Expansion and reversing gears can change steam-valve events by altering the motion delivered to a valve. This calculator does not solve a gear train; it linearly interpolates between two entered cutoff percentages and reports two ideal ratios derived from that selected percentage.
Variable Expansion Gear Interactive Calculator
Enter two cutoff endpoints and a position between them. Results are an arithmetic interpolation—not actual valve timing, reverser position, steam consumption, mean effective pressure or gear design.
Equation Used
- Both entered cutoff values are percentages of one piston stroke.
- The selected cutoff is assumed to vary linearly between the entered endpoints solely for this interpolation.
- The reciprocal 100/c is an ideal volume-ratio shorthand and omits clearance volume.
- The relative admitted-volume result is c/Cmax, not mass flow, steam consumption, efficiency or power.
- Valve lap, lead, port opening, eccentric phase, rod lengths, link curvature, clearance, pressure, condensation, exhaust, dynamics, wear and safety are omitted.
Documented Variable-Cutoff Link Topology
U.S. Patent 833,164 documents forward and backing eccentrics connected by rods to opposite ends of a Stephenson shifting link, with a link block and reversing lever used to vary valve motion. U.S. Patent 831,809 describes how movement of a link motion changes cutoff between forward, central and backward positions.
The animation identifies those parts schematically. Its displayed cutoff is not derived from their dimensions.
What This Calculator Represents
The tool treats the entered setting as an abstract percentage between two user-entered cutoff endpoints. It then reports the selected percentage, its reciprocal and its ratio to the entered long-cutoff endpoint.
Entered-endpoint Interpolation
ideal reciprocal cutoff ratio = 100/c
relative admitted-volume fraction = 100c/Cmax
The reciprocal ratio is an ideal zero-clearance volume shorthand. The admitted-volume fraction compares cutoff fractions only; it is not steam mass or fuel consumption.
Worked Arithmetic Example
With entered endpoints 15% and 75% and setting s=0%, selected cutoff is 15%. The ideal reciprocal cutoff ratio is 6.67:1 and the selected admitted-volume fraction is 20% of the entered long-cutoff value. At s=50%, the interpolation gives 45%, 2.22:1 and 60% respectively.
Model Boundary
- Calculated: linear interpolation, reciprocal cutoff fraction and a relative fraction.
- Illustrated: generic two-eccentric Stephenson shifting-link topology.
- Not calculated: actual cutoff from mechanism geometry, direction, valve displacement, lap, lead, port area, pressure, indicated work, steam flow, efficiency, power, load, wear or safety.
Frequently Asked Questions
Is the entered setting a real reverser position calibration?
No.
Does the calculator solve Stephenson link geometry?
No.
Is 100/c a complete thermodynamic expansion ratio?
No; it omits clearance volume and real valve events.
Does relative admitted volume equal steam consumption?
No.
Are forward and reverse valve events solved?
No.
Can these results set or approve a valve gear?
No.
References
- U.S. Patent 833,164, Valve-gear: forward/backing eccentrics, rods, Stephenson shifting link, link block and reversing lever.
- U.S. Patent 831,809, Valve mechanism for engines: link-motion position and changing cutoff through forward, central and backward positions.
- U.S. Patent 386,285: slotted-link expansion valve gear with a movable block for varying cutoff.
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