Category: Knots

Palomar knot
Category	Hitch
Releasing	Non-jamming
Typical use	Fishing

The Palomar knot (/ˈpæləmɑːr/ PAL-ə-mar) is a knot that is used for securing a fishing line to a fishing lure, hook, or swivel.^[1] It is strong and easy to tie and with practice can even be tied in the dark.^[2] If tied properly, it leaves the hook free to rotate in the knot.^[2]

To tie the knot first double 20-30 cm (8–12 in) of line into a loop and pass it through the eye of the hook, lure or swivel. Tie a very loose overhand knot using the doubled loop and the doubled section of line leading back to the fishing rod. Pass the object to be tied through the remaining loop of the overhand knot and slide the loop up onto the line just above the eye of the hook. Moisten the knot to lessen the friction and pull on the tag and standing ends evenly to snug the knot down. Trim the free end of the line to a length of about 3 mm.

This knot is good for all kinds of light fishing lines, especially braided Dacron, and retains almost all of the original line strength, even with monofilaments. It also is nearly impossible (if tied correctly) to “pull out”. It is equally effective with other fastening applications – such as a dog clip to a rope – provided the object being tied to can pass through the loop, and the line or rope is not too thick to pass through the object twice, and, with practice, it can be tied in the dark with cold hands.

The Palomar Knot was developed by Chester J. “Chet” Palomar, a Scout leader and public servant from Pomona, California. He introduced the knot at a Fred Hall fishing show in 1971, where it impressed reps from DuPont so much that they adopted it as one of their best knots.^[3]

• 
  Make a bight and pass it through the ring.
• 
  Form an overhand knot
• 
  Pass the ring through the loop
• 
  further back
• 
  to the doubled line.
• 
  Trim the knot .
• 
  Finished.

• List of knots

• How to Tie a Palomar Knot, a how-to article from wikiHow

Category	Hitch
Related	Bowline
Typical use	attaching a line to a relatively inaccessible object, such as a vehicle axle
ABoK	#162, #1850

The axle hitch is used to tie a hitch in a hard-to-reach place, or for extra security by having a double hold on an object. When the initial bight is passed around the object, the rest of the knot can be completed out away from the cramped location.^[1] The knot is finished with a bowline knot or other reliable knot that connects the working end to the standing part.^[2]

It provides distributed strength and is useful when a shock load needs to be spread along an anchor point, since it provides four lines distributed across two points, in which case a double bowline or water bowline should be used as the security knot.

• List of knots

Packer’s knot
Names	Packer’s knot, Packing Knot
Category	Binding
Related	Corned beef knot, Butcher’s knot
Releasing	Jamming
Typical use	Baling, parcel tying, butchery, cooking
Caveat	Less secure than the corned beef knot
ABoK	#187, #408, #2083

The packer’s knot is a binding knot which is easily pulled taut and quickly locked in position. It is most often made in small line or string, such as that used for hand baling, parcel tying, and binding roasts. This latter use, and its general form, make it a member of a class of similar knots known as butcher’s knots.^[1][2]

A lightly tightened figure-eight knot is formed around the standing part of the line such that both ends emerge from the same point. Pulling on the standing part tightens the binding. After the desired degree of tension is reached, a locking half-hitch is added over the working end and pulled taut.

Even without the locking half-hitch the knot will generally maintain tension while additional tying is accomplished, such as putting a second, perpendicular, wrap on a package.^[3][4]

A similar knot made with an overhand knot instead of a figure-eight works almost as well.^[5] Many other variations also exist finishing with this style of locking half-hitch. In fact, Clifford Ashley claimed that there were more knots of this type to be found than any other used for a single purpose.^[1]

• Corned beef knot
• List of binding knots
• List of knots

• Diagram of a packer’s knot Archived 2010-12-24 at the Wayback Machine

In the mathematical subject of knot theory, the average crossing number of a knot is the result of averaging over all directions the number of crossings in a knot diagram of the knot obtained by projection onto the plane orthogonal to the direction. The average crossing number is often seen in the context of physical knot theory.

