Measuring cf and applying an analysis to the Munter

[KC]

I totally key into follow the forces.
From that perspective I think where force is carried in  the rope : internally, externally or both in all seatings to host.  Along with if flattens(3/8 Tenex, paracord 550 etc.) or maintains round.
Yes, and then too the external mating surface / condition (glazing, fraying etc.), and whether that is a rigid load carrying part, are consistently overlooked aspects of making sure aren't comparing apples to oranges.
.
'Purifying' to this extent should sharpen view of real actual working pivotals, to then filter out of contrast with what used to be included as sames , to then further define impact of glaze, flatten, fluff, internal or externally carried load force etc.

[DerekSmith]

Hi mcjtom,  absolutely love your 'working protype' - lovely piece of demonstrative work.  What is the package you are using to produce the graphics?

Re:-

One of the consequences is that using Derek's data and his method of estimating rope on rope friction coefficient indirectly from Munter tensions themselves, probably underestimates it by a factor of about two (need to confirm).

Given that I have used loads directly from the hitch itself and contact angles for the hitch 'in tension' - i.e. loads or friction could not have come from any other sources, I would be interested in your rational as to why you feel I might have underestimated the cf by a factor of about two?

I do not refute the fact that I may be wrong in my analysis, I have been wrong in hte past and will doubtless be wrong again in the future, so I am open to seeing where you think the x2 factor comes from...

Derek

[DerekSmith]

I started this thread with the intention of sharing a very simple (and cheap) method of measuring the total grip of a hitch on its stator and with the objective of using the data to calculate cf factors for the cord on a bina,  then use the same method to measure the total grip of the Munter hitch.  By making measurements of multiple turns I also hoped to be able to demonstrate the additive characteristic of cf factors, then use this to determine the cf contribution from cord to cord friction.  After measuring  the contact angles of the cord on cord the plan was to derive a cf for cord on cord.  This I think we did, although mcjtom has concerns that I have somehow underestimated the cord on cord cf, but I hope we can resolve his concerns.

AgentSmith requested that the cf be used to demonstrate the workings of the Munter. He then expanded this to a request for the data  to be used to predict the increased grip the munter would have when the brake end was swung through 180 degrees to take up a parallel alignment with the SP (loaded end).  I hope to cover this request in this post.

@Mark, you have subsequently stipulated a far tighter set of requirements which I will address in a later post.

I am only interested in testing the "Munter hitch" using human rated EN892 and EN1891 ropes.
I care little for testing done with anything else - and I don't care what arguments are tendered to the contrary.
Within the realm of vertical rescue / rope access / rock climbing / canyoning / caving / etc etc, I am of the view that if you going to the trouble of testing and publishing results to the world, you should test using PPE (ie rope + carabiner) that accurately reflects what those various user groups actually use at their various 'workplaces'.
But that's my personal view... and others may hold conflicting views, but I still don't care

So, in theory, all we need to do is to calculate the effect of adding another 180 degrees of wrap ( π radians) to the total cf of the basic Munter.
From the earlier work we measured the Munter ∑cf for 550 paracord on DMM bina to be 1.55 to 1.65 and taking the cf for 550 against bina as 0.095, we need to add on another  π x 0.095 = 0.298 to the measured Munter ∑cf, giving us a theoretical Munter + 180 degree wrap ∑cf of 1.85 to 1.95

To get these Munter ∑cf values into real world load amplification values we have to use the e^x function on your calculator.  Doing this we get 6.35 and 7.03 respectively, this is the ratio of SP load / Holding load.   So, if you had a 1 kg holding force, it could hold a 6.4kg to 7 kg load, whereas without the 180 degree turn, it could only hold around 5 kg

But that is just a prediction based on the assumption of additive cf functions.  We should be able to confirm the prediction by measurement...

