Rope

[theTreeSpyder]

We make knots to hold solid, but then quick release is great too.
i find 2 types: pop-off/explode free or quick release to controlled belay.
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This was invented by knot guru knudeNoggin that visits some arbo forms occasionally and VERY well thought of at IGKT, perhaps top knotting mind seen.
It is specifically made to offer more than Highwayman Hitch of daisy chain quick release that can be found to be untrustworthy and problematic.
In just over a decade this has become renowned as probably the BEST quick-release of the pop-off/exploding free hitches!
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[lxskllr]

I like the looks of that. I'm gonna play around with it when I get some cord in-hand. I need to start carrying a piece of paracord in my pocket for practicing knots, and trying stuff out that I see. I have the need more often than one might expect. I carry a paracord prusik looped through my belt loops at work, but that only covers work, and I don't want to untie it all the time, cause it's primary purpose is to be a loop.

 

[DMc]

Thanks for posting that, Kenny. Even though this highwayman variant has been around a decade, I have somehow missed it. I use the original often on short redirects and it has served well. It is interesting that the load end reverses. That is something I might like.

 

[theTreeSpyder]

YW.
To get the clean pop-off effect needs some weight thru main frame green from load pull
>>when pull release pin yellow .
So just on finger not pulling load end or just weight of keys may not give the total picture.
>>paracord or puny diam flexible double braid, many other
virtually only deformity to most loaded part is the mount itself (inescapable) not so much other rope parts.
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Note if last leg of green thicker mainframe bearing most force had lest leg out
>>would invert lacing on support to form Muenster automatically if less than let's say 22# resisting the 25# load
cuz needs matching plus to invert to belay load , here the slip and then pin just match back and prevent that..until pin pulled
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Quick Release to controlled lower more like number_i below.
i have found this page to be cause of much recent insomnia in it's building:
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This is more towards what i'm trying to draw to in re-examination of all hitches etc. to focus on number of arcs and if/how crossed;
where understand a group of similarly based hitches and how their differences lend to different scenarios.
Seeing the base parts becomes a mnemonic whereby remembering sets of familiar moves to tie, rather than all individual nuances that must be traced to form the lacing. Trying to show things not generally shown together, but can be compared. And very logical genealogy of family builds and the properties of the mechanics passed on etc.
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i try to show there are only 2 primary parts of knots: straight extensions and arcs(2x90degree turns as single unit reaching halfway around a circumference), really arcs cuz extension is just an extension of force carried.. So pic below traces (GREEN) thru uncrossed forms to find workhorse 3arc Round Turn and it's 2 crossed forms : Backhand and Crossed Turns, drilling down Backhand Turn path we find our subject matter of 1 or both legs thru OFF host crossing and then knot derivatives from there.
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As a family the OFF host crossing grouping of Muenter and Cow etc. shows across forms inheritance of notably easier untie than uncrossed or crossed ON host forms due to counter-torque reverse of these not seen in continuous uncrossed and crossed forms(w/o reverse direction). Yet about as secure, and less tendency to walk to end of line/self tighten etc. due to anti-torque reverse thingy. Also ABoK notes several times only needs single pass around host for double bearing that can be a key balancing and angled pull mechanic.
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(smaller version)
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Uncrossed Forms
A>line extension primary form
B>Turn consists of a simple re-direct arc (primary form) and A>line extension to each side(arc ends stop half-way around host and line segments take over)
C>Round Turn (RT)gets into real working class force and grip control of 3arcs and extension
D>Dbl.Round Turn is simply super form of RT
E>Coil is likewise Dbl.Round Turn super form
>>>Can call RT as 2 arcs, 3rd is re-direct turn back; but short math is 3arc is most usable form, and accentuates, firms the forces even more to what look for from RT anyways..
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Following GREEN 3arc UNCROSSED workhorse RT to descendants and find 2 crossed forms that seem to reduce grip but increase frictions to the 3arc from RT.
F>Backhand Turns where crossing is OFF host and 1 or both legs thru as a group (focus of page)
G>Crossed Turns where a riding turn bears likewise across other rope parts but this pressure is ON host, 'pasting' turns tighter to host for more friction force contact ; like would make better electrical contact to be tighter (page in some stage of lack of progress)
