130 Kane et al.: Impact Force and Rope Tension Figure 2. Least squares means (whiskers represent SE) of percent cut for each rope tension (from left to right, columns correspond to 111, 156, 200, 267, 311, 356, and 400 N) within each swing. Swings followed by an asterisk (*) indicate percent cut varied among rope tensions within that swing by orthogonal polynomial comparison (p < 0.0001). Within Quarter, Half, and Three-Quarters swings, the quadratic comparison among rope tensions had the greatest F-value. The overall least squares mean of percent cut () was also significantly different (p < 0.0001) among swings (S); the best-fit line (r2 + 0.3101S - 8.9563. = 0.57) was quadratic: percent cut = -0.0002S2 entails a pole saw falling from a branch and contacting the climb- ing rope; this could generate large impact forces, depending on the mass of the pole saw and how far it fell. Impact force of the blade on the rope is considered in each of these examples. Impact cutting of a rope under tension likely does more damage to the rope than either slowly cutting the rope (under the same tension) or cutting the rope and then applying static or dynamic tension, as observed on nylon kernmantle ropes (Contri and Secchi 2002). Regardless of the circumstances when the rope and blade come into contact, it is important to remember that for the amount of damaged fibers in the rope, cutting reduces rope strength more than fibers lost through normal abrasion (Flory 2008). The negative quadratic best-fit lines relating percent cut to (a) the overall effect of increasing impact force, and (b) the effect of increasing rope tension within half and three-quarter swings, indi- cate impact forces greater than 267 N are very likely to completely sever the rope, regardless of rope tension. In contrast, the positive quadratic relationship between percent cut and increasing rope tension within quarter swings demonstrates that, at small impact forces, increasing rope tension increases the likelihood of com- pletely severing one’s climbing rope. Curvilinear trends were ex- pected because the mechanical behavior of rope is typically non- linear (McLaren 2006). It is speculated that there is a rope tension, even at small impact forces, at which all ropes would be com- pletely severed. When an 81 kg climber is tied-in to a tree with the conventional doubled rope technique, there is approximately 400 N of tension throughout the rope. Ascending into the tree using the single rope technique (SRT), however, means the climber’s full weight (800 N) tensions the rope. Thus, doubling the rope tension may more than double the risk of completely severing one’s climb- ing rope at small impact forces. Climbers who use SRT for ascen- sion should be extremely cautious when using their handsaw dur- ing an ascent, for example to remove a sucker blocking their path. The lack of difference between Poison Ivy and XTC, which have different diameters and constructions, supports previous findings where these ropes did not differ when cut by several dif- ©2010 International Society of Arboriculture ferent blades (Kane et al. 2009). It is unclear why this occurred, but it is speculated that the different constructions impart dif- ferent degrees of friction between fibers and yarns within each strand. In their numerical simulation of cutting kernmantle ropes, Contri and Secchi (2002) predicted that as friction coefficients in- creased, transverse displacement of the rope into the blade would decrease. They also observed significant transverse displacement of ropes in the direction of the blade during experimental tests in which the rope was transversely unconstrained, which caused a deeper cut (Contri and Secchi 2002). Since their test method was similar to the method used in the current study, greater friction among strands in the sheath of Poison Ivy may have reduced its transverse displacement into the blade, reducing the depth of cut. The authors do not intend to understate the danger of cutting oneself out of a tree using a handsaw. However, assuming a rough- ly one-to-one relationship between the degree to which a rope is cut and its subsequent loss in strength (Kane et al. 2009), it is helpful to remember a 50% cut would reduce the average tensile strength of Poison Ivy and XTC to roughly 14 kN. This value still exceeds the 12 kN impact force at which the human body would presumably suffer life-threatening damage (Anonymous 1953), and which is used as the maximum impact force in standard drop tests (Anonymous 2004). Thus, even relatively severe cuts do not always and immediately imply rope failure and climber injury. Future tests should consider used ropes, since normal wear and tear gradually reduces the number of rope fibers and weaken the rope. In the near term, it is impractical to cost-effectively manufacture cut-resistant rope that also maintains the current balance of strength, abrasion resistance, and energy absorption. A simpler approach to avoiding accidents involving climbers cutting their ropes is to raise awareness of the possibility of such accidents, and training climbers to consider where their rope is in relation to where they are cutting. Acknowledgments. We thank Bartlett Tree Experts for funding this proj- ect, Yale Cordage for donating rope, and Wesley Autio and Dan Pepin (University of Massachusetts) for statistical advice and designing and building the pendulum, respectively. LITERATURE CITED Anonymous. 1953. Force distribution in a parachute harness (interim report). Equipment Laboratory, Directorate of Laboratories, Wright- Patterson Air Force Base, Ohio. U.S. Air Force Technical Memoran- dum Report WCLE-53-292. Anonymous. 2004. Mountaineering equipment—dynamic mountaineer- ing ropes—safety requirements and test methods. European Commit- tee for Standardization CEN-EN 892. Contri, L., and S. Secchi. 2002. Snapping of ropes under stress. In: Nylon and ropes for mountaineering and caving, Italian Alpine Club Techni- cal Committee, Turin, Italy. Flory, J. 2008. Assessing strength loss of abraded and damaged fiber rope, pp. 227–234. In: Oil Companies International Marine Forum. Mooring Equipment Guidelines 3rd Ed. Witherby Seamanship Inter- national, London, England. Georgia Arborist Association. 2009. Industry Incidents in Georgia. . Kane, B., M. Cloyes, M. Freilicher, and H.D.P. Ryan. 2009. Damage Inflicted on Climbing Ropes by Handsaws. Arboriculture & Urban Forestry 35(6):305–310. McLaren, A.J. 2006. Design and performance of ropes for climbing and sailing. J. Materials: Design & Applications 220:1–12.
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