To measure the Munter + 180 deg ∑cf values I needed to modify the test setup.  As it stands the SP load and the holding load are 180 degrees opposite, but to measure the Munter + 180 deg we need both holding and SP to be parallel to each other.  to achieve this I hung the bina on the scales, loaded the Munter with 2kg and tensioned the holding end until the munter stopped slipping.  At this point the scale was holding both the 2kg load and whatever load the holding end needed to stop cord flow.  The weight recorded was 2.28kg.  As the static load is 1.98kg, it leaves 0.30kg for the holding load.  1.98 / 0.3 = 6.6 nicely within the range of our prediction.

Derek

[DerekSmith]

I have a problem and I am hoping that you folks out there might be able to cast an explanation on it for me.

I was preparing to mark up Mark's Munter image with the points where the forces congregate, but first, as I had used two methods to determine the cf's for various numbers of turns, I thought I had better compare the two sets of results to make sure that one method did not have a bias over the other.  The even number of radian were measured by one method and the odd number by the other method.  There was no offset between the two, but I did notice that the first reading for each series (the lowest number of radians)was consistently higher than the rest...  So I ran the trials backwards - same result, the lowest number of radians had the highest cf.

Was it the fact that the first turn had the highest load?  Nope, I ran the test with 1kg load and same profile.
Was it the fact that the first turns would be drawn faltter than subsequent turns, giving a greater surface area?  Nope.  Reducing the contact area reduces the pressure / unit area , so the frictional effect remains constant - try doing the test with two strands parallel - same results.

So what is it and why does it matter?
Here is a typical list of results for 550 on Aluminium bina.

Contact angle     cf/radian
1π                        0.104
2π                        0.101
3π                        0.098
4π                        0.099
5π                        0.085
6π                        0.096

Notice the drop from 1π radians to 3π radians (i.e. 180 degrees to 540 degrees).  It is only small, but it is repeatably consistent.  The 1π value is an average frictional coefficient from the first π radians of contact.  The 3π value however is the contribution from the first measured block, plus the contribution from the next two π radians of contact averaged across all three.  This means the later two had to have been significantly lower to have pulled the value down from 1.04 to 0.98.
If the is so, then why does it matter and how large is the effect?

Well, it matters because I hoped to be able to follow the forces into the Munter and calculate the drop in tension as the cord flows through the hitch.  If I use a single average cf for the whole of the analysis, then I would be seriously underestimating the power loss in the very first contact points.

To better see the magnitude of this effect, I set about using the data to extract the cf for eack segment without the averaging input from the previous turns:-

Contact zone        Mean cf.radian for this segment.

0 to π radians                    0.124
π to 2π radians                  0.087
2π to 3π radians               0.086
3π to 4π radians               0.074
4π to 5π radians               0.09
5π to 6π radians               0.068
6π to 7π radians               0.068

So my questions are :-
Anyone know what caused this effect?
and
Does this effect happen at every  meeting of cord with a new surface?
and
If it only manifests once - why?

Of course, it is entirely possible that my method of measurement has caused this artefact, and if it is then I would welcome any clarification and advice.

Thanks to those with the knowledge, understanding and time to chip in on this conundrum.

Derek

[agent_smith]

This post is directed towards Derek (more than anyone else):
I note that you are using a carabiner manufactured by DMM in Wales.
I presume you are aware that various models of carabiners have different profiles (cross-sectional profile).
More specifically, these days, it is getting harder to purchase a carabiner with a purely round profile (not impossible though...)
For example, the Black Diamond 'Rocklock' appears to be perfectly round (but in fact it isn't)
Link: https://www.blackdiamondequipment.com/en_US/product/rocklock-twistlock-carabiner/  (I own a bunch of these carabiners and
I can confirm that they are definitely not perfectly round).

Most carabiners tend to be; I beam, C channel, Ovoid/Oblate, T bar, etc...
Obviously, the shape/profile of the metal stock the rope is bending around will effect your results.
Your indicated "DMM belay biner" is not drilling down to a precise model/type... and so perhaps the metal profile is not purely round?

