Monday, November18, 2019 L-36.com

Knot Strength: The Study Of Knot Performance



Note:

This is the new page for displaying documents. It allows documents to display on devices without pdf viewers specifically mobile devices, a new Google requirement. Note also that some documents have blank pages. Just click on "Next Page" if that happens.
Previous Page    Next Page Go to page number Note: Page number may not agree with index page numbers


Previous Page    Next Page
Go to page number
Note: Page number may not agree with index page numbers

PDF to Text.

This is "Knot Strength" from www.allaboutknots.com                                    Page 1 of 23 pages




                               The Study of Knot Performance
            Exploring the Secrets of Knotted Cordage to Understand How Knots Work




                                         Knot Strength
          Structures that Make a Natural-Fiber Knot Strong or Weak




              Revised December 29, 2005. Copyright  2005 AllAboutKnots. All Rights Reserved
This is "Knot Strength" from www.allaboutknots.com                                          Page 2 of 23 pages




      We can never achieve the strength we require.
                                                      Stanley Barnes
                                                       Anglers' Knots, 25

      Any knot in rope will weaken it. Knots with the greatest load applied to very sharp
      bends are weakest. The strongest knots spread the load gradually over some
      distance before there is a grip.
                                                      Charles Warner
                                                       A Fresh Approach to Knotting, 23

      A rope practically never breaks within a knot. . . . It appears to be true that a rope
      is weakest just outside the entrance to a knot. . . . On testing [the Bowline Bend] I
      could find no tendency to break at the point of crossing. The material broke each
      time at a point just outside one of the Bowline Knots.
                                                      Clifford Ashley, 17, 30

      It is evident that some factor other than a harsh curve is present when string is
      broken in the manner described. It seems probable that this is the shearing effect
      exerted by the taut cord where it is hacked across the section that is held rigid.
                                                      Clifford Ashley, 30

      Every knot diminishes the strength of rope to some degree. The reason for this is
      that in any sharp bend of a rope (less than four times the diameter of the rope), the
      rope fibers on the outside of the bend carry the majority of the load on the rope.
      The fibers on the inside of the bend will carry very little of the load or none at all.
                                                      Vines and Hudson
                                                       High Angle Rescue Techniques, 54

      The higher the curvature, the lower the tensile load required for the crack
      formation.
                                                      Pieranski et. al.,
                                                       Localization of Breaking Points, 6

      All knots reduce the strength of the rope in which they are tied, generally by 20%
      to 40% of the unknotted strength. . . . A rough estimate of a knot's strength can be
      made by examining the severity of its bends. . . . Bending a rope around a
      carabiner is likely to cause a greater strength loss than any common knot.
                                                      Neil Montgomery,
                                                       Single Rope Techniques, 10, citing Link 1958

      The more severe the curved parts of the knot, the tighter the nip, the greater the
      chance the rope will break
                                                     Geoffrey Budworth, Knots and Crime, 28

      A law is useful if it predicts behaviour which would not, otherwise, be obvious.
                                                     Geoffrey Budworth, Knots and Crime, 34
This is "Knot Strength" from www.allaboutknots.com                                             Page 3 of 23 pages




  Key Words. knot strength, entry point, first curve, severe curve, gentle curve, collar,
anchor, anchor point, Bowline, Overhand Bend, Flemish Bend, Double Fisherman's Knot,
Blood Knot, core-and-wrap structure
Summary
   Knot strength refers to the ability of a loaded knot to resist breaking. It is one of the basic
elements of knot performance and of knot safety. Assuming uniform materials and conditions
of use, the procedures of structural analysis show how the structures of a knot interact with
mechanical forces to make a knot strong and how to estimate the comparative strength of
different knots. A straight segment of rope is the strongest because it distributes the load
evenly on each of the fibers and stresses them uniformly. A curved segment weakens the rope
because it distributes the load unevenly, which strains some fibers and compresses others.
The relative strength of a knot is determined by the severity of the first curve in the most
heavily-loaded segment. The more the first curve deviates from the axis of tension of the
knot, the weaker the knot. Core-and-wrap knots such as a Double Fisherman's Knot are
stronger than most knots of the Bowline type because the stem curves deep inside the knot;
in that location, the wrap squeezes against the stem, reducing the load on the first curve. The
location of the first curve affects both its breaking point and strength, but the severity of the
first curve affects only its strength. Curves and loads in other parts of a knot do not affect its
strength. This discussion pertains to the strength of knots tied in ropes made of natural fibers
such as manila. Some of the concepts and conclusions of this analysis may apply to knots
tied in ropes made of artificial fibers such as nylon.




              This study of knot strength can be read alone, but it is easier to understand if you've read
          the introduction and the previous studies on terminology, knot security, knot stability and
          the breaking point of knots. Click to view a .pdf file and download a reader.
              If your analysis is different from mine, or if you have found a better way of stating things,
          let me hear from you via email. Click here to send an email message.
This is "Knot Strength" from www.allaboutknots.com                            Page 4 of 23 pages




                       Introduction: The Comparative Strength of Knots

   People who use knotted ropes under a heavy load need to know that while all knots reduce
the strength of ropes, some knots are stronger than others.
   During the past century, numerous specialists have tested knots to determine how the
strength of one knot compares to the strength of another. Their results do not agree exactly,
but allowing for the conditions of the tests, such as unavoidable variation in the qualities of
the rope and the way the knot was snugged and tightened, there is general agreement.
   A review of previous studies of the strength of knots followed by close examination and
analysis of several knots shows why some knots are stronger than others and increases our
understanding of knot behavior.
Knot Strength Varies Widely
   Most of the study of knot strength has focused on tests of a few knots. A striking fact
that tests have turned up is that strength varies so much from one knot to another. As shown
by both experience and numerous tests, some knots weaken a rope by more than 50%, while
others weaken it by less than 10%.
   The following table, which I have extracted from various reports, compares the relative
strength of a few familiar knots. A straight or un-knotted rope is assumed to have 100%
strength. While the exact figures should not be trusted, the general range of strength is
corroborated by other tests and by experience.
   Strong Knots
   Blood Knot            8590% (Barnes); 80% (Day)
   Flemish Bend          81% (Frank and Smith)
   Figure Eight Loop 80% (Frank and Smith)
   Double Fisherman's 79% (Frank and Smith)

