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tahoe_rock_master
Feb 26, 2004, 1:49 AM
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I was wondering what Fall Factor was. I saw it mentioned as "Factor 2 fall". Although I have been climbing for about two years I have never heard of this expression.
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curt
Feb 26, 2004, 2:17 AM
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In reply to: I was wondering what Fall Factor was. I saw it mentioned as "Factor 2 fall". Although I have been climbing for about two years I have never heard of this expression.
Although the search engine on this site leaves something to be desired, you might try searching for "fall factor" because this topic has been covered several times.
Basically the fall factor is the distance fallen divided by the length of rope that is available to absorb the kinetic energy generated by the fall. The number is constrained between some number approaching zero on the low end, and 2 on the high end. It is used to calculate the force "seen" by the gear, climber and belayer in different fall scenarios. The higher the fall factor--the higher the force. Hope this helps a bit.
Also, you may want to reference this thread -
http://www.rockclimbing.com/forums/viewtopic.php?t=52735&postdays=0&postorder=asc&topic_view=&start=0
Pay particular attention to the posts by rgold (Rich Goldstone) who was one of the top climbers of the 20th century and is also a PhD. and Professor of mathematics.
Curt
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drkodos
Feb 26, 2004, 2:44 AM
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I think the concept of fall factor is much underappreciated and misunderstood.
Most falls people will ever take are much lower than a 1.0 on the scale that goes to 2.0, because you cabn never fall farther than twice the length of the rope itself, if you are tied in and want it to be used a safety measure by having it running through a system of protection.
Fall factor is feet fallen over amount of rope. It is an easy ratio to understand, I think despit the fact that I have no PhD in mathmatics for this is really arithmetic.
10 foot fall 100 feet up a climb would be:
10/100 = Fall Factor .10
10 foot fall 50 feet up? 10/50 = Fall Factor .2
The higher the number, the higher the force. Also, notice how the fall distance is not as important as the ratio. Certainly a 10 foot fall on 150 feet of rope is much more palatble than a 10 foot fall while only 10 feet off the deck! It's ll about the ratio.
A 20 foot fall while 22 feet off the deck would be: 20/22 == FF .909
In order to have a factor above 1, a person must fall lower than an anchor and be on an upper pitch, else a 30 foot fall 30 feet off the deck and you crater.
But high up a cliff, on a multipitch route, it is possible to be 50 feet off the belay and fall only to end up 20 feet below the original belay anchor. This 70 foot fall would then be: 70/50 = A fall Factor of 1.4 !!! Very dangerous! As anything over 1.0 is some sever sheet.
While I am not a PhD in manthematics, I feel this is an easy ratio to understand, and though I am sure to have oversimplified, I welcome any corrections, additions, or rearticulations of my layman's blatherings.
In 30 years of climbing and over 750 leader falls I have only one time ever taken a fall with a factor in excess of 1. I have taken over 10 falls with factors of 1, all of them right into the ground itself.
That probably explains much............
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curt
Feb 26, 2004, 2:54 AM
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750 leader falls? Good God man, I hope you were wearing a helmet. Hahahahahahahahahaha. Have you considered shuffleboard instead? :lol:
Curt
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drkodos
Feb 26, 2004, 3:08 AM
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In reply to: 750 leader falls? Good God man, I hope you were wearing a helmet. Hahahahahahahahahaha. Have you considered shuffleboard instead? :lol: Curt
There are some tough routes at the Gunks that I have fallen all over..... :lol: and up. (Many of them with Dr. Goldstone's nome de plume on the FA)
Perhaps lack of helmet has conribulated to my latest affloctions, but I donut think it has hade an efect atoll.
I am stupefyingly proud that I have already logged 11 falls and a crater shot this year already!
Although recently an aquaintance suggested the actual idea inherrant in the pursuit of climbing was to make progress upwards, so I am thinking of giving that a try one of these daze.....
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allthetime
Feb 26, 2004, 7:48 PM
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Most falls people will ever take are much lower than a 1.0 on the scale that goes to 2.0, because you cabn never fall farther than twice the length of the rope itself.
Just to be accurate: the maximum fall factor is infinite. You can very easily fall more than twice the distance of the amount of rope out at impact.
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allthetime
Feb 26, 2004, 7:52 PM
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In reply to: I think the concept of fall factor is much underappreciated and misunderstood. Most falls people will ever take are much lower than a 1.0 on the scale that goes to 2.0, because you cabn never fall farther than twice the length of the rope itself
Just to be accurate: the maximum fall factor is infinite. You can very easily fall more than twice the distance of the amount of rope out at impact.
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allthetime
Feb 26, 2004, 7:57 PM
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In reply to: I think the concept of fall factor is much underappreciated and misunderstood. Most falls people will ever take are much lower than a 1.0 on the scale that goes to 2.0, because you cabn never fall farther than twice the length of the rope itself...
just to be accurate: the maximum fall factor is infinite. you can very easily fall more than twice the distance of the amount of rope out at impact.
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drkodos
Feb 26, 2004, 7:59 PM
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In reply to: Most falls people will ever take are much lower than a 1.0 on the scale that goes to 2.0, because you cabn never fall farther than twice the length of the rope itself. Just to be accurate: the maximum fall factor is infinite. You can very easily fall more than twice the distance of the amount of rope out at impact.
Incorrect.
Max fall factor with a rope in a climbing system and used properly is 2.0
I explained this in my first post. If both people are tied in and protection is being used and the rope and anchors work, the maximun fall is twice the length of the rope. Period.
Free soling does not count. There is no such thing as fall factor if there is no rope involved.
Any fall that does not weight the protection system does not count. Fall factor is all about force being transfered to the protection system and/or anchor.
Please think about it.
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allthetime
Feb 26, 2004, 8:13 PM
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In reply to: Incorrect. Max fall factor with a rope in a climbing system and used properly is 2.0...I explained this in my first post. Please think about it.
ok, fair enough...thinking...thinking...ahhhah! a climber is on the second pitch of a route, and is 20 feet out from the belay. as it's starting to get difficult the climber looks for the next bolt or place to put pro. the belayer sees his partner's legs start shaking and readies the belay. the climber slips and falls before finding any pro, and the belayer takes in one armfull of rope, say 3 feet, and locks off, and braces for the impact. what's the fall factor?
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voriand
Feb 26, 2004, 8:18 PM
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The INCREASE of fall factor would be small and pointless.
Besides you should be locking off for the impact. Not messing around trying to pull in rope.
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olderic
Feb 26, 2004, 8:54 PM
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This monthly topic seems to have surplanted long discussions on how to mark the middle of the rope, what shoes to buy, or whether or not to use the harness bealy loop to (gasp) belay off of. There will follow much arm waving and chest thumping as to whether 2.0 is the max. Foreign languages - via ferrata - will be invoked and the thread will lurch off in that direction. Then the idea of reeling in rope while a leader is falling will be spouted - could you, would you, should you... on and on an on
Question first - reserach later
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drkodos
Feb 26, 2004, 9:03 PM
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In reply to: In reply to: Incorrect. Max fall factor with a rope in a climbing system and used properly is 2.0...I explained this in my first post. Please think about it. ok, fair enough...thinking...thinking...ahhhah! a climber is on the second pitch of a route, and is 20 feet out from the belay. as it's starting to get difficult the climber looks for the next bolt or place to put pro. the belayer sees his partner's legs start shaking and readies the belay. the climber slips and falls before finding any pro, and the belayer takes in one armfull of rope, say 3 feet, and locks off, and braces for the impact. what's the fall factor?
2.0
If you fall from above the anchor to below the anchor it is always above 1.0
20 feet up and you fall with no gear and end up falling "ONTO" the anchor itself is a factor 2 fall, by definition, regardless of rope amount. It is a ration. Whatever rope is out, all of it, the leader falls the distance above PLUS the distance of that same amount below. Thus the formula which is:
Length of fall/Amount of rope
Were the first is X and rope is Y we substitute:
Y = 20 feet up. So feet of rope minus 3 yarded in is 17 feet.
Therefore Y = 17
Fall then would be the 17 feet of rope to the anchor PLUS the 17 feet the climber falls below the anchor. The additions of strecth is a little complicated,so befroe some jumps in a yells, I admit to an obversimplification here just to try to get at the basic os the ratio.
Therefore X = 34.
x/y = fall factor
34/17 = 2.0
The point is that it is a relationship between the amount of rope in the system and the distance fallen. And this ratio is more important in many cases than the actual amount someone may fall.
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allthetime
Feb 26, 2004, 9:08 PM
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In reply to: The INCREASE of fall factor would be small and pointless.
first, the increase in fall factor is potentially large-- infinite in fact. second, i would argue any increase in force when you get near the limits of your anchor is extremely significant. i think it's down to each climbing team to determine their level of risk, but to not know about a potential risk means you are precluded from making a decision as to whether it's acceptable or not.
In reply to: Besides you should be locking off for the impact. Not messing around trying to pull in rope.
what if there is a ledge 20 feet below the belay? what if the climber placed one shaky piece of pro before falling?
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allthetime
Feb 26, 2004, 9:14 PM
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In reply to: Fall then would be the 17 feet of rope to the anchor PLUS....
re-examine how far the climber is above the anchor when he starts falling. you said it earlier in your post:
In reply to: 20 feet up and you fall with no gear and end up falling "ONTO" the anchor... |
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drkodos
Feb 26, 2004, 9:15 PM
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In reply to: what if there is a ledge 20 feet below the belay? what if the climber placed one shaky piece of pro before falling?
These are two seperate questions.
If you hit a ledge, all bets are off. Fall factor is calculated based on not having momentum stopped by anything other than the protection system.
Two.
Placing a piece changes things. Let us pretend it holds and this is our new scenario.
Climber is up 20 feet and has shaky gear at 12 feet up. He then falls from 8 feet above the last piece and it holds. Now the factor is calculated thusly.
8 feet above the piece X 2 equals a fall of 16 feet.
We originally had 20 feet of rope out. So X/Y becomes 16/20 = .8 Fall factor.
Much better than 2.0!!! Anything under 1. is manageable, but anything over 1 becomes a nuisance.
Hitting a ledge anywhere in this process and now we have to talk impact physics without the use of dynamic ropes and protection systems, or some gray area in between.
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olderic
Feb 26, 2004, 9:20 PM
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[quote="drkodos"][quote="allthetime"][quote="drkodos"] Incorrect.
Were the first is X and rope is Y we substitute:
Y = 20 feet up. So feet of rope minus 3 yarded in is 17 feet.
Therefore Y = 17
Fall then would be the 17 feet of rope to the anchor PLUS the 17 feet the climber falls below the anchor. The additions of strecth is a little complicated,so befroe some jumps in a yells, I admit to an obversimplification here just to try to get at the basic os the ratio.
Therefore X = 34.
x/y = fall factor
34/17 = 2.0
I just have one question - was the leader a little upset when he was 20 feet out and you yarded in 3 feet of rope and pulled him down 3 feet before he fell?
In your over simplified version the numbers would still be 37/17 which is >2.0.
In the real world people can and do take rope in on a falling (hopefully not until afer (s)he falls) leader and produce factors greater then 2.0. Probably even more common is to give dynamic belays to lesson the fall factor - intentionally on steep sport routes - unintentionally in cases where a real fall on to the anhor is in progress.
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allthetime
Feb 26, 2004, 9:23 PM
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In reply to: In reply to: what if there is a ledge 20 feet below the belay? what if the climber placed one shaky piece of pro before falling? These are two seperate questions. If you hit a ledge, all bets are off. Fall factor is calculated based on not having momentum stopped by anything other than the protection system.
i'm afraid you missed the point. those lines of mine were in response to the person who said you should be locking off and not trying to take in rope. i gave two situations where a belayer might consider it appropriate to take in rope when the climber falls. can you see why? the first one is fairly obvious. how about the second one?
