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TRANSCRIPT
A Simulation of Climbing and Rescue Belays
Tom Moyer
2006 International Technical Rescue SymposiumThis presentation and the associated model can be downloaded at
http://www.xmission.com/~tmoyer/testing (© Tom Moyer)All images in this presentation were generated with RescueRigger (rescuerigger.com)
SALT LAKE COUNTYS H E R I F F ’ S O F F I C E
SEARCH RESCUE
1
How do TTRL belays compare to climbing belays?
2
46 N min209 N average 425 N max
No load above which 100% of the population can grip
Mauthner - Gripping Ability on Rope in Motion study
3
What gripping ability is required to hold the load statically?
F
f
F
f
F / f = force multiplication factor (FMF)
For a brake bar rack with 5 bars, FMF ≈ 20 with 6 bars, FMF ≈ 25
For an ATC, FMF ≈ 7.5
Force Multiplication Factors of Friction Devices
4
80 kg climber
66% efficiency over biner
ATC FMF = 7.5
Hand Force T0
80 kg rappeller
Rope tension T1
Hand Force T0
ATC FMF = 7.5
Rope tension T2
T1
Rappelling
T1 = 80 kg * 9.81 m/s2 = 785 N
T0 = 785 N / 7.5 = 105 N
Belaying
T2 = 80 kg * 9.81 m/s2 = 785 N
T1 = 785 N * 0.66 = 518 N
T0 = 518 N / 7.5 = 69 N
Climbing Scenarios –Static Loads
5200 kg load
50% efficiency over edge
Brake bar (5 bars) fmf = 20
Hand holds 49N
Vertical TTRL Belay
T2 = 200 kg * 9.81 m/s2 = 1,962 N
T1 = 1,962 N * 0.50 = 981 N
T0 = 981 N / 20 = 49 N
Vertical TTRL Scenario
6
35°
600 kg load
Brake bar (6 bars) fmf = 25
Rope tension T1
Hand holds 135N
Low Angle TTRL Belay
T1 = 600 kg * 9.81 * sin (35 °) = 3.38 kN or 760 lb
T0 = 3.38 kN / 25 = 135 N
Low Angle TTRL Scenario
7
Dynamic Models
Model dynamic events and compare to test data
Why model?• Repeatable• Cheaper than testing• Can study one variable at a time• Can study parameters that are difficult to test
Comparison Data
• No Hand• Weber - PMI drop tests• Moyer - cordelette tests• Manufacturer’s ratings
• With Hand• Petzl fall simulator• CMT test data & simulation (live belayers)• Rigging for Rescue TTRL tests (mechanical hand)
Lead Fall
0
1000
2000
3000
4000
5000
6000
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Time (s)
Forc
e (N
)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
Dis
tanc
e (m
)
Runner load
Rope Load
Belay site load (N)
Climber position (m)
Slide Distance (m)
8
Gravitational potential energy = strain energy in the rope
Rope Modulus M = T/strain or TL/δPotential Energy = mg(h+δ)Strain Energy = ½T δ
Simple Linear ModelConservation of Energy
h
L
δ
m
FmgMmgmgT 21max ++=
where fall factor F = h/L Forc
e (N
)
Distance (m)
Strain Energy
δ
Fmax
9
Detailed ModelIterative Dynamic Motion Equations
Includes:• Nonlinear rope elasticity• Knots• Rope damping• Carabiner friction• Belay device friction• Slipping in belayer’s hand• Lifting of belayer
Iterative solution approach:• From current rope tension, calculate a = T/m +g• Calculate ∆v = a dt and ∆x = v dt• From new positions, calculate new rope strains ε = ∆L/L• From new strains, calculate rope tensions• Calculate slip distances at friction devices to limit tension ratios to allowed values• Calculate new rope strains and new rope tensions
10
Model ParametersFall Parameters
mc
L 1
L 2
h
d
FMFα
η
δs
Fall equationsFall height h = d + L2Fall factor F = h / L
Parameters at static loadLs = L + δshs = h + δsFs = hs / Ls
Climber mass (kg) mc
Belayer mass (kg) mb
Time step (s) dtRope span angle (deg) α
