A duplex steam-actuated air compressor has two parallel cylinder trains. In the Ingersoll-Sergeant arrangement shown by Hiscox, an air cylinder is tandem with each steam cylinder, with a crankshaft and flywheel linking the reciprocating motion.
This cutaway shows both trains, their common rods, guided crossheads, phased cranks and shared shaft. The calculator measures geometric swept volume and its rate of change. Swept-volume rate describes piston displacement; calculating force or actual air delivery requires additional pressure and gas-behavior data.
Duplex Steam-actuated Air Compressor Interactive Calculator
Inspect two tandem steam/air cylinder trains on one crankshaft. Compare bore, stroke, rod area and phase using geometric swept volume and its rate—not an actual compressed-air delivery rating.
Equation Used
- Two identical double-acting air cylinders, one rod-side annulus each.
- Tandem steam/air piston rods; L/r=4 exact slider-crank.
- Fixed phase on a shared shaft.
- No compression, clearance re-expansion, valve timing or steam-force model.
Hiscox figures 644 and 645 arrangement with illustrative internal cutaways. Geometric chamber-volume reduction excludes gas compression, clearance and valve events. No force or actual delivery is predicted.
Two tandem trains on a common crankshaft
Each steam piston and its air piston move together on one rod. A crosshead supports that rod, and a fixed-length connecting rod joins the crosshead to the crank. The two cranks maintain the selected phase difference on the common shaft. The single flywheel represents the wheel shown between the two trains in the historical plan.
The blue air cylinders are double acting in this illustration. Moving right reduces the full-bore right chamber; moving left reduces the annular chamber around the rod. The rod-area correction is therefore applied to only the rod side. Steam cylinder width, governor omission and frame proportions are explanatory choices.
Real air valves open according to pressure differences, and trapped gas compresses or re-expands. Those events are not modeled. The rate graph is the instantaneous reduction of the geometrically shrinking air chambers, before clearance, compressibility, leakage or valve restrictions.
Use phase to compare geometric pulsation
Adjust air bore and stroke to change the volume displaced. Rod diameter changes the annular swept area. Shaft speed scales all rates but does not change volume per revolution. Crank phase shifts the two waveforms relative to one another, changing the combined peak and minimum without changing the mean.
At zero rpm the rates are zero while the displacement and geometry remain available. Scrub the stopped model to inspect the mechanism. The volume results account for the bore, stroke and rod area of both cylinders.
Rod-corrected swept volume
For air bore D and rod diameter d, full piston area A=πD²/4 and rod area Ar=πd²/4. With stroke S, one double-acting cylinder displaces (2A−Ar)S geometrically per revolution. There are two identical cylinders.
Pair volume per revolution=2(2A−Ar)S
Divide mm³ by 1,000,000 for liters. Multiplying liters per revolution by rpm gives the mean geometric rate in L/min.
Crank radius r=S/2, rod length L=4r and piston coordinate x=r cosθ+√(L²−r²sin²θ). Its exact velocity is ω[−r sinθ−r² sinθ cosθ/√(L²−r²sin²θ)]. The second cylinder uses θ+φ.
For positive velocity the shrinking chamber has area A; for negative velocity it has area A−Ar. Sum |v| times the applicable area for both cylinders. Peak and minimum are sampled every 0.25° over a revolution; the mean is the exact swept-volume result. Ripple here is (peak−minimum)/mean, expressed as a percentage. At zero rate it is displayed as zero by convention.
Default displacement
A 100 mm air bore, 16 mm rod diameter and 80 mm stroke give approximately 2.4811 liters of geometric swept volume for the pair per revolution. At 60 rpm the mean geometric rate is about 148.87 L/min.
Changing crank phase changes the combined instantaneous curve, not this mean displacement. These figures are not a free-air-delivery rating: actual delivery requires pressure, temperature, clearance and valve data.
What this cutaway leaves out
Hiscox figures 644 and 645 document the tandem steam/air trains, common crank arrangement and central flywheel. The internal cutaways and dimensions are illustrative assumptions. Steam bore is drawn as 1.2 times air bore; connecting rod length is four crank radii. No steam pressure, power balance or governor response is solved.
The slider-crank geometry determines piston position and velocity. Bore and rod area convert these into chamber displacement and swept-volume rate; crank phase determines how the two cylinders combine.
The graph shows geometric swept-volume rate only. Valve delay, clearance re-expansion, pressure-dependent discharge, thermal behavior, leakage, stress and shaft torque are outside its scope. Playback is slowed for inspection.
Duplex compressor questions
Is the graph actual air delivery?
No. It shows the volume reduction of the shrinking chambers. Actual delivered flow depends on gas compression, clearance and valve behavior.
Does phase change average displacement?
No. Each piston still completes the same stroke. Phase changes when the two contributions occur.
Why subtract rod area on only one side?
The illustrated air cylinder has a rod entering its left end and a full-bore right end. The left chamber therefore has annular swept area.
Can swept volume determine piston force?
No. Piston force depends on chamber pressures and effective areas; load data are also needed to determine the resulting mechanism forces.
Can this show a stopped mechanism?
Yes. Set rpm to zero and use the cycle scrubber. Volume per revolution remains defined, while all rates are zero.
Historical construction reference
Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 173, figures 644 and 645, shows the Ingersoll-Sergeant duplex steam-actuated air compressor in plan and elevation, with each air cylinder tandem to a steam cylinder.
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