I note you appear to favor testing in very thin, non human rated ropes (likely due to cost and availability issues?).
Thinner diameter cord that does not meet stringently defined standards could also be a factor.
Larger diameter human rated ropes that are built to exacting standards (tighter tolerances compared to para cord) - should provide better consistency.
Para cord link: https://www.paracordplanet.com/blog/paracord-strength-sizes-and-types/  (It is unclear if you are using 'Mil-Spec' para cord?).
Even if it is Mil-Spec, it is still not the same level of stringent design/quality as per human rated rope.
I imagine that if you ran a test with thin paracord using a #206 Munter hitch, and then repeated the same test using 10.2mm EN892 dynamic rope,
the holding power of the hitch in one rope compared to the other might be different?
I just tried it with EN564 certified 6.0mm cord versus EN892 certified 11.0mm Edelrid dynamic rope... can you guess if there was a difference in brake holding power?
EDIT NOTE:
I tested EN564 6.0mm Sterling accessory cord in comparison to EN892 Beal 9.1mm 'Joker'.
[ ] 6.0mm cord = 5.0kgf to hold a 20kg mass
[ ] 9.1mm rope - 4.0kgf to hold a 20kg mass
This shows that larger diameter ropes provide increased brake/holding power compared to thinner cords.

You don't have a photo of your test rig setup (the reader has to try to visualize your setup based on your description).
A clear and detailed photo - or a clear and easy to understand diagram might reveal something you overlooked...?
I'm not suggesting that your test rig was incorrectly configured... I am simply saying that humans are not infallible, and its within the realm of possibility
that you overlooked something?

EDIT NOTE:
I have been using a 'Rock Exotica' Pirate carabiner.
It has a perfectly round cross-sectional profile.
Link: https://www.rockexotica.com/pirate-auto-lock
This ensures that the rope contact angle with respect to the carabiner is continuous.
Not all carabiners have a perfectly round profile - in fact, its getting harder to find such carabiners.
In my view, a perfectly round profile carabiner will help remove variability in testing...

With respect to the rope-on-rope U turn, I have found that it is not perfectly 180 degrees (ie Pi radians).
I've attached a photo with a close-up view of the 'U turn' - where it can be seen that it is not perfectly 180 degrees.
I've played around with various types of human rated ropes... and I've found that the contact angle varies according to:
[ ] the stiffness of the rope
[ ] how the rope is gripped/held by the belay person (the rope position is influenced by the belay persons grip and hand position - which appears to alter the rope-on-rope contact angle).
[ ] the test mass (higher test mass = greater compression of the #206 Crossing hitch structure)
This suggests that the test rig must be carefully setup and controlled to ensure a consistent geometric form and position of the Munter hitch).
Scaling up to heavier test mass seems to alleviate some of the variables (but in doing so adds burden to the tester who must have a way to manage the higher test mass).
Slight variations can effect the measured results...

[mcjtom]

I do not refute the fact that I may be wrong in my analysis, I have been wrong in hte past and will doubtless be wrong again in the future, so I am open to seeing where you think the x2 factor comes from...

Derek

I take it back.  I now think that it may be underestimated but by some 50%, not a factor of two.   It comes down to the contact arcs angles - mine turn out to be smaller.  Please take a look at the Munter Model and see what makes better sense:

https://forum.igkt.net/index.php?topic=7397.0

It allows you to easily modify the two fixed angles involved (under Fixed Parameters).  You can also modify all other angles, but that's a bit convoluted as they are computed internally based on the vector equilibrium of forces at the rope-on-rope junction of the Munter Hitch. 

The full range of the brake hand angles is already displayed as the red line, so you can read the holding tension value for any angle off the graph.

p.s. It's also worth looking at the uncertainties of inputs and how that propagates to the results (the Model does it now), especially if you want to use measured Load/Hold ratios to calculate rope-on-rope friction factor.  If you look at it closely, the difference in the calculated rope-on-rope friction factors (yours and mine) may not be that great.

