Since I would NEVER nitpick, ....
....Conclusion: with the setup shown in the picture, the tension in the rope would change very little where it passes through the loop, and therefore that bent passage should be the weakest spot in the entire system.
I'll take those comments as mostly true, with pretty good analysis on the loaded legs. I don't think that at 120° angles, that all the legs must be equally loaded. It is only essential that the "bight end" have a force on it equal to the force applied by deflecting the loaded side of the rope, and that the sum of the vector forces of the "after bight" and the "bight end" equal the loaded leg. Some of the load is absorbed by friction going around the log, which would be converted to torque on the log. Not all logs are free floating. Some are rigidly mounted to the ground. The torque on this log might very well be hidden by the log not wanting turn; as in say, a tree being pulled over?
Sure, the main line MUST be weakened where bent, even if only a little. OK! Technically, the weakest point.
But how much does that little bend weaken the rope? Not much, I'll bet. And beyond that bend, the load is carried by two legs of rope. So any imperfections in the rope closer to the log than the bight become moot.
Then you must compare that bend-point against the other possibilities along the entire length of the rope. Given that most ropes are used when we load them to breaking (after all, when they were new, they were strong enough to not break!), then there must be other imperfections along their length. So the problem now becomes a statistical analysis: what is the probability that there is another imperfection along the length of loaded rope that exceeds the weakening that occurs at the loop where the loaded line is tied to the log?
That probability on a well-used rope is pretty good, hence The Dan's observation that they usually break in the middle.
My own personal observation is that they ALWAYS break where they bend most sharply around the strongest piece of rigging in the system. Bumper hitch, figure-8, or the half-hitch holding the timber hitch securing the giant log that really shouldn't have been cut off at that size. I don't think I have ever broken a rope "at the knot", since I never use a knot to carry a rope breaking load (they are such a b**** to untie afterward!). I always try to isolate the loads on the rope around structural items that are stronger than knots.
Really though, I can't remember breaking enough ropes to qualify as an expert on the topic. We usually end up cutting them with a chainsaw, or destroying them in some other fashion than breaking them.
opcorn:
