Bend radius for rigging

Keeth

Participating member
Location
NC
I was taught long ago to maintain a 4:1 ratio when running lines. Anything less could damage the rope with repeated use. For a typical 1/2-inch rope, you’d need at least a 2-inch diameter for your pipe, bollard, pulley, or ring. Has the industry standard changed? I see guys running 3/4-inch lines through rigging rings on a regular basis. A local here rappels off a single carabiner when doing crane work. Has the standard changed or is it just being ignored?

Don’t get me wrong, I’m no purist. I’ve certainly used a figure eight, friction savers, and smaller than 2-inch rings and pulleys with 1/2-inch line in various applications for decades. I just try to minimize the less than 4:1 ratio use when loading the a line with a significant load. For me, “significant” with 1/2-inch is more than a 500-lb static, or a 200–lb dynamic load.

I asked a related question about this in the jail-brake thread, but I didn’t want to create a derail as my question is more broad.
 
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I would say it's ignorance due to convenience. Guilty here as well Keeth.

As far as I understand maintaining a 4:1 bend radius created almost no loss of strength to the cordage. By tying knots we're creating tight bend radius' as well.

We work with such big margins that we're probably going to wear a rope out long before we break one. Other industries are pushing they're ropes to the limit and need to be mindful of maximizing strength at bends and connections.

That all being said it still makes me cringe to see guys using a steel carbiner as a rigging point.
 
I was taught long ago to maintain a 4:1 ratio when running lines.
It might shock you to learn that rope manufacturers, at least Samson, recommend an 8:1 bend ratio for rope. The 4:1 is an educated compromise of sorts in my opinion. Minimal strength loss to size of block we need.

I like to use discretion. Light duty rigging, I'm ok with fudging the 4:1 (1/2" line in a pinto rig). I'd even climb off a pinto.
 
Thanks for asking this question. I observe a great variety of practices followed in the field on this subject.

I would say the danger is not so much potential breaking of rope, but undue wear and tear. I try to be responsible about my use of rope, both for my wallets sake, and the burden on our planet to refine petroleum to create that product.

A double headed extra large X ring on a sling gives a very generous bend radius. I was taught this is a must at the terminal rigging point and have found it an easy rule to follow. At redirects, a single X ring is acceptable. A block is usually my preferred terminal rigging point unless I’m getting into very large wood.

Industry approved crane slings built on two rings offer little more bend radius than a carabiner. But bombing out of that as a climber is a pretty small burden on a rope rated for 23kn.
 
It might shock you to learn that rope manufacturers, at least Samson, recommend an 8:1 bend ratio for rope.

Of course bigger is better, but not very practical. I love the Omni 2.6 for its extra girth and kN, but I’m under no illusion that the strength increase with bend radius is not really appreciable over the 2.0. I’m just curious if rope technology is that much better (it’s NOT,) or if the guidelines have shifted (maybe?)

I'd even climb off a pinto.

That is better than the standard double-ring friction saver I still use occasionally. However, I’m seeing more devices come out that are well below the 4:1 threshold for both rigging and climbing. I’m a bigger climber, so I pay close attention to mbs when trying new ropes and devices. It just seems much of the innovation in both areas doesn’t reflect the inevitable reduction in ‘cycles to failure’ that many of us think about constantly. For someone new to the industry, this is subtle, but for me it looks like a red flag. What do you guys think?
 
Of course bigger is better, but not very practical. I love the Omni 2.6 for its extra girth and kN, but I’m under no illusion that the strength increase with bend radius is not really appreciable over the 2.0. I’m just curious if rope technology is that much better (it’s NOT,) or if the guidelines have shifted (maybe?)