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jt512
Feb 26, 2004, 9:24 PM
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In reply to: The INCREASE of fall factor would be small and pointless. Besides you should be locking off for the impact. Not messing around trying to pull in rope.
The mathematically inclined belayer will instantly realize that, if the leader is 10 feet above the anchor with no pro in, that the best course of action is to just let go of the rope and let the leader take the maximum 210-foot fall. The rusulting 1.05-factor fall yields the minimum impact force.
HTH
-Jay
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dirtineye
Feb 26, 2004, 9:37 PM
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In reply to: In reply to: The INCREASE of fall factor would be small and pointless. first, the increase in fall factor is potentially large-- infinite in fact. second, i would argue any increase in force when you get near the limits of your anchor is extremely significant. i think it's down to each climbing team to determine their level of risk, but to not know about a potential risk means you are precluded from making a decision as to whether it's acceptable or not.
In the first place, like Drkodos has said about twice now, the fall factor RATIO of fall length to rope length out depends on rope and anchor working correctly, or it is meaningless.
Please explain how this ratio can grow large, as in much larger than 2, let alone approach infinity. If you can sucessfully show that the increase in fall factor can be infinite under any circumstance where fall factor has meaning, you will have invented a new math and a new physics, and your Nobel prize is waiting. More than likey you will just win an Ignoble prize.
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cracklover
Feb 26, 2004, 9:42 PM
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In reply to: In the first place, like Drkodos has said about twice now, the fall factor RATIO of fall length to rope length out depends on rope and anchor working correctly, or it is meaningless. Please explain how this ratio can grow large, as in larger than 2, let alone appraoch infinity. If you can sucessfully show that the increase in fall factor can be infinite under any circumstance where fall factor has meaning, you will have invented a new math and a new physics, and your Nobel prize is waiting. More than likey you will just win an Ignoble prize.
Oh please. He's already done so (and it's been done countless times before). Please check my math for me, dirt. By my calculations 37/17 is roughly 2.18.
Allthetime's point about the ledges is merely that if you know there's a ledge below you, as a belayer you may choose to take that risk and haul in rope, knowing that it may save your climber from decking, despite putting a larger force on the anchor.
But unless it's some kind of monster fall, the whole idea of yarding in is, or should be, purely theoritical. Do the calculations yourself as to how long a fall takes (they're not hard, you don't need anything more than simple multiplication, division, and the formula 10m/s/s.) Anyway, my point is that you're just going to have time to brace yourself for impact and hang on for a nasty ride - the idea of taking in rope in such a situation is really silly.
GO
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alpnclmbr1
Feb 26, 2004, 9:44 PM
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In reply to: 20 feet up and you fall with no gear and end up falling "ONTO" the anchor itself is a factor 2 fall, by definition, regardless of rope amount. It is a ration. Whatever rope is out, all of it, the leader falls the distance above PLUS the distance of that same amount below. Thus the formula which is: Length of fall/Amount of rope Were the first is X and rope is Y we substitute: Y = 20 feet up. So feet of rope minus 3 yarded in is 17 feet. Therefore Y = 17 Fall then would be the 17 feet of rope to the anchor PLUS the 17 feet the climber falls below the anchor. The additions of strecth is a little complicated,so befroe some jumps in a yells, I admit to an obversimplification here just to try to get at the basic os the ratio. Therefore X = 34. x/y = fall factor 34/17 = 2.0
37/17 = 2.176
Yarding in the rope can increase a fall factor beyond 2.0
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dirtineye
Feb 26, 2004, 9:47 PM
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And last tiime I looked, 2.18 or even 2.2 .r even 2.3 is not a lot bigger than 2.0.
This guy is claiming the increase can be infinite.
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jt512
Feb 26, 2004, 9:55 PM
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In reply to: And last tiime I looked, 2.18 or even 2.2 .r even 2.3 is not a lot bigger than 2.0. This guy is claiming the increase can be infinite.
I think he's claiming that theoretically it can. You can never actually achieve infinity. You could achieve a large increase in the fall factor if the belayer could take in slack fast enough and the fall was short enough.
-Jay
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cracklover
Feb 26, 2004, 9:58 PM
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In reply to: And last tiime I looked, 2.18 or even 2.2 .r even 2.3 is not a lot bigger than 2.0. This guy is claiming the increase can be infinite.
Okay, you can now see how it is possible to increase a FF over two. As a purely theoretical problem (because that's all it is) you should now be able to see how you can give a ff = 4, ff = 10, 100, etc. (infinite is hard).
GO
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timpanogos
Feb 26, 2004, 10:04 PM
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Heck, you guys are dealing with sissy + factor 2 fall scenarios.
Ok, My leader climbs up 200', no pro off the anchor and pitches.
Rope elongation on the lead rope is 7%, so, technically my leader falls 414 feet before bungy bounching back up.
so 414/ 200 = 2.07
But what is really the danger for the leader here, is after he climbs/jugs back up to the anchor, I punch his lights out for being an idiot.
Fall distance over rope out, and oh yea if you fall below your last fixed point (2, 2.07, 2.whatever) you're going to need to clean out your pants (and maybe get your ribs/spleen looked at).
Hey, it's not just a good idea - it's the law!
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drkodos
Feb 26, 2004, 10:07 PM
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Wrong.
20 feet above the anchor, as measured from where? You can't be 20 feet above the anchor unless there is 20 feet of rope out.
Then 20 feet above to below would be a 40 foot fall on 20 feet of rope.
40/20 = 2.0
You guys that got 37 feet are crazy. Your ARITHMETIC is faulty.
Yarding rope does not increase fall factor. Here is why:
It reduces both the fall AND THE LENGTH OF ROPE. Both variables are affected, not just one as in the above fallacious analysis.
It is simple arithmetic. Not mathematics.
When you pull ion rope there is less rope out and there is less distnace one can fall. Period.
You can never be farther from the belay than the amount of rope you have out.....if there is 17 feet or rope then you are 17 feet (or less!) off the belay.
It is possible though to be 17 feet up and have more rope due to slack. This DECREASES fall factor and is why people like me like having SLACK when I push my limits.
Then 17 feet up with 25 feet of rope and falling below the anchor would be this.
17 feet + 25 feet below the anchor = 42 feet.
42 feet over 25 feet...42/25 = 1.64
Fall factor can never be above 2.0 by its definition.
Both theoretically and in the real world.
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dirtineye
Feb 26, 2004, 10:13 PM
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In reply to: In reply to: And last tiime I looked, 2.18 or even 2.2 .r even 2.3 is not a lot bigger than 2.0. This guy is claiming the increase can be infinite. I think he's claiming that theoretically it can. You can never actually achieve infinity. You could achieve a large increase in the fall factor if the belayer could take in slack fast enough and the fall was short enough. -Jay
Sadly, I don't think he is being theoretical. I agree with the point that unless the fall is long, the belayer does not have much time to do a lot of reeling in.
What are you calling a large increase?
I've only seen about 3 feet be taken in in a 20 foot fall.
Something that is not theoretical however is the effect of friction on the rope running through the pro and rubbing against the rock. that can raise the fall factor, but in a fall on the anchors, I guess this is not an issue.
I've read in more than one place that actual fall factor can't even pass 1.77.
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drkodos
Feb 26, 2004, 10:14 PM
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In reply to: Heck, you guys are dealing with sissy + factor 2 fall scenarios. Ok, My leader climbs up 200', no pro off the anchor and pitches. Rope elongation on the lead rope is 7%, so, technically my leader falls 414 feet before bungy bounching back up. so 414/ 200 = 2.07 But what is really the danger for the leader here, is after he climbs/jugs back up to the anchor, I punch his lights out for being an idiot. Fall distance over rope out, and oh yea if you fall below your last fixed point (2, 2.07, 2.whatever) you're going to need to clean out your pants (and maybe get your ribs/spleen looked at). Hey, it's not just a good idea - it's the law!
rope stretch DECREASES fall factor by making both variable longer. You need to add the lenght of stretch to both sides of the equation. It is arithmetic. You cannot just add to one side and not the other willy nilly.
As the falls becomes longer, so does the rope!
The definition of fall factor is a closed end system that goes from 0 to 2.0.
Until quantitative analysis is presented in the form of some higher physics and mathematics, I maintain my position.
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jt512
Feb 26, 2004, 10:15 PM
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[quote="drkodos"]Wrong.
20 feet above the anchor, as measured from where? You can't be 20 feet above the anchor unless there is 20 feet of rope out.
Then 20 feet above to below would be a 40 foot fall on 20 feet of rope.
40/20 = 2.0
You guys that got 37 feet are crazy. Your ARITHMETIC is faulty.
Yarding rope does not increase fall factor. Here is why:
It reduces both the fall AND THE LENGTH OF ROPE. Both variables are affected, not just one as in the above fallacious analysis.
That is why it does affect the fall factor. More precisely, the fall factor is a ratio, and when you pull in slack, you reduce the numerator and denominator by the same addititive amount. In order for the ratio to not change, the ratio would have to be 1. Otherwise, the numerator and denominator are not changed proportionately.
(a - c) / (b - c) does not equal a/b, unless a = b.
-Jay
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drkodos
Feb 26, 2004, 10:18 PM
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I will add 10 perecnt stretch:
20 feet above the anchor. 20 feet of rope out. Fall.
The 20 feet of rope streches 2 feet and becomes 22.
the fall then becomes ten percent larger and becomes instead of 40, 44.
Now our formula:
x/y = ff
x= 44
y= 22
44/22 = 2.0
It is simple arithmetic. It is a ratio, folks. That is the nature of a ratio.
Some of you guys are using math straight out of Spinal Tap.
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cracklover
Feb 26, 2004, 10:28 PM
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Doc, you are right. As the climber begins to fall, gravity will anticipate that the belayer will take in 3 feet of rope over the course of the 40 foot fall, and cause the climber to only accelerate for 37 feet, rather than the usual 40. :roll:
And can I just mention two other things:
1 - FF uses the fall length before the rope begins to catch you.
2 - In a high fall factor expect the rope to stretch 30% or more.
GO
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jt512
Feb 26, 2004, 10:32 PM
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In reply to: I will add 10 perecnt stretch: 20 feet above the anchor. 20 feet of rope out. Fall. The 20 feet of rope streches 2 feet and becomes 22. the fall then becomes ten percent larger and becomes instead of 40, 44.
No. The fall becomes 5% larger.
42/22 = 1.91
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shakylegs
Feb 26, 2004, 10:34 PM
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Ah yes, the famous fall factor going up to 11.
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dirtineye
Feb 26, 2004, 10:34 PM
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In reply to: I will add 10 perecnt stretch: 20 feet above the anchor. 20 feet of rope out. Fall. The 20 feet of rope streches 2 feet and becomes 22. the fall then becomes ten percent larger and becomes instead of 40, 44. Now our formula: x/y = ff x= 44 y= 22 44/22 = 2.0 It is simple arithmetic. It is a ratio, folks. That is the nature of a ratio. Some of you guys are using math straight out of Spinal Tap.
Actually the rope does not stretch til you fall on the pro right?
So 20 feet above the anchor, plus 20 feet below plus 2 feet for rope stretch would be 42/22, or less than 2.
There is a more advanced fall factor calcuation on the Beal web page, that takes into account things that the theoretical calc does not.
http://www.impact-force.info/anglais/impact.html
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olderic
Feb 26, 2004, 10:38 PM
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Stretch doesn't enter in to it - the ratio denominator is the unweighted length of the rope at the instance that the falling weight comes on it. But even assuming that stretch can be factored in you are failing to grasp or at least acknowlege that the length of rope between the belay and the faller can change between the time the fall begins and the time it starts to get caught. In the case of a free fall it might be unrealistic to expect that it will change much, but in the case of a sliding slab fall it is common - there are plenty of real like stories of unanchored belayers sprinting down the hill to take it in on a slab fall - and yes yarding some in too. Of course in the case of a sliding slab fall the fall factor is not especially important in talking about the severity of the fall. But since you seem to be hung up on the actual mathamatics - and it is obvious tfat FF-s > 2 can easily be produced in real word situations. I do not comprehend how you don't grasp the flaw in your own 20 feet out, no pro, belayer yards in 3 example.
the fall is 37 feet, the length of the rope decreased 3 feet while the fall was in progress. Oh I give up - I am going actually climbing - does anyone here do that?
