Category: Knots

Heaving line knot
Category	Stopper
Releasing	Non-jamming
Typical use	To serve as a weight, making a rope easier to throw
ABoK	#538[1]

Stopper knot[2]
Names	Stopper knot[3], Franciscan knot,[4] monk’s knot,[4] Heaving line knot[4]
Category	Stopper
Related	Stevedore knot, Double overhand knot
Releasing	Non-jamming
Typical use	To serve as a weight, making a rope easier to throw
ABoK	#2004

A heaving line knot^[1] is a family of knots which are used for adding weight to the end of a rope, to make the rope easier to throw. In nautical use, a heaving line knot is often tied to the end of a messenger line, which is then used for pulling a larger rope, such as a hawser. There are several distinct knots which all share the common name, heaving line knot.^[1] The monkey fist is a well-known heaving line knot.

Make a bight in the tail end of the rope. Wrap the working end around the tail toward the bight end, with multiple turns. Complete the knot by passing the tail end through the bight loop.

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  Make a bight
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  Wrap the working end around
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  Put the end through the bight
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  Tighten by pulling on the standing part to close the bight

• 
  ABOK #2203
• 
  Hangman’s knot
• 
  ABOK #427
  Scout coil

• List of knots
• Hangman’s knot
• Heaving line bend – Type of bend knot

• How to Make and Throw a Heaving Line
• Animated Knots by Grogg

The Heneage knot is a decorative heraldic knot,^[1] the badge of the Heneage family of Lincolnshire, England.^[2] It was awarded to Sir Thomas Heneage by Queen Elizabeth I in 1594.

Heaving line bend
Names	Heaving line bend, messenger-line bend
Category	Bend
Related	Sheet bend, Racking bend
Typical use	To attach a lightweight line to a heavier line
ABoK	#1463

The heaving line bend is a knot for securely joining two ropes of different diameter or rigidity. It is often used to affix playing strings to the thick silk eyes of an anchorage knot in some stringed instruments. In nautical use, the heaving line bend is used to connect a lighter messenger line to a hawser when mooring ships. It is knot number 1463 in The Ashley Book of Knots,^[1] and appeared in the 1916 Swedish knot manual Om Knutar.^[2]

The heaving line bend is similar to the sheet bend and the racking bend, and may be used to pass a thick rope to a distant receiver by first throwing the end of a thinner rope which may be weighted with a monkey fist or a heaving line knot.

The heaving line bend is tied the same way as the sheet bend with one difference: the final crossing of the thin end is done in the opposite direction, so the thin end points away from the thin line, essentially in the same direction as the thick end, towards the thick line. This avoids jamming when the thin line is pulled to carry the thick end out of reach.

1. Make a bight in the larger line.
2. Pass the lighter line around the standing part of the bight.
3. Cross between the larger and the lighter line on the back side.
4. Finish by tucking the end between its turn around the standing part of the bight and that leg; pull tight.

• List of knots
• List of bend knots

Zeppelin bend
Names	Zeppelin bend, Rosendahl bend, Rosendahl’s knot
Category	Bend
Related	Zeppelin loop, Hunter’s bend, Ashley’s bend, Alpine butterfly bend
Releasing	Non-jamming
Typical use	Joining two ropes of similar size
Instructions

A zeppelin bend (also known as the Rosendahl Bend) is an end-to-end joining knot formed by two symmetrically interlinked overhand knots. It is stable, secure, and highly resistant to jamming.^[1] It is also resistant to the effects of slack shaking and cyclic loading.

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  Front view
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  Back view
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  Loosening / untying

The name “Zeppelin” was given to this knot in a Boating (1976 March) article by editors Bob & Lee Paine, ostensibly reporting the testimony of someone claiming knowledge of the knot’s history in the US Navy. The article asserts that then Commander Charles Rosendahl, commander of the airship Los Angeles, insisted that only this knot was to be used in joining airship ropes. However, in a note to a newsletter editor seeking permission to re-publish their article, Lee Paine wrote that then-retired Vice Admiral Rosendahl commented on the Boating article to say that he knew nothing of the knot (and he also corrected where airship training occurred). Giles Camplin, a student of airships, notes that a rolling hitch (#1735) is a more likely method used by ground handlers to join ropes. Other historical sources show that a ‘toggle’ was used to connect mooring lines with fixed eye splice terminations. Camplin’s report was published in issue #60 of ‘Dirigible’ in 2010. In a small publication, Potomac Caver, Bob Thrun published his discovery in 1966, calling it (his article title) simply ‘An easily untied bend’.^[2] Bob Thrun was well known in the caving community as fastidious for details in mapping caves.

