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Rock climbing in the Southeastern USA |
FAQ: Climbing Physics - Climbing Forces - An Overview
An understanding of the impact forces in a roped climbing system on the gear, anchors, belayer and climber generated when the climber falls is enlightenment that should be at least marginally understood by all climbers. The roped climbing system is continuously evolving as it has since it's earliest inceptions in alpine mountaineering. Climbers adapt methods and gear in response to lessons learned primarily through failures, often fatal, of the current practices. Over time, gear and methods have improved greatly increasing the safety of the climbers. Even so, it still contains the element of risk which is inherent if not defining to the sport. In earlier times, many of the things we now take for granted such as the integrity of our ropes were areas of great concern. Early natural fiber ropes were always questionable. It is impossible to consistently determine the characteristics of natural fibers. Strength would vary throughout the length of the rope, impacts such as rot and deterioration could only be guessed. The security of these ropes was so questionable the cardinal rule of the day was "the leader must not fall". Ropes did tragically fail in numerous circumstances. Fortunately, the survivors learned from these incidents. As technology improved, equipment was modified and redesigned to better address climbing situations. Modern dynamic synthetic climbing ropes are specifically designed for the sport and may now be used with confidence. As with ropes, all other gear has evolved and continues to be improved upon. Factors which complicate the calculations At best, we can closely estimate the forces in an individual climbing system. Assumptions must be made based on the known characteristics of new gear. All gear does degrade with time and use. In particular, the primary shock absorbing mechanism in the climbing system, the rope, loses a bit of it's effectiveness with each fall. Old ropes which have been previously stressed will make for harder falls than a fresh new rope. Other dynamics should be recognized which make calculations less than perfect. While our calculations are based on the characteristics of a new, fresh rope, they make assumptions the the belay anchor is fixed (static) instead of dynamic. A dynamic belay can reduce the forces in the system in several ways. One way is if the rope is permitted to slip a bit through the belay device. A system where the movement of the belayers body weight is incorporated helps dissipate the loads more gradually. If the belayer actively jumps in the direction of rope tension (i.e. jumping upward in a top rope situation), a significant degree of load is relieved throughout the system. Another important assumption is friction, most specifically, the friction of the rope running over a carabiner. Simple calculations can be made if we assume the top carabiner acts like a perfect frictionless pulley. In reality the actual friction generated will vary with the diameter of the carabiner, the diameter of the climbing rope, as well as the friction characteristics of the sheath of the rope and the degree of rope core / sheath slippage. For most climbing calculations a general assumption of top carabiner - pulley friction is assumed as 1.66 (source - Petzl catalogue). A few other factors which are difficult to incorporate are the amount of energy the falling climber's body absorbs (we are not solid masses), the energy dissipated as the knots in the system tighten, the type of belay device used, whether one or two ropes are used, and friction caused as the rope runs through additional carabiners within the climbing system. Simplifying - Using an online calculator The point of all the picky little details above is to indicate that we are not going to derive exact answers to the mathematical questions presented by climbing situations even with some involved calculus. There are just too many variables and complexities. However, it is possible to understand some basic principles and derive working solutions that tell us a lot about what forces we can expect to find in a variety of instances. We'll be looking at two basic elements: The amount of energy produced during a fall, and the impact force felt by the climber. The amount of energy produced during a fall is determined by the weight of the climber and how fast he is falling when the rope catches him. It is expressed mathematically as: Energy of Motion = ½ mass x velocity² As a climber falls, he accelerates. The longer the fall, the faster he is going when the rope comes tight, therefore more energy must be absorbed by the system. The impact force is how much force is felt by the climber, belayer, or the individual components of the system. It is determined by the length of time over which the fall is stopped determined by the energy absorbing characteristics of the rope and the weight of the climber as well as all those subtle nuances mentioned above. If there were not elongation designed into dynamic climbing ropes, or if a static rope with essentially no stretch is used, the force of stopping the climber almost instantaneously is enough to break gear and rock, snap your spine, and cause deadly internal injuries. Fortunately, dynamic climbing ropes are built to absorb the energy of a fall by stretching. They are specifically designed to insure a climber is able to withstand the forces of a worst case factor 2 fall (See FAQ: Fall Factor) without serious injury. Thanks to the energy absorbing design of dynamic climbing ropes, while a longer fall produces more energy (the climber is falling faster when the rope comes tight), the longer amount of rope in play allows more of the energy to be absorbed keeping the forces within survivable limits (See FAQ: Fall Factor). A dynamic climbing rope must be designed to absorb enough energy so that the maximum force on an 80 kg. (180 lb.) climber in a factor 2 fall is not more than 12 kN. (2698 lb.) (See What is a Kilonewton). Calculating the impact force in a fall requires some relatively complicated math, at least for most of us. Variables include the length of the rope, the length of the fall (ratio of these two factors = the fall factor), the static elongation characteristics of the rope (modulus), and the weight of the climber. Fortunately, there are several good climbing impact force calculators on the Internet, one of the best of which is found at http://www.myoan.net/climbart/climbforcecal.html. I'll try to spare you the impact force calculations by referring to the online calculator when needed when we look at the following:
Rather than get too specific, my goal is give you a basic understanding of what kinds of forces arise in climbing systems and how they are generated. With this knowledge, you can better understand how to evaluate and accommodate these forces as you climb. You can go further and experiement with the Impact force calculator by adding the specifics of your weight and rope characteristics to see what you can personally expect to experience in specific instances. Rope Systems Analysis (a 13 page DETAILED discussion, complete with physics): http://www.amrg.org/Rope_system_analysis_Attaway.pdf The Physics of Climbing (for the truly mathematically minded, A very technical explanation of how physics applies to rock climbing) http://student.kuleuven.be/~m9916724/physics/physics.htm Loads, Energy & Ropes (the discussion is about caving, but the principles are the same): http://www.bstorage.com/speleo/Pubs/rlenergy/Default.htm Fall Factor
and Climbing: Impact force calculator
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