Geometric definition of a Bowline

[agent_smith]

I will just repeat that I [b]feel [/b]that the expression "nipping loop" implies a single loop.

Obviously I dont know you on a personal level and we have never met. I am proceeding on the assumption that English is your first language (keep in mind that many people on this forum do not speak English as a first language). You use the word "feel". I have to state up front that [u]facts don't care about feelings[/u]. Your interpretation is false. The definition is not restricted to the existence of only one (1) loop. Logically, if there are two (2) loops, this implies there must be at least one (1) loop present. So for example, Ashley #1013 is a Bowline with 2 loops. It is still a 'Bowline' - and it has more than one loop (ie it has 2 loops). Singular versus plural is irrelevant.

I do not see how it allows a Clove Hitch, a Round Turn, or a Girth Hitch (none of which meets the definition you give for a "loop").

False. [u]Refer to attached image below.[/u] A Clove hitch actually consists of 2 superposed loops of the [i]same [/i]chirality. Do you acknowledge this as a fact? Yes / No ?

A Girth hitch actually consists of 2 superposed loops of opposite chirality.
Do you acknowledge this as a fact? Yes / No ?

I want all of these to be included into the "family of bowlines" and so I am trying to argue for the definition to say "nipping part" or "nipping structure"...

Your argument makes no sense, it is illogical. All 'Bowlines' that have ever been published since the dawn of mankind have certain geometric characteristics. You can objectively test this yourself. Take some time, and examine 'Bowlines' published by Ashley, CL Day, Budworth, et al. You will notice some geometric elements that are common to all 'Bowlines'. The only exception is the anomaly found in Ashley at illustrations #1057 and #1058. I am of the view that this was a [i]logic error[/i] (likely caused by following some previous publication or historical artefact - or an editing error). I could also mention the so-called 'circus Bowline' (which isn't a Bowline - its actually the [u]Farmers loop[/u]).

I don't think the Girth Hitch has the structure of a helix or that it is very circularized.

Why is the concept of a [i]helix [/i]necessary? Although I concede that a 'loop' is the beginning of a helical structure (and has the elementary shape of a helix). And so it is a useful term to explain what a 'loop' is. In Ashley #1013, there is a double loop. I say "double loop" rather than 2 superposed loops. We can say that the double loop in Ashley #1013 has the form of a helix. But, this misses the key point:- it is the presence of a [i]loop [/i](or more than 1 loop) that matters. It just happens to be that a double loop has the form of a helix.

The Karash structure is just a half-twisted loop that seems almost closer to the original Bowline than a Girth Hitch Bowline. I would like the definition to include all of these

The so called 'Karash' eye knot [u]is actually a quasi Bowline[/u] (refer to attached image below). I use and interpret the term 'quasi' as per the standard English dictionary. Definition: [i]Used to show that something [u]is almost, but not completely, the thing described[/u].[/i] This is an example of a nipping structure (rather than a nipping loop). In this case, the nipping structure is a [i]crossing hitch[/i] (same form as #206 Munter hitch). And so here, the term 'nipping structure' is appropriate.

And again, your epistemological understanding of what a loop is requires investigation.
A ‘Girth hitch’ is topologically just 2 superposed loops of opposite chirality.
Do you not see this?
And a Clove hitch is topologically just 2 superposed loops of the same chirality.
Both consist of loops.
What differs is how they are geometrically aligned with respect to each other.

---

[KC1]

i Think

in terms of 2 forms of Half Hitch (HH): Terminating immediately by Nip or at the next flow by an opposing force of the next rope part. Or Terminating vs Continuing forms of force flow.
Both forms leave a shrinking loop. If this loop is on a non rope part host, the loop just gets those Frictions to that rope part. But shrinking loop on a working rope part of the system build, then that rope host also gets Frictions against displacement and is a Nipping Loop. All actions have an Equal & Opposite(E&O) effect expressed in concert to total sum; when the host is rope get the Frictions from both ways to control. But loop on wood etc. host; such as a preceding HH passing to another terminating rope part, there is only 1 sided rope control by contrast. The E&Os are the compression by the loop of Frictions acquired and the host standing against the compression; instead of compressing another rope part with the secondary action giving Friction to both rope parts.