Runner angle (deg) βBelayer tie-in slack (m) b_slack
Belayer-biner distance (m) L1
Climber height above biner (m) dRope length (m) LBiner efficiency η
Rope 2nd order modulus (N/strain2) BRope 1st order modulus (N/strain) A
Damping coefficient (N/strain/s) λka/kb k_ratio
Number of knots #_knotsKnot 2nd order stiffness (N/m2) E
Knot 1st order stiffness (N/m) DKnot minimum force (N) C
Reaction time (s) Tr
Force multiplier FMFGrip (N) grip
Fall height (m) hFall factor F
δd
11
Three Components are Critical to Understand
The Rope
The Friction Device
The Hand
12
Rope Properties2nd order curve fits – Weber PMI Data
Elongation of Ropes2nd-order Curve Fits
y = 1,390,589x2 + 0x
y = 60023x2 + 4024x
y = 43072x2 + 4603x
y = 366035x2 + 318x
0
5,000
10,000
15,000
20,000
25,000
30,000
0% 10% 20% 30% 40% 50%
strain
Forc
e (N
)Weber PMI 12.5mm staticSterling Superstatic (TM)BD/PMI 10.5 dynamic (TM)Weber PMI 10.6
• Model results with nonlinear properties match Attaway’s analytical predictions
• Nonlinear rope still obeys fall factor rule. Impact force is a function of fall factor.
• Impact force for a zero ff drop on nonlinear rope is 3 x weight instead of 2 x weight.
13
Knot Properties2nd order curve fits – Weber PMI Data
Knot Elongation2nd-order Curve Fits
y = 260,435x2 + 7,462x + 783
y = 1,154,688x2 + 0x + 783
0
5,000
10,000
15,000
20,000
25,000
30,000
0 0.05 0.1 0.15 0.2 0.25Extension (m)
Forc
e (N
)PMI 12.5mm staticPMI 10.6mm dynamic
• Knots modeled as rope sources rather than compliance terms
• Knots are much more significant on short ropes
14
Rope Properties - Damping
What is damping?
• Elastic force is proportional to deflection (strain)
• Damping, or viscous force is proportional to velocity (strain rate)
• Elastic energy is returned on rebound.
• Damping energy is lost to heating in the rope.
• Damping causes oscillations to die out.
C. Zanantoni - CMT
15
Pavier Damping Model
• Spring in series with a spring/dashpot combination
• Simple spring/dashpot combo produces unrealistic results.
Initial impact forces too high.Damping values too low (too underdamped)
• Real ropes are close to critically damped.
• Damping values ka/kb and λ determined by trial and error to produce reasonable model behavior.
• Overall spring rate k from slow-pull testing
• Damping values could be determined experimentally with good force/deflection measurements in drop tests or fast pull-tests.
ka
kbλ
16
Comparison to Weber PMI Data Example Load Profile
• Drop-test values give maximum force, elongation, and energy.
• Data points are very close to the rope-only curve.
• Without damping, rope and rope + knots curves do not store sufficient strain energy.
• Therefore they over-predict both force and elongation.
Weber - PMI Drop Tests #92 & #13112.5mm PMI Static - hs = 5ft, Ls = 20ft
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Position (m)
Load
(N)
ModelWeber PMI Drop-testsSlow-pull, rope & knotsSlow pull, rope only
17
Impact ForcesPMI 12.5mm Static Rope, M = 80 kg, Ls* = 6.1m (20 ft)
0
5,000
10,000
15,000
20,000
25,000
0 1 2 3 4 5 6 7
Drop Distance* (m)
Forc
e (N
)
Second-Order Rope
Linear Rope k = 178 kN (40,000 lb)
Second Order Rope with Knots(Attaway)This Model (Second Order Rope withKnots & Damping)Weber Drop-Test Data
Linear Rope k = 67 kN (15,000 lb)
Comparison to Weber PMI Data
* Ls Length is at static resting point. Drop Distance is height above free (unstretched) length of rope.