That is better than the standard double-ring friction saver I still use occasionally. However, I’m seeing more devices come out that are well below the 4:1 threshold for both rigging and climbing. I’m a bigger climber, so I pay close attention to mbs when trying new ropes and devices. It just seems much of the innovation in both areas doesn’t reflect the inevitable reduction in ‘cycles to failure’ that many of us think about constantly. For someone new to the industry, this is subtle, but for me it looks like a red flag. What do you guys think?
I think, like @Phil says, I would climb off a Pinto - for that matter, I do about as often as I climb. My crane tie in is based on a Pinto, and I’ve never had any real issues with running on it. Only problem I have is that it runs so smooth my ZigZag gets a little jerky from the lack of TIP friction.

Cycles to failure is a concern, and so is rope wear, except that the rope I climb on has a MBS of nearly 7k lbs, and I weigh 200. I’ll never take a 6’ fall to a dead stop which is what is necessary to hit 5k lbs. If I did take that fall, my back would likely break before the rope did.
 
i think we are actually comparing separate apple/orange things that have some similarities.
i think the 4/1 standard is more towards pulleys than frictions type force flow, and is also just a guide for 'standard' stiffness ropes. A stiffer rope would need more caring/babying (larger)ratio for the same amount of (d)effects. This is to wear/chafe but also an old standard (to best of my memory) quoted out also for 50% strength/efficiency loss as well shown on pulley by Samson. Thumbruling 50% loss of strength/efficiency in the knots used anyway as then, matched components thru the system type logic. Much more drastic losses in arcs also in dyneema etc. So materials, construction matter, not just diameter in the (d)evaluation.
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Pulley float/roll more tolerated than a bark friction grind, especially at lower host diameters ratio. Pulley and rope as a wearpoint rolls as one together as frictions more displaced to axle(larger sheave giving more efficiency/leverage over same diameter axle frictions). Capstan would model more towards continuous directions roll wearing at rope as capstan sits still and rope turns; more of a fight at more co$t i think as outer part of rope arc turns 1 way and inner part of rope arc is held/pushed the opposite way essentially i think. Then to 8x ratio model for 'full'(but not quite, always assume some loss) strength in standard, not stiffer ropes etc. Our knots are hopefully stronger than 50%, but closer to a wash tho in 4-10x safety margin/SWL's given, and can always go to larger pulley/capstan to help.
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But rack bends kinda yet even another different animal to me, and not seen 2" or larger rack bars on anything from same manufactures and engineers to same quoted usages over time.. I view rack as not the same as capstan, that i view as a radial list of arcs; where rack would model as more as linear list of arcs to compare, but actually more of a linear gauntlet/list of bends. i think the continuous direction turns of capstan more likely to twist rope etc. is not in rack because of the counter torque of the opposing arc directions in rack as like flaking, fig8ing, opposing turns type storages or even counter torque in Cow. In either the radial list of 180 arcs on capstan or linear list of arcs/bends in rack, very important that each arc apex does pull/serve to opposite direction of the previous and subsequent arc/bend apex in chain/list.
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Sweating is shearing across tight rope to leverage, then capturing the 'purchase'(ABoK) behind frictions perhaps to sweat harder now with stiffer line if load did not move, so friction points give more chance of usage. As the rope gets tighter linearly it presents a less rubbery lever to sweat more powerfully with. Might be able to hang on line, and pull part of rope up from after first bar at same time to pretighten to bodyweight from hang + pull up on end of rope force + equal and opposite of that effort expressed back on body hang hand for bodyweight + 2xEffort potential tightening, decreased by friction that initial pull up on rope has to go thru to lessen, but not the bodyweight nor equal opposite of the pull up effort. then sweat with that now less rubbery lever, pinch rope to bar as capture purchase. So, then sweat again or pull thru rest of arc gauntlet/list before release thumb pressure to first bar hold of purchase sweated(of rope from loaded bank of rope to unloaded side/bank on capstan tailer/people side of frictions buffer from load force).
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Across the (p)ages of time, ABoK distills out millenniums of lessons handed down, as Mr. Ashley saw these jewels threatening to disappear, that have been so loyal to us, and in fact perhaps human intellect built along with these things as a first/primary technology leading to many basic understandings.
For terminations/hitches on a small radius, ABoK lesson#1720:
"Round Turn & Two Half Hitches is named by Steel in 1794. If a spar is small a RT is preferable to a single turn. It makes a stronger knot and dissipates the wear."
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Kinda same in lesson#1883 on hooks always a smaller host arc(linear sides of hook of less consequence than linear force line to arcs).
"A ROUND TURN AND Two HALF HITCHES. Any HOOK HITCH: with a double bearing is stronger than one that passes through the hook but once."
(double bearing would be the 2 apex arcs of resistance on opposing side of host from load, how load hangs as if from 2 separate hooks instead of 1)
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lesson#1074. "The BOWLINE with a bight is tied in the end of a pendant to
which to hook a tackle. Whenever possible a hook should have a double bearing when it is to be hitched to a rope..."
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Later to this 'double bearing' concept to broaden wear notes a few times like in lesson#1690.
"A BACKHANDED HITCH. The next two knots, although they
have a double bearing, require but a single pass around the spar...."
as another key insight and help handed across thru the (p)ages of time, distilled from millenniums of experience and what made it thru the gauntlets to be handed down so confidently. And again this double bearing noted as significant; when sometimes just mentions such a mechanic 1x.
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In fact several times invites using Round Turn:
In Tree Surgeon/small section leads off with lesson#478
"There is unsuspected virtue in a few turns of line. A single
ROUND TURN on a branch will allow a man to lower several times his
own weight. The device is much simpler to manipulate than a tackle
but, of course, will not serve for hoisting."
And again lesson#1732:"There's a lot of virtue in a round turn."
All these hints to usage woven in, as we only count knots, and take any advice as specific to a knot, not a general mechanix lesson in rope workings...


