multiple knots in a line

[mainebingo]

I apologize in advance for my inability to understand basic physics (I accepted my own limitation a long time ago in college. My answer to a Physics 101 thought experiment on relativity: I guess I'll be a philosophy major).

Is a rope with two (hypothetically) exact same knots, equal strength as a rope with just one knot?

[SS369]

Good day.

The rope is just as strong as it always was.
It is the the knot that sees the greatest load that will be the weak link.
I suspect that it will be the knot that is first to receive that load.
It will have to tighten first to then pass the load to the following knot.
And I guess that the test design may influence the outcome, i.e., drop, slow/fast pull, around an object, rope material.....
Just my opinion...

SS

[mainebingo]

Good day.

The rope is just as strong as it always was.
It is the the knot that sees the greatest load that will be the weak link.
I suspect that it will be the knot that is first to receive that load.
It will have to tighten first to then pass the load to the following knot.
And I guess that the test design may influence the outcome, i.e., drop, slow/fast pull, around an object, rope material.....
Just my opinion...

SS

Just making sure I understand.  Your opinion is: yes?

[roo]

I apologize in advance for my inability to understand basic physics (I accepted my own limitation a long time ago in college. My answer to a Physics 101 thought experiment on relativity: I guess I'll be a philosophy major).

Is a rope with two (hypothetically) exact same knots, equal strength as a rope with just one knot?

Yes, excluding minor knot differences.  The load on each knot will be proportional to the local stretch/strain of the line (see Hooke's Law), which should be uniform on a single line.  The single knot rope will have a little more length and overall stretch, of course.

Somewhat related:
https://igkt.net/sm/index.php?topic=6329.msg42529#msg42529

[mainebingo]

Yes, excluding minor knot differences.  The load on each knot will be proportional to the stretch/strain of the line (see Hooke's Law), which should be uniform on a single line.  The single knot rope will have a little more length and stretch, of course.

Then (and assuming hypothetically exact same knots), in the two knot line both knots would fail at the same time?

[roo]

Then (and assuming hypothetically exact same knots), in the two knot line both knots would fail at the same time?

Conceptually, perhaps, but in even with the most uniform rope and the most identical knots, you'd probably have better odds at winning the lottery 10 times in a row. 

[SS369]

Good day.

The rope is just as strong as it always was.
It is the the knot that sees the greatest load that will be the weak link.
I suspect that it will be the knot that is first to receive that load.
It will have to tighten first to then pass the load to the following knot.
And I guess that the test design may influence the outcome, i.e., drop, slow/fast pull, around an object, rope material.....
Just my opinion...

SS

Just making sure I understand.  Your opinion is: yes?

Theoretically, maybe, in reality - no. In my opinion.
I just don?t think that real knots in a line will tighten Exactly at the same rate.

A few people, including myself have done ?tug-of-war? knot pull tests of the same knots and One has always lost. Whether that is because one of the knots was a smidge tighter, had a small rotational difference in the tying, a speck of dust or moisture, etc., very hard to say.

[mainebingo]

Theoretically, maybe, in reality - no. In my opinion.
I just don?t think that real knots in a line will tighten Exactly at the same rate.

A few people, including myself have done ?tug-of-war? knot pull tests of the same knots and One has always lost. Whether that is because one of the knots was a smidge tighter, had a small rotational difference in the tying, a speck of dust or moisture, etc., very hard to say.

It was a purely theoretical.  I understand it will not play out that way in the real world. Thank you for the replies.

[Dan_Lehman]

It was a purely theoretical.  I understand it will not play out that way in the real world. Thank you for the replies.

Some people might suggest that there are theories
that cover such physical conditions, and will give a
different answer.
Practically, and this DOES come to bear, for those of us
who'd prefer to have two knots in a single specimen,
so to have a survivor to analyze,
must be chary of effects of a knot on the fibres of a
line that, if the knots are closely spaced, could induce
failure partly on account of the closeness.
Beyond that, there are at times some dynamic movement
of tightening in some knots at high loads which might occur
at different loads between a pair of alike-as-one-can-tie-them
knots.

Consider one test scenario that has (mis)led some authors
to claim that a triple fisherman's knot is "stronger than the
rope" it's tied in :: the test specimen is a ring formed by tying
its ends together; the round sling is tested  and a deduction
is made that the knot (being in one side) is half the total
strength of the tested sling.
But in fact the knotted side will compress and feed out material
to its side which will NOT be (well) equalized/shared around the
anchor pins, so the knotted side might be at 60% tensile while
the unknotted side is at 90% (or whatever) --and giving some
merit to the naive thought that one adds knotted strength to
100% for the figure!

But it is NOT the case that if one knot weakens rope 40% and
a 2nd is also tied that the rope's now weakened 80%!  --if that
was what your *theoretical* question was about.


--dl*
====

[agent_smith]

Thanks for your question Mainebingo:

Is a rope with two (hypothetically) exact same knots, equal strength as a rope with just one knot?

Answer = Yes (in my view)

Further commentary:
Why don't you setup and perform a series of experiments to prove or disprove the predicted results.

I started down this path quite some time ago when I noticed that knot testers never report which knot reaches its MBS yield point first (in a dual knot test where identical knot specimens are tied at each end termination).
The typical (and default) test rig setup is a fixed anchor point on side and a force generating machine at the opposite end.
In 100% of knot tests that I have carried out, one of the specimen knots always reaches its MBS yield point first (ie one knot always breaks first and the other survives).
This surviving knot provides an opportunity to investigate its response to load right up to moments before it reaches its MBS yield.
I have been quite interested in the 'surviving' knot specimen. Particularly which one survives - ie, the one closest to the force generating machine or the one closest to the fixed anchor point? Again, it is never reported and to the best of my knowledge, no one has conducted peer reviewed tests with scientific rigor (particularly tests that use a 'control').
Many home brew type tests from hobbyists/enthusiasts dont use a 'control'.

The typical default mindset of a knot tester is to look only at the MBS yield point of a knot - that is, they are generally fixated on simply increasing the load until the knot breaks - and then they pop the champagne cork. It is hard to find knot tests that steer away from this default thinking.

Your question is interesting - and a series of tests ought to be carried out to investigate this with some scientific rigor.
I can confirm that one knot always reaches its MBS yield point before the other. There is never a situation where both knots reach their MBS yield point at the exact same instant in time.

By the way, I was happy to see signs that some individuals are starting to investigate properties other than the MBS yield point of a knot.
Although not related to your question, it is refreshing to see a different mindset fora change!
Link: https://www.youtube.com/watch?time_continue=7&v=QAr-uHd8h8o&feature=emb_title
(hopefully the link works)...

[mainebingo]

But it is NOT the case that if one knot weakens rope 40% and
a 2nd is also tied that the rope's now weakened 80%!  --if that
was what your *theoretical* question was about.

No, my thought was if they were different, the two knot line would be (oh so slightly) stronger than the one knot line.

[Dan_Lehman]

No, my thought was
 if they were different,
 the two knot line would be (oh so slightly) stronger than the one knot line.

What was your reasoning for this?

 

[mainebingo]

What was your reasoning for this?

 

Because when you add something to a system, it generally changes how it works. Knots distribute force differently than a linear rope. If more tension is directed within the knots than the rest of the line, when you add knot #2 you have directed some force away from the other knot.  This is not a perfect analogy, but you have two points consuming more force than the rest of the line without weakening each other. 
I am not saying that is correct.  I can also think of how both lines would be the same.

[DDK]

Because when you add something to a system, it generally changes how it works. Knots distribute force differently than a linear rope. If more tension is directed within the knots than the rest of the line, when you add knot #2 you have directed some force away from the other knot.  This is not a perfect analogy, but you have two points consuming more force than the rest of the line without weakening each other. 
I am not saying that is correct.  I can also think of how both lines would be the same.

The elements of the rope include the straight sections of rope and the knots. These elements are in a series configuration as opposed to a parallel configuration. Being a series configuration, the tension is transferred completely from one element of the rope to the next so that the full tension is the same in and must be withstood by each element and does not depend on the number of elements (either knots or straight sections). If any one element is unable to withstand the full load (i.e. the "weak link"), it will fail.

In a parallel configuration, the loading/tension is shared by the elements and does depend on the number of elements (for example, the four legs of a chair each support roughly one-fourth of the full weight of the person sitting in it).

[agent_smith]

Mainebingo:
Have a look at the attached images.
There are several possible test configurations...I've only picked 2.

In a series configuration (with 2 knots tied in a linear length of rope) - the second knot does not cause a cumulative weakening of the rope.

In the parallel configuration, twice the force is required (because load is divided 50% across each leg).

Note that in both of these particular configurations, the force generating machine exists on one side.
Knot testers rarely report which knot reaches its MBS yield point first (in fact, the default approach is to ignore this issue).
There is never a result where both knot specimens fail at the exact same instant in time. There is always a 'survivor' knot.

Edit Note:
When using a series test configuration with multiple knots in a row, only end-to-end joining knots can be used OR; an eye knot that can be 'through-loaded' (SPart-to-SPart).  #1053 Butterfly knot is an example of an eye knot that can be through-loaded.
#1047 Figure 8 eye knot could not be used for such a test (although #1058 directional F8 could be used).
Note: Ashley erroneously describes #1058 as a "single Bowline on the bight" (it isn't a 'Bowline').