   Moderately Strong Knots
   Butterfly          75% (Frank and Smith)
   Bowline            60% (Day)
   Overhand Knot      60-65% (Luebben )

   A Weak Knot
   Overhand Bend            (My guess is less than 50%)
This is "Knot Strength" from www.allaboutknots.com                              Page 5 of 23 pages




Widespread Interest in Knot Strength, but Little Progress
   The results of tests of knot strength are frequently reported in knotting literature, and
many people ask about knot strength. But while it is generally agreed that most knots reduce
the strength of a rope, little study has been devoted to the reasons for variation in knot
strength. As Cyrus Day commented several decades ago, few people "have any precise
notions regarding the . . . breaking strength of knots" (15). Dan Lehman commented in
Knotting Matters, the quarterly publication of the International Guild of Knot Tyers (KM
55.10), that assertions about knot strength are often false. Cy Canute (KM 63.21), agreeing,
commented further that "so-called experiments are often little more than haphazard
observation and amateurish guesswork." The consensus is that the tests of knot strength may
be useful as general indicators but are not accurate.
   Only a few publications have tried to explain the factors that make a knot strong or weak.
Among these are books of more than half a century ago by Clifford Ashley and Cyrus Day,
and especially a study of fishing knots by Stanley Barnes. A recent detailed study by
Pieranski and others, noted by Alan King (KM 74.4243), found that "the main reason of the
weakening of a knotted string is the curvature of the string" (10.2). A recent study by Adam
Long, Malcolm Lyon, and Graham Lyon concluded that a knot's strength is determined by
the severity of curve at the point the standing part enters the knot (16). Except for these
studies, the structures that make a knot strong or weak remain largely unexplored.
The Aims and Method of this Study
   The aim of this study is to follow up these previous studies to determine the
characteristics of knots that make some knots strong and others weak. It inquires why there
is such great variation between the strength of knots. Assuming knots tied in rope made of
uniform fibers and used under uniform conditions, why do some knots break under less load
than others? What structures in a knot reduce its strength?
   The concepts and procedures of structural analysis which were used in previous studies
provide a way to assess the strength of knots and to understand the factors that determine
their strength. The procedures are intended to increase the general knot sense of knot users by
helping them become more aware of the anatomy and physiology of knots.

   This study of knot strength has been hampered by problems of inadequate terminology, a
lack of widely-accepted concepts, and faulty traditional concepts. As Charles Warner (A
Fresh Approach to Knotting and Ropework 34) noted recently, "There seems to be no theory
that will reliably predict the strength or security of a knot from a knowledge of the structure
of the knot and the conditions of the test."
   This study does not purport to reach definitive conclusions, but to develop general
principles and new methods for understanding the performance of knots. I have verified the
results of this study through a review of the literature, a series of interviews with knot users,
and correspondence with knotting authorities. Many of the conclusions, however, have not
been confirmed by tests and remain unproved.
This is "Knot Strength" from www.allaboutknots.com                              Page 6 of 23 pages




                           Assumptions and Limitations of this Study

    In this study, I make the same assumptions and impose the same limitations as in the
previous studies of knot performance. These are detailed in "The Breaking Point of Knots."
    While the discussion analyzes the system of forces that determine the strength of knots of
all types, many of the variables that affect the strength of knots are beyond the scope of this
study. Holding constant the effect of various materials and conditions of use, it is assumed
that the strength of a knot is determined by the way critical structures are affected by their
form and arrangement, by their contact with other structures, and by the load that falls on
them.
    Following the findings of Ashley, Day, Barnes, and others, I assume that most knots
usually break just outside the knot, at the point where the standing part enters the nub.
Following Barnes, I assume that a Blood Knot breaks in the center of the knot.
    Hitches around objects introduce an entirely different set of variables, particularly
concerned with the effect of environment and conditions of use. This group of knots, which
includes Two Half Hitches and the Constrictor Knot, are not discussed here.
    The most significant limitation of this study is the assumption that the knots analyzed
here are tied in rope made of natural fibers such as manila. Although the discussion attempts
to move toward principles that would apply to knots tied in any cordage, the conclusions do
not pertain to many of the properties of knots tied in nylon or other synthetic materials
    It is instructive to note, however, the difference between the causes of knot failure in
natural fibers and in nylon fibers, as explained by a correspondent. While the fibers of
knotted rope made of natural materials rupture because they are overstressed, the fibers of
knotted rope made of nylon break because of nylon's high coefficient of friction and slow rate
of thermal conductivity. A load causes the outer strands to stretch and move in relation to the
adjacent strands, creating friction that heats the fibers, weakens them, and causes them to fail.
Nylon fibers do not rupture because of overstressing, the way natural fibers do, because they
are so highly elastic. Under load, the fibers stretch and move, creating enough friction to melt
them.
    These properties of stretch, dynamic friction, and response to heat in nylon and other
synthetic materials are beyond the scope of this analysis. Yet although these variables
present more complex problems than structural analysis can account for, I suggest that in
addition to melting caused by internal friction, the strength of knots tied in nylon rope may
also be affected by the unequal distribution of load on the first curve, as in natural-fiber
ropes.
This is "Knot Strength" from www.allaboutknots.com                                Page 7 of 23 pages