Even taking Round Turn(RT) 3x180arcs concept on host to Standing Part(SPart) rather than host focus:
"If the rope is weak and the hoist is heavy, a round tum on the standing part adds
materially to the strength of the knot"
Working that backwards, in rigging i'll ALWAYS consider Round Turn around SPart, might not do every time; but will weigh and measure shituation w/that advice on how to upgrade on da'fly.
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knudeNoggin lends can't maximize both lessons at once w/RT on host and SPart. To me this would be because less force left over after RT on host to use RT to grip Standing Part. i think it does some anyway, and there is some 'virtue' in using RT in both positions, for the RT on SPart still grips the SPart to more pull along with it inline properly as grips with the 3x180arcs of RT, rather than not grip but rather just 'slide down the fire pole' to seat more against the host, rather than pull away from it at this 'seam' of drawing end back into works to secure. But now (do to sliding down to host) is decidedly shearing across the single column of SPart support more radically at the Samson Angle to to disrupt that support column. Note how at the seam is generally a linear rope part; so can ONLY max host grip by deforming SPart more to less efficient strength OR max towards strength w/less deformed SPart but less grip on host with this portion of rope, as antagonistic reciprocals of increase of 1 means decrease of other.
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i think there are more unlisted 'virtues' to an RT, and from all this seek to have at least 3x180 arcs in pro level knots on host and/or SPart as a key locking and spreading of wear quotients for right angle pulls, grip, frictions and nips and then those 3x180 arcs be needed specifically on host required for lengthwise pulls. All this as support geometry, where the support material just happens to be rope. ABoK chapterr__22 dedicated to 'lengthwise' pulls on host/load/support, and notes this 90degree usage of rope is worst angle to work rope at; this is true of any material tho, rope simply no different..
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ABoK very voluminous to climb thru, hard to read as lessons, that the knots are just examples of, especially when lessons named by those knots. Much more to be found tho by digging and sifting out the consistent mechanix of those lessons, that the presented knots are just examples of, rather than a challenge of seeing how many can tie as wade thru ABoK. Kinda Mr. Ashley's version of the journey, not destination as focus i think; especially as presents so much journey in the text. Looking at this as more of a comprehensive, than itemized reading of the same text(s)/volume.
 
