SIngle Fishermans bend (Ashley #1414)

[agent_smith]

I need assistance in tabulating all of the possible orientations in which a Single Fishermans bend (Ashley #1414) can be tied in Hawser laid rope.

The concordant form can be tied in:

S/S chirality

Z/Z chirality

Refer to image below for specimen knot that I am referring to.

Hawser laid rope generally consists of 3 twisted strands in either a Z (RHOL) direction or S (LHOL) directional. These types of ropes may also have a ‘Langs lay’ - which is a further orientation of yarns within the 3 strands (refer to images below).
NOTE: There are anecdotal reports of MBS (strength) differences in ‘concordant’ versus ‘discordant’ bends tied in Hawser laid rope.

I have not seen any historical data pointing to the various orientations in which a SIngle Fishermans bend can be tied in Hawser laid rope (in a coherent table form).

This table would form the basis of determining a rationale for why one particular chiral orientation may yield a higher MBS relative to another in Hawser laid rope. The next logical step would be to undertake actual MBS break tests to collect data to either prove or disprove any theoretical positions.

As the alleged ‘owner’ of this topic post, I encourage and welcome lively debate and discourse. It is essential that the marketplace of ideas is free of speech policing - as this would retard the seeking of truth and meaning. I have no objection to the use of CAPITALS and innuendo if a person wishes to strongly emphasise a point.

[Dan_Lehman]

@agent_smith

I need assistance in tabulating all of the possible orientations in which a Single Fishermans bend (Ashley #1414) can be tied in Hawser laid rope.

In a similar quest, I had a broader reach of figuring
out what test cases would be needed for seeing the
effects (or not) of chirality on esp. strength tests
–i.e., of the hand of the component OH knots
given any of a trio of general rope types : Z-lay,
S-lay, & no-lay (braided). One needs a trio of
ropes (well, both lays) to bring up some interesting
cases. And if one looks at a Fisherman’s Eye Knot
where the Returning Eye Leg can be a different
rope type from the rest (S.Part & Outgoing ELeg),
… more interesting (or maybe just more numerous).

I lay out the needed combinations below. Note that
I will give information in a specific order, with hands
of the knot given in a right / left ordering to match
the stated rope types.
Because of using ropes of opposite lays (plus braid),
we need just one particularly specified combination
of OH components; I chose Right-handed OHs for
the concordant Fisherman’s knot (and of course the
discordant one has one of each, but in my order here
it’s R-hand + L-hand (not vice versa) --that matters,
though it seems as though one is over-specifying
or else missing cases. The use of both lays makes
things work out.

The evaluation of needed cases must come from seeing
what of matched hand (“=”) & opposite hands (“X”) and
no hand (braided ; “O”) occur individually for the two
general forms (con- & dis-cordant). I.e., look in the
left column up’n’down to find redundancies there,
and the right (discordant) column for its duplicates.
See that, e.g., in the left column there are 3repeats :
O, = with =, O, then =, X with X, =, and X, O with O, X.
((yes my head hurts trying to keep this figured!))

With spine-v-spine it doesn’t matter which OH
component is one way with the other one different
–you’ve got the one of each.
The interesting cases to me come with discordant
form now --i.e.,using opp. lay ropes-- able to be
with same = or X in this belly-v-spine version.

. . . . . . . . . . . . . Concordant. . . . . . . . . . . Discordant . . . .
. . . . . . . . . . . . . (Spine-v-Spine) . || . . (Belly-v-Spine). . . . . . . . . . . . . .
.. . . . . . . . . . . . . R-OH vs R-OH . . || . . R-OH vs L-OH . . . . . . . . . . . . . . . . . . . . .
.ROPES . . . . . . . .. . . . . . . . . . . . . . . . || . . . . . . . .
. Z-lay + Z-lay. . . .= . . . . . . = . . . . . . ||. . . . = . . . . . . . X . . . . . . . . .
. . . . . . + S-lay . . . .= . . . . . . X . . . . . . ||. . . . = . . . . . . . = . (2 novel!)
. . . . . . + braid. . . .= . . . . . . O . . . . . . ||. . . . = . . . . . . . O . . . . .
. S-lay + Z-lay. . . .X . . . . . . = . . . . . . ||. . . . X . . . . . . . X . (2 novel!)
. . . . . . + S-lay. . . .X . . . . . . . X . . . . . . ||. . . . X . . . . . . . = .
. . . . . . + braid. . . .X . . . . . . O . . . . . . ||. . . . X . . . . . . . O . . . . .
braid + Z-lay. . . .O . . . . . . = . . . . . . ||. . . . O . . . . . . . X . . . . . . . . .
. . . . . . + S-lay. . . .O . . . . . . X . . . . . . ||. . . . O . . . . . . . = . (~= above)
. . . . . . + braid. . . .O . . . . . . O . . . . . . ||. . . . O . . . . . . . O . . . . .

There are 3 redundancies in each column (resp. con-/dis-cordant),
so 18 - (2x3) = a dozen are unique.

