A compound air compressor raises pressure in successive stages. The first cylinder takes in a larger volume of low-pressure air; the later cylinder handles a smaller volume at higher pressure. Cooling between stages reduces the temperature entering the next cylinder. This calculator shows an ideal equal-ratio pressure split and the corresponding cylinder proportions under explicitly stated assumptions.
Compound Air Compressor Interactive Calculator
Compare ideal interstage pressure and cylinder sizing, then watch the linked pistons, inlet and delivery valves, and the route through the intercooler. The smaller HP bore responds to the entered pressure ratio. All pressures are absolute.
Equation Used
- Two stages, ideal gas, equal inlet temperatures after perfect intercooling, equal compression exponents and no line/valve pressure losses.
- Same strokes, rotational speeds and volumetric efficiencies in the two cylinders.
- Illustrative valve timing uses polytropic exponent 1.3 and clearance equal to 5% of swept volume in each stage.
- Crank radius and connecting-rod length remain fixed; HP bore changes with pressure ratio. Playback is slowed to eight seconds per revolution.
Ideal two-stage pressure split and cylinder ratio, not a compressor rating. The illustration uses two parallel cylinders connected to their crank drives. The explanatory valve cycle uses n=1.3 and 5% clearance with no losses; these are illustrative assumptions, not measured data.
Two connected compression stages
The animation shows a generic pair of single-acting cylinders in section. Each piston is pinned to a connecting rod whose length stays constant as the crank turns. The two cranks are half a revolution apart. The low-pressure cylinder has the larger bore. Its discharge pipe leads through an intercooler to the smaller high-pressure cylinder’s inlet.
Gas left in the cylinder’s clearance volume first re-expands as the piston withdraws. The inlet opens once cylinder pressure has fallen to inlet pressure. On the return stroke the inlet closes, pressure rises, and the delivery valve opens only when cylinder pressure reaches its discharge pressure. The arrows therefore do not show uninterrupted flow through a closed valve.
The pressure readouts inside the drawing describe an illustrative cycle with a polytropic exponent of 1.3, 5% clearance and ideal valves. They are not measured pressures from a particular compressor. The geometric-mean pressure and bore-ratio results follow the stated ideal two-stage assumptions.
Historical compound compressors used several arrangements. Hiscox’s figure 646, for example, shows tandem single-acting pistons with opposite compression directions. The generic parallel-cylinder illustration here explains staged compression without claiming to reproduce that exact machine. Practical equipment additionally needs cooling, lubrication, controls and protective provisions appropriate to its design; those are not sized by this tool.
What the calculator is useful for
Use the model to understand why later compression stages have smaller swept volumes and why equal stage ratios are a useful ideal starting point. Changing the inlet or final pressure updates the interstage pressure, both cylinder pressure cycles and the illustrated HP bore.
The tool does not select an operating pressure for existing equipment or specify its capacity. Actual compressor selection requires the manufacturer’s rated pressure, flow, duty and cooling conditions.
Ideal pressure split and bore ratio
For two ideal stages with the same inlet temperature, compression exponent and efficiency, and negligible pressure loss between them, minimum compression work occurs at equal stage pressure ratios. Thus P₂/P₁ = P₃/P₂ and P₂ = √(P₁P₃). All three pressures must be absolute.
With equal inlet temperatures and equal volumetric efficiencies, conservation of mass gives V_LP/V_HP = P₂/P₁ = r. If the strokes are equal, swept volume is proportional to bore squared, so D_HP/D_LP = 1/√r.
These relationships set ratios, not dimensions. Imperfect intercooling, unequal efficiencies, clearance or pressure losses can change the preferred interstage pressure and cylinder sizing. The illustration uses the same fractional clearance and pressure ratio in both stages, so its ideal volumetric efficiencies are equal.
Example: 1 to 30 bar absolute
Set the pressures
Use inlet pressure P₁ = 1 bar absolute and final pressure P₃ = 30 bar absolute.
Find the interstage pressure
P₂ = √30 = 5.477 bar absolute. Both stage pressure ratios are approximately 5.477:1.
Compare cylinder sizes
The ideal LP/HP swept-volume ratio is 5.477:1. With equal strokes, HP bore is 1/√5.477 = 0.4273 times LP bore, or 42.7%. This is a relative size, not a recommended bore or a pressure rating.
Ideal sizing versus a real machine
Staging allows heat to be removed between compression steps. It also introduces additional cylinders, valves, pipework and cooling equipment. Those features have pressure losses and maintenance needs which are absent from this ideal calculation.
Clearance gas re-expands before fresh air enters. The demonstration includes that sequence so the valves and piston motion remain understandable. It does not calculate delivered flow, leakage, shaft power or discharge temperature; those require more information than the two pressure inputs.
Questions about two-stage compression
Why is the HP cylinder smaller?
After compression and cooling, the same mass of gas occupies less volume. With the stated equal-stroke and efficiency assumptions, the HP bore decreases as the fourth root of the overall pressure ratio increases.
Can gauge pressures be entered directly?
No. Convert them to absolute pressures using the local atmospheric pressure before using the ratio equations.
Why is a valve closed during part of the outward stroke?
Gas remaining in the clearance space re-expands first. Fresh inlet flow begins when the cylinder pressure has fallen to inlet pressure.
Does this calculate motor size or a safe pressure rating?
No. The tool provides an ideal pressure split and size ratios. It does not calculate power, structural strength, cooling capacity or the allowable pressure of equipment.
References
- NPTEL: Pneumatic Systems, multistage compressors, the sequence from first stage through intercooling to the next stage.
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 173, figure 646: a historical tandem compound compressor with two single-acting stages.
The present parallel-cylinder geometry is an explanatory arrangement. The equal-ratio equations follow the ideal assumptions stated above, rather than the dimensions of the historical machine.
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