Knot testing - Life support knots - procedures and results

[Dan_Lehman]

I can confirm that after the test was completed, the #515 stopper knots were loose and easily untied.
When I used 20mm diameter pins with a 6 wrap tensionless hitch, the #515 stopper knots were cinched tight ... .
In my view, this is a indication that the relative distribution of force was not concentrated around the pin,
but rather at the linear portion of the cord (which is what I wanted to test).

Does this make sense?

It is expected, but does NOT make sense in terms of the objective of getting
the break strength of the rope.  A larger pin, YES; more wraps, NO.  Again,
all the added wraps do is consume material and ease the tension into the
terminus--but that isn't the point of the exercise.  Maybe it doesn't much matter
for strength determination:  in the few-wraps case, material moves around
the pin and builds tension at the terminal side and tightens the knot;
in the many-wraps case, material moves around the pin until it just
gets exhausted by continued friction, leaving the terminal side slack.

My hunch, though, was that the many-wraps case will give excessive
material movement, which if nothing else, will delay the rise of tension,
putting material at-tension (whatever) longer, and that tends to lead
to lesser break figures (with some balance between the allowing of
fibres to settle into an evenness of sharing load--though I think one
might need cyclic preloading at say 50% to achieve this--, and the
added weakening agent of duration).  --and that few-wraps deprives
the specimen of this material contribution into the main loaded part,
and reaches higher forces sooner.  In either case, it's expected that
the break won't come on the terminal side.

As for photos, I still do not have the proper lighting conditions...I want to take quality photos.
Dont worry, all the knot specimens are packaged & preserved in their original condition after failure...
I recognise the importance of photography!

This sounds like perfection being the enemy of good:  SOMEthing is better than nothing;
I can't imagine that any modern camera--from $80, 3mb P&S, to <sky's the limit>--won't
produce  d e c e n t  photos for capturing the knot geometry during test, and the
positions of the marker threads (and the photo of the broken knot showing such
markers).  We're not insisting on Medium-Format Hasselblads or a Nikon D3 w/14-24mm lens!
Post-mortem  specimens have lost the transitional state (and also much of
the high-tension geometry, since tension is gone, SPart/eye-legs relaxed).

With respect to the higher forces to break a loop, it doesn't matter what the geometry is (ie a 2:1 pulley)

It matters to the force on the hauler and partner anchor, though resistance on the
opposite anchor will be doubled; recoil should be half-load to each of them,
but that pulley sure wants to be constrained!!

What steps are you aking to redress recoil?
I could see tying some anchor line, perhaps w/shock cord in its system, and that
to a 5#  bag of <sand?>, to the midpoint of line between knots (or having actually
a pair of lines tied at this point, each angled to resist recoil in one direction).

Good job, this is enlightening!

(-;

[DerekSmith]

Might I be allowed to indulge in a little 'dot counting' or 'pixel-peeping' as Dan calls it.

1.   MBF, in my book it stands for Mean Breaking Force, not Max.  There would be no value in comparing the strength of knots against the single highest figure recorded for the breaking of the cord, when the majority of the knots would likely never have been tied in that one strongest piece of cord.

2. Expecting two knots to break simultaneously is like expecting a needle to balance on its point.  Both are possible, but the probability of all forces and factors being so perfectly balanced is just a little bit improbable.  You should expect one to break but if both broke, then you should look carefully for a fault in your set-up to explain why the the near impossible just happened.

3. If you test two knots against one another the weaker one will always fail first.  If the two knots are essentially the same (in statistical terms you would say they were from the same population), then by testing one against another, you are filtering out the weakest knots and almost never testing the strongest.  This will skew your results into the lowest quadrants of results.   If you do enough tests, eventually you will test a strong knot against another strong knot and get what seems to be a spuriously high result, while all the tests involving weak knots will be recorded in your data.  You can compensate for this filtering effect, but it is far better not to inject it into the results in the first place.

You might argue that it is important to measure only how weak a knot is, because only the weak knots will fail.  That is a logical argument but it is weak science.  If a knot has a broad slew of possible strengths, then we should determine this and give ourselves the opportunity of also discovering just what it is that both imparts and takes away this strength.

