch chain. the simplest definition of force is mass*acceleration. you are going to have a lot more acceleration with a stiffer system.

I guess what he is saying is: What are the relative lengths of the dynamic elements relative to the lengths of the static elements. If in the original system you have 1 foot of dynamic cord and fall from 1 foot above the attachment point (full extension) to full extension at the bottom you have a total fall length of 2 feet being caught by 1 foot of dynamic cord a force factor of 2. If you have 1 foot of dynamic cord and 2 inches of static cord and the mass being held falls from 1 foot above the attachment point to full extension at the bottom you have a total fall of 26 inches being caught by 12 inches of dynamic cord a force factor of 2.16. If you have 1 foot of dynamic cord attached to 1 foot of static cord again the same fall from 1 foot above the attachment point to full extension below you have a 3 foot fall being caught by 1 foot of dynamic cord a force factor of 3.

FF is the distance from where the object falls to the point at which the rope BEGINS elongating divided by the initial total rope out, not just the length of the "dynamic" piece. there isn't really such thing as a "static" or "dynamic" piece. they just both have different stiffnesses.

in your case, where you have 12 inches of 'more stiff' rope and 2 inches of 'less stiff' cord, you will have a fall of 28 inches with a total of 14 inches of rope out. still a FF of 2. if you have a foot of stiff rope and a foot of less stiff rope, you have a fall of 4 feet and total rope of 2 feet, again a FF of 2. the notion of a 'static' material is false.

again, what it really comes down to is definition of force. you can look at it in terms of stiffness*displacment or mass*accelleration, where acceleration is change in velocity over change in time. what I am saying, is that a long fall (ie higher velocity) combined with a relatively stiff system (ie the change in velocity will occur brutally quick) will result in higher force than equivalent fall onto a soft sytem.

i'm not sure what rgold means when he comments about 'undefined' terms. if he is talking about 'system stiffness', then i would like to know what kind of rock he has been hiding under, as it is a very commonly used term in system dynamics testing and modeling. it is kind of ironic that he is assuming you can use a 'rigid' link to somehow increase the FF beyond 2. also, his saying that the FF is the essential ingredient is like saying a lady pressing on the gas pedal is the essential ingredient to making a car go down the street. it doesn't describe the underlying, basic laws that govern the propulsion system.

Slim, are you arguing on semantic grounds? If so, it might be worth saying: Guys maybe you should avoid calling this fall factor because you're muddying the definition.

Traditionally dynamic ropes are defined as ropes with 5-10% elongation. Static ropes are usually in the .5-2% range. Static elongation of the steel chain you mention is even less.

I agree that fall factor is just an approximation that climbers use as a stand in for force under the assumption that we are talking about a dynamic climbing rope which elongates in a linear fashion. We are certainly misappropriating the term fall factor when we talk about falling on a system which is a mix of dynamic and static elements (as I have defined them above using their common climbing meanings). This does not however mean that the calculations are not representative of the forces exerted on the system relative to falls on the original dynamic system. Therefore the relative numbers we are talking about are are meaningful even if they are technically not fall factors.

Playing around with the fall factor is just an approximate stand-in for working with the real elongations.

no, i am arguing about your calculation of fall factor, which is false. using your methods, if a belayer let rope through his device, and a person's total fall was 10 feet with only 1 feet of rope out, you would call it a FF of 10, which is false (it would still be 2 if the person fell from 1 foot above the anchor). using your method this FF of 10 would indicate more force than if the rope only slipped 5 feet. obviously this is incorrect.

also, your last sentence talks about using FF to describe elongation. FF and elongation are two totally separate things. FF doesn't describe elongation. Elongation is somewhat a function of FF, but there are too many other variables to directly describe elongation via FF.

