Rope arcs happen inside of knots whar ya can't see'em. But, they also happen in rigging. Because a pulley has 2 legs of loaded line on it, it has a potential loading of 2x Load. But, because the sling/rope holding the pulley, only resists inline not perpendicular tensions, we only need to calcualte the inline forces of the rope angle from the sling X 2 legs. This means that we take 2x Load X cosine of half the spread. And we are done.

This also explains a pulley with weight on a horizontal clothesline, or leveraging tighter by swigging or sweating purchases. For, this is the same math, in reverse, we are now just initiating force by the bend, not the end, into the system.

Thus; if we place 175 degree spread in angle box, we will see very little load on pulley; so pulley has leverage over the line at that angle. Thus, if we anchor leg and pull bend, we can incite those kind's of forces. The calculator crunches by radians, so calcs by hand in degrees all the way through might be slightly different. For code testers/breakers i allowed negative/floating load weights, but not angles< Zer0 nor >= 180.

calcPulleyLoadings.swf