Max Redirect Angle for a Block WLL
The inverse of the block-redirect tile: the largest direction change a block or anchor of a rated WLL can turn a line without the resultant exceeding the rating, angle = 2 x asin( WLL / (2 x line tension) ). A 3,000 lb line through a 5,000 lb block can turn up to 112.9 degrees; if the WLL is at least twice the line tension, any turn up to 180 degrees is within rating. Answers 'how far can I turn it' instead of the resultant from a set angle. Keep margin for shock; the qualified rigger and the tags govern.
Formula and source
max_direction_change = 2 x asin( block_wll / (2 x line_tension) ), the inverse of resultant = 2 x line_tension x sin(angle / 2); solvable only when WLL < 2 x line_tension, else any turn up to 180 degrees is within rating.
ASME B30.26 and standard rigging statics by name; first-principles vector resultant, solved for the angle.
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