ACCT 2008 Dynamic Rope Behaviorweb.mit.edu/sp255/www/reference_vault/acct_rope_behavior.pdf ·...

ACCT Rope Behavior 1

ACCT Rope Behavior 2

objective

ACCT Rope Behavior 3

structure

ACCT Rope Behavior 4

my sinister puppeteers

ACCT Rope Behavior 5

climbing, teaching, research,

modeling, consumption

of German beer, napping through

UIAA meetings

I’m not a guide, so I can’t tell you how to climb.

ACCT Rope Behavior 6

ACCT Rope Behavior 7

dynamic rope standard

pictorial images © P Schubert & N McMillan; from http://www.theuiaa.org/uiaa_safety_labels.php

ACCT Rope Behavior 8

low stretch rope standard

EN 1891• Definition: 8.5-16 mm, kernmantel, for use “in work access,

rescue and in speleology,” hem + haw, types A (general use) and B (not as good as A)

• Melting point > 195°C; knotability < 1.2; sheath slippage; sheath/kern ratio

• Fall performance in 0.6 m fall on 2.0 m rope (fall factor 0.3): peak force < 6 kN, drops held > 5

• Static strength: with terminations, 15|12 kN; without terminations, 22|18 kN

Additional UIAA requirements• > 80% solid color & single direction of spiraling 2nd color(s)

ACCT Rope Behavior 9

ACCT Rope Behavior 10

kilo-newtons, einstein, physicskN ~one BIG climber on a bathroom scale

equivalence principle: when you jump on the bathroom scale, it reads a much higher than body weight

• Energy • Force• Kinematics• Momentum• Material properties

ACCT Rope Behavior 11

fall geometry

ACCT Rope Behavior 12

fall properties

ACCT Rope Behavior 13

energy conservation

ACCT Rope Behavior 14

ugh

ACCT Rope Behavior 15

more complicated

Friction over the topcarabiner increases therope modulus.

Belayer behavior and damping (to somedegree) reduce thequantity under the radical sign.

Small falls are governed by belayer behavior.Severe falls are governed by rope properties.

ACCT Rope Behavior 16

Pavier model & damping

Spring in series with spring/dashpot parallel combo

Provides general idea of damping coefficient

Produces close match between model and experiment

Matches with the observation that climbing ropes are not far from critical damping/morethan half the energy is lost in each cycle

No model for why this works

35 kN

20 kN3 kNs

ACCT Rope Behavior 17

Pavier spring/spring-pot model

ACCT Rope Behavior 18

kinematics graphs

ACCT Rope Behavior 19

GROMF conditions

Table #: Generic, run of the mill fall (GROMF) characteristics

quantity symbol Value UnitsMass of climber mc 80 kgAcceleration of gravity g 10* m/s2

Rope modulus M 24 kNRope length L 30 mFree fall height H 2 mFall factor ff 1/15

Spring constant of rope k=M/l 800 N/m

ACCT Rope Behavior 20

GROMF result estimatesApproximate GROMF results based on modeling the rope as a simple spring

quantity symbol value units

Time of free fall tf 0.6 s

Time from rope engagement to dead-point tδ 0.1 s

Time of rope stretch (total) tr 1.2 s

Time, top to bottom of fall (tf +tr/2) 1.2 s

Rope stretch ymax 3.2 m

Total fall height (free fall height + rope stretch) h+ ymax 5.2 m

Velocity at the end of free fall v0 6.3 m/s

Velocity at dead-point vmax 7.1 m/s

Maximum deceleration amax 30 m/s2

Frequency (angular) ω 3.2 s-1

Maximum rope tension on climber Tmax 3.2 kN

ACCT Rope Behavior 21

goldilocks and the three belayers

ACCT Rope Behavior 22

fracture toughness,water,

strong acids,and heat transfer characteristics

ACCT Rope Behavior 23

experimental data

-200

20406080

100120140160180

0 5 10 15 20

Series1Series2

ACCT Rope Behavior 24

experimental verification:Mägdefrau

data

Maegdefrau Datasqrt fall factor vs.

anchor load

0

2

4

6

8

0.00 0.50 1.00

sqrt fall factor

anch

or lo

ad (k

N)

Single Rope

Rope Pair

Maegdefrau DataLoad Rate vs. sqrt F/l

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.00 10.00 20.00 30.00 40.00

load rate (kN/s)

sqrt

(F/l)

(m-1

/2)

ACCT Rope Behavior 25

statistical analysis of test facility data: expected error

ACCT Rope Behavior 26

ACCT Rope Behavior 27

experimental verificationCAI data

C. Zantoni et al, CAI,UIAA Meeting Minutes2005

ACCT Rope Behavior 28

CAI experimental verificationbelaying forces with slip

C. Zantoni et al, CAI,UIAA Meeting Minutes2005

ACCT Rope Behavior 29

experimental verificationCAI fixed point anchor force data

C. Z

anto

niet

al, C

AI,

UIA

A M

eeti

ng M

inut

es2

00

5

ACCT Rope Behavior 30

CAI results from experiments with sharp edge & energy absorption

C. Zantoni et al, CAI,UIAA Meeting Minutes2005

ACCT Rope Behavior 31

effects of use

Rope properties decay exponentially with use.

The half-life for 10.5 mm rope is ~5 km of use, whether ascending or descending.

Larger diameters have larger half lives;smaller diameters have shorter half lives.

ACCT Rope Behavior 32

effects of humidity: force

ACCT Rope Behavior 33

effects of humidity: drops held

Again, from A.B. Spierings, et al. in the International Journal of Impact Engineering

ACCT Rope Behavior 34

effects of humidity: elongation

Again, from A.B. Spierings, et al. in the International Journal of Impact Engineering

ACCT Rope Behavior 35

ACCT Rope Behavior 36

ropes don’t break

ACCT Rope Behavior 37

but ropes do

Cut & fray

Succumb to strong acids

Suffer misuse, abuse & new use

ACCT Rope Behavior 38

the failure mode is more likely to be

Failure of equipment other than the rope

Injury to the climber

ACCT Rope Behavior 39

the shape of rope performance space• Human physiology• Standard performance• Degradation due to use and abuse• Water• Strong Acids• Sharp Edges• Fall geometry• Belay behavior• Rope properties

ACCT Rope Behavior 40

bibliography/references

M Pavier Experimental and theoretical simulations of climbing falls

O. Henkel, M. Schmid, A.B. Spierings Water absorption and the effects of moisture on the dynamic properties of synthetic mountaineering ropes

A Wexler, The theory of belayingUIAA, Standard 101, dynamic ropesEN1891, PPE for prevention of falls from height—Low

stretch kernmantel ropesS Attaway, Rope System AnalysisC Zantoni et al., UIAA SafeCom minuteshttp://www.theuiaa.org/act_safety.html

ACCT Rope Behavior 41

questions

ACCT Rope Behavior 42

friction over the top carabiner

The dependency of the friction coefficient on mass, velocity, diameter, rope coating, rope type (static vs. dynamic), and temperature has not been investigated