                             Terms Used for Studying Knot Strength

   Many quasi-technical terms are essential for discussing the strength of knots. Some of
these terms are well established in current usage, some are newly coined, and some are re-
defined. All of them are discussed in the separate part on terminology and some have been
used in the previous study of the breaking point of knots. I have tried to clarify the
discussion of knot strength by using terms that are least likely to be ambiguous.
Anchor
   The anchor is the structure of indefinite length in the nub of a knot. The top of the anchor
merges with the lower end of the stem. The anchor has two functions: 1) it gives the standing
part a firm mooring to pull against; 2) it holds the lower end of the stem in a particular
position that determines how far it is forced to deviate out of a straight line. If the anchor is
positioned so that the stem makes a severe curve, the knot will be severely weakened. The
form and function of the anchor are also described in the previous study, "Knot Security."
Anchor Point
   The anchor point is the place at the lower end of the first curve where the stem merges
with the top of the anchor. The location of this juncture vitally affects the severity of the
first curve and thus the strength of the knot.
   The anchor and the anchor point are of central importance in the study of knot strength,
but so far as I am aware, they have not previously been identified.
Axis or Axi s of Tension
   The axis or axis of tension is the main line of longitudinal force in a knot. In a bend tied in
free-standing ropes, for example, the axis is the line from one standing part to the other. In a
tug-of-war, the opposing teams pull the rope taut along the line of axis.
Collar
    The collar is the first structure that the stem crosses over as it enters the nub of the knot.
It is an obstacle that the stem has to curve around. The configuration of the collar is one of
the factors that determine the severity of curve in the stem. The other two are the angle of the
standing part and the location of the anchor point.
Curve
   A curve is a segment of a knot that deviates from a straight line; most of the segments of
knots are curved. I use the word curve instead of the typical knotting term bight, because
bight is so often associated with specific knots such as Bowline on a Bight or with a doubling
of the standing part of a rope, not with a curve inside a knot. I use the word curve rather than
bend, fold, or coil, which mean the same thing but which are often used with other meanings. I
use bend to mean a knot that joins two pieces of rope, fold only as a verb, and coil for
connected loops of rope, not for a part of a knot.
This is "Knot Strength" from www.allaboutknots.com                              Page 8 of 23 pages



Deviation
   I use the expression "deviation from the axis of tension" in place of radius, which is used
by Day and by Long et al. Although the terms are not exactly equivalent, I think they both
refer to the same kind of configuration in the stem. I've discussed this question in Blog 12.
First Curve
   The term "first curve" as used here refers to the first curve in the most heavily-loaded
segment in a knot, and it refers to only the initial part of the first curve, not to portions that
go deeper into the knot or wrap around other structures. The first curve of all knots is in the
stem. It is fairly easy to determine by inspection where the first curve begins, but the location
of the place it ends and merges with the anchor is hard to pinpoint. I assume that it ends soon
after it has crossed over the collar, and it clearly does not reach further than a centimeter or
two into the knot.
Gentle
   I use the term gentle curve to refer to a segment of rope that deviates more or less slightly
from a straight line. A gentle curve deviates by an angle of only a few degrees from the axis of
the knot, but like a curve ball hurled by a major league pitcher, its slight arc can have a major
effect on the strength of a knot.
Severe, Severity
   I have found that the words severe and severity of a curve, used by Geoffrey Budworth
and Neil Montgomery, appropriately suggest a relatively high amount of deviation from a
straight line. The severity of the curvature of a segment of rope can often be observed directly
and estimated in degrees of angle.
   Some studies of knots use the terms "sharpness," "magnitude of curve," or "maximal"
curvature or refer to "tight," "gradual," "high," "highest," or "greatest" curves. I do not use
these terms because it is often difficult to tell exactly what they mean. I use the words severe
and gentle. For example, I use the term severe curve instead of sharp curve to refer to a
segment of rope that deviates in a wider angle from a straight line.
   I use the words sharp, sharply, and sharpness only in direct quotations from other writers.
In other cases, I use the words severe, severely, and severity because I have found that the
other terms are used imprecisely and ambiguously.
Stem
   The stem is the structure in a knot that merges at its upper end with the standing part at
the place where the rope first enters the knot. It merges at its lower end with the anchor at
the anchor point. In knots of the Bowline type, the stem begins to curve at the entry point,
where it first begins to cross over the collar. In knots of the core-and-wrap type, such as a
Double Fisherman's Knot, the stem extends deeper into the knot before it begins to curve.
Strength
   By a knot's strength, we mean the knot's ability to resist breaking when the rope is
loaded. Strong and weak are relative terms: saying that a knot is strong means only that it
resists breaking under load more than other knots.
This is "Knot Strength" from www.allaboutknots.com                              Page 9 of 23 pages



Stress, Strain, and Stretch
   In this study, the words stress, strain, and stretch are as they are in physics.
   Stress refers to an applied force that tends to strain a segment of rope. The stresses that
cause a knot to break are set up by loading a curved segment. The most important kinds of
stresses in a knot are tensile, that is, stresses created by pulling.
   Strain refers to a deformation produced by a stress. Stress causes strain.
   Stretch refers to the lengthening of fibers when they are stressed by a load. In studying
knot strength, stretch is the most important kind of strain. (These definitions are derived
from The American Heritage Dictionary. See also Giancoli, Physics, 240242.)
Wide
  The term wide pertains to the angle that a curve deviates from the axis of the knot. A wide
angle deviates by more than a few degrees.
Wrap
   In general, the word wrap refers to a segment of rope that passes around another segment.
I use it specifically to refer to the helix of a core-and-wrap knot that circles around the stem.
Wraps can be very powerful devices. In knots such as a Double Fisherman's Knot, a pigtail or
corkscrew encircles a central segment of rope like the tendrils of a grapevine. Warner also uses
the word wrap in this sense (A Fresh Approach 30). Ashley uses the word turn (17).
This is "Knot Strength" from www.allaboutknots.com                            Page 10 of 23 pages




                          Factors that Determine the Strength of Knots

   The chart of knot strength above shows that knots vary in strength from about 50% to
about 80% or more of the strength of unknotted rope. Why do knots vary so widely from
very weak to very strong?
   To discover factors that determine knot strength, we review the principles established in
previous studies, then we analyze the structures of several examples, particularly the
characteristics of the first curve in the stem, which determines how strong a knot is.
Throughout, we will search for both the principles that affect specific knots and a general
principle that explains the strength of all knots.
Principles of Knot Performance Established in Earlier Studies
   Earlier studies in this series have established several principles concerning knot structure
and mechanics. These observations pertain directly to knots tied in rope made of natural
fibers, but many of them apply to knots tied in any material.
    The performance of a knot is determined by the type of materials the knot is tied in, the
      conditions of use, the laws of mechanics, and the knot's structure.
    We can analyze the form of a knot to determine how its structure affects its
     performance. In straight segments of a knot, such as in the standing part, the load is
     distributed evenly on the fibers, while in curved segments it is distributed unevenly.
     When a load falls on a curved segment of rope, the uneven distribution of load over-
     stretches some of the fibers and the segment is weakened.
    A knot breaks when an excessive load falls on a structure that is weakened by
     curvature. When overloaded, the weakened fibers in the first curve are stretched and
     stressed until they cannot withstand the strain, then break.
    In any knot, the standing part bears the full load, while the load on segments of rope
     inside the knot is always less than 100%.
    A break occurs because of a weakness created by the curve in the stem. Knots usually
     break at the first curve in the most heavily-loaded segment.
    In a Bowline and most other knots, the first curve is at the place where the standing part
     enters the nub of the knot and the stem crosses over the collar. In a few knots of core-
     and-wrap construction, such as a Blood Knot and a Double Fisherman's Knot, the first
     curve is well within the nub. Knots of the Bowline type break just outside the nub,
     while knots of the core-and-wrap type break well within the nub.

