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Impact factor calculations and microwire placement

dhunchak

22-Nov-2009
1:27:16 AM

In an effort to determine how safe it is to place small gear I’ve been reading up on impact factors and
fall factors. I decided to post my results to get some feedback, and to pass on the information as I
have found it quite interesting. I hope the maths are not too boring for most…

Impact Factor:

IF = [mg(h1 + h2)]/h2
Where m = mass
g = acceleration due to gravity
h1 = length of fall
h2 = amount of rope stretch

This is derived from PE = mgh, which gives you the kinetic energy in Joules achieved in the freefall
phase, converted to the force in Newtons felt by the decelerating climber by dividing by the distance
over which fall arrest occurs. The stopping distance (rope stretch) must be included in the total
distance fallen (hence h1 +h2). Note that the units for a Newton are kg.m/s2

Rope stretch:

h2 = l x DE
Where l = length of rope in the system (from belay device to climber)
DE = Dynamic Elongation

Most dynamic climbing ropes have a dynamic elongation of ~30%, but this is calculated under UIAA
conditions of a factor 1.78 fall on a brand new rope – not the usual fall circumstances. I discovered
that on the internet people have been using 10% DE in their calculations, and have decided that this
made empirical sense to me and my experiences with falling; you may choose otherwise. Note that
increasing DE decreases the force felt at the anchor.

Force felt at the anchor:

Because an anchor point is a fixed pulley, theoretically the force the climber exerts on one end of the
rope is equal to the force the belayer applies at the other end, and therefore the anchor point feels 2x
the impact factor. In reality, this effect is diminished due to friction, and Petzl apparently reckons the
anchor feels 1.66x the IF.

Example 1)

Climbing a 30m pitch, you decide to run it out the last 5m and fall off the top. Note I have used my
own body weight of 70kg in these examples.

IF = [(70kg)(9.8m/s2)(10m + 3m)]/(3m)
= 3.0kN
The anchor then feels a force of 3.0 x 1.66 = 4.9kN

Example 2)

Climbing 10m up, you fall from 2m above your gear.

IF = [(70kg)(9.8m/s2)(4m + 1m)]/(1m)
= 3.4kN
The anchor then feels a force of 3.4 x 1.66 = 5.7kN

Example 3)

You can also use these equations to calculate the maximum distance you can fall to generate a force
of 2kN at the anchor point. This would correspond to the maximum distance you can safely climb
above a microwire for a given amount of rope in the system (maths not shown).

i) With 30m of rope out, a 70kg climber falling from 1.1m above a microwire will generate 2kN of force
on the wire.
ii) With 10m of rope out, a 70kg climber falling from 0.35m above a microwire will generate 2kN of
force on the wire.

Conclusions:

Fall factor plays a very significant roll in the force generated at the anchor point. Because h2
(representing the rope stretch – directly affected by the fall factor) is in the denominator, there is an
inverse relationship between force and amount of rope in the system. Since a fall of the same distance
generates 3x more force 10m up the climb compared to 30m up the climb, run outs at the top of the
climb are much safer – assuming no massive ledges trying to attack your ankles.

Microwires are difficult to use safely. My #3 BD wired nut is rated to 5kN, but both #1/2 stoppers are
2kN. When climbing above microwires, it is useful to know how far you can expect to climb before you
are in the gear failure zone. By placing multiple wires at the same level you may be able to reduce
your risk – presumably each piece that snaps absorbs 2kN of force from the fall. Therefore in example
#2, you would want to place at least three microwires to catch that fall. If preplacing gear, a strategy to
limit the number of draws you have to clip while on lead is to sling multiple wires together then place a
single draw on that sling. Then you need only clip the one draw to be protected by your multiple small
wires.

I have found it strategically quite useful to know the approximate force generated in several size falls
from various positions on a climb. For example, knowing that I can generate around 6kN from a fall
only 2m above my gear (example 2), I will be much more careful placing 00/0 Metolius Ultralight TCUs
– rated to 5kN – while low down on a climb. Hopefully some of you will find this info similarly helpful
and will be able to climb more safely because of it. If there are any mistakes of logic math or
otherwise I apologise. I am not a physicist or mathematician, nor is this an academic paper. There are
many assumptions / approximations contained within – please approach this with a generous amount
of scepticism.


salty crag

22-Nov-2009
9:11:21 AM

Hope you don't run through these calcs. every time you place some pro.
Good food for thought though, gut feeling and a strong aversion to falling usually has me backing up micro's.

