Two Legs Against the Head: Discharge Bounds for the Treadle Pump by Depth

A treadle pump is driven by the legs and body weight of a standing operator, and its usefulness for household supply and garden irrigation depends on how its discharge falls as the suction head grows. This study models a two-cylinder treadle pump under stated assumptions: a sustainable treadling power of 75 W, an overall efficiency of 0.62 giving 46.5 W of hydraulic power, and a displacement cap of 4.283 m^3/h set by the cylinder geometry and treadling rate. Delivered discharge holds at the displacement cap of 4.283 m^3/h from a head of 1 m through a head of 3 m, passes a crossover head of 3.98 m at which power and displacement limits coincide, and then declines with head to 3.413 m^3/h at a head of 5 m and 2.438 m^3/h at a head of 7 m, equivalent to 40.63 L/min at the deeper head. The operator cost rises correspondingly, from 0.233 operator-hours per cubic metre in the displacement-limited range to 0.410 operator-hours per cubic metre at a head of 7 m. Against stated daily needs of 200 L for domestic use, 1000 L for a garden plot, and 1200 L for the two combined, with delivery required within 2.0 hours of treadling, the power-only depth bounds are far beyond any suction pump's reach, at 28.44 m for the combined need, while the assumed practical suction limit of 7.0 m governs in practice: at that limit the combined daily need still takes only 29.5 minutes to deliver. For a larger comparison plot requiring 4000 L per day, the power bound is 8.53 m and delivery at a head of 7 m takes 1.64 hours, still inside the allowed treadling time but with little margin. The central finding is that, under the stated assumptions, suction physics rather than leg power sets the useful depth of a treadle pump for household and garden needs, and leg power becomes the governing constraint only when the daily volume is large.