[mcjtom]

I think that you'd do well if your tested-rope collection
had some noticeable differences of:
1) firmness
2) sheath slickness (from new, to normal-used, to *hairy*)
3) diameter (as in your stated cordage you'll go from, what,
8.x to 11mm?

One does see remarks by climbers of differences one might
want to beware when using a new, slick rope in a belay or
abseil device.
(... musing about some sort of quick'n'dirty measure
 for bending resistance : hanging a weight on a U-fold
of rope, seeing how much the legs are drawn towards
each other?!)

I think the good news is that although the stiffness, roughness, and rope/bollard diameter ratio of your particular rope/carabiner pairs may all affect how it slides through the Munter, a lot of the variation is already accounted for by the measured friction factors.  Stiffer ropes may need a little reduction of some contact arc angles involved in the model (or maybe not in most cases...).

The bad news is that those properties seem to vary wildly between rope/carabiner pairs regardless of a certification stamp a rope is displaying when new, and even more so as they age. 

AFAIK EN standards are not interested in measuring/restricting/reporting them, with the exception of EN1891 for low-stretch ropes Knottability value (a ratio of daylight to rope diameter in a loaded overhand knot - a misnomer as the lower values indicate softer rope) but this is only to make sure that such ropes don't leave the factories too stiff.  Classifying rope friction properties by their safety certifications is almost as unhelpful as doing it by their colour. :-)

That being said, there is no harm in experimenting (and reporting on) with any subset of ropes that one may cherish. 

[mcjtom]

EDIT NOTE:
I tested EN564 6.0mm Sterling accessory cord in comparison to EN892 Beal 9.1mm 'Joker'.
[ ] 6.0mm cord = 5.0kgf to hold a 20kg mass
[ ] 9.1mm rope - 4.0kgf to hold a 20kg mass
This shows that larger diameter ropes provide increased brake/holding power compared to thinner cords.

I'm afraid it doesn't show this.  You would need to measure two coefficients of friction for each of your ropes first to even consider the potential effects of rope diameter.

But more importantly, even if you do, that still has little chance to work because your load cell display resolution is 1 kgf.  This imprecision will at least double when you use your cell in the best of experimental setups. 

What it roughly means is that you can't detect tension differences of less than a few kilograms-force (and conversely, you will be spuriously 'detecting' differences of such magnitude even if there is none of the consequence - which is likely the case here).  You're measuring the noise, not the signal.

To see what level of experimental 'noise' you can expect in experimenting with your gauge, take a look at the plateau sections of the graph on page 87 of this paper - it's the same resolution gauge.

One usefulness of models such as The Munter Hitch Model is to simulate your intended experiments, varying parameters, and look at predicted (but quite realistic) tension uncertainties that it computes to see if your gauge+setup is sensitive enough to be able to measure what you're after.

[agent_smith]

I'm afraid it doesn't show this.

??

Wow, were you there standing next to me while I performed the test?
I don't recall seeing you standing next to me...

EDIT NOTE:
Some additional test results... Test conducted 09 Jan 2023
Test mass = 40kg
Load cell: Linescale 3 (running latest firmware)
Set to 'relative zero' prior to each test series.
Sensor scan rate (cycle rate) set to 40hz (to make it easier to read the LCD screen).
Carabiner: Rock exotica 'Pirate' (I chose this carabiner because it has a perfect round cross sectional profile).
NOTE: All tests conducted with a single strand of rope formed into a #206 crossing hitch (Munter hitch).

EN564 6mm Sterling accessory cord
Test 1: 0.08kN
Test 2: 0.06kN
Test 3: 0.07kN
Test 4: 0.07kN
Test 5: 0.07kN
Test 6: 0.07kN

EN892 dynamic 9.1mm Beal 'Joker'
Test 1: 0.05kN
Test 2: 0.06kN
Test 3: 0.07kN
Test 4: 0.06kN
Test 5: 0.05kN

EN892 dynamic 11mm Edelrid
Test 1: 0.04kN
Test 2: 0.05kN
Test 3: 0.05kN

NFPA Sterling HTP static rope 13mm
Test 1: 0.03kN
Test 2: 0.05kN
Test 3: 0.04kN
Test 4: 0.03kN

The results suggest a trend... in that the brake force induced by the #206 Italian/Munter hitch
scales with increasing rope diameter.
A possible explanation for this is that larger diameter rope has a larger surface contact area bearing across the carabiner.

