"gear to slow you down"

[G-spotter]

If you are falling and a piece rips there's a chance the next piece won't because you will stop.

 

But if one piece rips in an poorly equalized (and they are almost always poorly equalized if you use a cordelette) anchor it's not a 7kn minus 6 kn = 1 kn left situation.

 

7kn is applied to the first piece, which can withstand 6, it fails - then 7 kn is applied to the next piece and so on

[layton]

i agree (and I took my 3 semester of college physics fyi)

 

 

I think people are assuming the "pieces" i'm talking about are worthless. I'm saying these theoretical "pieces" are sketchy, but still have some holding power (like a micro nut).

 

I just don't feel satisfied by the statements made that the pieces that blow don't absorb much force (the friction of the piece blowing or distortion/snapping or metal/wire is negligible). Is it because the rope (or anchor cord) is now fairly static, and/or the acceleration between pieces (let's say two feet) is enough to bring the forces back up close to original levels?

 

edit: dru's post snuck in between chirps and this one. Ok, thank you!

 

So the point of this thread is that most (I'd say almost all) climbers don't realize this. Like me, it makes sense to assume that each piece reduces the force - on down the line. And this assumption probably creates some dangerous anchors or lead decisions.

 

So, is there any point to putting in a marginal piece to "slow you down" or to have an unequalized anchor made up of a bunch of crappy pieces? If there is a valid reason, please explain why.

Edited September 29, 2012 by layton

[bd2510]

Regardless of what you all have said... I'm an engineer at Rensselaer Polytechnic Institute, and the answer is that the decrease in for has to do with impulse, or forceXtime. When climbing companies rate equipment in terms of kN, this is a force. This force is the maximum allowable force on the piece. If, for example the rating is for 6kn, and the piece holds for 1 second, the resulting change in momentum is 6kN sec, which can be translated to a change in momentum. To summarize, no matter what the piece is rated for, it matters how long it holds. A 12kN piece that holds for 50% the time of a 6kN piece changes the force on the other pieces exactly the same amount. More pro is better in general, and everything takes energy out of the system, even the friction of a cordelette over a biner attached to a weak piece.

 

Also, for the mathematicians, the change in momentum is equal to the integral of the force in terms of time, and since momentum is mass times velocity, the change in velocity is the integral of Fdv/m.

[Off_White]

 

Young man, the answer you seek is simple: the leader must not fall.

[layton]

I violated that rule about 15 times today

[Buckaroo]

You didn't answer the main part of his question.

 

Are the ropes dynamic properties reduced when it's stretched out from the piece that blows, thus putting more force on the next piece?

[stevetimetravlr]

Not much it seems. Good answer BD2510, thank you.

[kurthicks]

didn't read this whole thread, but here's some relevant recent research:

 

http://amga.com/resources/various/Sequential_Failure_Paper.pdf

[mmeyers]

we're headed straight into Nerdville!

 

and BD2510 has it right. ('sup, I got my MS at RPI, too).

 

so, let's play around with this:

http://hyperphysics.phy-astr.gsu.edu/hbase/flobi.html

 

if you put 100kg and 5m height, you'll get 4900J for impact energy.

 

the impact *force* is calculated using the distance to stop, and you'll see how much it changes when you change the stopping distance. this is why rope stretch is so important, since this is the single largest component of elasticity (and hence stopping distance) in the system. the more the rope stretches (analogous to increasing the stopping distance), the lower the impact *force*. the elasticity in the system defines the impact force. but we all know that already.

 

let's say your system can only stretch the equivalent of 1m (I'm simplifying a lot here, but that includes the rope, slings, the elasticity in the pro that's being loaded, your body, etc). the *average* impact force is 4.9kN. this is *average*, not peak.

 

impact force looks like a bell curve with respect to time and distance. here is a highly simplified example:

http://imageshack.us/photo/my-images/834/48273249.jpg/

as you can see, the average force (what's calculated above) will be *less* than the peak force.

the less the system stretches, the higher the peak force is, and the higher the average force is.

BTW, all of this crap is nonlinear.

 

so, if your piece is rated at 5kN, it has probably blown, b/c the peak load is higher than the average of 4.9kN.

 

so now what happens? well, we can make some simplifying assumptions (ie, make up some bullshit numbers) about the elasticity of the system. we'll assume linear elasticity (not realistic), and an impact profile similar to what is above (laziness mostly), and some other bullshit assumptions I've made, plus we know that the deceleration would occur in 0.2 sec (to reach 1m). we could then estimate that the peak force is 7.3kN (which is entirely dependent on the impact profile and my other made-up numbers). 5kN is reached in about 0.06s (again, entirely dependent on my assumed impact profile), or maybe about 0.3m (ditto), at which point your velocity has decreased to about 6.8m/s (ditto), which means you lose about 3m/s, and about half of your kinetic energy (ditto).