I guess you didn't read or understand my post above. I'm sorry if you didn't understand it.

slim wrote:no, i am arguing about your calculation of fall factor, which is false. using your methods, if a belayer let rope through his device, and a person's total fall was 10 feet with only 1 feet of rope out, you would call it a FF of 10, which is false (it would still be 2 if the person fell from 1 foot above the anchor). using your method this FF of 10 would indicate more force than if the rope only slipped 5 feet. obviously this is incorrect. also, your last sentence talks about using FF to describe elongation. FF and elongation are two totally separate things. FF doesn't describe elongation. Elongation is somewhat a function of FF, but there are too many other variables to directly describe elongation via FF.

I never suggested that this is a FF 10 fall because the amount of dynamic rope catching the climber is 9 feet (10 foot fall less the 1 foot the climber was above the belayer implies 9 feet of rope in the system even if you didn't explicitly say it). Total fall is 10 feet being caught by 9 feet of rope is actually a fall factor of 1.11.

The question is how far are you falling on to how much spring (the dynamic rope). Your chain example a few posts above has the climber falling onto 0 spring. The force ends up being absorbed primarily by the climbers body.

In the wikipedia entry: en.wikipedia.org/wiki/Fall_…

They have the following section:
In falls occurring on a via ferrata, fall factors can be much higher. This is possible because the length of rope between harness and carabiner is short and fixed, while the distance the climber can fall depends on the gaps between anchor points of the safety cable.

Effectively, you fall and the whole system slides down to the prior connection point. If you have a two foot tether attached to the cable and your biner is 4 feet above the prior anchor point, you fall 6 feet before your 2 foot tether starts to arrest you. Inserting a static element into the dynamic system can have a similar result, increasing the length of your fall before the dynamic system begins to catch you.

Following me now? Do we actually have a disagreement? What is it?

anthony, your first example in your last post isn't consistent with your 3rd example above (ie 1 foot above falling onto 1ft of 'dyn' cord and 1 ft of 'static' cord equalling an FF of 3, when it would actually be 1.5.

also, in my example the FF would be 2 as the distance of the fall until the point at which the rope BEGINS to slip or stretch is 2 feet and the INITIAL amount of rope out is 1 foot. this is a great example of where the FF isn't very helpful in calculating the actual load. it is very limited to specific boundary conditions.

a via ferrata is a completely different beast because your tether isn't tied in a serial connetion with the rail. with a via ferrata i agree that you can achieve FF significantly greater than 2. it is better to consider the anchor as a moving object in this case so that you can add it into the fall distance.

slim wrote:anthony, your first example in your last post isn't consistent with your 3rd example above (ie 1 foot above falling onto 1ft of 'dyn' cord and 1 ft of 'static' cord equalling an FF of 3, when it would actually be 1.5. also, in my example the FF would be 2 as the distance of the fall until the point at which the rope BEGINS to slip or stretch is 2 feet and the INITIAL amount of rope out is 1 foot. this is a great example of where the FF isn't very helpful in calculating the actual load. it is very limited to specific boundary conditions. a via ferrata is a completely different beast because your tether isn't tied in a serial connetion with the rail. with a via ferrata i agree that you can achieve FF significantly greater than 2. it is better to consider the anchor as a moving object in this case so that you can add it into the fall distance.

Let's try it another way. What if you change my via ferrata example to the following. You have a 2 foot tether attached to 2 feet of steel chain attached to some fixture in the wall. You fall. How is the force different on your body than in the original example (two foot tether binered into a cable with an anchor point 4 feet below your biner)?

My calculations are consistent, please reread or directly illustrate my error. (3 feet of fall on 1 foot of dyn cord) (10 feet of fall on 9 feet of dyn cord)...

