The science
The engine is not pushed by steam pressure. Steam at about atmospheric pressure fills the cylinder; a spray of cold water condenses it, the cylinder pressure falls towards a partial vacuum pc, and the outside air pushes the piston down with force F = (patm - p) A. The beam then lifts the pump rods. Ideal work per stroke is (patm - pc) A s, and the useful pumping power is η W n / 60 with η = 0.70 and stroke s = 0.55 m (same constants as the 3D page); the water flow follows from P = ρ g H Q for a 22 m lift.
The animation integrates the piston: M x'' = (patm - p(t)) A - Fload - c x' with the pressure decaying exponentially (τ = 0.5 s) toward pc while the cold water is injected.
Simplifications: lumped condensation time constant, constant load force equal to η(patm - pc)A, rigid beam, constant 0.55 m stroke, no heat-loss or boiler model, fixed 22 m lift. Illustrative, not a reconstruction of a specific engine.
Made with ChatGPT · 2D companion of the 3D page; same solver and numbers.