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I did the math and figured out that according to the laws of physics, for any specific type of wire between poles a given distance apart, the more slack the wire has, the less its weight between those two poles gets magnified into tension force. When there's a buildup of ice on the wire and the wire has very little slack, the weight of the ice is already a lot heavier than the wire but the weight of the ice also gets greatly magnified into a force of tension that's much bigger than the weight of the ice on the part between those two poles. My question is

Did most of the places where part of a power line that fell down during a freezing rain storm fell down only from the weight of the ice on the power lines and not from a tree branch that fell down from a buildup of ice on it bringing down a power line with it? If so, did most of the spots where part of a power line fell down only from the weight of the ice on it have very little slack?

If so, this fact might be so useful for research. Maybe in the future, power lines could be built with more slack to account for the possibility that so much ice might build up on them during a freezing rain storm.

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  • $\begingroup$ Why not increase the slack so the cable lays on the ground - that would reduce the weight even more.... $\endgroup$
    – Solar Mike
    Feb 9, 2019 at 19:57
  • $\begingroup$ Have you looked at the literature? Google Scholar, for example, can point you to hundreds of research studies on icing of catenaries, including optimum geometry, stochastic analysis, and mitigation measures. More slack requires higher poles and more wire—a substantial penalty to consider in conjunction with the likelihood and potential damage of icing. One alternative is to heat the wire. $\endgroup$
    – Chemomechanics
    Feb 9, 2019 at 20:11

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Slack means length of wire is longer than the distance between the towers, means more ice accumulation: more weight. I don't know what kind of calculation you did. I'd say you managed to get the exact wrong answer.

The geometry of a wire or cable suspended between the supports under self weight, meaning not supporting a bridge or deck, is a catenary. the span and slack and tension in the wires are highly standard and optimised for many factors, only a sub section of it is elements, wind, icing, earthquake, thunder, dynamic vibration and resonance in gusty storms, etc.

There is always room for improvement, but that shouldn't start with wrong assumptions.

Edit

After some comments by OP, I think this will help.

Let's call the sag in the wire S and the distance at post or tower between the insulators X. Under certain wind condition the wires will vibrate and swing around the insulators possibly into a paraboloidal kind of surface.

At no moment these individual surfaces shouldn't get closer than is likely to touch or even close enough to create an electrical arc and start a fire. This mean one restriction for the sag, 2*S < X+ arcing distance. This is just one of concerns

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  • $\begingroup$ A gear system can be used to enable a person to life much heavier weights than they normally can. I've seen poles not very far apart with wires on them and the amount they were hanging down was a very small fraction of the height of those wires. I think they could have been made with more slack than that without causing a problem. I think that when they have that little slack, the system is like a gear system making the force of tension in the part of the wire between those two poles much greater than the weight of the wire. You're technically correct that the more slack, the more weight of $\endgroup$
    – Timothy
    Feb 11, 2019 at 3:17
  • $\begingroup$ ice during a freezing rain storm. However, I think that when there's that little slack, the weight gets magnified into tension by a larger factor. I don't think your answer solves my problem. $\endgroup$
    – Timothy
    Feb 11, 2019 at 3:19
  • $\begingroup$ @Timothy, as I said in my answer, the standards for electrical transportation on aluminum or coper cables have been studied in depth with consideration to many aspects of structural, electrical, electromagnetic, radio frequency emitions, spark control at insulators, etc. I would recommend couple of references, but before anything I encourage you to brush up on high school math and trig specially hyperbolic trig, to be able to benefit from free material on the subject. BTW our answers are to point to correct solution not affirmation of wrong hypothesis. $\endgroup$
    – kamran
    Feb 11, 2019 at 3:44
  • $\begingroup$ Maybe your answer is good and I just don't fully understand it. I actually got high marks in a lot of math courses in in high school and university and then got a book prize for getting such high marks in math when I graduated from university. I realize that doesn't mean I know everything in math. I struggled to understand what the textbook for my differential equations course and needed help from my professor to understand it because the book wasn't written clearly. I suppose some really good math experts unlike me probably could have figured out some math statements entirely mathematically $\endgroup$
    – Timothy
    Feb 11, 2019 at 3:49
  • $\begingroup$ that were related to what they read in the book as a result of seeing what the book said. I don't think that was one of the math courses that I did so well in. The equations for a hanging chain actually weren't taught at all in any math course I took. In grade 12 Physics, I think I might have had homework problems involving a weightless string with things pulling on different parts of it. The equations for a hanging chain might be more complicated because we don't neglect its weight. I'm pretty sure that if you pull on a chain with one fixed end, the harder you pull, the less curved it will $\endgroup$
    – Timothy
    Feb 11, 2019 at 3:55

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