Hong Life CalculatorsUnderstanding the compression ratio to cranking pressure calculator — concept and principle
A compression test gauge reads cylinder pressure while the engine is cranked. This calculator estimates that reading from the static compression ratio, using the dynamic compression ratio after the intake valve closes and a polytropic compression model.
How it is calculated
- Crank angle at intake closing: θ = 180° − intake closing angle (° after BDC).
- Piston distance from TDC: s = a + l − (a cos θ + √(l² − a² sin² θ)), with crank radius a = stroke ÷ 2 and rod length l.
- Dynamic compression ratio DCR = 1 + (rc − 1) × s ÷ stroke.
- Absolute pressure p = patm × DCR^n; gauge reading = p − patm.
The principle
Compression only starts when the intake valve closes, which happens after bottom dead centre, so the effective stroke is shorter than the full stroke. The slider-crank geometry gives how far the piston still has to travel at that moment. During cranking, heat flows to the cylinder walls and some gas leaks past the rings, so the pressure rises less steeply than in an adiabatic compression; a polytropic exponent around 1.2 is a common educational assumption.
Worked example
Default inputs: static ratio 10:1, intake closes 50° after BDC, stroke 86 mm, rod 145 mm, atmosphere 14.7 psi, n = 1.2.
- θ = 180 − 50 = 130°; a = 43 mm.
- s = 43 + 145 − (43 cos 130° + √(145² − 43² sin² 130°)) ≈ 74.4 mm, so 86.5% of the stroke remains.
- DCR = 1 + 9 × 0.8655 ≈ 8.79.
- p = 14.7 × 8.79^1.2 ≈ 199.6 psi absolute, so the gauge reads about 185 psi (12.7 bar).
- Using the static ratio instead: 14.7 × 10^1.2 − 14.7 ≈ 218 psi.
| Static compression ratio (:1) | Estimated cranking pressure (psi gauge) |
|---|---|
| 2.5 | 25 |
| 5 | 74 |
| 7.5 | 127 |
| 10 | 185 |
| 12.5 | 245 |
| 15 | 308 |
| 20 | 440 |
How to read the result
Real readings depend on cranking speed, battery, ring and valve sealing, altitude, temperature and gauge hose volume. The most useful check is consistency between cylinders: many service guides look for readings within about 10% of each other. A cylinder well below the others suggests a leak.
Common mistakes
- Comparing a real gauge reading directly with this estimate.
- Using the advertised intake closing at a lift threshold that differs from the actual seating point.
- Forgetting that the gauge shows pressure above atmosphere.
- Testing a cold engine with the throttle closed, which lowers readings.
Frequently asked questions
What compression should a 10:1 engine have?
Typically somewhere around 150–200 psi on a gauge depending on cam timing and conditions; compare cylinders rather than chasing one number.
What is dynamic compression ratio?
The ratio of compression from the moment the intake valve closes, not from bottom dead centre.
Why use n = 1.2 instead of 1.4?
During slow cranking, heat loss and leakage make the compression less than adiabatic.
Sources: Heywood, J. B., Internal Combustion Engine Fundamentals, 2nd ed. McGraw-Hill (2018) (slider-crank kinematics, compression) · Stone, R., Introduction to Internal Combustion Engines, 4th ed. Palgrave Macmillan