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ensonik
Aug 31, 2010, 1:52 AM
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I am currently reading through the ANAM 2009. On page 32, the analysis of an accident that happened during a pendulum fall is pretty thorough, but mentions the following: "..., if you fall from, say, ten feet to one side of and level with your pivot point, you will have the same speed at the lowest point of your swing as you falling straight down ten feet ..." To say the least, this is surprising to a physics layman like me. To describe this and be sure I really understand the full impact of a pendulum (yes, I over protect them even though I wasn't aware of this small yet non inconsequential detail), I drew up something a small child could have done better but nonetheless illustrates it well: In other words, on both fall types, when I hit point B, I will be going at the same speed? (distances between A and B being equal of course). (Yes, I know, I know: It's in the book ...., but you never know ... errors can slip in. So I want to confirm this on the internets where it's well known that errors are weeded out and only the real information bubbles through to the top)
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bill413
Aug 31, 2010, 2:13 AM
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ensonik wrote: I am currently reading through the ANAM 2009. On page 32, the analysis of an accident that happened during a pendulum fall is pretty thorough, but mentions the following: "..., if you fall from, say, ten feet to one side of and level with your pivot point, you will have the same speed at the lowest point of your swing as you falling straight down ten feet ..." To say the least, this is surprising to a physics layman like me. To describe this and be sure I really understand the full impact of a pendulum (yes, I over protect them even though I wasn't aware of this small yet non inconsequential detail), I drew up something a small child could have done better but nonetheless illustrates it well: In other words, on both fall types, when I hit point B, I will be going at the same speed? (distances between A and B being equal of course). (Yes, I know, I know: It's in the book ...., but you never know ... errors can slip in. So I want to confirm this on the internets where it's well known that errors are weeded out and only the real information bubbles through to the top) As I read that statement, your diagram is in error. "Fall from...level with your pivot point...." So, in your pendulum diaram, point A should be at the same height as your anchor (and as the A in the straight down fall).
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nailzz
Aug 31, 2010, 2:33 AM
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What Bill said ... plus: The distance from what you have marked as A->B in your second diagram (the pendulum) would be greater than 10ft. The distance between point A and your anchor would be 10ft. The circumference of the circle would be 2(Pi)r. Your radius is 10ft and you are falling 1/4 of the circle, so your fall distance would be 2(Pi)10ft/4, or 15.7ft. More than 50% longer. I think what the book is saying, though, is that in either case you are moving downward for 10ft. Gravity is constant. It doesn't matter if you fall those 10ft straight downward or at an angle. At the bottom you are going to be travelling at the same speed (not counting things like friction and such). At least that's what I'm taking away from the quoted text.
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patto
Aug 31, 2010, 3:19 AM
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ensonik wrote: To say the least, this is surprising to a physics layman like me. Its conservation of energy. If you fall 10meters and weigh 100kg then your body will have E=mhg worth of kinetic energy (~speed energy). E= 100 * 10 * g(~9.8) = 9800J of energy. In practice a climbing rope stretches so a pendulum fall will be slightly slower as its not a perfect pendulum.
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majid_sabet
Aug 31, 2010, 3:30 AM
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sounds like a case in yosemite . is it ?
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TarHeelEMT
Aug 31, 2010, 4:51 AM
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Your chart is wrong. It's 10 vertical feet. The motion of the pendulum just redirects the force that you gather in those ten vertical feet of falling into horizontal motion. At the base of the pendulum, you're traveling sideways with the amount of energy one gathers when falling ten vertical feet - just as if you hadn't been redirected by the pendulum and fell straight down. The pendulum just changes the direction of the force.
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cantbuymefriends
Aug 31, 2010, 8:45 AM
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I guesstimate that the speed at the bottom of the the pendulum will be roughly the same as in a straight-down fall before the rope starts to stretch. As mentioned above, the velocity will be in the horizontal direction and not vertical though.
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socalclimber
Aug 31, 2010, 10:44 AM
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Let us not forget that a pendulum low down can take your straight into the deck. I saw it happen once. The person was lucky because it was just dirt. Now if there had been talus, it would have been a whole different story. Also bare in mind that if the swing ends in a corner, the end result can be very bad. You will likely be receiving a "trunk" blow. In other words, slamming the side of your body against the wall. Lot's of vital organs there that can get punctured or ruptured. Good question.
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ensonik
Aug 31, 2010, 10:49 AM
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majid_sabet wrote: sounds like a case in yosemite . is it ? It is.
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devkrev
Aug 31, 2010, 10:53 AM
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ensonik wrote: I am currently reading through the ANAM 2009. On page 32, the analysis of an accident that happened during a pendulum fall is pretty thorough, but mentions the following: "..., if you fall from, say, ten feet to one side of and level with your pivot point, you will have the same speed at the lowest point of your swing as you falling straight down ten feet ..." To say the least, this is surprising to a physics layman like me. To describe this and be sure I really understand the full impact of a pendulum (yes, I over protect them even though I wasn't aware of this small yet non inconsequential detail), I drew up something a small child could have done better but nonetheless illustrates it well: [image]http://imgur.com/memJH.png[/image] In other words, on both fall types, when I hit point B, I will be going at the same speed? (distances between A and B being equal of course). (Yes, I know, I know: It's in the book ...., but you never know ... errors can slip in. So I want to confirm this on the internets where it's well known that errors are weeded out and only the real information bubbles through to the top) Watch the opening scene in hard grit. Actually watch the whole movie, its good.
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Toast_in_the_Machine
Aug 31, 2010, 11:39 AM
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So this got me thinking about if there was an easy formula for pendulum. Especially looking at it with rope and a drop to calculate the velocity into a vertical wall. It was easy to get to the speed of a full pendulum. (Best web example is here:http://www.worsleyschool.net/...sement/pendulum.html) But my question was more: Knowing the height up and the distance over (and of course the rope length), was there an easy way to calculate (1) the force / tension when the rope "caught" and you began to swing and (2) what would the velocity be when you hit the wall. So I started to put pen to paper, but before I did, I did a quick look on the web and found this gem: What is the proper equation for maximum tension force in a rope for a falling load With the reference to the person's question being, you guessed it RC.com:
answers.yahoo.com wrote: Fall Factor source: The Standard Equation for Impact Force. Goldstone, R. (PDF, 2009) ref: http://www.rockclimbing.com/cgi-bin/forum/gforum.cgi?do=post_attachment;postatt_id=746 http://www.rockclimbing.com/...hment;postatt_id=746. I thought that was funny. (Now back to my pen and paper....)
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majid_sabet
Aug 31, 2010, 1:48 PM
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ensonik wrote: majid_sabet wrote: sounds like a case in yosemite . is it ? It is. Man, my memories is good but there was a similar case in late 90's on El Cap where a guy took a 15 feet pengi and crushed his side to the wall except he had tons of gear on his shoulder harness ended up with two broken ribs. Rescuers rapped 900 feet and jugged with the injured climber up to the top. pengi falls are extremely dangerous cause you are dealing with down and side forces simultaneously and you can not predict where you may end up.
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gunkiemike
Aug 31, 2010, 3:49 PM
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patto wrote: In practice a climbing rope stretches so a pendulum fall will be slightly slower as its not a perfect pendulum. That's the key. The other statements (ANAM, nailzz, tarheel) that speed would be equal because you've fallen the same vertical interval are only true in the theoretical case of a rigid, frictionless pendulum arm. So now the question becomes: for a typical rope modeled as a Hooke's Law spring, can we (er...rg?) model the final speed of a pendulum fall? The rope stretches (absorbing energy) as it does work against the climber. The tension in the rope increases proportionally (sinusoidally I suspect) as the fall angle increases from vertical. But the calculations are way beyond my pay grade.
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fresh
Aug 31, 2010, 5:40 PM
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ptlong2
Aug 31, 2010, 6:49 PM
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Ha ha ha! But the Hooke's Law version is an easy enough problem to solve. Stretch does subtract some of the energy but it also adds to it by increasing the fall distance. The answer is that the difference between the a stretchy rope and a truely static rope is negligable, in theory. Real life, with real ropes and slack added, there's going to be more of a difference but I can't say how much. Either way a big pendo fall into a corner is a bad idea, RG will concur.
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darkgift06
Aug 31, 2010, 7:04 PM
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all the calcs & no one added the increase of forces based on the centrifugal force generated by the fall.
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gunkiemike
Aug 31, 2010, 7:50 PM
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"Centrifugal" force is simply the climber's perception of the tension in the rope.
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Rudmin
Aug 31, 2010, 7:59 PM
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gunkiemike wrote: "Centrifugal" force is simply the climber's perception of the tension in the rope. Centrifugal force would actually be the climber's perception of a field (similar to gravity) pulling hair cloths, everything away from the axis of the pendulum. It is an artifact of adopting a rotational frame of reference. The tension in the rope is a centripetal force, and is an actual force no matter your frame of reference.
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patto
Aug 31, 2010, 9:16 PM
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I can't believe this is still being discussed. For a perfect pendulum with a perfectly static rope the speed is the same. The tension on the rope simplifies to the extraordinarily simply F=3mg. In other words 3 times the person's weight. For a perfect pendulum with a dynamic rope the speed is less. The tension on the rope will induce stretch the rope and absorb energy. For an imperfect pendulum with a dynamic rope it is all too complicated to work out, too many variables.
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jt512
Aug 31, 2010, 10:12 PM
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patto wrote: I can't believe this is still being discussed. For a perfect pendulum with a perfectly static rope the speed is the same. The tension on the rope simplifies to the extraordinarily simply F=3mg. In other words 3 times the person's weight. For a perfect pendulum with a dynamic rope the speed is less. Maybe you're satisfied with the answer "less." It's obviously still being discussed because others want a little more specific answer.
