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Topic Date User

Impact factor calculations and microwire placement 22-Nov-2009 At 1:27:16 AM dhunchak

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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.