[mcjtom]

The results suggest a trend...

I'm afraid they don't, please see above, but what are you trying to find out anyway?  There may be a better way.

[DerekSmith]

@mcjtom  thank you for bringing us this fantastic piece of work - it is a gem and will find a home alongside my pdf copy of ABoK.

 Physics for Roping Technicians by Richard Delany

Do you by any chance know the author? and, would they be interested in contributing to this thread?

Derek

[mcjtom]

You may want to ask him: http://www.ropelab.com.au/#
He used to be a contributor here.

[DerekSmith]

This post is directed towards Derek (more than anyone else):

Hi Mark, apologies for not responding sooner - Frozen pipes have had me busy with repairs of the extensive damage caused by the subsequent flooding.

I note that you are using a carabiner manufactured by DMM in Wales.
I presume you are aware that various models of carabiners have different profiles (cross-sectional profile).
More specifically, these days, it is getting harder to purchase a carabiner with a purely round profile (not impossible though...)

My Wales DMM is 12mm full round section rated at 25kN.  I also have a BlackDiamond 12mm 'T' section (25kN) and will publish the significantly different values I get from using it.

I note you appear to favor testing in very thin, non human rated ropes (likely due to cost and availability issues?).

Yes, I am using Mil spec III 7 core 550.  I am using it purely for 'Proof of Method Principle' and ease of testing.  I also have access to 6.0mm Sterling accessory cord, 12.5 mm climbing rope and a coreless ultra soft 12mm braid for my VT lanyard.  But first, I will use the 550 to discover and identify the factors which throw the simplistic 'Capstan equation' out of whack.

I imagine that if you ran a test with thin paracord using a #206 Munter hitch, and then repeated the same test using 10.2mm EN892 dynamic rope,
the holding power of the hitch in one rope compared to the other might be different?

I certainly would not bet against that suggestion - my aim however, is to attempt to understand  WHY any such variations exist, and if possible, to quantify them.

I tested EN564  in comparison to EN892 Beal 9.1mm 'Joker'.
[ ] 6.0mm cord = 5.0 kgf to hold a 20kg mass
[ ] 9.1mm rope - 4.0 kgf to hold a 20kg mass
This shows that larger diameter ropes provide increased brake/holding power compared to thinner cords.

Unfortunately, the 1kgf resolution of your measuring system means that each value could be +- 0.5kgf, in other words, the 6mm cord could have a real value of 4.5 kgf and the 9.1mm rope could have a real value of 4.4 kgf i.e. indistinguishable from each other (even though there may be a real  difference at work here)
NB of interest, if you repeated this with a 40kg load, we should be able to predict holding forces of 10 kgf and 8 kgf respectively while your subsequent tests with a 40kg load showed holding forces of 7 kgf and 6 kgf respectively.  A disparity well beyond the ability of the scale to resolve).

By only measuring the total knot amplification factors ( x4 holding for the 6mm cord and x5 holding for the 9mm rope).  Personally I believe that you are indeed showing an actual trend, but what is causing it?  Stiffness, diameter, surface structure, rope to bina cf, rope to rope cf, or some factor we have not yet managed to pinpoint and quantify.  For sure you have set us a complex challenge.

You don't have a photo of your test rig setup (the reader has to try to visualize your setup based on your description).

Yes, I feel shamed by that.  Your graphics set us all to shame and an Iphone is not ideally suited to get images into a computer, then they have to be resized to meet the IGKT forum limits.
However, I will attempt to make a short video of the test rig and the test method.  If successful, I will post it to Youtube and put a link on here.