In reply to: For an imperfect pendulum with a dynamic rope it is all too complicated to work out, too many variables. Too complicated for whom? Are you seriously suggesting that the problem is so complicated that it can't be solved? Jay
(This post was edited by jt512 on Aug 31, 2010, 10:14 PM)
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ptlong2
Sep 1, 2010, 12:20 AM
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patto wrote: For a perfect pendulum with a dynamic rope the speed is less. The tension on the rope will induce stretch the rope and absorb energy. Yes, less. But the stretch also lengthens the fall which adds energy to the system, nearly enough to make it a wash. For a Hookian rope the difference is maybe a percent or two, depending on the rope modulus you select. If you add damping to the rope it reduces the speed a bit more, but not much.
In reply to: For an imperfect pendulum with a dynamic rope it is all too complicated to work out, too many variables. Got a computer?
(This post was edited by ptlong2 on Sep 1, 2010, 12:29 AM)
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jt512
Sep 1, 2010, 1:25 AM
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ptlong2 wrote: patto wrote: For a perfect pendulum with a dynamic rope the speed is less. The tension on the rope will induce stretch the rope and absorb energy. Yes, less. But the stretch also lengthens the fall which adds energy to the system, nearly enough to make it a wash. For a Hookian rope the difference is maybe a percent or two, depending on the rope modulus you select. If that's true then can you solve for the peak tension as follows? The potential energy (PE) of the fall is converted to kinetic energy (KE) and strain energy (SE) in the rope. That is, (1) PE = KE + SE . (2) PE = mgh = mg(L + s) , where L is the length of the unstretched rope and s is the maximum rope stretch in the fall. (3) KE = (1/2)mv² , (4) SE = (k/2L)s² (from rgold's paper), where k is the rope modulus. Substitute (2), (3), and (4) into (1), to give (5) mg(L + s) = (1/2)mv² + (k/2L)s² . From rgold's paper (6) s = TL/k , where T is the maximum rope tension. Now, substitute (6) into (5), compute v assuming an ideal pendulum, and solve for T. Jay
(This post was edited by jt512 on Sep 1, 2010, 1:26 AM)
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ptlong2
Sep 1, 2010, 1:38 AM
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jt512 wrote: compute v assuming an ideal pendulum, and solve for T. If you're assuming the speed of an ideal pendulum then you don't need the energy balance equation. T=(k/L)s is also equal to the centrifugal force plus the weight (assuming no vertical component of the velocity at the bottom of the swing). It's easy enough to take that force balance and combine it with the energy balance to get a quadratic in s. Then you have s and v, as well as T.
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Rudmin
Sep 1, 2010, 3:25 PM
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s and T are quite linearly related. You solve one and you have the other. The problem is that the centrifugal component of T is a function of v. That is m*v^2/(L+s). Simple enough to solve recursively, but it puts a crimp in your solution. To run it through some simple numbers. Let's say 10 metres of rope with a 100 kg climber and a stiffness of 24 kN per metre. (that's assuming that only the 10 metres of rope is being used). What I get is a velocity of about 50.2 km/hour and a rope tension of about 3kN. In essence, the rope stretch does next to nothing. If we take a quarter of the stiffness, as if you had almost a full rope length out, we get a velocity of 49.8 km/hour. So looks like no amount of climbing rope will help you in a pendulum.
(This post was edited by Rudmin on Sep 1, 2010, 3:26 PM)
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ptlong2
Sep 1, 2010, 4:49 PM
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What I posted above is wrong. That is, you can't expect a force balance at the bottom of the pendulum. By coincidence it gives an answer that is very close to that of a numerical approach, at least for the first swing. Rudmin, I'm not sure exactly what you did but when I run your numbers the machine gives slightly lower results. Same basic answer though. Interestingly the tension peak occurs after the bottom of the swing. Now in a real pendulum fall you have a real rope, a belayer and some initial slack. I think it would still hurt.
(This post was edited by ptlong2 on Sep 1, 2010, 4:50 PM)
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clc
Sep 1, 2010, 6:37 PM
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I was belaying my friend when he took a small pendulum fall. He swung down and across maybe 5 ft. Anyway its was a slow hobble back up the route and trail with a broken heel bone.
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Rudmin
Sep 1, 2010, 7:27 PM
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What the question is now, is where is the transition between a pendulum style fall and a normal fall. Would you actually be safer if your belayer fed out slack, making your fall longer, but lessening the pendulum? Say you are horizontally 8 feet from an anchor in an overhang. If you fell with the rope tight, you would be flying pretty fast in an arc, but suppose your belayer gave you 4 feet of slack. It could turn your pendulum fall into a regular fall and actually make you safer. It all depends on what the terrain is like of course, but it's something to consider.
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jt512
Sep 1, 2010, 7:44 PM
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Rudmin wrote: What the question is now, is where is the transition between a pendulum style fall and a normal fall. Would you actually be safer if your belayer fed out slack, making your fall longer, but lessening the pendulum? Say you are horizontally 8 feet from an anchor in an overhang. If you fell with the rope tight, you would be flying pretty fast in an arc, but suppose your belayer gave you 4 feet of slack. It could turn your pendulum fall into a regular fall and actually make you safer. It all depends on what the terrain is like of course, but it's something to consider. As a rule, I generally leave extra slack in the rope when the leader is off to the side of his pro to reduce the swing. Jay
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ensonik
Sep 1, 2010, 7:55 PM
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jt512 wrote: Rudmin wrote: What the question is now, is where is the transition between a pendulum style fall and a normal fall. Would you actually be safer if your belayer fed out slack, making your fall longer, but lessening the pendulum? Say you are horizontally 8 feet from an anchor in an overhang. If you fell with the rope tight, you would be flying pretty fast in an arc, but suppose your belayer gave you 4 feet of slack. It could turn your pendulum fall into a regular fall and actually make you safer. It all depends on what the terrain is like of course, but it's something to consider. As a rule, I generally leave extra slack in the rope when the leader is off to the side of his pro to reduce the swing. Jay Ok, I just came back on board. Really? Is this common for others?
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raingod
Sep 1, 2010, 8:12 PM
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ensonik wrote: jt512 wrote: Rudmin wrote: What the question is now, is where is the transition between a pendulum style fall and a normal fall. Would you actually be safer if your belayer fed out slack, making your fall longer, but lessening the pendulum? Say you are horizontally 8 feet from an anchor in an overhang. If you fell with the rope tight, you would be flying pretty fast in an arc, but suppose your belayer gave you 4 feet of slack. It could turn your pendulum fall into a regular fall and actually make you safer. It all depends on what the terrain is like of course, but it's something to consider. As a rule, I generally leave extra slack in the rope when the leader is off to the side of his pro to reduce the swing. Jay Ok, I just came back on board. Really? Is this common for others? I do that as well
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ptlong2
Sep 1, 2010, 8:15 PM
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Is this the situation where you would add slack?
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ptlong2
Sep 2, 2010, 12:18 AM
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Like this? About how much slack would you add?
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jt512
Sep 2, 2010, 12:44 AM
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ptlong2 wrote: Like this? About how much slack would you add? I don't know. My gut reaction would be five feet, maybe six. In addition, I'm going to dynamically belay, which I think will also reduce the swing into the wall. Edit: Actually, as drawn, it looks like I can't dynamically belay. Jay
(This post was edited by jt512 on Sep 2, 2010, 12:50 AM)
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brokesomeribs
Sep 2, 2010, 12:50 AM
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ptlong2 wrote: Like this? [img]http://img825.imageshack.us/img825/3360/horizontala.jpg[/img] About how much slack would you add? I'd like to preemptively comment that this thread has among the highest SNR's of any active thread I've seen here recently. Kudos, RC! But I digress... The second scenario isn't as "hopeless" as the first scenario, but still "shitty." Adding slack in this situation would depend primarily on the topography of the rock between the belayer and the climber. My benchmark for adding slack is when the addition of said slack will reduce the arc of the pendulum, but not forseeably add any danger to the climber. As an example, if there were a ledge approximately 10' below the illustrated roof, I would not add any slack. That would further increase the already high likelihood of decking and shattering ankles. A scenario where I might add some extra slack would be if there were a large feature/abutment projecting out from the cliff face, located below the "10 feet" text in the image. In that scenario, adding some slack would allow the climber to fall further before beginning the pendulum, hopefully placing him below the abutment, instead of swinging right into it for a side impact.
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ptlong2
Sep 2, 2010, 2:26 AM
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brokesomeribs wrote: I'd like to preemptively comment that this thread has among the highest SNR's of any active thread I've seen here recently. One person's signal is another's noise. Not everybody thinks geek threads are valuable.
In reply to: Adding slack in this situation would depend primarily on the topography of the rock between the belayer and the climber. I think it's simpler if this obvious complication is ignored. Pretend there are no ledges below and no obstacles in the way, other than that vertical wall or big corner that the climber could pendulum into. Is adding slack (how much?) going to reduce the speed that the climber impacts the wall/corner?
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brokesomeribs
Sep 2, 2010, 2:37 AM
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ptlong2 wrote: brokesomeribs wrote: I'd like to preemptively comment that this thread has among the highest SNR's of any active thread I've seen here recently. One person's signal is another's noise. Not everybody thinks geek threads are valuable. In reply to: Adding slack in this situation would depend primarily on the topography of the rock between the belayer and the climber. I think it's simpler if this obvious complication is ignored. Pretend there are no ledges below and no obstacles in the way, other than that vertical wall or big corner that the climber could pendulum into. Is adding slack (how much?) going to reduce the speed that the climber impacts the wall/corner? I don't think that you can ignore the complication of topography, however I understand you're asking as an exercise in academic thought. And despite the fact that I enjoy participating in geek threads, I'm only an armchair geek at best and I have absolutely no idea how to calculate (or even surmise) an answer to your question. I was a liberal arts major. Color me stumped.
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ptlong2
Sep 2, 2010, 3:01 AM
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brokesomeribs wrote: I don't think that you can ignore the complication of topography Not in practice. If you said, "an infinite amount of slack", then you would have had the technically-right answer and forced the issue. But the question, without the obstacles, still has merit. Do you feed some slack (how much?), or not?
