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.
Example
You enter
- Apex load (lb) 1200
- Leg 1 east offset (ft, - west) 6
- Leg 1 north offset (ft, - south) 0
- Leg 1 rise (ft) 8
- Leg 2 east offset (ft) -3
- Leg 2 north offset (ft) 5.196
- Leg 2 rise (ft) 8
- Leg 3 east offset (ft) -3
- Leg 3 north offset (ft) -5.196
- Leg 3 rise (ft) 8
You get
- T1 (lb) 500
- T2 (lb) 500
- T3 (lb) 500
- Angle1 (deg) 53.13
Checked against published worked examples from: Entertainment rigging bridle statics.
Details, formula, and sources
ScopeThe 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 or tableLi = 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).
Source and editionEntertainment rigging three-point bridle geometry (static 3-D resolution), by name.
Free accessStatic bridle resolution is a public statics result; ASME B30.9 governs rigging practice. An ESTIMATE only; the hardware ratings and a qualified rigger govern.
What governsEstimate. Head rigger and manufacturer working-load-limit charts govern. Inspect every piece of hardware before the show.
API field namesapex_load_lb, e1_ft, n1_ft, r1_ft, e2_ft, n2_ft, r2_ft, e3_ft, n3_ft, r3_ft, t1_lb, t2_lb, t3_lb, angle1_deg
- Three-dimensional statics single apex, three straight legs to fixed points, load acts straight down; ropes carry tension onlybridle statics
- Estimate only the hardware working load limits and a qualified rigger govern the actual pickASME B30.9