# Reef knot

"Square knot" redirects here. For the mathematical version of this knot, see square knot (mathematics). For another knot known as "square knot", see friendship knot..
Reef knot
Names Reef knot, Square knot, Hercules knot
Category Binding
Category #2 Bend
Origin Ancient
Related Thief knot, Granny knot, Grief knot, Surgeon's knot, Shoelace knot
Releasing Jamming
Typical use Joining two ends of a single line to bind around an object.
Caveat Not secure as a bend. Spills easily if one of the free ends is pulled outward. Does not hold well if the two lines are not the same thickness.
ABoK #74, #75, #460, #1204, #1402, #2096, #2573, #2574, #2577, #2580
Instructions [1]

The reef knot or square knot is an ancient and simple binding knot used to secure a rope or line around an object. Although the reef knot is often seen used for tying two ropes together, it is not recommended for this purpose because of the potential instability of the knot, and over-use has resulted in many deaths.[citation needed]

A reef knot is formed by tying a left-handed overhand knot and then a right-handed overhand knot, or vice versa. A common mnemonic for this procedure is "right over left; left over right", which is often appended with the rhyming suffix "... makes a knot both tidy and tight". Two consecutive overhands of the same handedness will make a granny knot. The working ends of the reef knot must emerge both at the top or both at the bottom, otherwise a thief knot results.

## Naming

The reef knot is at least between 4,000 and 9,000 years old. The name "reef knot" dates from at least 1794[1] and originates from its common use to reef sails,[2][3] that is to tie part of the sail down to decrease its effective surface area in strong winds. To release the knot a sailor could collapse it with a pull of one hand; the sail's weight would make the collapsed knot come apart. It is specifically this behavior which makes the knot unsafe for connecting two ropes together.[4]

The name "square knot" is found in Dana's 1841 maritime compendium A Seaman's Friend, which also gives "reef knot" as an alternative name.[5][6]

## Uses

The reef knot is used to tie the two ends of a single line together such that they will secure something, for example a bundle of objects, that is unlikely to move much. In addition to being used by sailors for reefing and furling sails, it is also one of the key knots of macrame textiles.[7]

The knot lies flat when made with cloth and has been used for tying bandages for millennia. As a binding knot it was known to the ancient Greeks as the Hercules knot (Herakleotikon hamma) and is still used extensively in medicine.[8] In his Natural History, Pliny relates the belief that wounds heal more quickly when bound with a "Hercules knot".[9]

It has also been used since ancient times to tie belts and sashes. A modern use in this manner includes tying the obi (or belt) of a martial arts keikogi.

With both ends tucked (slipped) it becomes a good way to tie shoelaces, whilst the non-slipped version is useful for shoelaces that are excessively short. It is appropriate for tying plastic garbage or trash bags, as the knot forms a handle when tied in two twisted edges of the bag.

The reef knot figures prominently in Scouting worldwide. It is included in the international membership badge[10] and many scouting awards.[11] In the Boy Scouts of America demonstrating the proper tying of the square knot is a requirement for all boys joining the program.[12] In Pioneering (Scouting), it is commonly used as a binding knot to finish off specialized lashing (ropework) and whipping knots.[13] However, it is an insecure knot, unstable when jiggled, and is not suitable for supporting weight.

A surgeon's variation, used where a third hand is unavailable, is made with two or three twists of the ropes on bottom, and sometimes on top, instead of just one.

## Misuse as a bend

The reef knot can capsize (spill) when one of the free ends is pulled outward.

The reef knot's familiarity, ease of tying, and visually appealing symmetry conceal its weakness. The International Guild of Knot Tyers warns that this knot should never be used to bend two ropes together.[14] A proper bend knot, for instance a sheet bend or double fisherman's knot, should be used instead. Knotting authority Clifford Ashley claimed that misused reef knots have caused more deaths and injuries than all other knots combined.[15] Further, it is easily confused with the granny knot, which is a very poor knot.

## Physical analysis

An approximate physical analysis[16] predicts that a reef knot will hold if $2\mu e^{\mu\pi} \ge 1$, where μ is the relevant coefficient of friction. This inequality holds if $\mu \gtrsim 0.24$. Experiments show that the critical value of μ is actually somewhat lower.[17]

## Notes and references

1. ^ David Steel (1794), The Elements and Practice of Rigging and Seamanship, London: David Steel, p. 183
2. ^ Lever, Darcy (1998) [1819], The Young Sea Officer's Sheet Anchor (2nd ed.), Mineola, NY: Dover Publications, p. 83, ISBN 978-0-486-40220-8
3. ^ Cyrus Lawrence Day (1986), The Art of Knotting and Splicing (4th ed.), Annapolis: Naval Institute Press, p. 42
4. ^ Ashley, Clifford W. (1944), The Ashley Book of Knots, New York: Doubleday, p. 258, ISBN 978-0-385-04025-9
5. ^ Ashley, p. 220.
6. ^ Richard Henry Dana, Jr. (1997) [1879], The Seaman's Friend: A Treatise on Practical Seamanship (14th revised and corrected ed.), Mineola, NY: Dover, p. 49, ISBN 0-486-29918-X
7. ^ Ashley, pp. 399-400.
8. ^ Hage, J. Joris (April 2008), Heraklas on Knots: Sixteen Surgical Nooses and Knots from the First Century A.D., World Journal of Surgery 32 (4): 648–655, doi:10.1007/s00268-007-9359-x, PMID 18224483
9. ^ Pliny the Elder, Bostock, John; Riley, H. T., eds., The Natural History, p. 28.17, retrieved 2009-08-23
10. ^ See File:World Scout Emblem 1955.svg for an image of the emblem.
11. ^ Square Knots - Meaning and Placement, retrieved 2009-08-17
12. ^ Boy Scouts of America, Boy Scout Joining Requirements, retrieved 2009-08-23
13. ^ "Foolproof Way to ALWAYS Tie a Square Knot Right". www.scoutpioneering.com. Retrieved 2013-06-17.
14. ^ International Guild of Knot Tyers, Sea Cadet Knots, retrieved 2009-08-23
15. ^ Ashley, p. 18.
16. ^ Maddocks, J.H. and Keller, J. B., "Ropes in Equilibrium," SIAM J Appl. Math., 47 (1987), pp. 1185-1200
17. ^ Crowell, "The physics of knots," http://www.lightandmatter.com/article/knots.html