In reply to: I'm only an armchair geek at best and I have absolutely no idea how to calculate (or even surmise) an answer to your question. Computer models are only so good as well. I know what mine says. Anecdotal reports, while suspect, have some value in the absence of solid data. What do climbers do, and how do they perceive that it works (or doesn't)?
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skiclimb
Sep 2, 2010, 3:59 AM
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jt512 wrote: ptlong2 wrote: Like this? [img]http://img825.imageshack.us/img825/3360/horizontala.jpg[/img] About how much slack would you add? I don't know. My gut reaction would be five feet, maybe six. In addition, I'm going to dynamically belay, which I think will also reduce the swing into the wall. Edit: Actually, as drawn, it looks like I can't dynamically belay. Jay In both cases with pro or with short pro adding slack will increase the speed and therefore impact force ..unless maybe you add the full ropelength of slack in the with pro diagram.. in that case the climber might not hit the wall at all.. but then again..if he does which he probably will anyway....ouch
(This post was edited by skiclimb on Sep 2, 2010, 4:02 AM)
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jt512
Sep 2, 2010, 4:34 AM
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skiclimb wrote: jt512 wrote: ptlong2 wrote: Like this? [img]http://img825.imageshack.us/img825/3360/horizontala.jpg[/img] About how much slack would you add? I don't know. My gut reaction would be five feet, maybe six. In addition, I'm going to dynamically belay, which I think will also reduce the swing into the wall. Edit: Actually, as drawn, it looks like I can't dynamically belay. Jay In both cases with pro or with short pro adding slack will increase the speed and therefore impact force ..unless maybe you add the full ropelength of slack in the with pro diagram.. I doubt it. At least not in the case with pro. Your reasoning does not take into account that as you increase the slack you decrease the angle at which the pendulum starts. By your own admission, there must be an amount of slack that will reduce the impact force into the wall, but I doubt that it really is a whole rope length. My guess is that the impact force against the wall decreases monotonically with the amount of slack. I assume that ptlong2 will eventually run the numbers and give us his solution. I just had a vague recollection of a similar problem coming up on rec.climbing a long time ago. My memory might be playing tricks on me, but I seem to recall someone claiming that the amount of slack should be greater than the horizontal runout. Jay
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blondgecko
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Sep 2, 2010, 5:01 AM
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ptlong2 wrote: Like this? About how much slack would you add? One somewhat unintuitive thing the climber could do in this situation is, if possible, launch himself back towards the belayer as he comes off. The closer to directly underneath the last anchor point he is when tension comes onto the rope, the better off he's going to be.
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skiclimb
Sep 2, 2010, 5:12 AM
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jt512 wrote: skiclimb wrote: jt512 wrote: ptlong2 wrote: Like this? [img]http://img825.imageshack.us/img825/3360/horizontala.jpg[/img] About how much slack would you add? I don't know. My gut reaction would be five feet, maybe six. In addition, I'm going to dynamically belay, which I think will also reduce the swing into the wall. Edit: Actually, as drawn, it looks like I can't dynamically belay. Jay In both cases with pro or with short pro adding slack will increase the speed and therefore impact force ..unless maybe you add the full ropelength of slack in the with pro diagram.. I doubt it. At least not in the case with pro. Your reasoning does not take into account that as you increase the slack you decrease the angle at which the pendulum starts. By your own admission, there must be an amount of slack that will reduce the impact force into the wall, but I doubt that it really is a whole rope length. My guess is that the impact force against the wall decreases monotonically with the amount of slack. I assume that ptlong2 will eventually run the numbers and give us his solution. I just had a vague recollection of a similar problem coming up on rec.climbing a long time ago. My memory might be playing tricks on me, but I seem to recall someone claiming that the amount of slack should be greater than the horizontal runout. Jay If i remeber my old physic correctly a pendulem only redirects force it does not mitigate it. the amount of vertical fall is the sole generater of speed. more slack means more speed = more force at impact. the reason i meantioned that a full ropelength fall might be safer (but probably not) is that other forces can come into play ..such as glide and air friction may allow a person to hit the rope at a point directly under the pro without hitting the wall first. then again it could make it worse if the person falls in such a way that they push away from the wall.. they key is the direction of fall in regarding slack..if they fall toward the wall such that they aproach nearly directly below the pro point once the slack runs out then they have a chance to not hit the wall at all. However if they fall straight down or only slightly towards the pro or worst of all away from the pro then the slack just increases the speed at which they impact the wall. best case would be an aproximately 30 foot freefall towards and slightly past the pro with moderate slack such that you hit the rope at a point between the wall and the pro perhaps about 1ft past the pro on the wall side.. the resulting pendo would actually take you away from the wall... However realworld best bet in this case is a tight belay and the old rule.."the leader must not fall" If the leader must fall he should try to use the last couple second or so of control before failure to jump/pushoff towards the pro
(This post was edited by skiclimb on Sep 2, 2010, 5:21 AM)
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curt
Sep 2, 2010, 6:32 AM
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ptlong2 wrote: brokesomeribs wrote: I don't think that you can ignore the complication of topography Not in practice. If you said, "an infinite amount of slack", then you would have had the technically-right answer and forced the issue. But the question, without the obstacles, still has merit. Do you feed some slack (how much?), or not? In reply to: I'm only an armchair geek at best and I have absolutely no idea how to calculate (or even surmise) an answer to your question. Computer models are only so good as well. I know what mine says. Anecdotal reports, while suspect, have some value in the absence of solid data. What do climbers do, and how do they perceive that it works (or doesn't)? I have little doubt we'll see the "correct" answer posted here in short order: http://www.theclimbinglab.com ...as soon as the proctor, the advisory board and the dumbass get around to it. Curt
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jt512
Sep 2, 2010, 10:20 AM
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skiclimb wrote: jt512 wrote: skiclimb wrote: jt512 wrote: ptlong2 wrote: Like this? [img]http://img825.imageshack.us/img825/3360/horizontala.jpg[/img] About how much slack would you add? I don't know. My gut reaction would be five feet, maybe six. In addition, I'm going to dynamically belay, which I think will also reduce the swing into the wall. Edit: Actually, as drawn, it looks like I can't dynamically belay. Jay In both cases with pro or with short pro adding slack will increase the speed and therefore impact force ..unless maybe you add the full ropelength of slack in the with pro diagram.. I doubt it. At least not in the case with pro. Your reasoning does not take into account that as you increase the slack you decrease the angle at which the pendulum starts. By your own admission, there must be an amount of slack that will reduce the impact force into the wall, but I doubt that it really is a whole rope length. My guess is that the impact force against the wall decreases monotonically with the amount of slack. I assume that ptlong2 will eventually run the numbers and give us his solution. I just had a vague recollection of a similar problem coming up on rec.climbing a long time ago. My memory might be playing tricks on me, but I seem to recall someone claiming that the amount of slack should be greater than the horizontal runout. Jay If i remeber my old physic correctly a pendulem only redirects force it does not mitigate it. the amount of vertical fall is the sole generater of speed. more slack means more speed = more force at impact. the reason i meantioned that a full ropelength fall might be safer (but probably not) is that other forces can come into play ..such as glide and air friction may allow a person to hit the rope at a point directly under the pro without hitting the wall first. then again it could make it worse if the person falls in such a way that they push away from the wall.. they key is the direction of fall in regarding slack..if they fall toward the wall such that they aproach nearly directly below the pro point once the slack runs out then they have a chance to not hit the wall at all. However if they fall straight down or only slightly towards the pro or worst of all away from the pro then the slack just increases the speed at which they impact the wall. best case would be an aproximately 30 foot freefall towards and slightly past the pro with moderate slack such that you hit the rope at a point between the wall and the pro perhaps about 1ft past the pro on the wall side.. the resulting pendo would actually take you away from the wall... What the fuck are you smoking?
In reply to: However realworld best bet in this case is a tight belay... Please don't ever belay me. Ever. Jay
(This post was edited by jt512 on Sep 2, 2010, 10:21 AM)
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sbaclimber
Sep 2, 2010, 10:51 AM
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jt512 wrote: In reply to: However realworld best bet in this case is a tight belay... Please don't ever belay me. Ever. +1
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blondgecko
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Sep 2, 2010, 11:24 AM
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ptlong2 wrote: Like this? About how much slack would you add? Just another random thought on this picture: what if the draw in the roof was extendable by (say) 3-6 feet, but held in a short configuration by a link set to fail at low force (I'm thinking not much more than bodyweight). The idea is to start the pendulum enough to get some (but not too much) sideways momentum, then trigger a period of freefall as the weak link breaks. If you're moving sideways during that freefall, then by the time the rope pulls tight again, the new vector is far more vertical and so more of the fall energy goes into stretching the rope rather than accelerating you sideways. Just rambling. Seems to make sense to me though.
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skiclimb
Sep 2, 2010, 2:43 PM
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sbaclimber wrote: jt512 wrote: In reply to: However realworld best bet in this case is a tight belay... Please don't ever belay me. Ever. +1 By tight belay i did not mean tension i meant keeping as much slack as possible out of the rope without interfering with the lead.
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sp00ki
Sep 2, 2010, 5:10 PM
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ensonik wrote: non inconsequential If only there were a word for that...
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ensonik
Sep 2, 2010, 6:56 PM
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sp00ki wrote: ensonik wrote: non inconsequential If only there were a word for that... I'd suggest a bit Douglas Adams to brush up on your grammatical sense of humour. It sounds like you may need a bit of help in that department. You seem to be doing fine on irony though. Carry on.
