Test of hitch tension reduction methods

[mcjtom]

I'm not sure if this is allowed or in good form (could please the Moderators delete this post if it's not).

There is a short article in the Knotting Matters #146 (March 2020): pp.: 24-30 describing tests of a number of spar wrapping techniques reducing the tension on the final object hitch (or one could consider those wrapping techniques as an integral part of the hitches as in the 'round turn and two half-hitches' or the 'backhand hitch').  Either way, while not ground-breaking I think it's an interesting enough quantitative dataset on friction, without which no knot would work, to include in this sub-board.

How to Reduce Jamming - KM146:pp.24-30

p.s. I just re-read it and discovered some minor typos, notably Figure 2 is referred to in the text as Figure 1.

[DerekSmith]

@mcjTom

Good piece of work and method development, and excellent paper.  I hope the Editor finds a place for it in KM.

I will, if I may, in light of recent work, make a few comments...

I am a lifelong Analyst (Chemical and Physical).  From experience, two issues come to mind -
1)  Human bias is a massive source of error.  For this reason we would normally set samples for both random and anonymous measurement.  However, simply being aware of this natural propensity for bias is sometimes enough for us to consciously resist recording anything but the displayed value.
2)  Variation in results for replicate assays is ALWAYS due to some real parameter, it is never simply random noise.  By careful identification and elimination of these 'subliminal' variables, most of the 'noise' usually attributed to statistical variation can be accounted for and often will lead to a greater understanding of the system under test.

I noted from your results that you employed regression analysis to eliminate 'noise'.  In line with my above comment, I reanalysed the raw data you published to give individual cf values for each of the 15 simple round turn variables you tested.  Plotting the cf values against the number of turns for each of the four load values highlighted three anomalies.
i) The two highest loadings of 147 and 99.1 both exhibited near identical reducing trends from 1 turn (0.17 and 0.15 resp)  to 0.14 and 0.13 resp for 7 turns.
ii)  The 19.9 load measurements all sat roughly 0.04 higher than the 147 and 99.1 traces.
iii) The 52 load test for 1 turn gave an anomalously low cf value (by ca 0.05).

Q1  What could cause the consistently reducing trend of approx 0.02  from 1 turn to 7 turns?
Q2  What could have caused the 19.9 load values to be ca +0.04 across the set of turns?
Q3  Could the single very low value have been caused by misreading the display / load bsing partially caught up / rough part of the bamboo surface ...

Bamboo is a natural, organic material often having a slightly oily surface and an irregularity where the side shoot joins and distorts the rod to form a groove to the next node.  Could any of these type of factors indicate the direction Q2 and Q3 could be investigated?

As for Q1, I believe it may be due to a one off constant factor introduced by loaded straight cord being forced into loaded curved cord.  This force would impart a greater point Normal force and so create a single point of greater friction.  Each measurement would then be a composite of the point contact and the turns contact..  As each measurement was a series of increasing turns, the effect of the single point contact would be shared over more turns giving an overall reducing cf value experience in these tests.

I have had an idea of how to create multiple spot points by stacking two carabinas.  I will report back if this turns out to be a reality.

Derek

[Dan_Lehman]

@mcjTom

Good piece of work and method development, and excellent paper.
I hope the Editor finds a place for it in KM.

Derek, note tense & citation!
>>> There is a short article in the Knotting Matters #146 (March 2020): pp.: 24-30

The (former) editors DID find space.

(-;

[mcjtom]

Plotting the cf values against the number of turns for each of the four load values highlighted three anomalies.
i) The two highest loadings of 147 and 99.1 both exhibited near identical reducing trends from 1 turn (0.17 and 0.15 resp)  to 0.14 and 0.13 resp for 7 turns.
ii)  The 19.9 load measurements all sat roughly 0.04 higher than the 147 and 99.1 traces.
iii) The 52 load test for 1 turn gave an anomalously low cf value (by ca 0.05).

Q1  What could cause the consistently reducing trend of approx 0.02  from 1 turn to 7 turns?
Q2  What could have caused the 19.9 load values to be ca +0.04 across the set of turns?
Q3  Could the single very low value have been caused by misreading the display / load bsing partially caught up / rough part of the bamboo surface ...

I couldn't find a reason to call any of those measurements an outlier and made them all contribute to the 'overall' cf via regression - which I estimated to be 0.15 +/- 0.03 at 95% CI for my setup, perhaps optimistically.  Removing one or two values wouldn't make much difference. 

