Exploring the Secrets of Knotted Cordage
to Understand How Knots Work
We do not know
half of all there is to be discovered about knots.
Under the circumstances, it behooves the layman to speak
skeptically rather than dogmatically about why knots behave the way they do.
For all puzzles
there is always a beautiful solution.
When Thor asked the mayor why he had never before revealed the secret of hauling the moai upright, he replied, ÒNobody asked me.Ó
Knots were among the first practical devices created by
human beings and one of the few primitive inventions we continue to use. They
are part of our common humanity. Surprisingly, few people show much interest in
them or how they work.
People tie knots, use them, teach them, but rarely stop to analyze them.
– aak
The characteristic
that distinguishes knots from other objects created by mankind is their
structure. Analysis of the structure of several familiar knots and how they
bring to bear mechanical forces reveals the devices that determine their
performance. From this analysis, answers are emerging to the question ÒHow does
a knot work?Ó
Knots work by
creating friction between intertwined strands of rope. They fail to work in
three ways: when they slip apart under a normal load, when they deform and slip
apart under an abnormal load, and when they break under an excessive load. By
examining how particular structures of knots harness universal mechanical
forces, we can come to understand the factors that make knots hold together and
those that cause them fail.
The original
studies of knot performance collected here lead you to an understanding of how
any kind of knot works. They show you
¥ How to use
the step-by-step procedures of structural analysis to examine the structure of
knots.
¥ How to
understand the elementary principles of mechanics that affect knot performance.
¥ How to
understand the interaction of structure and mechanics that makes a particular
knot behave the way it does.
¥ How to
examine the three essential properties of practical knots, their security,
their stability, and their strength; and, as part of the background to the
study of knot strength, how to examine the breaking point of knots.
The focus throughout these studies is on the interaction of
mechanical forces with the structure of knots tied in standard materials and
applied in uniform conditions. Some of these studies pertain only to knots tied
n ropes made of natural materials, but many of the concepts and procedures
apply to all knots. Although the
results of the studies can be useful for analyzing the various ways to tie
knots and to use them in rope systems, they are not directly concerned with
these skills.
Learning these
techniques for analyzing knots can develop your concepts of knot performance,
improve your selection and use of knots, and increase your knot safety.
Anyone who drives
an automobile probably knows more about what goes under the hood of a car than
inside a knot. Even many people who depend on knots to support life or heavy
loads fail to take an interest in their inner workings. The way they function
often seems as mysterious as a computer, where the mechanisms are complex and
hidden from view. While the structures that make knots perform the way they do
are simple and open for all to see, they have become so familiar and
commonplace that we usually fail to notice them. In addition, they interact in
subtle ways. Because few people have asked how knots work or have devised
fruitful ways to study them, their inner workings are little understood.
As far
as I have discovered, no one has previously developed a systematic method for
analyzing the structure and mechanics of a knot to determine its holding
properties, and no one has presented a general explanation of how knots work
and why they behave they way they do.
In developing these
studies during the past several years, I have been surprised that so few people
are aware of how a knot works. Even among persons who depend on knots for
supporting life and loads, the study of knot performance is often neglected.
Inquiring about the essential characteristics of knots has not become part of
habitual patterns of thought. When I describe the procedures and results of my
studies of knot performance, the usual response—even from experienced
knot users who are engineers—is, ÒI had never thought of that.Ó
These paper move
toward answers to several questions about knots that have often been neglected:
¥ How do a
Bowline or a Double FishermanÕs Knot perform under a normal load?
¥ Can you tell
whether a knot is secure just by examining and analyzing it?
¥ Of common
knots, which are the most secure? What structures make them secure? How do
these structures work?
The study of knot
stability focuses attention on the distinction between stability and security. These two aspects of knot performance
are frequently confused and even more frequently entirely ignored.
¥ How does a
particular knot behave when subjected to an abnormal load?
¥ How does
deformation of a knotÕs structure lead to failure?