18
UIAA Test
80 kg weightFall Factor 1.712.8 meter rope
Cordelette is at the direction change anchor
Black Diamond 10.5mm rope- rated impact force of8.4 kN (1888 lb)
Comparison to Moyer Cordelette Testing
19
Comparison to Moyer Cordelette Testing
20
Comparison to Moyer Cordelette Testing
UIAA Drop - 10/15/00 Boulder, CO
0
2000
4000
6000
8000
10000
12000
0.0 0.5 1.0 1.5 2.0
Time (s)
Forc
e (N
)
Runner load
Runner load (data)Rope load
Rope load (calc from data)Belay site load
Belay site load (data)
5mm Gemini Drop #1
UIAA drop, Boulder 80 m c80 m b
0.0005 dt36 α14 β
0 b_slack0.4 L1
1.96 d2.67 L0.78 η
62252 B2657 A2800 λ
6 k_ratio4 #_knots
260,435 E7,462 D
783 C0.00 Tr
6000.0 FMF1 grip
4.23 h1.584 F
21
UIAA Drop - 10/15/00 Boulder, CO
0
2000
4000
6000
8000
10000
12000
0.0 0.5 1.0 1.5 2.0
Time (s)
Forc
e (N
)
Runner load
Runner load (data)Rope load
Rope load (calc from data)Belay site load
Belay site load (data)
Same Drop –Damping Removed
The Effect of Damping
5mm Gemini Drop #1
1st peak slightly shifted
Bigger effect on 2nd peak
22
Comparison to Moyer Cordelette Testing
0
1000
2000
3000
4000
5000
6000
7000
8000
0.00 0.50 1.00 1.50
position
Load
(N)
ModelData
UIAA Drop – 10/15/00 Boulder Colorado5mm Gemini Drop #1
23
Drops with a Hand in the System
• Hand slipping makes rope properties relatively unimportant
Italian CMT has done extensive study of the behavior of the belay hand in climbing falls
• Force measurements in falls compared to slow-motion video of the belayer
• Three phases of belay-hand behavior identified• Inertial Phase• Muscular Phase• Slipping Phase
24
“INERTIAL” PHASEThe hand moves fast
THE UPPER BODY STANDS STILL
THE HAND MOVES FAST
25
“MUSCULAR” PHASEThe hand moves slowly
THE UPPER BODY MOVES
THE HAND MOVES SLOWLY
26
“HAND SLIPPING” PHASEPossible rope slipping in the operator’s hand
NOTE THE SLIPPAGE IN
THE HAND
27
FIX POINT BELAYFIX POINT BELAY
0
100
200
300
400
500
600
700
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4time ( s )
load
( d
aN )
0
1
2
3
4
5
6
7
8
9
10
disp
lace
men
t ( m
) -
spe
ed (
m/s
)
runner load (model) sliding length in the brake falling mass speed
fallig mass displacement hand speed
inertial phase
muscular phase
no more sliding in the brake
28
Comparison to CMT Belay Simulation and Data
CMT Fall Parameters given:• Mass m = 80 kg• Fall height h = 8 m• L1 = 7.15 m• Belay Device FMF = 7.5• Hand mass = 2.5 kg
CMT Lead Fall80 mc
0.0005 dt7.15 L1
4 d11.15 L0.58 η
0 B20920 A3000 λ
50 k_ratio0.15 Tr
7.5 FMF290 grip
8 h0.717 F
CMT Lead Fall
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Time (s)
Forc
e (N
)
0.00
0.40
0.80
1.20
1.60
2.00
2.40
2.80
3.20
3.60
Dis
tanc
e (m
)
Runner load
Rope Load
Belay site load (N)
Climber position (m)
Slide Distance (m)
29
CMT Conclusions on Belaying
• Hand acts as an inertial load for the first few hundred milliseconds.
• Slip distance is proportional to fall height, not fall factor. Confirmed.
• Peak force occurs at maximum hand acceleration, not at lowest climber position.