This is always similar to me as with Backhand type constructions; whereby the Turn around Standing Part(SPart) is of duel actions affecting 2 rope parts at once vs. the arc in Backhands that is on an ‘external’ non-rope wood etc. host by contrast. But when even that rope section(usually on non-rope host) is around a rope part in the system; the mechanics do change. The same E&O forces thru the Geometry are the same, but used/exploited/harvested differently to task. What was once a ‘byproduct’ just secured to wood/externally expressed host is now folded back into the system to use again with the conservation of the E&O promise of forces, now just not externally expressed.

Kinda as like a ‘dumbwaiter’ concept of not lifting something else with a redirect pulley, but lifting yourself for a 2:1 (-Friction and stretch etc.)effect. The system is ‘closed’ to conserve both the E&O products, not ‘open’ leaking 1 part of the E&O product externally.

[agent_smith]

@KC1

in terms of 2 forms of Half Hitch (HH): Terminating immediately by Nip or at the next flow by an opposing force of the next rope part. Or Terminating vs Continuing forms of force flow.

I re-read your opening paragraph - the punctuation/sentence structure was difficult for me… but I think I grasped what you were attempting to communicate.

To ‘steel man’ your position:

The nipping loop which encircles and crushes the rope segments within its circumference is loaded at both ends and progressively shrinks as load increases (which has a corresponding increase on the crushing effect on the encircled rope segments).

If there are two nipping loops:

1. both are loaded at both ends and both encircle and crush all rope segments within their respective circumference.

2. the nipping loops may exist in a linear series (one followed by another) or be superposed in a parallel configuration (eg as per Ashley #1013 Double Bowline).

Have I got this right so far?

You are losing me on the ‘frictions’ part of your explanation. I am unclear if your model accounts for transfer of energy into heat (energy cant be destroyed, only converted from one form to another).

We know for sure that heat build up occurs as load increases in all knots. In the hundreds of load tests I have performed, there is always evidence of melting/fusing of rope fibres - which points to heat build up. So energy transfer through the knot core is being ‘lost’ in the form of conductive and radiative heat,

In general terms. tension force propagates through a knot and eventually reaches zero at the tail end protruding from the core (or 2 tail ends in the case of a ‘bend’). So the force goes from some initial input value to zero at the tail(s).

Your mention of “loop on wood” could not occur in a standalone simple Bowline (Ashley #1010) - there is no ‘wood’.

Your mention of a Crossing hitch (Munter hitch) - aka ‘Backhanded hitch’ has nothing to do with a standalone eye knot (eg Ashley simple Bowline #1010) - the Munter being describer by the Capstan equation (the U turn of the rope around its own S.Part is = Pi radians). There is also bending/turns around a carabiner (aluminum + nylon rope friction coefficient). - in the case of a Munter hitch used by climbers.

I did not see any use of cosine and sine in your post? Have you dropped the use of these trig functions?

NOTE: Nothing in my reply post is intended to cause offense or harm. The concept that words can cause harm is subjective - and in the eye of the beholder. Technical disagreements are not a form of hate speech - mere disagreement ought not to be construed as being hateful. The source of a disagreement is rooted in the pursuit of truth and meaning (in this case - about finding truth and meaning about knots).. The pathway to finding truth and meaning by definition involves engaging with others who may not share your worldview about knots. In order to fully engage with someone means risking being offended if your worldviews do not align. Mismatched worldviews is not proof of hate or hate speech.

[KC1]

Very sorry about my grammar(one reason started drawing), and delay over the holidays.

i was, kinda s always, looking at HH(Half Hitch) alone, outside of Bowline as study; to then add it in more into the orchestration as better understood for comparative analysis later. At that point noting we have been handed down 2 things called HH; one that terminates by an cross pull on SPart(Standing Part) using only 1 arc90. Then the one with another arc90 turn and back to continue some force flow to the next position or separate HH type from Bitter End of the first

The terminating type has less friction effect(but has Nip), as only has 1 arc180, but does use friction with that arc180; and use that same friction again on SPart. So using the friction and it’s E&O(Equal & Opposite) result too. Where by the arc180 on the nonRope/wood etc. host would only deliver the friction of rope 1x, E&O is on the ‘external’ host.