¥ Which common
knots are the most stable? What makes them stable?
¥ How can the
instability of a knot be used for a desirable purpose?
¥ How does the
stability of a knot affect its security? Can a knot be secure but unstable?
¥ When placed
under an excessive load, a Bowline tied in a rope made of natural fiber usually
breaks at a point just outside the knot. Why does it break there?
¥ Under an
excessive load, where does a Double FishermanÕs Knot tied in the same
natural-fiber rope usually break? Why does it break there?
¥ Can the
findings about natural-fiber ropes be applied directly to artificial-fiber
rope? Or do they have to be adapted? Or abandoned?
¥ Are there
general principles that determine where any knotted rope will break?
¥ What have
tests shown about the comparative strength of knots?
¥ What
structures make some knots stronger than others?
Finding answers to
these questions entails close examination and analysis of several knots against
a background of other writings.
The current studies
focus on only a few practical knots tied in rope made of natural fibers and
used in standard conditions. For this reason, the procedures and concepts
developed here apply only in a limited way to knots tied in other materials and
used in different conditions.
The long-range aim
is to develop a set of concepts and procedures to discover fundamental
principles that apply to all practical knots tied in any material under any
conditions of use and in any atmosphere. These studies attempt to lead in that
direction, however distant the goal may be.
Many of the
procedures can be applied to the study of individual knots regardless of the
materials or conditions. Their chief value for these kinds of knots may well be
that they draw attention to aspects of knots that are usually overlooked and
provide a way to study them. In this way, they help to arouse interest
in knot performance and to extend the boundaries of our understanding.
These studies
contribute to our understanding of knot performance in several ways. They
¥ Emphasize
knot performance, an aspect of knot study that is poorly understood and often
neglected.
¥ Bring
together what is known about knot performance and present the results of an
original examination of the relation between knot structure and mechanics and knot
performance.
¥ Provide a
method for estimating how well a knot will perform.
¥ Analyze a
few familiar knots to help knot users understand the way that any practical
knot works and how it fails to work.
¥ Supplement
what we have learned about knots from tests and from experience.
¥ Help to
raise awareness of the way knots work and to develop habitual ways of thinking
about them.
¥ Reduce the
risk of using knots for life support.
¥ Demonstrate
a way to discover general principles of knot performance.
¥ Develop
hypotheses that can be demonstrated and tested further.
¥ Provide
concepts and appropriate terminology to facilitate discussion among people who
use knots and those who study them.
¥ Suggest
several questions and lines of thinking for further study of the properties of
knots.
¥ Suggest
principles that can be used for more scientific and technical study of knot
performance.
¥ Provide a
conceptual basis for further research.
In addition to
these practical applications, a valuable effect of this kind of knot study is
to increase our wonder at knots. Although their structure and performance are
usually overlooked by people who use them daily, they are marvelous little
devices.
I have found it
necessary to introduce several new terms and to narrow or re-define several
others. All of the terms used in these studies are explained in the separate
paper on terminology as well as in the individual studies.
These studies are
arranged in a sequence that builds a comprehensive scheme for studying knot
performance, but each paper can be read without reference to the others. To
make the individual studies intelligible, I have repeated some of the key
concepts and terminology.
The focus in these
studies of knot performance is on a systematic way of thinking about knots
which is based primarily on observation and analysis. The study focuses on how
a knot works rather than
how to tie it or how to use it. The analysis leads to conclusions about
the performance of individual knots, but the general aim is to show how to use
procedures that lead to the conclusions, not only the conclusions themselves.
People usually
think about knots in two ways, 1)
how to tie them, 2) how to use them. These studies on knot performance include
these two ways of thinking but focus on a third: knots are devices that can be
analyzed into their functional parts to see how they work.
Consider how
learning about knots is like the typical stages of learning about driving a
car.