In reply to: I will add 10 perecnt stretch: 20 feet above the anchor. 20 feet of rope out. Fall. The 20 feet of rope streches 2 feet and becomes 22. the fall then becomes ten percent larger and becomes instead of 40, 44. Now our formula: x/y = ff x= 44 y= 22 44/22 = 2.0 It is simple arithmetic. It is a ratio, folks. That is the nature of a ratio. Some of you guys are using math straight out of Spinal Tap. |
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alpnclmbr1
Feb 26, 2004, 10:55 PM
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Doc, I assume by this point you will concede the numbers.
As far as fall factors
If you take a static fall onto a anchor sling it is easy to surpass FF2
via ferrata equipment is designed for fall factor 7
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drkodos
Feb 26, 2004, 11:38 PM
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Via Ferrata and rope free climbing are not comparable systems for fall factor.
It is possible to have a greater number than 2 in Via Ferrat, I concede that.
But it is not possible in a roped free climbing system. The roped climbing system is a close ended system. Via Ferrata is not.
I will, however, accept whatever definition a legitimate PhD of mathematics and physics has to say on the matter.
Until then, I maintain my position, but remain open minded as I have stated my bar level for burden of proof.
And that position is: In a closed system of free climbing with proper use of a dynamic rope and a system of protection, it is impossible to exceed fall factor of 2.0
I am willing to be shown the light, but it must be very clear and bright, for I am dense and deeply wooded in the mind.........
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dirtineye
Feb 26, 2004, 11:39 PM
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I found this link
http://www.geocities.com/Yosemite/Trails/8700/ropes.html
that details the fall factor testing method of the UIAA. Since they have a little rope (.3 m) between their carbiner like device and they only use a 2.8 meter length of rope( only 2.5m in the fall), they have a 1.77 ff in their 5 m test fall
So applying this to our belayer, he would have to be right up against the anchor biner or you will have to count that bit of rope between atc and anchor biner. Of course this little bit will make less difference as more rope is out.
As far a this discussion goes, ti was not about via ferrata or aind falls on daisys or falls on slings or anything but fall factors on climbing rope. Someone did predict that via ferrata woud lbe brought up and they were right hahaha.
As far as slab falls and belayers running down the slab, that is also not relevant to this discussion.
The 20 feet up with no pro except the anchor and the belayer yarding in three feet seems plausible. The situation where you have a ledge 20 feet below and no pro for 20 feet above this belay station sounds like one to avoid, but it is true that the theoretical FF would be 2.18 or so.
But what difference does this make?
Time to use the impact force calculator...
Using the calculation given here
http://www.impact-force.info/anglais/impact1.html
And a rope max impact force rating of 9,500N, I got for a ff of 2.18, 10,446N and for an ff of 2 10,041N
Still acceptable, and that is with a fairly high impact rope.
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jt512
Feb 26, 2004, 11:52 PM
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In reply to: Via Ferrata and rope free climbing are not comparable systems for fall factor. It is possible to have a greater number than 2 in Via Ferrat, I concede that. But it is not possible in a roped free climbing system. The roped climbing system is a close ended system. Via Ferrata is not. I will, however, accept whatever definition a legitimate PhD of mathematics and physics has to say on the matter.
By my count you've been corrected by one mathematician, one statistician, and one engineering student. Maybe it is time to take the hint.
In reply to: Until then, I maintain my position, but remain open minded as I have stated my bar level for burden of proof.
I've already stated an informal proof above. Here's a more rigorous one:
Let a, b, and c be positive numbers. Then, as c approaches the smaller of a or b:
If a < b, then (a - c)/(b - c) approaches a limit of 0, or
If a > b, then (a - c)/(b - c) approaches infinity.
-Jay
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vegastradguy
Feb 27, 2004, 12:05 AM
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If a climber falls frm 20 feet up and has no gear, and the belayer manages to yard in a 3 feet of slack, the fall factor is 2.18.
The climber falls from 20 feet up. He falls 20 to belay, during this time, the belayer yards in the slack. He then falls 17 feet past belay before the belayer catches him.
This translates to a 37 foot fall. 37 feet on 17 feet of line is a Factor 2.18 fall.
Of course, this sort of thing is rare at best, and for all intensive purposes, a factor 2 is about as bad as it can get, but not the worst it can get.
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drkodos
Feb 27, 2004, 12:05 AM
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In reply to: In reply to: Via Ferrata and rope free climbing are not comparable systems for fall factor. It is possible to have a greater number than 2 in Via Ferrat, I concede that. But it is not possible in a roped free climbing system. The roped climbing system is a close ended system. Via Ferrata is not. I will, however, accept whatever definition a legitimate PhD of mathematics and physics has to say on the matter. By my count you've been corrected by one mathematician, one statistician, and one engineering student. Maybe it is time to take the hint. In reply to: Until then, I maintain my position, but remain open minded as I have stated my bar level for burden of proof. I've already stated an informal proof above. Here's a more rigorous one: Let a, b, and c be positive numbers. Then, as c approaches the smaller of a or b: If a < b, then (a - c)/(b - c) approaches a limit of 0, or If a > b, then (a - c)/(b - c) approaches infinity. -Jay
I publically stand corrected.
Thank you for your patience as I did state that I am densely wooded in the brain.
That being said, I still have only ever taken 1 fall above factor 1.0 Of that I remain certain.
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dirtineye
Feb 27, 2004, 12:18 AM
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Jay that is not a proof, that is a set of statements that now must be proved.
Depending on what you will accept as true, a proof could get really tedious haha.
I think with a little more nudging though, drkodos will accept that you can contrive a ff of a little greater than 2. I'm not going to accept that you can get a really big ff by any action the belayer can take in reality, so let's leave out the idea about aproaching infinity, or even ff of 3.
One more time, climber places no pro above anchor, climber falls 20 feet above anchor, belayer yards in 3 feet, climber falls the 20 feet down to the anchor plus the 17 feet past for 37 feet. 37/17 is about 2.18.
This adds about 440 Newtons or so the the impact force the climber feels in a factor 2 fall, as I calculated above using the impact force calculation I linked to.
Now unless you can come up with a REASONABLE way to get a much higher ff, enough to get over an impact force of 12kN, it don't matter.
By the way, for the example of running down the slab, that will not really raise the theoretical ff even if your belayer were jumping off a ledge, because THE ROPE IS STILL IN THE SYSTEM.
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shut_up_and_climb
Feb 27, 2004, 12:30 AM
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do you know how to find the resting "kn" on the fall of an 8" draw from a 4' fall on an 11mm static rope? lets say the climber weighs 120 pounds.
-kyle
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dredsovrn
Feb 27, 2004, 12:31 AM
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In reply to: In 30 years of climbing and over 750 leader falls I have only one time ever taken a fall with a factor in excess of 1. I have taken over 10 falls with factors of 1, all of them right into the ground itself. That probably explains much............
Holy Crap! They should build a statue of you. I am going to guess that you have gotten over your feer of falling on gear. I hope to do the same someday.
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allthetime
Feb 27, 2004, 3:27 AM
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i don't think a belayer yarding in one armful of rope is "theoretical". The natural movement of bringing your brake hand from in front of you to back by your hip in a lock off position can take in 1-2 feet of rope. In addition, if the belayer is paying attention it can be readily apparent when a climber is going to fall, and if you anticipate the fall, you can easily yard in a full arm's length of rope.
good dr., now that you've gotten some of the intricacies of fall factors straightned out, how about revisiting the case where the leader is able to get one sketchy piece of pro in before falling. should the belayer take in rope if possible during the fall?
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drkodos
Feb 27, 2004, 3:39 AM
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In reply to: good dr., now that you've gotten some of the intricacies of fall factors straightned out, how about revisiting the case where the leader is able to get one sketchy piece of pro in before falling. should the belayer take in rope if possible during the fall?
I have already conceded this one as well, but I will do so here again publically.
Damn' it, Jim, I am rhetorician, not a mathmatician!
A piece is better than no piece.
Fall factor can be higher than 2.0.
What other hot button topics I am on the cannabis-addled-brain side of?
Act now, while I am down and ready for a good kicking. A window of opportuntiy like this is fleeting.
http://www.rottentomatoes.com/...&dateline=1054664104
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jt512
Feb 27, 2004, 3:44 AM
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In reply to: i don't think a belayer yarding in one armful of rope is "theoretical".
No, it isn't theorectical. Gumby belayers do it all the time.
In reply to: The natural movement of bringing your brake hand from in front of you to back by your hip in a lock off position can take in 1-2 feet of rope.
I disagree with that. The natural movement -- or at least the correct one -- is to bring your hand directly to your hip, which doesn't pull in any slack at all. To pull in slack, the belayer would have to straighten out his arm, which is neither natural nor correct, unless the situation really calls for pulling in slack.
In reply to: In addition, if the belayer is paying attention it can be readily apparent when a climber is going to fall, and if you anticipate the fall, you can easily yard in a full arm's length of rope. some people do that as a reflex.
Yes, that is a common gumby mistake, and the main reason I am very selective about who I allow to belay me. Pulling in slack like this can slam the leader violently into the wall, as has been discussed many times on this site.
Whether or not pulling in a foot or two of slack would make any practical difference in a factor-2 fall is not clear to me, though. Using a non-auto-locking belay device, a lot of rope is going to slip throught the device, resulting in an impact force much less than that which would result from a statically belayed factor-2 fall. Perhaps with a grigri, pulling in slack would be a problem, but then again, taking a factor-2 fall on a grigri is a problem itself.
In reply to: good dr., now that you've gotten some of the intricacies of fall factors straightned out, how about revisiting the case where the leader is able to get one sketchy piece of pro in before falling. should the belayer take in rope if possible during the fall?
I was going to go into that next, but I'll hold off to give drkodos a chance to respond.
-Jay
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vertical-rockrat
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Feb 27, 2004, 3:49 AM
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Anyone got a calculator?
Hmm 50 feet up and i don't think fall factor is running thru my head about then lol. Im shaking with a possible 15 foot fall knowing its gona hurt some if i land hard and my harness shifts.
OHHHHH wait ya i need to know this so when i make my first homemade rope i will know if it can take the fall.. LOL
I can understand wanting to know what fall factor is but i think what is most important is to know how many falls you have taken on your 6 fall rated rope.
just my opinion. alltho i would like to thank those for explaning it simple and giving the ratios. nice knowledge.
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allthetime
Feb 27, 2004, 3:52 AM
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In reply to: A piece is better than no piece.
yes, I think we might all agree on that. i'm not trying to brow beat you. the question I posed is what happens to the fall factor and therefore the force on that sketchy piece of pro if the belayer takes in rope vs. just locking off? try doing the math and see what you come up with.
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jt512
Feb 27, 2004, 3:59 AM
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In reply to: Hmm 50 feet up and i don't think fall factor is running thru my head about then lol. Im shaking with a possible 15 foot fall knowing its gona hurt some if i land hard and my harness shifts. I can understand wanting to know what fall factor is but i think what is most important is to know how many falls you have taken on your 6 fall rated rope. just my opinion. alltho i would like to thank those for explaning it simple and giving the ratios. nice knowledge.
Funny, but your opinion and mine are diametrically opposed. Your 6-fall rope will withstand 100s of falls if you take care of it, so there is no reason whatsoever to know how many falls it has held. On the other hand, if you understand fall factors, you would know not to worry about getting hurt on a clean 15-foot fall with 50 feet of rope out, since it would only be a factor-0.3 fall; but, that that same fall, when 15 feet above your first belay, would result in a factor-2 fall, that could not only hurt you, but could cause your belayer get injured also, possibly lose control of the belay entirely, or in the worst case scenario, cause your anchor to fail.
