Sizing the Flywheel of a Treadle Lathe: Stroke Energy, Cutting Torque, and a Speed-Sag Criterion with a Worked Wheel

A treadle lathe is powered in pulses: the operator's leg drives on the down-stroke and the machine coasts on the return, while the cut draws power continuously. The flywheel must bridge that gap without letting the spindle slow enough to spoil the cut. This paper sizes the wheel from first principles using a speed-sag criterion: during the 0.6 s unsupported part of each cycle the spindle may lose at most 10 percent of its speed. A treadle stroke of 180 N over 0.22 m delivers 39.6 J, or a mean input of 26.4 W after linkage losses. A moderate cut — 30 N tangential force on 60 mm diameter stock at 600 rpm — draws 56.5 W and needs 33.9 J during the unsupported interval, which requires 178.6 J of stored kinetic energy and a moment of inertia of 2.26 kg·m² on a wheel shaft turning at 120 rpm. A cast-iron rim of radius 0.45 m and mass 11.2 kg meets the requirement; an oak disc alternative weighs 22.3 kg at 50 mm thickness. The same arithmetic sets the machine's ceiling: the maximum cutting force sustainable on average is 28 N, and an 80 N cut makes the spindle sag by 29.8 percent in a single cycle. Heavy roughing cuts are therefore outside this machine's range, however large the wheel.