OK you physics wizards...

[plexus]

Alpinist 14 was the catalyst for this mode of question.

 

Here's the scenario:

 

I've just finished the xx pitch of a climb and set up a hanging belay with three downward pulls (two nuts and a cam) and one upward pull (my favorite #10 nut). Partner comes up, we rack out and up she races. She gets in three pieces and takes a fall. Lets say there is 25 feet of rope up to the last piece and she falls 12 feet.

 

How much force is put onto that upward piece? To complete the scenario, the three downward are tied off on a cordellete and the upward piece is clipped in seperately to the belay. All of her pieces hold.

 

I was just thinking back to some hanging belays in the past and was wondering, should I have had more then one upward piece since if the person falls the initial pull is going to be up.

 

Blind me with science.

[foraker]

Need to know her mass.

[Gary_Yngve]

Physics really doesn't help. Yes, you can calculate the fall factor (which by the way is the distance fallen (12) over the total rope out (which goes beyond the last piece, so should be 25+6=31). That's the worst-case scenario, and your piece should be plenty strong enough.

 

But the belay's dynamic, the there's friction through the biners, and your partner likely weighs less than what the standard tests use (75 kg, I think). So the forces are much less.

 

The bigger issues would be rock quality and angle of pull.

[Gary_Yngve]

Need to know her mass.

 

And her age too.

[Alpinfox]

 

I haven't done any calculations, but I doubt the force of a factor ~0.4 fall (after friction on top biner is taken into account) will exceed the weight of the hanging belayer, therefore the upward-oriented piece will see 0kN.

[foraker]

Physics really doesn't help.

 

This reminds me of two almost direct quotes from professors that I heard in college, within the same week:

 

1) Physics prof: This is the chemists do it, but it's just not right.

2) Math prof: This is the way the physicists do it, but it's just not right.

 

Talk about hubris.

 

You only need to know her age if you are worried about Cf, the coefficient of skin friction.

[Toast]

Need to know her mass.

 

I want to see her ass

[Figger_Eight]

Need to know her mass.

 

I want to see her ass

 

I like fishing for bass.

[scrambled_legs]

The biner friction where the rope reverses direction, will take a lot of the force out of the fall. Combine that with the inertia of the still belayer and the rope stretch and it'll take a lot to pull someone off the ground let alone pop a nut. how many times have you become airborne catching a fall without jumping? If you and your partner have a similar weight, I wouldn't be too concerned.

[John Frieh]

I was just thinking back to some hanging belays in the past and was wondering, should I have had more then one upward piece since if the person falls the initial pull is going to be up.

 

Blind me with science.

 

I would think that unless the leader weighs a ton they are not going to generate enough force to pull you the belayer up so high that you put force on the the directional piece... unless of course you placed it so that the sling attaching you to it was already super tight (no slack).

 

Even then it is almost physically impossible to generate enough force for the directional piece to fail... the rope, the pieces and slings in the system, the rope slippage through your device (no device stops the rope immediatly)... all absorb some of the force generated in the fall so that the forces put on that piece are fairly small... if anything you need to worry about the piece failing from shitty rock/shitty placement... not the cable/whatever it is failing... make sense?

[ken4ord]

Need to know her ass.

 

And her age too.

 

Name and phone number might help too.

[crackers]

I've been looking at a some studies done over in Italy in the last year or so that present some interesting perspectives on this. I'll see if i can find them when I get home.

 

Basically, it appears that the standard idea of how dynamic forces are generated in a climbing system is not too good.

 

Have you seen the 14 bazillion pieces of gear in 21 feet paper? As i recall, that paper basically posits that you need a piece of gear every half: ie: place gear at 1', 3', 6', 12',24'. But that's insane at first glance. Then again, the same paper says that if you do that you can run it out the last 60' of a 200' pitch.

 

The italians have been working on the effects of friction on the system through both rock rubbing and through inefficient and efficient rope systems. Their work seems more grounded in reality than the other and they've been doing some interesting empirical tests with load meters and different length slings.

 

of course, ymmv, and she gathers herself after falling. She leads the pitch and you guys get down okay after that. That's when the problems start. Taking the advice of cc.com, you plant one on her before you remember she plays winger for wazzu's rugby team. She slaps you down and then reports you to your fiance.

 

I wish i had my bookmarks...argh.

[catbirdseat]

It is not insane at first glance. If you want to minimize fall factor you really do have to sew up the early part of your pitch. Run it out all you want after you get some altitude. The main reason we are taught to build a redundant, bomber anchor is because for practical reasons we don't generally put enough protection early in the pitch and we want to guard against the possibility of ripping out all gear and sustaining the dread fall factor 2 fall onto the belay.