Kenny, I wish I had your mental energy and typing stamina. Want to mix it up a bit? How's about itty bitty pinch points in devices like grigri and related copy devices? Penny for your thoughts.
 
Kenny, I wish I had your mental energy and typing stamina. Want to mix it up a bit? How's about itty bitty pinch points in devices like grigri and related copy devices? Penny for your thoughts.
A typical ascender cam, like on a Petzl basic, desheaths the rope or breaks at about 1300 lbf.
 
Lost during some trimming, the point of ABoK more turns for spread out wear, applies to capstan, porty etc. of even more turns than a knot adding just 1 to bear wear more focused to less as shown in ABoK..
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But the original 4xDiameter host was for standard @ the time stiffness, material for rope; on a pulley to best of my memory. More of rope working in 1 direction on pulley than bollard/capstan. Fight displaced to the axle in pulley usage. In Friction Braking on wood(thermal insulator), metal (thermal heatsink)etc. hosts/ without axle function; fight is more disruptively at rope level mating to host as major change.
Pulley allows bottom portion of rope in arc to carry more forward with the top of rope arc as more 1 contiguous unit, but much less so when host of capstan/bollard etc. type function where tope of rope cranking one way and bottom of rope essentially cranked opposite direction by comparison, working rope more 2 ways than pulley model i believe.
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A linear list of geometric arcs in a rack can give brake force similarly as radial list on bollard/capstan type devices due to both having opposing direction arcs from a linear imposed load. But linear list of arcs/rack type strategy offers counter torque , so is either balanced or 1stroke=half cycle off at most as 'cleaner' travel than other strategies sometimes. A linear list of arc apex's each sit 90degrees to a bollard/capstan arc's most controlling apex. So they both can be seen as working opposite ends of the 90degree radial paradigm as avenues to the same friction target.
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i look for 3x180arcs for RT as pro basic usage/knots even extends to minimal brake device of wood or metal. Bollard capstan take arcs step further as a list of arcs, and can even then hand or motor powered winch, but always want at least 3x180 if not 4x180s always on capstan crank drum friction buffer to the termination, just as winch butt connector to spool always keep 3-4 minimum 180 arcs. It just consistently works across all these forms with reasonable friction co-efficient(ie. much less in dyneema that has co-efficient of about Teflon!), gives Nature enough much more proper geometries to correctly capitalize on than simpleness of single turn strategies. Note direction of usage, Input force to radial can be concentrated to more focused linear pull like hand crank winch. But, also opposite is true, focused linear input from a load can be radially dispersed , to control the load by controlling a small part of the radial lever chain diluted down to, by stopping the lever at any point, @ far end of chain with least effort. This is 2D radial aspect, but holds even more true in 3D radial concentrated down/gathered to focused 1D linear aspect as an explosion in a cylinder or barrel is taken from even more so dispersed 3D radial and made to a focused, higher power linear push of piston or projectile of 1D pathing. Rope Brake devices, knots etc. go instead from focused linear to radial dispersed, as how things work in everything type concept ruling all. Knots/bollards/capstans/racks capitalize strongly on this 1 pivotal concept.
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To me, any of the pawl, gibb, 1way cams, are another different strategy class.
Utilizes geometry a different way to make a Nautilus Shell/golden ratio/Fibonacci/growth spiral/'equiangular spiral'/'eternal line' (many names) type radial to most Naturally mechanically COMMAND the effect in the Naturally progressive/organic changes cos/sin of the rotation; very workable in its premium powerband of mated headshell size vs. Nautilus shell cam size to what size rope sandwiched and load range.
gear-geek-cam-style-belay-devices. This Math is relative to Euler's number etc., these math/geometry things constantly come up as pivotals; as in any material, rope simply no different.
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gotta run..
 