A clear and detailed photo - or a clear and easy to understand diagram might reveal something you overlooked...?
I'm not suggesting that your test rig was incorrectly configured... I am simply saying that humans are not infallible, and its within the realm of possibility
that you overlooked something?

Never a truer word spoken, and this forum is the perfect place for other minds, eyes, perceptions and levels of experience to spot mistakes and to throw in new perspectives.  I am all for constructive discussion, no matter how critical...

With respect to the rope-on-rope U turn, I have found that it is not perfectly 180 degrees (ie Pi radians).
I've attached a photo with a close-up view of the 'U turn' - where it can be seen that it is not perfectly 180 degrees.

Yes, I found it hard to quantify this.  In the end I loaded the hitch and 'froze it' with Superglue, then slipped it off the bina in order to more precisely measure the contact angles for cord on bina and cord on cord.  There are also straight (non contact) sections I was able to quantify, once the hitch could be studied in 'frozen' 3D

I've played around with various types of human rated ropes... and I've found that the contact angle varies according to:
[ ] the stiffness of the rope
[ ] how the rope is gripped/held by the belay person (the rope position is influenced by the belay persons grip and hand position - which appears to alter the rope-on-rope contact angle).
[ ] the test mass (higher test mass = greater compression of the #206 Crossing hitch structure)
This suggests that the test rig must be carefully setup and controlled to ensure a consistent geometric form and position of the Munter hitch).
Scaling up to heavier test mass seems to alleviate some of the variables (but in doing so adds burden to the tester who must have a way to manage the higher test mass).
Slight variations can effect the measured results...

I think there you have captured the essence of the challenge you have set us, and for sure, 'it's complicated'

Derek

[agent_smith]

Derek,
I've looked at the DMM website.
Link: https://dmmwales.com/climbing-products/locking-carabiners
There doesn't appear to be any carabiners with a perfect round cross-sectional profile.
Maybe you have an old (no longer manufactured) design?
I am using a Rock Exotica 'Pirate' - it has a perfect round profile.
Note: If grooves are milled into the carabiner, this obviously removes metal - and this creates small areas where the rope is not in contact with the metal.
The DMM 'belay master': https://dmmwales.com/climbing-products/locking-carabiners/belay-master  has grooves milled into the metal stock.

I chose to use a Rock Exotica 'Pirate' carabiner to reduce variables in my testing.

I am also using a Linescale 3 load cell - running latest firmware (factory calibrated).
I reset absolute zero - and also set relative zero for each test series.
The load cell is accurate to +/- 0.01kN (which is perfectly okay for my budget restrictions and needs).

For each test series, I carefully balanced the 40kg mass.
I used two (2) 20kg barbell gym weights - so I am confident that the mass is 40kg.

I was careful to gently ease the 40kg mass on to the rope and #206 Crossing hitch (ie Italian / Munter hitch). I was also careful to avoid shock loading the Italian / Munter hitch.

Principal issues that affected my measured results:
1. The first test in each series generally had the lowest measured kN value.
As I repeated the same test, I noticed a trend toward slightly higher measured forces.
It occurred to me that the section of rope subjected to load was being stretched, and it became slightly stiffer (and slightly narrower - due to being stretched/loaded).
And so in subsequent tests, the rope was slightly stiffer and narrower relative to the first test.
This induces a slightly reduced 'footprint' of the Munter/Italian hitch in terms of total surface area contact with the metal carabiner. And this might explain why I tended to get slightly higher results as the test series progressed.