Fish Boy

22-Nov-2009
10:10:01 AM

screamers are good


pmonks

22-Nov-2009
10:21:53 AM

On 22/11/2009 Fish Boy wrote:
>screamers are good

Screamers or screamers?


dimpet

22-Nov-2009
11:58:56 AM

That's not a screamer, this is a screamer :P
http://www.youtube.com/watch?v=Iy42ndIUHrA&feature=fvw


miguel75

22-Nov-2009
9:44:14 PM

Thanks for posting these calculations. As a pretty "new" lead climber I've often wondered if I could use
less pro when climbing as I usually back up every piece and burn through the rack pretty. I'll likely keep
placing stacks of pro as i find it great practice..

Cheers,

Mike

Mike Bee

22-Nov-2009
11:11:53 PM

On 22/11/2009 miguel75 wrote:
>Thanks for posting these calculations. As a pretty "new" lead climber I've
>often wondered if I could use
>less pro when climbing as I usually back up every piece and burn through
>the rack pretty. I'll likely keep
>placing stacks of pro as i find it great practice..

As you progress through the grades you'll stop doing this out of neccessity, I reckon.
When it gets vertical or steeper, you simply don't have the strength to hang around and place more than one piece of gear.
Also, these numbers only show that smaller nuts and cams could fail due to the force of a fall. If you check the numbers printed on the slings of your larger cams (eg .4BD and higher) and your medium to large nuts, you'll see that most of the gear is rated to 8kN plus, with 12kN being the standard.

To the OP, these calcs are interesting to have a read of and a play with, but don't go placing too much emphasis on them, they are far too simplistic to model a real world trad fall.
Things like deformation of the nut, deformation of the body, tightening of the tie in knot, the dynamicness of the belay and maybe most importantly, the condition of the rope, all contribute to the impact force experienced by the top piece.

For example, a leader climbing on a rope with a stated impact force of 7.3kN (eg Beal Booster) will generate significantly less force than a climber who experiences the exactly the same fall but is using a Mammut Tusk (9.1kN impact force). This significant factor isn't included in your model.

mikl law

23-Nov-2009
7:23:42 AM

Ittake a while to churn through that doesn't it.
The important point is that if a piece pulls it doesn't really absorb much energy or slow you down much:- Attaway did a nice paper where he showed that with equally spaced equally bad gear and the top piece fails, they will all fail. So you need to eiother equalise a bunch of bad gear, or climb on doubles (the load is spread over 2 pieces if they are within a meter or two so only half the load comes on each, and the impact force of a thin rope is less).
Or get your belayer to let slip the rope.
The Wexler equation covers all this, I don't have a web reference for it, but it was a neat piece of work which invented the "fall factor" long before we had nylon ropes.
Attaway also had a more accurate fit to rope forces
http://web.mit.edu/sp255/www/reference_vault/second_order_rope_fit.pdf


IdratherbeclimbingM9

23-Nov-2009
2:59:10 PM

On 22/11/2009 dhunchak wrote:
>Conclusions:

It is good to see people seriously looking at the application of their equipment and its limitations.
Apart from the specification/technical aspects another couple of points to consider are the actual placement and the quality of the rock it is placed in.
The maths is only good for the ideal placement, and many real life applications are less than ideal...

gjoh

23-Nov-2009
4:01:23 PM

Just out of interest does anyone know what factor of safety the manufacturers use when quoting a maximum force?

Also, how much energy would be absorbed by the slings and uplifting of the belayer?


ado_m

23-Nov-2009
5:24:48 PM

also what percentage of microwires break significantly above their rated strength?
(ie where manufacturers indicate a lower breaking strain to ensure eg 99% hold at that force?)


ambyeok

23-Nov-2009
5:56:55 PM

Perhaps the real point is... who has broken microwires and what were they doing when they broke. I dont remember reading any accident reports about people decking after microwires broke. Do we really need to be worried?


miguel75

23-Nov-2009
8:40:59 PM

Too true Mike. You're right in that it takes more energy to hang around longer and the rope drag can get
nasty though I plug everything in mainly because I love placing gear. The act of climbing is awesome,
though to me, standing on a hold somewhere along a multipitch climb just plugging gear into the wall is a
hoot! It makes me happy!


southcol

23-Nov-2009
10:27:15 PM

On 23/11/2009 mikl law wrote:

So you need to eiother equalise a bunch of bad gear, or
>climb on doubles (the load is spread over 2 pieces if they are within a
>meter or two so only half the load comes on each, and the impact force
>of a thin rope is less).