The continuing HH type (like in Bowline) uses tail/Bitter End of terminating HH to stretch the mechanism open for 2 arc180’s frictions AND cashes in on the nipping loop host rope parts as well. i do recognize the double nipping loop as another progression of this same theory.

ALL of this is cos:sin to me of Same Dimension:Crossing Dimension ratio parts to the total sum of the whole. To me these are implicit in definition of arc0,90,180; as all Dimensionally defined. The numbers don’t command but are a math language to decode for us what is going on. To me cos:sin pair is not just statically applied positionally on a paper, but also applied dynamically. The ONLY way for rope to support against a pull is to present opposing force (Direction) in the SAME Dimension of the system. Just as would be found in rigid materials in a system. Rope lives by the same rules except only works in 1 Direction(tension) and only in the Load Dimension. Rope is just another material of choice to work with. With rope you only have to unload to form a simple support geometry; not drill, heat, grind, glue, nail etc. etc.

Cosine% of the rope efficiency of same Dimension as support against Load is a retained strength against the Load, is the SAME, no matter what direction the Load pulls. So the cos% Dimensional value is Unique in the system, then there is everything else too; type of logic.

[agent_smith]

Happy new year ‘KC1’.

Not sure if you are aware that the title of this topic thread is:

“Geometric definition of a Bowline”

It is unclear to me which parts of your post strictly relate to the topic? In the first instance, there is no wood in a ‘Bowline’…

Were you intending or preferring to start your own topic thread based on hitches? (This is a genuine question, not a slur).

Also, your explanation and use of the trig functions Sine and Cosine make no sense to me (from a mathematical standpoint). What coordinate reference frame are you using?

[KC1]

HNY to all; am trying to make resolutions last longer than the leftovers once again!

The "coordinate reference frame " i use in simple models is the Linear Force Input Dimension as Benchmark of cosine, crossing as sine. Kinda like straight(forward or back) vs crossing(left or right) from any axis/Dimension chosen as Benchmark.

Please see that cos:sin pair is intrinsic to the Geometry definitions as becomes analytical Geometry and trig. cos:sin ratio decode/translate the happenings to show how much reach and force is expressed to the same UNIQUE Dimension vs. not in the containing system. The concepts put the Geometry search and it’s fruits on steroids, as shows relationships between the geometric bodies.

The wood Friction reference was to show and respect different values of different frictions; they serve of the promised Equal&Opposite(E&O) forces of the rope friction to an external non-rope part; like wood parts of the system. Or, if plural sections of rope each get all the frictions/so none expressed outside of rope system. Like they do inside the microcosm of a nipping loop on a single rope(or better seen/expressed with plural/not singular rope’s diameters as host).

i tried to show, that this same geometry of rope reach and force expresses singled out as a separate component for study outside of revered Bowline. Then, to understand better as a component inside the sum total of the orchestration of a Bowline’s components. Such component isolations; to then re-assemble and know the whole better is how have found/ mimicked to understand best everything from chemistry, electronics, machines, tree hinges, ropes, rigging, engines etc. etc. Thus, then too, showed HH terminating and then taking ‘tail’ from being a Bitter End to a non-terminating passer of force as in Bowline etc. Both forms have been handed down with the same name…to then segregate to then respect their individual traits as well as their commons. Knowing what small differences make big differences , grooming the geometries more purposefully.

A ‘sinusoidal waveform’ on graph of organic cos:sin change as on charts, is the SAME Dimensional change as organic fall of voltage, wind, magnetism, water wave etc. etc. from Full expression to baseline/Null expression. If not followed for gradient change of shadows, movement, color change, sound change etc. for Virtual Reality, will look fakey. Even tho advanced part of brain may fumble with these concepts that we are surrounded by, the deeper grunt level can tell innately is not what has always seen! The ‘sinusoidal waveform’ is the organic Universal, cycle(circle) of change. This change is not consistent degree to degree, not jagged, not sudden, but subtley rolling in change as the organic form of change. Rope is no different, nor Earth even. The Ancients literally found and defined these things in ‘the heavens’ for even planetary movements Universally. 360° is the rounded version of 365.24xxxxx days in a year.