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Rudmin
Sep 2, 2010, 7:08 PM
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I made up a quick numerical calculator in excel to drop a climber at some distance horizontally from an anchor with a given amount of slack. The surprising thing was that adding slack increased peak horizontal velocity. When I charted out the fall path, it quickly became apparent that as the climber fell the rope (modeled as a spring) would bounce them pretty hard like a spring would. I figured that the problem was that the rope was acting like a perfect spring, so I added a dampening factor that opposed rate of stretch and then jigged the stiffness and dampening factor to roughly match some UIAA numbers for popular retail ropes. This would allow the rope to bleed energy out of the system. I also added a wind resistance proportional to velocity^2 sufficient to give a terminal velocity of 55 m/s. After all that, still the same result pretty much. My final results were for a test with a rope with stretch and dampening to give it approximately similar characteristics to a UIAA approved rope. 80 kg climber 10 metres from protection. Slack [m]/Peak Tension [kN]/Peak Horizontal Velocity [m/s] 0/2.1/13.0 1/2.0/13.3 2/2.4/13.2 3/2.8/13.0 4/3.1/12.8 6/3.7/12.2 8/4.2/11.6 10/4.7/11.1 20/6.4/9.1 50/9.3/6.3 (climber reaches vertical speed of 100 kmph and wind resistance is dominant energy sink) What I can conclude, is that pendulum speed doesn't depend so much on rope stiffness or rope length, but on how much energy can be removed by the time that swing occurs. Because my rope is simplified down to two numbers, this model probably doesn't accurately represent reality, but it is probably somewhat close. If you want to reduce forces on your anchor, don't give slack to a pendulum fall. If you want to reduce pendulum velocity, you need to give out a lot of slack, or think of a smarter way to do things. Here is what a fall 10 metres out with 6 metres of slack looks like:
(This post was edited by Rudmin on Sep 2, 2010, 7:33 PM)
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gunkiemike
Sep 2, 2010, 9:12 PM
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curt wrote: I have little doubt we'll see the "correct" answer posted here in short order: http://www.theclimbinglab.com ...as soon as the proctor, the advisory board and the dumbass get around to it. Curt Jesus, give it up already...
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gunkiemike
Sep 2, 2010, 9:18 PM
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ptlong2 wrote: I think it's simpler if this obvious complication is ignored. Pretend there are no ledges below and no obstacles in the way, other than that vertical wall or big corner that the climber could pendulum into. Is adding slack (how much?) going to reduce the speed that the climber impacts the wall/corner? If we think like physics students and resolve the fall into horizontal and vertical components, I suspect we see that the horizontal component of the climber's ultimate (bottom of fall) motion is unaffected by slack. So he impacts the wall with V(sub)h. Adding slack merely increases his V(sub)v, the vertical component of the fall. In other words, with slack he strikes the wall at a glancing blow; without slack he hits it perpendicularly. I think I'd want the former. Within reasonable limits.
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Rudmin
Sep 2, 2010, 9:20 PM
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how would you get a vertical component of velocity at the bottom of a fall? If you are still moving vertically you are still falling.
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gunkiemike
Sep 2, 2010, 9:31 PM
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Rudmin wrote: how would you get a vertical component of velocity at the bottom of a fall? If you are still moving vertically you are still falling. Good point - I'm picturing the rope tension being sufficient to produce the horizontal motion of the climber BEFORE the tension rises high enough and long enough to arrest the vertical component. That may not be the case. [goes back to scratching his head]
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blondgecko
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Sep 2, 2010, 11:46 PM
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blondgecko wrote: ptlong2 wrote: Like this? About how much slack would you add? One somewhat unintuitive thing the climber could do in this situation is, if possible, launch himself back towards the belayer as he comes off. The closer to directly underneath the last anchor point he is when tension comes onto the rope, the better off he's going to be. So, I decided to some quick back-of-the-envelope calculations on this idea (sorry, don't have time to do a real analysis). To simplify, say you're on a perfectly inelastic rope with no slack 3m horizontally from a pivot point. You drop and start to pendulum until you're 1m vertically below your starting point. At this point your anchor instantly extends by 1m. Under this scenario, according to my calculations at the instant the anchor extends, you're travelling at ~4.2m/s vertically, 1.5m/s horizontally, and you're 1m vertically and 2m horizontally from your anchor. Once the anchor extends, however, you're in free-fall and not being accelerated by the rope until it pulls tight again (ie. when the distance from the original pivot point = 4m). Until that happens, it's just plain old parabolic trajectory: V(horizontal) = 1.5m/s; V(vertical) = 4.2m/s + 9.81*t. If I haven't made a mistake along the way, this means that you re-engage the rope after a little over 0.4 seconds, by which time you're ~2.75m lower, and 0.65m closer to the wall. At that instant, you're moving at ~8.5m/s vertically, but still moving at just 1.5m/s horizontally. By comparison, at this time in the straight pendulum, your fall would be almost over and you'd be about to hit the wall at a little over 7m/s. So not only are you going far slower in the direction that's going to hurt, but your angle with the anchor point at the instant of re-engagement is now only about 20 degrees from vertical (it was 65 degrees when the anchor shifted) - meaning that a far greater fraction of the fall energy will go into stretching the rope rather than accelerating you sideways. It's been a long, long time since I had anything to do with spring calculations, so I'll leave it to someone else, if interested, to do the detailed calculations.
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blondgecko
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Sep 3, 2010, 1:10 AM
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blondgecko wrote: blondgecko wrote: ptlong2 wrote: Like this? About how much slack would you add? One somewhat unintuitive thing the climber could do in this situation is, if possible, launch himself back towards the belayer as he comes off. The closer to directly underneath the last anchor point he is when tension comes onto the rope, the better off he's going to be. So, I decided to some quick back-of-the-envelope calculations on this idea (sorry, don't have time to do a real analysis). To simplify, say you're on a perfectly inelastic rope with no slack 3m horizontally from a pivot point. You drop and start to pendulum until you're 1m vertically below your starting point. At this point your anchor instantly extends by 1m. Under this scenario, according to my calculations at the instant the anchor extends, you're travelling at ~4.2m/s vertically, 1.5m/s horizontally, and you're 1m vertically and 22.8m horizontally from your anchor. Once the anchor extends, however, you're in free-fall and not being accelerated by the rope until it pulls tight again (ie. when the distance from the original pivot point = 4m). Until that happens, it's just plain old parabolic trajectory: V(horizontal) = 1.5m/s; V(vertical) = 4.2m/s + 9.81*t. If I haven't made a mistake along the way, this means that you re-engage the rope after a little overunder 0.4 seconds, by which time you're ~ 2.752.3m lower, and 0.650.56m closer to the wall. At that instant, you're moving at ~ 8.57.9m/s vertically, but still moving at just 1.5m/s horizontally. By comparison, at this time in the straight pendulum, your fall would be almost over and you'd be about to hit the wall at a little over 7m/s. So not only are you going far slower in the direction that's going to hurt, but your angle with the anchor point at the instant of re-engagement is now only about 2035 degrees from vertical (it was 6570 degrees when the anchor shifted) - meaning that a far greater fraction of the fall energy will go into stretching the rope rather than accelerating you sideways. It's been a long, long time since I had anything to do with spring calculations, so I'll leave it to someone else, if interested, to do the detailed calculations. Murphy's law strikes (it's sin, not cos). I think that's right now.
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curt
Sep 3, 2010, 1:11 AM
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gunkiemike wrote: curt wrote: I have little doubt we'll see the "correct" answer posted here in short order: http://www.theclimbinglab.com ...as soon as the proctor, the advisory board and the dumbass get around to it. Curt Jesus, give it up already... Hey, thanks for the unsolicited and unwanted advice. Curt
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blondgecko
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Sep 3, 2010, 2:02 AM
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blondgecko wrote: blondgecko wrote: blondgecko wrote: ptlong2 wrote: Like this? [img]http://img825.imageshack.us/img825/3360/horizontala.jpg[/img] About how much slack would you add? One somewhat unintuitive thing the climber could do in this situation is, if possible, launch himself back towards the belayer as he comes off. The closer to directly underneath the last anchor point he is when tension comes onto the rope, the better off he's going to be. So, I decided to some quick back-of-the-envelope calculations on this idea (sorry, don't have time to do a real analysis). To simplify, say you're on a perfectly inelastic rope with no slack 3m horizontally from a pivot point. You drop and start to pendulum until you're 1m vertically below your starting point. At this point your anchor instantly extends by 1m. Under this scenario, according to my calculations at the instant the anchor extends, you're travelling at ~4.2m/s vertically, 1.5m/s horizontally, and you're 1m vertically and 22.8m horizontally from your anchor. Once the anchor extends, however, you're in free-fall and not being accelerated by the rope until it pulls tight again (ie. when the distance from the original pivot point = 4m). Until that happens, it's just plain old parabolic trajectory: V(horizontal) = 1.5m/s; V(vertical) = 4.2m/s + 9.81*t. If I haven't made a mistake along the way, this means that you re-engage the rope after a little overunder 0.4 seconds, by which time you're ~ 2.752.3m lower, and 0.650.56m closer to the wall. At that instant, you're moving at ~ 8.57.9m/s vertically, but still moving at just 1.5m/s horizontally. By comparison, at this time in the straight pendulum, your fall would be almost over and you'd be about to hit the wall at a little over 7m/s. So not only are you going far slower in the direction that's going to hurt, but your angle with the anchor point at the instant of re-engagement is now only about 2035 degrees from vertical (it was 6570 degrees when the anchor shifted) - meaning that a far greater fraction of the fall energy will go into stretching the rope rather than accelerating you sideways. It's been a long, long time since I had anything to do with spring calculations, so I'll leave it to someone else, if interested, to do the detailed calculations. Murphy's law strikes (it's sin, not cos). I think that's right now. OK, colour me obsessed, but I worked out the "perfect" case (where the climber hits the wall just as the rope comes taught again, which unless I'm missing something will give the lowest possible horizontal speed) for two scenarios: a 1m or 2m extension at the anchor. Here it is graphically (trajectories are a bit rough, but distances and velocity vectors (the blue arrows) are to scale): Basically, if you do nothing your horizontal velocity at impact is 7.7m/s. If you instantaneously release 1m of slack when the climber's at the point of the trajectory marked by the rightmost orange circle, he'll be going at 5.8m/s horizontally when he hits the wall (at the point marked by the bottom orange circle). If you release 2m of slack at the point of the rightmost purple circle, he'll be going just 4.5m/s at the wall. Since kinetic energy scales as the square, that's a 42 and 66% reduction in horizontal impact energy, respectively.
