Fall factor physics question

[obsydian]

If a person uses 9/16" webbing as a personal anchor and takes the hardest fall available, what is the force excerted and does this system have enough redundancy to be considered strong enough?

 

What has been published so far:

----------------------------------------

160 lb climber - 72.6 Kg Climber

Gravity Acceleration - 9.8 m/sec^2

Time to fall 4 feet - 0.5 seconds

Peak velocity - 4.9 m/s

sudden deceleration from 4.9 m/s to 0 m/s

A newton is the force required to impact a 1 kg mass to an acceleration of 1 m/sec^2

Applied in opposite - to decelerate a mass from gravity (9.8 m/sec^2) to zero velocity

72.6 kg x 9.8 m/sec^2 = 711.2 Newtons or .7112 kN

strength is decreased with knots -- including the water knot - 20-30% reduction per FOH

This would drop the strength of the webbing from 6.8kN to 4.8 kN. This also assumes no knicks in the webbing or other areas where the webbing is bound that would further weaken the strength of the personal protection.

 

Factor of safety for 9/16" webbing - 6.8. However, this does not take into account accelerations due to falling in an arc and additional accelerations and shock that would occur.

Repeated stressing of the webbing.

Any weakening of the webbing that may occur due to UV exposure over time

Knicks in the webbing

 

Suggest only daisy chains or 1" webbing.

-----------------------------------------------------

What is wrong this logic? Thanks

[cracked]

Your logic is grossly mistaken:

Applied in opposite - to decelerate a mass from gravity (9.8 m/sec^2) to zero velocity

72.6 kg x 9.8 m/sec^2 = 711.2 Newtons or .7112 kN

This makes no sense whatsoever. You are 'decelerating' from acceleration to acceleration. Which makes no sense, you want to accelerate from one velocity to another.

 

You're concerned about the impulse, defined as the integral of force over time, which is equal to the change in momentum. I don't know the elasticity of webbing.

 

Either way, the above calculation makes no sense whatsoever.

[Freeman]

I just ran over to the Petzl page and ran their fall simulator on this one. For a 72.6 kg climber falling 2.2 meters on 1.1 meter of "static" rope (fall factor 2) on a static anchor (12 mm bolt and Grigri) the calculated force is 17.1 kN. As you know, the UIAA rating for climbing rope is 12 kN with a fall factor of about 1.7 - the assumption is that a human body can take 12kN. Anything more (like 17) would result in probable injury.

 

Just one more reason to not fall on runners (or a daisy chain)

[Freeman]

The breaking strength of 9/16 climb spec runners is given in one source as 2250 lbs (10 kN) and 9/16 spectra as 6075 lbs (27 kN). It is likely that this short factor 2 fall would be enough to fail the runner. The source did not say if this was sewn, tied, or just the breaking strength of the webbing - it did call it "impact force and breaking strength that...components... can withstand".

[matt_m]

If a person uses 9/16" webbing as a personal anchor and takes the hardest fall available, what is the force excerted and does this system have enough redundancy to be considered strong enough?

 

 

I think what's being asked here is if the leader takes a factor two onto the the anchors and the belayer is attached to the anchor via a homemade PAS, will that be considered strong enough...

 

Short answer - NO

Long answer - You shouldn't just be using as PAS, sling or daisy (worst) as your sole attachment point to an anchor. I use a PAS (strong) AND equalize with the rope in a simple 2 bolt setup common around here. I could go on and on about different ways to build and attach yourself to an anchor but the bottom line is to have some sort of redundancy if at all possible. Now this question does lead one to focus on the great issues at hand... Factor 2s on the anchor are BAD. We're talking REALLY REALLY bad. It's the place where gear can be stressed at it's maximum and thus closest to its breaking point. It is very important for the leader to place a piece of protection quickly after leaving the belay. Some of my more terrifying moments have been on runout slab 20+feet above the belay looking for the bolt. Not as much because of the fall but of the fact that I'd be hitting the belay HARD. Not fun.

Petzl had a brief article on other risks associated with falls close to the belay.

Petzl Belay Info

Only thing they kinda dance around is the higher forces associated with the grigri but apparently, the thing starts slipping (more dynamic) around 4.5kn.

 

Summary - Factor 2s onto the belay are one of the worst things you can do in climbing. Protect yourself (leader) properly ASAP. Use strong and redundant connections to the belay (belayer) and be aware of the high forces you could encounter. I know I'll get some flack for this BUT - Daisies are for personal connivence only - if you like to use an adjustable connection as part of your anchor - like myself - go get a PAS - they're just better for what most people do with them.

[selkirk]

There's lots of stuff you should be able to use for a personal anchor.

9/16th Climb Spec is supposed to hold 11 kn

(however you've got two strands of it so long as your using a tied sling it should hold 22kn. somebody let me know if i'm wrong here)

the Metolius PAS is at 18kn,

9/16th Spectra Sewn Runner at 27

Mammut Dyneema Sewn Runner at 22

You could also use Spectra Accessory Cord at 20 kn,

 

Generally all of these things should be fine for a

Personal Anchor. The sticking point is you really don't want to fall directly onto your personal Anchor. Your going to generate a shit load of force. So you definitely want it backed up.

 

Take a look at if your interested.

http://flash.lakeheadu.ca/~lurock/factor2.html

 

They're analysis comes out to 18kn for a 1.2 m factor 2 fall onto static rope/runner

The other thing to remember is that the rest of the climbing system will fail at about the same point

 

Anchors -- 25 kN

Carabiners -- 20 kN

Slings -- 22 kN

Harnesses -- 15 kN

 

So not only might your personal anchor fail, but you could quite easily pull your pro, blow your harnes or break your biners. Best thing to do is keep the personal anchor snug and you below the anchor your attached to so you can't take a factor 2 onto it.

And definitely back it up! Take your climbing rope and tie it directly into the anchor ASAP.

 

The other thing to watch with Daisies is that the stitching in the pockets blows out well before the whole runner (i've heard at around 300 lbs? for some). So there's the whole threat that if your clipped through 2 loops (say the end loop and an intermediate loop to shorten it) you could potentially blow the stitching at a low force and detach the daisy from an anchor.