Simulation of Climbing and Rescue Belays

8/2/2019 Simulation of Climbing and Rescue Belays

http://slidepdf.com/reader/full/simulation-of-climbing-and-rescue-belays 1/48

A Simulation of Climbingand 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 compareto climbing belays?



2

46 N min209 N average425 N max

No load abovewhich 100% of

the populationcan grip

Mauthner - Gripping Ability on Rope in Motion study



3

What gripping ability is required tohold the load statically?

F

f

F

f

F / f = force multiplication factor(FMF)

For a brake bar rack with 5bars, FMF ≈ 20 with 6 bars,FMF ≈ 25

For an ATC, FMF ≈ 7.5

Force Multiplication Factors of Friction Devices



4

80 kgclimber

66% efficiency overbiner

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



5

200 kg load

50% efficiencyover edge

Brake bar (5 bars) fmf = 20

Hand holds49N

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 kgload

Brake bar(6 bars)fmf = 25

Rope tension T1

Hand holds 135N

Low Angle TTRL BelayT1 = 600 kg * 9.81 * sin (35 °)= 3.38 kN or 760 lb

T0 = 3.38 kN / 25 = 135 N

Low Angle

TTRLScenario



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)

F o r c e ( N )

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

D i s t a n c e ( m )

Runner load

Rope LoadBelay 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/ δ

Potential Energy = mg(h+δ)

Strain Energy = ½T δ

Simple Linear Model

Conservation of Energy

h

L

δ

m

F

mg

M mgmgT

21max ++=

where fall factor F = h/L F o r c e ( N )

Distance (m)

StrainEnergy

δ

Fmax



9

Detailed Model

Iterative 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

L1

L 2

h

d

FMFα

η

δs

Fall equations

Fall height h = d + L2

Fall factor F = h / L

Parameters at static load

Ls = L + δs

hs = h + δs

F s = hs / Ls

Climber mass (kg) mc

Belayer mass (kg) mb

Time step (s) dt

Rope span angle (deg) α

Runner angle (deg) βBelayer tie-in slack (m) b_slack

Belayer-biner distance (m) L1

Climber height above biner (m) d

Rope length (m) L

Biner efficiency η

Rope 2nd order modulus (N/strain ) B

Rope 1st order modulus (N/strain) A

Damping coefficient (N/strain/s) λ

ka /kb k_ratio

Number of knots #_knots

Knot 2nd order stiffness (N/m2) E

Knot 1st order stiffness (N/m) D

Knot minimum force (N) CReaction time (s) Tr

Force multiplier FMF

Grip (N) grip

Fall height (m) h

Fall factor F

δd



11

Three Components areCritical to Understand

The Rope

The Friction Device

The Hand



12

Rope Properties2nd order curve fits – Weber PMI Data

Elongation of Ropes

2nd-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

F o r c 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 Elongation

2nd-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 0.25

Extension (m)

F o r c 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 forceis proportional to velocity

(strain rate)

• Elastic energy is returnedon rebound.

• Damping energy is lost toheating 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 unrealisticresults.

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 trialand error to produce reasonable model behavior.

• Overall spring rate k from slow-pull testing

• Damping values could be determinedexperimentally with good force/deflectionmeasurements in drop tests or fast pull-tests.

ka

kb

λ



16

Comparison to Weber PMI Data

Example Load Profile

• Drop-test values give

maximum force,

elongation, and energy.

• Data points are veryclose to the rope-only

curve.

• Without damping,rope and rope + knotscurves do not store

sufficient strain energy.

• Therefore they over-

predict both force andelongation.

Weber - PMI Drop Tests #92 & #131

12.5mm 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)

L o a d ( N )

ModelWeber PMI Drop-tests

Slow-pull, rope & knots

Slow 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)

F o r c e ( N )

Second-Order Rope

Linear Rope k = 178 kN (40,000 lb)

Second Order Rope with Knots

(Attaway)

This Model (Second Order Rope with

Knots & 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. DropDistance is height above free (unstretched)length of rope.



18

UIAA Test

80 kg weightFall Factor 1.71

2.8 meter rope

Cordelette is at the directionchange anchor

Black Diamond 10.5mm rope

- rated impact force of 8.4 kN (1888 lb)

Comparison to Moyer Cordelette Testing



19




20


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)

F

o r c 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, Boulder80 m c

80 m b

0 .0005 d t36 α14 β

0 b_s lack

0.4 L11.96 d2.67 L0.78 η

62 25 2 B2657 A2800 λ

6 k_ra tio

4 #_kno ts260 ,435 E

7 ,4 62 D783 C

0.00 r

6000.0 FMF1 grip

4.23 h

1 .5 84 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)

F o r c 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 peakslightlyshifted

Biggereffect on2nd peak



22


0

1000

2000

3000

4000

5000

6000

7000

8000

0.00 0.50 1.00 1.50

position

L

o a d ( N )

Model

Data

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 thebelay hand in climbing falls

• Force measurements in falls compared to slow-motionvideo of the belayer

• Three phases of belay-hand behavior identified

• Inertial Phase• Muscular Phase• Slipping Phase



24

“INERTIAL” PHASE

The hand moves fast

THE UPPER BODY STANDS STILL

THE HAND MOVESFAST



25

“MUSCULAR” PHASE

The hand moves slowly

THE UPPER BODYMOVES

THE HAND MOVESSLOWLY



26

“HAND SLIPPING” PHASE

Possible rope slipping in the operator’s hand

NOTE THESLIPPAGE IN

THE HAND



27

FIX POINT BELAY

FIX POINT BELAY

0

100

200

300

400

500

600

700

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

time ( s )

l o a d

( d a N

)

0

1

2

3

4

5

6

7

8

9

10

d i s p l a c e m e n t ( m )

- s

p e e d

( 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 Fallmc

0.0005 dt7.15 1

4 d11.15 L0.58 η

0 B20920 A3000 λ

_ra o

0.15 r

7.5 FMF290 grip

8 h

0.717 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)

F o r c e ( N )

0.00

0.40

0.80

1.20

1.60

2.00

2.40

2.80

3.20

3.60

D i s t a n

c e ( m )

Runner load

Rope Load

Belay site load (N)


Slide Distance (m)



29

CMT Conclusions on Belaying

• Hand acts as an inertial load for the first few hundredmilliseconds.

