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Block and tackle breaking strength

I'm interested in how reeving a line through blocks affects the whole system's breaking strength.

Suppose I have a line with breaking strength B and I produce a block and tackle with mechanical advantage A (i.e. pull A feet to move the moving part 1 foot).

To simplify things, for now, imagine the blocks and attachment points have infinite breaking strength and zero friction, and that the curve in the rope at all points (including knots and splices) does not decrease the breaking strength of the rope.

I would guess that in this idealized scenario, the breaking strength of the whole system is now A x B, since to achieve a tension of B in the line, I would have to load the moving part with a tension of A x B.

The first thing that doesn't feel right is that, at the points where the line turns around the block, the line has tension in opposite directions of equal magnitude, which should add up. Imagine a 2:1 purchase, rove to disadvantage. The moving part has two bits of line sticking out, straight up. If I put a weight W on the moving part, each bit of line supports W/2, which initially support the above reasoning for the breaking strength being A x B (since the line will break when W = 2 x B).

But the "two bits of line" are really just two ends of the same line being pulled away from another, each with tension W/2, so in between them, surely the tension is now W. At the very least, the block in the moving part is pressing down (across) the line with force W. So this seems to imply that the breaking strength is now just B again.

An important thing that I don't know how to account for here is how strong a line is when a force is applied transversely, rather than longitudinally. I would imagine it depends on how the line is assembled (single braid, double braid, three strand, etc.).

Finally, as an application: I put together a soft shackle last night from 3/6-in dyneema with a breaking strength of 5,400 lbs. The open shackle has the line doubled up, and the closed shackle is doubled up again, so it seems the breaking strength of the whole thing (by the original A x B argument) should be 21,600 lbs, minus whatever loss in strength is created by the knot, and assuming that all parts share the load equally.

Thoughts?

 degreeoff 01-29-2011 01:55 PM

Just kidding bout the cold but it did make my head hurt.

It made my head hurt thinking about it, too, so I decided to share the pain. I think it would be good to know the SWL of my various tackles, though I suspect that in many cases it will be greater than the SWL of the hardware attaching them to the boat :P

 sailingdog 01-29-2011 02:07 PM

Quite a bit depends on the line and the diameter of the sheaves, as well as the type of line it is and what it is made from. Some lines don't like being bent and if you bend them under a minimum radius, they will be severely damaged.

A lot also depends on how much friction is in the system. A large diameter block with higher friction will probably take more of a load than a small diameter block with very low friction sheaves, given all other things being equal.

Also, there are often other factors to consider. For instance, in a mainsheet setup, you don't only have to worry about the strength of the shackles, becket, sheaves and line, but also the strength and durability of the cam cleat that is used when the mainsheet is cleated off. The system is only as strong as its weakest link.

I don't know how to consider most of the other factors, so I'm looking at an idealized picture for now. As long as my basic understanding (A x B) is correct I suppose next I'd consider the effects of sheave diameter on the problem.

 Liquorice 01-29-2011 03:23 PM

In 50 years of sailing I've never had a block and tackle break!
With a 27 ft Catalina I doubt you will either.

I'd suggest you ponder more important stuff - like how come I have to pay \$38 for a bottle of rum in Alberta, but it's \$6.38 in the caribean?

Scoff. Mathematicians do not ponder "important stuff".

 tommays 01-29-2011 04:04 PM

http://i565.photobucket.com/albums/s...s/P4192441.jpg

You do need to keep and eye on the bits and pieces ;)

 nemier 01-29-2011 09:28 PM

Grab a cappuccino. :)

The Block & Tackle will come with a certificate stating what load it is certified to safely use (SWL). The Breaking Load with be significantly higher. (Man Riding applications have a sfety factor of 8)

This information should also be stamped on the side of the cheek plates.

As long as the line is sized correctly, you will not have to worry about the line breaking under load. If the Breaking Load is exceeded, the Block & Tackle will fail before the line parts. Unless this is a 'shock' load, you will have plenty of warning before that happens.

Over simplifying it, every time the line passes over a set of pulley's, you will half the load. Hope I actually answered your question.

Quote:
 Originally Posted by nemier (Post 692440) Over simplifying it, every time the line passes over a set of pulley's, you will half the load.
Certainly that's not the case, since then mechanical advantage would always be a factor of two.

Anyway I guess it makes sense that blocks would be marked with their SWL or whatever, but I'm wondering what happens when I mix and match things and combine them in clever ways. For example, what do you think about the soft shackle problem? The original line's breaking strength was listed, but I'm trying to understand when, in this case, I double the line up twice.

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