                       Determining the Strength of Bowline-Type Knots

   The analyses of a Bowline, an Overhand Bend, and a Flemish Bend on the next sections
summarize the principles of knot strength for all knots of the Bowline type. These knots are
selected for illustration because they represent the extreme range of strength in knots of this
type. In addition, these pages illustrate many of the structural principles that determine the
strength all knots.
This is "Knot Strength" from www.allaboutknots.com                              Page 11 of 23 pages




                        Figure 1. The Moderate Strength of a Bowline
   Reference is made throughout these studies to a Bowline because it is a familiar knot with
moderate performance characteristics and an interesting structure. The shape of the curve in
the stem, which governs the strength of all knots, is determined by the configuration of the
standing part, the collar, and the anchor. The conclusions stated here are explained in more
detail in the discussion that follows.

SP The Standing Part, the straight segment of rope leading to
the nub, bears 100% of the load. In this part of the knot, the load
is distributed evenly on all the fibers. The standing part enters the
nub at an angle determined by the collar and the anchor.
X The Entry Point , where the standing part merges with the
stem and the rope curves as it enters the knot, is the place where
a Bowline usually breaks under excessive load. Virtually 100% of
the load falls on this point. The severity of this first curve
determines the strength of the knot.
Parts of the Nub The nub is the knotted part of the knot. In a
Bowline, it is composed of the stem, the bight, and the hitch.
   S The Stem, the segment between the dotted lines, merges
   with the standing part at the entry point; it is moored to the
   hitch below. As the stem crosses over the collar, it forms the
   first curve. This fully-loaded curve distributes the load
   unevenly on the fibers of the stem, causing an overloaded
   knotted rope to fail at the entry point.
   B The Bight is the curved segment that forms a collar around
   the stem just below the entry point. The stem forms the first
   curve as it passes over the collar.
   C The Crossing of the Hitch forms an anchor that moors the
   stem and determines the slight amount that it curves around
   the collar.
   H The Arc of the Hitch, the curved segment opposite the
   crossing, wraps around the legs of the bight and squeezes them
   together.
T The Tail bears no load except its own weight.
L The Loop . While the loop bears the entire load, each leg bears
only about 50% of the load.

                    Structures that Determine the Strength of a Bowline
      As shown in the figure, a Bowline is a fixed-loop knot tied in a single length of
      rope. It is made up of the standing part, the loop, the tail, and the nub. The nub, or
      the knotted part, is composed of the stem, a hitch, and a bight. The bight forms a
      collar around the stem and forces the stem to make the first curve. All of the load
      on a Bowline falls on the standing part, and nowhere else within the knot.
      The strength of a Bowline is determined by the configuration of the standing part,
      the stem, the collar, and the anchor, which is in the lower arm of the hitch. These
      structures determine the severity of the first curve and the strength of the knot.
      The text explains that a Bowline is stronger than some knots and weaker than
      others because of the characteristics of its first curve. The principles detailed here
      apply to other knots of the Bowline type, which includes most knots.
This is "Knot Strength" from www.allaboutknots.com                              Page 12 of 23 pages




                  Figure 2. The Extreme Weakness of an Overhand Bend
   The analysis of the Overhand Bend below illustrates other aspects of knots of the Bowline
type. We do not have test results for the Overhand Bend, but experience and analysis both
show that it is very weak. Despite its weakness, it is used by climbers because "it's the
fastest and simplest knot to tie rappel ropes together, admirable qualities when a storm is
bearing down" (Raleigh 14). I use it here because it admirably shows extreme curves in the
stems, which cause it to be so weak.




                                       The Overhand Bend.
   The Overhand Bend is probably the most common knot for tying two pieces of cordage
together. Its cousin the Thumb Knot, used as a terminal knot, must also be familiar to
everyone. Here the segments are rearranged as a bend. I think of the Overhand Bend as the
kite-string knot, because as a boy I used to tie random pieces of string together to fly my
home-made kites.
   While numerous knot books report on tests of the strength of several knots in common
use, few of them explain why one knot is stronger than another, and none that I know of
mention the Overhand Bend. Analysis of this knot makes the principles of knot strength
evident.
Description of the Overh and Bend
   To follow this description, tie an Overhand Bend in a length of rope and orient it as shown
in the figure, with the nub standing upright at a right angle to the axis and the tails emerging at
the right. The white standing part in the illustration, which joins the stem and enters the nub
from the left, curves at a extremely severe angle, something like 90. The blue standing part,
extending under the tails to the right, curves somewhat less severely, but still at a wide angle.
Parallel strands pass across from the top of the nub and down to the right. These strands then
pass under the stems, come around from the left, and pass under and emerge to the right as
the twin tails.
This is "Knot Strength" from www.allaboutknots.com                             Page 13 of 23 pages



   The curves in the stems of this knot are as severe as any I know of. Keeping the weakening
effect of a severe curve in mind, inspection of the first curves in an Overhand Bend indicates
clearly why the Overhand Bend is found to be such a weak knot.
   The Overhand Bend shows especially well the structures that create a weak knot. The
standing parts enter the knot at an extreme angle to the nub, the opening in the collar is
oriented at a right angle to the axis of the knot, the first curve is extremely severe, and the
anchor point draws the stem at this wide angle.
   The Overhand Bend is a prime example of a secure and stable knot that is extremely weak.


                           Figure 3. The Strength of the Flemish Bend




                                         The Flemish Bend
  Of Bowline-type knots, the Flemish Bend, or Figure Eight Bend is probably the strongest
bend. The stem curves very little as it enters the knot and crosses over the collar.