• Slip distance is proportional to fall height, not fall factor.Confirmed.

• Peak force occurs at maximum hand acceleration, notat lowest climber position.

• Only a small amount of belayer lifting is helpful (~20cm). More lifting increases fall distance and does notdecrease 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 2.2Time (s)

F o r c e ( N )

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

D i s t a n c e

( m )

Runner load

Rope Load

Belay site load (N)


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 Comparisonmc

0.0005 dt

10 L1

8 d18 L

0.67 η

0 B44100 A

0 λ . _rat o

1 #_knots260,435 E

7,462 D783 C0.00 r

5.0 FMF

400 grip16 h

0.889 F



31

Belay Device Details - FMF Values

240°

120°

120°

120°

120°

80°

Attaway Friction

Analysis

T2 /T1 = e

µ β

Total = 800°

4.4π

T1 = T2 /31

T2

T1

Friction deviceproperties arevery important to

the modelpredictions



32

Belay Device FMF ValuesBlack Diamond Testing

M o t i o n

BelayDevice



33

Friction Device Force Multiplier Values (10.8mm rope)

0.0

5.0

10.0

15.0

A T C

A t o g a

S h e r i f f

B u g

A i r b r a k e

A i r s t y l e

M u n t e r

P y r a m i d

J a w s

V C

R a p t o r

C u b i k

F i x e

F o r c e M

u l t i p l i e r

Low Friction

High Friction

Belay Device FMF ValuesBlack Diamond Test Data



34

Friction Device Force Multiplier Values

Variation with Rope Diameter - (HF side of variable devices)

0.0

5.0

10.0

15.0

A T C

A t o g a

S h e r i f f

B u g

A i r b r a k e

A i r s t y l e

M u n t e r

P y r a m i d

J a w s

V C

R a p t o r

C u b i k

F i x e

F o r c e M u

l t i p l i e r

10.8 mm

9.9 mm9.4 mm

8.1mm




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

A T C

A t o g a

S h e r i f f

B u g

A i r b r a k e

A i r s t y l e

M u n t e r

P y r a m i d

J a w s

V C

R a p t o r

C u b i k

F i x e

F o r c e M

u l t i p l i e r

1.0 lb

18.4 lb

37.7 lb




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)

F o r c e ( N )

0.0

0.5

1.0

1.5

2.0

2.5

D i s t a n c e ( m )

Rope Load


Slide Distance (m)

• Brake BarFMF determinedby trial anderror.

• FMF = 14.3gives a slidedistance equalto the measuredvalue

• Thisunderpredictsthe measuredpeak force

RFR Drop #2

1m drop3m rope length

200 kg test mass

210N hand setting

7/16 Sterling SS rope

RFR Drop #2200 mc

90 θ0.001 dt

3.00 L1.00 h366035 B

318 A10000 λ

_ra o

1 #_knots1,154,688 E

0 D783 C0.20 r

14.3 FMF

210 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)

F o

r c e

( N )

Rigging for Rescue

3/5/05: DT-62 Hand

Average 299 N

Comparison to Rigging for Rescue Drop-Test Data

• Slide distance is afunction of the average

mechanical hand force.

• Peak rope tension is afunction of the peakmechanical hand force.

• Any spikes in themechanical hand forcewill cause highermeasured peak forcevalues.

Rigging for Rescue Data – ITRS 2005



38

Brake Bar FMF - 5 bars - Function of Hand Force

0

10

20

30

40

50

60

0 100 200 300 400 500

Hand Force (N)

F M F

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

M

o t i o n



40

Brake Bar FMF Testing at Black Diamond

Brake Bar FMF - 5 bars - Function of Hand Force

0

10

20

30

40

50

60

0 100 200 300 400 500

Hand Force (N)

F M F

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 bars

at 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

F M

F

Brake Bar FMF Testing at Black Diamond



42

Back to the Original Question

How do TTRL belays compareto climbing belays?

Gripping Ability Required for



43

Required Gripping Ability

for 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)

S l i d e D i s t a n c

e ( 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 forClimbing and Rescue Scenarios

How much slip is too much?

• BCCTR belay standard, 1mmaximum total extension.

• Petzl rope burn warning, 1800J

• Some belay device slip is good -

reduces peak force.

• Too much sliding increaseschance of collisions.

• A reasonable limit might be slidedistance less than fall height.

Averagehuman

gripping ability

Rope Stretch



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)

T o t a l r o

p e e l o n g a t i o n ( m )

Low Angle Belay

Vertical Belay

Low Angle TTRL

Vertical TTRL

Edgetransition

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 Belaysand Climbing Belays



46

• TTRL grip requirements are similar to climbing.

• Teams who prohibit manual devices should alsoprohibit them for lead climbing and rappelling.

• Brake bars are not very high friction devices.

• Unlikely that TTRL belay would ever meet 1mextension 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

Simulation of Climbing and Rescue Belays

Documents

Transcript of Simulation of Climbing and Rescue Belays