Spanned Cable Minimum Sag for a Tension Limit

d_min = w L^2 / (8 sqrt(T_allow^2 - (w L / 2)^2)). A 100 ft span at 1 lb/ft held to a 502 lb rope WLL needs at least 2.5 ft of sag; pull it tighter and the tension climbs past the limit, because tension is inversely proportional to the sag. The allowable must exceed the w L / 2 support vertical reaction, or no sag can carry the load. Enter the rope WLL or anchor capacity with the design factor applied. A planning screen; the WLL, the anchors, and the head rigger govern.

d_min = w x L^2 / (8 x sqrt(T_allow^2 - (w x L / 2)^2)); the inverse of T_support = w L^2 / (8 d) sqrt(1 + (4 d / L)^2) solved for the sag.

Shallow-cable parabola statics (by name) with ASME B30.9 / Wire Rope Users Manual rigging practice; first-principles, no edition cycle.

The shallow-cable parabola (H = w L^2 / 8d) is a public statics result; ASME B30.9 governs sling and rigging practice. An ESTIMATE only; the certified rope WLL and the head rigger govern.

Estimate. Head rigger and manufacturer working-load-limit charts govern. Inspect every piece of hardware before the show.

Field names used by the API: span_ft, load_lb_per_ft, allowable_tension_lb, min_sag_ft, horizontal_tension_lb

• Support-tension limit the allowable limits the support (anchor) tension and must exceed the w L / 2 vertical reaction; below that no sag can carry the loadcable statics
• Shallow parabola valid where the resulting sag is under about a tenth of the span; a deep sag trends toward the catenarycable statics
• Uniform load, level supports the load is uniform along the horizontal span and the two supports are at the same heightcable statics
• Estimate only the certified rope WLL, the anchor capacity, and the head rigger govern the actual pickASME B30.9