Three Legs and a Load: Buckling, Splay Angle, and the Safe Load of a Well-Digging Tripod

A tripod of three wooden poles, lashed at the top and splayed over the mouth of a well, is the lifting structure most often available where a well is dug or a pump is serviced by hand. This design study models it as three identical solid round poles carrying a vertical suspended load, resolves the load into axial force in each leg as a function of splay angle, adds the self-weight of the legs before sharing the load, increases the worst leg's share by a stated factor of 1.25 for uneven ground and an off-centre load, and limits each leg by the Euler buckling load of a round wooden column with an elastic modulus of 10.0 GPa, divided by a safety factor of 3.0. Safe suspended loads are tabulated for pole diameters of 60, 80, 100, and 120 mm, lengths of 3, 4, and 5 m, and splay angles of 10, 15, 20, 25, and 30 degrees. Across the grid the safe load runs from 152 kg to 8,904 kg, but the useful lesson sits at the working end: length costs capacity much faster than splay does, and one ordinary-looking arrangement — 60 mm poles, 5 m long, at 30 degrees — cannot carry the 200 kg design working load adopted here, failing the buckling criterion with a utilisation of 1.271, and carries even the 140 kg pump-cylinder case only at a utilisation of 0.933. The study closes with a setup rule: for a design working load of 200 kg, use poles of at least 80 mm diameter and no more than 4 m long, splayed at 20 degrees — a configuration whose safe load is 914 kg, whose worst leg carries 1,027 N under the design load, and whose utilisation is 0.249. The rule deliberately steps up from the thinnest pole that passes on paper, because the 60 mm pole at the same length and angle passes with a safe load of only 280 kg.