Page 206 - J. C. Turner - History and Science of Knots

Studies on the Behaviour of Knots 195

rope would break through creep within a few years [20, p. 242]; in practice,
of course, weathering would have weakened the rope sufficiently to cause a
break before that. Laid nylon rope is less susceptible to creep; when exposed
to a load of 75% of the breaking strength, it took about 10 days to break
[25]. It is suspected that the creep effect is influenced more by the ultimate
elongation of the fibres rather than the rope structure; manila stretches much
less than nylon for a comparable degree of loading and so attains its limiting
stretch well before the nylon, and therefore breaks sooner [20, p. 240]. I know
of no experiments on the effect of creep on the strength of knots. Could it
be that a knot tied tightly in a rope some time before testing would show a
lower efficiency? It would be interesting to examine the behaviour of a knot
exposed for a long time to a high constant load, as suggested by Chisnall [15],
including testing strength and security from time to time and examining what
might turn out to be a slow-motion breaking of the rope.

Shock Forces

It remains to consider the effects of a sudden jerk, such as applied by a falling
weight. This topic is of particular interest to people who might find themselves
falling from a height, with only a rope to arrest their fall; that is, to climbers
and other users of life support ropes (see Chapter 9) The earliest tests of this
property of a rope that I have found were described by the Alpine Club Special
Committee in 1864 [1]. They wanted to be able to recommend appropriate
available ropes to their members. They first eliminated all ropes that would
not hold a 12 stone (76 kg) weight falling 5 feet (1.5 m) and examined those
remaining. They finally recommended a rope which they said would hold a
weight of 12 stone (76 kg) falling 10 feet (3 m), or 14 stone (89 kg) falling 8
feet (2.4 m); any rope that would hold 14 stone falling 10 feet was considered
to be too thick and heavy for convenient use. No details of the experimental
conditions are given, and the results are now difficult to interpret.
It was not until ropes made of synthetic fibres, much stronger and more
extensible than natural fibres, were available that climbers felt at all confident
that their climbing rope might hold them in a substantial fall. The UIAA, the
international association of alpine clubs, sponsored a study by Prof. Dodero of
the physics involved in a fall, and eventually devised a standard for climbing
ropes described below.
Physics of a Falling Weight held by a Rope
Consider a rigid weight mg where m is the mass and g the force of gravity,
attached to an extensible rope of unextended length l fixed at the other end
to a rigid anchorage. The weight is allowed to fall freely a distance h before
the load is first taken by the rope, at which time the energy in the body can