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Wrathchild
Big Wall climber
Lee NH
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Aug 28, 2005 - 04:58pm PT
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Falling a full rope legnth, onto the belay, and you grabbed a big rock off the ledge on the way by...
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deuce4
Big Wall climber
the Southwest
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Aug 28, 2005 - 09:03pm PT
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Apologies in advance for bringing this up again, but it occured to me that what Karl was asking for was something like the following analysis. I was getting too wrapped up in the energy analysis.
Here's the simple force analysis of what's happening with a adjustable daisy based on Fish's test:
Neglecting second and higher derivatives related to the forces involved (acceleration and changes in acceleration).
Fish could test this further by putting the load cell in line with the climber or the pulling side.
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Wrathchild
Big Wall climber
Lee NH
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Aug 28, 2005 - 09:06pm PT
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I think I did the PO with that guy in Pic #2.
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rgold
Trad climber
Poughkeepsie, NY
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Aug 28, 2005 - 10:49pm PT
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I don't think there is much I can add, but I can say it in a somewhat different way---if anyone is interested.
Let's forget about the precise definition of mechanical advantage. That may be fun to argue about but isn't the real point.
For clarity, consider how much force the climber has to exert to hold herself in place. If she wants to move upwards, she will have to accelerate, and this will require a force higher than the holding force. How much higher depends on how fast she wants to get moving, and isn't a property of the adjustable daisy system. Once moving, the force exerted can, in principle, drop back to the holding force level. If you're winching yourself up on an A5 placement, you'll be keenly interested in keeping the peak force very close to your holding force.
Since it has been much discussed, consider the frictionless case. The climber is, at any moment, supported by two strands. (The fact that one strand goes to the climber's harness and the other to the climber's arm is irrelevant.) The tensions in each of these strands are equal because of the assumption of no friction at the pulley point. The sum of these tensions has to equal the climber's weight, so the tension in each strand must be half the climber's weight. This means that the force exerted by the climber's arm is half the climber's weight, as many have already said.
Third, consider the friction case. The situation is complicated by the nature of the buckle. There is a cam that increases the friction significantly. When the climber pulls on the free end, the cam has to be unloaded and then the strap slides over the buckle surface. I suspect it takes more force to retract the cam than it does to hoist the climber once the cam is retracted, but the weight test doesn't allow us to make that distinction. In any case, it is all we have.
In the weight test, it takes 250 lbf to begin moving 100 lbf. This means, glossing over the mechanism by which it is created, that there is a frictional force of about 150 lbf and so an effective coefficient of friction of 150/250=0.6, once the weight starts moving. (I think a smaller value for coefficient of friction might be more appropriate here, because the 250 lbf value is what is required to "break" the cam's locking action.)
Let c denote the coefficient of friction, whatever it is, and consider the climber holding her weight W, having retracted the cam. Suppose she has to exert a force F to do this. Then the buckle mechanism provides a friction force of cF, which means the tension on the side of the daisy attached to her harness must be F-cF or (1-c)F in order for the forces at the buckle to be in equilibrium. Adding the tensions on both sides and equating the sum to the climber's weight gives (2-c)F = W or
F = W/(2-c).
Note that if c=0, we are back in the frictionless case and get the same result, F=W/2, mentioned above. If we use the value c=0.6 estimated from the weight test, we get approximately
F = 0.71 W,
in other words the climber has to pull with a bit less than 3/4 of their body weight, not the 1/2 bodyweight you'd expect from the frictionless case.
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deuce4
Big Wall climber
the Southwest
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Aug 29, 2005 - 10:39pm PT
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Thanks Rich-
Are you a mathematician? Nice analysis. I needed the sketches to figure out what you did by logical progression.
I think the problem you mention in the beginning is significant, that the "jerk" factor in initiating the adjustable daisy will in fact increase the load on the piece considerably more than gingerly stepping up and clipping your static daisy.
cheers
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Karl Baba
Trad climber
Yosemite, Ca
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Aug 29, 2005 - 10:47pm PT
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That's assuming that the climber hauls himself up with a jerk. Climbers getting on dicey stuff don't jerk. That folks are hauling themselve up reguarly with adjustable daisies is a myth.
Here's another example of what they're good for. You are rapping the east ledges with your pig attached to your rap device. When you get to the anchor, you clip in with the adjustable. When it's time to do the next rap, you snug up your device and voila, you are able to release the daisy under a load and go on rappel without bag hoisting.
How about a little poll. How many folks have done at least one whole wall with Yates adjustable daisies and then gone back to static? I don't trust metolius and don't know Fish's.
Peace
karl
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yo
climber
NOT Fresno
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Aug 30, 2005 - 12:17am PT
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"Climbers getting on dicey stuff don't jerk."
Chris! Baba's in the gutter!
The key to adjustable efficiency, which apparently escaped all the eggheads, but not KB, is the wild gyrations (as in wg=3x). Drive with the legs, hip thrust (gently), flick of the wrist, and you're up the steepest shizz like a ring-tailed lemur.
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Watusi
Social climber
Joshua Tree, CA
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Aug 30, 2005 - 12:25am PT
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Wazzat Holmes?
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'Pass the Pitons' Pete
Big Wall climber
like Oakville, Ontario, Canada, eh?
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Aug 30, 2005 - 01:31am PT
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Duecey!
Look at your pulley in #3. Ya can't have 143 pounds on one side and 57 on the other! The forces have to be equal on both sides!
Sheesh...
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WBraun
climber
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Aug 30, 2005 - 01:34am PT
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Look again Pete it's not what you're seeing.
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deuce4
Big Wall climber
the Southwest
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Aug 30, 2005 - 09:48am PT
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Pete--it's not a pulley. It's a.....
Adjustable Daisy!
The free body diagram is showing the forces the moment movement begins.
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Prod
Trad climber
A place w/o Avitars apparently
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I especially like the part where Ed gets a little antsy with Karl and calls himself an over eduicated idiot.
Talk about analog vs digital personalities!
Prod.
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John Mac
Trad climber
Littleton, CO
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Karl,
In regards to your poll ... I've gone full circult from standard to adjustable and no back to standard. I'm a lot smoother and faster using standard daises!
Cheers
John
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