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112
Sep 3, 2010, 2:40 AM
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I think you are modeling a dynamic belay with no slack to start. I thought the question was regarding how much initial slack to add, and then the motion would be mostly rotational there after. I see it as: fall, initial catch, and then penji. 45 degrees seems optimal (as jt512 stated); slack to pay out would be roughly 40% of the distance from last pro. But, if someone worked out an equation to optimize, that would be cool!
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blondgecko
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Sep 3, 2010, 3:37 AM
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112 wrote: I think you are modeling a dynamic belay with no slack to start. I thought the question was regarding how much initial slack to add, and then the motion would be mostly rotational there after. I see it as: fall, initial catch, and then penji. 45 degrees seems optimal (as jt512 stated); slack to pay out would be roughly 40% of the distance from last pro. But, if someone worked out an equation to optimize, that would be cool! Yes, I'm modelling an alternative scenario. The basic idea I'm putting forward is that the best time to provide slack isn't before the fall. It's during the fall, once the climber has built up some sideways momentum.
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jt512
Sep 3, 2010, 3:45 AM
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blondgecko wrote: 112 wrote: I think you are modeling a dynamic belay with no slack to start. I thought the question was regarding how much initial slack to add, and then the motion would be mostly rotational there after. I see it as: fall, initial catch, and then penji. 45 degrees seems optimal (as jt512 stated); slack to pay out would be roughly 40% of the distance from last pro. But, if someone worked out an equation to optimize, that would be cool! Yes, I'm modelling an alternative scenario. The basic idea I'm putting forward is that the best time to provide slack isn't before the fall. It's during the fall, once the climber has built up some sideways momentum. That seems counterintuitive. Jay
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blondgecko
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Sep 3, 2010, 3:54 AM
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jt512 wrote: blondgecko wrote: 112 wrote: I think you are modeling a dynamic belay with no slack to start. I thought the question was regarding how much initial slack to add, and then the motion would be mostly rotational there after. I see it as: fall, initial catch, and then penji. 45 degrees seems optimal (as jt512 stated); slack to pay out would be roughly 40% of the distance from last pro. But, if someone worked out an equation to optimize, that would be cool! Yes, I'm modelling an alternative scenario. The basic idea I'm putting forward is that the best time to provide slack isn't before the fall. It's during the fall, once the climber has built up some sideways momentum. That seems counterintuitive. Jay Yes it does - so don't take my word for it, but do the working yourself. The basic idea is simple, though - as long as the falling climber is moving sideways without being supported by the rope, they're reducing the horizontal fraction of the force imparted by the rope once it comes tight.
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jt512
Sep 3, 2010, 4:06 AM
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blondgecko wrote: jt512 wrote: blondgecko wrote: 112 wrote: I think you are modeling a dynamic belay with no slack to start. I thought the question was regarding how much initial slack to add, and then the motion would be mostly rotational there after. I see it as: fall, initial catch, and then penji. 45 degrees seems optimal (as jt512 stated); slack to pay out would be roughly 40% of the distance from last pro. But, if someone worked out an equation to optimize, that would be cool! Yes, I'm modelling an alternative scenario. The basic idea I'm putting forward is that the best time to provide slack isn't before the fall. It's during the fall, once the climber has built up some sideways momentum. That seems counterintuitive. Jay Yes it does - so don't take my word for it, but do the working yourself. The basic idea is simple, though - as long as the falling climber is moving sideways without being supported by the rope, they're reducing the horizontal fraction of the force imparted by the rope once it comes tight. Actually, now that I think about it, not only is it intuitive, but I have always performed a variant of it. As I said in an earlier post, when the leader is to the side of his pro, in addition to leaving slack in the rope, I also give a dynamic belay. The latter accomplishes something similar to what you are suggesting: lengthening the fall at the last instant before impact with the wall. Intuitively, I always suspected that the dynamic belay part was more important than the initial slack. But whatever method one choses to lengthen the fall at the last moment, one can still leave initial slack in the rope, and so the question of the effectiveness of that remains open. Jay
(This post was edited by jt512 on Sep 3, 2010, 4:07 AM)
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hafilax
Sep 3, 2010, 5:14 AM
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I think that for this kind of problem one can learn more with a fishing bob and an elastic or a piece of string than from crunching numbers.
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Rudmin
Sep 3, 2010, 2:55 PM
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112 wrote: I think you are modeling a dynamic belay with no slack to start. I thought the question was regarding how much initial slack to add, and then the motion would be mostly rotational there after. I see it as: fall, initial catch, and then penji. 45 degrees seems optimal (as jt512 stated); slack to pay out would be roughly 40% of the distance from last pro. But, if someone worked out an equation to optimize, that would be cool! I answered this question about a page ago. Slack doesn't help unless you add a lot of it, at least with a theoretical rope in a theoretical situation.
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112
Sep 3, 2010, 3:12 PM
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Rudmin wrote: 112 wrote: I think you are modeling a dynamic belay with no slack to start. I thought the question was regarding how much initial slack to add, and then the motion would be mostly rotational there after. I see it as: fall, initial catch, and then penji. 45 degrees seems optimal (as jt512 stated); slack to pay out would be roughly 40% of the distance from last pro. But, if someone worked out an equation to optimize, that would be cool! I answered this question about a page ago. Slack doesn't help unless you add a lot of it, at least with a theoretical rope in a theoretical situation. Yeah, you stated that, I guess I just didn't follow your proof. I am not doubting you. I just don't yet see the truth.
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Rudmin
Sep 3, 2010, 3:20 PM
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112 wrote: Rudmin wrote: 112 wrote: I think you are modeling a dynamic belay with no slack to start. I thought the question was regarding how much initial slack to add, and then the motion would be mostly rotational there after. I see it as: fall, initial catch, and then penji. 45 degrees seems optimal (as jt512 stated); slack to pay out would be roughly 40% of the distance from last pro. But, if someone worked out an equation to optimize, that would be cool! I answered this question about a page ago. Slack doesn't help unless you add a lot of it, at least with a theoretical rope in a theoretical situation. Yeah, you stated that, I guess I just didn't follow your proof. I am not doubting you. I just don't yet see the truth. My proof was a an excel sheet of forces, velocities, and positions calculated with a 1 ms time step. I can email it to you if you want..
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blondgecko
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Sep 3, 2010, 8:06 PM
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Rudmin wrote: 112 wrote: Rudmin wrote: 112 wrote: I think you are modeling a dynamic belay with no slack to start. I thought the question was regarding how much initial slack to add, and then the motion would be mostly rotational there after. I see it as: fall, initial catch, and then penji. 45 degrees seems optimal (as jt512 stated); slack to pay out would be roughly 40% of the distance from last pro. But, if someone worked out an equation to optimize, that would be cool! I answered this question about a page ago. Slack doesn't help unless you add a lot of it, at least with a theoretical rope in a theoretical situation. Yeah, you stated that, I guess I just didn't follow your proof. I am not doubting you. I just don't yet see the truth. My proof was a an excel sheet of forces, velocities, and positions calculated with a 1 ms time step. I can email it to you if you want.. If you're feeling enthusiastic, I'd love to see what your model says about my scenario(s) above.
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Rudmin
Sep 3, 2010, 9:00 PM
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You can mess around with it all you like. To simulate what you said, I just took a 0 slack fall, and then took the position and velocity part way through and used those as initial conditions for a 3 metre slack fall. Not a very big difference. Here is the excel sheet: http://FastFreeFileHosting.com/...45/pendulum-xls.html
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blondgecko
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Sep 3, 2010, 9:20 PM
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Rudmin wrote: You can mess around with it all you like. To simulate what you said, I just took a 0 slack fall, and then took the position and velocity part way through and used those as initial conditions for a 3 metre slack fall. Not a very big difference. Here is the excel sheet: http://FastFreeFileHosting.com/...45/pendulum-xls.html It won't let me download it - I get a message about the server not allowing proxies to download.
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112
Sep 4, 2010, 12:24 AM
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I have been trying to put something together, but want to proof it before posting. But, it appears that adding up to 10% initial slack (of distance from last pro) increases the horizontal velocity at impact. Adding 20% slack is roughly the same as no slack and anything greater than 20% reduces the total horizontal velocity at impact. I might be wrong (typically am), and this doesn't address which single form of mitigation (initial slack or dynamic belay) is better. I guess that analysis would be per foot of extension; which method is is more effective? I am off for a 5-day weekend! I might post something when I return... Thanks so much for such a fun thread! EDit to add: Rudmin's number show the same thing but a cross over around 30%.
(This post was edited by 112 on Sep 4, 2010, 1:29 AM)
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112
Sep 4, 2010, 1:49 AM
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And, if you have to give 30% initial slack to just start seeing benefits, then a dynamic belay has to be better!
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jt512
Sep 4, 2010, 2:38 AM
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112 wrote: And, if you have to give 30% initial slack to just start seeing benefits, then a dynamic belay has to be better! Again, a dynamic belay does not negate leaving slack. And 30% slack is no big deal. If the leader were laterally out, say, six from his pro, it would be no big deal to have as much as six feet of slack in the rope: 100%. Jay
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jt512
Sep 4, 2010, 2:44 AM
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Question for the physics people: Does fall factor matter? Jay
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curt
Sep 4, 2010, 3:51 AM
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jt512 wrote: Question for the physics people: Does fall factor matter? Jay It should. If the belayer is not anchored at the base of the roof (as in ptlong2's diagram above) and is instead belaying from 100ft farther below (for example) there is already a mechanism in the system that mimics paying out slack--i.e., greater rope stretch. Curt
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skiclimb
Sep 4, 2010, 5:35 AM
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oh oh oh .. PTFTW..my first claim:) Ok so we have a great real world question. We have quite a few seriously considered answers ie Hypothesis. Now we need experimental evidence. I actually would like to see this tested. Setting up a good fall for this seems pretty simple. But how do we get useful measurement of the result? I suppose if the differences are big enough they might be clearly visible just to the naked eye. ie massive impact vs barely bumped. beyond that testing it seems more difficult to setup. any ideas?