Although some users regard (what might be better named) “Thrun’s Joint” as a nearly ideal rope joining knot,^[3][4] it is not very well known; it is not added into the (1944) The Ashley Book of Knots (although “Hunter’s/Rigger’s” bend was added ca. 1983).

Fundamentally, the zeppelin bend is formed from two superposed loops of opposite chirality. This is in contrast to the rigger’s bend (AKA Hunter’s bend, #1425A) which is formed from two inter-linked loops of the same chirality.

Chirality refers to the “handedness” of the loop, which can be either left (designated “S”) or right (designated “Z”). The chirality of a loop cannot be changed by flipping or turning it over – in the same way, a left shoe cannot be transformed into a right shoe by flipping or turning it over (it is always a left shoe).

The zeppelin bend is difficult to tie while ropes are under tension (which is further obvious evidence that it wasn’t used with mooring lines during ground handling of airships). In fact, with any ‘end-to-end joining knot’ (i.e. bend), existing tension in the ropes makes the tying process extremely difficult (if not impossible). The zeppelin is therefore tied with two loose ends (i.e. no existing tension) ending with a simple knot on each, but woven to each other in a pattern specific to zeppelin. Butterfly bend, Hunter’s bend, and Ashley’s bend also weave one simple knot on either end but use their own different patterns.

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  Ends held together, inner main part forward
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  Outside end bent out and over both ropes
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  Outside end under both ropes and up through own loop
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  Inner end under inner main part, and through loops along outside end
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  Tighten by pulling opposite ends and main parts.

1. Form a loop in each of the ends of rope (one loop must be “S” and the other must be “Z” chirality)
2. Superpose (overlay) one loop over the other, orienting each loop so that both working ends face outwards/away from the central overlap.
3. Feed each working end though the central overlap of the two loops, ensuring that each working end goes in opposite directions.
4. Dress and set the knot by sequentially pulling on all four rope segments.
5. To untie, loosen the collars that form around each Standing Part (SPart).

Another method of remembering this knot is to visualize a “69”. To tie the knot with this method, follow the steps below:

1. Make a “6” with one line (rope) end. It is important that the working end (the free, short end) winds up on top of the standing end for the “6”.
2. Make a “9” with the other line end. Make sure that the working end (the free, short end) winds up on the bottom of the standing end
3. While keeping the 6 and the 9 intact, place the “6” over the “9”, with the holes of each number lining up, making absolutely sure the working ends are on opposite sides of the holes, and both working ends are outside, not in between the standing ends.
4. wrap the “tail” of the “6” first down, around both lines/hole edges, and up through the middle (circle) part of your “69”.
5. wrap the “tail” part of the “9” up, around both lines/hole edges, and down through the middle (circle) part of your “69”, it should pass along to the other working end in the opposite direction.
6. Pull each standing end while ensuring that the working ends are not pulled back out from the “69” holes to tighten. Pull each working end to tighten even more.

• 
  Simplest and therefore the slimmest version of Zeppelin bend
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  Zeppelin bend where the ends are secured with a stopper knot each
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  Zeppelin bend tied with bights creating two fixed loops protruding from the knot core
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  Zeppelin bend on bight with three very reliable fixed loops at the knot
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  Double slipped zeppelin bend with stopper knots at the ends
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  Double slipped zeppelin bend with slips locked using the knotted ends
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  Zeppelin knot—the working ends on the bend version create a bight/loop on the knot version
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  Zeppelin loop

• List of bend knots
• List of knots

The harness bend is a general purpose bend knot used to join two ropes together. The knot can be tied under tension and will not capsize.^[1][2]

The harness knot is essentially one half hitch and one crossing hitch each made by one of the two joined ropes, around the other ropes body. The ends get caught in between the two ropes and these two hitches, at the elliptical eye in the middle of the knot.

There are two other variants to this bend: a double harness bend with ends pointing in opposite directions, and a double harness bend with parallel ends i.e. with ends pointing in the same direction. The starting side of one of the hitches has to be different, in order to have the ends approach the elliptical eye in the middle, from the prescribed direction.

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  Double harness bend ABOK #1420 – untightened
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  Double harness bend with parallel ends ABOK #1421 – untightened
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  2 – sometimes ends are crossed, sometimes are not – like in abok 1420

The double harness bend is an unfinished Fisherman’s knot (or even a Double fisherman’s knot): the end needs to go through its own half hitch (twice) to form a (double) overhand knot.