1. Learning to tie
a knot is like learning the location and function of the instruments of a
car, the gear shift lever, the
steering wheel, the brake pedal, and so on. YouÕre not actually driving, but
youÕre preparing to by becoming acquainted with how to manipulate the controls.
2. Learning to use
a knot in practical applications is like learning to drive a car. You learn
skill at steering, signaling
direction change, accelerating, and braking. You also learn how to follow the
rules of safety and motor vehicle laws. You can pass your driver education
course and get your license.
3. Learning to
understand how a knot works is like learning what goes on under the hood of a car,
in the engine, the gear box, the differential. Few people become knowledgeable
about how a car works, fewer how to repair it or make it perform better. Fewer
still learn that sort of thing about the knots they tie and use. In fact, I
have found very few people who have thought much about the matter.
The discussion on
the next page shows how structural analysis goes beyond the traditional ways of
thinking about knots and builds new concepts.
Expanding
Our Ways of Thinking About Knots
Despite the introduction of numerous inventions that replace
knots, knot use appears to be alive and well around the world. But whatÕs
missing in almost every case I have observed is an interest in understanding
how they work—what makes them secure and stable, where they break, and
what causes some to be stronger than others.
These studies on knot performance develop a new and
broader way of thinking
about knots. Consider how we can develop new perspectives on learning knotting
skills:
1. Beginning Learners Think of Knots as
Ways of Tying.
The main interest of anyone learning to tie knots, from a
Cub Scout to an adult candidate for a rescue squad, lies mainly in learning the
procedures for tying a particular knot. Most of the instruction found in knot
books, on the web, and in training courses is about how to tie knots. This is, of course, the first and basic
skill. But few people seem to get beyond that stage.
2. More Advanced Learners Think of Knots
as Applications.
At a more advanced stage of learning, a studentÕs range of
vision broadens and interest shifts to learning how to use the knot for a
specific purpose or application—perhaps by tying a Timber Hitch to move a
heavy log or to tie a Prussic Hitch for lowering a litter from a mountainside.
At this stage, includes interest in mastering the procedures of knot tying continues, but moves beyond
that perspective to focus also on an application of the knot.
At this level, Scouts and rescue workers share the way of
thinking with mountaineers, arborists, ski patrollers, sailors, and the dozens
of other users of practical knots. The applications range from practical uses
around the house to recreation and professional uses.
3. The New Perspective: Think of How
Knots Perform.
At the most advanced stage of learning about knots, we bring
the way knots work to
the center of our attention.
Each stage of learning about knots adds a perspective on
knots that engages the mind in a different way. Rope no longer remains just a
piece of rope but becomes the material for tying a knot and using it to perform
a task. Pretty soon, these ways of thinking become habitual.
As a matter of fact, at every stage of learning and in every
application, knot performance has been at the heart of the knot-tying
experience. A beginning learner ties a Square Knot, then pulls on the ends to
see that it holds. A candidate for the Merit Badge uses the Taut-Line Hitch to
pitch a tent. A rock climber hitches in with a Figure Eight Loop. But few
people seem to have noticed the performance of the device they have created and
tested and used.
We can add a new dimension
to our knotting skills by applying the principles and techniques of structural
analysis to study knot performance – this new aspect of knot study
Be sure to notice that we do not abandon skill at tying
individual knots nor do we cease to use them skillfully in applications. By no
means. But we broaden our point of view and cultivate new understanding. The
remarkable fact is that beginners, even small children, can develop all three
of these perspectives simultaneously, right from the start.
Large areas of knot
study remain beyond the scope of these studies. It is important to recognize
that I have deliberately adopted several limitations to devise a project
that could be reasonably managed.
A full understanding of the way a knot works would take into
account all of the factors that affect knot performance. But we can more easily
study the interplay of the first two factors, structure and mechanical forces,
while holding constant the other two. This means that for the moment, we
disregard the effect of various materials, uses, and weather.
I have made several
assumptions about the knots themselves.
¥ I have
examined only a few well-known knots.
