acct 2008 dynamic rope behaviorweb.mit.edu/sp255/www/reference_vault/acct_rope_behavior.pdf ·...
TRANSCRIPT
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ACCT Rope Behavior 1
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ACCT Rope Behavior 2
objective
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ACCT Rope Behavior 3
structure
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ACCT Rope Behavior 4
my sinister puppeteers
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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.
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ACCT Rope Behavior 6
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ACCT Rope Behavior 7
dynamic rope standard
pictorial images © P Schubert & N McMillan; from http://www.theuiaa.org/uiaa_safety_labels.php
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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)
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ACCT Rope Behavior 9
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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
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ACCT Rope Behavior 11
fall geometry
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ACCT Rope Behavior 12
fall properties
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ACCT Rope Behavior 13
energy conservation
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ACCT Rope Behavior 14
ugh
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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.
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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
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ACCT Rope Behavior 17
Pavier spring/spring-pot model
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ACCT Rope Behavior 18
kinematics graphs
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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
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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
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ACCT Rope Behavior 21
goldilocks and the three belayers
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ACCT Rope Behavior 22
fracture toughness,water,
strong acids,and heat transfer characteristics
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ACCT Rope Behavior 23
experimental data
-200
20406080
100120140160180
0 5 10 15 20
Series1Series2
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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)
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ACCT Rope Behavior 25
statistical analysis of test facility data: expected error
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ACCT Rope Behavior 26
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ACCT Rope Behavior 27
experimental verificationCAI data
C. Zantoni et al, CAI,UIAA Meeting Minutes2005
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ACCT Rope Behavior 28
CAI experimental verificationbelaying forces with slip
C. Zantoni et al, CAI,UIAA Meeting Minutes2005
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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
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ACCT Rope Behavior 30
CAI results from experiments with sharp edge & energy absorption
C. Zantoni et al, CAI,UIAA Meeting Minutes2005
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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.
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ACCT Rope Behavior 32
effects of humidity: force
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ACCT Rope Behavior 33
effects of humidity: drops held
Again, from A.B. Spierings, et al. in the International Journal of Impact Engineering
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ACCT Rope Behavior 34
effects of humidity: elongation
Again, from A.B. Spierings, et al. in the International Journal of Impact Engineering
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ACCT Rope Behavior 35
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ACCT Rope Behavior 36
ropes don’t break
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ACCT Rope Behavior 37
but ropes do
Cut & fray
Succumb to strong acids
Suffer misuse, abuse & new use
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ACCT Rope Behavior 38
the failure mode is more likely to be
Failure of equipment other than the rope
Injury to the climber
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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
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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
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ACCT Rope Behavior 41
questions
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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