| Physics for Cavers: Ropes, Loads, and Energy |
 |
By William Storage & John Ganter
Everyone knows that force is what breaks a rope. But some might not realize
that the force a rope experiences depends heavily on the properties of the rope
itself. Few aspects of caving cause as much confusion as so-called shock
loads. When cavers use this term they are usually talking about dynamic
loads resulting from stopping a fall. When scientists talk about shock loads
they are concerned with extremely rapid load application, such as that
encountered in ballistics studies—nothing like what cavers mean. To a scientist,
our loading conditions are simple physics, the stuff Newton worked on. But this
"simple" Newtonian physics has important implications for rigging and vertical
technique.
Dynamic loads arise from acceleration or deceleration of a mass. Weight is
merely a static load, the consequence of gravity pulling on a mass. The
relationship between the weight of an object and the force generated by its
acceleration is more subtle. A falling body accelerates because of gravity, but
this does not cause a dynamic or "shock" load. The dynamic load is caused when
the body stops falling; when it is decelerated by an applied force. This force
can come from a rope, or the ground. As the rope begins to store the energy of
the falling climber, the load increases. It then decreases, during the rebound,
down to a static load, the climber’s weight.
Unlike popular usage, engineers and scientists have specific meanings for the
commonly used terms. This is not merely jargon, because it prevents some of the
misunderstandings that can lead to bad conclusions—a valid concern for cavers. A
force is simply a load; a push or pull on an object. It can be thought of
as a muscular effort. Formally, work is the product of force and
distance; the distance through which the force acts. When a 180-lb climber
ascends ten feet up a rope, he does 1800 lb-ft of work against gravity.
Energy is the capacity to do work. The amount of energy something
possesses is exactly equal to the amount of work it can do. These concepts are
needed to understand the way a rope behaves during a fall.
When a force is applied to an object, it deflects. Most objects deflect
elastically, like a spring, up to a point. When the applied force is removed,
the deflection goes away. Energy is stored in the elastic deformation. Think of
stretching a Slinky toy. Beyond an elastic limit, plastic deformation, or
yielding occurs. Think of ruining a Slinky by stretching it too far.
Energy is consumed in the yielding process; the object doesn’t go back to
its original shape.
Figure 1: Rope characteristics represented graphically: The curve shows the
elongation of a 10-foot length of 10-mm caving rope under loads increasing to
the point of failure. The energy of a falling climber is merely a consequence of
his static weight and the distance fallen. With these rope characteristics, the
load resulting from deceleration can be determined graphically.
Every object can be viewed as a spring. It has a spring rate, a
measure of the force required to deflect it an incremental amount. With some
objects and materials, the spring rate is not constant, such as a rubber band
that at same point suddenly gets very hard to stretch any farther. Steel does
the opposite; once plastic deformation begins to occur, small increases in load
have much larger effects on elongation. Most ropes have a fairly constant spring
rate. Spring rate is easily seen graphically. It is the slope of a graph of
force versus deflection (load vs. elongation).
Static rope is designed to have low stretch. Therefore, it has a high spring
rate, compared to dynamic rope. A force versus deflection curve for a 10-ft
length of typical 10-mm static caving rope is shown in Figure 1. It is important
to note that this curve, and the spring rate derived from it, are for a specific
length of rope. As with a coil spring, increasing the length decreases the
stiffness, thus decreasing the spring rate. Cavers notice a lot of bounce at the
bottom of a long, free pitch. Nearer the top, the effective "spring" length is
short and the spring rate is higher; you don’t bounce as much.
An interesting aspect of the curve in Figure 1 is that since work (or energy)
is the product of force and distance, the area under the curve equals the energy
required to break the rope.