Also, given your hypothetical scenario, I assumed that the rope was being fed through the device as the climber fell before the climber was caught resulting in a 10 foot fall with 9 feet of rope out. FF computations assume a static belay.

anthony, there is a significant difference in the configuration with a via ferrata. with the VF when you fall and hit the rail support, you are NOT stretching or really even loading the rail, so there is basically no strain in the rail. therefore, the length of your fall is going to be 6 feet (until the beginning of elongation), and your lenght of rope out will be the 2 foot tether. this results in an FF of 3.

with the analogy of connecting a 2 foot rope to a 2 foot chain and falling from 4 feet above the anchor, the fall (until the beginning of elongation) will be 8 feet, and the amount of rope out is 4 feet (the sum of the lenght of chain and the length of rope). the FF is 2. you can't discount the length of chain, even though it is a lot more stiff than the rope. you have to look at it in terms of a system, from start to finish.

as to the error (inconsistency) in your calculations, in the first parenthesis you are only considering the length of the less stiff portion of the rope (not correct, use both pieces), and it is the INITIAL length of the rope (which is correct). in the second parenthesis the length of the rope is the FINAL length of the rope (which is incorrect).

again though, a via ferrata can't be compared to a typical anchor situation. they are completely different.

also, another example of why the FF isn't really a clean method of comparing forces generated by falls is a comparison of rated forces provided by rope manufacturers. if you take 5 different 10mm ropes, the fall forces will be different.

FF is a decent method for getting a relative idea of force trends, but not a good method of actually calculating an accurate force.

My question was "How is the force different on your body than in the original example?".

Also, I should have said "the length of your fall is going to be 8 feet" not "6 feet" (two feet of fall past the binner, four feet down the cable and 2 feet until your tether starts to catch. The forces on your body are identical. Using fall length/length of dynamic element results in the same tooth rattling 4.0.

Again, like I have been saying for four posts now I realize that the real definition of Fall Factor is Length of fall/Length of rope, but the calculation Lenghth of fall/length of dynamic rope can be used as a stand in where static elements are present to compare relative force exerted on the climber.

Definitions are, to a certain extent, arbitrary, but some are more useful than others. The most useful way of defining fall factor puts the (effective) length of the fall at the numerator and the amount of rope involved in absorbing energy at the denominator.

In the canonical case in which the rope is locked off at the belay and all types of friction are ignored, all non-nonsensical definitions of FF agree. For cases in which the belayer gives slack or takes, in which the rope is stuck at some intermediate point between belayer and leader, and many others the difference between one definition and a less useful one is that the former allows easier modeling and analysis.

Since the ratio of the energies stored in two springs connected in series is the reciprocal of the ratio of their elastic constants, the definition that looks at the rope involved in absorbing energy suggests that in first approximation one can usually ignore all that is not the dynamic rope.

One does not have to. Instead, one can easily compute an equivalent rope from an ideal rope and a rigid link. If one considers 100 feet of static rope tied to 20 feet of dynamic rope, obviously one shouldn't disregard either contribution. However, whenever one compares situations in which the dynamic rope is assumed to be the same model, it's much handier to be able to suppose that all energy is stored in the dynamic rope. Doing so allows that kind of qualitative reasoning, which, maybe in spite of appearances, is the main application of the concept of fall factor.

anthony, in your 2 cases the resulting force will not necessarily be the same. in fact, i will say they will most probably not be the same, unless you tweak the stiffnesses of the 2 systems and force the final outcomes to be the same.

brent, define 'effective length' of the fall, ie in your definition is it the fall until elongation begins to occur, or total length of fall with elongation and/or letting rope through with friction?

slim wrote:they will most probably not be the same, unless you tweak the stiffnesses of the 2 systems and force the final outcomes to be the same.

Given that Young's modulus for dynamic ropes is a couple of order of magnitudes lower than for steel, I suspect it would be a very minor tweak.

slim wrote:define 'effective length' of the fall, ie in your definition is it the fall until elongation begins to occur, or total length of fall with elongation and/or letting rope through with friction?

Yes, it is the length of the fall when the rope comes taut. If there is significant slippage through the belay device, the notion of fall factor is not very useful.

The "effective" modifier is a minor detail of little import to the current discussion. It's just there to remind us that what really matters is the kinetic energy of the falling body when the rope comes taut. That energy can be converted into an effective height by dividing by mg. Usually, that just gives the height of the fall, but if, say, a piece or two of pro popped during the fall, there would be a difference.