[selkirk]

Even crappy gear that pulls out above the belay absorbs energy and will prevent a true factor 2. Just thing of those initial nuts and little cams like screamers! Sacrificial energy absorbition!

[Gary_Yngve]

Yes, if you want to minimize fall factor, you'd theoretically have a Xeno's paradox going right down to the belay. But the theory fails because there are all sorts of things that absorb a constant amount of energy that is significant when compared to the total energy in a short fall, but insignificant in a long fall. Such absorbers would include the body, the harness, and the tie-in knot.

[DirtyHarry]

I would think that unless the leader weighs a ton they are not going to generate enough force to pull you the belayer up so high that you put force on the the directional piece...

 

Obviously. With rope stretch and shit, there won't be much upward pull at all.

[scrambled_legs]

But the theory fails because there are all sorts of things that absorb a constant amount of energy that is significant when compared to the total energy in a short fall, but insignificant in a long fall. Such absorbers would include the body, the harness, and the tie-in knot.

Not true if I'm understanding what you're saying. If you think that a knot, harness and body will recieve the same amount of force regardless of where you fall from, you're incorrect. The rope stretch acts in the same way on that end as it does on the individual pieces. The further you fall with the less rope out, the higher the impact forces will be on every single point and the shorter that duration will be. If you take a short 5 meter factor two fall, you'll receive high forces on the belay, belay device, rope, knot, harness and body, but it'll be a sharp quick fall. If you have 30m of rope out and then take the same 5 meter fall, you'll receive a long soft fall and both the piece that you fell on the, rope, the knot, the harness and the body, will all receive low impact forces but for a longer duration.

[sobo]

Need to know her mass.

 

I want to see her ass

 

Here ya go, Toast...

 

[Gary_Yngve]

But the theory fails because there are all sorts of things that absorb a constant amount of energy that is significant when compared to the total energy in a short fall, but insignificant in a long fall. Such absorbers would include the body, the harness, and the tie-in knot.

Not true if I'm understanding what you're saying. If you think that a knot, harness and body will recieve the same amount of force regardless of where you fall from, you're incorrect. The rope stretch acts in the same way on that end as it does on the individual pieces. The further you fall with the less rope out, the higher the impact forces will be on every single point and the shorter that duration will be. If you take a short 5 meter factor two fall, you'll receive high forces on the belay, belay device, rope, knot, harness and body, but it'll be a sharp quick fall. If you have 30m of rope out and then take the same 5 meter fall, you'll receive a long soft fall and both the piece that you fell on the, rope, the knot, the harness and the body, will all receive low impact forces but for a longer duration.

[Drederek]

The biner friction where the rope reverses direction, will take a lot of the force out of the fall. Combine that with the inertia of the still belayer and the rope stretch and it'll take a lot to pull someone off the ground let alone pop a nut. how many times have you become airborne catching a fall without jumping? If you and your partner have a similar weight, I wouldn't be too concerned.

Well at some point the distance fallen and the speed generated will start putting more force on the belayer - I've caught a 25+ footer hanging from 2 bolts from 2' slings with about 80' of 11 mm rope out and been pulled up to the limit of the slings, somewhere between 3 and 4 feet. I outweigh the falling climber by about 10%. Hanging there seemed to make a difference (unscientifically) to me in that the initial force seemed to be greater.

[ZimZam]

Need to know her mass.

 

I want to see her ass

 

Here ya go, Toast...

 

 

Baby's got back. I'm gonna go smoke some grass.

[Buckaroo]

I think most of the time the upward pull piece is just to hold the downward pieces from being pulled out.

 

An easier/quicker belay might be one nut and two cams, with the cams more resistant to pull out from any direction.

 

I weigh 135 and have never been pulled upwards more than 3 ft. even with a 200 lbs person. This has usually been on the ground but if it was at an anchor you wouldn't imagine that it would be a heavy upward load, if it ever even loaded the anchor at all.

 

Gravity is on the anchor's side in this case, a car brakes quicker going uphill.

[scrambled_legs]

The worst case scenario is that your partner falls clipping his second piece while you're at a hanging belay. He has a factor 1 or more fall which launches you hard enough upwards that the upward piece fails, and the upward pull causes all the pieces making up the downward belay to dislodge. Now, both the climber and the belayer are hanging off the first piece that was placed on the pitch and in a world of hurt if it releases.

 

I think in reality the amount of force ever exerted on an upward piece and the possibility of a belay with a cam or two, to completely dislodge, are slim to nothing. I wouldn't waste good gear on a bunch of upward pieces. An exception might be a belay consisting of straight nuts and only suspect upward placements, then you might want to place 2.