• Only a small amount of belayer lifting is helpful (~20 cm). More lifting increases fall distance and does not decrease peak force. Confirmed.
30
Comparison to Petzl Fall Simulator
Lead Fall - Comparison to Petzl
0
1000
2000
3000
4000
5000
6000
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Time (s)
Forc
e (N
)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
Dis
tanc
e (m
)
Runner load
Rope Load
Belay site load (N)
Climber position (m)
Slide Distance (m)
Peak Force - on rope 3000 N
- on anchor 5000 N - on belayer 2000 N
- on belayer's hand 400 N Slide distance 4.95 m
Petzl Simulator values:• Hand Grip = 400N• Rope Burn Warning = 1800J• Reverso FMF = 5.0• Munter Hitch FMF = 7.5• Grigri FMF = ∞ (no slipping)
• 11mm rope modulus ≈ 44.1 kN• Carabiner efficiency = 66.6%• Knot elongation included
• No rope damping• No lifting of belayer
Petzl Comparison80 mc
0.0005 dt10 L1
8 d18 L
0.67 η0 B
44100 A0 λ
3.6 k_ratio1 #_knots
260,435 E7,462 D
783 C0.00 Tr
5.0 FMF400 grip16 h
0.889 F
31
Belay Device Details - FMF Values
240°
120°
120°
120°
120°
80°
Attaway Friction Analysis
T2/T1 = eµβ
Total = 800°4.4π
T1 = T2/31
T2
T1
Friction device properties are very important to the model predictions
32
Belay Device FMF ValuesBlack Diamond Testing
Mot
ion
Belay Device
33
Friction Device Force Multiplier Values (10.8mm rope)
0.0
5.0
10.0
15.0A
TC
Ato
ga
She
riff
Bug
Airb
rake
Airs
tyle
Mun
ter
Pyra
mid
Jaw
s
VC
Rap
tor
Cub
ik
Fixe
Forc
e M
ultip
lier
Low FrictionHigh Friction
Belay Device FMF ValuesBlack Diamond Test Data
34
Friction Device Force Multiplier ValuesVariation with Rope Diameter - (HF side of variable devices)
0.0
5.0
10.0
15.0
ATC
Ato
ga
She
riff
Bug
Airb
rake
Airs
tyle
Mun
ter
Pyr
amid
Jaw
s
VC
Rap
tor
Cub
ik
Fixe
Forc
e M
ultip
lier
10.8 mm9.9 mm9.4 mm8.1 mm
Belay Device FMF ValuesBlack Diamond Test Data
35
Friction Device Force Multiplier Values (10.8mm rope)Variation with Hand Force - (HF side of variable devices)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
ATC
Ato
ga
Sher
iff
Bug
Airb
rake
Airs
tyle
Mun
ter
Pyr
amid
Jaw
s
VC
Rap
tor
Cub
ik
Fixe
Forc
e M
ultip
lier
1.0 lb18.4 lb37.7 lb
Belay Device FMF ValuesBlack Diamond Test Data
36
Comparison to Rigging for Rescue Drop-Test Data
• Measured values:5,626 N Peak Force, 184 cm slide distance, 231 cm FAS Extension
• Model values:3003 N Peak Force, 184 cm slide distance, 219 cm FAS extension
Rigging for Rescue Drop-Test #2
0
500
1,000
1,500
2,000
2,500
3,000
3,500
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Time (s)
Forc
e (N
)
0.0
0.5
1.0
1.5
2.0
2.5
Dis
tanc
e (m
)
Rope Load
Climber position (m)
Slide Distance (m)
• Brake Bar FMF determined by trial and error.
• FMF = 14.3 gives a slide distance equal to the measured value
• This underpredictsthe measured peak force
RFR Drop #21m drop3m rope length200 kg test mass210N hand setting7/16 Sterling SS rope
RFR Drop #2200 mc
90 θ0.001 dt
3.00 L1.00 h
366035 B318 A
10000 λ5 k_ratio1 #_knots
1,154,688 E0 D
783 C0.20 Tr
14.3 FMF210 grip
37
"Two Rope Mech Hand" set at 210 N 80kg mass 0 cm drop of 11 mm Sterling
Superstatic straightline pull through hand
0
100
200
300
400
500
0 0.4 0.8 1.2 1.6 2.0 2.4
Time (s)
Forc
e (N
)
Rigging for Rescue3/5/05: DT-62 Hand
Average 299 N
Comparison to Rigging for Rescue Drop-Test Data
• Slide distance is a function of the average mechanical hand force.
