The Shoulder Carrying Pole as a Spring: A Stiffness Window and a Sizing Rule for Two 20 kg Baskets

A flexible pole carried on one shoulder, with a load hung from each end, is one of the oldest load-carrying tools in the world, and its users insist the spring in the pole does part of the work. This paper treats the pole and its two loads as a spring–mass system driven at the walker's step frequency and derives the stiffness window in which the pole reduces the peak force on the shoulder relative to a rigid carry, for two baskets of 20 kg each (40 kg total, static weight 392.4 N). Isolation requires the bounce-mode natural frequency to lie below the step frequency divided by √2: at a step frequency of 1.9 Hz, the pole stiffness must be below 2,850 N/m. Usefulness requires the static sag to stay below a stated limit of 0.18 m, which requires a stiffness above 2,180 N/m. The window is therefore narrow — 2,180 to 2,850 N/m — and it vanishes entirely for a slow walker at 1.6 Hz, for whom no stiffness satisfies both conditions. At the centre of the window (2,515 N/m, natural frequency 1.262 Hz, sag 0.156 m) the peak shoulder force is 502.6 N, only 5.1% below the 529.7 N peak of the modelled rigid carry, although the dynamic increment above static weight is reduced by 19.8%. The failure side is severe and is reported in full: a pole stiff enough to resonate at the step frequency (5,700 N/m) gives a peak force of 1,092.7 N — 2.79 times the static weight and 106.3% above the rigid carry — and several ordinary pole dimensions fall in or near the amplification region. The sizing rule that follows is: for 2 × 20 kg, use a bamboo pole about 1.9 m long and 29 mm in diameter (centre stiffness 2,515 N/m, bending stress 81.5 MPa against a stated allowable of 100 MPa), accept a sag of about 0.16 m, and treat the benefit as a modest smoothing of peak force, not a large one.