An argument can be made that when you look at the scatter of 3-4 observations (the chance that the next observation will be even higher or lower than the min-max of 4 observations is 40% regardless of distribution) that trends are weak, if any, but the cf values calculated from the lowest load may stick out a bit from the rest and that small arc contact angles tend to scatter the observations a little more (but the very Munter hitch uses angles of similar magnitude so that is likely fitting).

I think that the main trouble in trying to measure the single 'best' value of a cf between two materials is that it is unlikely constant.  The constant cf friction model is baked into the capstan equation, but it is likely that the cf itself depends at least on how hard the two surfaces are squeezed (normal force) - cf often becomes lower when the load increases significantly.  There is also 'bending rigidity' effect that the regular capstan equation doesn't account for.   How large those effects may be is debatable but the model equations can be modified to account for them.

This paper more or less summarises the improvements that people were trying to make:

http://ningpan.net/publications/101-150/146.pdf

Great ideas but a little impractical.  If the bending rigidity and power-law friction were introduced to the model, you would require 4 extra measured parameters further describing your rope-carabiner system as an additional input to the model in an attempt to (probably slightly) improve the accuracy of predictions.

As it is, The Munter Hitch Model, once calibrated, requires only two parameters (two estimated cf's assumed constant, but a little fuzzy...) to make all the tension reduction predictions - and even those two are not that easy to measure honestly.  The net cost of it is that the predictions are also a little fuzzy, but allow you to read what's happening in the Munter hitch well enough, I think. :-)

p.s. Coincidently, the reasonable 'fuzzines' of inputs (cf and contact angles) results in the fuzziness of predicted tensions which is in the similar range as the precision of measuring them in practical setups such as the Munter - i.e. you may not be able to detect improvements to the model too well.  So it all seems to fit reasonably well in practice.

[KC]

To me most all these things are simplest 3parts: input connection(SPart), machine of change('pivot') and output connection to 'tailer' function.  These are tension reduction machines with real capstan arc reductions to output ; just not to tailerman, but hitch here after the machine of tension reduction (same outputs to tailer of man or hitch).
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Played backwards (from whatever is greater input tension end as domain ruler), the lesser,tailing force of hold whether man or hitch ; gets leveraged greater thru the 'friction buffer', (in direction of reverse view) machine (radial list of arcs as capstan or linear list of arcs as rack), to eventually bear/ ballast against the greater raw peak input force .  Only pure matching balance gives hold load/initiating force at bay.  In contrast to imbalance against load of less/ or more than matching the initiating/ruling force imposed , gives movement.
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The initial chart is incomplete (to point of very smooth with large hole)without a Crossed (on host)Turn I think.  As 3rd key 3x arc180/ PI radian.  Chart has Round(not crossed)Turn and Backhand (crossed off host) Turn very nicely, but I think Crossed (on host)Turn would complete the logical triad(and somewhat more faithfully to what Ashley lends).  This is in Hitch and Bend USAGES (irrespective of name of knot used) as have linear force input vs. radial input of Binding against swell where ; arcs don't decrease tension (in contrast to linear inputs to arc conversion)until nip. 
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i prefer arc180 naming (even tho math proper does say PI radian)as part of just 3elements to describe loaded rope forms: arc0(linear) and arc180 each maintain the input power axis(just in opposing directions on that axis); and arc90 that shears across the input power axis.  Rope is so simple it can't present more elements as is without cross-axis rigidity /only working on inline axis and only in tension/not compression direction on that axis.  In this view as minimal structure , rope offers the most simplistic not most complicated force lessons.  Especially round (ultimate organic undifferentiated equilateral geometry)rope on round host models. 180 arc key in rope friction as is in bridge support , for same reasons geometrically.  Rope is just a different material to form the geometries in.
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Tension reduction of output, also makes that section of rope less rigid/easier for the greater input to nip , not just by war of tension but also rigidity when rope crosses self as another machine aspect.  This is another difference of (constant) rigid vs. flexible(variable rigidity) device forces. 
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To me it is Natural for the stiffness of rope as a rod to tip scales of how well rope seats to host especially at lower tensions, to then get less return of usable byproducts: frictions, nips and grips.  The host interrupts the linear flow of force thru rope, deflecting to less properly aligned column of support against load; getting byproducts in  traded place of tensile efficiency.