Strength of a rope, in relation to its curved path.

[xarax]

   I do not believe that the wire ropes are so different from the ropes we use... because, at the end of the day, they are also nothing else but long strings, that are supposed to resist tension forces - just as the ropes we use are. So, the knowledge acquired on wire ropes could possibly be used by the knot tyers - and vice versa.
   There is this well known diagram that relates the ( deterioration of the ) strength of the wire rope, to the diameter of the sheave/pulley it is forced to follow ( See the attached picture ). I wonder if a similar diagram would also apply / be useful for our ropes... Of course, the deterioration of the strength of the ropes we use is not so pronounced - but this does not mean that a possibly quite similar curve should not apply in our case, too.

[squarerigger]

Hi Xarax,

Thanks for the graph - can you tell us the original source please?

SR

[xarax]

http://www.manchestersling.com/index.php?target=pages&page_id=blockrigging

  ( However, I have seen essentially the same graph at other sites as well...See, for example ; http://practicalmaintenance.net/?p=576)
  I think that, if we could have a similar graph for our ropes, that might also apply to the curvature of the standing part s path inside a knot s nub. Knowing/measuring the tensile forces at each and every point of this path, and the corresponding curvatures of the line at those points, we could possibly estimate the total deterioration of the strength of the rope for each knot... It would also be interesting to compare the relative graphs for different ropes. For a givem knot and fiber material, are the laid ropes as sensitive to strength deterioration as the braided or kernmantle ropes ?

[squarerigger]

Thanks xarax,

The idea you propose (identifying the tensile forces at each point in a line's path through a knot) is a grand one and may take some considerable testing to identify.  However, using ANOVA or some other (perhaps better) form of statistical analysis may enable elimination by correlation studies of such a vast field.  The effects mentioned may be found for several different sizes of the same manufacturer of line, then compared for any significant variance with the same or a different manufacturer and then compared as to any difference between sizes and then analyzed with respect to any difference in types of knots; hitches on different shapes (and types) of base material, such as hexagonal, square, round, oval and so on; bends between similar and different line-types.  All this would be predicated on having some accurate data on the surface and interstitial characteristics of each type of line (surface friction, wet/dry condition, partial degradation, affected by chemicals in a range, structural make-up, fiber lay and twist if different, molecular composition, surficial treatments, effects of dyes, effects of tracers, effects of different manufacturing equipment, pre-loaded line and so on) used so as to have a relatively complete picture of what goes into a piece of line.  Should make for an interesting doctoral defense!  At the end of the day, the application of an amount or lack of dressing of the knot to achieve a certain undefined level of tightness or position may be the downfall of such testing.  If subject A tightens a, say, square knot, in one way and subject B tightens in a different manner, which is correct and under what circumstances of loading (static, dynamic, gradual and calibrated loading, static followed by dynamic and so on) is that correctness defined?  Things to think about!  Thanks,

SR

[xarax]

   Thank ou Squarerigger,

   You show me the peak of Everest, and tell me how irrelevant is to make a first step to reach there ? 
    All your remarks are very true, of course. I am also especially interested in the particular type of braiding of a braided rope . I think that the way the bundles go around each other, matters a lot on how the braided rope bends,  and how it is re-distributing the tensile and compression forces inside its body.
   

[squarerigger]

Hi xarax,

No, no, I did not say how irrelevant it is to reach Everest  - I simply said that there is more to consider in how we reach it, i.e. what new knowledge we have gained (Everest has already been climbed so all other efforts are merely repeats that show little or nothing new and are possibly even self-aggrandizement) when we get there?  Science always asks for repeatability of course (as in climbing Everest) so that predictions may be formed into a theory and perhaps into a rule or a law.  If one different element of tying a knot, no matter which one, is the person tying the knot, then that is something to think about - how do we deal with it scientifically?  Should there be some method of tightening or dressing the knot that goes with the knot itself to guarantee consistent tightening?  Does it matter at all?  I would like to know your thoughts.  Also, tell us more, if you will, about the different types of braiding - do you refer to the different numbers of warps, perhaps an over-under-pattern that differs, or to the incorporation of different fibers into the individual yarns or is it something else and how would we test for it's presence or influence?  You also speak about the re-distribution of tensile and compressive forces inside the body - are you referring to different cores or to the arrangement of the yarns so as to spread the load differently?  It certainly sounds like an additional element to add to the mix!
Getting back to the original post - the forces of wire rope as they negotiate a pulley or sheave - can we, in fact, relate this to the bending of fibers in a knot, hitch, bend or splice?  The transition from one part of a sheave where the line enters to the part where it leaves is usually quite firm, smooth and slow - how does this relate to the bending of a line inside a knotted structure?  In the aforementioned knotted structure it may not be unusual to see a bend, a twist and an accidental hockle, all within the same piece, none of which even closely resemble a smooth and firm pulley.  Do you have a suggestion for how we could proceed?   

