This partial calculator evaluates ideal indicated work rate for one hypothetical cylinder with two equal full-area work strokes per revolution, using entered mean effective pressure, bore, stroke and speed. It does not predict actual steeple-engine power, shaft power, steam consumption, stresses or safe operation.
Steeple Engine - Ideal Equal-Area Double-Acting Cylinder Ledger
Explore ideal equal-area cylinder work rate, force and selected piston travel.
Equation Used
- Mean effective pressure, bore, stroke and rotational speed are entered values.
- One hypothetical cylinder has two equal full-bore-area work strokes per revolution.
- The rod-side annular-area reduction is omitted because no rod diameter is entered.
- Indicated power is ideal cylinder work rate and is not brake or shaft power.
- Thermodynamics, valves, losses, loads, structure and safety are excluded.
The secondary figure is an ideal selected cylinder/stroke ledger, not a steeple-engine reconstruction.
Ideal equal-area cylinder ledger
Ideal piston area is pi d squared over four. Entered mean effective pressure times area gives an ideal mean force. Each assumed revolution contains two full-area work strokes of selected length, so indicated work rate is p A L times 2N divided by 60. Mean piston travel rate is 2LN.
What the calculator determines
Use it to inspect the stated ideal work-rate arithmetic and selected cylinder geometry only. It is not an engine rating or reconstruction.
Selected relationships
A=pi d^2/4; F=pA; P_i=pAL(2N)/60; horsepower=P_i/745.6999; mean piston travel rate=2LN.
Selected-input example
At 1.5 bar entered mean effective pressure, 1000 mm bore, 1.2 m stroke and 31.65 rpm, the ideal equal-area ledger reports about 149.147 kW and 200.010 horsepower.
Not an actual engine model
A real rod side has annular rather than full bore area. Indicator-diagram differences between ends, clearance, cut-off, expansion, condensation, valve events, leakage, friction, pumping, auxiliaries, mechanical efficiency, torque ripple, structure, bearings, flywheel, steam rate and safety are excluded.
Questions
Is this brake or shaft power?
No. Indicated power is cylinder work rate; NASA distinguishes brake power as indicated power minus friction and other losses.
Why call the two strokes equal-area?
ORNL notes that a real double-acting return stroke uses annular area after subtracting the rod. No rod diameter is entered here.
Does mean effective pressure equal constant cylinder pressure?
No. It is an equivalent mean pressure representing the same work as the varying pressure cycle.
Authoritative references
- U.S. Department of Transportation engine handbook — explains indicated mean effective pressure and the pressure-area-stroke-work-strokes power relationship.
- NASA NDARC Theory, Appendix 3 — relates mean effective pressure, swept volume and indicated power and distinguishes brake from indicated power.
- ORNL MEASUR double-acting piston formula — states that the return stroke uses annular area between bore and piston rod.
- NIST Guide to the SI, Appendix B.9 — gives horsepower (550 ft lbf/s) as 745.6999 watts and bar as 100000 pascals.
References & Further Reading
- Wikipedia contributors. Steeple engine. Wikipedia
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