¥ All of the
knots are properly tied, arranged, and tightened, and the ropes are of uniform
thickness and condition.
¥ Except as
otherwise noted, I assume that the amount of load, rate of loading, and period
of loading remain constant and that the knots are loaded in the standard
way—a Bowline, for example, with the standing part anchored at the top
and the load well distributed on the loop.
¥ I do not
take into account the effect of backup knots because backups obscure the
characteristics I want to expose and examine.
¥ The most
important limitation of these studies concerns the type of cordage. While the
range of materials that knots are tied in is virtually limitless, I assume that
the knots studied here are tied in rope made of natural fibers. This means, of
course, that the conclusions do not apply simply or directly to knots tied in
rope made of artificial fibers or of other types of cordage. This limitation is
especially important in the discussion of the breaking point of knots tied in
climbing and rescue work. As is well known, ropes made of artificial fibers
behave in very different ways from those made of natural fibers. But I have
found it feasible to examine only one set of variables, and leave for later
study the analysis of other variables such as the properties of different types
of cordage.
¥ I assume
that the rope is not deformed in any way that would hinder the motion of
surfaces in contact.
¥ The knots
are used in standard environmental conditions. I do not take into account the
effect of varied conditions of temperature or humidity or of lubricants on the
bearing surfaces of the rope.
¥ This inquiry
is limited to two aspects of knot performance, the knotÕs structure and the
mechanical principles that come into play when a load is placed upon it. Other
factors that affect performance are held constant.
¥ I have
applied only elementary principles of mechanics.
¥ I have
examined the interplay of structure and mechanical forces by means of
observation and analysis alone.
¥ The study is
guided by a series of procedures, but it does not make use of specialized
technical knowledge, simulations, controlled laboratory tests, or numerical
calculations.
At times, the discussion is based on meager evidence. This is
because so few studies about knot performance have been published and I have
not conducted original laboratory research.
Structural
analysis is a series of
procedures that reveal how the structure of a knot affects its performance. It
uses the techniques of reverse engineering, that is, taking a completed device
apart systematically to see how it works In these procedures, we examine the
way the segments of rope are intertwined so that they produce sufficient
friction to keep the knot from slipping apart and coming untied. The aim is to
raise awareness of the relation between the way a knot is built and the way it
performs.
Structural analysis
focuses our attention on basic questions about the inner mechanisms in a
particular knot. How is it built? What mechanical principles come into play?
How do the structural devices work together to create friction and make a knot
secure? Under a normal load, how does the knot effectively resist slipping
apart? How does it behave under and abnormal load? The result is a set of
concepts that can be applied to any practical knot.
By supplementing
the results of tests, the recommendations of experts, and our own personal
experience, this kind of examination of the shape and function of the parts of
a knot helps us develop new understanding of knot performance.
I have developed
the procedures of structural analysis over the past several years. I began to
investigate the performance of knots by posing questions about how knots work,
reviewing the knotting literature, and devising a set of step-by-step
procedures for observing individual knots and for analyzing their structure and
determining their mechanics.
Analysis of a few
knots led to conjectures and surmises about their behavior, which then led to
further analysis and tentative conclusions. As I developed the procedures in
interviews with dozens of knot users, I sharpened and refined the questions and
my conclusions. My own understanding has been enlarged through these interviews
and through correspondence with persons knowledgeable about knots. The method
of structural analysis is described in full in the study titled ÒKnot
Security,Ó and it is applied in all of these studies.
The procedures used
here for analyzing the structure and performance of knots are similar to those
used in systematic inquiry of any kind:
¥ Begin by
stating presuppositions and known or assumed general principles.
¥ Identify a
research question to guide the inquiry; define terms and state the problem precisely.
¥ Limit the
inquiry to manageable proportions by holding some variables constant.
¥ Select a
specimen for analysis.
¥ Develop a
series of increasingly clear and logical steps; using these steps, examine the
specimen, both its parts and their function.