• Peak rope tension is a function of the peak mechanical hand force.
• Any spikes in the mechanical hand force will cause higher measured peak force values.
Rigging for Rescue Data – ITRS 2005
38
Brake Bar FMF - 5 bars - Function of Hand Force
0
10
20
30
40
50
60
0 100 200 300 400 500Hand Force (N)
FMF
RFR Drop Tests - peak force
RFR Drop Tests - slide distance
Comparison to Rigging for Rescue Drop-Test DataBrake Bar FMF varies with Hand Force
39
Brake Bar FMF Testing at Black Diamond
Mot
ion
40
Brake Bar FMF Testing at Black Diamond
Brake Bar FMF - 5 bars - Function of Hand Force
0
10
20
30
40
50
60
0 100 200 300 400 500Hand Force (N)
FMF
RFR Drop Tests - peak force
RFR Drop Tests - slide distance
SMC slow pull tests - 11mm
Slow Pull Tests
41
Brake Bar FMF - function of # of barsat 223N (50 lb) Hand Force
4.0
6.0
8.0
10.0
12.0
14.0
16.0
3 4 5 6 7# of bars
FMF
Brake Bar FMF Testing at Black Diamond
42
Back to the Original Question
How do TTRL belays compare to climbing belays?
43
Required Gripping Abilityfor Different Belay Scenarios
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 50 100 150 200 250 300 350 400
Gripping Ability (N)
Slid
e D
ista
nce
(m)
Vertical TTRL, 5 bars, 200 kg, h=1, L=3
Toprope, ATC, ff0, L=45
UIAA fall, ATC, ff1.71, L=2.8
Low Angle TTRL, 6 bars, 600 kg,preloaded drop, L=3Petzl Rope Burn
Gripping Ability Required for Climbing and Rescue Scenarios
How much slip is too much?
• BCCTR belay standard, 1m maximum total extension.
• Petzl rope burn warning, 1800J
• Some belay device slip is good -reduces peak force.
• Too much sliding increases chance of collisions.
• A reasonable limit might be slide distance less than fall height.
Average human gripping ability
44
Rope Stretch
• Rope stretch is very important at longer rope lengths• A preloaded rope is much better
Rope Elongation in Rescue Belay ScenariosLocked Belay - Sterling Superstatic Rope
0.00
2.00
4.00
6.00
8.00
10.00
12.00
0 10 20 30 40 50 60
Rope Length (m)
Tota
l rop
e el
onga
tion
(m)
Low Angle BelayVertical BelayLow Angle TTRLVertical TTRL
Edge transition
1 m extension
45
• The hand is preloaded in a TTRL belay• A TTRL belayer can optimize brake bar setup
• Reaction time may be longer for a TTRL belay.• TTRL belay may already be sliding.• TTRL belayers typically wear gloves.• TTRL belayers are not expecting to catch falls.
Differences Between Rescue Belays and Climbing Belays
46
• TTRL grip requirements are similar to climbing.• Teams who prohibit manual devices should also
prohibit them for lead climbing and rappelling.• Brake bars are not very high friction devices.• Unlikely that TTRL belay would ever meet 1m
extension limit in the BCCTR test.
• The ideal rescue belay would be autolocking, force limiting and preloaded.
Conclusions
47
• Chuck Weber – PMI• Paul Tusting and Kolin Powick –
Black Diamond Equipment• Carlo Zanantoni - CMT• Mike Gibbs – Rigging for Rescue• Dave Custer – UIAA• Steve Achelis – RescueRigger• Garin Wallace – SMC• Marc Beverly and Steve Attaway
Thank You