In rock climbing, a belayed fall is a common occurrence. In a belayed fall
much of the energy of the falling climber is converted to heat, because of rope
drag through the carabiners at each point of protection. Because of rope stretch
between the belayer and the climber, this is true even if no rope slippage
occurs at the belay point (a "static" belay as viewed by the belayer). But
usually, a lot of additional energy is absorbed or converted to heat by the
belayer (a "dynamic" belay). These factors significantly reduce the resulting
loads. In caving, falls are rare, but often result in a perfectly static belay,
as is the case when a rebelay or secondary anchor fails. Even if climbing rope
were used for underground rigging, the loads resulting from anchor failure would
be much greater than the loads resulting from a fall of the same length in a
normal rock climbing situation.
Consider a caver, who falls from his anchor point, with some amount of slack
in the rope. From the definition of energy we see that he possesses energy (of
falling: kinetic energy) equal to the product of his weight and the distance
fallen. In this situation friction is negligible; his energy must be absorbed by
the rope. If his energy is greater than the rope’s energy storage capacity (the
area under the curve), the rope will break.
If his energy is less than the energy storage capacity of the rope, he will
experience an impact force, a dynamic load, when the slack goes out of the rope.
His impact force (the force he and the rope and all the other rigging components
experience) can be determined by starting to shade in (from left to right) the
area under the rope’s load-elongation curve. When the area shaded equals the
area represented by the falling climber’s energy, we can read the impact force
(cavers’ "shock load") right off the graph. To be accurate the climber’s weight
must be added to the resulting load, since it exists independent of the fall and
dynamic load. For simplicity, we’ll deal only with the dynamic portion of the
load.
In the example of Figure 1, a 180-lb person takes a 5-ft fall, yielding 900
lb-ft of energy. From the graph we see that this energy results in a load of
about 1900 lbs and a rope elongation of about 1 ft. This exercise shows, without
the use of equations, that the dynamic loads on ropes and belay anchors are the
consequence of rope characteristics.
Figure 2 shows another version of the load-elongation curve. This time the
elongation axis of the graph has been normalized to express elongation as
a fraction (of the original, unstretched length) for a variety of ropes, etc.
One foot of elongation in a 10-ft rope results from the same force that will
cause 2 ft of elongation in a 20-ft rope; on this graph each elongation would be
0.1.
Now, remembering the definition of energy, we’ll note that doubling the
amount of slack in the rope before falling will double the distance fallen
before the slack is used up, thus doubling the kinetic energy.
Combining these concepts lets us conclude that any increase in energy caused
by increasing the amount of rope slack will correspondingly increase elongation,
leaving the percent elongation unchanged. No change in percent elongation means
no change in load; and the concept of fall-factor is born.
Fall-factor is the ratio of distance fallen to available rope slack (Figure
3). From this simple physics exercise we conclude that all falls of the same
fall factor result in the same deceleration rate, regardless of the absolute
distance fallen. In practical caving applications, conditions such as knot
tightening, deflection of the human body, and harness movement on the body tend
to significantly reduce loads in short-fall and low-fall-factor situations. But
for our purposes we’ll use this conservative and simplified model of reality.
The climber in the examples above who fell from his belay point had a fall
factor of one, regardless of the amount of slack.
In Figure 2 the energy storing capabilities of the ropes, webbing and chain
can be used to determine the load (force) experienced by a climber falling with
various fall factors.
For the chain the total area under the curve, to the point of failure, is
about 120 lb-ft per foot of rope/chain. That represents the energy, per
foot of unstretched chain, that will result in enough load to break the chain.
Fall factor, the total number of feet you can fall, per foot of rope, equals the
area under the curve divided by the climber’s weight.
In the case of the chain, a 180 lb-climber would break the chain with a fall
of fall factor 0.67 (120 lb-ft per foot divided by 180 lbs. equals 0.67).
Unfortunately, humans cannot survive deceleration forces of 7800 lbs, the
strength of the chain. At best, they can take about 15 G’s (a force of 15 times
their weight). The Union Internationale des Associations d’Alpinisme (UIAA) uses
2650 lbs as a maximum tolerable load for evaluating climbing ropes. For 2650 lbs
on the chain, we calculate a fall factor of about 0.07. Helpful hint: do not
belay with chains.
From the climbing rope curve, we calculate that a fall factor of 2.3 (by
definition, fall factor 2 is the maximum possible) would be needed for a 180-lb
climber to experience a deceleration load of 2650 lbs. In other words a fall of
any length on a climbing rope might be survived if the faller didn’t hit the
ground or a ledge before being decelerated by the rope. Hence the survival rate
of bungee jumpers.
From the curve for a 10-mm caving rope, we calculate that 2650 lbs equates to
a fall factor of 0.7 for a 180-lb climber. This confirms what rope manufacturers
tell us; lead climbing with caving rope can be risky and painful. A fall on a
10-mm caving rope will end in a load about three times greater than that
resulting from the same fall on a climbing rope. A stronger 11.5-mm caving rope
would result in a load about 10% higher yet, because its spring rate is
10% higher.
The issue of rope softening
Readers should be aware that the curves in Figures 1 and 2 are roughly
accurate for new ropes. A lot of attention has been given to the reduction in
rope strength that occurs with age. However, very little has been done to assess
the change in spring rate, and the energy handling capability of an old rope.
Unfortunately, spring rate is in most ways much more important for surviving
falls than the strength value. Tests by Smikmator (1986) and Kipp (1979) clearly
show that old rope is stiffer and produces higher loads than a new rope subject
to the same fall. Testing by Stibranyi (1986) on Czechoslovakian climbing ropes
produced the opposite results. Theory would tend to support the former
conclusions, though. Testing by the German Alpine Club (Microys, 1977) showed a
significant increase in stiffness of new climbing ropes that were cold and wet.
Tests conducted in a study by Smith (1988) indicate that treatment with
concentrated fabric softener reduced the strength of a new rope. Frank
(1989) showed that certain ropes treated with dilute softener (per
manufacturer’s recommendations) were stronger than the same rope without
softening, after aging and washing. Frank reported that the likely mechanism at
work explaining these results is that the fiber lubricants contained in new rope
are lost with age, allowing the fibers to cut one another. Fabric softener
replaces some of the lubricants. Excess softening leaves the rope effectively
wet, with the corresponding loss in strength.
With this mechanism in mind, a further argument for treatment with fabric
softener would be its effect on spring rate. Since a rope’s spring rate is
determined by both nylon material properties and fiber weave, it is likely that
fabric softener will help prevent stiffening due to loss of internal
lubrication. In dynamic situations, the underlying physics shows that preserving
the spring rate is as important as preserving its strength toward the goal of
avoiding rope breakage. Probably more importantly, preserving the spring rate
will avoid the higher climber loads in falls that would come from a rope that
had become stiffer with age.
Strength misconceptions
Now that everyone understands the science, let’s go back and look at the
popular misconceptions. Much of the caving literature uses such terms as "shock
strength." This probably originated from intuitive physics, which while
frequently accurate, has failed us miserably here.
The fallacy probably came from a situation like this. Two ropes, one nylon
and one polyester, had the same strength, as measured by pull testing. But in a
fall-factor = 1 situation, the polyester snapped like a twig and the nylon was
unharmed. The obvious conclusions are that "shock strength" is a radically
different property than tensile strength, that dynamic testing is needed to
evaluate it, and that polyester has lower "shock strength" than nylon.
To an extent the latter conclusion serves us; we avoid belaying with
polyester rope. But the first two conclusions are dead wrong, and have
encouraged us to do a lot of unscientific dynamic testing, sometimes drawing
even more inaccurate conclusions. Misinterpretation of test results has led
cavers and rescue enthusiasts to believe that the speed of load application
encountered in falls greatly affects the strength of the rope. Testing of nylon
materials and seat belts by the aircraft industry simply does not support this (Figucia
1969). As we have seen, the speed of load application affects the value of the
load (because of the deceleration rate), not the strength of the rope.
Probably the most harmful result of this situation is that "shock strength"
has encouraged us (and equipment manufacturers, through competition) to make
everything stronger. Some have advocated making caving rope stronger, to resist
being cut by ascenders in the event of an anchor failure. Unfortunately, if low
stretch is to be retained, stronger static rope will necessarily be stiffer, and
the benefits of higher strength may not be realized because the greater
stiffness causes higher deceleration loads. The probable end result is that
there is a negligible reduction in chance of rope failure and a significant
increase in chance of victim injury from high deceleration loads.