The double harness bend is an unfinished Blood knot: The half hitches need to take one or several turns around both ropes before going through the eye in the middle.

The double harness bend with parallel ends is an unfinished Reever knot: The ends need to go through the opposite half hitch, to be lined up with its own rope body.

All these knots are more secure than the harness knot but they are not as easy to untie.

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  From double harness bend ABOK #1420 to Fishermans bend: ends through own half hitch
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  From double harness bend ABOK #1420 to Blood knot: ends take full rounds around both ropes before the half hitch
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  From double harness bend with parallel ends ABOK #1421 to Reever bend: ends through opposite half hitch

The harness bend is useful when one needs to tighten the slack in a binding loop before locking the knot in the tight position. The name probably comes from the use in fixing the saddle on the back of the horse, tightening as soon as the horse that has learned to inhale at first move, exhales.

In situations where a more professional quick and secure packing is required, it may be more proper not to tie a harness bend starting with a crossing hitch and locking with a half hitch, but another more reliable combination of loop to tighten in, and hitch to lock with, such as these:

• a Packer’s knot starting with a figure-eight knot and locking with a half hitch,
• a corned beef knot starting with a buntline hitch and locking with a half hitch,
• another alternative is starting with a bowline and locking with a sheet bend

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  Harness of leather and blue fabric band
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  Packers knot
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  Sheet bend to bowline’s loop

• List of bend knots
• List of knots

• How to tie

Hangman’s knot
Names	Hangman’s knot, hangman’s noose, collar
Typical use	Hanging
ABoK	#1119, #366

The hangman’s knot^[1] or hangman’s noose^[2] (also known as a collar during the Elizabethan era) is a knot most often associated with its use in hanging a person.

This knot was typically used as a method of capital punishment. The pull on the knot at end of the gallows often resulted in a cervical fracture. Another method intended to result in the mass of the knot crushing closed (occluding) neck arteries, causing cessation of brain circulation, which was not always rapid. The knot is non-jamming but tends to resist attempts to loosen it.

Surviving nooses in the United Kingdom show simple slipknots that were superseded in the late 19th century with a metal eye spliced into one end of the rope, the noose being formed by passing the other end through it. The classic hangman’s knot was largely developed in the United States. Filmed hangings of war criminals in Europe after World War II, conducted under US jurisdiction, show such knots placed in various locations.

Each additional coil adds friction to the knot, which makes the noose harder to pull closed or open. When Grover Cleveland was the sheriff of Erie County, he performed two hangings. Cleveland was advised by a more experienced Sheriff to grease the rope with tallow and run it through the knot a few times to ensure rapid closure with the drop. The number of coils should therefore be adjusted depending on the intended use, the type and thickness of rope, and environmental conditions such as wet or greasy rope. One coil makes it equivalent to the simple running knot.

Woody Guthrie sings of the hangman using thirteen coils:^[3]

Did you ever see a hangman tie a hangknot?
I’ve seen it many a time and he winds, he winds,
After thirteen times he’s got a hangknot.

• List of knots

• The Ashley Book of Knots discusses this knot in the entry for drawing #1119

• Media related to Hangman’s nooses at Wikimedia Commons
• How to tie a Noose Knot using Step-by-Step Animations

Handcuff knot
Names	Handcuff knot, Hobble knot
Category	Loop
Related	Tom fool’s knot, Fireman’s chair knot
ABoK	#412, #1134, #1140, #2292

A handcuff knot is a knot tied in the bight having two adjustable loops in opposing directions, able to be tightened around hands or feet. The knot itself does not possess any inherent locking action, and thus is not as easy to use for such purposes as the name might suggest.

The knot is also known as a hobble knot for similar reasons, from the idea that the knot was sometimes used on the legs of horses to limit the distance their riders had to walk in the morning to retrieve them.

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  1. Two loops
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  2. Pull through
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  3. Tighten

The knot consists of two simple loops, overlaid, and with the ends pulled through. At that stage, the knot is slippery and easy to adjust. The knot can be “locked” by making one or more overhand knots with the loose ends in the manner of a square knot.^[1]

The sizes of the two loops can also be fixed by making half hitches with each end over the necks of the loops. This configuration is known as the fireman’s chair knot.