>>>>Sailor/Sailor Gripping, Pile/Icicle are then seen as hybrid group each containing Backhand and Crossed Turn forms in 1 lacing.
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Find F>3arc crossing OFF host form; itself have 2 subforms(focus of page)
H>Backhand Turn proper, pretty much applying Muenter/Italian (belay) Hitch to host mount
i> Cow based forms of both legs thru the OFF host crossing as stop over-ride of belay function of 1 leg thru OFF host crossing
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Other 1 leg thru crossing forms :
J>Tumble Hitch: knudeNoggin improvement of Highwayman Hitch's betrayals. After holding strong this releases totally cleanly
K>Slipped Backhand in contrast to Tumble Hitch is quick release to controlled lowering
L> Backhand and 2 HH's offered by ABoK (shown as opposing halfs to keep page theme). So gives also 1 leg thru OFF host crossing form with sister both legs thru OFF host crossing
M>Muled Muenter is similar, release 2 HH's (opposing shown) to Muenter control. Usually in doubled bight of long rope as shown
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Cow Hitch (i) is also very recognizable base form, 2nd leg thru crossing stops belay function
N>Girth is same only use both legs to hold load
O>Bale/Choker Sling/Hitch is same with loop that allows legs to carry load evenly to both legs to maximize and rotate wear, also cleaner on/off motions
P>Opposing Halfs very secure, lots easier untie than continuous halfs in more of Clove finish
Q>Lobster Buoy is 'innie' form of above much more secure, MUCH easier untie than similar Clove innie finish of Bunt Line (Bunt Line is much better slip than Lobster slipped tho)
R>Stillson is a mix of old friends brought together for very secure form, as such shows theme of whole page of recognizing base forms to assemble, not each itemized move to trouble over..
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ALL above show the proper right angle of pull across host mount; for pulling 'lengthwise' along /not across host is WORST angle of possible pull.
Friction Hitches can thus pull right angle but also can help on the 'lengthwise' pulls.
Another game changer of friction hitches is that most knots hold, some belay, but this class holds/slides/holds on command unlike any other knot species!
S>Prussic : a basic friction hitch as simply 3arc rt to each side of choker instead of single Turn as leading OFF host crossing friction hitch.
T>ABoK shows a 1 leg pull form of same
U>6 Coil Prussic >>Can add more turns for more grip but also pushes the side pull to higher leverage
V>Schwab tames some by adjusting amount of turns, but side pull is from lowest turn so less side leverage distortion
>>>Of above friction hitches, would expect only T>single leg pull to be same diameter as host support line grabbed. Other forms shown of dual pulls on hitch favor hitch 50-75% of host diameter to make up for the divided force to 2 legs of hitch grabbing the full force tightness of host
>>Forming separate Friction Hitch page starting with these and parallel Clove type friction hitches etc. as base to that world
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W>note all friction hitch openings (single leg pull) and 'tracks' (host line) should be terminated so don't 1> run off line or cord, also 2> so stop is early enough so can't run into ground etc. Fig.8 stoppers shown as reminder!
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Strength notes finish with focus on age old shipping dock methods for most strength from simple sling.
X>Bull Hitch(stronger than choke) control side pulls more along loaded side more, doesn't cut across loaded line of force like simple choke
Y>alternative ways to make Bull Hitch and Cat's Paw from simple choke.
Z>Cat's Paw takes this even further and ABoK boasts 100% strength of loop. Also says if one side failed, the other side might hold until got to ground and tension came off. This was in more frictive(knudeNoggin) line AND hook pinches together to stop unravel of 'loose splice'. Small ring would expect similar then, but flat log seems could unravel 1 side etc. if failed as top not pinched together.
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i think ABoK was trying to preserve things for us from really a past time even in his day before they slipped into eternity un-noticed. In 1940 writing about the generation before of 1900 or earlier. When the newest 12yr.old boy joining ship might be only one that could read much; and likewise simple knot tying inaccuracies could phenomenally change the day.
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i think knotting came before controlling fire, speech, lever or wheel and is root to many mechanix; and the first time could combine properties outside self to something larger with more attributes. i think these are the things to bring forward and not lose as Ashley lent. Just as have tried to show Yoga as tracing the root stages of animate existence to not lose the powers of the lessons of each stage as we go forward. The forgotten principles simply don't change, so can haunt if forsaken! Every generation sees this worry in some way or other; things easier on offspring as a blessing, but some curse of raw lessons lost that are closer to pivotal functions and truths and the advancements buffer us from. As like health food, these lost lessons can be as dis-guarded fiber in over-processed world..

