Full Nelson loop and exploding bend - are these new?

[Hilary Mark Nelson]

I've developed a couple of knots that I think may be novel designs, and I'd like to invite the IGKT members to take a look and let me know if they have been previously described. I've posted diagrams, descriptions, and videos showing how they can be tied on my personal website at http://hilarynelson.com/Hobbies/Knots. Here are a couple diagrams showing the basic knots (the website includes improved versions of each):

Full Nelson Loop

Full Nelson Exploding Bend

What I am calling the Full Nelson Loop is, I think, both more secure than a bowline, and at least as strong. The Full Nelson Exploding Bend comes apart immediately and completely when the ripcord is pulled, with no tendency to tangle, as with Peter Suber's exploding knots.

While I hope that these will survive your scrutiny and turn out to be genuine innovations, I'd be happy to be proved wrong, and will be very interested in any antecedents that you may turn up.

-Hilary Mark Nelson
West Lafayette, Indiana, USA

[Nadiral]

I visited your page some time ago and read that you had find that your exploding bend wasn't original.  I haven?t find it anywhere else, nor the loop.

Best wishes.

[Nadiral]

I went to your site and now it is all clear to me.  In my opinion, both are new knots.

[Dan_Lehman]

On your WWWebsite you claim that, for one/both? of the Full Nelson loopknot
 "Tests I conducted at Purdue have shown it to be at least as strong as a bowline."
1) Which knot was tested?
2) What sort of testing was done (and how was  this compared w/the Bwl)?

As for the bend(s), why not just slip the Lapp Bend?

--dl*
====

ps:  "Now these things kind of creep me out."  They shouldn't--they're graceful.

[Hilary Mark Nelson]

In the summer of 2006 I was allowed to use the materials testing lab at Purdue University's School of Materials Engineering to test the strength of a variety of knots. I just dug up my data and discovered that I didn't test the bowline. Here's the list:

    * Unknotted Line (as a control)
    * Zeppelin Bend
    * Double Figure 8 Bend
    * Johnson Hitch
    * Full Nelson Loop
    * Full Nelson Bend
    * Full Nelson Bend Simple
    * Fixed Noose

The FN Loop was probably version 1. One of the 2 FN Bends was the basic FN Bend that I have on my site, the other would have been either the same with an extra wrap, or the same with one less wrap. I took before and after photos of all the samples, and if I can find them I may be able to tell which it was. The easy-releasing elaboration of the FN Bend that I just discovered was not included.

The Fixed Noose was another knot I came up with. It looks like like a hangman's noose, but doesn't slide. I'd hoped that all the turns would make it stronger, but it turned out to be one of the weakest of the bunch. So it goes.

The tests were performed on a big, expensive, computer-controlled machine whose name I can't recall (MTS 810 servohydraulic system?). It had two large hydraulic rams that lifted a heavy cross-bar. The test samples were attached to grippers on the machine's base and cross-bar, and the test program slowly extended the rams, taking measuremnts of the strain through a load cell, and continuing until the sample broke.

I tested at least 3 samples of each knot (and the unknotted line), using some utility cord (10mm?) purchased from a local sporting goods store.

Note that the highest strain wasn't necessarily the last line of data. The strain would generally drop off a bit near the end, when a lot of the strands had broken and the last few were stretching toward failure and unable to provide much resistance. As the samples approached their failure point they'd typically show at least 2 or 3 sudden drops in the strain as fibers in the core snapped. The strain would usually go through a few peaks of increasing height, followed by drops, before finally failing completely.

The unknotted line failed between 570 and 580 lbf., and was, of course, the best result from all the tests.  The Zeppelin Bend made it to 365-371 lbf., and the Double Figure 8 reached 362-385 lbf.

The FN Loop highest strains were 408-428 lbf., which really surprised me. I'd expected the Double Figure 8 to be quite a bit better than anything else, but the FN Loop exceeded it by a significant margin.

The FN Bend rated 354-401 lbf., and the simple version ranged from 349-407 lbf. I have 4 samples for the simple FN Bend, and the lowest test is significantly lower than the other 3. I believe that's because that was the test where one of the grippers failed.

The Johnson Hitch only reached 314-365 lbf., and my Fixed Noose ranged from 319 to 380 lbf.

