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ben123324
Nov 21, 2012, 12:31 AM
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Registered: Oct 9, 2012
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hey,
after seeing somebody at the crag trying to set a top rope anchor with two points at a 120-160 degree angle from each other, i decided it was about time to show those of us exactly why not to do that. this also explains why slack-lines have such huge constant forces on the points and even bigger ones while you jump.
to put it simply, when you have a rope in a straight line hanging between two points, any forces exerted perpendicularly to that rope on the rope will be magnified in the horizontal direction. you pull the center of a 10m long rope with 1 Newton of force, and the force exerted in the tension on both anchor points will be massively larger than 1N.
i've gone ahead and derived a simple equation that can be applied by any rock climber or slack liner:
(perpendicular force)/(2*tan(theta))
so if you're on a slack line 10 meters long, and the point where you stand sags .1 meter, then the angle of the rope below the horizontal is ~1.15 degrees.
say that i weigh 60kg(63.5 irl) and gravitational acceleration is rounded to 10m/s^2.
now if i stand at the center of the line, i put 600N of force perpendicularity to the webbing.
600N/(2*tan(1.15)) = 14944N
that's 15kN!!! and that's just me standing on a decently tension-ed line! now what if i jump and put a peak of 1200N on the line. assuming the line doesn't stretch to more than 1.15 degrees again, my tension is now 30kN, which passes the ratings on most standard gear. true that the line will obviously stretch more, but that's a huge force on your gear...
it goes to show that when slack-lining, don't use your good biners and then go climbing on them. don't be setting tr anchors 100 degrees from each other. think! its easy enough to guestimate the force you exert on your gear just by knowing simple trig and physics. so next time you go climbing/lining, your mass *10 over 2tan(theta) just may save your life!
-ben
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moose_droppings
Nov 21, 2012, 1:02 AM
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ben123324 wrote: hey, after seeing somebody at the crag trying to set a top rope anchor with two points at a 120-160 degree angle from each other, i decided it was about time to show those of us exactly why not to do that. this also explains why slack-lines have such huge constant forces on the points and even bigger ones while you jump. to put it simply, when you have a rope in a straight line hanging between two points, any forces exerted perpendicularly to that rope on the rope will be magnified in the horizontal direction. you pull the center of a 10m long rope with 1 Newton of force, and the force exerted in the tension on both anchor points will be massively larger than 1N. i've gone ahead and derived a simple equation that can be applied by any rock climber or slack liner: (perpendicular force)/(2*tan(theta)) so if you're on a slack line 10 meters long, and the point where you stand sags .1 meter, then the angle of the rope below the horizontal is ~1.15 degrees. say that i weigh 60kg(63.5 irl) and gravitational acceleration is rounded to 10m/s^2. now if i stand at the center of the line, i put 600N of force perpendicularity to the webbing. 600N/(2*tan(1.15)) = 14944N that's 15kN!!! and that's just me standing on a decently tension-ed line! now what if i jump and put a peak of 1200N on the line. assuming the line doesn't stretch to more than 1.15 degrees again, my tension is now 30kN, which passes the ratings on most standard gear. true that the line will obviously stretch more, but that's a huge force on your gear... it goes to show that when slack-lining, don't use your good biners and then go climbing on them. don't be setting tr anchors 100 degrees from each other. think! its easy enough to guestimate the force you exert on your gear just by knowing simple trig and physics. so next time you go climbing/lining, your mass *10 over 2tan(theta) just may save your life! -ben
I'm quite slow and require a pic (please) of what your getting at.
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ben123324
Nov 21, 2012, 1:23 AM
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here you go :)
misspellings, woohooo!
(This post was edited by ben123324 on Nov 21, 2012, 1:25 AM)
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moose_droppings
Nov 21, 2012, 1:44 AM
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So that bit of a deflection in the rope multiplies the force on the anchors that much?
I didn't think that small of angle change increased it as much as you have it penciled out to be. It's still much less then a 90 (more like a 30) degree angle change on both anchors.
Also, isn't the increase your saying it has split betweeen the two anchor points?
Thanks for the pic. I thought that was what you were saying, but like I said, I'm slow and still don't see as much of a dramatic increase in forces.
spelling edit
(This post was edited by moose_droppings on Nov 21, 2012, 1:48 AM)
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acorneau
Nov 21, 2012, 2:09 AM
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No, it's not the change of the angle, it's the angle at any given time.