SR

[Dan_Lehman]

Knowing/measuring the tensile forces at each and every point of this path,
and the corresponding curvatures of the line at those points,
we could possibly estimate the total deterioration of the strength
of the rope for each knot...

There are many factors to strength and many
definitions of what strength is --over time/usage,
in immediate slow-pull testing, or in ... dynamic testing,
for some.  --and without or, in contrast, with much loading
beforehand (maybe "strength" is the duration of some
sub-tensile-capable threshold loading that can be sustained
--that seems a more *practical* measure than peak loading).

I've seen it said that breaks occur outside of a knot,
sometimes; we might learn that this happens only
because that material had been internal and got
damaged --frictional abrading & heat-- on being pulled
out under such pressure.


--dl*
====

[xarax]

maybe "strength" is the duration of some bsub-tensile-capable threshold loading that can be sustained--that seems a more *practical* measure than peak loading

Are you speaking about fatique ?
I will use nylon ropes in my tests, just for this. As 1) reports, nylon rope suffers less from fatique than any other synthetic high tensile rope.

1) http://user.xmission.com/~tmoyer/testing/High_Strength_Cord.pdf

[roo]

maybe "strength" is the duration of some bsub-tensile-capable threshold loading that can be sustained--that seems a more *practical* measure than peak loading

Are you speaking about fatique ?
I will use nylon ropes in my tests, just for this. As 1) reports, nylon rope suffers less from fatique than any other synthetic high tensile rope.

1) http://user.xmission.com/~tmoyer/testing/High_Strength_Cord.pdf

I don't think that report is correctly approaching material fatigue.  There is no attempt to determine a cyclical stress profile in isolation from abrasion damage or local contact stress damage.

Typically the crack-propagating phenomenon of material fatigue is examined in ranges with much higher numbers of cycles, too.

[Dan_Lehman]

maybe "strength" is the duration of some sub-tensile-capable threshold loading that can be sustained--that seems a more *practical* measure than peak loading

Are you speaking about fatique ?

We're talking about **knots**, not materials, here
(though of course knots live in materials, not en vacuo!).

I'm talking about how a bowline might pull in & out
of its collar on changes in tension, but that collar's pressure
and friction isn't so great as to matter much, and the turn
of the knot sort of takes the tail with the rotation rather
than rubbing against it.  So, cumulative wear might be minimal,
compared to some other knot.  In that Dave Merchant e-book
it's suggested that the greater compression and rope-movement
in fig.8 & fig.9 eyeknots lessens their strength vis-a-vis
the overhand eyeknot in shock loading; so, that's a contrast
with test-bed, new-rope, slow-pull testing.

--dl*
====

[xarax]

  Science always asks for repeatability of course ...so that predictions may be formed into a theory and perhaps into a rule or a law.

Science also - and this is perhaps THE most important, forgotten nevertheless  element of the scientific method- tears the whole into many parts, examine those parts, and then tries to glue them into the original thing again !  We have to isolate as many elements as we can in this most complex problem, and then examine each and every one, and see what we can say about it. The curvature of the rope as it runs into a knot, is a most important element I believe in relation to the strength of the knot, and that is the element about which I was talking about in the first post of this thread.

If if one different element of tying a knot, no matter which one, is the person tying the knot, then that is something to think about - how do we deal with it scientifically?  Should there be some method of tightening or dressing the knot that goes with the knot itself to guarantee consistent tightening?  Does it matter at all?

It matters, of course, but not much. It is the structure of the knot itself that is much more important I believe. If two different knots are tied by two persons in their own way, and the strength results are separated by a, say, 10% strength gap, I do not believe that any swap of the persons involved can reverse this result. I do not believe we should start our long journey to the peak from there - but of course I do not doubt we will meet this problem at a higher altitude. We have not even reached the first base, we should not worry about all problems we are going to confront with at once - because then we will not make any  step forward.

do you refer to the different numbers of warps, perhaps an over-under-pattern that differs, or to the incorporation of different fibers into the individual yarns or is it something else and how would we test for it's presence or influence?
...the arrangement of the yarns so as to spread the load different