-Jay
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dirtineye
Feb 27, 2004, 4:24 AM
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In reply to: Whether or not pulling in a foot or two of slack would make any practical difference in a factor-2 fall is not clear to me, though.
It won't, assuming your anchor is a good 25 kn anchor. I calculated this for the 20 foot above the anchor adn a three foot reel in. you add 440 N over what the factor 2 fall would do, and it is still under 10.5 kN impact force. Evein if you let the guy be ten feet over the anchor and reel in thre feet, that still does not break 11kN, and I don't think anyone can do better than 3 feet off a 20 foot fall. If you wnat to check what I did, look at taht psot above adn use the link to the formula. I used 80kg as the mass, and all the other stuff I used I gave in the other post. Multiplying by 1.66 and the worst case of 11 kN the total force on the anchor is less than 25 kn, in fact it is 18.26 kN.
In reply to: In reply to: good dr., now that you've gotten some of the intricacies of fall factors straightned out, how about revisiting the case where the leader is able to get one sketchy piece of pro in before falling. should the belayer take in rope if possible during the fall? I was going to go into that next, but I'll hold off to give drkodos a chance to respond. -Jay
First, these intricacies are stupid. First you have to have someone dumb enough to climb up over an anchor for so many feet with no pro, but with a ledge the same number of feet below the anchor (the reason you gave to haul in line as I recall). Second, as I calculated, it won't matter, unless you can't build a decent anchor and so the anchor fails. By the way, I want to hear of a possible situation where the fall factor can get even close to 3, because even in the three foot reel in on a ten foot over the anchor fall 17/7 = 2.42, and that is nowhere near infinity, and still safe impact force as I calculated, so please stop with the infinite or even very large fall factor until you can DEMONSTRATE one that has a snowball's chance in hell of happening.
Second, jay, drkodos isn't playing any more haha. he alreadt said a piece is better than no piece and left it at that.
Third, real fall factor becomes complicated when a piece pulls, but here is a link from rgold about rope recover and blowing pieces:
http://groups.google.com/groups?q=%22shock+wave%22+group:rec.climbing&hl=en&lr=&ie=UTF-8&group=rec.climbing&selm=wk66oazj4l.fsf%40cline116.dsl.frii.com&rnum=6
But then real fall factor is much more complicated to start with if there is any friction between the rope and biners and or rock. You can ponder this at the beal links I gave above.
What are the details of the sketchy pro fall now? You had better read that link from a physicist about rope stretch recovery before stating the problem I think.
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dirtineye
Feb 27, 2004, 4:49 AM
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By the way, I used a slanted example to get the 11 kN impact force of the climber and the 18.26 force on the anchor. That was 80 kg climber(180 pounds), lousy 9.5kN impact force rated rope as opposed to a nicer 6 or 7 kN rated one, a three foot take in when the climber falls from ten feet over the anchor...
This 11 Kn might not be very comfortable, but it should be survivable. And that is an extreme case. a factor 2 fall measures about 10 kN impact force using the same parameters as I used to check the other fall factors.
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squish
Feb 27, 2004, 4:56 AM
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In reply to: Via Ferrata and rope free climbing are not comparable systems for fall factor.
Fall factor is a reality that can't be denied in either case. It has a strict definition, and it applies to both kinds of climbing. The only difference is the generally accepted upper limit of 2.0 in standard belayed climbing.
In reply to: It is possible to have a greater number than 2 in Via Ferrat, I concede that. But it is not possible in a roped free climbing system. The roped climbing system is a close ended system.
... But not always.
I believe DMT brought this up in the last fall factor thread I saw, and it's worth repeating here, seeing as we're repeating the same old argument:
When simulclimbing, the second must not fall.
Illustration: Assume steep terrain. Leader and follower are simulclimbing on a 60m rope with only a few pieces between them. The second falls and pulls off the leader. Together, they fall some distance (up to a maximum of 60m), and the leader is stopped when his tie in knot impacts the protection piece: severe injury or death for the leader. The second is OK, since he has the full length of the rope to absorb his fall.
Leader's fall distance: up to 60m.
Leader's rope length: approximately zero.
Leader's fall factor: approximately infinite.
Second's fall distance: up to 60m.
Second's rope length: exactly 60m.
Second's fall factor: up to 1.0.
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dirtineye
Feb 27, 2004, 5:43 AM
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We are NOT talking about via ferrata, we are not talking about simul climbing, we are talking about falling on an anchor and drkodos conceded that in thiscase the fall factor can be greater than 2.
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curt
Feb 27, 2004, 5:58 AM
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Well, I am glad we got that settled. Yes, it is theoretically possible for a belayer to reel in slack and force the fall fctor to exeed 2.0 although the normal definition does not account for this.
Similarlya belayer can pay out slack and lower the fall factor. If a climber is 20 feet above his belayer and falls with no gear in--and the belayer pays out an extra 10 feet of rope, he has decreased a potential 2.0 fall factor situation to one that is now 1.67.
In real life this is more likely to happen (decreasing of the theoretical fall factor) due to movement of the belayer, slippage of the belay device and perhaps even anchors, etc.
Curt
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drkodos
Feb 27, 2004, 6:34 AM
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The only time I ever have my belayer "take" in rope is to keep me off a ledge or the ground.
Whatever the facts may be, I prefer to have a losse belay and have the belayer pay out rope. That is my preference.
As for definitons. A cursory check did show, however, that the definition of fall factor varies from source to source, but seems consistant that 2.0 is the working upper limit by definition, whatever theory may hold.
please see that this is copied from a link
In reply to: How to fall How to fall? You just let go and drop, right? Not if you want to stay safe! Falling is actually a technique itself - and worth practice! The key ideas to remember when falling: Don't grab the rope or any other gear - you might pinch your fingers or unclip the rope! Put your feet and arms out in front of you to catch the wall when you meet it. Fall Factor Calculator -------------------------------------------------------------------------------- This calculator will determine the fall factor and impact force on a climber. The fall factor is the ratio of the distance you fall to the length of the rope. The highest fall factor possible is a 2, which puts the maxmimum strain on your rope. A fall factor of 1 is moderate, and a fall factor of less than 1 is light. Dynamic rope considerably decreases the shock a climber feels because it has the ability to stretch and absorb more of the force.
********************************************************
From The Petzl Page:
- Petzl home page -
--------------------------------------------------------------------------------
In reply to: Fall Factor Explained... A lot of climbers don't really understand the fall factor concept; however, it's pretty simple, even if you hated math (this is math you can use in later life. In fact , you can use it to have a later life) Fall Factor is simply the length of the fall divided by the length of the rope from faller to belayer. The equation looks like this; Fall Factor = Length of Fall __________ Length of Rope Fall Factor 2 is the maximum you should encounter in a typical climbing fall, since the height of a fall can't exceed two times the length of the rope. Normally, a Fall Factor 2 can only occur when a leader who has placed no protection falls past the belayer, or the anchor if it's a solo climb. As soon as protection is placed, the distance of the fall as a function of the rope length is lessened, and the Fall Factor drops below 2. Your life depends on the stretch of the rope... Shock load is the result of three factors; The nature of the rope, the fall factor, and the weight of the falling object. That is you. Obviously, the only part of this equation that can reduce the force of a fall is the bungee-like stretch of the dynamic rope (unless, of course, you can lose weight really fast). Thus, climbing safety systems are designed around the shock-absorbing quality of dynamic rope. It cushions the fall, reducing the impact force and the chance of system failure. In fact, the dynamic rope is the one "given" in the whole system. It is designed to limit the force of one climber's weight (80 KG) in a worst-case fall (Fall Factor 2) to not more that 12 kN. Thus, the rest of the gear can be designed to work with this known maximum force. More rope means more stretch to absorb a fall. Which explains why a Fall Factor 2 drop of 4 meters develops the same shock force - 9 kN - as one of 20 meters, assuming a dynamic rope is used that conforms to UIAA standards. What's happening is that the increasing length of the fall ( and the greater shock force that goes with it) is compensated by the greater length of the rope available to cushion its arrest.
These pieces of information are what I was basing my argument upon. I accept that factors of 2.0 are theoretically, and possibly even realistically attainable in tests, but for all purposes rhetoric I will continue to consider the scale to be close ended, as it was intended to be to laymen such as myself.
As for other esoteric incidents, you gentlemen have convinced me to stay on the porch when it comes to arguing the physics of climbing and focus instead on the politics of it. :lol:
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dirtineye
Feb 27, 2004, 3:10 PM
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In reply to: Well, I am glad we got that settled. Yes, it is theoretically possible for a belayer to reel in slack and force the fall fctor to exeed 2.0 although the normal definition does not account for this. Similarlya belayer can pay out slack and lower the fall factor. If a climber is 20 feet above his belayer and falls with no gear in--and the belayer pays out an extra 10 feet of rope, he has decreased a potential 2.0 fall factor situation to one that is now 1.67. In real life this is more likely to happen (decreasing of the theoretical fall factor) due to movement of the belayer, slippage of the belay device and perhaps even anchors, etc. Curt
I just don't want this thread to die yet.
http://www.geocities.com/Yosemite/Trails/8700/ropes.html
IF you read how the UIAA test is conducted, you will notice that they use 2.8 meters of rope for a 5 meter fall. WELL, you might also notice that 2 x 2.8 is not 5, so what is going on here?
What is going on is that the rope runs over a "carabiner like thing", and there is three tenths of a meter of rope that must be taken into account as rope out. So even though the fall is from 2.5m above to 2.5 m below the "anchor', the fall factor is not really 2, but 1.77, because 5/2.8 is 1.77.
Now clearly there is some rope betwen the belayer and the anchor point that all these FF 2 scenarios are not taking into account. Just as clear is the fact that as more rope is paid out, this little bit between belay device adn anchor point has less influence on the fall factor.
Let's see how it affects the 20 foot fall on the anchor, Assuming one foot of rope from belay device to anchor point, and a PERFECT lockdown by the belayer, our fall factor becomes not 2 but 40/21 = 1.9. Now let there be this ledge to hit and let the belayer yard in his three feet. OF course Mr. belayer is not going to give up that one foot between himself and the anchor, so 37/18 = 2.06. The calculation without the one foot or rope in the system between belay device and anchor biner gave an FF of 2.18.
So, this one foot can make a difference.
Now in reality, as shown on this link
http://www.impact-force.info/anglais/impact3.html
Real fall factors must take into account friction between rope, biners and even rock. This makes for a more difficult calculation and a higher fall factor. Other real factors such as harness give and belayer movement towards the anchor as the impact hits would tend to lower the fall factor.
To maximize the value of this discussion, let's look at some relevant points:
It's bad to belay directly off the anchor. That one foot of extra rope makes a difference in the fall factor when you need it most.
It's bad to zig zag your rope by using short runners, this increases the real fall factor considerably. Ideally the rope should run straight from the anchor to the top piece, without touching the rock.
The real fall factor may be higher than the theoretical one, because of the friction over the first biner. the rope on the belayer side of the top biner loses at least 40% of it's ability to respond and that is as good as it gets, according to the impact force link.
Yarding in rope, except to prevent a ground or ledge impact, is a bad idea. This raises the fall factor and the impact force on the top piece and the faller.
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cracklover
Feb 27, 2004, 3:59 PM
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Dirtineye, you don't want this thread to die, despite having embarrased yourself in it? Odd.
And having extricated yourself out of the last one, I'm afraid you seem to be digging yourself into a new hole.
No-one said anything about the rope manufacturers tests because... they are not ff2 tests. All the tests say quite clearly that they are ff = 1.77.
A ff 2 would happen when you are belaying directly off your harness or directly off the anchor, not when you use a redirect.
