Simulation of Climbing and Rescue Belays v3tmoyer/testing/... · • From current rope tension, calculate a = T/m +g • Calculate ∆v = a dt and ∆x = v dt • From new positions,
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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
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
• 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