I really wish I'd had time to test a bowline or other common loop knot. (I had my kids with me, and after a few hours they started getting cranky.) The FN Loop looks good compared to the bends, but maybe loops in general fail at higher strains than bends. In that case, the FN Loop might turn out to be at the low end of loop strength. (The relatively weak Fixed Noose would argue against that interpretation, however.)

At the moment I can't say, but I can say that it was stronger than a Double Figure 8, which I've always heard was considered to be very strong.

I've made all the data from those tests available as a .zip file, and it's free for anyone to review and share as long as the accompanying ReadMe.txt file is included. I just added a link to it from my knot page, and someday I hope find time to graph all the results and include photos of the samples. Here's the location: http://hilarynelson.com/Hobbies/Knots/KnotLoadTests.zip

As for slipping a Lapp bend... I can't say because I'm not familiar with it. I tried to find something about it on the web, but all I could locate were text descriptions, which I couldn't quite follow. Can you point me to any place where I can see a diagram or photo of one?

Thanks!
-Hilary

[Dan_Lehman]

In the summer of 2006 I was allowed to use the materials testing lab ...

I hope you didn't wear out your welcome?!

The Fixed Noose was another knot I came up with. It looks like like a hangman's noose, but doesn't slide.
I'd hoped that all the turns would make it stronger, but it turned out to be one of the weakest of the bunch. So it goes.

An image would be good, or maybe just the tying description.

using some utility cord (10mm?) purchased from a local sporting goods store.

Knowing this, too, would be helpful.  Given the reported strengths and size, it must've been
natural-fibre cord.

The unknotted line failed between 570 and 580 lbf.,

Do you recall where it failed?  (E.g., amidst the open span, or at the pins?)

The Zeppelin Bend made it to 365-371 lbf., and the Double Figure 8 reached 362-385 lbf.

65%-ish.  Common enough of a value.

The FN Loop highest strains were 408-428 lbf., which really surprised me.

72%, not bad.

The FN Bend rated 354-401 lbf., and the simple version ranged from 349-407 lbf. I have 4 samples for the simple FN Bend, and the lowest test is significantly lower than the other 3. I believe that's because that was the test where one of the grippers failed.

Hmmm, but in one case, anyway, there is quite a range?

The FN Loop looks good compared to the bends, but maybe loops in general fail at higher strains than bends.

There was a fellow who tested all sorts of bends against each other,
anchoring the test specimens with Fig.8 loopknots--which never broke!

I can say that it was stronger than a Double Figure 8, which I've always heard was considered to be very strong.

I take it from your having Budworth's Ultimate Encyc.... that by this name you
mean something unlikely to be the intended referent to what you "always heard"
--for the pull-together knot w/Fig.8s (rather than Overhands, as for the common Fisherman's Knot)
isn't very common.  Rather, such a name has been used for the Flemish/Fig.8 bend, as well as
for the Offset Fig.8 bend.  Still, one might expect that pull-together one to be stronger?  Although
it can impart significant torsion, maybe?!

As for slipping a Lapp bend... I can't say because I'm not familiar with it. I tried to find something about it on the web, but all I could locate were text descriptions, which I couldn't quite follow.

A text description should be simple and quite easy:  Reverse Sheet Bend.
(reversing the so-called same-side Sheet bend (hence, ends, resp. SParts, lie
on same side after reversal))

Thanks,
--dl*
====

[Hilary Mark Nelson]

Lab access: whether or not I'd be welcome to use the lab again is an open question, and one that I haven't explored yet.

As I mentioned, one of the grippers partially failed during the tests. The gripper had a sort of horizontal bollard or mandrel that you wrapped the sample around, and the end was then secured in a small vice that was part of the gripper. The whole body of the thing appeared to be cast iron. At one point I was tightening the vice's knob on a sample when it suddenly got easier and easier to turn, and then the knob an part of the vice came off in my hand. The part tha the vice's adjuster thread went through had fractured and fallen off.

I was able to keep testing by anchoring the ends of the samples with a few wraps around the body of the gripper, so the failure didn't put a halt to everything.

Thinking that the gripper would be maybe a couple of hundred dollars, I happily volunteered to pay for it. Imagine my shock when I found out that a replacement would be something like $2,000! The lab manager said he was going to try to get the part welded back together, and I haven't heard more from him about it since, so I'm hoping it was repairable.