 

[pantheraba]

i think these are the things to bring forward and not lose as Ashley lent. Just as have tried to show Yoga as tracing the root stages of animate existence to not lose the powers of the lessons of each stage as we go forward. The forgotten principles simply don't change, so can haunt if forsaken! Every generation sees this worry in some way or other; things easier on offspring as a blessing, but some curse of raw lessons lost that are closer to pivotal functions and truths and the advancements buffer us from. As like health food, these lost lessons can be as dis-guarded fiber in over-processed world..

Well put thoughts there. And "forgotten principles....can haunt"....so true....physics persists. I like the exploding knots....I"ll explore them. Thanks.

 

[kevin bingham]

a Japanese climber just taught me that tumble hitch as an excellent retrievable redirect. really effective. it is a knot that can't be released under tension which is a good attribute of a redirect.

 

[theTreeSpyder]

i've mentioned this very little, tho some over time about clevis wet ground numbers off of, basically cuz as says, NOT tested 1000x yet personally and was still feeling this one out.
At end of my run was playing with this idea ~15yrs or so ago.
Not an everyday thing, was slowing down too, and at some point it was so good, it grew legs and wandered out on it's own to parts still unknown..
Gives good mechanix and food for thought i think. Started as Clevis Brake but being smartazz quickly became Air Brake of Floating Brake (kinda a sky hook extension) . So originally thought AFB was Air Friction Brake when saw...and tend to read it to self instead of 'Aerial'.
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Best on straight support line to it, if support is not right over load, rig is angled, will still work, but then as slanted rope 'arm' takes load , it folds to under support and this does give some slack and downward slide to load/loss of clearance some, but favour between 5 and 7 o'clock/best at 6; from center of clock hang. Way to beat that is krab SOFT redirect of line from opposite side that allowed line with brake to then serve better over target. i always had ground help like not swimming alone, but could trick out more by self while they were otherwise occupied and out of range, but still could see each other etc. Did that even on some cake 30mins. stuff w/no (real) haul, 'extra' man could clean truck, saws, hand out biz cards, handle gear, take lessons etc. or just get an easy deal (even Sorry game board has Slide Zone!) as long as watched and could come up with the phone number to nineEleven if need arose...
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The pre-tightening strategy shows my personal fave, perhaps even signature pattern of employing bodyWeight + effort
>>PLUS equal and opposite of effort thru re-direct position to take that promised part of force running away from work and redirect it around to target along side effort for ~2x from effort part of input. But as SEPARATE force also have bodyWeight working on load.
The effort pair presents 2 points but same force/at same time. But the bodyWeight force can be worked independently.
Sometimes this allows holding with effort and impacting with bodyWeight if orchestrate right vice/versa etc.
>>or even orchestrate to drop down weight and snatch up on Load hand at same time etc.
More flexibility and options realizing the separation of forces to place against target AND hit with all 3 in MANY scenarios of martial arts like motions of maximizing what ya got.
Recomend none of precious bodyWeight resource on lifeLine, but it is there w/slack to catch a/n.
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If stretchable length below clevis to load, can help to climb up as shows to get most stretch into rope length before frictions.
This pulls up at hitch point, sometimes more advantageous to go further out on load and pull up, once again if flexes link upwards some, only this time is wood.
With lanyard thru inside elbow of hang arm , under load farther out than hitchpoint and pull up on lanyard, can capture the purchase pinching load and control legs together, then paste rope to clevis after drop lanyard, then chase out slack with hang hand to real/final control leg .
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GAME CHANGER is to lock load side hand (shown as LEFT) and instead of input motion effort there, input from legs thru cam as to do leg lift input to system and left hand instead of effort input against load who's E/O goes thru bod and also pulls down on control leg with bodyWeight, now LEFT load side hand is locked and is passive receiver of E/O of leg lift , PURE (if iron hand receiver), unfiltered, no friction leg lift, as the input raw leg input itself is reduced by frictions of redirect (as is bodyWeight).
>>This was my pre-tighten etc. dance on so many things as best inventorying and orchestrating of avail. personal inputs collected when can connive a redirect out of shituation, just applied here.

 

[stig]

It is "Sir Francis Bacon" not Beacon.

 

[lxskllr]

How do you maintain tension when you take up the slack from the "hang" side? You have a moment where you need to fix the free end, and also get your hand off the shackle. Seems like it would be easy to lose the tension you put on it.

 

[Tree09]

@lxskllr , it's called sweating a line, old sailing trick for tensioning lines such as halyards. You simply pull sideways on the line and then pull the slack by pulling the bitter end. You lose a little bit when you pull to capture the progress, but you would be surprised at how efficient it actually is. By pulling sideways you are using the highline force multiplier to tension far beyond the effort, and even capturing a part of it makes it worthwhile. With older ropes that stretch, such as 3 strand, arborplex, e.t.c you can really get it tight. Once you have it tensioned enough you hold the progress by simply pushing the rope against the object, another sailing trick.

 

[theTreeSpyder]

