ACCT Rope Behavior 1 objective ACCT Rope Behavior 2 structure ACCT Rope Behavior 3 my sinister puppeteers ACCT Rope Behavior 4 climbing, teaching, research, modeling, consumption of German beer, napping through UIAA meetings ACCT Rope Behavior 5 I’m not a guide, so I can’t tell you how to climb. ACCT Rope Behavior 6 dynamic rope standard ACCT Rope Behavior 7 pictorial images © P Schubert & N McMillan; from http://www.theuiaa.org/uiaa_safety_labels.php 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 8 ACCT Rope Behavior 9 kilo-newtons, einstein, physics kN ~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 10 fall geometry ACCT Rope Behavior 11 fall properties ACCT Rope Behavior 12 energy conservation ACCT Rope Behavior 13 ugh ACCT Rope Behavior 14 more complicated Friction over the top carabiner increases the rope modulus. Belayer behavior and damping (to some degree) reduce the quantity under the radical sign. Small falls are governed by belayer behavior. Severe fallsACCT are Rope governed Behavior by rope properties. 15 Pavier model & damping Spring in series with spring/dashpot parallel combo 35 kN 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/more than half the energy is lost in each cycle 3 kNs 20 kN No model for why this works ACCT Rope Behavior 16 Pavier spring/spring-pot model ACCT Rope Behavior 17 kinematics graphs ACCT Rope Behavior 18 GROMF conditions Table #: Generic, run of the mill fall (GROMF) characteristics quantity symbol Value Units Mass of climber mc 80 kg Acceleration of gravity g 10* m/s2 Rope modulus M 24 kN Rope length L 30 m Free fall height H 2m Fall factor ff 1/15 Spring constant of rope k=M/l 800 N/m ACCT Rope Behavior 19 GROMF result estimates Approximate 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 2 Maximum deceleration amax 30 m/s Frequency (angular) ω 3.2 s-1 Maximum rope tension on climber Tmax 3.2 kN ACCT Rope Behavior 20 goldilocks and the three belayers ACCT Rope Behavior 21 fracture toughness, water, strong acids, and heat transfer characteristics ACCT Rope Behavior 22 experimental data 180 160 140 120 100 Series1 80 Series2 60 40 20 0 -20 0 5 10 15 20 ACCT Rope Behavior 23 Maegdefrau Data sqrt fall factor vs. experimental anchor load verification: 8 6 Mägdefrau Single Rope 4 Rope Pair data 2 anchor load (kN) load anchor 0 0.00 0.50 1.00 sqrt fall factor Maegdefrau Data Load Rate vs. sqrt F/l 0.30 0.25 0.20 0.15 0.10 sqrt(F/l) (m-1/2) 0.05 0.00 0.00 10.00 20.00 30.00 40.00 ACCT Rope Behavior 24 load rate (kN/s) statistical analysis of test facility data: expected error ACCT Rope Behavior 25 ACCT Rope Behavior 26 experimental verification CAI data C. Zantoni et al, CAI, UIAA Meeting Minutes 2005 ACCT Rope Behavior 27 CAI experimental verification belaying forces with slip C. Zantoni et al, CAI, ACCT Rope BehaviorUIAA Meeting Minutes 28 2005 experimental verification CAI fixed point anchor force data C. Zantoni et al, CAI, UIAA Meeting Minutes 2005 ACCT Rope Behavior 29 CAI results from experiments with sharp edge & energy absorption C. Zantoni et al, CAI, ACCT Rope BehaviorUIAA Meeting Minutes 30 2005 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 31 effects of humidity: force ACCT Rope Behavior 32 effects of humidity: drops held ACCT Rope Behavior 33 Again, from A.B. Spierings, et al. in the International Journal of Impact Engineering effects of humidity: elongation ACCT Rope Behavior 34 Again, from A.B. Spierings, et al. in the International Journal of Impact Engineering ACCT Rope Behavior 35 ropes don’t break ACCT Rope Behavior 36 but ropes do Cut & fray Succumb to strong acids Suffer misuse, abuse & new use ACCT Rope Behavior 37 the failure mode is more likely to be Failure of equipment other than the rope Injury to the climber ACCT Rope Behavior 38 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 39 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 belaying UIAA, Standard 101, dynamic ropes EN1891, PPE for prevention of falls from height—Low stretch kernmantel ropes S Attaway, Rope System Analysis C Zantoni et al., UIAA SafeCom minutes http://www.theuiaa.org/act_safety.html ACCT Rope Behavior 40 questions ACCT Rope Behavior 41 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 ACCT Rope Behavior 42.