A single-stage compressor loses delivery as pressure rises, because of clearance volume: the compressed air left at the top of the stroke re-expands and fills part of the next intake. With 5% clearance a single cylinder delivers about 80% of its swept volume at an 8:1 absolute ratio and about 63% at 16:1, and at 7 bar gauge a 100 mm bore puts 5,498 N on the piston and connecting rod.
Part of Pneumatic Systems
Designing a one-cylinder air compressor: sizing the sweep, controlling clearance volume, and checking the load on the parts that carry it.
Clearance Volume Is What Limits One Cylinder
At top of stroke the piston cannot touch the head, so some compressed air stays in the gap and in the valve passages. On the next stroke that air expands back down before fresh air can enter, which wastes part of the stroke. The standard result, recalled from compressor texts and not from this corpus, is
Volumetric efficiency = 1 - c x (r^(1/n) - 1)
where c is the clearance volume as a fraction of the swept volume, r is the absolute pressure ratio and n is the exponent of re-expansion, about 1.3 for air in a real cylinder.
Worked example. Take c = 0.05, which is a 5 mm gap on a 100 mm stroke. This is an assumed value for illustration; measure yours.
| Ratio r | Gauge pressure | r^(1/1.3) | Volumetric efficiency |
|---|---|---|---|
| 2 | 1 bar | 1.70 | 96.5% |
| 4 | 3 bar | 2.90 | 90.5% |
| 8 | 7 bar | 4.95 | 80.2% |
| 16 | 15 bar | 8.42 | 62.8% |
Check r = 8: 8^(1/1.3) = e^(2.0794 / 1.3) = e^1.5995 = 4.95, so the efficiency is 1 - 0.05 x (4.95 - 1) = 0.80. The cylinder stops delivering altogether where c x (r^(1/n) - 1) reaches 1, which for this clearance is r = 52. So the cylinder delivers about 80% of its swept volume at 8:1 and about 63% at 16:1. Heat and power set the practical limit long before the cutoff, which is why this article stops at about 8 bar and the two-stage design takes over beyond it.
Reducing clearance. Shave the piston crown and head so that they meet to within a millimetre or two, keep the valve plate thin, and keep the valve passages short.
Sizing the Cylinder
The carrier gives 75-150 mm bore and 100-150 mm stroke. At 300 RPM (5 revolutions per second), swept volume and the ideal power at 7 bar gauge (adiabatic, r = 8, working in Gas Laws in Practice) are:
| Bore x stroke | Swept volume | Free air at 300 RPM | Ideal power at r = 8 |
|---|---|---|---|
| 75 x 100 mm | 0.442 L | 132.5 L/min | 636 W |
| 100 x 100 mm | 0.785 L | 235.6 L/min | 1,130 W |
| 150 x 150 mm | 2.651 L | 795.2 L/min | 3,814 W |
Check the 150 x 150 row: swept volume = π / 4 x 0.15² x 0.15 = 0.002651 m³; flow = 0.002651 x 5 = 0.01325 m³/s; power = 101,325 x 3.5 x 0.01325 x 0.8114 = 3,814 W. Before choosing the large cylinder, ask where 3.8 kW comes from; the corpus’s 785 W water wheel falls far short. Multiply by the volumetric efficiency for the real delivery.
The Loads the Parts Must Carry
The pressure on the piston crown is gauge pressure times area. For the 100 mm bore:
- Area = π / 4 x 0.1² = 0.007854 m²
- Force at 7 bar gauge (700,000 Pa) = 700,000 x 0.007854 = 5,498 N
That load goes through the connecting rod, the crank pin, the main bearings and the head studs. The rod works in compression and must not buckle; the arithmetic is in Piston and Rod Design. The head studs together must hold at least that force plus a margin. The corpus offers a safety-factor band of 4-8 for machine components under repeated loading (Safety Factors).
Valves and Seals
- Valves: reed or plate valves of 0.3-0.5 mm spring-steel strip per the carrier. A valve that opens late loses delivery; one that slams shut breaks.
- Piston rings: cast iron rings in cast iron grooves. The corpus notes that a cup-shaped leather piston seal works to 5-7 bar (Compressed Air), so leather is an option at the low end but not for 8 bar.
- Cylinder finish: the carrier specifies better than 0.8 μm Ra and 0.05 mm piston clearance.
Common Mistakes
- Large clearance volume. A thick gasket or a deep valve pocket costs delivery, and the loss grows with pressure.
- Sizing the crank for the average load. The rod and crank see the peak, 5,498 N for the 100 mm bore, on every stroke.
- Raising the relief setting to get more pressure. The cylinder will deliver less air at the higher ratio while the heat and the load climb.
Safety
The head joint carries the full pressure force
The cylinder head is pushed off by gauge pressure times bore area, 5,498 N for a 100 mm bore at 7 bar gauge. Use studs of known strength, tighten them evenly in a cross pattern, and do not reuse stretched or cracked studs. Never run the compressor without the relief valve, and never place a shut-off valve between the cylinder and its relief valve.
What’s Next
- Learn next: Two-Stage with Intercooler — beyond what one cylinder can do
- Combine with: Receiver Tank Construction — where the air goes