More precisely, if K is a smooth knot, then for almost every unit vector v giving the direction, orthogonal projection onto the plane perpendicular to v gives a knot diagram, and we can compute the crossing number, denoted n(v). The average crossing number is then defined as the integral over the unit sphere:^[1]

${\displaystyle {\frac {1}{4\pi }}\int _{S^{2}}n(v)\,dA}$

where dA is the area form on the 2-sphere. The integral makes sense because the set of directions where projection doesn’t give a knot diagram is a set of measure zero and n(v) is locally constant when defined.

A less intuitive but computationally useful definition is an integral similar to the Gauss linking integral.

A derivation analogous to the derivation of the linking integral will be given. Let K be a knot, parameterized by

${\displaystyle f:S^{1}\rightarrow \mathbb {R} ^{3}.}$

Then define the map from the torus to the 2-sphere

${\displaystyle g:S^{1}\times S^{1}\rightarrow S^{2}}$

by

${\displaystyle g(s,t)={\frac {f(s)-f(t)}{|f(s)-f(t)|}}.}$

(Technically, one needs to avoid the diagonal: points where s = t.) We want to count the number of times a point (direction) is covered by g. This will count, for a generic direction, the number of crossings in a knot diagram given by projecting along that direction. Using the degree of the map, as in the linking integral, would count the number of crossings with sign, giving the writhe. Use g to pull back the area form on S² to the torus T² = S¹ × S¹. Instead of integrating this form, integrate the absolute value of it, to avoid the sign issue. The resulting integral is^[2]

${\displaystyle {\frac {1}{4\pi }}\int _{T^{2}}{\frac {|(f'(s)\times f'(t))\cdot (f(s)-f(t))|}{|(f(s)-f(t))|^{3}}}\,ds\,dt.}$

• Buck, Gregory; Simon, Jonathan (1999), “Thickness and crossing number of knots”, Topology and Its Applications, 91 (3): 245–257, doi:10.1016/S0166-8641(97)00211-3, MR 1666650.
• Ernst, C.; Por, A. (2012), “Average crossing number, total curvature and ropelength of thick knots”, Journal of Knot Theory and Its Ramifications, 21 (3): 1250028, 9, doi:10.1142/S0218216511009601, MR 2887660.
• Diao, Yuanan; Ernst, Claus (2001). “The Crossing Numbers of Thick Knots and Links”. In Jorgr Alberto Calvo; Kennrth C. Millet; Eric J. Rawdon (eds.). Physical Knots: Knotting, Linking, and Folding Geometric Objects in R³. Contemporary Mathematics. Vol. 304. Las Vegas, Nevada. ISBN 0-8218-3200-X.{{cite book}}: CS1 maint: location missing publisher (link).
• O’Hara, Jun (2003). Energy of knots and conformal geometry. K&E Series on Knots and Everything. Vol. 33. Singapore: World Scientific Publixhing Co. Pte. Ltd. ISBN 981-238-316-6.

Overhand loop
Names	Overhand loop, Loop knot
Category	Loop
Origin	Ancient
Releasing	Jamming
ABoK	#1009, #1046, #518

The overhand loop is a simple knot which forms a fixed loop in a rope. Made by tying an overhand knot in the bight, it can be tied anywhere along a rope (does not need any working end). The knot can be used for attaching clips, hooks, other rope, etc., but has the disadvantage that it is likely to jam tight when the rope has been pulled and the knot may need to be cut off. It also has some uses in kite-flying, though other knots may be better. It is commonly disapproved by cadets because of its tendency to be misused as an alternative to the bowline.^[1] (Reference 1 also contains a sequence of images that show how to tie an overhand knot.)