                   Developing Concepts of Strength in Bowline-Type Knots

   This section applies the principles of structural analysis to develop concepts of the
strength of knots of the Bowline type such as the three knots illustrated above. The strength
of knots of the core-and-wrap type is discussed in a later section, where many of the same
principles apply.
The Stem and Adjacent Parts
  The first task in studying the strength of knots is to become familiar with the stem and the
parts adjacent to it.
The Stem is Attached at Both Ends
   Identifying the stem is essential to the study of knot strength because that is where most
breaks occur. The lower end of the standing part merges with the upper end of the stem,
which then crosses over the collar, creating the first curve. Further into the nub of the knot,
the lower end of the stem merges with the anchor.
This is "Knot Strength" from www.allaboutknots.com                             Page 14 of 23 pages



The Position of Three Point s Determines t he Severity of the First Curve
   To determine the relative strength of a knot, the question to ask is how far the first curve
deviates from a straight line.
   In knots of the Bowline type, the severity of the first curve depends on the angle formed
by three points: 1) the entry point, where the standing part begins to merge with the stem, 2)
the place where the first curve crosses over the collar, and 3) the anchor point. The relative
location of these parts causes the stem to curve more or less from the axis of the knot. If
these parts are way out of line, the stem is forced into a wide angle and a severe curve. If they
are in virtually a straight line, the stem curves very little.
   The effect of various positions of these three points can be seen most clearly in the
extremely severe first curves in both stems of a Overhand Bend, where the three points form
an angle of something like 90. In a Bowline, these points are much less out of line, so that
the first curve is more gentle. In a Flemish Bend, which is a very strong knot, the standing
part is virtually in line with the nub of the knot. Its stem curves very gently as it passes on to
the anchor point.
   A load on this curve in the stem creates the stresses that weaken the knot by distributing
the load unequally on the fibers. It compresses some of them and stretches and strains others.
A Load on the Stem Forces it into a Curve
   The stem is pulled from both directions, with a load coming from the standing part at its
upper end and from the anchor at its lower end. As the stem passes over the collar, these
loads force it to curve out of a straight line so that it deviates from the main line of
longitudinal force of the knot.
An Excessive Load on the First Curve Causes a Knot to Break
   As shown in the preceding study of the breaking point of knots, a knot doesn't necessarily
break at the most severe curve. It breaks at the first curve of the most heavily-loaded segment
of rope, however severe or gentle that curve may be. In knots of the Bowline type, the first
curve is at the entry point, where the standing part merges with the stem and begins to cross
over the collar.
   Keep in mind that throughout these studies, the term first curve refers to the first curve in
the most heavily-loaded segment of rope.
Curves Redi stribut e the Load and Weaken the Knot
   Any curve in a loaded segment of rope distributes the load unequally on the fibers. The
load falls more heavily on the outside fibers of the curve than on the inside fibers. By
stretching some fibers and compressing others, a curve loads the fibers unevenly. The uneven
distribution of load creates strains that weaken the knot at that point. The outside fibers,
carrying more of the load than the inside fibers, are placed under greater stress. Under an
excessive load, these outer fibers are stretched until they break, just as they are in a green
stick if you bend it to the breaking point. The inner fibers, unable to support the increasing
load, break soon after. In this way, the curve of the stem creates a weak point that causes a
knot in an overloaded rope to fail.
Severity of the Curve of the Stem Determines Knot Strength
This is "Knot Strength" from www.allaboutknots.com                              Page 15 of 23 pages



   The relative strength of a knot is determined by the severity of the first curve. The
strength of any knot is determined by the severity of the angle that the first curve veers from
the axis. If the stem deviates very little from the main line of longitudinal force in the knot and
the first curve is gentle, the knot will be stronger.
   In knots of the Bowline type, the standing part merges with the stem at the entry point so
that the stem is forced into a curve as soon as it begins to enter the knot. The full load on the
standing part falls directly on the upper part of the stem, but on no other structure in the
knot. This is because as soon as the rope enters the nub, contact with other structures
reduces the load on every segment of rope inside the knot.
   A gentle curve gives little resistance to the pull from the standing part. This means that a
good bit of the load is transferred to the anchor below and the fibers are not strained a great
deal by unequal loading. A stem that crosses over the collar in a gentle curve, such as in a
Flemish Bend, is stressed very little, so this knot is quite strong.
   A severe first curve does not transfer so much of the load further into the knot. Knots with
a severe first curve are weaker than knots with a gentle first curve. An Overhand Bend is very
weak because the stems at both ends of the knot are extremely curved. A Bowline is
considerably stronger than an Overhand Bend because the first curve is so gentle.

                      Determining the Strength of Core-and-Wrap Knots

   This section applies the principles of structural analysis to develop concepts of the
strength of all knots of the core-and-wrap type. Two knots with a core-and-wrap
construction illustrate the principles of this small group of knots.
                Figure 4. The Great Strength of the Double Fisherman's Knot
This is "Knot Strength" from www.allaboutknots.com                          Page 16 of 23 pages




                                        Double Fisherman's Knot

  The Double Fisherman's Knot is the best known of knots of core-and-wrap construction
and is among the strongest of knots. The stem does not curve until it has passed three-
quarters of the way through the knot, and a series of four wraps squeeze tightly against it.
The upper view shows it before the slide-and-block parts have been drawn together.


                    Figure 5. The "Fisherman's Favorite," the Blood Knot




                                      The Blood Knot, loosely tied

   Little known except among anglers, this Blood Knot is among the strongest of bends. Like
other core-and-wrap knots, the stem does not curve until it is a good way into the knot, and
the wraps squeeze it.
This is "Knot Strength" from www.allaboutknots.com                              Page 17 of 23 pages