An unweighted slack-line has an "angle" of 180 degrees (left and right) so any force in the center will result in huge forces at each anchor.
Think of a two-point anchor with a weight in the middle. At an 80 degree angle each anchor point sees ~70% of the load in the middle. At 120 degrees each anchor point sees ~100% of the load in the middle. For 180 degrees it's theoretically infinite.
Edit to clarify.
(This post was edited by acorneau on Nov 21, 2012, 2:25 AM)
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USnavy
Nov 21, 2012, 5:51 AM
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ben123324 wrote: hey, after seeing somebody at the crag trying to set a top rope anchor with two points at a 120-160 degree angle from each other, i decided it was about time to show those of us exactly why not to do that. this also explains why slack-lines have such huge constant forces on the points and even bigger ones while you jump. to put it simply, when you have a rope in a straight line hanging between two points, any forces exerted perpendicularly to that rope on the rope will be magnified in the horizontal direction. you pull the center of a 10m long rope with 1 Newton of force, and the force exerted in the tension on both anchor points will be massively larger than 1N. i've gone ahead and derived a simple equation that can be applied by any rock climber or slack liner: (perpendicular force)/(2*tan(theta)) so if you're on a slack line 10 meters long, and the point where you stand sags .1 meter, then the angle of the rope below the horizontal is ~1.15 degrees. say that i weigh 60kg(63.5 irl) and gravitational acceleration is rounded to 10m/s^2. now if i stand at the center of the line, i put 600N of force perpendicularity to the webbing. 600N/(2*tan(1.15)) = 14944N that's 15kN!!! and that's just me standing on a decently tension-ed line! now what if i jump and put a peak of 1200N on the line. assuming the line doesn't stretch to more than 1.15 degrees again, my tension is now 30kN, which passes the ratings on most standard gear. true that the line will obviously stretch more, but that's a huge force on your gear... it goes to show that when slack-lining, don't use your good biners and then go climbing on them. don't be setting tr anchors 100 degrees from each other. think! its easy enough to guestimate the force you exert on your gear just by knowing simple trig and physics. so next time you go climbing/lining, your mass *10 over 2tan(theta) just may save your life! -ben
http://www.slacklineexpress.com/force.htm
Also, your example is completely unrealistic. A 10m line with less than four inches of sag in the middle?! Clearly you dont know much about slacklining. The amount of tension required to get that little sag would likely be in excess of the failure strength of the webbing. You would have to tension the line with a truck!
Fortunately I have actually done quite a bit of force testing on slacklines so I can tell you the actual forces subjected to a slackline. A primitive line that is 10m long is generally tensioned to somewhere between 350 and 500lbf. When standing in the middle, you can expect around 600 to 900lbf, maybe a tad more if you are fat. If you jump around you might flirt with 1,000lbf for a few mS if you had it tighter than normal. But really, a 1" nylon slackline that long probably wont get you above 4kN unless you set it as a trickline.
Also, your assumption about the angle not changing on a jump because the webbing does not stretch is completely false. Of course the webbing is going to stretch when you jump on it! Do ropes stretch more on a lead fall than on a TR fall? Yea, and slacklines stretch more on a jump than when standing static. That is how nylon and polyester works, the greater the load the greater the elongation, the greater the elongation the shallower the angle.
This graph shows a test where I stood on the line on three different points. The first peak represents standing 20% downline of the anchor from the side without the load cell. The middle peak represents standing in the middle of the line. The last peak represents standing 20% downline of the anchor from the side with the loadcell.
(This post was edited by USnavy on Nov 21, 2012, 7:17 AM)
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ninepointeight
Nov 21, 2012, 1:56 PM
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Registered: May 14, 2012
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Regurgitating the formula for calculating the force doesn't explain 'why' it happens at all. You're just restating an observation.
If you walk up too a stranger and start speaking tangents at them, they are going to tell you to fuck off. The 'why' is much simpler. When there is small angle between the anchors, the anchors are exerting force in the same direction (almost). When the angle is great, they exert more and more of that force on the opposite anchor.
(This post was edited by ninepointeight on Nov 21, 2012, 1:57 PM)
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bearbreeder
Nov 21, 2012, 7:28 PM
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Registered: Feb 2, 2009
Posts: 1960
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are ya another toppu roperu tofu guy at the crag screaming about other peoples top rop anchors ????
they seem to pop up all the time on this site 
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moose_droppings
Nov 21, 2012, 11:35 PM
Post #9 of 9
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Thanks acorneau , that's a great explanation.
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