Thank you for the numerous replies. I hoped someone would have a little more insight on the industry/innovation movement away from the 4:1 ratio. At the end of the day it seems the consensus is “live and let live.”

There are three discussions occurring at this time. Ropes running 1-over a pulley, 2-around a bollard, and 3-pinching the rope (climbing devices.) The third is related, but not really the focus question regarding rigging.

For the record, I would encourage newer folks in tree work to think through these concepts. Running a rope at sharp angles on a regular basis will greatly decrease the rope’s life. Maybe it’s the planned-obsolescence model so people will buy ropes and devices more often. I wouldn’t be surprised.

With rigging, sometimes you have to learn the hard way. Avoidable mistakes in climbing are much less forgiving.

If someone is really interested in a more rigorous (physics/math) dialogue, just send a DM sometime. Thanks!
 
i think we perhaps see a perfect storm of :
Hard stating numbers opens door wider to litigation and so the long game would be to play the hand more conservative, as the survivors do. Could be more conservative food freshness date all the same.
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Also, newer materials and stiffer constructions capable of more power in smaller construction/denser power outrightly demand more care in arc. While expanding scope of work found rope used for at same time/potential audience . Such as some ropes not up to tree work rigors etc.
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And Voila this raises the average mean of care when quoting general/nonspecific, blind, global recommendations given more headroom!
For the record, I would encourage newer folks in tree work to think through these concepts. Running a rope at sharp angles on a regular basis will greatly decrease the rope’s life. Maybe it’s the planned-obsolescence model so people will buy ropes and devices more often. I wouldn’t be surprised.

With rigging, sometimes you have to learn the hard way. Avoidable mistakes in climbing are much less forgiving.
In my head I model that each rope is as links of chain, some with larger links/more resistance and wear to arcX bend per that chain link size to arc ratio. Higher tension exemplifies the base effect to express stronger. I consider a 4x4 corners as inorganic, non flowing abomination as a host, bollard etc., but round host to be the flowing, organic, Natural model by extreme contrast. Arc is the key shape in any material, the rope gets this from a form/mold like plastic or metal does, only this form is host and can't be removed. But still gives rope proper arc shape all the same.
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To 2nd part, I sought to get a feel for rigging a load, from being the rigged load/feeling how ropes pull on a load, when hanging in ropes myself climbing. Especially after kicked off spurs, and really had to L-earn to use rope better, in so many more expanding ways, it made me a better rigger.

Ropes made for tree work tend to be outstanding in grittiest of such work vs. other constructions of same materials, diameters and tensile strengths. Rope is the wearable, elastic /soft link utility in work cycles, as fanbelt is. Just not rotated out as often as on great ships before synthetics.
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Different color ropes make id easier in rigging but also easier to remember individual histories and peak loadings. Have downgrade path ready, to take especially dirty wear off better and longer rope histories. Harvest a short climbing line at opportune time, ropes for dragging or at least modular section to take abuse, keeping such heavier abuse off even medium ropes etc. Key asset to plot moves ahead, and few paths ready, as on chessboard. Always have a rope in bag ready paid for at home so never any bluffing, downgrade as/when needed w/o blinking, sort and re-load later.
 
Dan, do you remember those old test videos with ascenders mangling ropes in drop tests? Or were they pull tests?

I figure there's some sort of accelerated wear factor that could be come up with for normal rope use in pinch devices (normal use, as we're already aware of the catastrophic fail case).
 
1761846236345820a653380bb57e58a5.jpg

I found this text box in TCIA Best Practices for Rigging. I appreciate how the authors do not hide the discrepancy between manufacturers guidelines vs. common practice in the tree care industry.


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I have a question about impact rigging block design. Most (all?) have what DMM calls an “anchor thimble” to improve the bend ratio but it’s significantly smaller than the main sheave. If I want to follow best practices and use a larger sling than my rigging rope this makes the bend ratio very unfavorable on the anchor thimble. Why wouldn’t designers want a 4:1 ratio on the thimble also? Is this to prevent users from getting the ends mixed up? Save weight and keep the cost down?