  I have realized that the industry follows more or less the same path as regards the types of braidings it uses for a rope, and I think that this is not something that is dictated by any exhaustive research ...It is more a follow through along the same traditional paths, and a result of considerations about many things, the last  of them being the strength of different knots tied on that rope !
  Let me talk about an example. let us say we have those 12 bundles of fibers, and we want to make a solid braided rope out of them. How many different patters are there that we could possibly use ? MANY, I can assure you !  Do you believe that the industry has studied all those pattern, regarding how they influence the strength or the rope when curved around this or that diameter ? I do not...and I would like to investigate the subject a little further. How many patterns ? How many bundles ? Which angles ?
   I have made some naive experiments, weaved some braided segments of a rope with the same number of yarns following different patterns/paths  ( "arranged  so as to spread the load differently", as you say) - and I have seen that , when those braided ropes are forced to turn around the relatively tight curves we meet in the knots, the tensile and compression forces are manifestly different...Precisely, it is "an additional element to add to the mix !"  , yet another one... I could not find something to read and learn on this matter.

the forces of wire rope as they negotiate a pulley or sheave - can we, in fact, relate this to the bending of fibers in a knot, hitch, bend or splice? The transition from one part of a sheave where the line enters to the part where it leaves is usually quite firm, smooth and slow - how does this relate to the bending of a line inside a knotted structure?

Yes, I believe we can, and it relates a lot, because it is the minimum diameter alongside a curved path that matters most, regardless if this curve is around a sheave or inside a knot s nub.

It is an unchartered side of the mountain that we are speaking about, so we should walk carefully and slowly - but keep walking ! 

[xarax]

There are many factors to strength and many definitions of what strength is --over time/usage, in immediate slow-pull testing, or in ... dynamic testing, for some.  --and without or, in contrast, with much loading beforehand

test-bed, new-rope, slow-pull testing.

   I speak about what I can possibly study, i.e. the macimum breaking strenght under slow pulling of a knot that has been loaded only once, up to some portion of that strenght ( 50 %, perhaps ? ) That, the test bed, new rope, slow-pull I can try to measure. Do not forget how many bends and bowline-like loops we have...and then we should examine hitches and binders as well.  

[Dan_Lehman]

There are many factors to strength and many definitions of what strength is --over time/usage, in immediate slow-pull testing, or in ... dynamic testing, for some.  --and without or, in contrast, with much loading beforehand

   I speak about what I can possibly study, i.e. the macimum breaking strenght under slow pulling of a knot that has been loaded only once, up to some portion of that strenght ( 50 %, perhaps ? ) That, the test bed, new rope, slow-pull I can try to measure. Do not forget how many bends and bowline-like loops we have...and then we should examine hitches and binders as well.

I'm aware of the huge number of test cases that a statistician
might want, in order to take consideration of all of the various
factors that might affect strength.  I've thus sought some better
(= briefer, in test cases) statistics!  (E.g., Derek was all upset when
I recommended testing eyeknots by tying one in BOTH ends of the
test specimen, so as to have TWO knots make the break strength,
and one survive (as a count of knots, and as an examinable token
intact).)

With the apparent limits to validity of testing, I thus think that
what might be the better information to seek --not statistically
valid range of by-some-application-of-force break strength, in
just SOME material tested-- is WHERE (and maybe by some
analysis, How) DOES THE BREAK OCCUR?
My effort to determine this was to stitch brightly colored threads
into parts of the test specimen at points near where I expected
the break to occur; to photograph the knot when tied & set (I
used a pulley to set with considerable force), and to photograph
the knot after testing (I was not present for the testing, alas)).
I think that by gaining more data on WHERE... , we can start
to build theories on Why... and go on to project outcomes and
check these, based on the theory.

In some cases, we might infer from our inchoate theory, "If the
material were more slick/flexible/compressible/static/... , then
this would be the behavior" and put such conjectures to test
--hoping to find success and build upon it.

Attached: set, pre-tested, "False Bowline-8" (& Semi-Symmetric Fig.9)
eyeknots; and tested (broken & surviving) FB8s.

--dl*
====

[xarax]

have TWO knots make the break strength, and one survive (as a count of knots, and as an examinable token intact)

With my universal test machine, I plan to do something even less expensive ! 
Tie two knots(bends) with the ends of two segments of a rope ( each segment about 1.20 m = 4 ft long ), pass the closed loop around two sheaves, then pull the sheaves apart by means of one or more hydraulic cylinders.  That way you do not spend ropelength to fasten the two ends, as it is the common practice. ( Of course, you will now need twice the tensile force to reach the ultimum and maximum breaking strengths,  but that is no problem if you use hudraulic bottles/jacks).

P.S. At last, some (great) pictures ! Good.