   The core-and-wrap construction, in which a series of turns or wraps encases the core, is
described in detail in the study titled "The Breaking Point of Knots." This knot structure is
not to be confused with the sheath-and-core construction of some rope, which has a "heart
enclosed in a braided outer cover" (Budworth Crime 200).
   These knots are quite different in both structure and performance from Bowline-type
knots. In addition to the general principles of knot strength which pertain to all knots, an
additional principle determines their performance. The strength of core-and-wrap knots is
affected not only by the severity of the first curve but also by the length of the core and how
tightly the wrap is bound around it, as well, apparently, as the severity of the first curve.
   Knots of this type are stronger because the stem curves only after passing part-way
through the knot. Why would this be so? As the stem enters the nub of a core-and-wrap
knot, it remains straight for some distance before making the first curve further inside the
knot. The wraps squeeze the core, which is actually the straight part of the stem. Pressure
from the wraps reduces the load that reaches the first curve; this diminished load reduces
stress on the first curve, which and increases the knot's strength. The greater the length of the
straight portion of the stem and the tighter the wraps, the greater the strength of a core-and-
wrap knot.
   Although Ashley did not describe the inner workings of knots with the core-and-wrap
structure, he suggests the secret of their outstanding performance in his comment that "there
is unsuspected virtue in a few turns of line" (77). The strength of a Double Fisherman's Knot
shows forth that virtue.
The Core-and-Wrap Construction Makes a Blood Knot Strong
    Stanley Barnes examined another core-and-wrap knot, the Blood Knot that he identified as
the "Chaytor type." This is what Day called a Barrel Knot (110) and it is similar to the one
that Ashley called a Barrel Knot (#295). Barnes labeled it "the most important knot used in
angling." He particularly valued it for "its great strength" and rated it at 8590% (95), while
Day rated it at 80% (110). Either of these ratings is considerably stronger than most knots of
the Bowline type.
    The core-and-wrap construction makes a Blood Knot especially strong in two ways. First,
it creates a straight-line knot. Unlike the standing part of knots of the Bowline type, the
standing part of a Blood Knot does not curve as it merges with the stem at the entry point.
Instead, the stem enters directly into the nub without forming an angle with the main line of
pull of the knot. As Barnes noted, cordage is "at its strongest" when it is in a straight line
(23). The core, which is the extension of the standing part, lies in a direct line with the axis or
the main longitudinal force of the knot and does not curve until it has reached the center of the
nub.
    Second, the core-and-wrap structure makes a Blood Knot strong because as the stem
passes to the center of the knot, three tightly-drawn wraps grip it and progressively diminish
the load that falls on it. By the time the stem makes its first curve at the center of the knot,
pressure has reduced its load to considerably. This diminished load at the first curve contrasts
with the virtually full load that falls on the stem in knots of the Bowline type. But although it
is diminished, this load is nevertheless the heaviest load that falls on any curve.
Strength of Other Knots of the Blood Knot Type
This is "Knot Strength" from www.allaboutknots.com                              Page 18 of 23 pages



   It appears to be true that other knots which are built with the core-and-wrap structure not
only break within the nub of the knot but are stronger than most other knots. Tests that Day
reported show that hitches are stronger than bends and fixed loops (Table 4, 15); this strength
is apparently because of their straight-line construction and wraps. Robert Chisnall makes a
similar observation. As summarized by Charles Warner, Chisnall (Manual) notes that "in
general hitches were stronger than loops because in a hitch the standing part passes straight
through the knot, with no bight in the load-bearing side of the knot" ("Behaviour" 192193).
("Standing part" here refers to the segment of rope that enters the knot, then becomes the
core-cum-stem.)
   The way the core-and-wrap construction works can be seen even better in a Double
Fisherman's Knot. Climbers have extended the core-and-wrap principle in the Triple
Fisherman's Knot, which creates a good hold in slick and stiff cordage such as Spectra and
Kevlar (Raleigh 20). This knot is constructed so that a load draws the six wraps tightly
around the core, a structural device that creates a knot that approaches the strength of those
super-strength ropes.

                        Corroboration of this Analysis of Knot Strength

   Several discussions of knot strength in the knotting literature jibe with this analysis.
Ashley: Knot Strength and the Location of the Nip
   Ashley asserts that a knot is stronger--that is, it is better able to resist breaking--if the
nip is "well within the structure" (17). He offers no example or explanation of this assertion,
but I suggest that he may have had in mind knots of the core-and-wrap type, where the first
curve is "well within the structure." These knots are indeed stronger. According to the
analysis here, this comment would not pertain to the strength of knots of the Bowline type.
Day: Knot Strength and the "Radius of the Sharpest Curve"
   Day supports the view that severe curves (his term is "sharp") inside a knot play no part
in weakening it to the breaking point. (I assume that he refers to knots of the Bowline type.)
     It is sometimes asserted that the breaking strength of a knot depends on the radius
     of the sharpest curve within the knot. When rope is bent under tension, the outside
     fibers are supposed to be the first to give way. From this it is inferred that the
     outside fibers of the sharpest curve within the knot--the curve with the smallest
     radius--will be the first to break. As a matter of fact, however, a knot seldom
     breaks internally; the break usually occurs in the standing part of the rope, at the
     point where it enters the knot. The curve at this point is seldom very sharp,
     especially as compared with some of the curves within the knot itself, yet it is
     there that failure occurs (1516).
   Day's statement supports the conclusion that severe or "sharp" curves inside a knot play
no part in knot strength. His comment that "the outside fibers are supposed to be the first to
give way" applies to fibers in the first curve, as others have shown, but not to fibers of
"curves within the knot itself."
Barnes: "How Sharply the Weakest Coil is Bent"
This is "Knot Strength" from www.allaboutknots.com                                Page 19 of 23 pages



   Barnes concludes that the loss of strength in a knot "will be in large degree dependent on
how sharply the weakest coil is bent" (19) and that a knot will break where the core forms
"its first sharp coil" (51). I assume here that "coil" means curve and "bent" means curved.
The analysis above shows that in all knots, the "weakest coil" is the first curve in the most
heavily-loaded segment of rope, regardless of how it is curved. The "weakest coil" would be
either the curve of the stem, as in the Bowline, or the curve at the center of the knot, as in the
Blood Knot.
   It is useful to keep in mind that for all knots, while the severity of the first curve affects its
strength, it does not affect its breaking point, and the severity of curves elsewhere in the knot
affects neither its strength nor its breaking point.
Warner: the Severity or Gentleness of the Curve
   Warner states that "the strongest knots spread the load gradually over some distance
before there is a grip" (Fresh, 23). I surmise that the "grip" is the structural device that I have
identified as the anchor, which holds the first curve in position. The concept that "spreading
the load gradually over some distance" creates a strong knot would apply to core-and-wrap
knots. A Double Fisherman's Knot, for example, is one of the strongest because the stem
passes through four wraps before it makes a curve. The concept also applies to the strong
Flemish Bend where the first curve makes a broad sweeping arc as it passes under the two
hitches and into the nub. In addition, it applies to weak knots such as an Overhand Bend
which curves at the entry point and the load is not spread gradually over some distance
further inside the knot.
Long, Lyon, and Lyon
   Long, Lyon, and Lyon arrive at the same conclusions about variation in knot strength: The
curve at the entry point varies from knot to knot, the curvature at that point does not have to
be severe to cause the knot to break, and variation of curvature at the entry point causes
variation in knot strength.

