In reply to jkarran:
Indeed. But I think the "bigger arc" is often confused with the "soft catch," although in principle different concerns are at play. The ankle-shattering short fall happens when the climber swings into the rock at relatively high velocity because if the short pendulum arm. If (and this is critical) the rock is continually overhanging, then lengthening the fall will allow the climber to be at a point in the swing past the low point of the pendulum arc, a point where they will be moving up and slowing down. If the rock overhangs enough and/or enough rope is let out, they won't hit the wall at all. All this happens as a result of more rope in the system, but is not directly related to belayer behaviors such as jumping, whose primary goal is not to lengthen the fall (although that is a consequence) but to engage energy-absorbing mechanisms other than rope stretch.
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I can also offer an old-timey perspective on belay testing with dead weights. It was very common in the US in the late fifties and early sixties when I learned to climb. I think the primary reason was a booklet published by the Sierra Club in 1956 (the year before I started climbing), "Belaying the Leader---An Omnibus on Climbing Safety," by Richard M. Leonard, Arnold Wexler, William Siri, Charles Wilts, David Brower, Morgan Harris, and May Pridham. The lead article, by Leornard and Wexler , was a reprint of one they wrote for the Sierra Club Bulletin ten years earlier (Sierra Club Bulletin 32 (7) (December 1946). Four years later, Leonard wrote an article for the 1950 American Alpine Journal entitled “The Theory of Belaying” that contained a mathematical account of his approach to belaying. At that time the first kernmantel rope (by Edelrid) was still three years away. Laid nylon climbing ropes were first employed in the US by the military in the early 1940’s for the 10th Mountain Division troops, after testing virtually every possible fiber. But in 1946, climbers were still transitioning from manila to laid nylon ropes and the idea that a leader fall might break a rope was still in the air.
In the introduction to the mathematics in the AAJ article, Leornard says, “The methods of rope-handling that serve to absorb this energy can be used to classify the belay into three fundamental types: the rigid or static belay, the resilient or indirect belay, and the dynamic or sliding belay. The static belay is one in which the kinetic energy of a fall is absorbed by the rope alone, one end of which is fixed to a rigid support, such as a tree or horn of rock. In the resilient belay, the support as well as the rope absorbs energy by yielding or “giving” under load, as in the case of the belayer snubbing the rope around his body. In the dynamic belay, the rope is allowed to slide over the support so that the friction of the sliding rope absorbs energy in addition to the energy absorbed by the rope in stretching. It will be shown that the dynamic belay is the most efficacious for it is capable of fully absorbing the energy under loads easily tolerated by men and equipment.” You can read the text of the AAJ article at
http://publications.americanalpineclub.org/articles/12195037900/print but the transfer to the web has obliterated all the mathematics.
So what Leonard proposed, demonstrated mathematically, and verified by belay tests with steel weights was that climbing loads could be kept within “reasonable” limits by allowing rope to side under tension through the belay. (The UIAA’s 12 kN limit was, of course, not known then, but it would have been regarded as too much for the equipment of the day.) Leonard calculated how much rope should be allowed to slide, and with those guidelines advocated for belay practice to learn how to do this.
Subsequent development of climbing ropes made Leonard’s dynamic belay seem less relevant. Although belay device engineering (until the Gri-gri) included explicit “safety-valve” considerations that would allow the rope to slip through the device when loads reached a certain level, it is no longer deemed necessary to practice what to do if such extreme circumstances occur. But back in the fifties and sixties, almost everyone getting into climbing in the US learned the dynamic belay by catching steel weights. It was obvious that you had to practice this to achieve Leonard’s ideal rope runs. As college undergraduates, my friends and I set up a system on a stadium catwalk that provided UIAA-level falls, with the weight plummeting past the belayer. Almost no one could stop these falls the first time they tried, which made the practice seem like it meant something. In my case, the experience seemed to pay off, as I have had to catch one factor-2 fall and one factor 1.7 or so fall, both of which were accomplished without a hitch and with no rope burns or injuries to the me as the belayer. (The leader wasn’t so lucky on the factor 1.7 fall.)
Perhaps this rather universal US belay practice leaked over to the UK, although maybe not accompanied by all the theory justifying the practice?