4. Photography is critical just before failure in the loaded situation, because an unloaded knot cannot be expected to display the same geometry as it would under load.  Images also have to be captured from different perspectives because one shot cannot capture the 3D nature of the directions, angles and vectors involved in a knot.  This is especially important when you consider the time effort and cost going into creating a single breaking strain figure and the fact that photography today is ridiculously inexpensive per picture (ca 10p per gigabyte), takes but a few seconds to record, and offers a means of sharing the information of the event via the internet.

5.  The suggestion that anchor point diameter influences MBL and knot strength.  The 'Weak Point' of a cord  depends on two factors a) the physical strength of the cord at any given point and b) the focus or magnitude of force at that point.  A physically strong point can become a weak point if there is a concentration of load at that same point.

In testing a straight piece of cord, the weakest point can be anywhere along it.  The chance that the physical weak point being at the anchor point goes down proportional to the length of the test cord (increasing the MBL) and the longer the cord the greater the chance it will contain a a rare weak point (decreasing the MBL).

Increasing the anchor point diameter will reduce the load concentration so it will lessen the effect of stress concentration upon happenstance location of a physical weak spot at the anchor 'bend'.  However, this should not translate into the cord in such a way as to alter knot characteristics unless core / sheath characteristics have a propagation ability and this reaches a closely tied knot.

Happy knotting
Derek

[Dan_Lehman]

Might I be allowed to indulge in a little 'dot counting' or 'pixel-peeping' as Dan calls it.

1.   MBF, in my book it stands for Mean Breaking Force, not Max. ...

Clean your glasses before peeping at anything:  nOne has said "max", but, rather,
"MIN"; and the question is What does "Minimum Breaking Strength"  mean
--it might be defined statistically re standard deviations, and not as a lowest datum.

2. Expecting two knots to break simultaneously is ...

..., again, not part of any discussion here:  so, what's the point of discussion?
(What we expect is that two knots enduring tension X are better than having
one do so, re data/stat.s, and also yield the benefit of a survivor.)

3. If you test two knots against one another the weaker one will always fail first.

--a tautology.

4. Photography is critical just before failure in the loaded situation, because an unloaded knot cannot be expected to display the same geometry as it would under load.  Images also have to be captured from different perspectives because one shot cannot capture the 3D nature of the directions, angles and vectors involved in a knot.

I'm thinking of a mirror involved, like the extra knot in a test specimen:  two things
for the effort for one!

--dl*
====

[DerekSmith]

Might I be allowed to indulge in a little 'dot counting' or 'pixel-peeping' as Dan calls it.

1.   MBF, in my book it stands for Mean Breaking Force, not Max. ...

Clean your glasses before peeping at anything:  nOne has said "max", but, rather,
"MIN"; and the question is What does "Minimum Breaking Strength"  mean
--it might be defined statistically re standard deviations, and not as a lowest datum.

--dl*
====

Thanks for the kind words Dan, but I think it must be the clot behind the glasses that is at fault here - either I am going to have to lay off that 30 yo Glenfarclas or there has been a sneaky Edit ? ?

Anyway, we probably need to bottom this one out before moving on to any strength calculations.

In terms of defining a ropes usable strength, manufacturers declare the rating that fewer than one rope in a thousand will fail to reach.  It is called the 3-Sigma Minimum Breaking Strength, and you are right that it is not the lowest datum, it is in fact much lower than the lowest recorded value.  The manufacturer measures a number of break strengths, then calculates the average (Mean) and the Standard Deviation (Sigma).  They then step down from the Mean by three Standard Deviations which (for a 'Normal Distribution') gives the once in a thousand safety limit. (see http://www.sterlingrope.com/faq.asp )

However, for the purpose of declaring knot strength, this figure is nearly as meaningless as a Max BS because you are comparing the knot breakage with rope you are almost never going to come into contact with.

For the purpose of assessing the effect of the knot on the rope, we should compare like with like, i.e. the strength of the rope unknotted with the strength of the rope knotted, and for this comparison when there are not many test values, the mean is the most meaningful comparison (calculating Sigma on two or three values is as silly as reading max when the text says minimum).  We should be careful not to mix up rope safety strength claims with what is being performed here - a comparative test.

Derek
AKA 'Dot Counter'

[DerekSmith]

snip...

2. Expecting two knots to break simultaneously is ...

..., again, not part of any discussion here:  so, what's the point of discussion?
(What we expect is that two knots enduring tension X are better than having
one do so, re data/stat.s, and also yield the benefit of a survivor.)