An autoblock (or autobloc or “third hand”) is a rope device used in climbing and caving for both rappelling (downward) and ascending (upward).^[1][2]

While rappelling, it slides freely down the rope when pushed downward by the hand, allowing a controlled descent, but jams in the event of a sudden drop or loss of control, stopping the descent. This prevents uncontrolled falls in the event of an accident in which the rappeler loses control of the rope.^[3] For ascending, it likewise can be pushed up the rope manually when unweighted, but jams and holds when weighted by the body.

It is made using a friction hitch around the rope, connected by a carabiner to the climber’s harness, and may be combined with other climbing equipment for further safety.^[4] For instance, it is typically used as a backup while rappelling using a tube belay device.^[1]

The term autoblock is also used for a specific type of friction hitch,^[5][2][6] which is also known as a French prusik or Machard knot, named after its inventor, Serge Machard.^[7][8]

Other friction hitches that can be used to build an autoblock system include the Prusik knot, Klemheist knot, and Bachmann knot.

The Ashley Book of Knots #505.

• List of knots

• Grog. “The Klemheist”. Animated Knots. Retrieved May 5, 2013.
• Backing up an Abseil

Overhand knot with draw-loop
Category	Hitch
ABoK	52

A slipped half hitch^[1][2] is a knot in which the weight of the load the rope carries depresses the loop sufficiently to keep it in place until the load item is placed in its location. When no longer required the free end may be pulled and draw the loop through and so release the load.

• 
  Tying onto a ring.
• 

The Overhand Noose^[3]
is sometimes used as a Slip Knot to form the loops of a Trucker’s Hitch, or as a Stopper. Double Noose is used in arboriculture to fix a rope to a carabiner. Today this knot is mistakenly named like Barrel Hitch.

• 
  Make an eye, the working end is shown on the right.
• 
  Bring the eye left and down, in front of the standing part.
• 
  Pull the standing part through the eye, forming a bight. The working end is shown below the standing end.
• 
  Tighten

• 
  Noose
  ABOK 43
• 
  Slip knot
  ABOK 529

• List of knots

An Austrian knot (or Hungarian knot), alternatively warrior’s knot or vitézkötés, is an elaborate design of twisted cord or lace worn as part of a dress uniform, usually on the lower sleeve. It is usually a distinction worn by officers; the major exception is the hussars, in which Austrian knots are worn by all ranks. British cadet under officers wear Austrian knots as part of their rank insignia.

Of Hungarian origin, the vitézkötés (in English “warrior’s knot”) evolved as an indicator of rank among hussars of the Hungarian army, and became part of the Hungarian noble attire since the 16th century. Later, as other nations added hussars to their armies, they started to use the knot as well. The reason for this was that hussar regiments were often established by Hungarian nobles and some retained the name of their founder; for example the Ladislas Ignace de Bercheny.

In the Austrian (later Austro-Hungarian) army of the 18th century epaulettes were widely perceived as foreign (due to their French origin) and thus unacceptable. In the hussar regiments ranks came to be denoted by braided gold cords on the sleeve, with the number of gold cords representing the seniority of the officer. Other branches of the Austrian Army used a system of waist-sashes and collar stars to distinguish commissioned rank.

Austrian knots soon appeared as part of the distinctive uniform of hussar regiments in the armies of other European nations but did not gain wider popularity until the last decades of the nineteenth century. First the French army, then the Dutch,^[1] Romanian, Japanese,^[2] Turkish^[3] and several Latin American armies adopted this insignia to distinguish officer ranks. British officers of most regiments wore Austrian knots of a simplified pattern in gold braid on the cuffs of their full-dress tunics^[4] until this order of uniform ceased to be generally worn after 1914.

Along with most other elaborate and conspicuous indicators of rank, Austrian knots fell into disuse during the First World War and were not revived in everyday wear. An exception was the French Army where the kepis still worn by most officers have Austrian knots in cruciform pattern on the top crown. French officers of North African regiments such as the zouaves and the Algerian tirailleurs continued to wear Austrian knots in gold braid on the sleeves of their colourful full-dress uniforms until 1939. They are still worn on some parade uniforms in France, where they are called nœuds hongrois (“Hungarian knots”).

