Archimedes Screw Pump — Bucket Ladder & Efficiency Curve

This is a 2D-native companion to the 3D Archimedes screw pump model. Instead of a tilted, rotating helix rendered in perspective, the screw is "unrolled" into a straight ladder of discrete water pockets climbing from the sump to the discharge lip, with each pocket's fill wedge and leak droplets driven by the same volumetric-leakage and fill-loss formulas as the 3D engine. A second panel plots overall efficiency against rotation speed as an explicit curve — the same trade-off between volumetric efficiency (rising with speed) and fill efficiency (falling above ~35 rpm) that makes the 3D model's efficiency peak, but here the peak is a visible feature of a parameter-space plot rather than something read off a single number. Adjust rotation speed, tilt angle, intake submergence and casing gap and watch both panels respond together.