Thanx, Stig no telling how many more times woulda copy/pasted that blindly, thought originally copied from my sig that is correct.
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lxskllr would hold rope to 'paste' rope to clevis 'firmer', for better friction contact(just like if held hot or electric force firmer get more burn/shock here get more friction force transfer with the same better force conducting , firmer contact) as 'hold fast'(sailor speak fer secure, 'make fast' i believe is when can hitch and release hand and still holds)
>>hold with hand to maintain 'purchase' of some line (ol'sailor speak just as allowing load to pull back line some from control side is 'paying out' line of belay etc.) of line from load side to control side 'banks'(my term to fit lingo).
>>Now pull slack thru 2nd, 3rd arc now(only tightening thru 1st arc, and maintaining that 'purchase' thru hold of later arcs)
Can have ground control help work 1st arc to max LINEAR effort tensioning and then preserve purchase etc.
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Tree09 actually brings another fave in, to sweat/swig force from the line for even more purchase as input force across line rather than along it..
note how pic actually shows Linear tightening up/down column of rope, hand pulls in equal/opposite directions around redirect arc_1 on clevis
>>invoking bod weight, effort and promised equal and opposite of effort as complete inventory of raw input forces available (and then can impact them)
Once line is super tight from linear efforts, then would still hang down on hang hand but as Kyle states pull across line path on load side, raising tension,
(at leveraged angle /non-linear across rope column type tightening now as Samson against columns, after did all could with linear tighten down column of line)
>>then in 1 move try to release (or even push load side hand up) with 'slack' gained with relieve of bend SUDDENLY
>>while QUICKLY snatching as much relieved /slack line from load side to control side as further purchase, before load side retensions from relief of arc.
There will be some loss /spillage of the precious purchase as he says.
>>But line will be tighter now (or load moved as less rope on load side); which means it is more leverage-able(as tighter) to sweat more, as it resists bend more
>>For have less rubbery/much firmer leverage-able rope span now
So note linear tighten rope hard first to firmer leverage 'bar' before bending , snatch purchase, harder to bend gives more leverage, snatch again etc.
Some real olds-cool chit of only way some starving sailors made it home is using this to command sails after capstan crank broke or washed over..
But as like cranking a capstan, needs a tail-er man, to secure 'purchases' leveraged thru system to control side.
Write up below talks of same force science as frapping turns/ crossing turns like if making wall and bind 2 logs side by side around TIGHT several turns, then cut across those tight lines binding front and back of turns together between logs; are wrenching across to tighten, only works if linear part of wrenching resists bend!
This is commanding minimal tools properly, olds-cool!

 

[Tim_B.]

Hey, @theTreeSpyder! I'm posting the link below because I think it fits in with the way that your mind works, and that therefore you might find it interesting. I have to confess that I have not been keeping up with this thread, so I will have to go back through and read it wherever I left off last time I was here. I just wanted to add the link to the end of this thread in hopes that you might see it. I'd love to hear what you think of the article. Best wishes, Tim.

How strong is your knot?

MIT mathematicians and engineers have developed a mathematical model that predicts how stable a knot is, based on several key properties, including the number of crossings involved, and the direction in which the rope segments twist as the knot is pulled tight.

news.mit.edu

 

[theTreeSpyder]

Thanks, perhaps i don't get out enough but really think this is great and going to reveal things.
i'm constantly visualizing 'heat' colors as force loading patterns in ropes (and hinging too i guess).
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This new toy will show secrets not seen before thru it's viewport into secret world inside knots.
>>Seems they talk of 'strength' and don't mean efficiency, but rather security tho, as different than usually expressed.
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i think sheet metal, loaded across; would give stretch pattern to where we minimize to beams of about same strength
>>so, i don't visualize rope forces as same thru the visible form either, and try to squint to see the loading secrets
Here i show such colors for properly adjusting Sailor's Hitch to Top Crossing and even Top Nip i try to highlight often.
>>Sailor Hitch very unique study from many angles besides this Top Crossing (rare to maintain) and Top Nip especially in one
>>Also Sailor (and Pile and Icicle) is hybrid between like Clove and Muenter i believe, so many insights into this powerful family of knots
i can't think of any hitch that force diminishes so quickly, like at the top of 2nd drawing where Sailor adjusted properly
>>and i show 'hot' purple flip to 'almost cold ' light blue:
Grabbing the tail from pic_1 and pulling up to crank the X crossing properly to top of pic_2, is like a friggin' gear shift the way the knot forces change!!
>>Strength/efficiency and security JUMP
i think the color changing spaghetti will show much, much more in all !

Note how Nipping and Crossing Turns both most intense on opposite side of host mount than loaded pull
>>as closely related for in Nip function Working End serves under greater tension, Crossing Turn WE goes over
This top, 'prized' location is hard to maintain in either, but Sailor Hitch does so in both
>>Rope of Sailor's Hitch seems to lend contours to the host mount to keep the rope fairly aligned to these magics
Any other knot used as hitch or bend i think can show fuller purple 'hook' to 9 o'clock, than this where purple stops at top/high noon to me
>>find force change that immense, and unique here.
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Older youtube thermal view:

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i think knotting is the original engineering of steps outside of body;
that if did out of order , failed etc.
Probably knots to at least to clothe and shelter if not tool before organized language
>>most sure before commanded fire, wheel, lever; perhaps even before confident walking upright.
Also, very importantly, the first linking of properties etc. outside of body.
Controlled series of linked connections is how we do most all, even computer commands.
>>amazing what we don't know about knots and how use computer evolution to look back to see what missed for so long of perhaps start of technology.
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But, like i said; in finding that amazing, i probably don't get out much!

 

[theTreeSpyder]

New IGKT "A Glossary for Practical Knot Tyers"

 

[theTreeSpyder]

Single Hitch mostly overlooked as doesn't work on simple round spar,
knot is so minimal depends on host mount for more 'services' of 'edge or shoulder' to Nip against.
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But is VERY different than 'Half Hitch'
whom Nips on load side of host mount, rather than the ante/opposing side of host mount/support like Single

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The Slippery Hitch crossing will want to rotate to the Load Leg side (from Control Leg side shown)
toward source of pull(Load), just like a Clove Hitch crossing placed on top will pull towards center of Load Leg side
>>use the increase to tighter forces in rope to hold crossing on Control Leg side half way point, so doesn't rotate to Load Leg side half way point!
CONSTANT, PURE DOWNWARD PRESSURE MUST BE MAINTAINED
Works better on larger mount, with more distance between radial degrees of change...

 

[theTreeSpyder]

MIT Spring Paradox: Connections of Series or Parallel and elastic response change
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MIT Schematic Sketch:

In series both springs are carrying full weight;
in parallel each carries half is where the twist here is...
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In ropes, 500# on single leg stretches further on impact than pulley setup against same load
>>pulley rig now has ~2x as much power, so it's ceiling is encroached on less , leaving more 'max headroom' of clearance/capacity.
>>This gives less elastic dampening from the pulley setup
>>more shockload to rest of connected chain, testing knots, ropes, supports etc. more
The single/series leg stretches further, gives more elastic dampening/stretch
>>some days this buffering is what outruns/wins over the stronger 2:1 pulley setup.
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Elastic response is per loading percentage of capacity, and not a nice even increments of change
>>so can't forecast that 250# gets half the elastic response of 500# nice and neat
So, 2x250# does equal the same single leg 500#, but former ( 2x250# )is stiffer/less elastic response ; than latter (1x500#).

 

[Eric H-L]

Hello Kenny,
I don’t know if you want this added as a comment on your mind-blowing thread or would prefer somewhere else? I have just learned that the oldest three strand cordage has been discovered. Not made by Homo sapiens but our cousins the Neanderthal. The scientists are suggesting that this probably means they had knot skills as well.

Direct evidence of Neanderthal fibre technology and its cognitive and behavioral implications - Scientific Reports

Neanderthals are often considered as less technologically advanced than modern humans. However, we typically only find faunal remains or stone tools at Paleolithic sites. Perishable materials, comprising the vast majority of material culture items, are typically missing. Individual twisted...

www.nature.com

 

[ruel]

Fascinating finding. Interesting to wonder about what other perishable technologies our relatives possessed.

 

[theTreeSpyder]

If take common 8' 2x4 w/2"sq.block each end we neatly have 8x12" + 2x2" =100" column
>>as a FINITE usable length that can be 'expressed' vertically or horizontally w/hybrids of each in between ranges.
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If from center of clock, 2x4 w/blocks column rises to TDC/12 noon,
>>all of the potential length is 'expressed' vertically, none sideways
>>thus cosine is 1 (efficiency of vertical rise 100%) and sine is 0 for side drift
BUT if this pure vertical column drifts to the side 6degrees (12:01 on clock)
>>cosine drops 1% to .99 efficient, thus column reach upward loses an inch vertically
>>while at same time sine JUMPS to 10% drift/side force
As board now 'only' rises to 99", it also JUMPS to 10" drift at top, thus the major change is the drift/side force horizontal
>>@ 12:02 minute hand angle board now reaches 98"(cos.9 but drifts another 10" to side (sine.20)
FORCE uses the same maths, just to different potential force in equation, and is just as real JUMP sideways
>>just as the length in equation is a potential, with percentages expressed to cosine column and not
>>the amount of force borne by device is the finite force potential, percentages of which are expressed vertically and horizontally all the same by same calculation, just to the different potential of force in the equation
In motion to these positions (tree felling etc.) , we thus can incur very harsh sudden impacting side force that in first few 'minutes' on clock as a very counter-intuituve point as eye sees height more or less same not decrease.
>>or only a hair, and with out study i think totally don't imagine that potent jump to side, that also happens in forces!
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The ruling 360 degree circle and the clock were both made by the Babylonians 4000 yrs ago to be handed down.
>>they used a base_60 math, as shown on clock, so each hash/tick/minute/second is 360/60=6 degrees
For hand-grenade close rule of thumb i simply use clock marks as angles and then numbers as cos/sin mnemonic.
>>hand grenade close as in errs in the hundreths to model all around 360 circle from 10pts. in first 45 degrees!
This is how i EASILY calc angle and percentages, using common clock:

sample usage of thumbrule:​

@Noon/ 0degrees cos:100%, sine:0%, tang:0% (TDC)

@1min/ 6degrees cos:99%, sine:10%, tang:11%

@2min/12degrees cos:98%, sine:20%, tang:22%

@3min/18degrees cos:95%, sine:30%, tang:33%

@4min/24degrees cos:91%, sine:40%, tang:44%

@5min/30degrees cos:86%, sine:50%, tang:55%

@6min/36degrees cos:81%, sine:59%, tang:66%(2%err)

@7min/42degrees cos:74%, sine:50%, tang:77% (ERR do not use!)

