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mountainmonkey
Dec 4, 2003, 6:18 PM
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What belay devices are you guys using? The huge forces possible with a factor 2+ fall is not achievable with most belay devices that I know of. ATC is only capable of holding about 2kN and the Munter is only a little stronger at 2.5-3kN. GriGri starts slipping at 9kN. Only with knots will the forces exceed the strength rating for the normal use of gear. If the belayer is tied to the anchor with the rope and the belay device is connected through the tie-in loop, that rope also acts to absorb some of the fall - making a factor 2+ fall very difficult. If you have a re-directed belay, you reduce the fall factor and you increase the force on the top piece by ~160%.
Always try to avoid a factor 2 by clipping into an anchor piece and by placing pro as soon as possible.
There are times when wheeling in slack are necessary to keep injury to a minimum. Slabs. The forces are always lower because the sliding, grating, and scraping slow down the falling leader.
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tedc
Dec 4, 2003, 6:19 PM
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In reply to: Jay, ...I have no way of knowing if these are offsetting or not, but the friction in a real-life fall situation can be 30% of the total force of the fall--and I doubt that the fall factor is increased by 30% from friction through gear. Curt
Actually, it is not to complicated to evaluate how the friction forces interact with the fall forces. Jay's post was accurate but a bit hard to evaluate. SIMPLIFY and ISOLATE. Assume (correctly) that friction decreases (dissipates) the overall forces in a fall situation. So lets up the ante (up the friction). Lets make the coef of friction between rope and biner ohhhh, 1.0 (100%). To put in lead climbers terms, the leader just clove hitched the last piece (100% friction=zero sliping). FALLLLLLing. What happens? Well the belayer is happy. His force went to zero. But the climber and the top piece just saw FACTOR 2. The actual situation of many biners and lower friction factor is just more math to do but the conclusion is the same. Friction reduces the overall energy but only the bealyer benefits and everyone else suffers.
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iltripp
Dec 4, 2003, 7:08 PM
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In reply to: The climber 10 metres up without pro loses contact and falls. His belayer somehow manages to take almost all of the rope. (Yeah, he's endowed with very fast hands.)
I've heard stories of belayers who, faced with the possibility of the leader decking, have taken a leap of faith, locked off, and jumped off the belay ledge. This would take the rope in very fast (although it doesn't quite apply to a factor two on the anchor situation that you're talking about). So, what effect will this have on the fall factor and fall forces? Whatever piece is loaded, I imagine, will be hit with significantly more force, so this is probably a horrible idea unless the consequences of not doing so would be the leader decking.
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cracklover
Dec 4, 2003, 8:43 PM
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In reply to: What belay devices are you guys using? The huge forces possible with a factor 2+ fall is not achievable with most belay devices that I know of... GriGri starts slipping at 9kN.
Most single ropes have an impact force of between 8 and 10 kN, and double ropes are even less. For all intents and purposes, this means that in real life scenarios the grigri is a static belay device - in other words, equivalent to a knot.
In reply to: There are times when wheeling in slack are necessary to keep injury to a minimum. Slabs. The forces are always lower because the sliding, grating, and scraping slow down the falling leader.
Perfect example. Climbing safely is not about rules, it's about making intelligent, informed choices. The fact that many people's choices seem to be informed by misunderstandings is a little scary. A couple of interesting points:
If you do the math, you will find that the fall factor for a smaller (< ff1) fall gets _smaller_ if you take up any slack, while taking up slack in a larger (>ff1) fall _increases_ the fall factor.
For anyone who's interested, here's an example of a >ff1 fall, using the petzl fall simulator for the complex calculations:
Lets say the leader leaves the belay, clipping into the best piece of the anchor as he does. Let's say this piece is 1 meter above the belayer's device. The climber then proceeds to run it out an additional 5 meters before a foothold breaks off and the climber is airborn. So there's 6m of rope out, and the climber is 5m above his last piece of gear.
Scenario 1 - belayer locks off and hangs on tight. Climber falls 10m on 6m of rope. FF = 1.67. Acording to the Petzl fall simulator, an 80kg leader with a ff 1.67 using a 10.5mm single rope feels 7.8kN of peak force, and generates 13kN of force at his top piece.
Scenario 2 - belayer is able to pull in 1 meter of rope as the leader is falling. Climber falls 9m on 5m of rope. FF = 1.8. Acording to the Petzl fall simulator, this leader feels 8.1kN of peak force, and generates 13.5kN of force at his top piece.
Both of these are serious falls, and even well placed gear may fail at these forces. Is the additional 115 lbs of force going to make a difference in whether the piece fails or not? Maybe, or maybe not. Of course if it does, then you're in a world of trouble, as you're now looking at a fall directly on the belayer, who's now hanging from a compromised anchor.
Just some food for thought.
GO
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noshoesnoshirt
Dec 4, 2003, 9:23 PM
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j_ung wroteIn reply to: Sorry, but you're all wrong. In this scenario, if the belayer takes in 2m of rope, leavine 8m out, then the fall is only 16m, and still the same factor of 2. To fall 18m, the amount of rope in system has to be 9m. And even in that case, 18 divided by 9 is still 2.
draw a picture. if the climber falls from 10m up, and the belayer reefs in 2m of rope, the fall will be 18m (neglecting stretch). the climber will fall 10m to the anchors, and an additional 8m to the extent of the rope. fall factor = 18/8 = 2.25.
btw reno, 1/2 m*V^2 is kinetic energy, not force.
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curt
Dec 4, 2003, 9:37 PM
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In reply to: Friction reduces the overall energy but only the bealyer benefits and everyone else suffers.
Curt
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mountainmonkey
Dec 4, 2003, 10:11 PM
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In reply to: In reply to: What belay devices are you guys using? The huge forces possible with a factor 2+ fall is not achievable with most belay devices that I know of... GriGri starts slipping at 9kN. Most single ropes have an impact force of between 8 and 10 kN, and double ropes are even less. For all intents and purposes, this means that in real life scenarios the grigri is a static belay device - in other words, equivalent to a knot.
I don't know what your point was. I was referring to falls that are greater than factor two (ie 2+). The ropes are tested with a fall factor close to 2, but never greater than a factor 2. A factor 2+ fall would cause forces greater than the rated inpact force of the rope.
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jeffers_mz
Dec 4, 2003, 10:23 PM
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The key question posed by the thread's author requires a comparison of the peak forces imposed on a climber's falling body under two different scenarios.
On one side of the comparison, we have the kinetic energy a given fall imparts to the climber in terms of the distance fallen (fall energy), and on the other side of the comparison we have the rope's ability to absorb this energy over time (fall factor). Although these are the two starting points, neither one directly translates to peak force.
Force would seem to be the way to go regarding the kinetic energy a given fall distance will impose on the climber, but it it leads into a box canyon. Force equals mass times acceleration. Acceleration is change in velocity with respect to time. An instantaneous stop is delta V over zero, or infinite acceleration. Under infinite acceleration, the force also goes infinite, with decidedly less than pleasant side effects.
The best way to calculate "total fall energy" is to look at how much work it took to get the climber from the point he falls to up to the point he falls from. It takes 9.8 Newtons of force to raise one kilogram against the force of gravity. To raise one kilogram one meter requires 9.8 joules of work. To raise an 80 kilogram climber (176 pounds) 20 meters requires 9.8 Newtons times 80 kilograms times 20 meters, or 15,680 joules of work.
Ignoring atmospheric friction, the rope will have to do 15,680 joules of work to stop the falling climber. What goes up must come down. When a person climbs, kinetic energy is converted to potential energy (altitude in this case) and in returning to the original elevation that precise amount of potential energy is converted back to kinetic energy.
In arresting the climber's fall, the work done by the rope converts his kinetic energy into potential energy which is stored in the spring. The work necessary to stretch a spring a given distance can be expressed by:
Work equals 1/2 times the Force times the Stretch Distance.
Here we start getting into deep water because the Stretch Distance figures given for the rope are expressed as dynamic elongation, how much stretch will occur during the arrest of a 1.78 fall factor drop, in percentage of the rope's total length. This figure will change, possibly dramatically, if the fall factor changes.
In the simple case, using the dynamic elongation figures given by Climbing magazine (9/15/2003) for ropes ranging from 9.3 to 9.8 mm and a 1.78 fall factor, a reasonable average will be 31 percent.
Using 10 meters of rope, a 31% Stretch Distance translates to 3.1 meters. If the total work done by the rope is 15,680 joules, and the Stretch Distance is 3.1 meters, then by the above formula:
Work (15,680 joules) equals Force times the Stretch Distance times one half, or:
Force equals two times (Work divided by Stretch Distance), or:
Force equals 2 x (15,680/3.1), or
10116.12 Newtons
Since Force also equals mass times acceleration, then:
10116.12 Newtons equals 80 kg times Acceleration, or
Acceleration equals 10116.12 divided by 80 kilograms, or
126.45 meters per second per second.
Since 1.0 G equals 9.8 meters per second, this acceleration figure translates to 12.90 G .
Therefore, a climber falling 20 meters, with 10 feet of rope out will be subject to a 12.9 G negative acceleration.
A climber falling 18 meters will require that 14112 joules of work be done to arrest his fall. The dynamic elongation of 8 meters of rope would be 2.48 meters, and would impose a force of 11382 Newtons, or 142.25 meters per second per second, or 14.52 G on the climber.
The answer then, to the original question, "should I take two meters or lock off immediately?", in the simple case, involving an 80 kg climber and a 10 meter runout, ignoring variable dynamic elongation and friction effects, is:
"It doesn't matter. Either way the climber will be dead, but he'll deader if you take."
Interestingly, when you play with the formulae, you see that the acceleration imposed on the climber becomes a constant times the quantity: distance fallen over 31% of the rope out. To reach the break even point, the distance fallen ( which is twice the rope past the last piece) would be roughly one third the length of of the rope in use.
Since the distance fallen is twice that of the rope runout, the guideline would then become:
If the runout is less than one sixth of the total length of the rope in use, take.
If the runout is more than one sixth of the rope in play, lock off immediately, or better yet, give the climber a soft catch.
Even better, if the runout/total rope in use (times 100 to get a percentage) is less than half the of the dynamic elongation figure, take.
If the runout/total rope x 100 is more than half the dynamic elongation, give a soft catch.
Of course, since this is based on a static dynamic elongation figure that does not change with the fall factor, and does not take any friction effects into account, it is still useless, but not as useless as it was before.
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xanx
Dec 4, 2003, 10:35 PM
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...i smell a great senior thesis for aspiring physics majors...
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j_ung
Dec 4, 2003, 11:53 PM
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Now the more I think about it, the more wrong I'm certain I was. The belayer can actually increase the fall factor by pulling in rope during the climber's fall.
I can even think of a practical example:
Sport climber blows second clip. To keep him/her off of the ground the belayer squats away from the fall to quickly take up rope. The resulting catch is harder on both the climber and belayer.
This a great thread. I've been thinkin' about all day.
j_ung
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jt512
Dec 5, 2003, 12:52 AM
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In reply to: Now the more I think about it, the more wrong I'm certain I was. The belayer can actually increase the fall factor by pulling in rope during the climber's fall.
The relevant math is simple.
When you pull in slack during a fall, you decrease both the numerator and the denominator of the fall factor by the same amount. The consequence of this is that the fall factor gets further from 1. Thus, if the initial fall factor was less than 1, pulling in slack reduces the fall factor, and the peak impact force is reduced. On the other hand, if the original fall factor was greater than 1, then pulling in slack increases the fall factor and the peak impact force is greater.
Does this mean you should pull in slack if the fall factor is less than 1 in order to reduce the impact force? The answer is no. Pull in rope if the leader is going to hit something or if he's sliding down a slab. Otherwise, you should dynamically belay, letting out rope or jumping at the instant the leader's weight comes onto the rope. This will reduce the impact force more effectively than trying to haul in rope while the leader is in freefall. Should you let out rope to reduce the fall factor of a hard ( > factor-1) fall? Probably not. In reality, you'll be locking off with all your might praying that you can maintain control of the belay.
Being really bored, I'll post the math:Let:
a > 0 = the fall distance if no slack is pulled in
b > 0 = the amount of rope out if no slack is pulled in
s < min(a,b) = the amount of slack pulled in
Therefore,
a/b = the fall factor if no slack is pulled in, and
(a-s)/(b-s) = the fall factor after slack is pulled in.
If a < b (ie, fall factor < 1), then
(a-s)/(b-s) --> 0 as s --> a (1)
If b < a (ie, fall factor > 1), then
(a-s)/(b-s) --> inf. as s --> b (2)
Eq. (1) implies that if the initial fall factor < 1 then pulling in slack reduces the fall factor.
Eq. (2) implies that if the initial fall factor > 1 then pulling in slack increases the fall factor. |
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jeffers_mz
Dec 5, 2003, 1:38 AM
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In reply to: The relevant math is simple. When you pull in slack during a fall, you decrease both the numerator and the denominator of the fall factor by the same amount. The consequence of this is that the fall factor gets further from 1. Thus, if the initial fall factor was less than 1, pulling in slack reduces the fall factor, and the peak impact force is reduced. On the other hand, if the original initial fall factor was greater than 1, then pulling in slack increases the fall factor and the peak impact force is greater. Does this mean you should pull in slack if the fall factor is less than 1 in order to reduce the impact force? The answer is no. Pull in rope if the leader is going to hit something or if he's sliding down a slab. Otherwise, you should dynamically belay, letting out rope or jumping at the instant the leader's weight comes onto the rope. This will reduce the impact force more effectively than trying to haul in rope while the leader is in freefall. Should you let out rope to reduce the fall factor of a hard ( > factor-1) fall? Probably not. In reality, you'll be locking off with all your might praying that you can maintain control of the belay. -Jay
Excellent work, sir, for two reasons.