¥ Describe the
parts and functions in detail; look for relations among parts and functions.
¥ Search for
specific properties of the specimen and for universal principles that apply
generally.
¥ Proceed
systematically toward conclusions; state and record observations at each stage
of observation and analysis.
¥ Synthesize
your observations; drawing on intuition, make a conjecture about the way the
specimen works.
¥ Check the
conjecture by using the procedures to study other specimens and comparing the
results.
¥ Record your
revised conclusions.
¥ Have the
whole project reviewed by outsiders.
Structural analysis
supplements the knowledge and understanding about knot behavior that we have
accumulated through testing and experience. It can correct some false
and misleading concepts. It can
enrich knot instruction by raising awareness of the way knots work and helping
knot users judge the performance of these important tools. It can help to
reduce the risk of using knots. It provides terminology, procedures, and
concepts useful for further research and discussion among knot users.
Structural analysis
is a useful technique for knot study because it
¥ Raises
pointed questions about knot behavior
¥ Challenges
some traditional assumptions about the way knots behave
¥ Clarifies
concepts and procedures for studying knots
¥ Defines and
uses standardized terms
¥ Develops a
disciplined method of inquiry
¥ Produces a
set of conclusions that can be re-tested and verified or modified, then
abandoned or adopted.
¥ Develops
curiosity on the one hand and habits of observation and analysis on the other
¥ Suggests
directions for further study.
This method of
study was originally designed for persons who use life-support and load-bearing
knots, serious knot users such as climbers, ski patrollers, cavers, rope rescue
personnel, ropes course managers, anglers, sailors, and so on. It was also
designed for teachers and students of knot tying.
But this method has
far wider practical use. As described here, the procedures of structural
analysis may seem daunting at first. But they require only an ability to
observe, follow procedures, and apply elementary principles such as load,
pressure, and curvature. Both the procedures and the concepts can be widely
understood because they are stated in ordinary language, using no statistics,
formulas, graphs, or diagrams. For these reasons, the study of knot performance
can be undertaken by persons without specific technical training, and it is
beneficial at every level of knot use and knot instruction, from rank beginner
to professional. I have used the procedures with evident success with small
children as well as with mountain guides.
Many persons who
have followed the systematic procedures of structural analysis have commented
that this form of guided knot study increased their understanding. Some
procedures challenged their assumptions about knots and made them aware
of avenues for studying concepts
that had remained obscure. Other procedures brought to the level of awareness
ideas they had felt intuitively but had not thought of consciously or
verbalized. It appears that within the limitations of scope of the inquiry, the
procedures bring about the stated aims.
Although there has
been little criticism of the procedures themselves, some of my conclusions
about knot behavior expressed in earlier versions of these studies have not
been universally accepted. Some of these conclusions have been challenged on
the grounds that they do not apply to types of rope commonly in use and that
they fail to take into account some important mechanical principles.
In this revised
version of knot studies on allaboutknots.com, I have tried to meet these
criticisms by refining the method of inquiry, making clear the limitations of
scope, correcting some errors, and making my statements clearer. While I have
considered all of the changes that correspondents have suggested, I have not
adopted some of them. I continue to work toward more complete analysis and
accurate conclusions.
Although I offer
only tentative conclusions, a reliable understanding of knot performance seems
to be emerging. And although some of the conclusions do not apply
directly to other aspects of knots, I
am confident that the procedures lead to a greater understanding of the way all
knots work. If these studies can fill in some blanks in thinking about knot
performance and suggest avenues for further study, they will have filled their
main purpose. While all of the conclusions developed here have been carefully
considered, they remain open for further study.
Principles as
significant as the ones discovered by the procedures of structural analysis
ought not to be neglected. Both the procedures and the principles ought to be
adapted for use in every lesson in knot tying They ought to be applied
habitually, and every insight gained by this analysis ought to influence daily
decisions about ropes and knots, whether for utility or for life support.