So... even though I don't think I did anything wrong, they may not be eager to let me back in the lab. I'll just have to see what they say, should I ever want to try some more tests.

Fixed Noose: I'll try to make a drawing or post a photo on my site. I'll add a note here when I do.

Cord: it was some sort of synthetic kern/mantle type of utility cord. When I get my photos up, you should have a good idea of the sort of stuff it was.

Unkotted line failure: I'm pretty sure it was in the middle. Again, the photos may hold the answer. All the knots, of course, failed at the knot.

FN Bend-Simple: The 4 samples highest strains were 349, 362, 388, 407. That's quite a wide range, but most of the knots showed a fair amount of variation.

Double Figure 8: Yes, I meant the Flemish Figure 8 bend, as illustrated here: http://www.animatedknots.com/fig8joinrescue/index.php

A text description should be simple and quite easy:  Reverse Sheet Bend.
(reversing the so-called same-side Sheet bend (hence, ends, resp. SParts, lie
on same side after reversal))

Should be easy and simple, perhaps, but you're still losing me.     Knots are just an off-and-on hobby for me, and I haven't completely digested the terminology. A picture would nail it in an instant.

Just out of curiousity, have you tried tying any of my knots? Do you have any thoughts about their utility, practicality, ease of tying (or lack of it), etc?

Also, if anyone wants to put together a short list of knots that they think would make a good test suite, I'll keep them in mind if I ever get around to trying to visit the lab again. (I have to finish making a bedroom in the basement for our son first -- a project that's been dragging on for a year and a half now!)

-Hilary

[Pinrail]

Quote
The FN Loop looks good compared to the bends, but maybe loops in general fail at higher strains than bends.
There was a fellow who tested all sorts of bends against each other,
anchoring the test specimens with Fig.8 loopknots--which never broke!

As I was reading this, I thought of something; perhaps a little off topic.  Could it be that we see two "lines" taking the strain of the load in a loop and only one in a bend?  Is this a possible explanation why bends may fail before loops? 

My thought was this: 
Picture a fixed anchorage point on a ceiling.  This is the "Knot"
Fix a rope to the anchorage point, and apply a 100 Kg load to it.  This "knot" would be the bend, supporting 100kg.

Now, Fix a pulley to the anchorage point.  Pass a rope over the pulley, and attach a 50 Kg load to each end.  To me, this could be a model of a Loop knot.  The anchorage point, or "knot" is still supporting a total load of 100 Kg, but each line leading out of it is only responsible for half the total load.  Granted, I am making several empirical assumptions to make the model work...like an equally loaded loop. 

Of course, I see a flaw in my logic; that both bend and loop have but a single line leaving one side of the knot, which would be taking the same strain, and could be the failure point of each.  Not having the opportunity to be part of any quantitative analysis of rope/knot strength, I'd be curious to hear what the world at large has already learned.


-Abe

[Hilary Mark Nelson]

As promised, here's a drawing of my Fixed Noose loop knot:



Does anyone recognize this? Is it something that's been around for a long time, and I just haven't seen it before?

Update: I think I just found it. I went thumbing through my Ashley Book of Knots and spotted a Heaving Line knot (#538) on  pg. 88. It appears to be the same as mine, except that I pull out a loop before threading the working end through one of the bends in the S to start wrapping it.

Pinrail: I don't whether or not you're on to something there. All I can say is that the knots always seemed to fail right at the knot. I don't recall whether the loops only failed on the single stranded side, or if they also failed on the loop sides.

Thanks,
-Hilary

[Dan_Lehman]

Double Figure 8: Yes, I meant the Flemish Figure 8 bend, as illustrated here:

Argh, that's exactly the ambiguous/impossible "flat" form of the knot that is commonly presented
(which will not stay so perfectly aligned under tension).  But, in any case, you've answered the
question, and indeed it is somewhat surprising (though we are yet guessing at the geometry
of rope that met the strain).

A text description should be simple and quite easy:  Reverse Sheet Bend.
(reversing the so-called same-side Sheet bend (hence, ends, resp. SParts, lie
on same side after reversal))

Should be easy and simple, perhaps, but you're still losing me.   

IS ... !  Tie a Sheet Bend; load the ends--voila!

Just out of curiosity, have you tried tying any of my knots?
Do you have any thoughts about their utility, practicality, ease of tying (or lack of it), etc?