2. Lifting and then positioning the 40kg mass was done by hand - and I was very careful to avoid any shock loading. The 40kg mass was carefully eased on to the Italian/Munter hitch. However, there might be slightly different rates in which I eased the test mass on to the rope and Italian/Munter hitch.
EDIT NOTE:
I've done some more experimentation - and this is a reasonably significant issue.
If I allow the test mass to dynamically drop - it causes shock loading on the Italian/Munter hitch - and it slips and compresses, and settles. This induces higher loading
to the load cell.
If I carefully and gently ease the test mass on to the Italian/Munter hitch, there is (of course) no shock loading... the hitch slowly responds to the load and then settles. The measured force
is correspondingly lower than allowing the test mass to shock load the system.
I see this as an issue for any 'home-brew' backyard tester... in that; the way the tester transfers load to the Italian/Munter hitch will significantly impact the measured loads.
I am trying to imagine a professional lab tester... and I also think they will find inconsistencies in how they transfer load to the Italian/Munter hitch.
This in turn will produce variability in their measured results.
Slight variations affect the measured results.
I think shock loading the Italian/Munter hitch is not the best approach.
I think carefully and slowly easing the test mass on to the Italian/Munter hitch is probably going to produce the most consistent measured results...

3. On some occasions, the test mass would slowly rotate/spin - and there was a very slight swinging motion. I carefully damped out any spinning/swinging to settle the mass down to render it motionless.
The load cell would sometimes read 0.04/0.05 kN...the number oscillating and then finally settling down after about 1 minute.
Once the kN force had settled - I recorded the result.
NOTE: I set the sensor scan rate to 40Hz... I found that if I set it to higher scan rates, the measured force would be continuously switching between values 0.01 kN apart (eg 0.04 / 0.05 / 0.04 / 0.05 / 0.04 / 0.05...) - which made it hard to read. I did not set the load cell to measure and record peak load.
I wanted to observe the LCD screen and see the measured kN force in real time.
Link to load cell: https://www.linegrip.com/linescale-3/

[KC]

i think this is always an aspect, and that is why Mr. Ashley found to define as to rail or ring host in separate chapters.
Linear or radial always matters, in this aspect too; my questions is always in ratio to what extent on this not neutral aspect.
To the right angle grip of the rope, radial is neutral/equivalent ultimate equilateral that leverages from all angle across center evenly that load could invoke;
>>by contrast tho in the breadth across that round, linear is neutral, arc sides can give side pressures that are not load invoked, that round linear does not propose.   We could also show this on round stock host formed into box end , with linear base across to linear sides that hugged rope some; giving 3 not 1 side(s) of friction.
.
If we look at the output of the Munter/Backhand as finishing on the opposite side of the host as input(and turned back over host again to pull in input direction as a Backhand Turn):
How well does our L-earning these numbers carry into a HH modeled as a self-seized Munter/Backhand to then Fig.8 Hitch, Timber, Fig.8 Timber and
ABoK Lesson# 1669/pg.290: (fave)fig8+RT , then w/dual legs thru as Cow/Girth/Prusik for both legs thru single or RT around SPart(s)?  Then rail or ring host? 
.
Viewed like this we see the odd numbered arcs of single arc of simpler Turn, then a triad of 3arcs of RT, Crossed Turn, BackHand Turn as repetitive forms in many, many times as we form knots.
.
For me a consistent naming is that odd numbers of arcs are called/get a suffix of (re)Turn as the system output pulls in same direction as system input.
Like if just hold a weight pulling in simplest OPPOSITE direction than input, don't employ spar is 0arcs, not on chart.
But take a (re)Turn over spar against Load and pull in the SAME direction as the input.
If 2nd arc cross nowhere is (a)Round,     then 3rd arc is a Round (+) Turn.
If 2nd arc cross on host  is (a)Crossed,   then 3rd arc is a Crossed (+) Turn
If 2nd arc cross off host  is (a)Backhand, then 3rd arc is a Backhand (+) Turn
Ashley points out several times that 3arc Round Turn or Crossed Turn take '2 passes' around host, but echoes several times that Backhand Turn takes but 1 pass around host.
.
550 paracord does not maintain round on host.
Like some other ropes (3/8" hollow Tenex etc.) can have round profile on straight pull, but flatten on host.
But doubled either does fair kinda as round host as is about half as thick as wide; just not quite total ultimate organic equilateral of round.
.
Linear vs. Radial matters in all aspects of the ruling geometries.




test: