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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?

s/v Laelia - 1978 Pearson 365 ketch

Last edited by AdamLein; 01-29-2011 at 12:42 PM.