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The concept - wear is from deformation x under load x under motion (with a velocity/power/heat limitation too). Bend radius is a subset of the factors. To ponder when you're bored. :)


Maybe it's a little ok to scrimp on the thimble because there's no motion there.
 
Well spliced thimble is termination as Hitch not continuation as Bend so yes different mechanic, but still dual legs; now of shared support to eye w/o deforming primary column of Standing Part(SPart)have always thought.
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i always read rope from just that same most responding point of arc apex to host, is half loaded as eye at that point compared to pulley, and eye is static as isn't being cranked/ground thru the arc as greater level of complexity. Primary Arc is always go to for reading rope as most responding ropePart as read forces, get best nip at apex of 2/1 pulley effect and highest wear point (usually) all in one.
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Bowline to make seam/close of eye loop still 2 legs to eye, but deforms primary support column of SPart. But would use on hook etc. of less than 2" commonly. Partially because SPart deformity is weak link determining strength now anyway.
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Splice or Friction Hitch( perhaps Half Hitch preceding) as seam give least disturbance to primary support column of SPart to eye.
 
Across the (p)ages of time, ABoK distills out millenniums of lessons handed down, as Mr. Ashley saw these jewels threatening to disappear, that have been so loyal to us, and in fact perhaps human intellect built along with these things as a first/primary technology leading to many basic understandings.
Beware the belief of any accuracy in most knots books --including Ashley's. Mostly what is indeed "handed down" is simply what was there to (easily) *hand* down (in contrast to authors having the wit to do real research or even thinking!). Perhaps the most egregious tome of rubbish is Hensel & Gretel's make-believe word in their Encyclopedia of Knots & Fancy Ropework --somehow published, re-printed, expanded, and still published. It is both amazing & appalling.
I'm abashed to admit it took a small booklet, A Letter to Lester, to open my eyes to this.
Pieter van de Griend remarked, there :
"Knot tyers --and esp. knot-book authors--
propagate initial falsehoods sufficiently often to establish them as truths."


(e.g. "The constrictor knot will bind so tightly that it must be cut off!")
Kinda same in lesson#1883 on hooks always a smaller host arc(linear sides of hook of less consequence than linear force line to arcs).
"A ROUND TURN AND Two HALF HITCHES. Any HOOK HITCH: with a double bearing is stronger than one that passes through the hook but once."
I can't find it in a quick image-search now, but there is a now pretty old (1980s?) knots-strength table produced IIRC by Samson showing --unusually, despite its relevance!-- the Anchor Bend (aka "Fish.BEND") & 2HHitches (again, IIRC, it was this sans a "round turn") for both a 5/8" ring & a 4" (?!) spar in, hmmm, 1/4"(?!) rope :: the former was weaker on the ring, and a bit stronger on the spar. .:. My surmise (all I got) is that on the larger dia. object the Anchor Bend pulled out enough tail so that its SPart ran pretty straight into tangent contact & around, whereas the 2HHs would give some bite into the SPart and have more weakening (though IIRC the diff. wasn't all so much).
Interestingly, in his first writing on knots --The Sailor & His Knots(?)-- in 1926 A. opined that the Anchor Bend should be finished w/HH and then the tail seized to the SPart ; that this would ensure that the turns didn't tighten around the anchor and ... have that wanted double bearing, really, more like a double eye knot than an hitch. --though this opinion seems to have been forgotten on writing ABoK decade plus later.
lesson#1074. "The BOWLINE with a bight is tied in the end of a pendant to
which to hook a tackle. Whenever possible a hook should have a double bearing when it is to be hitched to a rope..."
And I'll go with this and remark that the same rationale seems to apply to, well, what should be the same eye knot, viz. #1016, got from Luce & Ward --actually, not in the older (Luce I think is who) but in Ward's revision of Luce)--, who recommended that GRAPHICALLY PRESENTED (as) single-eye knot as the proper one for rigging a light tackle for heavy pulls (no reason given what made it so). IMO, it was the 2-eye knot intended, and the artist wasn't clear on the concept (there's a lot of that going around). Hmmm, struggling w/computer ignorance (lotta that ...) --voici! (Ward)

[pardon :: I tried to isolate the bottom knot --what Ward added to Luce's work, on revision--, but apparently that takes smarts, and I've been l00king all over for them for ages.]