(This post was edited by skiclimb on Sep 4, 2010, 5:36 AM)
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jt512
Sep 4, 2010, 11:42 AM
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skiclimb wrote: oh oh oh .. PTFTW..my first claim:) Ok so we have a great real world question. We have quite a few seriously considered answers ie Hypothesis. Now we need experimental evidence. I actually would like to see this tested. Setting up a good fall for this seems pretty simple. But how do we get useful measurement of the result? I suppose if the differences are big enough they might be clearly visible just to the naked eye. ie massive impact vs barely bumped. beyond that testing it seems more difficult to setup. any ideas? To measure speed? High-speed camera? Jay
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skiclimb
Sep 4, 2010, 3:26 PM
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That could work pretty well with high shutter speeds, if framerate is a known and you have an accurate way measure distance within the the frame. That seems like a fairly simple way to get a reasonably accurate speed measurement. Scale models might make this easier to do..perhaps find some line with the proper dynamic stretch under smaller loads.. say 10 pound weight and perhaps some 3mil ..dunno exactly..test for proper stretch under static and fall situation. (might have to replace the line after each fall test as i suspect a small diameter lines dynamic properties could change dramatically after each fall.)
(This post was edited by skiclimb on Sep 4, 2010, 3:34 PM)
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jt512
Sep 4, 2010, 7:01 PM
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skiclimb wrote: That could work pretty well with high shutter speeds, if framerate is a known and you have an accurate way measure distance within the the frame. That seems like a fairly simple way to get a reasonably accurate speed measurement. I think that in practice you'd need the elapsed time, the ratio of the filming speed to the playback speed, and a background with grid lines of known size. This is a pretty cool: link.
In reply to: Scale models might make this easier to do..perhaps find some line with the proper dynamic stretch under smaller loads.. say 10 pound weight and perhaps some 3mil .. dunno exactly.. That's the problem. An assumption you make about how to scale the problem could affect the validity of the results. Jay
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skiclimb
Sep 4, 2010, 8:48 PM
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jt512 wrote: skiclimb wrote: That could work pretty well with high shutter speeds, if framerate is a known and you have an accurate way measure distance within the the frame. That seems like a fairly simple way to get a reasonably accurate speed measurement. I think that in practice you'd need the elapsed time, the ratio of the filming speed to the playback speed, and a background with grid lines of known size. This is a pretty cool: link. In reply to: Scale models might make this easier to do..perhaps find some line with the proper dynamic stretch under smaller loads.. say 10 pound weight and perhaps some 3mil .. dunno exactly.. That's the problem. An assumption you make about how to scale the problem could affect the validity of the results. Jay I agree you would have to test the stretch both dynamically and statically to see that it was the same as regular rope. Now we don't need accuracy to 50 gagillion significant digits here.. Basically we need accuracy to say at worst 3M/sec to get good useful information about what would be the safest way to belay the situation.
(This post was edited by skiclimb on Sep 4, 2010, 11:12 PM)
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gunkiemike
Sep 4, 2010, 11:04 PM
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skiclimb wrote: oh oh oh .. PTFTW..my first claim:) Ok so we have a great real world question. We have quite a few seriously considered answers ie Hypothesis. Now we need experimental evidence. I actually would like to see this tested. Setting up a good fall for this seems pretty simple. But how do we get useful measurement of the result? Wouldn't it be cool if someone could set the fall up and monitor/record rope tension at really high data rates and synch it up with a video? Oh never mind - he just left rc.com this past month.
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curt
Sep 5, 2010, 6:19 AM
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gunkiemike wrote: skiclimb wrote: oh oh oh .. PTFTW..my first claim:) Ok so we have a great real world question. We have quite a few seriously considered answers ie Hypothesis. Now we need experimental evidence. I actually would like to see this tested. Setting up a good fall for this seems pretty simple. But how do we get useful measurement of the result? Wouldn't it be cool if someone could set the fall up and monitor/record rope tension at really high data rates and synch it up with a video? Oh never mind - he just left rc.com this past month. And yet I can still hear his balls slapping against your chin from here. Curt
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blondgecko
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Sep 6, 2010, 11:16 AM
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skiclimb wrote: oh oh oh .. PTFTW..my first claim:) Ok so we have a great real world question. We have quite a few seriously considered answers ie Hypothesis. Now we need experimental evidence. I actually would like to see this tested. Setting up a good fall for this seems pretty simple. But how do we get useful measurement of the result? I suppose if the differences are big enough they might be clearly visible just to the naked eye. ie massive impact vs barely bumped. beyond that testing it seems more difficult to setup. any ideas? In the absence of high-speed cameras or load cells, there's a few more low-tech approaches that can still give you fairly consistent relative impact force results. For instance, make your "climber" a reasonably large steel ball bearing, and have it impact into a wall of clay or plasticine. Impact force can then be inferred from the depth of the dimple when it hits.
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skiclimb
Sep 6, 2010, 2:10 PM
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blondgecko wrote: skiclimb wrote: oh oh oh .. PTFTW..my first claim:) Ok so we have a great real world question. We have quite a few seriously considered answers ie Hypothesis. Now we need experimental evidence. I actually would like to see this tested. Setting up a good fall for this seems pretty simple. But how do we get useful measurement of the result? I suppose if the differences are big enough they might be clearly visible just to the naked eye. ie massive impact vs barely bumped. beyond that testing it seems more difficult to setup. any ideas? In the absence of high-speed cameras or load cells, there's a few more low-tech approaches that can still give you fairly consistent relative impact force results. For instance, make your "climber" a reasonably large steel ball bearing, and have it impact into a wall of clay or plasticine. Impact force can then be inferred from the depth of the dimple when it hits. Thanks BG. This seems very workable on a small scale. I think a scale model should be able to answer the basic and important real world question. What is the best way to belay in this clearly dangerous situation? We don't need to find out actual force of impact we just need impact ><=. The one variable to test for is amount of slack. After some thought I concluded that any line with stretch would allow us to model the situation? Such that a line (perhaps small diameter bungie) with even higher stretch qualities could give us more easily interpreted but still acurate data? (unless bounce becomes a major factor) I think more stretch could amplify the absolute difference between fall impacts without changing ><= relationship. I'm gonna go get some line, some clay and stuff today and try this out. See if I can set something up on the ceiling that I'm happy with. I'll try a few different lines with different stretch qualities to see if that changes things.
(This post was edited by skiclimb on Sep 6, 2010, 2:12 PM)
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curt
Sep 6, 2010, 5:12 PM
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blondgecko wrote: skiclimb wrote: oh oh oh .. PTFTW..my first claim:) Ok so we have a great real world question. We have quite a few seriously considered answers ie Hypothesis. Now we need experimental evidence. I actually would like to see this tested. Setting up a good fall for this seems pretty simple. But how do we get useful measurement of the result? I suppose if the differences are big enough they might be clearly visible just to the naked eye. ie massive impact vs barely bumped. beyond that testing it seems more difficult to setup. any ideas? In the absence of high-speed cameras or load cells, there's a few more low-tech approaches that can still give you fairly consistent relative impact force results. For instance, make your "climber" a reasonably large steel ball bearing, and have it impact into a wall of clay or plasticine. Impact force can then be inferred from the depth of the dimple when it hits. Actually, that's going to be a fairly difficult calculation and the relation of the result to the impact force of a falling climber may not be all that good. If you're only looking to establish whether the impact force increases or decreases with slack though, it might be OK. I would think the best test would be to use an actual test tower like those used for UIAA rope testing (as John Long did for his anchor modeling) and adapt it for this particular test. Curt
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skiclimb
Sep 6, 2010, 10:23 PM
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Of course. It is Labor day.. I hate holidays. No one that might have the bearings is open. So gonna be a few days with work and such but I will be testing this. Nope won't be able to give real world impact forces but we MAY be able to determine how much if any slack should be safest. If i can't get good results with clay or similar material. (due to attaching it vertically and consistantly) I may try carbon paper on various backings.
(This post was edited by skiclimb on Sep 6, 2010, 10:27 PM)
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jt512
Sep 6, 2010, 10:29 PM
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skiclimb wrote: If i can't get good results with clay or similar material. (due to attaching it vertically and consistantly) I may try carbon paper on various backings. Carbon paper still exists? Jay
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bill413
Sep 6, 2010, 10:30 PM
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Hmmm, several alternating layers of carbon paper & regular paper might give you a measure, by counting how deep the mark penetrates. A weight of almost any sort might be substituted for the ball bearing - perhaps a light dumbbell?
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skiclimb
Sep 6, 2010, 10:38 PM
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Need something without corners.Bearing is perfect just put it in a sandwich bag or maybe some light hankerchief fabric and tie it off. I'll do some straight drop tests from 3 different heights to see if i get good consistant distinguishable imprints with either clay or carbon paper. was thinking a neoprene backing with paper and carbon paper on top. I'll play with it in clay and carbon till i get something that gives consistent and easily distinguishable results. I've always enjoyed this type of lab-work.. whats boring and mind-numbing is once you get the method down.
(This post was edited by skiclimb on Sep 6, 2010, 10:47 PM)
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jt512
Sep 6, 2010, 10:45 PM
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bill413 wrote: A weight of almost any sort might be substituted for the ball bearing - perhaps a light dumbbell? I casually tried it with a dumbell. It was difficult to suspend the dumbell so that it struck the wall in a predictable and consistent orientation. Jay
(This post was edited by jt512 on Sep 6, 2010, 10:45 PM)
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skiclimb
Sep 6, 2010, 10:50 PM
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never completely discount the ole MII eyeball. Have you tried a dumbell pendo with and without slack of various lengths? the difference might be fairly visible or audible.