@7.5mins/45degs cos:70.7% sin:70.7% tang:100% (mid point)

In simplest gravity direction models

In simplest, Natural gravity force direction:
i use cosine to show % of 'displaced' space & force from the available potential length/force used VERTICAL
likewise sine to show % of 'displaced' space & force from the available potential length/force used HORIZONTAL
While tangent (not focus of this model but a freebie)
>>@ 12 degrees/2 mins on clock and holding 100", will 'express' ~22# to the side
>>@ 18 degrees/3 mins on clock and holding 100", will 'express' ~33# to the side etc.
SO rigging sideways on hinge almost cut thru, limb bearing down 400# on rope
>>gets 44# instead of Zer0 pulling sideways if can get rope angle to 1 minute/not vertical
>>if can connive 1 more minute/click that sideforce doubles to 88#, about what 1 man pulling tree might give..
The clock hand angles and minute marks lend very well to this, cant believe i'm the only ever to see this
>>but cant find elsewheres when look. Wonder if purposeful guide coded in 4000yrs ago..
It is MOST accurate in first 5mins, that mostly use, then can flip that 12-1 to find the 2-3 numbers
>>leaving center 1-2o'clock mid range as most err , in most unused zone of primary 90
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This 'primary 45 degrees' can be flipped to define the rest of the 'primary 90 degrees' .
>>then the primary 90 can be flipped around to all 4 corners of the squared circle model
>>thus PI is simply 4 - 21.5% loss ea. corner . 4-(4x 21.5%)=~3.141592
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In my force imagery models, i project the need of the unique, simple, single dimension of the cosine first against the linear force
>>as necessarily conjured against opposing force, then sine force as a trailing responder
This is in keeping with also the unseen waveforms all around of air, water, electricity, light etc. who's sine waves are ALWAYS preceded by their corresponding cosine waves.
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The numbers given by the Ancients are all around us, but especially magnified in force and leverage of that force in this thing that we do with virtually the heaviest, longest, most rigid leverage-able force in a life form known. Especially as we work with the simplest of tools rope & friction pivot to command the beasts. A front row seat of magnified view of how all much else works, as perhaps greatest persisting gift of this work, persisting far beyond the paycheck.
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They eventually cast PI as 3 1/8, 3.125 , so as to be .01659 short
>>so s/light 1-2% err found a bit here and there/mitigate, seems likely reality.
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Each generation's cast luxuries to children, risk taking them further from the unspoken lessons of the rawest of forces.
These peoples had no such buffering, and engaged forces most rawly, with fewer distractions and simplest of tools to do battle with.
What they decoded in the sight of such rawness, rules the world, and beyond the stars; let alone a simple tree in said context.
i truly hope this simple clock model gives a look into this key/pivotal world;
as it has allowed me to read the code and l-earn from much around me!
Further definement takes protractor and calculator/slide rule, tables etc.
>>But at a glance of the clock, can answer many questions on the fly!

 

[theTreeSpyder]

These numbers show how much respect (and fear) to give produced forces and their directions
Cosine/Sine TOTALLY RULE AND DICTATE, all physical displacements of space and force thru devices as mediums of transfer
(even in sound wave forms thru air as medium of transfer, electric wave form thru wire as medium, light,thermal etc. ALL WAVE FORMS)
The Ancients somehow defined that there is no other deeper pivotal concept/'common denominator' to drill to know these forces, as they span out to all.
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Examples: 100# Load/2 support legs = 50#support needed from each support leg;
if 2 straight legs cos:100%, sine:0
>>50# needed divided by cosine 100%(1) = 50# line tension
>>50# line tension x0%sin=0 side force
>>just as 50# line tension x 100%cos = 50# support column force against load (each side)
If each support leg deflects 30 degrees (60degree spread total) cos:86%, sine:50%
>>50# needed divided by cosine 86% = ~58# line tension
>>58# line tension x50%sin=29# side force
>>just as 58# line tension x 86%cos = 50# support column force against load (each side)
This could just as easily be a trailer nose pull geometry of same forces

(http://mytreelessons.com/images/cos...-vs-sine-across-that-must-also-be-carried.png)

120° spread both legs gives 60° deflection from load force center axis, to each support axis/side
This 60o of support is very easy, memory-able benchmark: cos=.50%, sin=86%
So, 2 legs of support at 50% efficiency each, GIVES LINE TENSION = LOAD
Therefore: any more vertical angle, line tension is less than load vs an more flatter gives line tension greater than load
As more vertical increases cosine contribution from line tension etc.
NOTE: sine at 60° is greater than cosine, and the sine softens as more vertical rope column given
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In clock metaphor , the rope angle is past halfway point of 45°
so counting backwards towards center from 3o'clock/15mins. to 2o'clock/10mins (5 mins)
is 50% cosine, and sine=100-2-3-4-5=86%
(just as reversed at 1 o'clock cosine =100-2-3-4-5=86% and sine =50% last example before pic)
Any of the sines can be felling side force(horizontal), cosines are the straight vertical part of tree force on vertical gravity force line
.
Just as support pull upward is a reverse of downward direction force on load axis,
going from 1o'clock angle to 2o'clock angle is a reverse/swap of mechanical pivotal (cos/sin)forces

 

[theTreeSpyder]

Hello Kenny,
I don’t know if you want this added as a comment on your mind-blowing thread or would prefer somewhere else? I have just learned that the oldest three strand cordage has been discovered. Not made by Homo sapiens but our cousins the Neanderthal. The scientists are suggesting that this probably means they had knot skills as well.

