Oscillating steam engine (2D)

What you see

The oscillating steam engine in its plane of motion. The piston rod is pinned straight to the crank pin; instead of a connecting rod and a slide, the whole cylinder rocks on a trunnion (green). The yellow bar is the piston and the shaded steam follows the pressure on the working face.

Kinematics

The crank pin moves on a circle of radius R = 0.171 m about the crankshaft. The distance from the pin to the trunnion is d = sqrt(D^2 + R^2 - 2 D R cos(theta + alpha)), so the piston travels 2R = 0.342 m and the cylinder tilts by about asin(R/D) each way. The page calls the same updateOscillator closure as the 3D model, so the piston and tilt numbers are identical.

Steam indicator diagram (added here)

The 3D page has no steam model, so this 2D page adds a simple ideal one: steam is admitted at boiler pressure up to the cut-off point, then expands with p V = constant (isothermal approximation), then is exhausted at 1 bar. Work per stroke is the area of the loop: W = p0 Vc (1 + ln(1/c)) - p_back Vs. A double-acting cylinder works twice per turn, so power is 2 W n.

Why short cut-off saves steam

Closing the valve early lets the steam do work while it expands, so more work is obtained per kilogram of steam, but the engine produces less force at low speed.

Simplifications

No clearance volume, wire-drawing, heat loss, friction or valve timing (the valve here is idealised). Treat the power figures as an illustration of the method, not as a rating of a real engine.