Yes.  The bends are rather tedious to tie, and although the easier-to-release version
seemed to me also to be such, I don't see why it won't in fact become as tight, really
(I only played around a little with it), as the same jamming part has if anything less
resistance to its tightening than otherwise.  Re the utility of such "exploding" knots,
I remain skeptical (both of need and reliable function--slipped knots often require huge
forces to pull free).

Re the noose, that should be easily seen to be weak:  the SPart dives through those
hardly-so-tight-as-to-take-off-load wraps to make a 1dia u-turn against a loaded part.

As for the FNLoop, improved version, I was awaiting any sign of others' awareness,
for that has had some bit of presence on the WWWeb.  --to wit:



So, yeah, I've been tying some of your knots for quite a while.  The Locktights were
designed w/rockclimbing & caving kernmantles in mind.  Never had them tested, though.

 

[Hilary Mark Nelson]

IS ... !  Tie a Sheet Bend; load the ends--voila!

But the ends are so short! How're you going to attach a load to them?  

Repetition works. I think I get it now. (Of course, I might just be stupid enough to only think I get it.) Thanks!

Re the utility of such "exploding" knots, I remain skeptical (both of need and reliable function--slipped knots often require huge forces to pull free).

Fair enough. I'll have to see if I can come up with some real-world applications. To be honest, in the several years since I invented it, I haven't run across a situation where I really needed it.

Re the noose, that should be easily seen to be weak:  the SPart dives through those hardly-so-tight-as-to-take-off-load wraps to make a 1dia u-turn against a loaded part.

Yes, in retrospect that seems obvious. Being a rank amateur, though, I had to test it before I could see the obvious.

As for the FNLoop, improved version, I was awaiting any sign of others' awareness, for that has had some bit of presence on the WWWeb. ... So, yeah, I've been tying some of your knots for quite a while.  The Locktights were designed w/rockclimbing & caving kernmantles in mind.  Never had them tested, though.

Ha! I knew this was the place to come!

The Locktight Loop I is definitely the same as my FNLoop v2, albeit with one more wrap than mine. (And I'm sure it's a better knot for having the extra turn.) Thanks for setting me straight - I've updated my Knots page (http://hilarynelson.com/Hobbies/Knots) with references to your prior publication of the Locktight Loops at http://www.iland.net/~jbritton/KnotPhotoContributions.html. (The Lehman 8 looks really nice, too!)
Updated Link > www.pssurvival.com/PS/Knots/Knot_Knowledge_Photo_Illustrations_2004.pdf

I doubt that either of the FNLoops that I tested would have been exactly the same as the Locktight I, since even if I had the same number of turns, they would have been like my FNLoop v1, where the wraps don't all go over the standing part. Still, the data suggests that the Locktight I might be really strong. If I ever go back to the lab, would you like me to test it and see?

Thanks for the education, and I guess I'll just have to cross my fingers and let my hopes for a knotting legacy ride on the FNBend... useless and pointless as it may be.  

-Hilary

[Hilary Mark Nelson]

A footnote and correction: in my first post I mentioned that I thought the cord I used might have been 10mm.

I don't think in metric much, and I didn't have a clear image of what 10mm would look like. Had I even glanced at a ruler before writing, I would have known that 10mm was much larger than what I used. The cord I tied my samples in was more like 4mm.

Ooops.

-Hilary

[DerekSmith]

Hello Hilary,

It is good to meet you.  The moment I say your diagrams I new you were something special - they looked freehand, yet the line spacings were exact and some loops matched pixel perfect - how did you do that?  Then when I read your website I realised you were indeed a rarity (as indeed, sadly, all of us nutty knotologists are)  --  but an interest in knots, the Space Elevator, a programmer (with 3d skills) - all that AND access to a testing laboratory.  Well, I hope that we can encourage you to stay around and spend some more time on knots, while that great bag of other interests tries to drag you away.

At least, hopefully, you will stay long enough to teach us how to make diagrams like that !! and maybe over in Chit Chat share some thoughts on the Space Elevator (it is after all going to be the biggest and possibly most important, piece of 'cord' ever built), but hopefully, you will find the subject of knots so challenging you will stay around for much much longer.

Moving on then to the Nelson Loop and the Locktight II by Dan.  Although they are essentially similar, I have to wade in here and say that I believe that even discounting the number of turns variation, the two knots are NOT the same.