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Rudmin
Sep 6, 2010, 10:51 PM
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I've tried uploading my pendulum fall calculator somewhere new. If you really want to stop a fall, adding about a 100 metres of slack seems to give a pretty gentle catch and low pendulum speed of only 6 metres per second on the first swing. http://www.mediafire.com/?xt4dxdzkvs5tb0k Give it a try. Hopefully it is pretty self explanatory. Don't use a time step larger than 0.2 s or you will start to see some crazy resonances creep in. And note that the first set of numbers I posted were thrown off because dampening coefficient wasn't modulated with rope length, making longer ropes successively stiffer. It has since been fixed. EDITED TO ADD: So far the best course of actions seems to be to launch yourself towards whatever it is you will be pendulumming into as hard as you can when you fall. If you can manage to hit it or cross below your anchor before the rope comes under tension, you will greatly reduce your impact. You can enter an initial horizontal velocity by changing the first entry in the u column from 0 to whatever initial velocity you desire. Also, if the thing you don't want to hit is behind the anchor rather than right underneath it, you can greatly reduce the impact by pushing towards it and having about double the amount of rope out. It all depends on exactly where though.
(This post was edited by Rudmin on Sep 6, 2010, 11:05 PM)
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jt512
Sep 6, 2010, 10:55 PM
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skiclimb wrote: never completely discount the ole MII eyeball. Have you tried a dumbell pendo with and without slack of various lengths? the difference might be fairly visible or audible. Yeah, I tried. I couldn't really see or hear any difference, nor did I like what the dumb bell was doing to the wall of my garage. Jay
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blondgecko
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Sep 7, 2010, 12:42 AM
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Rudmin wrote: I've tried uploading my pendulum fall calculator somewhere new. If you really want to stop a fall, adding about a 100 metres of slack seems to give a pretty gentle catch and low pendulum speed of only 6 metres per second on the first swing. http://www.mediafire.com/?xt4dxdzkvs5tb0k Give it a try. Hopefully it is pretty self explanatory. Don't use a time step larger than 0.2 s or you will start to see some crazy resonances creep in. And note that the first set of numbers I posted were thrown off because dampening coefficient wasn't modulated with rope length, making longer ropes successively stiffer. It has since been fixed. EDITED TO ADD: So far the best course of actions seems to be to launch yourself towards whatever it is you will be pendulumming into as hard as you can when you fall. If you can manage to hit it or cross below your anchor before the rope comes under tension, you will greatly reduce your impact. You can enter an initial horizontal velocity by changing the first entry in the u column from 0 to whatever initial velocity you desire. Also, if the thing you don't want to hit is behind the anchor rather than right underneath it, you can greatly reduce the impact by pushing towards it and having about double the amount of rope out. It all depends on exactly where though. Just had a quick play around with this. First thing is that I'm pretty sure your rope stiffness is a bit high, and damping coefficient is way too low (which is why it bounces around a lot in the first few passes). Ropes tend to be pretty close to critically damped, meaning you should se very little oscillation. According to this (PDF) article - which admittedly uses a second-order model for stiffness - the damping coefficient (in your units) should be closer to 28 N/s/%. The stiffness you have of 185 N/% gives a bit over 5% stretch in the 10m fall, no slack case, which is closer to static rope - under real-world dynamic fall conditions, static ropes should stretch up to about 11%, dynamic ropes up to 40%. A value here of 60 N/% gives stretches in the 30-35% ballpark. Under these conditions, apparently anything below 2m slack makes the horizontal impact speed very slightly worse: no slack 12.13 m/s; 1m slack 12.28; 2m 12.14. I tested the initial-slack case against one instance of my scenario: no initial slack, on the rope until the climber is 10m down and 6m away from the wall, then free-fall from that point until impact. This takes the release of about 3m of slack at this point, and reduces horizontal velocity at impact to 8.9 m/s (which makes for a reduction of almost 50% in impact energy). It takes 10.3m of slack at the start to achieve the same - but there's a catch: in my scenario the vertical velocity at impact goes from zero to 15m/s (33 miles per hour), making for one hell of a scrape. So, to counteract this, I tried one further scenario: drop a bit more slack a bit earlier in the fall, but stop the period of freefall before contact with the wall, so that the rope takes most of the vertical fall energy back up. Starting again from the no-initial-slack scenario, if you initiate the period of freefall around eight vertical metres into the fall and allow 5m of extra slack, then you get a horizontal velocity at impact of ~8.4m/s and a vertical velocity of just 2m/s. So I'd say that in the ideal case the "slack during the fall" scenario works out substantially better than the "slack before the fall" in terms of amount of rope needed for the same impact force - the question is how the hell to do such a thing in the real world in a controlled fashion.
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acorneau
Sep 7, 2010, 12:46 AM
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blondgecko wrote: Rudmin wrote: I've tried uploading my pendulum fall calculator somewhere new. If you really want to stop a fall, adding about a 100 metres of slack seems to give a pretty gentle catch and low pendulum speed of only 6 metres per second on the first swing. http://www.mediafire.com/?xt4dxdzkvs5tb0k Give it a try. Hopefully it is pretty self explanatory. Don't use a time step larger than 0.2 s or you will start to see some crazy resonances creep in. And note that the first set of numbers I posted were thrown off because dampening coefficient wasn't modulated with rope length, making longer ropes successively stiffer. It has since been fixed. EDITED TO ADD: So far the best course of actions seems to be to launch yourself towards whatever it is you will be pendulumming into as hard as you can when you fall. If you can manage to hit it or cross below your anchor before the rope comes under tension, you will greatly reduce your impact. You can enter an initial horizontal velocity by changing the first entry in the u column from 0 to whatever initial velocity you desire. Also, if the thing you don't want to hit is behind the anchor rather than right underneath it, you can greatly reduce the impact by pushing towards it and having about double the amount of rope out. It all depends on exactly where though. Just had a quick play around with this. First thing is that I'm pretty sure your rope stiffness is a bit high, and damping coefficient is way too low (which is why it bounces around a lot in the first few passes). Ropes tend to be pretty close to critically damped, meaning you should se very little oscillation. According to this (PDF) article - which admittedly uses a second-order model for stiffness - the damping coefficient (in your units) should be closer to 28 N/s/%. The stiffness you have of 185 N/% gives a bit over 5% stretch in the 10m fall, no slack case, which is closer to static rope - under real-world dynamic fall conditions, static ropes should stretch up to about 11%, dynamic ropes up to 40%. A value here of 60 N/% gives stretches in the 30-35% ballpark. Under these conditions, apparently anything below 2m slack makes the horizontal impact speed very slightly worse: no slack 12.13 m/s; 1m slack 12.28; 2m 12.14. I tested the initial-slack case against one instance of my scenario: no initial slack, on the rope until the climber is 10m down and 6m away from the wall, then free-fall from that point until impact. This takes the release of about 3m of slack at this point, and reduces horizontal velocity at impact to 8.9 m/s (which makes for a reduction of almost 50% in impact energy). It takes 10.3m of slack at the start to achieve the same - but there's a catch: in my scenario the vertical velocity at impact goes from zero to 15m/s (33 miles per hour), making for one hell of a scrape. So, to counteract this, I tried one further scenario: drop a bit more slack a bit earlier in the fall, but stop the period of freefall before contact with the wall, so that the rope takes most of the vertical fall energy back up. Starting again from the no-initial-slack scenario, if you initiate the period of freefall around eight vertical metres into the fall and allow 5m of extra slack, then you get a horizontal velocity at impact of ~8.4m/s and a vertical velocity of just 2m/s. So I'd say that in the ideal case the "slack during the fall" scenario works out substantially better than the "slack before the fall" in terms of amount of rope needed for the same impact force - the question is how the hell to do such a thing in the real world in a controlled fashion. WHY HASN'T THIS BEEN MOVED TO THE LAB?!?!?!?!?!?!?
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blondgecko
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Sep 7, 2010, 12:48 AM
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acorneau wrote: WHY HASN'T THIS BEEN MOVED TO THE LAB?!?!?!?!?!?!? A good point, actually. Done.
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blondgecko
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Sep 7, 2010, 1:23 AM
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blondgecko wrote: Rudmin wrote: I've tried uploading my pendulum fall calculator somewhere new. If you really want to stop a fall, adding about a 100 metres of slack seems to give a pretty gentle catch and low pendulum speed of only 6 metres per second on the first swing. http://www.mediafire.com/?xt4dxdzkvs5tb0k Give it a try. Hopefully it is pretty self explanatory. Don't use a time step larger than 0.2 s or you will start to see some crazy resonances creep in. And note that the first set of numbers I posted were thrown off because dampening coefficient wasn't modulated with rope length, making longer ropes successively stiffer. It has since been fixed. EDITED TO ADD: So far the best course of actions seems to be to launch yourself towards whatever it is you will be pendulumming into as hard as you can when you fall. If you can manage to hit it or cross below your anchor before the rope comes under tension, you will greatly reduce your impact. You can enter an initial horizontal velocity by changing the first entry in the u column from 0 to whatever initial velocity you desire. Also, if the thing you don't want to hit is behind the anchor rather than right underneath it, you can greatly reduce the impact by pushing towards it and having about double the amount of rope out. It all depends on exactly where though. Just had a quick play around with this. First thing is that I'm pretty sure your rope stiffness is a bit high, and damping coefficient is way too low (which is why it bounces around a lot in the first few passes). Ropes tend to be pretty close to critically damped, meaning you should se very little oscillation. According to this (PDF) article - which admittedly uses a second-order model for stiffness - the damping coefficient (in your units) should be closer to 28 N/s/%. The stiffness you have of 185 N/% gives a bit over 5% stretch in the 10m fall, no slack case, which is closer to static rope - under real-world dynamic fall conditions, static ropes should stretch up to about 11%, dynamic ropes up to 40%. A value here of 60 N/% gives stretches in the 30-35% ballpark. Under these conditions, apparently anything below 2m slack makes the horizontal impact speed very slightly worse: no slack 12.13 m/s; 1m slack 12.28; 2m 12.14. I tested the initial-slack case against one instance of my scenario: no initial slack, on the rope until the climber is 10m down and 6m away from the wall, then free-fall from that point until impact. This takes the release of about 3m of slack at this point, and reduces horizontal velocity at impact to 8.9 m/s (which makes for a reduction of almost 50% in impact energy). It takes 10.3m of slack at the start to achieve the same - but there's a catch: in my scenario the vertical velocity at impact goes from zero to 15m/s (33 miles per hour), making for one hell of a scrape. So, to counteract this, I tried one further scenario: drop a bit more slack a bit earlier in the fall, but stop the period of freefall before contact with the wall, so that the rope takes most of the vertical fall energy back up. Starting again from the no-initial-slack scenario, if you initiate the period of freefall around eight vertical metres into the fall and allow 5m of extra slack, then you get a horizontal velocity at impact of ~8.4m/s and a vertical velocity of just 2m/s. So I'd say that in the ideal case the "slack during the fall" scenario works out substantially better than the "slack before the fall" in terms of amount of rope needed for the same impact force - the question is how the hell to do such a thing in the real world in a controlled fashion. Here's the graphical x-y profiles of the four scenarios: no slack, 10m slack at the start of the fall, 5m slack in the middle of the fall, and 3m slack right at the end: The first three scenarios really show what all this is about: postponing the vertical deceleration for as long as possible while reducing the angle at which the rope eventually catches the climber as much as possible, to maximise the vertical component of the rope tension and minimise the horizontal component.