                         Rejected Explanations of the Strength of Knots

   Several other reasons have been proposed to explain how knots break and what makes
them strong or weak. Some of these concepts continue to be asserted, and they may seem
intuitively true. But for reasons outlined here, these traditional explanations have to be
abandoned. A survey of some of the rejectamenta indicates that progress has been made in
understanding knot strength but that a great deal remains to be done.
Rejected: Knots Break Because One Segment of Rope Cuts Another Segment
   Discussion of the effect of curves on knot strength has a history that reaches back at least
to the 1860s and probably long before that. The idea that a knot breaks when one segment of
rope cuts through another appeared in the 1864 report of a Special Committee of the Alpine
Club, published in Volume I of The Alpine Journal. E. S. Kennedy and members of the
committee cautioned that
     It is very unsafe to join two pieces of rope by looping one end through the other,
     so that, when the jerk comes, they will be strained across each other as two links of
This is "Knot Strength" from www.allaboutknots.com                               Page 20 of 23 pages



      a chain are strained across each other. Unless a pad of some kind divides the loops,
      one will cut the other through (326).
    The idea that a severe curve causes one segment of rope to cut through another apparently
seemed reasonable to those alpinists, but it is now generally discarded in favor of other
concepts. Stanley Barnes, for example, concludes that while some knot users have "deduced
that in a nylon knot one filament breaks the companion coil by a cutting process," the failure
in a thumb knot is due to "a break at the convexity rather than a cut in the concavity" (26
27). Vines and Hudson (60) concur with this view, and it jibes with the analysis of in the
study, "the Breaking Point of Natural-Fiber Knots." Whatever may be the case with nylon
filament, the break in ordinary rope under normal conditions appears not to occur by a
cutting process.
Rejected: A Shearing Effect Causes String to Break
   After describing and illustrating a convenient way to break twine (30), Ashley comments
that
     It is evident that some factor other than a harsh curve is present when string is
     broken in the manner described. It seems probable that this is the shearing effect
     exerted by the taut cord where it is hacked across the section that is held rigid.
   From my analysis of knot strength and breaking point, it appears that Ashley's "other
factor" that causes the break is not the shearing effect of the taut cord but the full load falling
on the curve.
Rejected: Knots Break Where Loops Interlock
   In the passage from the Alpine Club report there also appears the idea that a break occurs
at interlocking loops: "to join two pieces of rope by looping one end through the other, so
that, when the jerk comes, they will be strained across each other as two links of a chain are
strained across each other." Although the explanation offered in the report is brilliantly clear
and graphic, a test conducted by Ashley showed that it is not so. He demonstrated that the
Bowline Bend (#143, #1455), in which two Bowlines are linked to join two pieces of rope,
showed "no tendency to break at the point of crossing." Instead, the linked loops "broke each
time at a point just outside one of the Bowline Knots." These breaks occurred at the stem of
one of the knots despite the fact that the "right-angle crossing provides the uneasiest curve
that is possible within a knot" (30). The knot does not break at the interlocking loops despite
the 180 reversal of directions of the legs of the loop and the stresses placed on the fibers at
the point where they link to each other.
   In a nearby passage, the Alpine Club committee expressed a preference for "knots in
which the folds are least sharply bent round each other; that is, in which the curves are large"
(325). This judgment agrees entirely with more recent concepts and with the present analysis.
Dissecting these brief statements shows how intermingled various problems are and how
complex and inconsistent our concepts can be. What was missing in the earlier concept of
knot failure was the idea of the full load falling on the first curve.
Rejected: Knots Break Because of Pressure Inside the Knot
   Intuition suggests to many people that a knotted rope will break because of excessive
pressure at curves inside the knot. Many assume that a Bowline would break at the arc of the
bight, at the arc of the hitch, or at the crossing of the hitch. These assumptions seem plausible
This is "Knot Strength" from www.allaboutknots.com                            Page 21 of 23 pages



for several reasons: 1) there are many curves in these places; 2) some of these curves are
severe and heavily loaded, as in the hitch of a Bowline; 3) snugging and tightening obviously
place stress on the segments there; 4) segments in the nub are apparently stressed both by
the load and the curves. But both tests and analysis show that they are not so.
Rejected: Knots Break Because of Friction Inside the Knot
   Following a similar intuition, others have thought that friction created at bearing surfaces
between segments causes a knot to break. The analysis in "The Breaking Point of Knots"
shows, however, that a break in a knot tied in natural-fiber rope occurs in the first curve and
is caused by an excessive load falling on fewer than all the fibers of that segment. Drawing on
that analysis, we can conclude that a break occurs at a weakness created by the curvature of
the stem, not by pressure and friction between structures.
   This concept appears to apply, however, to knots tied in artificial cordage.
Rejected: Knots Break Because of Severe Curves Inside the Knot
   Day commented that "It is sometimes asserted that the breaking strength of a knot
depends on the radius of the sharpest curve within the knot." (15) It may also be inferred that
the Alpine Club report would support the idea that a knot breaks at a severe curve inside the
knot. And Ashley observed that "One of the `laws' quoted in dictionary and encyclopedia
knot discussions ... is that `the strength of a knot depends on the ease of its curves' " (30).
Ashley's experiment with the Bowline Bend dramatically refutes the idea that severe curves
inside a knot weaken it. Except in knots of the core-and-wrap construction, curves well inside
a knot do not directly affect either the strength of the knot or the place where they break. For
example, a Bowline does not break at the severe curve where the arms of the hitch cross. This
is because the load that falls on the gentle curve at the entry point is virtually 100%, while
the load at the hitch is considerably less than that.
Rejected: Knots Break Because of Poor Dressing of a Knot
   Some knot users have sugged that poor dressing of a knot will cause it to break. That is, a
weakness is created in a knot that is not drawn up properly. "Dressing" a knot refers to
arranging the segments of a finished knot so that they lie where they are supposed to and do
not cross each other where they are not supposed to. Although knot books frequently
admonish readers to dress a knot, there seems to be no evidence that dressing a knot affects
its strength. Dressing would seem to improve knot strength only if it affected the first curve.
I surmise that this idea arose out of a desire to make the knot as neat-looking as possible
rather than from tests, analysis, or experience of knot failure.
Rejected: Tight or Compact Knots Are Stronger
   Knots that can be tightened compactly are sometimes thought to be stronger. These knots
may be more secure or more stable, but not necessarily stronger. There is apparently no
evidence that this factor contributes to knot strength.
Rejected: Knots of Great Bulk or Volume Are Stronger
  Contrary to the "tight knot" school, there are those who think that knots of great bulk or
volume are stronger. A lot of children and inexperienced knot tyers, following the adage "if
This is "Knot Strength" from www.allaboutknots.com                              Page 22 of 23 pages