Direct evidence of Neanderthal fibre technology and its cognitive and behavioral implications - Scientific Reports

Neanderthals are often considered as less technologically advanced than modern humans. However, we typically only find faunal remains or stone tools at Paleolithic sites. Perishable materials, comprising the vast majority of material culture items, are typically missing. Individual twisted...

www.nature.com

.
So Sorry i missed this, when dropped in and thought had something special must leave behind.
It is my basic conjecture that 'man' in whatever stage/form
mimicked birds nest to weaving for clothing and shelter, evolved to knotting/rope work
>>before so commanding fire, lever, full language and most probably before walking fully upright.
>>kinda even kid before speech, quieter time, man could peacefully make knots w/o woman saying was wrong-at least verbally!
Many things need taught, even upright walking, for when 'feral children' (ouch) are discovered; they don't walk upright w/o example...
(kinda like riding a bike, whoever thought of that 'stupid chit' first, that would not be duplicated w/o example/urging input to you)
.
That lacing and then knotting are original engineering of critical part series that must be done in right order or fail (of outside own body experience)
>>Also being able to collect things to greater some of same(bundle or extension), or varied properties to larger whole(hammer, spear etc.)
(and see a computer program as list of ordered steps leveraged in connection all the same, rope as the start of this connectivity)
So, learning the ropes, is starting this education where our minds started it originally, and all lessons evolving from.
>>so scouts etc. teaching to kids in working form, gives basic lessons, some of which are nonVerbal/must be experienced to put it all together
Just as l-earned yoga traces animate stages of existence to bring back what was skipped at that stage (cobra, lion etc.)
>>so to, allow kids to trace our own evolvemeant of thought to gain the unspoken knowings, in contiguous chain to bring forward in fullest understanding
>>kinda like sports competition and all its lessons growing up
Thus rope work can be considered integral to a certain type of development of understandings and knowings
>>following now latent logical paths of human development from its roots
So l-earn in a few things to assert same forces in different ways to different affects, without being a 'fumble-bum'
>>handy i think they used to call it, as can make the connections between now and experience
>>and then to be on time, not off-beat with delivery of that quantity
>>for even best machine, or team as a machine; ain't chit w/o that proper timing!
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i find tree work to be such a basic pivotal lessons too, all the grunting forward and it's nonVerbal lessons it welds in
>>on your toes or die adrenaline, reaching down deep to come up with enough from a jar already scraped clean 6x...
>>As working with/around raw basic forms of both flexables(rope) and rigids(wood) in raw force forms etc.
.
And soon now, back to our (ir)regular (de)programing; (this rope heritage fave topic tho fer'reals!)

 

[theTreeSpyder]

To me, ropework/knots is about the straight line extensions and working 180 arcs.
>>So much so that describe 180arc as primary, and straight line as a non-arc of just simple extension.
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Binding USAGE of rope, is radial arc force INPUT reflected back full to Equal & Opposite of usual radial arc control
>>any other usage of radial arc control, does NOT have radial input DURING USAGE (not measured during presetting)
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ABoK's other knot classes of non Binding, not radial input to radial control but rather linear input into same radial control:
Hitching as forceline termination at node-deformity and
>>Bending as continuation of forceline thru node-deformity
Have LINEAR input force, imposing force from outside world into knot internals thru primary straight line (Standing Part)
>>that converts to Primary Arc that opposes Standing Parts introduced/imposing forces
>>Conversions always have a co$t, so are less forces after conversion co$t than mirroring E&O of radial to radial of Binding
Primary Straight as outer world interface + Primary Arc of internals are the most rigid, defining parts of Bends and Hitches to me
>>together as one i always look for the hook formed, rest of knot just helps keep interface in place to task
While frictions reduce tension flow to Bitter End Nip, that (reading backwards thru knot
>>Form Bitter End Nip as a ballast against load, small ballast given leverage thru frictions; against load

.
Example of using this model is to show why Zeppelin not so easy to seize, while Faux-Zepp can roll out;
While Rigger's Bend can seize, but Alpine Butterfly offers Faux-Zepp relief to keep from seizing..

.
Same raw forces, names and effects, with normal extra dressings:

Zeppelin:Strong, non-Jamming w/ full rigid SPart parts as side guards, equal to each side
>> False/Faux Zeppelin allows conversion to side force to exit thru least guarded side/rollout
Rigger's so intense can jam, but cousin B'fly has 1 weak side as Faux-Zepp, but w/o side force in it's pure inline focus
>>so B'fly wants to stay inline from pulls, but has some force limiter/steam escape to side not pressing/rolling towards, 'cuz side force

 

[cory]

That link re Neandrethals and cordage was amazing, both from the caveman POV as well as the scientists who study them.

And safe to say there is but one Kenny on this earth.