3. If you test two knots against one another the weaker one will always fail first.

--a tautology.
snip...
--dl*
====

"so, what's the point of discussion?"  The point is that if AS is intending to publish his results he should not expose himself to criticism that he failed High School Stats.  Even the claim that the method generates a valuable surviving sample is questionable because the shockwave caused by failure might have altered the structure in some way impossible to predict.

Luckily the problem is very easy to demonstrate.

Assume we have a length of reasonably uniform cord, we divide it up and make ten test samples.  If we test each one to destruction we might for example get the following set of results (modelled roughly on a Normal distribution) --

47, 53, 44, 56, 59, 47, 41, 51, 49, 53.

The average strength of these samples is 50.

Now let's do a paired test, you can do it easily for yourselves.  Write the values on scraps of paper and put them into a hat, pull out two at random and write down the lowest of the two, then throw them both away (tested).  Repeat this four more times till you have the five double knot test results.

Here are a set I drew out.

53 vs 47    result  47
44 vs 53    result  44
47 vs 59    result  47
51 vs 56    result  51
49 vs 41    result  41

Average              46

@A Fluke of the draw' you cry - OK do it again several times and you will see that you are getting a result which is focussed towards the average of the low values, or roughly 10% lower than the true average for that knot in that cord.  The reason is that the method filters out the high values and discards them, biasing the result away from the real value.

If you counter argue that you want to declare the statistically weakest strength, then again you have to measure all ten individually to be able to determine the mean and a value for Sigma, then take the 3-Sigma value, but agian you must not skew the data before calculating the mean and sigma.

Derek

[agent_smith]

Just some comments here...

[ ] Photography: I have preserved all the knot specimens - the surviving knots (from the dual knot test series) have been cinched very tight - and their shape and structure has not altered with the passage of a few weeks. There are a few very good reasons why i haven't taken photos; i) I ran out of time - I am currently at work and away from home; ii) I want to take photos in the right conditions (using combination of flash + natural sunlight) but North Queensland (Australia) has had a deluge of rain/storms the past month. There are a few  perfectionists on this forum and I for one dont want to send out sub-standard images of my work!

I'm on to it guys, just be patient a bit longer - I will be back home in 3 days and it will be the weekend...

[ ] The lever action winch: I purchased a $AUD 100.00 winch and it consists of a 2:1 pulley configuration. I always mount the load cell at the knot specimen side - so it measures what is going on right there at the knot. I cant be specific about the speed of increasing load - I simply crank on the lever and keep cranking away. I cant for example state a speed of say 300mm per minute or whatever. So there is always going to be some degree of lack of measurable quantities in my tests... The 2:1 configuration of the winch doesn't alter the force bearing down on the specimen knots...and there is still cable length run out from anchor point to anchor point...whichever way you look at it, there is force in the system and it has to be treated with respect.

[ ] Recoil at instant of knot failure: Linear type knot tests with 5.0mm diameter accessory cord are easy to manage - the anti-recoil system I use is simple. I have an old punch bag (boxing) which I lay down on the driveway to which is attached an old (retired) dynamic climbing rope. The punch bag acts as a 'dead weight' - and absorbs the shock. I also lay down foam padding underneath the load cell - because it jumps a bit - I don't like it jarring on a concrete surface. The recoil force in the loop style tests a little more scary due to the force hovering around 7-8kN. I use the same system, only with more caution thrown in. Hearing protection is not required. I don't bother to wear eye protection in the linear tests, but I do wear them in the loop tests.

[ ] Dual knot testing: I still support the concept of testing dual knots - because there is always a surviving specimen. With tracer threads woven in both knots, it makes it easy to draw comparisons and determine the region of knot failure. Its just that I HATE inserting the cotton threads. I now know that my calling in life wasn't sewing! I wish that I could mail all my knots to Dan Lehman (by the bag full) and let him do the weaving (and then mail them all back to me)...

i find it hard to understand the test results of loop style tests - eg 2 x ABoK #1415 Double Fishermans joined from 2 x 500mm lengths of cord. Sterling report an MBL of 5.2 for their 5.0mm diameter cord...but the test results are up around 7-8kN... I would have to get a harness manufacturer in Australia to form a loop out of the cord by using a stitched join. Then I'd have to break the darn loop (3 times) to get some figures...and then compare it to the looped knot tests... too expensive and too time consuming.

