Portable Ladder Setup Geometry (OSHA 1926.1053)

ladder-angle does the 4:1 setback and stops. Three more numbers decide whether a ladder is usable, and the first has arithmetic nobody does: the side rails must extend at least 3 ft above the landing, and that 3 ft comes out of the CLIMBABLE length along with the setback. At 4:1 every foot of height costs 1.0308 ft of rail, so a 24 ft ladder needs 25.8 ft of rail to serve a 22 ft roof -- it does NOT reach, and the highest landing it actually serves is 20.3 ft. A ladder never reaches its label. Where the 3 ft is impossible the ladder must be secured at the top AND a grasping device provided -- an alternative, not an excuse. Rung spacing is a WINDOW, 10 to 14 in, so too close fails as surely as too far. Clear width at least 11.5 in.

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Formula and source

rail per foot of height at a b:1 setup = sqrt(1 + 1/b^2); base setback = height / b; rail to the landing = height x that factor; total rail = (height + 3 ft) x that factor; the highest landing served = ladder length / factor - 3 ft. Rung spacing must fall between 10 and 14 in between centrelines; clear width between side rails must be at least 11.5 in; side rails must extend at least 3 ft above the landing unless the ladder is secured at its top to a rigid support with a grasping device provided.

OSHA 29 CFR 1926.1053, Subpart X - Stairways and Ladders. A US federal regulation in the public domain, quoted directly. The rail-budget arithmetic is geometry from the setup ratio, not a code value.

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