Mechanics 101 question - splicing line to chain

[DBBPhysics]

TL;DR Summary

Connect a 3 strand line to anchor chain either by weaving the line into the chain or putting the line through the 1st link and then weaving the line into itself.

This question is about splicing a 3 strand line to a chain rode on an anchor on a boat. There’s two ways under consideration. One is simply weaving the three strands into the rings of the chain for about 12”. With this approach, the weave connects the line to the chain and a force of x lbs on the anchor translates to a force of x lbs on the line or 1/3 of x for each strand.

A second way of doing it is to put two strands through the first link with those two strands doubling back toward the line. (Since a third strand will not fit in the link with two other ones, the 3rd strand just joins the other two going toward the line) The three strands are now weaved into the line, back towards the boat. The benefit of this is that the chain and line easily go through the windlass (winch) unobstructed whereas with the previous design, the chain links are widened by the line woven into the links and therefore can get hung up in the windlass. Now, there are four lines going backwards toward the boat, I.e. two going up to the chain link and two going backward.

So now, load x is supported at the chain link by 4 strands and therefore each strand carries 1/4 x lbs - a lower value than the previous design. Therefore this last design is the better one since it will hold a higher x before breaking at the splice. Of course at the end of the weave going toward the boat, there are only 3 strands so the line before the splice will break first.

That theory seems plausibly correct, however when one looks at the latter design, it looks like there are only two strands connecting the line to the chain instead of 3 strands and that gives reason to pause. I’d like to use the trimmer design in order to go through the windlass easier but I don’t trust it. Is there anything wrong with my logic?

 

[Lnewqban]

Now, there are four lines going backwards toward the boat, I.e. two going up to the chain link and two going backward.

Which means to me that only two lines are carrying the load.
What matters is the effort of the chain link to break each line where is wraps around the link.

 

[Tom.G]

Can you put a larger repair link on the end of the chain, one that the 3 strands of rope will fit through?

Also, be sure to use a thimble where the rope joins the chain. This reduces the stress concentration on the rope, greatly increasing its life. Without a thimble, the force concentration at the sharp bend tends to cut thru the rope at repeated high loads.

http://www.google.com/search?&hl=en&q=rope+thimble&oq=rope+thimble

Cheers,
Tom

 

[Baluncore]

There is always a third way. You might mediate between the two by making a Dutch splice and a thimble in the end of the soft rope. Join the chain end-link to the thimble with a spliced torus of wire rope, of a size that will fit through the chain.

To make the torus, remove one of the six outer bundles from a wire rope with a length that is about ten times the circumference of the intended torus. Tape the cut ends to prevent it separating. Thread the wire through the thimble and the chain end-link, pull it to the approximate circumference, to where it lies neatly against the first pass, then continue threading, winding, and laying neatly, until after six loops, it looks like the original wire rope. Hide the two ends of the wire inside the torus, where the core would have been in the original rope.

 

[DBBPhysics]

Thanks for the replies. This splice is in between 50’ of chain and 250’ of line so it MUST go through the windlass which means all connectors won’t work.

Lnewqban said: “Which means to me that only two lines are carrying the load”
Yes, if the two lines went straight through the link and was secured to the chain then clearly two lines are carrying the load. But those two lines then go back toward the boat making 4 lines that are carrying the load. That’s my conundrum - what does physics say?

 

[Baluncore]

But those two lines then go back toward the boat making 4 lines that are carrying the load. That’s my conundrum - what does physics say?

It says that the two lines that run back, must be spliced into the rope sufficiently that, when wet or dry, they lock before they pull out of the splice. The third line must also be buried in the splice so it will share the load and will not pull out.

 

[Lnewqban]

Lnewqban said: “Which means to me that only two lines are carrying the load”
Yes, if the two lines went straight through the link and was secured to the chain then clearly two lines are carrying the load. But those two lines then go back toward the boat making 4 lines that are carrying the load. That’s my conundrum - what does physics say?

If only two loops are going through the chain link, the link is trying to break or separate only two lines by putting a huge tension in each loop.
The tension of the incoming line pulls in one direction, while the tension of the returning line pulls in the opposite direction.

The question may be, are two lines enough to resist the actual loads?
Perhaps three lines were more than enough.

 

[Baluncore]

The tension of the incoming line pulls in one direction, while the tension of the returning line pulls in the opposite direction.

That makes one balanced tension in the line, not twice the tension in the line. Beyond the splice, the rope has twice the tension.

 

[Lnewqban]

That makes one balanced tension in the line, not twice the tension in the line. Beyond the splice, the rope has twice the tension.

Correct for an ideal pulley.
Sharply bending two of the lines around the diameter of the bar conforming the last link of the chain, as described in post #1, induces shearing and bending loads besides the simple axial load to be resisted by the fibers of the lines.

The following previous idea is optimistic, IMHO:

Now, there are four lines going backwards toward the boat, I.e. two going up to the chain link and two going backward.

So now, load x is supported at the chain link by 4 strands and therefore each strand carries 1/4 x lbs - a lower value than the previous design.

 

[Baluncore]

An alternative would be to not pass the line through the link. Align the chain without twist over the last 10 links. Split the rope into its three lines, and run those up alongside the chain, in three of the four spaces. Then lash with a thin cord, each line to the sides of the alternate chain links.

 

[DBBPhysics]

The tension of the incoming line pulls in one direction, while the tension of the returning line pulls in the opposite direction.

I think I’ve got it. I believe this is what you are saying: Let’s look at one strand with my right hand holding the strand before it goes through the chain link and my left hand is holding the strand after it comes out of the link looped backwards on itself. My right hand would be resisting the force from the anchor and my left hand would be keeping the strand from being pulled back through the link, like the splice does. So the force in the line follows the strands, first the force is away from the link and then the force follows the strand through the link and then the force is in the opposite direction of the force applied by the anchor. Therefore, the 2 strand example I gave is weaker than the 3 strand. QED

Thanks for all the replies!

 

[Baluncore]

Therefore, the 2 strand example I gave is weaker than the 3 strand. QED

Your logic is confused.
The rope has a strength of three strands. The two folded strands that pass through the link have a total strength of four, since they are folded back and held in the splice.
The third strand in the rope, that does not pass through the link, needs to carry one third of the rope load, so it must be connected deep in the splice, to the two other strands.

The strength of a strand where it passes through the chain link will be determined by the amount of twist in the strand. One full turn of the strand passing through the link will result in all fibres in the strand having the same length, and therefore the same tension.

 

[Flyboy]

Eye splice it through the end of the chain.

 

[Baluncore]

Eye splice it through the end of the chain.

But only two of the three strands, that make up the rope, will fit through the end link.

 

[DBBPhysics]

Your logic is confused.

Therefore, the 2 strand example I gave is weaker than the 3 strand.

Yes, I think that conclusion was wrong. After a long discussion with Google’s Gemini AI app in which even it came to wrong conclusions, I’m now going with the conclusion that the 2 strand looped design theoretically is stronger than the 3 strands woven into the chain. BUT, because of the secondary, weakening effects of having the strands looped around the link (as Baluncor mentioned), the 3 strand woven is the better overall design for me.

I just don’t have confidence in the 2 loop design:

 

[Flyboy]

But only two of the three strands, that make up the rope, will fit through the end link.

Then you need either a smaller line spliced onto the end or a bigger end link.

 

[sophiecentaur]

Which means to me that only two lines are carrying the load.

I find this very confusing. There has to be a finite stretch in all the strands. Assuming the arrangement is in equilibrium and the strands have settled how could the forces (tensions) not be equal where the strands pass round the chain links? The way the situation has been described seems to imply there's a strand pulling one way and one pulling in the other. This seems to violate Newton's third law.

As in many of this type of question, a diagram is essential. Without one, we are all using different models in our heads. If the question is to do with the tensions in the lines within the splice then the division of forces between the 'arriving' strands and the 'returning' strands within the splice will change along the splice.

 

[DBBPhysics]

As in many of this type of question, a diagram is essential. Without one, we are all using different models in our heads.

Thanks for your reply. I’ll restate the question but in much more simplified way such that this will be a theoretical question, not applying to real life.

Assume two designs, A and B as below. Assume a line with 1 strand instead of 3 strands. Assume all effects of a woven splice and bending effects are negligible. Design A is simply one strand of line spliced to a chain with a force diagram as in the picture showing F1=F2. Design B is also one strand but is wrapped around a chain link and spliced to itself where F3=F4. The question is: Is design B a better connection design than design A? Practically, it doesn’t matter since the strength of the line would control. Is design B splice stronger since there are effectively two strands supporting the force?

In real life, if design B splice is better, then except for bending effects, a three strand line spliced to a chain would be a better splice since, in the example given originally there are 4 strands supporting the force at the splice rather than 3 lines in design A.

 

[sophiecentaur]

Assume all effects of a woven splice and bending effects are negligible.

A splice only works because of those effects. It relies on friction and finite stretching / distortion. There's been a lot of study of knots, ties and splices and you could always search those terms until you find something interesting / intelligible.

IMO the thing that counts is how many strands share the total load as they wrap over the link. The load on each strands would be F/n where F is the tension in the rope and n is the number of strands. It's seems obvious to me that the strongest arrangement will be with all strands passing through the steel link.

PS Your diagrams don't actually show any internal details of individual strands or a chain link. Probably a bit hard to know how to make a good diagram.. Most of what appears on the Web seems to be only loosely theoretical - only what riggers and practical rope users need to know.

 

[sophiecentaur]

After a long discussion with Google’s Gemini AI app in which even it came to wrong conclusions

I'm not surprised at all.

 

[Baluncore]

The benefit of this is that the chain and line easily go through the windlass (winch) unobstructed whereas with the previous design, the chain links are widened by the line woven into the links and therefore can get hung up in the windlass.

The windlass will have a chain sprocket as the gypsy wheel, and a capstan drum, adjacent, on the same driven axis. To weigh the anchor, you will pull in the rope, (cable), with two or three turns about the capstan drum, and then finally, with less than one turn of chain locked into the gypsy.

The transition between those two will stress the rope at the changeover, so a thimble, spliced onto the rope, (attached to the chain with a shackle), will raise the rope from the capstan drum, or the chain from the gypsy, which will help when stepping between the drum and gypsy on the windlass.

Not having a thimble will seriously reduce the life of the rope at the point of maximum wear and stress, and that will probably, every now and again, cost you a lost anchor and chain.

 

[Tom.G]

Not having a thimble will seriously reduce the life of the rope at the point of maximum wear and stress, and that will probably, every now and again, cost you a lost anchor and chain.

Especially with that rusty chain grinding its way thru the rope with every movement. That is why I mentioned a thimble back in post #3 https://www.physicsforums.com/posts/7249404

But it's your anchor.

Have Fun!
Tom

 

[RicoGerogi]

The second method is pretty common for windlass setups. Even with just two strands through the link, the load spreads out fine if it’s spliced right.

 

[sophiecentaur]

I agree that the squeeze in the splice would help but won't the maximum stress be on the two strands where they pass over the link? That would be 'the weakest link'.