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Re: [curt] Pendulum fall speed:
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Rudmin
Sep 2, 2010, 7:08 PM
Views: 8169
Registered: Mar 29, 2009
Posts: 606
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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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Edit Log:
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Post edited by Rudmin
() on Sep 2, 2010, 7:33 PM
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