The essential difference is that in the Nelson, the SP takes a straight line through the coils before taking its first turn around the loop legs, while in the Locktight, the SP makes a full OH turn around one of the loop legs before starting its return coils and that is enough to define them as different knots even if you were to hold that leniency should be exercised over the number of body turns involved.  Yes, they are sisters, but they are not identical twins.

Keep them coming.

Derek

[Hilary Mark Nelson]

Derek,

I hate to argue against a claim that my knot is novel, but I think you may be confused by the drawings. Dan's drawing is of what would be the backside of my drawing, and I had to tie one of each and put them side-by-side to make a proper comparison. (I was bumping up against the limits of my spatial imagination.)

Also, I haven't posted a drawing of the Full Nelson v2 here, and it differs significantly from the FNv1 above. Here's the FNv2:



After a second review, I am quite convinced that if you take one coil off Dan's Locktight Loop I, you will have my Full Nelson Loop v2. (The FNv1 would be a different knot, but I think it's probably inferior.)

So thanks for the support, but I'm going to have to agree with Dan.  :-)

As for the drawings... I do them in Adobe Illustrator, and the technique is not as easy as I'd like it to be.

The basic idea is simple: I use a pen tool to make a single line that just follows the path of the cord in one solid stroke, crossing and curving as necessary. That line is black, maybe 10 points in width, with square ends that stop right at the last point in the line.

Then I copy it, paste it in front, change the color to white, and reduce the width by 2 points (to 8 pt., in this example). That gives you the perfectly parallel 1 pt. outline around the white cord.

The trick is getting the crossings. As described so far, all you have is a sort of black aura around the white silhouette of the cord -- there's no internal details that show what crosses what.

To get those, I start by making note of where the crossings will need to be. Then I copy sections of the black line that I need to form the crossing parts and place them on new layers above the base layer. To do that, I have to make sure that the original line has points at each place that I'll need to "cut" to get the pieces that form the crossing parts.

Once the black lines for the crossing parts are on a new, higher layer, I copy those sections, paste them in front, change the color of the pasted lines to white, reduce the width by 2 pts., and change the end style to rounded ends. That last step is important, because it prevents each of the crossing parts from having a black "end" that would appear to cut the line of the cord.

The technique is fairly easy for a single crossing, but when you have a knot with many parts crossing over each other in the same area, it can lead to a lot of layers, and planning where to place your points can be tricky.

It's also hard to revise once you start building your layers. If you get partway through and discover that you need to adjust a curve, or need another point somewhere, the best thing to do is just delete everything but the initial black line, make the adjustments, and start building layers all over.

If there's enough interest in the technique, I could probably find time to make a little demo page on my site that would illustrate the steps.

Thanks for the kind words, and I'll try to stay active on the site!

-Hilary

[DerekSmith]

Diagram reflected and reversed and I find that I have to make my apologies to both Dan and yourself - I was wrong, it is the same knot --

0/10 Derek, must try harder. 

I guess that my 'spatial imagination' ran into stack overflow as well.

As for the diagrams, well, I am impressed.  I work with Adobe Illustrator every day so I am well aware of the huge amount of work that you have had to put in to create these lovely diagrams.  Many many times harder than just drawing the thing with a pencil and paper.  Clearly you are both diligent and a perfectionist.  I am sure others would like to read the details of how you created them, but I doubt many will have the patience to create them for themselves.

That brings me round to FCB4 and your skills at 3D programming.

I don't know if you have followed the attempts at creating a knot diagram utility over at http://knotcyphers.pbwiki.com/  It is ultra simplistic but is none the less effective at creating diagrams very quickly.  However, because it is based on a very limited set of 18 predefined image tiles, it lacks the wonderful 3D freedom you have with the 'freehand' drawing method you have utilised.



 Creating the program and latterly the ability to generate a knot 'crossings signature' has taught us a lot about spatial mapping to generate the 'essence' of a knot and we are currently working on reflection, rotation and auto lookup in a Library of Knots.  However,the next big step would be to discard FCB4 and move to a system that allowed the knot to be viewed in 3D, rotated and 'filled out', that is, have the cord thicken so that the knot could 'dress' itself.

Perhaps such an undertaking is a long way off yet, but to even start thinking about it we would need 3D programming skills on board.  Would a challenge like this be of interest to you?

Derek