[ ] Knot security/stability Vs raw strength - Although its interesting to go through this exercise, at the end of the day I think security and stability are more important factors with life support knots. I don't think any knot is ever going to break in the field...

[ ] MBS: Minimum Breaking Strength.. have not researched into how Sterling derive their published figures (ie 5.2kN for 5.0mm diameter cord). I dont know about the technical detail of the composition & weave pattern of the sheath either. Perhaps Dan/Derek could write to Sterling and aks for more detail???

[ ] Anchor pins / tensionless hitch: Can we ask how Sterling anchor the standing Parts of their cordage for linear pull tests? I used 30mm diameter anchor pins with the 5.0mm accessory cord, and I found this worked for me...I got an immediate increase to 5.48kN using an 8 wrap tensionless hitch around a 30mm diameter pin... again, what do Sterling use?



agent smith

[Dan_Lehman]

2. Expecting two knots to break simultaneously is ...

..., again, not part of any discussion here:  so, what's the point of discussion?
(What we expect is that two knots enduring tension X are better than having
one do so, re data/stat.s, and also yield the benefit of a survivor.)

3. If you test two knots against one another the weaker one will always fail first.

--a tautology.
--dl*
====

"so, what's the point of discussion?"  The point is that if [A_]S is intending to publish his results he should not expose himself to criticism that he failed High School Stats.  Even the claim that the method generates a valuable surviving sample is questionable because the shockwave caused by failure might have altered the structure in some way impossible to predict.

Ah, well, implying that we expected simultaneous/equal breaks was an odd
way of stating this concern.  But I don't give it much value, anyway.

Luckily the problem is very easy to demonstrate.  ...
the following set of results (modelled roughly on a Normal distribution)

Holy haphazard hypothesis, Batman!!
You are spewing results that differ in extremes of the lowest being 75% of the highest!!
That is quite some diversity, which makes your lament seem worthwhile.

But even so, the conclusions you want to draw are simply not those that should
be drawn.  Knowing that the surviving knot is stronger, one can (as I suggested
above) toss in some bit of statistical hocus-pocus to adjust for that; it is of some
comfort to realize that one's data is in this sense a bit of "worst-case" values.
Given a more reasonable set of values, there isn't all that much difference to
have to worry about, anyway.  (Perhaps one could take Dave Richards's
results from kernmantle-rope breaking and figure a reasonably likely maximum
difference--it will be well shy of 25%!!--, and then use that to guesstimate some
2- or 3-stnd-dev. below Mean value (by bumping Mean; or, by going just 2 vs. 3
stnd. dev. below.)

What you miss is that this project requires EFFORT of breaking, COST or MATERIALS:
PER UNIT TEST SPECIMEN WE FIND A VALUE THAT **TWO** KNOTS ENDURE
rather than just one.
Now, taking my logic to extreme, I guess we should urge a stringing together
of some 10-20-50-100 knots in a row, and ... .  That goes beyond practical,
but might give a more believable Min value than statistical figuring from merely
5 knots.

you must not skew the data before calculating the mean and sigma.

Sad to think that adding information degrades the result; I don't.

And I also don't lose sight of the purpose of this plan,
which is to:
  compare various knots (this consistent method does so);
  learn about knot behavior (statistics aren't invited here);
  and gain confidence in some seldom-tested, "new" knots.

Considering that other results to which these arguably improperly figured
values might be compared come without the basic information to assess
the tested items, I don't see any loss of value here.

As for the value of the surviving knot, photos can show whether there
is any deformation of structure from some shock wave--I doubt it.
--dl*
====

[Dan_Lehman]

[ ] Photography: I have preserved all the knot specimens - the surviving knots (from the dual knot test series) have been cinched very tight - and their shape and structure has not altered with the passage of a few weeks.
...  There are a few  perfectionists on this forum and I for one dont want to send out sub-standard images of my work!

A moderately good photo is infinitely better than none.  I reiterate prior urgings.
As for knot change, while I don't think so much of the post-rupture geometry will
be lost, I do not believe that in-tension geometry survives rupture--especially for
bowlines, whose collar won't hold the full tension of the SPart.

