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"Joe",
I'm not sure what your inferring there, so I won't bother addressing your timeline accusation until you make that a bit clearer. I hope that you will consider in your clarification, that the TCIA publication was some time after the job.
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Angus, I'm not inferring anything other than I put a version of those trig equations on the web before your version was put in the TCIA publication(which were "published" incorrectly). There is no accusation being made about anything.
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What I will point out is that opposing pendulums is NOT for speed lines, and the formula posted by "Joe Hash" on the old forum in 2000, would NOT work accurately for speed lines.
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Those equations, just like the ones you wrote, can give a reasonable account of the tensions in a line when a weight is at a point along that line with 2 anchor points at different heights like when using speedlines. The equations represent differing tensions at the rigging points when the load is static. It's useful information when we don't have anything better.
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I will also point out that the day Joe Hash made that post, it included the same intentional arithmetic error we put into the formula.
Each time we see the same error replicated, we laugh and know how it got there, and who it was given to.
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You're more observant than I, I could use better information if you're willing to give it.
I used those equations to get an idea of what I could expect to experience when using a speedline. So, now, I set anchors on the lower side of the speedline and take even smaller pieces when I don't have a lower anchor point available. I could have learned this through experience, but the math made it much more clear for me.
Joe