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Boiler, condenser and cut-off
A shorter cut-off lets the steam expand and do more work per kilogram, but gives less power per stroke.
Expansion, clearance and size
Clearance volume wastes steam; the expansion exponent sets how fast the pressure falls after cut-off.
Model checks
The science
The indicator diagram
A steam-engine indicator draws pressure against piston position. The enclosed area is the work per stroke, W = ∮ p dV. Steam is admitted at boiler pressure until cut-off; the valve then closes and the trapped steam expands, p Vn = const with n ≈ 1.13 for wet steam. At release the pressure drops to the exhaust (condenser) pressure; near the end of the return stroke the exhaust closes and the remaining steam is compressed to cushion the piston.
Why short cut-off saves fuel
The steam used per stroke is m = ρ(p1) (Vcutoff - Vc pce/p1). Cutting off earlier reduces m faster than the work falls, so the steam rate in kg per kWh drops, until the clearance and the low end-of-stroke pressure dominate. The steam density uses the ideal-gas law with a small real-gas factor; the saturation temperature comes from the Antoine equation.
Power and torque
Indicated power is W · 2 N / 60 for a double-acting piston (two strokes per revolution). Crank torque follows from virtual work T = F dx/dθ and fluctuates strongly over a turn, which is why a heavy flywheel is needed.
Honest simplifications
- Instant valve events, no pressure drop in the steam chest and ports, no wall condensation (which in real engines is the largest loss), and no rod area on the back side of the piston.
- Efficiency compares the indicated work with the heat from feed water at 40 C to saturated steam, fitted from steam-table data; mechanical friction is not included.
What to try
- Load Economical short cut-off: the loop is thin but the steam rate is far better than Full admission.
- Raise the exhaust pressure from 0.15 bar (condenser) to 1.05 bar (atmosphere) and watch the work area collapse.
- In the torque graph note how the torque goes negative near the dead centres when compression is large.
- Increase the boiler pressure in the efficiency graph and compare with the Carnot limit.