I have an old punch bag (boxing) ...

This is good to know:  I will henceforth let Derek argue w/you about results.   

to which is attached an old (retired) dynamic climbing rope. The punch bag acts as a 'dead weight' - and absorbs the shock.

I don't follow.  There's (lots of!) mass, and a climbing rope:  but what's tied to what?

I HATE inserting the cotton threads. I now know that my calling in life wasn't sewing!
I wish that I could mail all my knots to Dan Lehman (by the bag full) and let him do
the weaving (and then mail them all back to me)...

Well, maybe it's the insertion at in-tension time rather than prior, making an
estimate of position (and a photo to document where they *happen* to end
up).  Again, I'm curious as to what sort of sewing you do.  At first, I thought
one would just pull a thread through once or twice; but then it occurred to
me that it might be better to just try to make a nipping loop of thread around
a few of the mantle fibres (thinking it less likely then that the thread would
be pulled in two directions--odds being that those few fibres would all go
in the same direction).

i find it hard to understand the test results of loop style tests - eg 2 x ABoK #1415 Double Fishermans joined from 2 x 500mm lengths of cord. Sterling report an MBL of 5.2 for their 5.0mm diameter cord...but the test results are up around 7-8kN... I would have to get a harness manufacturer in Australia to form a loop out of the cord by using a stitched join. Then I'd have to break the darn loop (3 times) to get some figures...and then compare it to the looped knot tests... too expensive and too time consuming.

  Um, the knots  broke under a load of the loop of 8kn, which implies a load
on the knot (i.e., on each side of the loop) of 4kN.  And we can wonder at the difference
between this derived value and that of the individual tests (which were higher).  It's not
huge, and I gave some reasoning that might explain.  --no reason to create a loop of
original material:  that makes no sense, unless your break is at the pin.

MBS: Minimum Breaking Strength.. have not researched into how Sterling derive their published figures (ie 5.2kN for 5.0mm diameter cord). I dont know about the technical detail of the composition & weave pattern of the sheath either. Perhaps Dan/Derek could write to Sterling and aks for more detail???

Re "MBS", yes, we (I) can.  Re weave:  you have busted (and cut) bits right in
your hands!  Can't you take a peek at this--esp. in the ruptures, the kern should
be plainly visible.  --and a collection of twisted (or braided?) strands, or maybe
a braided unit (sort of a rope within a rope (which would break my definition
of "kernmantle", but that's just me)).

Anchor pins / tensionless hitch: Can we ask how Sterling anchor the standing Parts of their cordage for linear pull tests? I used 30mm diameter anchor pins with the 5.0mm accessory cord, and I found this worked for me...I got an immediate increase to 5.48kN using an 8 wrap tensionless hitch around a 30mm diameter pin... again, what do Sterling use?

Okay.  Again, I question the value, to strength, of extra wraps;
they have value in absorbing force transmitted to the end,
but that isn't a great issue here.  (I suspect Sterling use an
even larger bollard--maybe 6" diameter?)

Cheers,
(-;

[DerekSmith]

snip...

I have an old punch bag (boxing) ...

This is good to know:  I will henceforth let Derek argue w/you about results.   

snip...

Dan, even in jest I am not here to 'argue' with anyone.  It is Agent Smith's project and he has posted here to attract input and comment from other minds.  From past contact with him I have found that he demands a very high standard of himself and for his publications, and to achieve this he willingly subjects his work to open review, then makes his own balanced judgement as to what his final publications will contain.

I have also found your good self to be a perfectionist, so I am more than a little surprised to see you advocating "Guestimation" and "hocus pocus" rather than the simple application of a little bit of rigour to eliminate an effect documented in studies which you have referenced before on this forum.

Just because a piece of work is not being carried out in an accredited laboratory does not mean that it has to be sloppy or that it cannot present the very highest standard of professionalism.  Often in the Amateur world, cutting edge work has been produced well in advance of any standard industry could afford to achieve.

This trial uses a concrete drive as its testbed and a hand winch as it force source, but what does that matter so long as these factors can be shown not to distort the results?  In my test rig, I use a 50 KN hydraulic car jack as the force source, but it does not detract from the quality of work that is possible, provided knowledge, ingenuity and peer input are fully utilised.