 

[theTreeSpyder]

Even i must admit that is 'prolly a good thing!
Hitch (& Bend) USAGES of linear force imposed thru primary linear SPart inputs into knot internals;
against the Primary Arc , both together comprise 'Hook' of most tensioned, thereby most rigid, key 'rope part'
>>'Rope Part' : mechanic from rope pool/puddle of rope
>>if working with rigid devices, could be separate device function linked to whole
>>rope simply allows each 'device' be formed in rope w/o heat, pin nor carving etc. each piece/funcion/rope part as rigids need per part
>>then rope also allows linking to next 'device'/event/rope part in tool set chain, against imposed loading.
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The Primary Hook is stabilized by rest of 'knot carriage'
>>to stabilize hook into place to task against imposed load w/grips even crossings sometimes
And also frictions that precede (final) nip/pinch to give greater more rigid rope parts
>>vs softer less tensioned rope parts
Rigid Tensioned rope pressure arc, seating against at least same rigidity host (can be rope part)
>>sandwiching a lesser tensioned, there by softer rope part to securely pinch it
.

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As 'parity check' verifier, forces should 'read' same backwards and forwards, thru the (connected) tool chain set comprising the knot/system..
.
Working flow backwards for answers of the maze/puzzle:
Small, securing Nip, can hold against much larger imposed load
>>thru frictions of 'knot carriage' holding 'Hook' giving enough leverage to tiny nip
>>to magnify/leverage that punitive effort against imposed load on system, thru Hook
Of course, if can give more leveraged frictions, and crossings to increase frictions etc.
>>and take that final low tension /soft BE and nip with greater pressure of Primary Arc
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Theory even functioning at what ABoK shows as worst angle of mechanical pull/lengthwise on support:

.
Is even better ratio of security of greater force, more rigidly applied to lesser,
>>softer part of 'tool chain set' of rope
>>in rigids this connected tool chain set would be individual connected devices
>>but rope is as all in 1(like saying 'batteries included' in software, no more needed)
.
In electronic hobbyist world of digital sensors, have only 0 & 1 off/on noted on wire
>>If sensing for switch close to HI / 1 signal of 5v+
>>can get some 'falsies', ghosts, drifts showing hits/closes from sensor left 'floating' w/o other connection
Dead Ballast sensor wire down with 10k resistor to ground/0 makes more lock sure definitive architecture
>>not a 'maybe baby', but a thriving one
The 'pull-down resistor' doesn't allow falsies from floating sensor
>>too much resistance for 5v to short when thrown high
>>more definitive 'kerplunk' when switches opens back up from 1 to what would have been floating but now 'anchored'
Following pivotal laws closest to source (like measuring cos/sin etc.) is more definitive, positive mechanix
>>of no maybe babys when ushered and commanded so completely to the true solid architecture maths

 

[theTreeSpyder]

In the geometries of space taken or force invoked, it is about DISPLACEMENT.
To control, with force, takes displacing into that space, with enough force to match or beat the existing force
>>for positively commanding displacement to rule/Nip situation ('in the bud')
.
The ruling rigidity is gained by matching linked target forces or being greater/not lesser.
>>The base/unloaded rigidity of the materials matters for this advantage
>>The amount of tension force
>>and how densely that force is packed into each part as yet another rigidity adjustment
Different force loads in diameters for the crossing over to be great enough to Nip the sandwiched ropePart

.
Sometimes see questioned if Square Knot should be still taught
>>i always think YES, for is a minimal structure study, with fewest parts
>>on edge of make or break(fail) and things that change that
(errant bend usage, unequal diameters, formations or disturbances that 'pull out of square' form etc.)

.
i first note many things in the minimalist study of Square family(Square/Thief/Granny/Grief)
>>and would usually forsake American upbringing and call as original name Reef in respects to how many knots born at sea
BUT, the name Square is so excellent to force chase, and constant reminder that all rope mechnix best if 'square' to purpose
>>the minimalist Square Knot, just more sensitive to that, as Thief/Granny/Grief fail by pulling out of square, as does tugging end.
The SheetBend invokes a locking hitch that can free stand off of host mount (unlike Square that is dependent on host to nip against)
>>so has another layer of simplest/base lessons, and how a more rigid locks on softer rigidity etc.

.
Friction Hitches show the matching or greater principle too
>>advise a single leg of pull (A) can match rigidity to single line and control (Taut-Line, ProLaska/Blake's etc.)
But dividing load to 2 legs pull on host /receiver and are trying to grab greater rigidity with lesser(B) can fail
>>using a smaller cord to pack lesser divided force into a denser/more rigid container can resolve(C)

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The smaller 'cord' can also be a more rigid /unyielding braid, too stiff to seat properly like this on own diameter
>>but flexible enough to seat well on larger diameter host
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i think the term (Friction) Hitch is accurate, as the function is to slide the hitch up/down to repeatedly grip
passive 'rail' whether rope or not , the rigidity examination tho is for rope on rope
.
Friction hitch grabs on smooth pole can slip some as rope can't 'dent' impose into the host