Another concern of dynamic loading is knot strength. Sharp bends in knots
result in some fibers being loaded much more than others—a stress
concentration occurs. Consequently they reach their ultimate load capability
first and fail, leaving the remaining fibers more highly loaded and subject to
failure. Knots used in caving reduce the rope’s strength by 30-60%. For normal
loading this is completely irrelevant. It only becomes important when the
knotted rope strength falls below the threshold of human load tolerance in a
dynamic situation such as a fall. Standard water knots, bowlines,
lasso-bowlines, and figure-8s will reduce strength by about one half. A knotted
8mm rope, then, can fail with loads less than 2000 lbs. Thus knots with more
gradual bends, causing less stress concentration, such as the figure-9 knot
(Figure 4), must be used. It is reported to cause a strength loss of about 30% (Marbach
1980).
In some circumstances, knot slippage can reduce dynamic loads by decreasing
deceleration rates. Use of shock-absorber knots has been advocated by several
caving texts. Alan Warild (1994, p. 54) presents convincing evidence that the
effect is too variable and unreliable to be used in caving. The shock-absorbing
knots, usually overhand loops, might reduce loads, but they will
definitely reduce strength of the whole system, provided the rest of the rigging
is done correctly.
Recommendations
In summary, while an investigation into dynamic loading might initially
appear to be merely an academic pursuit, several specific recommendations arise
from it. In addition, the general concept of "stronger means better" is further
revealed as dangerous and nonproductive. Some important implications of this
study are:
Acknowledgments
We would like to thank Dr. Walter Paul for his comments and observations on
the use of ropes in caving and climbing. Dr. Paul is a nylon rope specialist at
Martin-Marietta and an advisor to the US Navy on rope use. Dr. Peter Gibbs of
Gibbs Products shared his observations on the popular misconceptions of rope
physics and their implications. We would also like to thank Steve Hudson of PMI,
and fellow STC members Andy Grubbs and Steve Worthington for their assistance in
reviewing this article.
Bibliography
Brew, Brendon. 1977. Test Methods for Caving Equipment. Proceedings of the
7th International Speleological Congress. Sheffield, England.
Figucia, F. 1969. The Effect of Strain Rate and Ply Geometry on the
Stress-Strain Properties of
Nylon Yarns. Army Natick Laboratories, Natick, Mass. September 1969.
Frank, James A. 1989. Fabric Softener and Rescue Rope. Nylon Highway
128, July 1989.
Kipp, Michael. 1979. On the Practical Strength of Kernmantle Ropes. Caving
International 15, October 1979. pp. 37-40.
Marbach, G. and J.L. Rocourt. 1980. Techniques de La Speleologie Alpine.
Choranche, France.
Microys, Helmut. 1977. Climbing Ropes. American Alpine Journal 21:l:5I
pp. 137-147.
Smikmator, Ferdinand. 1986. Research of Properties of Ropes. Proceedings
of the 9th International Congress of Speleology. Barcelona, Spain.
Smith, Bruce. 1988. Effects of Rope Aging. NSS News 46:4, April 1988.
Stibranyi, Gustav. 1986. Tests and Practical Experiments with Czechoslovak
Climbing Ropes, Used in
Speleology. Proceedings of the 9th International Congress of Spe1eology.
Barcelona. Spain. pp. 324-328.
Warild, Alan, 1994. Vertical. Sydney, Australia: The Speleological
Research Council Ltd. pp. 64-66.
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Publication History
| 1990 | NSS News [National Speleological Society USA] 48:12, December 1990, pp. 316-319 | |
| 1998 | online versions (HTML and Adobe Acrobat) at http://www.bstorage.com/speleo/Pubs/rlenergy/Default.htm (v07, 3 September 1998). Images changed to higher resolution on 9 October 2000. | minor revisions |
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