Relating to things by Dimension , it’s attributes including cos:sin value pair of how much of Same vs. Not Dimensions; has made me a better rigger, driver, knottier, worker etc. as i do things more purposefully to these powers, L-earn from that, and can see reflections of the same common principle into the other skills. Then knowledge, familiarity in one can be reflected into others; as they each re-affirm each other’s functions in this model. To the point of seeing how could it be any different in rope, wen even stars and microbes follow this pattern.

Below is chart had made about force patterns too determined by if in Unique Same Dimension in system or not. Like cos:sin, only the expression patterns w/o those ratioed value pair, but still divided as to if in SAME or Crossing Dimension. This covers many things, some not rope; just trying to show the definitive dividing of IS vs. isNOT in SAME Dimension in system; that relates to all, even rope; as the most consistent principle.

Peace!

[agent_smith]

To ‘KC1’,

Given the title and intent of this topic thread is confined to the geometric definition of a ‘Bowline’ (ie Ashley #1010) - I am still confused as to which parts of your replies directly relate to a ‘Bowline’.

For example, you state:

The wood Friction reference was to show and respect different values of different frictions; they serve of the promised Equal&Opposite(E&O) forces of the rope friction to an external non-rope part; like wood parts of the system.

Which part of a ‘Bowline’ does this apply to?

Are you able to provide an image of a Bowline knot and show how your theoretical position directly applies to said ‘Bowline’?

I would request that you omit wood from any image you might upload.

Can you also show precisely where Sine and Cosine trig functions apply within a Bowline knot structure? (ie provide a photo - and clearly show where these trig functions exist).

Thank you…

[KC1]

Dear Agent Smith et al,
In both these points of apparent contention:
Friction external to wood etc.
And
Cosine vs. Sine value pair
The effort is to, once again brainstorm into this open forum, and define most comprehensively individual components working inside of any Bowline. I try to show this by what they are individually first and what they are not to the total sum of the whole across all ranges.

The drawing with wood was highlighting HH component singularly outside of Bowline, to understand it more comprehensively inside a Bowline. Also, in that discussion, to show/highlight by contrasting how hard frictions work in nipping loop of HH in Bowline conserved only to plural rope parts; vs. how frictions serve on singular rope part + externally (here to wood) by defining contrast as lesser. The contrasts more fully illuminating the facets of the target nipping loop, and respects for it as a marvel too when host is own rope parts; not a 3rd party.

And, then too, the measure of Geometric Dimensions (plural) contrasts between knot forces in the same UNIQUE Dimension as Load, vs expressing NOT in that UNIQUE same Dimension as Load. Like how much need to keep major Bowline parts working in same UNIQUE Dimension of Load to lock properly vs. spreading eye apart outside said Dimension, lending to unlock. Such as when choked up tightly to large log or other spreading force vs. the lock works spaced far enough from log to allow locking function to predominate. The log can be different sizes too necessitate Bowline lock works be spread different distances from wood to command competently. The truest measure of how much and why is by how hard the specific material in the Bowline geometry is pulled open or close is the angles of pull into the locking function. This could be enumerated to decipher to aha moments with cos:sin value pair to then eventually know more intuitively without the numbers. But to truly appreciate and comprehensively comprehend, seems must put in the work and see the contrasts as well; just as anything else in this life. Cos:sin value pair here is from an engineering toolset, to define the engineering marvel of a Bowline by it’s Geometric forces; as the scientific method of many disciplines.

i’m not saying i’d lace the Bowline to the log; but have seen done or left behind like that many times.

Also, with our ropes and knots, cos:sin examination shows why radial(round or roundish) face host (and ropes) are mucho better than linear face host(square etc.) and (flat, flattish) ropes(webbing). That is what this is about from : Model/Prism of only 3 repeated root elements for organic/cornerless rope works

i truly believe this is the hand of the magician to watch to catch the secrets in this ‘magic show’ of these doings.