IF one makes this table for the “artificial” Fisherman’s Eye Knot
where the RELeg can be of a different rope type, then these
cases are all unique (18). This is because now the OH components
are different in loading : that in the S.Part->OELeg is loaded on
both ends at 100% & 50%; but that in the RELeg->Tail is loaded
probably at about only 40% & 0% (Tail) --the RELeg being highly
nipped passing through the S.Part’s OH! And thus “X, O” doesn’t
replicate “O, X” : one has an opp.handed S.Part to the lay while
the latter a no-handed S.Part OH.
(I’ll guess that that being so, the strength pretty much is
determined only by the S.Part’s OH.)

–dl*
/====

[agent_smith]

I think you need to define some of your terms for this to make more sense to the casual reader.

eg Spine v Spine…. and Belly v Spine

What is the definition of ‘Spine’?

What is the definition of ‘Belly’?

Presumably, the underlying concept is with regard to surface area contact between opposing overhand knots. And the presumption being that imperfect contact between opposing knots may affect response to load (and ultimately the MBS)?

Also, what is the significance of the alleged “redundancies” in your tabulated data?

Note: None of my questions are intended to ‘wind’ you up or trigger you. I am seeking truth and meaning (as you are). We need to define our terms.

[Dan_Lehman]

The OH has been given the named parts “spine”
& “belly” by Harry Asher (for the pretzel OH form).
Agent_Smith’s photos in his OP show the abutting
of two spines of the concordant form on the right,
and on the left image the lower-positioned OH is
showing its belly abutting the upper OH’s spine.
Spine-vs-spine has, given the crossing of ends
forming the spine, a little more bulk in the
direct opposition, whereas a spine abutting a belly
gets some relief re that.
I wanted to be cute re “pretzel form” by showing such
an OH, but I can’t find any --pretzels are mid-flyp F8s
(or more, or no-knot!).
Here’s grabe showing the spine’s crossings at top;
I’ll let Agent_Smith note the claimed hands --wrong.

https://training.wasbc.org.uk/2021/04/07/overhand-knot/

the significance of the alleged “redundancies”

“alleged” ?! The redundancies were indicated clearly.
Surely one can see that where rope lay matches knot
hand, it doesn’t matter which chirality (S/Z) is in play,
and so on. The only “significance” is in showing the
excess of cases coming from my using that sort of
table.

Speaking of which, in our more common scenario
we don’t have S-lay rope; let’s put up a table for 2 ropes.
Now, lacking two lays --only Z–, we need to have
the opposite-handed concordant-knots case so to get
the “X” cases with our Z-lay rope.
The discordant column has nothing new to offer;
we cannot get the interesting X,X & =,= cases.

There are 3 redundancies ( =.O & O.= ; O,O & O,O ; X,O & O,X )
in the “table”, where we don’t show how the discordant cases
would all be redundant going from one had of OH to opposite.

. . . . . . . . . . . . . Concordant. . . . . . . . . . . Discordant . . . .
. . . . . . . . . . . . . (Spine-v-Spine) . || . . (Belly-v-Spine) . . . . . . . . . . . . . .
.. . . . . . . . . . . . . R-OH vs R-OH . . || . . R-OH vs L-OH . . . . . . . . . . . . . . . . . . . . .
.ROPES . . . . . . . .. . . . . . . . . . . . . . . . || . . . . . . . .
. Z-lay + Z-lay. . . .= . . . . . . = . . . . . . ||. . . . = . . . . . . . X . . . . . . . . .
. . . . . . + braid. . . .= . . . . . . O . . . . . . ||. . . . = . . . . . . . O . . . . .
braid + Z-lay. . . .O . . . . . . = . . . . . . ||. . . . O . . . . . . . X . . . . . . . . .
. . . . . . + braid. . . .O . . . . . . O . . . . . . ||. . . . O . . . . . . . O . . . . .

.. . . . . . . . . . . . . **L-OH vs L-OH . . || . . . . .
.ROPES . . . . . . . .. . . . . . . . . . . . . . . . || . . . . . . . .
. Z-lay + Z-lay. . . .X . . . . . . X . . . . . . ||.
. . . . . . + braid. . . .X . . . . . . O . . . . . . ||.
braid + Z-lay. . . .O . . . . . . X . . . . . . ||.
. . . . . . + braid. . . .O . . . . . . O . . . . . . ||.

–dl*
/====

[Dan_Lehman]

A short “executive summary” explanation for readers
not caring to bend brains trying to make sense of my
“tables” --a struggle I’ve had, alas–,
the takeaway is that “Fisherman’s Knot” can denote many
different things, in exact geometry & knot-workings. I’ve
never seen anyone go to the level of detail needed to
distinguish what case(s) mattered for the data/behavior
given in any report.
That we don’t know (a lot of) things re knotting
isn’t all so surprising; it’s sad that for the most part
we aren’t aware of what sh/could be known, though!

–dl*
/====