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hafilax
Sep 7, 2010, 4:53 PM
Post #98 of 100
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Registered: Dec 12, 2007
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blondgecko wrote: blondgecko wrote: Rudmin wrote: I've tried uploading my pendulum fall calculator somewhere new. If you really want to stop a fall, adding about a 100 metres of slack seems to give a pretty gentle catch and low pendulum speed of only 6 metres per second on the first swing. http://www.mediafire.com/?xt4dxdzkvs5tb0k Give it a try. Hopefully it is pretty self explanatory. Don't use a time step larger than 0.2 s or you will start to see some crazy resonances creep in. And note that the first set of numbers I posted were thrown off because dampening coefficient wasn't modulated with rope length, making longer ropes successively stiffer. It has since been fixed. EDITED TO ADD: So far the best course of actions seems to be to launch yourself towards whatever it is you will be pendulumming into as hard as you can when you fall. If you can manage to hit it or cross below your anchor before the rope comes under tension, you will greatly reduce your impact. You can enter an initial horizontal velocity by changing the first entry in the u column from 0 to whatever initial velocity you desire. Also, if the thing you don't want to hit is behind the anchor rather than right underneath it, you can greatly reduce the impact by pushing towards it and having about double the amount of rope out. It all depends on exactly where though. Just had a quick play around with this. First thing is that I'm pretty sure your rope stiffness is a bit high, and damping coefficient is way too low (which is why it bounces around a lot in the first few passes). Ropes tend to be pretty close to critically damped, meaning you should se very little oscillation. According to this (PDF) article - which admittedly uses a second-order model for stiffness - the damping coefficient (in your units) should be closer to 28 N/s/%. The stiffness you have of 185 N/% gives a bit over 5% stretch in the 10m fall, no slack case, which is closer to static rope - under real-world dynamic fall conditions, static ropes should stretch up to about 11%, dynamic ropes up to 40%. A value here of 60 N/% gives stretches in the 30-35% ballpark. Under these conditions, apparently anything below 2m slack makes the horizontal impact speed very slightly worse: no slack 12.13 m/s; 1m slack 12.28; 2m 12.14. I tested the initial-slack case against one instance of my scenario: no initial slack, on the rope until the climber is 10m down and 6m away from the wall, then free-fall from that point until impact. This takes the release of about 3m of slack at this point, and reduces horizontal velocity at impact to 8.9 m/s (which makes for a reduction of almost 50% in impact energy). It takes 10.3m of slack at the start to achieve the same - but there's a catch: in my scenario the vertical velocity at impact goes from zero to 15m/s (33 miles per hour), making for one hell of a scrape. So, to counteract this, I tried one further scenario: drop a bit more slack a bit earlier in the fall, but stop the period of freefall before contact with the wall, so that the rope takes most of the vertical fall energy back up. Starting again from the no-initial-slack scenario, if you initiate the period of freefall around eight vertical metres into the fall and allow 5m of extra slack, then you get a horizontal velocity at impact of ~8.4m/s and a vertical velocity of just 2m/s. So I'd say that in the ideal case the "slack during the fall" scenario works out substantially better than the "slack before the fall" in terms of amount of rope needed for the same impact force - the question is how the hell to do such a thing in the real world in a controlled fashion. Here's the graphical x-y profiles of the four scenarios: no slack, 10m slack at the start of the fall, 5m slack in the middle of the fall, and 3m slack right at the end: The first three scenarios really show what all this is about: postponing the vertical deceleration for as long as possible while reducing the angle at which the rope eventually catches the climber as much as possible, to maximise the vertical component of the rope tension and minimise the horizontal component. Is it possible to put equally spaced time points on those lines to get a feel for the velocity?
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blondgecko
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Sep 8, 2010, 12:50 AM
Post #99 of 100
(6671 views)
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Registered: Jul 2, 2004
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hafilax wrote: blondgecko wrote: blondgecko wrote: Rudmin wrote: I've tried uploading my pendulum fall calculator somewhere new. If you really want to stop a fall, adding about a 100 metres of slack seems to give a pretty gentle catch and low pendulum speed of only 6 metres per second on the first swing. http://www.mediafire.com/?xt4dxdzkvs5tb0k Give it a try. Hopefully it is pretty self explanatory. Don't use a time step larger than 0.2 s or you will start to see some crazy resonances creep in. And note that the first set of numbers I posted were thrown off because dampening coefficient wasn't modulated with rope length, making longer ropes successively stiffer. It has since been fixed. EDITED TO ADD: So far the best course of actions seems to be to launch yourself towards whatever it is you will be pendulumming into as hard as you can when you fall. If you can manage to hit it or cross below your anchor before the rope comes under tension, you will greatly reduce your impact. You can enter an initial horizontal velocity by changing the first entry in the u column from 0 to whatever initial velocity you desire. Also, if the thing you don't want to hit is behind the anchor rather than right underneath it, you can greatly reduce the impact by pushing towards it and having about double the amount of rope out. It all depends on exactly where though. Just had a quick play around with this. First thing is that I'm pretty sure your rope stiffness is a bit high, and damping coefficient is way too low (which is why it bounces around a lot in the first few passes). Ropes tend to be pretty close to critically damped, meaning you should se very little oscillation. According to this (PDF) article - which admittedly uses a second-order model for stiffness - the damping coefficient (in your units) should be closer to 28 N/s/%. The stiffness you have of 185 N/% gives a bit over 5% stretch in the 10m fall, no slack case, which is closer to static rope - under real-world dynamic fall conditions, static ropes should stretch up to about 11%, dynamic ropes up to 40%. A value here of 60 N/% gives stretches in the 30-35% ballpark. Under these conditions, apparently anything below 2m slack makes the horizontal impact speed very slightly worse: no slack 12.13 m/s; 1m slack 12.28; 2m 12.14. I tested the initial-slack case against one instance of my scenario: no initial slack, on the rope until the climber is 10m down and 6m away from the wall, then free-fall from that point until impact. This takes the release of about 3m of slack at this point, and reduces horizontal velocity at impact to 8.9 m/s (which makes for a reduction of almost 50% in impact energy). It takes 10.3m of slack at the start to achieve the same - but there's a catch: in my scenario the vertical velocity at impact goes from zero to 15m/s (33 miles per hour), making for one hell of a scrape. So, to counteract this, I tried one further scenario: drop a bit more slack a bit earlier in the fall, but stop the period of freefall before contact with the wall, so that the rope takes most of the vertical fall energy back up. Starting again from the no-initial-slack scenario, if you initiate the period of freefall around eight vertical metres into the fall and allow 5m of extra slack, then you get a horizontal velocity at impact of ~8.4m/s and a vertical velocity of just 2m/s. So I'd say that in the ideal case the "slack during the fall" scenario works out substantially better than the "slack before the fall" in terms of amount of rope needed for the same impact force - the question is how the hell to do such a thing in the real world in a controlled fashion. Here's the graphical x-y profiles of the four scenarios: no slack, 10m slack at the start of the fall, 5m slack in the middle of the fall, and 3m slack right at the end: The first three scenarios really show what all this is about: postponing the vertical deceleration for as long as possible while reducing the angle at which the rope eventually catches the climber as much as possible, to maximise the vertical component of the rope tension and minimise the horizontal component. Is it possible to put equally spaced time points on those lines to get a feel for the velocity? That's a great idea - unfortunately I had to get some real work done, and closed the spreadsheet without saving it. Here's an exercise if anyone wants to play around with it, though: The scenario I've been working with so far is pretty much the worst case: a 90-degree roof, with absolutely no pro between climber and belayer. What about the slightly more realistic case where there's a piece or two in - say the climber's 10m out from a piece placed 3m from the wall? In that case my suggestion is that the best option is to drop them a few metres so that the rope pulls taught just as they pass under the gear. This will maximise tension in the rope when it's actually acting to pull them away from the impact.
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112
Sep 10, 2010, 3:11 PM
Post #100 of 100
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Registered: May 15, 2004
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jt512 wrote: 112 wrote: And, if you have to give 30% initial slack to just start seeing benefits, then a dynamic belay has to be better! Again, a dynamic belay does not negate leaving slack. And 30% slack is no big deal. If the leader were laterally out, say, six from his pro, it would be no big deal to have as much as six feet of slack in the rope: 100%. Jay I was looking at it from a perspective of per length of extension and assumed a dynamic belay using 20-30% extension yielded some reduction in velocity (may be a bad assumption) were the initial slack didn't. I believe 0 initial slack may not be easily realizable and therefore some initial slack should probably be included in the analysis. Including the affect of a dynamic belay is giving me trouble...
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