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All tied up

Sunday, August 3rd, 2008 01:02 pm

I like knots.

I was always terrible at them as a Cub Scout: in my pack, knotting was taught via a series of "rabbit goes out of the hole"-style mnemonics, which I could never remember or apply. I suspect this was one of the reasons why I never went further in the Scouting movement. However, a couple of years ago I picked up Geoffrey Budworth's excellent The Knot Book, which takes an entirely different tack. He dispenses with mnemonics in favour of clear diagrams and (where possible) a breakdown of the knot into simpler components. I think very visually, and learn best by connecting new ideas to things I already understand, so this approach works very well for me. Just as good is the organisation of the book: each knot is accompanied by a discussion of its pros and cons, and cross-references to related knots. Knots are largely collected together by function, allowing for easier comparison. For a couple of weeks, I spent most of my spare time tying knots in things, and festooning my flat with knotwork. I was particularly proud of the barrel sling arrangement for hanging a cup of tea off a doorknob.

When choosing knots, the two most interesting factors are usually

The breaking strain - knots (which are essentially twists and kinks in rope on which pressure is exerted unduly) all weaken the rope, often substantially. Different knots weaken the rope to different extents. This tendency is usually expressed as a percentage of the breaking strain of the unknotted rope - a simple overhand knot, for instance, has a breaking strain of 40%, which means that a rope with an overhand knot tied in it can be broken with 40% of the force that would usually be required. A reef knot (US: square knot) has a breaking strain of around 45%, whereas sheet bends and double fisherman's knots have breaking strains nearer 65% - this is one of the reasons why the reef knot is not recommended for joining two lines together.
The security - the tendency of the knot to come undone, particularly when subject to random, inconstant loads. Knots with the same breaking strain might have wildly different securities - for instance, the left-handed bowline is as strong as the right-handed version, but much less secure. Security's harder to measure than breaking strain, but UIAA bounce tests give some idea.

Different groups prioritise these differently - anglers, for instance, work with very thin line and comparatively high forces, so have evolved elaborate knots with breaking strains close to 100%, whereas climbers will often choose a more secure knot with substantially lower breaking strain - modern climbing rope has such absurdly high breaking strain that your rope, however knotted, will probably still be the strongest part of your belay or abseil (US: rappel) system. See this discussion of the best bend¹ for joining two abseil ropes together for some idea of the considerations used. Other factors come into play too, of course: climbers value knots which are visibly correct from some distance away, such as the Figure of Eight Loop, and sailors prefer knots that can be tied one-handed (so you can use your other hand to hang onto something). The nature of the rope to be used matters, too: many knots which were secure in hemp or gut had to be abandoned after the switch to synthetic ropes after the Second World War.

Budworth devotes specific chapters to discussing the knots used by three groups: sailors (of which he is one), anglers and climbers (including cavers). Which is all very interesting, but there's an important (and growing) group of rope-users he leaves out, namely BDSM enthusiasts. While I'm not interested in BDSM per se², I am interested in their approach to knotting: what, I wondered, are the criteria that they use for selecting the knots that they use? Which ones do they select? (And are BDSMers welcome at knotting conventions?)

I tried to work it out from first principles. A human being would be very unlikely to exert enough force to snap a modern rope, so breaking strain probably wouldn't be a consideration. Security, on the other hand, probably would. But there, I got stuck.

I was forgetting something, of course. Now we have an Internet, we don't need to wonder about things any more: we can simply go and find out. A quick search turned up this page, which answered many of my questions. Many of the usual suspects turned up: the reef knot, the lark's foot, the bowline, etc. No bends - I suppose BDSMniks have little occasion to join ropes together. I was rather surprised to see the Prusik knot (used by climbers to ascend a rope) - the author advocates using it as an adjustable loop. I'd have used a Tarbuck knot for that, but I suppose the Prusik is easier to check visually. I hadn't come across the French bowline before, but it turned out that that was the key to the mystery, for I had failed to spot the two key factors at play. When your hitching post is a human limb, it's vitally important to (a) minimise the pressure (force/area) on the skin - this means using lots of turns or loops to maximise the area of rope in contact, and (b) choose a knot that doesn't tighten under load, or you could constrict blood vessels. The lashings (knots used to hold two struts, or in this case, limbs, together) used follow a similar pattern - many loops of rope where only a couple would usually do. I imagine this improves the security of the lashing, too.

Googling for "bondage site:igkt.net" suggests that the International Guild of Knot Tyers (whose Vice President, mathematicians may be interested to learn, is the Fields Medallist and famous knot theorist Vaughan Jones) is well aware of the use of knots in bondage, but somewhat divided about whether or not to discuss bondage ropework on their main forum :-) It also appears that the analysis of breaking strain above is too simplistic - the precise geometry of each instance of a knot matters too.

¹ A bend is a knot used for joining two ropes together. A hitch is a knot used for attaching a rope to a solid point. Annoyingly, the Fisherman's Knot is a bend, and the Fisherman's Bend is actually a hitch.
² Though judging from my friends page, quite a few of you are: perhaps you'd care to comment? This is a public post, but feel free to comment anonymously if you'd rather.

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