I used to subscribe to the theory of impact force on thin ropes is less until I read this: http://gravsports.blogspot.com/2006/11/single-and-half-rope-impact-forces_30.html (2nd time I posted URL, yawn..) However its interpreted, its important to realise that rope diameter alone does not determine impact force...spreading the load is the important part in double rope technique.

thanks for the report David. Yates screamers are worthwhile.

patto

23-Nov-2009
11:04:10 PM

On 23/11/2009 gjoh wrote:
>Just out of interest does anyone know what factor of safety the manufacturers
>use when quoting a maximum force?

No safety factor is used. Most gear is 3 sigma rated. Thus the rating is the force that 99.7% of will be able to withstand.

On 23/11/2009 ado_m wrote:
>also what percentage of microwires break significantly above their rated
>strength?
>(ie where manufacturers indicate a lower breaking strain to ensure eg
>99% hold at that force?)
>

From the above statement one would suggest that 99.7% would break above their rated strength.


Phil Box

24-Nov-2009
6:20:30 AM

Testing for impact forces is done using solid weights in a drop tower. This to some degree does NOT replicate real life forces out on the cliff. There is lots of spooginess in the system when out on the cliff. Your body absorbs impact forces as does the belayers body and the slippage that occurs in the belay device.

I've seen videos and looked at the graphs from some of the tests done on drop towers. The drop tower gives a consistency of results to be sure but what is sorely needed is some empirecal data on the relationship between that hard data and what actually occurs out on the cliffside.

The impact forces I suspect are much less out in the real world.

I haven't broken microwires but I have placed a piece on aid and when I looked closer at the placement I observed a broken off head of the same size piece. Man that clears out the nostrils. It was the tiniest size RP. Of course this was on Brown Corduroy Trousers at Frog and all the hard climbers throw themselves at this climb. Obviously someone had placed a confidence piece to hang the rope at the crux. Better to just climb on and not bother with that piece if you are not aiding. A great piece not far below and a stonker piece not far above.


IdratherbeclimbingM9

24-Nov-2009
10:41:21 AM

I have not broken any but I have cleaned broken micro-wires from placements while aid climbing. Some would have been broken during leader falls, but others I suspect had been broken by a funkness device during a cleaning attempt.

For the smaller RP's I note that usually it is one wire broken and this takes place up near the head. Mostly it is the wire that one would consider to be the lowest in a normal placement. This also makes me think that it is a result of damage to a wire incurred during previous successful cleaning of the piece in former placements.

~> I re-swage the wire of such pieces into a clipable loop and continue to use them in 'thin aid*'. (*bodyweight placements etc).

I tend to treat thin gear as marginal regardless of its rated strength.
The more marginal I think it is the more inclined I am to back it up* whenever possible.
(*That is what is great about thin aid ... ~> you get to back up the back-ups, and play equalisation games!)

ambyeok wrote;
>Perhaps the real point is... who has broken microwires and what were they doing when they broke. I dont remember reading any accident reports about people decking after microwires broke. Do we really need to be worried?

I think the more pertinent point would be 'How amazing is it, that thin gear often holds the falls that they take!'
;-)

patto

24-Nov-2009
10:51:19 AM

On 24/11/2009 Phil Box wrote:
>Testing for impact forces is done using solid weights in a drop tower.
>This to some degree does NOT replicate real life forces out on the cliff.
>There is lots of spooginess in the system when out on the cliff. Your body
>absorbs impact forces as does the belayers body and the slippage that occurs
>in the belay device.
>
>I've seen videos and looked at the graphs from some of the tests done
>on drop towers. The drop tower gives a consistency of results to be sure
>but what is sorely needed is some empirecal data on the relationship between
>that hard data and what actually occurs out on the cliffside.
>
>The impact forces I suspect are much less out in the real world.
>

Well that, and when was the last time you or anybody you know took a serious factor two fall? (well the test uses 1.77 but hey that is close enough!)

mikl law

24-Nov-2009
12:03:13 PM

What you REALLY need falling on crap gear is an 11mm rope, a Grigri, and a 100kg belayer, tied down. That should do the job.
Gotta get that gear outta the cliff you know.

egosan

24-Nov-2009
12:12:18 PM

Why stop there, Mike?

I have some 11mm "low stretch" static line here. Just in case you still can't get the piece
to pop. I find it useful in cleaning my #13 nuts.

-edited: Thanks, Andrew.... jackass

There are 29 messages in this topic.