 

see? it's all dependent on making up numbers (when you don't have real data to use), which is why no one wants to (or can) give anyone a specific answer, because even rules of thumb in dynamic systems are hard to come by. and that's why John Long's study is an interesting discussion starter, but not worth analyzing in detail, because in reality, gear is robust enough and over-engineered enough that it's pretty non-critical as long as you know what you're doing and you use a dynamic rope!

 

so, to answer the questions directly, as well as I think I can:

 

So, is there any point to putting in a marginal piece to "slow you down" or to have an unequalized anchor made up of a bunch of crappy pieces?

 

yes, gear blowing during a fall will reduce energy in the system, and therefore slow your fall. obviously, the more marginal it is, the less effect it will have. and an unequalized anchor of crappy pieces is better than no anchor at all, yes?

 

Are the ropes dynamic properties reduced when it's stretched out from the piece that blows, thus putting more force on the next piece?

 

yes to the first part (reduced properties), and no to the second (more force). I read somewhere that it takes a dynamic rope about 5-10 minutes to shrink back to its original length after a hard fall. so, the rope is viscoelastic, which in this case means that it takes measurable time for the rope to regain it's initial elasticity state. the time between blowing out one piece and hitting the next piece is small enough that the stretch will not rebound. the impact on the second piece will not be the *same* as the impact on the first piece, but that definitely does not mean that the force on the second piece will be higher than if the first piece did not exist. this is because, in typical situations (aha, more assumptions!) the rope will still retain a lot of it's elasticity (you're not going to max out the elasticity in one fall on one piece that rips out). hopefully I'm able to explain my thinking clearly here, and that I'm making sense.

 

[layton]

well thank you!

and great article kurt!

 

ok, i think we beat this one into a pulp

[Choada_Boy]

didn't read this whole thread, but here's some relevant recent research:

 

http://amga.com/resources/various/Sequential_Failure_Paper.pdf

 

 

Conclusion: "A residual velocity after the initial anchor point failure results in an increased effective fall factor for subsequent impacts. For equally spaced anchors of equal strength, this increased effective fall factor makes sequential failure highly likely."

[Choada_Boy]

we're headed straight into Nerdville!

 

and BD2510 has it right. ('sup, I got my MS at RPI, too).

 

so, let's play around with this:

http://hyperphysics.phy-astr.gsu.edu/hbase/flobi.html

 

if you put 100kg and 5m height, you'll get 4900J for impact energy.

 

the impact *force* is calculated using the distance to stop, and you'll see how much it changes when you change the stopping distance. this is why rope stretch is so important, since this is the single largest component of elasticity (and hence stopping distance) in the system. the more the rope stretches (analogous to increasing the stopping distance), the lower the impact *force*. the elasticity in the system defines the impact force. but we all know that already.

 

let's say your system can only stretch the equivalent of 1m (I'm simplifying a lot here, but that includes the rope, slings, the elasticity in the pro that's being loaded, your body, etc). the *average* impact force is 4.9kN. this is *average*, not peak.

 

impact force looks like a bell curve with respect to time and distance. here is a highly simplified example:

http://imageshack.us/photo/my-images/834/48273249.jpg/

as you can see, the average force (what's calculated above) will be *less* than the peak force.

the less the system stretches, the higher the peak force is, and the higher the average force is.

BTW, all of this crap is nonlinear.

 

so, if your piece is rated at 5kN, it has probably blown, b/c the peak load is higher than the average of 4.9kN.

 

so now what happens? well, we can make some simplifying assumptions (ie, make up some bullshit numbers) about the elasticity of the system. we'll assume linear elasticity (not realistic), and an impact profile similar to what is above (laziness mostly), and some other bullshit assumptions I've made, plus we know that the deceleration would occur in 0.2 sec (to reach 1m). we could then estimate that the peak force is 7.3kN (which is entirely dependent on the impact profile and my other made-up numbers). 5kN is reached in about 0.06s (again, entirely dependent on my assumed impact profile), or maybe about 0.3m (ditto), at which point your velocity has decreased to about 6.8m/s (ditto), which means you lose about 3m/s, and about half of your kinetic energy (ditto).

