## ARTICLE: Knot Theory, in Practice - Studying The Mechanics of Knots

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Experiments with psychedelic, colour-changing fibres and spaghetti might sound more akin to child's play than to serious scientific research, but a team of mathematicians and engineers at Massachusetts Institute of Technology in Boston have slowly disentangled the Gordian knot of understanding the factors which determine knot strength, using pressure-sensing fibres to develop a new mathematical model - with some help from everyone's favourite stringy carbohydrate. The team hope that their findings outlined in the paper 'Topological mechanics of knots and tangles' could help match particular knots to specific safety purposes in climbing, sailing and rope access work.

Can anyone explain what the + and - mean?

From the paper:

'Tight knots act on themselves by right-handed (positive) and left-handed (negative) torques.
Equally directed torques lead to rolling, whereas opposite torques promote locking and thus stabilize a knot against untying.'

I am particularly keen to make the acquintance of a "robotic flicker" !

Does raise the simple question as to how many accidents are caused by failing knots in climbing( not knots that people forgot to tie or even incorrectly tied knots... which are different issues)

I suspect very very low numbers.

Ig Nobel submission for the work on spaghetti?

Are you trying to make me feel inadequate?

Is this work tied to string theory?

> Is this work tied to string theory?

No, it's knot.

> could help match particular knots to specific safety purposes in climbing, sailing and rope access work.

Do sailors need much help with knots? I suspect they're probably already pretty heavily optimised after six or seven thousand years of trial & error.

Not even loosely?

I'm a frayed knot.

Yes and no - modern ropes (especially dyneema ones) perform differently to the hawser-laid natural fibre ones of yesteryear.  Anglers using dyneema line have had to learn new knots as the traditional knots for nylon monofilament simply don't work.  Even traditional knots like the half-blood knot are being replaced with others such as the Uni knot for mono as people realise the old ways aren't necessarily the best.

I did indeed have that suspicion/doubt in the back of my mind as I was writing, thanks for confirming

Post edited at 07:53

This article says nothing about the most important requirement of climbing tie-in knots, namely that they be stable and secure when they're not under load and being manipulated as they're clipped into gear, taken in and paid out ("shake-stability"). None of the standard tie-ins will fail under fall loads if correctly tied and still intact, unless they're cross-loaded.

Andy --esp., as you've done much testing-- there are various things that should give one pause in greeting this article as showing some advance in knotting.  (1) They refer to knot *strength* often where what seems to be at issue we'd call *security* (granted, if knot-K slips untied at loads < knot-M, it IS in a sense less strong, but …), (2) they have the opposite-sides sheet bend slightly more secure than what most folks regard as better, the (tails_on_)same-side version; (3) worse?, they've got the reverse of these knots (one of which is called the "Lapp bend") in more differing rating and with the less secure one higher (!) (cross-/ring-loading the bowline (tail-inside loop) is vulnerable to spilling, vs. the tail-outside version precisely because of this security difference!); and there are errors in the presentation of images and ratings --e.g., in fig.S3, for "As"(hley) Bend (#1452), columns 2 & 4 are identically THE knot (i.e., properly loaded), but in the figure's text they isolate col.4 as "warping" --which col. 2 would also do, iffff, and IMO both will look, loaded, much as is shown (unlike the carrick bends!); Hu(nter) Bends col.1 & 3 are the same (mirror'd) but are +/-1 diff. in rating (!); and the Bu(tterfly) col.s 1 & 3 are identical but ratings differ by 7(!??).

How can smart knots researchers end up calling the sheet bend series "Bo(wline)"s ???  Which knots both have been in the literature since Grog chisled stone, and are well known esp. to sailor set, which allegedly includes one of the authors???  --somewhat of a nit, yes, but it's so point-blank obvious & simple, why botch this obvious knot naming? (They're, sadly, not alone : some recent climbing-aimed on-line presentation also managed to find a sheet bend vice a bowline … .)-:

Then there is the nonsense about these being commonly used end-2-end joints : NONE of these knots is much used in practice, to my awareness (as one who liked to spend time observing knotted structures around a marine setting --commercial fishers have some nifty stuff!).  Indeed, though it permeates the knotting literature, it's hard to come to some actual-factual ground in seeing the carrick bend used (seized tails or otherwise); Alaskan crab fishers use it in their stiff pot warp, but tie it (judging from a single instance seen on Deadliest Catch) in a different manner --preforming one end into a sort of Munter hitch and then reeving the other into it appropriately, the rope stiff enough not to play well with the popularly presented capsizing of the (what article shows) lattice form.

Finally (yeah, I can rant long re knot stuff), the Science (printed magazine) article has some photo images of knots tied in braided line; they claim "20mm" but I've looked at many ropes and … it just doesn't look IMO like "rope" but "cord", so … '2.0mm' maybe (I would guess a bit larger).  Who would end up getting 2cm-dia. rope for the heck of loading some knots --that's rather big, IMO.

((Given the particular orientation of ends of the set of knots chosen, it's a shame that the two tangled pieces of material --red & blue-- and the B&W loading guides atop columns labeled 1-2 & A-B, better indicating connection of which end to which other.))

kN*