Three-Point Bridle Leg Tension (3-D)
The exact leg tensions of a three-point bridle from the apex load and each leg's east / north / rise offsets: the 3x3 static equilibrium T1 u1 + T2 u2 + T3 u3 = (0, 0, W) solved by Cramer's rule, with each leg's length and angle. Physical only while every tension is positive - the apex must hang inside the triangle of its attachment points (a rope can only pull), and an asymmetric hang splits 1,000 lb as 497 / 419 / 244, nothing like an even 333 each. A design aid, not a rigging sign-off.
Formula and source
Li = sqrt(e^2 + n^2 + rise^2); ui = (e, n, rise)/Li; T1 u1 + T2 u2 + T3 u3 = (0, 0, W) solved by Cramer's rule; angle_i = asin(rise_i / Li).
Entertainment rigging three-point bridle geometry (static 3-D resolution), by name.
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