 

see? it's all dependent on making up numbers (when you don't have real data to use), which is why no one wants to (or can) give anyone a specific answer, because even rules of thumb in dynamic systems are hard to come by. and that's why John Long's study is an interesting discussion starter, but not worth analyzing in detail, because in reality, gear is robust enough and over-engineered enough that it's pretty non-critical as long as you know what you're doing and you use a dynamic rope!

 

so, to answer the questions directly, as well as I think I can:

 

So, is there any point to putting in a marginal piece to "slow you down" or to have an unequalized anchor made up of a bunch of crappy pieces?

 

yes, gear blowing during a fall will reduce energy in the system, and therefore slow your fall. obviously, the more marginal it is, the less effect it will have. and an unequalized anchor of crappy pieces is better than no anchor at all, yes?

 

Are the ropes dynamic properties reduced when it's stretched out from the piece that blows, thus putting more force on the next piece?

 

yes to the first part (reduced properties), and no to the second (more force). I read somewhere that it takes a dynamic rope about 5-10 minutes to shrink back to its original length after a hard fall. so, the rope is viscoelastic, which in this case means that it takes measurable time for the rope to regain it's initial elasticity state. the time between blowing out one piece and hitting the next piece is small enough that the stretch will not rebound. the impact on the second piece will not be the *same* as the impact on the first piece, but that definitely does not mean that the force on the second piece will be higher than if the first piece did not exist. this is because, in typical situations (aha, more assumptions!) the rope will still retain a lot of it's elasticity (you're not going to max out the elasticity in one fall on one piece that rips out). hopefully I'm able to explain my thinking clearly here, and that I'm making sense.

 

The posted article provides evidence that contradicts a number of your points above.

[layton]

shit's not over yet

 

I've heard that article has some problems with it, as does John Long and Sterling's tests

[layton]

total basic high school science stuff

[obwan]

Another couple of pints and I might even get this.

[trumpetsailor]

tl;dr. Marginal placements are good and may help, badly equalized anchors with bad placements are bad.

 

 

 

 

I opened this thread expecting to find a discussion of heavy gear. Fromage is right. It's Nerdville.

 

Mike wanted a PhD physicist's opinion, so here's one (almost - this thread is an enjoyable distraction from finishing my thesis analysis):

 

While I know something about mechanics, my climbing qualifications have a lot more to do with skiing than trad rock anchorbuilding. Physicists frequently disagree. This post represents my best answer at present, but it is not valid without experimental confirmation. Don't die.

 

Rope stretch is the primary way energy is dissipated in a fall.

 

Mike's questions come down to rope relaxation. After loading, even partial relaxation will soften a subsequent load. I don't think a rope has the distance, not the time, to un-stretch very much in the case of a disintegrating anchor, but it does in the case of a failing marginal placement. Think about the stretch you get hanging from a dynamic rope. 5 kN will introduce at least 5 times that much stretch. If the rope remains mostly stretched before getting re-loaded, it won't stretch again.

 

Marginal placement:

 

yes, gear blowing during a fall will reduce energy in the system, and therefore slow your fall.

 

This is correct, excepting nonlinear properties of the rope/knots/body (on which I'm not expert and which were part of the original question). Pages 16 and 22 of Kurt's article addresses those effects (claiming that the rope unstretches fast); form your own conclusion.

 

As noted above, it's somewhat like using a Screamer.

 

The energy associated with a fall will be dissipated into heat, one way or another. The "work" (<-- technical term) done by stretching/relaxing the rope before/after the piece pops (mostly), and by ripping out the piece itself (a little bit), will consume some of the fall's energy. Again neglecting nonlinearities, the next piece down the line will then see loads equivalent to those of a fall that began at a lesser height.

 

Whether the second piece will rip will depend upon the initial runout above the first piece, the strength of the first piece, the distance to the second piece, and the strength of the second piece.

 

All else being equal, I'd put in the marginal piece. Your mileage may vary. Kurt's article is interesting.

 

 

Unequalized anchor:

 

This is a different story. The purpose of an anchor is never to absorb energy; that's the rope's job. The anchor's job is to never fail. Cascading failure scenarios are possible (three people can lift a piano together than one at a time cannot). To bank on the disintegration of an anchor for energy absorption is to ask for trouble. The energy consumed by anchor-component failure alone (and not a relax/stretch cycle of the rope) probably isn't very big. As an anchor comes apart, the rope may not relax significantly; it's still under load and being stretched. If there's not much stretching/unstretching going on, there's not much dissipation, and the anchor's just getting weaker.