Your comment about stacking multiple knots to find the weakest in a single test is completely valid, but it does not tell us how weak it was against the other knots and because it was destroyed in testing, we cannot infer anything from the structure of the remaining knots, because they were all stronger than it was.  Their structure may well have been different in some  significant aspect, such as to bestow the additional strength on them.  We just finish up with an unknown situation which weakens a knot to a known low value. 

You also state that "hocus pocus" can be utilised to take the biased 'pair results' back to full population results - fine, how about pointing us then to how this should be done or to someone who can do it as I would not be able to advise Agent Smith how to do it.

How many times have we seen reports from professional labs or Universities where the test set up and statistical analysis has been exemplary but all detail of knot structure, dressing etc has been ignored - virtually every time.  So when the job is approached from the other direction - from the knot tyers perspective, should we fall into the same trap of ignoring aspects which are not particularly interesting to us or not within our sphere of expertise, resorting to a little bit of "Guestimation" and "hocus pocus"?   I would suggest not, particularly when the solution is so easy to achieve.

How large is the effect?  I have no idea.  The hypothetical data set I used in the example was simply to demonstrate the existence and mechanism of the effect for you.  We cannot know the significance of this effect unless we have access to unbiased data and we cannot begin to postulate reasons for strength variations unless we have access to images of the knots from several perspectives under near terminal load.  Whether Agent Smith decides if any of this is relevant to his final report, is up to him, and I have no intention of arguing with him or yourself over the issue.  The facts are more than capable of arguing for themselves.

Derek

[Dan_Lehman]

I have also found your good self to be a perfectionist, so I am more than a little surprised
to see you advocating "Guestimation" and "hocus pocus" rather than the simple application
of a little bit of rigour to eliminate an effect documented in studies which you have
referenced before on this forum.

There is a simple matter of making X number of loadings of X test specimens:
I want to increase the information got from that, and believe that including two
knots per does that.  By your insistence on that pristine-for-statistics 1-per-1
work you have X broken knots & data; by the current test plan we have that
AND add X more load-enduring knots, which hold some form that can be
analyzed.   Statistics, as you point out, can point out that the latter sample
of 2X knots got data from the weaker of each pairing; well, then, we can
be happy that our results are more *solid* in finding minimum values (as
one tends to have a bigger complaint for things weaker than expected).
I'll surmise--w/o knowledge--that there is some statistical analysis that
can accommodate the unknown strengths of the surviving knots; and
that especially in a population where differences (stnDev) are small,
ultimate values are not going to change much:  and, again, one could
use the X-values-only and proceed with a confidence of conservatism.
As this method can be applied I think for all knots (bends--2 in line--,
hitches), they all can be compared.

And you would prefer to have half the number of knots tested?
(And, yes, yet, I have not urged FOUR knots per test.)

AND, again, we are not seeking to make huge inferences or promotions
with these values vis-a-vis other tested values, about which a great
deal is unknown (in some cases, e.g., I wonder at transposition of
the digits!).  And my Perfectionism relaxes there in realization that
such fine-tuned scrutinizing just cannot have much sway in anything
that matters (for one, conditions of material and loading in practical
cases will vary greatly).

I do urge the jettison of wanting photographer-studio conditions and
losing all capture of images in its absence--much is lost to us, now.

very highest standard of professionalism.

I've never thought that this was an issue, so I don't understand your words
on this point.

Their structure may well have been different in some  significant aspect,
such as to bestow the additional strength on them.

But this has nothing to do with examination of a survivor, but everything to do
with photographing knots during testing!

You also state that "hocus pocus" can be utilised to take the biased 'pair results'
back to full population results - fine, how about pointing us then to how this should be
done or to someone who can do it as I would not be able to advise Agent Smith how to do it.

I'll see if some statistically adept person has a definite answer,
beyond my remarks above about at least simply noting that the
data comes from a selectively weaker set than the survivor set.

"Guestimation" and "hocus pocus"?
I would suggest not, particularly when the solution is so easy to achieve.

You're making more of the words than is intended--I'm happy enough to use
them for statistics in general, after all.  The "solution" of losing results doesn't
appeal; I will hope that statistics shows some way(s) to deal.

The hypothetical data set I used in the example was simply to demonstrate
the existence and mechanism of the effect for you.  We cannot know the significance
of this effect unless we have access to unbiased data ...