you can't tie a knot tie a lot," tie knot on knot until they create a great wob. If those add-ons
are merely half hitches, they add little strength.

                  Summary: Factors that Determine the Strength of a Knot

   The strength of a knot is determined by two characteristics of the first curve.
   1. The relative proportion of full load that falls on the first curve.
   In knots of the Bowline type, in which the stem curves at the entry point, the first curve
bears virtually 100% of the load. In knots of the core-and-wrap type, the proportion of the
full load that falls on the first curve is determined by its location inside the knot and the
number and tightness of the wraps.
   2. The severity of the first curve, that is, how far it deviates from a straight line.
   A load falls more or less unevenly on the fibers in the stem, depending on the severity of
the first curve. Some of the fibers have to bear more of the stretch and strain than others.
Under an excessive load, this uneven stress weakens the knot and causes it to break.
Severity of the First Curv e Determines the Strength of a Knot
    The strength of knots depends on the severity of the first curve. The amount of deviation
from the axis of the knot determines the amount that the outer fibers in the first curve are
stretched. The more severe the first curve, the weaker the knot, and the gentler the first curve,
the stronger the knot. The reason is that the more severe the first curve, the more unevenly
the load is distributed in this vulnerable location and the more the outer fibers are stretched.
Adam Long et al., using somewhat different terminology, arrive at a similar conclusion. "A
knot's strength depends largely on the radius of the first bend as the loaded end of the rope
enters the knot," they comment. "A very tight bend will result in a weaker knot than one
with a more gradual bend" (16). As Warner put it, "knots with the greatest load applied to
very sharp bends are weakest" (Fresh, 23). The greatest load is always on the first curve. I
take it that these writers refer to the same configuration that I do and arrive at the same
conclusion.
    Tests of the strength of several knots confirm the assertion that their relative strength
varies according to the severity of the first curve. The Flemish Bend, with gentle first curve,
is rated at more than 80% of the strength of an unknotted rope, while experience shows that
the Overhand Bend, with a severe first curve, is extremely weak. Although this conclusion is
unsubstantiated by tests and remains unproved, analysis shows it to be the case.


                     Afterword: The Difficulty of Studying Knot Strength

   The analysis of knot strength has been the most challenging task in this study of knot
performance, and it remains the least certain part. Little has been written about the subject.
Few tests of knots with contrasting strength have been reported, and several observers have
questioned the reliability of published tests. The severity of a curve and the effect of a curve
on individual fibers are difficult to measure without laboratory instruments. The factors that
affect the strength of a knot are difficult to observe and analyze, and the differences in
This is "Knot Strength" from www.allaboutknots.com                              Page 23 of 23 pages



structure that account for greater or lesser strength are subtle. As Cyrus Day noted long ago,
the study of knot strength has been neglected. Part of the reason is probably that the study is
so difficult.
   Some of these conclusions about the strength of knots are not as firm as those about
security, stability, and breaking point. In writing this part, more than others, I have felt "This
explanation sounds reasonable, but I cannot explain why," and have had to leave it at that.
Perhaps a more technical analysis, using equipment such as a strain gauge and instruments
that accurately measure angles, curvature, and lengths would yield firmer results.
   I feel nevertheless that the questions, the method of analysis, and the principles developed
here are firm and suggest some of the right tracks for further research. I hope that my
comments will be useful for other studies of how knots work and why they work that way.
And I hope that my conclusions are sound and trust that readers will point out their
shortcomings to me.

   END


Ad by Google

Cookie Policy:
This webiste uses cookies to store settings on the weather pages so that you return to the same settings when you click the weather pages. This is necessary to save your setup information. There are also cookies used if you click the save location button. We do not sell or share any user data. Ads on this site are from Google. See Google for their policy. There are no cookies that are relevant to the EU as the weather site is for US territories only.
Privacy Policy:
I do not sell any data. I do host ads from Google. They may or may not sell your data. Please adjust your account settings with them if you wich..
Disclaimer:
The information on this web site has not been checked for accuracy. It is for entertainment purposes only and should be independently verified before using for any other reason. There are five sources. 1) Documents and manuals from a variety of sources. These have not been checked for accuracy and in many cases have not even been read by anyone associated with L-36.com. I have no idea of they are useful or accurate, I leave that to the reader. 2) Articles others have written and submitted. If you have questions on these, please contact the author. 3) Articles that represent my personal opinions. These are intended to promote thought and for entertainment. These are not intended to be fact, they are my opinions. 4) Small programs that generate result presented on a web page. Like any computer program, these may and in some cases do have errors. Almost all of these also make simplifying assumptions so they are not totally accurate even if there are no errors. Please verify all results. 5) Weather information is from numerious of sources and is presented automatically. It is not checked for accuracy either by anyone at L-36.com or by the source which is typically the US Government. See the NOAA web site for their disclaimer. Finally, tide and current data on this site is from 2007 and 2008 data bases, which may contain even older data. Changes in harbors due to building or dredging change tides and currents and for that reason many of the locations presented are no longer supported by newer data bases. For example, there is very little tidal current data in newer data bases so current data is likely wrong to some extent. This data is NOT FOR NAVIGATION. See the XTide disclaimer for details. In addition, tide and current are influenced by storms, river flow, and other factors beyond the ability of any predictive program.