During the American Civil War, Confederate officers often wore gold Austrian knots on their uniforms. More elaborate braiding indicated higher rank. This type of insignia was worn by officers of the US Army on the sleeves of the blue full-dress uniforms authorised until 1917. It is a feature of the blue mess-dress uniform adopted as optional wear for officers in 1937 and still worn for formal social or evening functions.

• Frog (fastening) – decorative fastener which originated from China and was adopted in the military clothing of Western countries.

Ashley’s stopper knot
Names	Ashley’s stopper knot, Ashley stopper knot, Oysterman’s stopper
Category	Stopper
Origin	Clifford Ashley, c. 1910
ABoK	#526
A/B notation	820

Ashley’s stopper knot, also known as the oysterman’s stopper, is a knot developed by Clifford W. Ashley around 1910. It makes a well-balanced trefoil-faced stopper at the end of the rope, giving greater resistance to pulling through an opening than other common stoppers. Essentially, the knot is a common overhand noose, but with the end of the rope passing through the noose eye, which closes upon it. It may be multiplied to form a larger knot with more than three bights appearing around the knot. It is the result of implementing a double wall knot in one strand.

Ashley developed this knot in trying to duplicate a knot he saw on a boat in a local oyster fishing fleet. When he had a chance to observe the knot up close at a later time he realized it was just a badly water-swollen figure eight stopper knot.^[1]

The oysterman’s stopper…It is a larger knot than the figure-eight, which has but one part around the stem. The oysterman’s stopper knot has three rim parts, and these are quite symmetrical when viewed from the underside. From this view it closely resembles a three-strand wall knot. The end is nipped by a single top part. It is easy to tie and practical to use when the hole that is to be filled is too large for the figure-eight.

1. Form an overhand noose, or simply tie an overhand knot around the standing part as shown.
2. Tighten the overhand portion of the knot around the standing part. Thread the working part through the loop.
3. First close the noose on the working part by pulling on the standing part, then remove any remaining slack in the knot by pulling on the working part. The knot should have a tidy, triangular shape where the standing part enters the knot. (See image at right.)

• List of knots

• Budworth, Geoffrey (2001). The Ultimate Encyclopedia of Knots & Ropework. Anness Publishing LTD. ISBN 9781859679111.

Ossel hitch
Category	Hitch
Related	clove hitch, ground-line hitch, snuggle hitch, Munter hitch

The ossel hitch^[1] is a knot used to attach a rope or line to an object. It was originally used on Scottish gill nets to tie small line to larger rope that supported the net. Ossel is actually the Scottish word for “gill net” and for the line attaching the net to the float rope.^[2][3]

Rather, the ossel hitch works only on objects that are approximately the same diameter as the line, as the tail must be nipped under the initial turn, which if made on a larger object will have a gap between line and object.

To what extent the true history of this knot can be learned is a matter of speculation; knots books are notoriously inaccurate. Examination of such “snood”/”gangion” hitches in commercial fishing in the present day will show that it is typical to tuck the hitching line (the snood) through the lay of the object line – which implies that braided lines are not used here. In such cases, various simple hitches – e.g., the clove hitch, the ground line hitch – can be used, with the tucked tail providing security of the knot against both loosening and shifting position along the line. In some areas, lobster fishing is done with long ground lines to which numerous lobster pots are connected via approximately 10′-long snoods. It is possible that the ground line will at times be hauled up from different ends, so hitches might need to endure pulls from either direction.

Place a turn around the rope or spar and come up to the left of the standing part of the line. Cross over the standing part and make a turn around the rope or spar in the opposite direction. Finally, pass the working end over the second turn and tuck it under the first turn. Set the knot and tighten the knot.

• 
  1. Turn and cross over…
• 
  2. Turn in opposite direction…
• 
  3. Tuck behind 2nd turn, through 1st…
• 
  4. Completed Ossel hitch.

• List of knots

• Video of knot being tied