View attachment 79706
Now, I lost the lovely PAINT art annotation I did on this, but words can work. What appears larger in ABoK's #1016 is what appears here (Fig.218) as a nearly fully contracted ring of the knot NNW of the "F" of "Fig.", crossing over the two eye legs to team up with the tail and take twin legs into a collar and out as the single eye's legs. (NB: So un-understanding were Hensel&Gretel (<-"Graumont", but, c'mon) that they photo'd their books image JUST like this but felt in necessary to point out (oh : just eye knot, no block/hook/right side) that the eye was the thing on the right end and not the (ridiculously large) twin collars! (Btw, load it, and the SPart's initial turn is going to pull back into the collar space --because the SPart's loop like that of a sheet bend has no resistance yet to make it tighten.
.:. IMO, Ashley's rationale is what made the correct(ed) version above --where that tiny loop is pulled out as a twin eye-- just the right knot for that heavy loading; oh, that and the doubled (2x2=) 4dia for the SPart to crunch around with its 100% of load --kinder to the rope, whether any gained strength was needed or not.
"If the rope is weak and the hoist is heavy, a round tum on the standing part adds
materially to the strength of the knot"
I think that this comes from a Timber H. variation, making an RT on the SPart and then dogging the tail. IMO, Ashley's assertions about strength are often speculation; I can see how these turns could result in a weakening, like the 2HH's biting into rope vs. the Anchor Bend's lesser interference --which, yes, we must note are untested speculations from me!
knudeNoggin lends can't maximize both lessons at once
kN can't make sense of what he's doing in this sentence! (-;

<somewhere something about
.
ABoK very voluminous to ...
... count every knot. BUT, I did push myself to try to do that, so to FINALLY work to cut out the forever-parroted nonsense about ABoK "containing over /nearly /roundabout 3,900 knots" --something one should hope that anyone consulting the book, understanding the image#s, and seeing e.g. in the Index that the Clove Hitch, Bowline, ... are presented MANY MANY times, usually getting an image #, ... . .:. My count (and I was generous --e.g., a clove loaded on both ends qua "crossing knot" (or on neither, qua binder; but A. doesn't give this) was counted along with it being loaded on one end only, end hitch (but not re-counted for each size hitched-to object (ring / spar / pile)) >>>>> about 50%, 1950 roughly. (And, man, I just pretty much punted on the numerous multi-strand button/knob knots and matts and ... --most all counted.)
[quote, for Knotting Matters #153 (Dec'21, winter)]

I count 3,858 image numbers and 1,932 distinct "knots":
so, about 50%. Note that the end number 3854 is added to by
three "1/2" #s (794.5, 1034.5, & 2585.5) and (in later editions
of the book) #1425a --the knot that tied the IGKT together
(and thus which should be our logo, the knot's ends assuming
the four cardinal compass directions!). Ch.33, Tricks & Puzzles,
gets my low count of 1
--same as for Ch.26's Holdfasts but over
twice the image #s. [One image # has only the remark that the
knot got lost!]
[edit to note : This is misleading. What I did was first count the "knots"
in those chapters grouping functional kin (end joints, eye knots,
multiple-eye knots, ...), and then proceeded to ones I expected
would be repeating these (Occupational knots, Tricks & ...).
So, that "low count" was net of things counted elsewhere.
]

But who asked?

*kN*
 
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