Horizontal Lifeline Tension and Anchorage (OSHA 1926.502)
A horizontal lifeline MULTIPLIES the force it is asked to catch, and the multiplier is set by SAG. An 1,800 lb arrest at midspan of a 30 ft line sagging 1 ft puts over 13,500 lb into each anchor -- 7.5 times the arrest force -- which is why a cable strung between two roof-hatch handles is not a lifeline. Halve the sag and the tension roughly doubles, so the line pulled drum-tight is the dangerous one and the slack that looks sloppy is what keeps the anchors alive. It also costs clearance below, which is the counterweight. The engineered demand at OSHA's factor of two routinely exceeds the 5,000 lb per worker everyone quotes.
Formula and source
static midspan cable: T = W x sqrt((L/2)^2 + s^2) / (2 s); horizontal pull at each anchor H = W x L / (4 s). Anchorage demand = T x the safety factor, compared against the prescriptive 5,000 lb per employee attached; the larger governs. Inverse: the sag for a target tension is s = W (L/2) / sqrt(4 T^2 - W^2), which has no solution for a target at or below W/2.
Cable statics, with the regulatory requirements from OSHA 29 CFR 1926.502(d)(8), (d)(15), and (d)(16). A US federal regulation in the public domain, quoted directly.
Audience
This tile is built for trades and the adjacent professions in the Cross-Trade Utilities group. The interactive calculator runs entirely in your browser. No account, no fee, no advertising, no tracking.
Related tools
Posture
Rough Logic answers the math question the working professional asks on the job. The site is a calm, fast, ad-free, account-free, ever-free reference. It does not interpret code. It does not replace the licensed professional. It does not store your inputs. The Authority Having Jurisdiction governs all installations and inspections.