Oh, but you can.  You have unbiased weakest-knot data--i.e., the range of values
of randomly selected pairings.  You also have Richards's results in some similar
cordage (i.p., 7mm accessory nylon kernmantle).
here:  www.caves.org/section/vertical/nh/50/knotrope.html
The largest stnDev in the 7mm (and about largest throughout, ignoring those
knots that required back-up knots to arrest slippage) is 3.2%.  The smallest
value is 93% of the largest; in your set, it was 75%.  Absent the exagerated
difference, there really is little to fuss about, other than the *purity* of the statistics
for statistics sake.  Again, I'm happy to put a footnote "* NB:  these values are
probably slightly understated." (or simply "understated").  We're not hiding
anything, anyway.

and we cannot begin to postulate reasons for strength variations ...

Oh?!  I distinctly recall someone's red-painting a "GeeSpot" and vowing to get
water from rock on that!  --even lacking some obvious aspects of the issue.
 

unless we have access to images of the knots from several perspectives under near terminal load.

It might well turn out  that for some knots the strength-determining geometry
is set well shy of near-terminal load; but it will take some scrutiny of knots
preferably with sharable photos in order to understand this.

--dl*
====

[DerekSmith]

So if I might paraphrase:-

You accept that you have corrupted your data by weakest pair testing, but you hold that, (based on someone else's unbiased data from different cord) that the corruption is small, and besides it is in the right direction (understating true mean strength).

And you have a set of destruction fragments with known failure strengths and a set of intact knots, known to be stronger than a given value but of unknown strength.

I don't think there is any point flogging this one any further, you understand the data is corrupt and want to stick with it.

Ho Hum

[Dan_Lehman]

Speaking of data, here's what we have, so far, concisely:
(avg. % values figured for both the rated, 5.2kN, & tested, 5.48kN tensile)

((interesting is the discrepancey between the Grapevine when tied to
join TWO ropes into a sling vs. tied in-line of single strand!?))
(((interesting is that A_S didn't re-test Rosendahl's bend similarly!)))

Bowline (#1010):
  3.98  3.78  3.76  avg.~= 3.84  ~= 74 {70}%  (per 5.2 rating  {or 5.48 test} )

Bowline (EBSB):
  3.84  4.02  3.96  avg.~= 3.94  ~= 76 {72}%

Grapevine (#1415) in LOOP:
  7.86  7.76  7.74  avg.~= 3.9   ~= 75 {71}%
in single-knot/-line:
  4.16  4.58  4.20  avg.~= 4.3   ~= 83 {78}%

Rosendahl's Zeppelin Bend in LOOP:
  6.62  7.22  6.48  avg.~= 3.4   ~= 65 {62}%

Fig.8 EyeKnot:
  4.00  4.26  4.32  avg.~= 4.2   ~= 80 {76} %


 

[DerekSmith]

snip...

((interesting is the discrepancey between the Grapevine when tied to
join TWO ropes into a sling vs. tied in-line of single strand!?))
(((interesting is that A_S didn't re-test Rosendahl's bend similarly!)))

snip...

Grapevine (#1415) in LOOP:
  7.86  7.76  7.74  avg.~= 3.9   ~= 75 {71}%
in single-knot/-line:
  4.16  4.58  4.20  avg.~= 4.3   ~= 83 {78}%

snip...

You state that TWO ropes were joined to make a sling, i.e. you are testing the weakest again so in that respect no surprise.

However, I am surprised at the magnitude.  Are you SURE that there was no friction at the sling anchor points which would have caused uneven tension in one leg over the other.  Even the slightest disparity will load one leg while releaving the other.  i.e. 4.3 + 3.5 = 7.8  only +/- 5% of the total load displaced.  unless the anchor pin is free to rotate under load, it is easy to generate this sort of disparity, but then, it is strange that the disparity is so reproducible ? ?  Short of seeing a video of the testing process it is hard to pinpoint what error is being incorporated.

Note : although I know what you mean, even the approximation notation does not give justice to the statement "7.86  7.76  7.74  avg.~= 3.9"

PS.  What method was used to test the single knot/-line bends ?