GO
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dirtineye
Feb 27, 2004, 4:08 PM
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In reply to: Dirtineye, you don't want this thread to die, despite having embarrased yourself in it? Odd. And having extricated yourself out of the last one, I'm afraid you seem to be digging yourself into a new hole. No-one said anything about the rope manufacturers tests because... they are not ff2 tests. All the tests say quite clearly that they are ff = 1.77. A ff 2 would happen when you are belaying directly off your harness or directly off the anchor, not when you use a redirect. GO
YOU know, I think you are great at missing the point. Why don't you actually read the thread and consider the ideas before spouting off?
I'm not embarassed at all, I said it would be hard to get a fall factof of much greater than 2 under normal climbin conditions, and it is.
The point about 1.77 ff is clearly that you should NOT belay directly off your belay device or the anchor, I would have thought that this would be obvious even to you.
Instead of addressing the intereseting points about real fall factors, and how to avoid the bad stuff, you'd rather be insulting.
Instead of being an A$$, why don't you try contributiing something to the discussion?
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cracklover
Feb 27, 2004, 4:17 PM
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In reply to: In reply to: Dirtineye, you don't want this thread to die, despite having embarrased yourself in it? Odd. And having extricated yourself out of the last one, I'm afraid you seem to be digging yourself into a new hole. No-one said anything about the rope manufacturers tests because... they are not ff2 tests. All the tests say quite clearly that they are ff = 1.77. A ff 2 would happen when you are belaying directly off your harness or directly off the anchor, not when you use a redirect. GO YOU know, I think you are great at missing the point. Why don't you actually read the thread and consider the ideas before spouting off?
Not only do I read, I also think. You should try that sometime.
In reply to: I'm not embarassed at all, I said it would be hard to get a fall factof of much greater than 2 under normal climbin conditions, and it is.
You want to know why I'm being an ass? Because you arrogantly stated incorrect information several times, though the truth had already been explained in this thread and others. And once you realized you were wrong, rather than admitting it, you edited your post from "Please explain how this ratio can grow large, as in larger than 2." to say "much larger than 2." That's lame, dude, real lame.
In reply to: The point about 1.77 ff is clearly that you should NOT belay directly off your belay device or the anchor, I would have thought that this would be obvious even to you.
You just can't stop putting your foot in your mouth, can you. How 'bout this, go to petzl's site and do a quick calc on the impact force on the anchor for the two scenarios and then report back. Oh, I mean then edit your post to make it seem like you were saying the opposite. Lame!
GO
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dirtineye
Feb 27, 2004, 4:33 PM
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THe change from larger than to much larger than was for clarity. Remember the subject was about infinite fall factor. I guess you mised that little point as well. Lsat time I checked, and you may correctt me if I am wrong here, Infinity or even approaching infinity is larger than as well as much larger than 2. Keep on twisting things.
As for the anchor calculation, IF you build your anchor to the recommended strength, it will withstand the pulley effect very well, as I have already dsescribed several posts ago, using less than favorable constants. Seems you missed that. But then you miss the point a lot, and you still have not contributed anything but crap.
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dirtineye
Feb 27, 2004, 4:36 PM
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So anyway, why don't you comment on the actual fall factor calulation in that impact force link from beal? That is actually interesting.
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cracklover
Feb 27, 2004, 5:11 PM
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C'mon dude, you're not fooling anyone, except maybe yourself.
You had a couple paragraphs where you showed how the extra foot between the belayer and the re-direct lowers the fall factor, but never mentioned that it increases the force. You even said:
In reply to: To maximize the value of this discussion, let's look at some relevant points: It's bad to belay directly off the anchor. That one foot of extra rope makes a difference in the fall factor when you need it most.
Need it for what? Who cares! It increases the force on the anchor!
So what's the Beal link you find interesting?
Okay, so you want a contribution to this thread that's covering the same old stale $hit?
How 'bout this:
The standard model of a redirected belay gives you a force on the anchor of around 1.6 or 1.7 times the force of the falling climber. This model is clean and accurate. However there is one important point that this static model leaves out. The real situation is not static. That is to say, on a hard fall, at the point of maximum rope tension, the belayer is moving. This obviously reduces the amount of tension in the rope on the belayer side, and thus the amount of force on the anchor. Unfortunately, this is a much harder equation to solve!
However, it would be simple to devise a test that would measure the force difference between the static model and the dynamic model. The way ropes are tested, the "belayer" end is fixed. (A nice test of the static model.) You would simply modify the testing apparatus such that the "belayer" end of the rope is attached to an 80kg weight that could either be fixed in place (static model) or allowed to move freely (dynamic model). Depending on the amount of friction in the "anchor", you would see different results. But nowhere in this range of results would you get a force as high as in the static model. Well I finally found a manufacturer who did exactly such a test.
I have seen some test data for the scenario I describe above as the "dynamic model". This model allows that the belayer will be lifted by the force of the fall, as opposed to the scenario in the rope tests used by manufacturers, in which the "belayer" is simply a knot tied to an immovable point. Anyway, the data shows a reduction in force to the anchor of about 20% from the standard (static) model. This makes sense intuitively, since the force generated on the belay-end of the rope is reduced by the movement of the belayer, *and* the force on the leader-end of the rope is reduced due to the extra stopping time produced by the movement of the belayer.
So, for example - take a fall factor 2 that generates a max force of 9 kN. Caught on your harness or directly on the anchor, the force on the anchor is ~ 9 kN. The standard model (static belayer) says that if you redirect through the anchor, the belayer contributes an additional force equal to that of the faller minus the force absorbed by friction over the carabiner, or .7 times that of the faller. According to this model, the max force on the anchor is 15.3 kN. However, the new model shows that the true peak force on the anchor would be closer to 12 kN. May not be intersting to anyone else, but it is to me!
Obviously, this is only really notable on hard falls where the belayer gets lifted. On lower FF falls, the static model works fine.
GO
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drkodos
Feb 27, 2004, 5:39 PM
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No.
My falls go to 11.
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rgold
Feb 27, 2004, 5:50 PM
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I'd be cautious about home-grown calculators. Remember this is the web---anyone can put up anything they want, but that doesn't mean it is what it says it is or does what is says it does.
This particular calculator doesn't report the correct value of the fall factor.
When you put in a number D for "distance from last anchor" and a number L for "length or rope," (a quantity which is nowhere defined), the calculator reports the quantity (D+L)/L as the fall factor, which is wrong (except for the single exception D=L, if you use a possible but non-standard definition for "length of rope").
I haven't bothered to check whether the impact calculated is the correct impact for the incorrectly reported fall factor, or indeed whether the impact is correct but the reported fall factor is wrong. The fact that the author of this site doesn't say what "rope length" means, the fact that he or she thinks forces can be "absorbed," the fact that there is no provision for entering the UIAA impact rating of the rope and no indication what rating is being used, and the fact that the reported fall factor is incorrectly calculated are more than enough reasons to seek reliable information somewhere else.
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jt512
Feb 27, 2004, 5:52 PM
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In reply to: In reply to: Whether or not pulling in a foot or two of slack would make any practical difference in a factor-2 fall is not clear to me, though. It won't, assuming your anchor is a good 25 kn anchor. I calculated this for the 20 foot above the anchor adn a three foot reel in. you add 440 N over what the factor 2 fall would do, and it is still under 10.5 kN impact force.
The reason I question whether pulling in slack in a factor-2 fall situation would have much effect is because, when the fall is that severe, the belay device limits the impact force, by allowing rope to slide through the device. Most impact force calculations, on the other hand, assume a completely static belay. I suspect that with any non-locking belay device, the total impact force on the anchor will be a fraction of what you've calculated.
In reply to: In reply to: In reply to: good dr., now that you've gotten some of the intricacies of fall factors straightned out, how about revisiting the case where the leader is able to get one sketchy piece of pro in before falling. should the belayer take in rope if possible during the fall? I was going to go into that next, but I'll hold off to give drkodos a chance to respond. -Jay First, these intricacies are stupid.
This particular intricacy -- the effect of pulling in slack when the fall factor is less than one -- actually has practical value. Pulling in slack in this case reduces the impact force. That's a good thing to know if your partner falls low on a pitch. of course you need to take in the slack quickly, before the leader's weight comes onto the rope; otherwise, you increase the impact force, instead.
-Jay
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dirtineye
Feb 27, 2004, 7:43 PM
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Cracklover,
The beal link is here:
http://www.impact-force.info/anglais/impact3.html
I refer you for the second time to the post where I calculated the extra force on the anchor in a conservative factor 2 fall, using a force multiplier of 1.66, and got 18 kN and said, this is fine as long as you have built a 25 kn anchor, which is what is recommended. (UIAA standard for anchor, 25 kN) That post precedes the one you refer to, but I assume you can follow ideas from one thread to the other.
Given your obsession with Petzl, I am surprized you didn't notice that in their new catalog, which is chock full of the kind of stuff we are discussing here, they show in every belay anchor, a rebelay.
I guess they expect you to build a good anchor too.
In reply to: The standard model of a redirected belay gives you a force on the anchor of around 1.6 or 1.7 times the force of the falling climber. This model is clean and accurate. However there is one important point that this static model leaves out. The real situation is not static. That is to say, on a hard fall, at the point of maximum rope tension, the belayer is moving. This obviously reduces the amount of tension in the rope on the belayer side, and thus the amount of force on the anchor. Unfortunately, this is a much harder equation to solve!
Haha, well you are now talking. Of course dynamics are more difficult than statics. Building such a model might not be so bad. Here's one guys' idea:
http://www.caimateriali.org/Eventi/Torino/computermodel.html
Another good question is, will this moving belayer counteract the actual higher fall factor caused by friction on the rope that is through the biners and rubbing the rock in a non factor 2 fall?
JT,
Yeah, I agree that a real belay device will give, a harness will give, your body will flex a little, and all this will help reduce the force.
In reply to: This particular intricacy -- the effect of pulling in slack when the fall factor is less than one -- actually has practical value. Pulling in slack in this case reduces the impact force. That's a good thing to know if your partner falls low on a pitch. of course you need to take in the slack quickly, before the leader's weight comes onto the rope; otherwise, you increase the impact force, instead.
I'm in a hurry, how about making a calculation and giving your parameters? I suggest you use the impact force equation on the beal site, adn here are the constancts I used: 80 kg mass of climber, 9.81 m/s^2 = g, rope max impact force = 9.5 kN for a rope K of 27100. Just give your actual fall factor ratios for each number you get please.
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cracklover
Feb 27, 2004, 8:16 PM
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In reply to: Another good question is, will this moving belayer counteract the actual higher fall factor caused by friction on the rope that is through the biners and rubbing the rock in a non factor 2 fall?
To the degree that they're related, it's actually the other way around. As the friction caused by out-of line protection increases, the belayer stops being lifted.
Regarding the Beal Site: I've seen that info before - sure it's interesting, but I haven't got anything to add.
By the way, just for $hit's and giggles, here's one answer to how you can get a large (much larger than 2) fall factor: Belayer brings up the second with gri-gri on the anchor. Belayer hands off remaining rack to the second (they're leapfrogging), but forgets to move the belay device to his harness. Second becomes leader and leaves the belay station to start leading the next pitch. Just then (let's say three feet up) the leader breaks off a handhold, and say's "falling!" Stupid belayer takes up all the slack and leader slams into anchor with nothing but his tie-in knot between him and the gri-gri. Ouch!
GO
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cracklover
Feb 27, 2004, 8:25 PM
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By the way, dirt, I'm not a particular fan of Petzl. I don't get their catalog, or any other gear catalog, for that matter. If you're referring to the post where I told you to check your math on their site, I did so with tounge in cheek. It was a goof, since you don't need to go to a force calculator to realize that a redirected close to FF2 fall is much harder on the anchor than a full FF2 force that's not re-directed.
Cheers,
GO
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drkodos
Feb 27, 2004, 8:31 PM
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I reassert my original contention:
If the system (including the humans in it) is working properly, there will not be a factor 2.0 fall. In all the incidents people are using in this thread in their attempts to win the argument, they hav failed to notice that they are bending out definitions like David Gilmour bends strings in a guitar solo to tweak small intertonal qualities out of a note.
If pigs had wings they would, no doubt, fly.
Anything above a factor 2.0 fall is an impossibility in the climbing world I have constructed for myself to live in.
Transmission over.
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cracklover
Feb 27, 2004, 8:53 PM
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In reply to: In reply to: This particular intricacy -- the effect of pulling in slack when the fall factor is less than one -- actually has practical value. Pulling in slack in this case reduces the impact force. That's a good thing to know if your partner falls low on a pitch. of course you need to take in the slack quickly, before the leader's weight comes onto the rope; otherwise, you increase the impact force, instead. I'm in a hurry, how about making a calculation and giving your parameters? I suggest you use the impact force equation on the beal site, adn here are the constancts I used: 80 kg mass of climber, 9.81 m/s^2 = g, rope max impact force = 9.5 kN for a rope K of 27100. Just give your actual fall factor ratios for each number you get please.
What JT is describing doesn't require a beal impact force site, or any complex math whatsoever. You don't need to know the weight of the climber, the springiness of the rope, or any of that jazz. Just the basics. For:
F = fall distance
R = rope available
T = rope taken up
FF = F/R
and
FF1 = (F-T)/(R-T)
You see that while FF > 1, as T increases, so does FF1. And while FF < 1, the reverse is true.
In reply to: If the system (including the humans in it) is working properly, there will not be a factor 2.0 fall.
With that, I agree 100% :)
GO
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squish
Feb 27, 2004, 9:08 PM
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In reply to: I reassert my original contention: If the system (including the humans in it) is working properly, there will not be a factor 2.0 fall.
Granted, and I hope to continue doing things properly myself, and never have to encounter anything approaching factor 2.
In reply to: In all the incidents people are using in this thread in their attempts to win the argument, they hav failed to notice that they are bending out definitions like David Gilmour bends strings in a guitar solo to tweak small intertonal qualities out of a note.
How can one bend a simple formula like rope_length/fall_length ? That is the strictest definition that you can't get around. There are, albeit stupid, situations where FF > 2.0 does happen.
In reply to: If pigs had wings they would, no doubt, fly.
If you ignore Exhibits A, B, and C, then fall factor > 2.0 is impossible. By discounting all data to the contrary, you have proven your hypothesis.
In reply to: Anything above a factor 2.0 fall is an impossibility in the climbing world I have constructed for myself to live in.
Good for you. Mine too.
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allthetime
Feb 27, 2004, 9:38 PM
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In reply to: As for other esoteric incidents, you gentlemen have convinced me to stay on the porch when it comes to arguing the physics of climbing and focus instead on the politics of it.
spoken like a true politician:
In reply to: A cursory check did show, however, that the definition of fall factor varies from source to source, but seems consistant that 2.0 is the working upper limit by definition, whatever theory may hold.
:(
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jt512
Feb 27, 2004, 10:58 PM
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In reply to: In reply to: In reply to: This particular intricacy -- the effect of pulling in slack when the fall factor is less than one -- actually has practical value. Pulling in slack in this case reduces the impact force. That's a good thing to know if your partner falls low on a pitch. of course you need to take in the slack quickly, before the leader's weight comes onto the rope; otherwise, you increase the impact force, instead. I'm in a hurry, how about making a calculation and giving your parameters? I suggest you use the impact force equation on the beal site, adn here are the constancts I used: 80 kg mass of climber, 9.81 m/s^2 = g, rope max impact force = 9.5 kN for a rope K of 27100. Just give your actual fall factor ratios for each number you get please. What JT is describing doesn't require a beal impact force site, or any complex math whatsoever. You don't need to know the weight of the climber, the springiness of the rope, or any of that jazz. Just the basics. For: F = fall distance R = rope available T = rope taken up FF = F/R and FF1 = (F-T)/(R-T)
Yeah, since we're talking about relative impact forces, not absolute ones, we shouldn't have to calculate the impact forces themselves, just the fall factors.
For example:
FF = 8/12 = .667
T = 2
FF1 = 6/10 = .6
FF1/FF = .9
So, if the belayer can take in 2 feet of slack, he can reduce the fall factor, and hence the impact force on the top piece, by 10%. Is that of practical value? I don't know. Perhaps, if the top piece is marginal.
What the belayer would really like to do in this situation is dynamically belay. Unfortunately, if this fall were to occur close to the ground or a belay ledge, the belayer might not be able to dynamically belay without risking decking the leader. On the other hand, if the belayer can pull in a couple of feet of slack as the leader is falling, the belayer may be able to let that slack out again as the leader's weight come onto the rope, and thereby give a dynamic belay...but that's another thread.
-Jay
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dirtineye
Feb 27, 2004, 11:46 PM
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In reply to: By the way, dirt, I'm not a particular fan of Petzl. I don't get their catalog, or any other gear catalog, for that matter. If you're referring to the post where I told you to check your math on their site, I did so with tounge in cheek. It was a goof, since you don't need to go to a force calculator to realize that a redirected close to FF2 fall is much harder on the anchor than a full FF2 force that's not re-directed. Cheers, GO
Since you never did go back and find it, here you go.
In reply to: In reply to: Whether or not pulling in a foot or two of slack would make any practical difference in a factor-2 fall is not clear to me, though. It won't, assuming your anchor is a good 25 kn anchor. I calculated this for the 20 foot above the anchor adn a three foot reel in. you add 440 N over what the factor 2 fall would do, and it is still under 10.5 kN impact force. Evein if you let the guy be ten feet over the anchor and reel in thre feet, that still does not break 11kN, and I don't think anyone can do better than 3 feet off a 20 foot fall. If you wnat to check what I did, look at taht psot above adn use the link to the formula. I used 80kg as the mass, and all the other stuff I used I gave in the other post. Multiplying by 1.66 and the worst case of 11 kN the total force on the anchor is less than 25 kn, in fact it is 18.26 kN.
Now this quote is from two pages ago I think. This calculation was sitting there all the time you were spouting off. I beleive I refered you to it two or three times.
I never said it was not harder, on the anchor in fact I calculated that is is harder, attempted tp geta sort of upper bound for just how hard and noted that you need a 25 kN anchor to get by. It's right there in the quote.
You didn't bother to comment on the dynamic belay paper, but it's probably no great loss given that you don't seem to pay much attention anyway.
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curt
Feb 29, 2004, 2:18 AM
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In reply to: In reply to: Pay particular attention to the posts by rgold (Rich Goldstone) who was one of the top climbers of the 20th century and is also a PhD. and Professor of mathematics. Yikes Curt! I think "a minor luminary from a bygone era" would be accurate and praise enough. The number of climbers from the twentieth century better than I ever was would fill many fat histories of climbing. Moreover, degrees or not, we all make mistakes, so I'd hold on to your scepticism and judge what you read by how much sense it makes rather than who said it, no matter how purportedly qualified they may be. But thanks for the compliment, deserved or not.
OK Rich,
Your continual modesty has forced me to post this:
http://www128.pair.com/r3d4k7/Goldstone.html
:lol:
Curt
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cowboychris
Jan 16, 2010, 9:35 AM
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First of all, let me say that I am a noob when it comes to climbing. I started bouldering a couple of weeks ago and loved it. As such, I am not the most qualified person to be discussing the topics here, but I felt that some insight form a fresh perspective would be good for this discussion.
As I understand it, Fall Factor is the ratio of Fall distance over total rope, or F/R. To then complicate matters, the beleayer can take in rope, and hopefully shorten the fall, but may also increase the FF.
We then get (F-B)/(R-B) or something to that effect. However, what was argued was that the Fall Factor can "theoretically" be infinite. Aside from the fact that actual infinities don't exist, the statement does not correspond to reality (at least as far as I can tell).
For example, to get a FF of 10, we must have a ratio of 10/1 or some sort. This means that the Fall distance must be 10 times the length of rope contained in the system. This assumes that no rope is taken in. If rope is taken in, the same result requires that (F-B)=10 and (R-B)=1. I would assume that this means the beleayer took in all but 1 unit of rope and that the fall was 10 + the taken in rope. I do not see how this is physically possible. Since reaching such a number as 10 seems far fetched (from what I understand of the math) a greater number of 100 or 1000 seems even more unlikely. Infinity is awful large to make the claim that anything approaches it. I would not even say the universe is infinite, maybe uncountable, but not infinite.
As or the "theoretical" nature of this problem. I noticed that it was an engineer, statistician, and another who said it was possible. I do not doubt the credibility of these individual, as I my self took many years of math in college, but I do doubt their reasoning. Case in point. It is "possible" to travel the speed of light provided one can generate an infinite amount of energy. It is also "impossible" to not traverse a distance between two point because one must always go half the distance first, and can therefor never reach the second point. These points seem more pedagogical than practical to me. If I am wrong please explain it to me clearly as, like I said above, I am very very new to this sport and am typing this right now with my first blisters on my hands.
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acorneau
Jan 16, 2010, 2:22 PM
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Wow, 6 year old thread revival!
cowboychris wrote: I do not see how this is physically possible. Since reaching such a number as 10 seems far fetched (from what I understand of the math) a greater number of 100 or 1000 seems even more unlikely.
It's very easy to get fall factors of 2 or greater in Via Ferrata.
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c4c
Jan 16, 2010, 2:26 PM
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acorneau wrote: Wow, 6 year old thread revival!
finally someone uses the search function instead of starting a new thread about an old topic and you mock him anyway???
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acorneau
Jan 16, 2010, 2:31 PM
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c4c wrote: acorneau wrote: Wow, 6 year old thread revival! finally someone uses the search function instead of starting a new thread about an old topic and you mock him anyway???
Not mocking him, just surprised.
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JimTitt
Jan 16, 2010, 7:04 PM
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A brave man that says `actual infinities don´t exist´!
To exceed the speed of light does not require infinite energy, all you require is to get a particle up to a reasonable speed in one medium and fire it into a medium with a lower "speed of light".
You can wow your wife with this one, especially on a romantic moonlit night- the speed of light in a vacuum is 299,792,458 m/s (or so) but when it whacks into that diamond on her hand you are holding in your sweaty grasp it slows down to about 124,000,000m/s. At the point of initial impact the light is going over double the speed of light without massive inputs of energy, only the cost of the diamond!
On the same lines but less likely to impress the wife you can climb up to the full length of your climbing rope, fall off and catch your tie-in knot on a spike near the bottom of the fall. This will give a fall factor up there in the tens or hundreds of thousands. You will not survive!
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cowboychris
Jan 18, 2010, 5:42 AM
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A brave man that says `actual infinities don´t exist´!
First of all, it is just a philosopher who says that infinities do not exist. Infinities must, by definition, have no limit. If it is countable, measurable, dividable or any such, it is not infinite. As to the "speed of light" issue, while a photon can travel at the speed of light, the mass in a photon is extremely small in comparison to the mass of a ship or person. Look at what it has taken for us to get a particle moving close to, but not at the speed of light, it is called the Large Haydon Collider.
That said, back to this fall factor issue being infinite. I did some looking, as I am still new to the sport on what Via Ferrata is before I made myself look like a complete idiot. As I understand the system of Via Ferrata, one is clipped onto a pre-existing cable/rope which is secured at points along the climbing surface. Assuming this set up has an extremely large distance between anchor points, the fall factor would be quite large.
For arguments sake, let us assume that a Via Ferrata cable is attached to the top of Mt Everest and an anchor point at the base of the mountain (sea level). Let us also assume that such a set up is possible.
Now, if the climber is almost at the summit, and is only clipped in with 1 foot of rope, we get:
29029/1= Fall Factor of 29029. This is still a finite fall factor. I understand that it would probably not hurt much as it would be akin to falling out of an airplane at 30000 without a parachute.
That all said, can one of you who is claiming that the fall factor is infinite please give a reasonable example of how fall factor can exceed a billion, trillion, or 10^100? By demonstrating that, I would be much more likely to believe it to be infinite. Thank you for you patience in explaining this to me.
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JimTitt
Jan 18, 2010, 8:43 PM
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Philosophers are divided about the existence of infinity.
Mathematicians also disagree (for example the controversy over Cantor´s theory) though this is again a more philosophical dispute. They still find the concept of infinity one of the most powerful and useful tools they have which is a strong argument for its existence.
Physicists don´t like infinity because it renders most physical laws inoperable, however even by ignoring it they still end up at infinity in some cases which is rather inconvenient.
These disagreements are all related to actual infinities, not conceptual ones.
When talking about fall factors and infinity we are talking about concepts (since fall factors are described and defined by mathematical symbols which in themselves are conceptual) and there is no reason to think that in this case infinity does not exist. The fact that someone on this thread thinks it does is irrefutable proof that it exists as an abstract concept (Descartes is your man here!).
As to the speed of light;- It is possible, in fact easy to exceed the speed of light even without challenging special relativity. The simplest way is to either remove the energy or the mass from the particle, (in this sense modern physicists would prefer to call the mass information) and there are a few ways to do this.
That this occurs is obvious if you take my example of light hitting a diamond, if the change in velocity is not instantaneous then in the diamond the photon has exceeded the speed of light at this point. If the photon is not allowed to exceed the speed of light then it must have changed it´s velocity instantaneously, that is it underwent an infinite deceleration. Special relativity tells us it then had an infinitely high mass or gave off an infinite amount of energy, both of which would be rather awkward! That it slows down without the world exploding tells us something interesting is happening.
Exceeding the speed of light has been demonstrated using sound waves and even more effectively with grouped laser puses, the guys at NEC have got to 300 times the speed of light this way.
And to go even faster, in fact infinitely fast, we can turn to quantum tunneling!
As to fall factors, if you´d clipped MY bolts you wouldn´t be worrying!
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robdotcalm
Jan 18, 2010, 10:45 PM
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«If it is countable, measurable, dividable or any such, it is not infinite.»
«Philosophers are divided about the existence of infinity.
Mathematicians also disagree (for example the controversy over Cantor´s theory) though this is again a more philosophical dispute. They still find the concept of infinity one of the most powerful and useful tools they have which is a strong argument for its existence.»
Mathematicians have dealt comfortably with infinities for well over a century. Objects that are commonly referred to as infinites are well defined entities that fit in with rigorous, axiomatic based mathematics. There aren’t really any disputes still around about “Cantor’s theory”.
The use of “countable” above is curious. In mathematics, the smallest infinity (yup, these things can be ordered from smaller to larger) is called “countable”. For example, the set of positive integers {1, 2, 3, ….} is a countably infinite set. So also is the set of positive even integers {2, 4, 6, …}. Note that these 2 sets can be put into one-to-one correspondence, 1 to 2, 2 to 4, 3 to 6, …. . Thus they are considered equal. If one considers all numbers including the irrationals, e.g., sqrt(2), pi, etc., then by a clever technical argument (going back to Georg Cantor) one can show this set of numbers is bigger than any countable set.
Historically, the need to deal with these issues started with a problem in heat transfer that Jean Fourier studied in the early 1800s. It led him to express values in terms of trigonometric functions. The problems associated with this had a life of their own independent of their origin. This eventually led to Cantor and his classification of infinities.
This raised a lot of other issues, but really by the mid-twentieth century these were resolved.
The type of infinity that one thinks of as the limit of an increasing quantity such as the impact force at the climber’s end of the rope as the fall factor increases is a different type of infinity, but again nothing mystical about it. The mathematical theory covering it is rigorous and logical.
Cheers,
Rob.calm
Disclaimer: What I’ve written doesn’t have anything to do with fall factors in climbing unless one wants to be poetic and say that any impact force sufficient to kill, say, 99% of the people at the end of the rope is “infinite”.
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cowboychris
Jan 30, 2010, 9:02 PM
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I do agree with the issue of "countable" sets. I apologize for incorrectly using the mathematical term. Semantically, I intended an idea of a thing which we can attribute a numerical value to, ie 1 orange, $2 trillion etc.
As for the issue of the existence of infinity. You will notice that I said no "actual" infinities exist. A conceptual infinity is a very real and existent item, as much as a concept has existence. The concept of a unicorn is a usable an coherent concept which (as best and as far as we know) has no "actual existence." It is very reasonable to talk about y -> infinity as x-> 0 in the equation y=1/x. The problem here is that no material thing exists with these properties. Just because a concept only has existence in thought and not reality does not mean it does not exist, but it does mean it does not "actually" exist.
While I enjoy the philosophical discussion about the existence of infinity, the ultimate statement that started the discussion was that fall factor could be infinite. No one has demonstrated that it is "actually" possible, but only "theoretically" possible. This is equivalent to saying it is not actually possible for me to grow wings and fly, but it is theoretically possible. The issue is the chasm between theory and reality, between thought and reality. I will fully concede that it is "theoretically" possible to have an infinite fall factor, but such a thing could never actually happen in reality.
Sincerely-
A n00b who stepped in it the first day here.
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jt512
Jan 31, 2010, 3:26 AM
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[quote "cowboychris"
As for the issue of the existence of infinity. You will notice that I said no "actual" infinities exist.
Your use of the word "actual' is problematic. If by "actual" you mean having a physical existence, then you should state that.
In reply to: It is very reasonable to talk about y -> infinity as x-> 0 in the equation y=1/x. The problem here is that no material thing exists with these properties.
Consider the following "material" line segment A: __________________ . How many unique line segments are there that are segments of A?
Jay
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cowboychris
Feb 1, 2010, 12:47 AM
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Definition of "actual" according to dictionary.com and very similar to the Webster's Unabridged on my shelf.
1. Existing and not merely potential or possible. See Synonyms at real.
2. Being, existing, or acting at the present moment; current.
3. Based on fact: an actual account of the accident.
Thus, a unicorn is not "actual." I used the term correctly.
Now, to deal with your line segment. The example you give in not a really an infinite, but only indefinite. Let us assume your line, but with two end points A and B (not a ray like you have listed with only one point). We thus have A_____________B. We can then find a point C on segment AB such that C lies on the segment AB and is between AB. (That is to say that segment AC is part of the same segment of AB and similarly for CB). We now have A_____C____________B, for any arbitrary point C between A and B. We can then pick another point between C and B on the segment CB and call that point D. We can then talk about segments AC, AD, AB, CD, and CB. We can continue to divide the line indefinitely. However, we never arrive at the infinite segment (that is, the ith segment were i is infinity).
Also notice that you cannot do this "thought" experiment in reality, but only in thought.
A working definition of an actual infinite: "a collection of definite and discrete members whose number is greater than any natural number 0, 1, 2, 3..." (W L Craig, Reasonable Faith, pg 116). After you understand this, do a quick search and reading on "Hilbert's hotel."
My contention was never that one could not demonstrate infinite fall factor "on paper" or "in thought," but was that in the real world (the place where things like fall factor take place) it is not possible to achieve an actually infinite fall factor.
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jt512
Feb 1, 2010, 2:09 AM
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cowboychris wrote: Definition of "actual" according to dictionary.com and very similar to the Webster's Unabridged on my shelf. 1. Existing and not merely potential or possible. See Synonyms at real. Thus, a unicorn is not "actual." I used the term correctly.
The question isn't whether unicorns are "actual"; it's whether infinity is. That's where you run into trouble with the word "actual." Is the set of positive integers "actual"? You can't write them all out. Guess why? Cause they're infinite. Seems to me that this is proof that infinity is "actual." After all if it didn't actually exist, then you could write out all the positive integers.
In reply to: Now, to deal with your line segment. The example you give in not a really an infinite, but only indefinite. Let us assume your line, but with two end points A and B (not a ray like you have listed with only one point). We thus have A_____________B. We can then find a point C on segment AB such that C lies on the segment AB and is between AB. (That is to say that segment AC is part of the same segment of AB and similarly for CB). We now have A_____C____________B, for any arbitrary point C between A and B. We can then pick another point between C and B on the segment CB and call that point D. We can then talk about segments AC, AD, AB, CD, and CB. We can continue to divide the line indefinitely.
And therefore the set of all line segments of AB is infinite. It actually is.
In reply to: However, we never arrive at the infinite segment (that is, the ith segment were i is infinity).
So, what. There are still an infinite number of segments. It's not my problem that you're trying to construct them by sequentially dividing the original segment.
In reply to: A working definition of an actual infinite: "a collection of definite and discrete members whose number is greater than any natural number 0, 1, 2, 3..." (W L Craig, Reasonable Faith, pg 116). After you understand this, do a quick search and reading on "Hilbert's hotel."
So, what, you're quoting some sort of Christian theological definition of infinity? Who fucking cares about that. I guess that explains why you keep using the bizarre phrase "actual infinite." I don't know what an "infinite" is supposed to be, and I don't care. I now see exactly where you are coming from. In your mind, if infinity really existed, then it would be possible that the Universe was not a creation of "God" (W L Craig's argument). But, since you believe that "God" created the Universe, then infinity must not exist. The usual circular Christian "logic," applied to the extended real number system!
As far as your hero's definition of "actual infinite" goes, as a definition of infinite set it is wrong for at least two reasons. First, an infinite set does not have to be comprised of members that are "discrete" in any mathematical sense that I know of. I suppose he's trying to refer to countable infinity, à la Hilbert's Hotel, but infinite sets need not be countable (eg, the set of all real numbers is uncountably infinite). Secondly, it contains a contradiction: there obviously is no natural number that is greater than any natural number. And, perhaps subtler, there is no real number that is, either.
So, what your hero has done is he has made up a concept ("actual infinite") and then "proved" its non-existence by defining it to be a contradiction.
Now, "after you understand this" look up the archimedean property of the real numbers.
Jay
(This post was edited by jt512 on Feb 1, 2010, 5:53 AM)
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rgold
Feb 1, 2010, 5:45 AM
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This argument dates back, at least, to the 4th century BC, when Aristotle distinguished between actual and potential infinity (and argued against actual infinity, claiming also that mathematicians didn't need it anyway, potential infinity was good enough).
Gauss took pretty much the same position, it wasn't until Bolzano and Cantor that people looked at something as simple as the integers as a single entity (and so an actually infinite thing) rather than as some kind of process that didn't have any prescribed end. We are so steeped in set theory that the idea that people didn't look at infinite sets as single entities now seems strange.
Cowboychris has aligned himself with Aristotle and Gauss (among the smartest people to have ever lived) in taking the human inability to perform infinite enumeration as an obstruction to speaking of an actually infinite object. (Never mind that the same argument essentially denies the existence of actually very large finite objects like the number of grains of sand on all the world's beaches.)
In any case, the instant the set concept was formulated, this obstruction simply vanished, as Jay keeps trying to point out. We're not in the fourth century BC or even in the 18th century any more CC!
Anyway, the whole thing seems to have been started by the comment that the fall factor can be infinite, which is a typical bit of internet imprecision and was, one hopes, never intended to mean anything other than the fact that there is no upper bound to possible fall factors. There is, of course, no infinite fall factor; the fall factor is a real number.
By the way, about the biggest fall factor you can get in a "normal" climbing situation (if we ignore the hypothetical arbitrarily long fall arrested when the harness loop catches and holds on something) occurs if you clip directly into an anchor with a sport draw and then take a "factor 2" fall, which is really more like a factor-six fall, since the energy of a six biner-length fall has to be absorbed by one biner-length of nylon draw material.
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jt512
Feb 1, 2010, 6:12 AM
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rgold wrote: This argument dates back, at least, to the 4th century BC, when Aristotle distinguished between actual and potential infinity (and argued against actual infinity, claiming also that mathematicians didn't need it anyway, potential infinity was good enough). [I]t wasn't until Bolzano and Cantor that people looked at something as simple as the integers as a single entity (and so an actually infinite thing) rather than as some kind of process that didn't have any prescribed end. We are so steeped in set theory that the idea that people didn't look at infinite sets as single entities now seems strange.
Very interesting.
Jay
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guangzhou
Feb 1, 2010, 6:18 AM
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rgold wrote: This argument dates back, at least, to the 4th century BC, when Aristotle distinguished between actual and potential infinity (and argued against actual infinity, claiming also that mathematicians didn't need it anyway, potential infinity was good enough). Gauss took pretty much the same position, it wasn't until Bolzano and Cantor that people looked at something as simple as the integers as a single entity (and so an actually infinite thing) rather than as some kind of process that didn't have any prescribed end. We are so steeped in set theory that the idea that people didn't look at infinite sets as single entities now seems strange. Cowboychris has aligned himself with Aristotle and Gauss (among the smartest people to have ever lived) in taking the human inability to perform infinite enumeration as an obstruction to speaking of an actually infinite object. (Never mind that the same argument essentially denies the existence of actually very large finite objects like the number of grains of sand on all the world's beaches.) In any case, the instant the set concept was formulated, this obstruction simply vanished, as Jay keeps trying to point out. We're not in the fourth century BC or even in the 18th century any more CC! Anyway, the whole thing seems to have been started by the comment that the fall factor can be infinite, which is a typical bit of internet imprecision and was, one hopes, never intended to mean anything other than the fact that there is no upper bound to possible fall factors. There is, of course, no infinite fall factor; the fall factor is a real number. By the way, about the biggest fall factor you can get in a "normal" climbing situation (if we ignore the hypothetical arbitrarily long fall arrested when the harness loop catches and holds on something) occurs if you clip directly into an anchor with a sport draw and then take a "factor 2" fall, which is really more like a factor-six fall, since the energy of a six biner-length fall has to be absorbed by one biner-length of nylon draw material.
A well crafted answer until your last paragraph. Last couple sentences really.
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jt512
Feb 1, 2010, 6:27 AM
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guangzhou wrote: rgold wrote: This argument dates back, at least, to the 4th century BC, when Aristotle distinguished between actual and potential infinity (and argued against actual infinity, claiming also that mathematicians didn't need it anyway, potential infinity was good enough). Gauss took pretty much the same position, it wasn't until Bolzano and Cantor that people looked at something as simple as the integers as a single entity (and so an actually infinite thing) rather than as some kind of process that didn't have any prescribed end. We are so steeped in set theory that the idea that people didn't look at infinite sets as single entities now seems strange. Cowboychris has aligned himself with Aristotle and Gauss (among the smartest people to have ever lived) in taking the human inability to perform infinite enumeration as an obstruction to speaking of an actually infinite object. (Never mind that the same argument essentially denies the existence of actually very large finite objects like the number of grains of sand on all the world's beaches.) In any case, the instant the set concept was formulated, this obstruction simply vanished, as Jay keeps trying to point out. We're not in the fourth century BC or even in the 18th century any more CC! Anyway, the whole thing seems to have been started by the comment that the fall factor can be infinite, which is a typical bit of internet imprecision and was, one hopes, never intended to mean anything other than the fact that there is no upper bound to possible fall factors. There is, of course, no infinite fall factor; the fall factor is a real number. By the way, about the biggest fall factor you can get in a "normal" climbing situation (if we ignore the hypothetical arbitrarily long fall arrested when the harness loop catches and holds on something) occurs if you clip directly into an anchor with a sport draw and then take a "factor 2" fall, which is really more like a factor-six fall, since the energy of a six biner-length fall has to be absorbed by one biner-length of nylon draw material. A well crafted answer until your last paragraph. Last couple sentences really.
You know, ln light of the expertise of the person whose argument you are criticizing, if you want to be taken seriously, you have to actually state your criticism explicitly.
Jay
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qwert
Feb 2, 2010, 7:11 PM
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So two questions:
Why has this old thread been dug up agin?
and:
Is the thing below correct? I am not reading that thread
olderic wrote: This monthly topic seems to have surplanted long discussions on how to mark the middle of the rope, what shoes to buy, or whether or not to use the harness bealy loop to (gasp) belay off of. There will follow much arm waving and chest thumping as to whether 2.0 is the max. Foreign languages - via ferrata - will be invoked and the thread will lurch off in that direction. Then the idea of reeling in rope while a leader is falling will be spouted - could you, would you, should you... on and on an on Question first - reserach later
qwert
(This post was edited by qwert on Feb 2, 2010, 7:29 PM)
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kennoyce
Feb 2, 2010, 7:34 PM
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I'm not reading all of this, but I just wanted to let you know that it is incredibly easy to get an infinite fall factor in normal climbing situations. Lets just say you fall, the rope contacts a sharp part of the rock and is severed. At this point you have zero rope to absorb the impact of the fall, so no matter how far you fall, the fall length divided by zero is infinity. There you go, infinite fall factor.
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ptlong
Feb 2, 2010, 8:10 PM
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kennoyce wrote: I'm not reading all of this, but I just wanted to let you know that it is incredibly easy to get an infinite fall factor in normal climbing situations. Lets just say you fall, the rope contacts a sharp part of the rock and is severed. At this point you have zero rope to absorb the impact of the fall, so no matter how far you fall, the fall length divided by zero is infinity. There you go, infinite fall factor.
Clever, Ken. But it doesn't work. In the limit as the fall factor becomes infinite the tension in the rope also is infinite. But that won't happen in your example.
How far above your last piece of pro (numerator of the fall factor ratio) are you when you have no protection? It's undefined, as is the fall factor.
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bill413
Feb 2, 2010, 8:58 PM
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ptlong wrote: kennoyce wrote: I'm not reading all of this, but I just wanted to let you know that it is incredibly easy to get an infinite fall factor in normal climbing situations. Lets just say you fall, the rope contacts a sharp part of the rock and is severed. At this point you have zero rope to absorb the impact of the fall, so no matter how far you fall, the fall length divided by zero is infinity. There you go, infinite fall factor. Clever, Ken. But it doesn't work. In the limit as the fall factor becomes infinite the tension in the rope also is infinite. But that won't happen in your example. How far above your last piece of pro (numerator of the fall factor ratio) are you when you have no protection? It's undefined, as is the fall factor.
False. FF = distance fallen / (effective) rope out.
distance above your last piece of pro contributes to the distance fallen, but is not the sole determinant (5 feet above pro with rope taut yields 10foot fall, 5 feet above pro with 5 feet of slack = 15 foot fall).
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ptlong
Feb 2, 2010, 9:24 PM
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bill413 wrote: ptlong wrote: kennoyce wrote: I'm not reading all of this, but I just wanted to let you know that it is incredibly easy to get an infinite fall factor in normal climbing situations. Lets just say you fall, the rope contacts a sharp part of the rock and is severed. At this point you have zero rope to absorb the impact of the fall, so no matter how far you fall, the fall length divided by zero is infinity. There you go, infinite fall factor. Clever, Ken. But it doesn't work. In the limit as the fall factor becomes infinite the tension in the rope also is infinite. But that won't happen in your example. How far above your last piece of pro (numerator of the fall factor ratio) are you when you have no protection? It's undefined, as is the fall factor. False. FF = distance fallen / (effective) rope out. distance above your last piece of pro contributes to the distance fallen, but is not the sole determinant (5 feet above pro with rope taut yields 10foot fall, 5 feet above pro with 5 feet of slack = 15 foot fall).
Oops, you're right, I did get it wrong. But now so have you. It isn't the distance fallen, it's the distance fallen before the rope begins to stretch. Otherwise you'd have to know the rope characteristics in order to calculate the fall factor.
The rope never stretches in Ken's example. So the fall factor is undefined.
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kennoyce
Feb 2, 2010, 10:27 PM
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okay, maybe my example doesn't give an infinite fall factor, but here is an example that does. All you have to do is climb with a rope made from a material with a negative youngs modulus, any fall on this rope would give you an infinite fall factor.
edit to add: even a rope with a youngs modulus of zero would give you an infinite fall factor regardless of fall length.
(This post was edited by kennoyce on Feb 2, 2010, 11:08 PM)
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ptlong
Feb 3, 2010, 12:00 AM
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kennoyce wrote: okay, maybe my example doesn't give an infinite fall factor, but here is an example that does. All you have to do is climb with a rope made from a material with a negative youngs modulus, any fall on this rope would give you an infinite fall factor. edit to add: even a rope with a youngs modulus of zero would give you an infinite fall factor regardless of fall length.
Ken, I like your "thinking outside the box" style. But the usual definition of fall factor does not include the distance fallen after the rope begins to stretch.
The discussion about actual infinity was a lot more interesting.
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knudenoggin
Feb 4, 2010, 12:04 AM
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rgold wrote: guangzhou wrote: A well crafted answer until your last paragraph. Last couple sentences really. Yes, I do start heading down the road to incoherence at the end, although I thank Jay for standing up for me.
do w/o the gratuitous full-post copy. And which goes against your
own advice to put aside "degrees or not, we all make mistakes,
so I'd hold on to your scepticism and judge what you read by how
much sense it makes rather than who said it, no matter how
purportedly qualified they may be."
I see a question in it at least that has bothered me, in that
FF has been touted as THE determining factor in impact force
to the exclusion of fallen-upon material. E.g., that a big
whipper on low-elongation rope would be no worse than some
shorter fall of the same FF (though worse than on climbing rope,
for sure). Now, RGold's above assertion
contradicts that; and I think then that he should throw in some
significant discount towards the FF calculation for the rather static
webbing (dogbone duobled/trebled material, even?), as is implied
for the pair of (not perfectly static) 'biners.
*kN*
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rgold
Feb 4, 2010, 2:22 AM
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*KN* wrote: I see a question in it at least that has bothered me, in that FF has been touted as THE determining factor in impact force to the exclusion of fallen-upon material.
The fall factor is obtained by assuming that the material behaves, during extension like an ideal elastic material, meaning that it obeys Hooke's Law. This approximation isn't too bad for nylon climbing ropes. It is worse for other materials (unless, somewhat paradoxically, they stretch so little that Hooke's Law is a good first-order approximation).
More accurate models assume the presence of viscous damping, although there is, as far as I know no theoretical basis for these assumptions. The "right" configuration of springs and dashpots appears to behave in the same way as actual ropes.
*KN* wrote: ... E.g., that a big whipper on low-elongation rope would be no worse than some shorter fall of the same FF (though worse than on climbing rope, for sure).
To the extent that internal frictional forces and/or frictional forces between the rope, the rock, and the protections system serve to dissipate fall energy, the actual height of the fall will matter in the final determination of maximum impact load, even if the rope is perfectly elastic. The model leading to the fall factor concept is the simplest in a chain of approximations.
*KN* wrote: I think then that he should throw in some significant discount towards the FF calculation for the rather static webbing (dogbone duobled/trebled material, even?), as is implied for the pair of (not perfectly static) 'biners.
Congratulations: I think you managed to surpass my not inconsiderable level of incoherence with this last remark. In any case, the original subject was about how fall factors greater than two can occur. You are complaining that my response doesn't address issues that were never part of the discussion, which could have gone on more or less as it did even if the fall factor had nothing to do with maximum impact.
In response to another question, I posted some references about rope behavior on Super Topo, which may relieve some of your discomfort with the simple model.
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jt512
Feb 4, 2010, 3:41 AM
Post #107 of 107
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Registered: Apr 12, 2001
Posts: 21904
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rgold wrote: *KN* wrote: I think then that he should throw in some significant discount towards the FF calculation for the rather static webbing (dogbone duobled/trebled material, even?), as is implied for the pair of (not perfectly static) 'biners. Congratulations: I think you managed to surpass my not inconsiderable level of incoherence with this last remark.
He has, indeed, but even his last remark failed to attain complete incomprehensibility; although, to understand it, it helps to have read hundreds of posts by David Kastrup on rec.climbing. They're still accessible via groups.google.com, if you need a refresher.
Jay
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