One, it greatly simplifies the math involved.
Two, it quantifies the indeterminate variable that robbed my effort above of usefulness, namely, the rate at which dynamic elongation varies with respect to fall factor.
Since your math is impeccable (not to mention elegant), then dynamic elongation must vary directly and linearly (within the limits imposed by an imperfect spring)with respect to fall factor.
Now I understand something that has always subconciously made me uncomfortable with the premise that fall factor alone, and not the distance of the fall, determines acceleration in arresting the fall, and further, understand the error in that previously subconcious line of thought.
The stretch variable itself varies so as to balance the equation, in effect becoming a mathematical shock absorber.
I stand in awe.
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fullahsiffur
Dec 5, 2003, 2:43 AM
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That's interesting. Everyone is chipping in physics formulas, with distance, time, newtons, joules, and g numbers. Then J_ung chips in with basic math difficulties (20 - 2 = 16) about a point covered in the first paragraph of the post.
Anyway, it is rare that in forums for other sports you will see people with these deep thoughts and (not too deep) physics.
Climbers are just smarter.
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curt
Dec 5, 2003, 3:21 AM
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Jay,
Nice work, as usual.
Curt
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slcliffdiver
Dec 5, 2003, 3:23 AM
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In reply to: In fact any friction will decrease rather than increase any forces experienced in the fall. Curt
It'll increase the force felt on the climbers side and decrease the force felt on the belayers side of the friction (another reason rope drag is a drag).
BTW the simple explaination of why fall factors are fairly accurate at predicting forces (for a tied of rope) is because the energy absorption capability of a rope increase linerally with the amount of rope out and the energy of a falling climber increase linerally with distance (the velocity increases as the square route of the "distance" fallen and the energy increases as the square of the velocity take the product and it gives a liner increase with distance).
Edit: BTW I'm with mountainmonkey for the most part what will happen in real life isn't a simple as fall factors.
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jonathanjcooke
Feb 16, 2007, 9:53 AM
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Well put.
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cantbuymefriends
Feb 16, 2007, 10:21 AM
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tedc wrote: In reply to: In fact any friction will decrease rather than increase any forces experienced in the fall. Curt Mostly right, however, the force that the climber feels is actually increased due to the friction of the rope in the top biner. This friction tends to issolate some of the force he/she creates from getting to the belayer's side of the rope where it could be better dissapated.
The OP asked about true factor 2 (or larger) falls, when the climber is falling straght onto the bely.
Then there will not be any "top biner" that the rope is running through. And there will not be any friction in the system at all, other than the belay device.
(Edited to fix quote)
(This post was edited by cantbuymefriends on Feb 17, 2007, 6:52 PM)
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deadhorse
Feb 16, 2007, 6:55 PM
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IN the really long post on this page- the one with the kinetic conversion to joules- you make a leap in there I'm not sure how you got, unless you were kidding.
[paraphrase]' should I take in rope or not, it doesn't matter, he'll be dead'
I hope you're not saying that 12.5 G is going to kill a person, I was under the impression that it took much much more than this... I have heard that avg car crashes are 60-70G and it takes 100G to break a neck. Fighter pilots get into the 10 G range if i'm not mistaken. I guess it was a physics joke over my head.
How come, in our calculation of the deceleration we haven't had to factor in the time in any of these? We looked at the amount of distance for a catch (elongation) but time plays just as critical a role- DOes it get factored w/ the speed of the fall / deceleration period?
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curt
Feb 19, 2007, 6:24 AM
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deadhorse wrote: ...How come, in our calculation of the deceleration we haven't had to factor in the time in any of these? We looked at the amount of distance for a catch (elongation) but time plays just as critical a role- DOes it get factored w/ the speed of the fall / deceleration period?
You can measure the time required to bring the falling climber to a rest--or the distance. The result is the same either way.
Curt
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paulraphael
Feb 21, 2007, 3:57 PM
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This is all interesting, but I suspect irrelevent. I'm willing to bet that the difference in forces between a factor 2 and a factor 2.25 fall are extremely low, and that it's unlikely that anyone is going to be able to yard in enough slack to make a bigger difference than that.
Consider that the difference in force between a factor 2 and a factor 1 fall is much less than 100%. We might be talking about a 5% or 10% difference (impossible to know without real world tests using a real belayer and device). Other factors probably make a bigger difference.
There's one way to create much larger than factor 2 falls, and it usually involves climbers not paying attention. If you have a belay rigged with generous lenghts of static material (cord, slings, etc.) and the belayer allows slack to form in the system, this can lead to huge fall factor increases in a short factor 2 fall.
Not much different than people wandering above an anchor while clipped with a daisy chain. People have broken carabiners by falling just a few feet.
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