Derek

[R Statistician]

The R in R Statistician stands for retired.  There are procedures for analyzing this type of data (some values known, other values are a lower limiit on the breaking strength).  The problem occurs in product life testing: the test is terminated before all the items fail.  Some times are failure times (when the item failed), other times are how long an item was on test, but it didn't fail.  The times for the non-failing items are called censored times or censored data.  The computations are very complicated, so they are done by a computer package.  The calculations depend on the type of distribution.  I compared the fit of Normal, Lognormal, Extreme Value, and Weibull distributions to the data listed in this thread.  Of the six small data sets (5 knots and re-test in single-knot line), the Weibull fit best in 2 cases, the Extreme Value fit best in 1.5 cases (the result of a tie between two distributions), the Normal fit best in 1.5 case, and the Lognormal fit best in 1 case.  I also checked the fit of these distributions to the 7mm accessory cord data: the Weibull fit best for 5 of the 8 knots, the Extreme Value for 2 knots, and the Lognormal for 1 knot.   So I used the Weibull distribution.  Here are the results.
 knot         mean   95% confidence interval (approximate)
Bowline       3.90   (3.79-4.02)
EBSB          3.98   (3.91-4.05)
Grapevie     3.91   (3.88-3.94)
in 1 line      4.31    (4.05-4.58)
Zeppelin     3.49    (3.31-3.68)
Fig 8 Eye    4.27   (4.16-4.39)

I believe that the retest of the grapevine in single-knot line gave a different result due to a calibration problem between the two levels of testing: the sling or rope ring requires twice the force to break it as does a single line.  If the re-test was done after all the other tests were finished, then there could have been a calibration problem between the times of the two tests.  The usual solution to this problem is to prevent it by testing all the knots once before testing any knot the second time, then test every knot the second time before testing any knot for the 3rd time, and so on.  The order of testing the knots within each set is often determined by a random draw (for example, ace-2-3-4-5-6 from a shuffled deck of cards for six knots).

I am not only retired, I have an old computer (Windows 95 operating system) and ancient software; I suggest you get somebody else to verify the results.  For Internet access I use the computers at the public library, so my Internet visits are short and infrequent.  I am interested in data abouts knots: strength, security, stability, ease of tying and untying.

[Dan_Lehman]

There are procedures for analyzing this type of data (some values known, other values are a lower limiit on the breaking strength).  The problem occurs in product life testing: the test is terminated before all the items fail.

Ah, good, thanks; I thought that there must be something to this effect.

I don't mean to go overboard in exercising your expertise,
but might you show the results for, say, a couple of the above
knots--i.p., one w/greatest variance (bowline?)--, and one with
much less--, as though those results were in fact for FOUR knots per specimen?
--just to get an idea of what we might be missing (probably not great) by the
current limit of two.  (Putting four knots into a specimen I think would raise
or aggravate concerns about physical proximity and other behavior.)

I believe that the retest of the grapevine in single-knot line gave a different result due to a calibration problem between the two levels of testing: the sling or rope ring requires twice the force to break it as does a single line.  If the re-test was done after all the other tests were finished, then there could have been a calibration problem between the times of the two tests.

Good points.  But, to reiterate, there is a valid thought that if the knots'
compression rates differed--say, side-A loses more material (maybe was
less tightly set)--, friction at the pins could sustain an imbalanced loading,
and perhaps have 100% + 80% of knot strength, giving a value (by halving
the total force pulling both sides of sling) of 90% of actual force in the breaking
side.  --conceivably.  Or, as you point out, other factors could be at work.

[edit:  It must be noted that by my reasoning above the in-loop values should higher, not lower! ]

The order of testing the knots within each set is often determined by a random draw
 (for example, ace-2-3-4-5-6 from a shuffled deck of cards for six knots).

Here is where Statistics & I have a disagreement:  IF there is some bias resulting from
test-device *ageing* during activity, I'd think that likely it is somewhat linear and going
from one state towards another (as it accrues usage); and that to balance results,
one must be deliberate in spreading particular knots-testing across this possible
range of readings--whereas random ordering could do poorly at this!

my Internet visits are short and infrequent.  I am interested in data about
 knots: strength, security, stability, ease of tying and untying.

We will enjoy what visits you can make, and hope to keep or build your interest
maybe to raise the frequency.  I just lost one computer and have yet to set up
its replacement, so I know well about this modern benefit of a local library!
--AND books, to boot (have two at hand from the 4-sale shelf).

Thanks, & happy to meet you,
--dl*
====