 

For Mike's original question, it's possible to assemble an equalized anchor that might hold 10-15kN out of three placements that can hold 5 kN each. Three incorrectly-equalized, but otherwise correct, pieces that each hold 5 kN are clearly safer than two (also unequalized; equalized can hold more than 5kN) or one, but whether it will hold a fall that exceeds 5 kN in initial load will depend on the details of the fall, the rope's properties, and the details of the anchor's construction and subsequent failure.

 

Equalization is a good thing. From a strength perspective, I can't think of a downside to proper equalization.

 

 

Force Vs. Energy:

 

BD2510 is correct.

 

A fall does not increase in force (kN) as it gets bigger (though the forces applied to the braking system will tend to increase somewhat.); the falling climber's momentum and kinetic energy increase.

 

To bring a climber to rest, his momentum must be changed with an "impulse" (<-- technical term meaning integrated force times time) and his kinetic energy must be converted to another form, usually heat, through "work" (integrated force times distance). More anchor strength, in kN, is better, but it's not the whole story.

 

System failure is determined by peak forces, not total dissipated energy, which is part of why dynamic rope is so important.

See this DMM video for 22 kN slings failing with an 8 foot fall.

[layton]

thank you!

[trumpetsailor]

No problem .

 

Looking at this stuff again this morning, I'd like to make an addendum.

 

In the case of the anchor, it's also useful to think about the peak load applied to the anchor. The stretching and unstretching of a rope doesn't just dissipate energy, it also provides a softer catch as it reloads again (spreading the impact over time and reducing the peak load on the anchor).

 

If the argument that the rope doesn't have the distance to unstretch as the anchor comes apart is correct, then the second and third pieces will see peak loads that are comparable to the one that forced the first piece to pop.

 

This may be similar to when a loaded rappel rope shifts a little; the jolt you feel is sharper than a similar (tiny) fall on an unstretched rope.

 

It's interesting to consider a mechanics problem from both momentum and energy perspectives. One is often more clear, or applicable, than the other. In the anchor's case, I now believe the momentum/impulse/peak load/impact-time perspective is more appropriate than energy/dissipation. Rope stretch is still the key.

 

 

 

 

Aside: In the first couple years of grad school, we had a course where the Physics Education folks would distribute questions like these (but simpler) to ~30 grad students, all of whom did well as undergrads. It was rare that more than half of the class would get the Just-So story correct. Similar studies with professors would see at most two-thirds get it right on the first pass.

 

These questions are simple to pose, but the answers are sometimes subtle and counter-intuitive. I'm amazed that nobody's countered my argument yet; it might be wrong. It's the internet, after all.

[layton]

and that's why I asked the question

 

a lot of know-it-all answers and jibs at it being a high school physics problem, but simple things we take for granted sometime provide very interesting surprises

[matt_warfield]

I have a Ph.D. in engineering.

 

Climbing presents numerous scenarios that can't be effectively analyzed.

 

-John Yablonski falling off a free solo and grabbing a tree

-Todd Skinner not knowing how old a harness can be before failing

-Dan Osman not knowing how long ropes can hang while doing repeated huge jumps on them.

 

Testing and experience are important as well as engineering and physics.

Edited September 30, 2012 by matt_warfield

[G-spotter]

Seems like most physicists designing the problem would assume a fully static rope and a frictionless carabiner and thus approximate the wrong answer

[mmeyers]

that's a good paper, imo.

 

here are some more interesting ones as well:

http://web.mit.edu/sp255/www/reference_vault/second_order_rope_fit.pdf

http://www.caves.org/section/vertical/nh/51/Multi-point%20pre-equal%20anchors.pdf

http://web.mit.edu/sp255/www/reference_vault/ITRS_02_force_eqn_analysis.pdf

 

if you're into that sort of thing....

[pcg]

Wow. The first paper (immediately above)appears to imply that knots make good energy absorbers. It doesn't discuss whether this is just the first time they're tightened in a fall, or if the effect continues after an initial stretching event.

So, if one is forced to rely on questionable pro and has no screamers handy, should one throw a few knots in the rope to act as energy absorbers?

I'm not expecting a definitive answer, just makes fun food for thought.

 

[layton]

knots do, but you have to untie/retie in

 

 

I don't think adding more knots to the rope is a good idea, but I do wonder if there is an on the fly way to improvise a screamer without added equipment like this product (http://www.e-climb.com/cintas_en/dissip_en)

[Rad]

You could also clip a screamer between yourself and the end of the rope if you expect to be on a series of questionable placements. The cost of replacing it might keep you from falling in the first place!