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  Handcuff knot “locked” with an overhand knot
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  Handcuff knot “locked” with half hitches, this is also known as the Fireman’s chair knot

• Tom fool’s knot, a similar knot sometimes incorrectly identified as a handcuff knot
• List of knots

In mathematics, especially in knot theory, a Wirtinger presentation is a finite presentation where the relations are of the form ${\displaystyle wg_{i}w^{-1}=g_{j}}$ where ${\displaystyle w}$ is a word in the generators, ${\displaystyle \{g_{1},g_{2},\ldots ,g_{k}\}.}$ Wilhelm Wirtinger observed that the complements of knots in 3-space have fundamental groups with presentations of this form.

A knot ${\displaystyle K}$ is an embedding of the circle ${\displaystyle S^{1}}$ in three-dimensional space ${\displaystyle \mathbb {R} ^{3}}$. (Alternatively, the ambient space can also be taken to be the three-sphere ${\displaystyle S^{3}}$, which does not make a difference for the purposes of the Wirtinger presentation.) The open subspace which is the complement of the knot, ${\displaystyle S^{3}\setminus K}$ is the knot complement. Its fundamental group ${\displaystyle \pi _{1}(S^{3}\setminus K)}$ is an invariant of the knot in the sense that equivalent knots have isomorphic knot groups. It is therefore interesting to understand this group in an accessible way.

A Wirtinger presentation is derived from a regular projection of an oriented knot. Such a projection can be pictured as a finite number of (oriented) arcs in the plane, separated by the crossings of the projection. The fundamental group is generated by loops winding around each arc. Each crossing gives rise to a certain relation among the generators corresponding to the arcs meeting at the crossing.

More generally, co-dimension two knots in spheres are known to have Wirtinger presentations. Michel Kervaire proved that an abstract group is the fundamental group of a knot exterior (in a perhaps high-dimensional sphere) if and only if all the following conditions are satisfied:

1. The abelianization of the group is the integers.
2. The 2nd homology of the group is trivial.
3. The group is finitely presented.
4. The group is the normal closure of a single generator.

Conditions (3) and (4) are essentially the Wirtinger presentation condition, restated. Kervaire proved in dimensions 5 and larger that the above conditions are necessary and sufficient. Characterizing knot groups in dimension four is an open problem.

For the trefoil knot, a Wirtinger presentation can be shown to be

${\displaystyle \pi _{1}(\mathbb {R} ^{3}\backslash {\text{trefoil}})=\langle x,y\mid (xy)^{-1}yxy=x\rangle .}$

• Knot group

• Rolfsen, Dale (1990), Knots and links, Mathematics Lecture Series, vol. 7, Houston, TX: Publish or Perish, ISBN 978-0-914098-16-4, section 3D
• Kawauchi, Akio (1996), A survey of knot theory, Birkhäuser, doi:10.1007/978-3-0348-9227-8, ISBN 978-3-0348-9953-6
• Hillman, Jonathan (2012), Algebraic invariants of links, Series on Knots and Everything, vol. 52, World Scientific, doi:10.1142/9789814407397, ISBN 9789814407397
• Livingston, Charles (1993), Knot Theory, The Mathematical Association of America

Studding-Sail Bend
Names	Studding-Sail Bend, Studding-sail Halyard Bend[1]
Category	Hitch
ABoK	#1678

Studding-Sail Bend^[2] is a way to attach the end of a rope at right angle to a cylindrical object such as a beam.

1. wrap the end two or more times around the object
2. make the end hook around the standing part and under all wrappings, to come out by the last wrap
3. make the end turn back and cross over the wrappings, to tuck/pass it under the first wrap

Halyard bend may be considered to be the “double-loop-around, and single-tuck-under” version of timber hitch which itself is usually tied as “single-loop-around, and double-tuck-under”.

• List of knots
• Topsail Halyard Bend
• Gaff Topsail Halyard Bend

In knot theory, Willerton’s fish is an unexplained relationship between the first two Vassiliev invariants of a knot. These invariants are c₂, the quadratic coefficient of the Alexander–Conway polynomial, and j₃, an order-three invariant derived from the Jones polynomial.^[1][2]

When the values of c₂ and j₃, for knots of a given fixed crossing number, are used as the x and y coordinates of a scatter plot, the points of the plot appear to fill a fish-shaped region of the plane, with a lobed body and two sharp tail fins. The region appears to be bounded by cubic curves,^[2] suggesting that the crossing number, c₂, and j₃ may be related to each other by not-yet-proven inequalities.^[1]

This shape is named after Simon Willerton,^[1] who first observed this phenomenon and described the shape of the scatterplots as “fish-like”.^[3]