Background
The indicator diagram is the fundamental graphical representation of an engine cycle. By plotting cylinder pressure against cylinder volume (or piston position), the diagram captures the entire thermodynamic process: compression, combustion, expansion, and gas exchange. The area enclosed by the loop represents the work done by gas on the piston during one cycle.
For most of engine engineering history, indicator diagrams were captured as paper records using mechanical indicators. Today, PMI systems capture diagrams electronically every cycle, with analysis software extracting parameters automatically.
This article covers the structure of indicator diagrams from slow-speed two-stroke marine engines, the parameters extracted, common pathological patterns, and the diagnostic interpretations.
Diagram phases
A complete two-stroke indicator diagram has these phases:
Compression
Starting from BDC (bottom dead centre) or scavenge port closing (whichever comes later), the piston moves upward. Cylinder volume decreases; pressure rises.
The compression process is approximately polytropic:
P × V^n = constant
For ideal adiabatic compression of air, n = 1.40. In a real cylinder with heat loss to walls, n is somewhat lower (typically 1.30 to 1.36). The polytropic index n can be extracted from the slope of the compression line on a log-P log-V plot.
Compression ends approximately at TDC. Pressure at TDC is Pcomp.
Combustion
Around TDC, fuel injection begins. After a short ignition delay (typically 1-3 ms), combustion begins. Pressure rises rapidly to Pmax.
The combustion phase has three sub-phases:
- Premixed combustion: ignition delay allows fuel-air mixing; mixture burns rapidly when ignited
- Diffusion combustion: continuing fuel injection burns at the spray-air interface
- Late combustion: tail-end combustion of remaining fuel
For modern engines, combustion is largely complete within 30-50°CA after TDC.
Expansion
After combustion, the piston descends and cylinder volume increases. Pressure decreases approximately polytropically:
P × V^n = constant (with n typically 1.25-1.30)
The expansion line is the longest part of the diagram and carries most of the work output.
Blowdown
When the exhaust valve opens (typically 95-115° BBDC), pressure drops rapidly as exhaust gas blows down to manifold pressure. The blowdown is brief (a few crank degrees) but pressure drops by 10+ bar.
Scavenging
The cylinder enters its scavenge phase. Scavenge ports open, fresh air enters, and combustion residuals leave through the exhaust valve. Cylinder pressure stabilises at scavenge receiver pressure (typically 3-4 bar absolute at full load).
Pre-compression
After both ports and exhaust valve close, the piston moves upward. Cylinder pressure rises along the compression line.
Loop closure
The loop closes back to its starting point, completing one cycle. The area enclosed is the cycle work.
Parameter extraction
IMEP (Indicated Mean Effective Pressure)
IMEP is calculated as:
IMEP = W_cycle / V_swept
where W_cycle is the area enclosed by the PV diagram (positive only above the gas exchange phase) and V_swept is the cylinder swept volume.
Modern engines achieve IMEP of 22-24 bar at full load. Differences between cylinders’ IMEP values reveal load imbalances.
Pcomp and Pmax
Pcomp is the pressure at TDC immediately before injection. Pmax is the maximum pressure achieved during combustion.
The ratio Pmax/Pcomp is approximately 1.3-1.5 for modern engines. Higher ratios indicate aggressive combustion; lower ratios indicate slower combustion.
Pressure rise rate
The maximum rate of pressure rise during combustion is calculated:
(dP/dCA)_max
For modern engines, target maximum pressure rise rate is below 10-12 bar/CA. Higher rates produce diesel knock and component fatigue.
Polytropic indices
The compression and expansion polytropic indices reveal heat transfer characteristics:
- n_compression: 1.30-1.36 typical (heat losses cool the compression)
- n_expansion: 1.25-1.30 typical (heat losses cool the expansion)
Significant deviations indicate cooling problems or chamber condition issues.
Heat release rate
By differentiating the cylinder pressure (with appropriate volume, mass, and thermodynamic corrections), the heat release rate dQ/dCA is calculated. The integral over the combustion phase is the cumulative heat release Q.
Modern analysis software produces heat release rate plots from each indicator diagram. The peak rate, the timing of peak release, and the duration of release are all important diagnostic parameters.
Indicated power
Indicated power per cylinder:
P_indicated = IMEP × V_swept × n_cycles_per_second
Sum across cylinders gives total indicated power. The difference between indicated and brake power is the friction power, indicating engine mechanical efficiency.
Common pathological patterns
Late combustion
If combustion continues into the expansion phase rather than completing near TDC, the indicator diagram shows:
- Lower Pmax than expected
- Slower pressure decay during expansion
- Higher exhaust temperature
- Reduced thermal efficiency
Causes: late injection timing, poor atomisation, low cetane fuel, excessive ignition delay.
Early combustion (knock)
If combustion begins too early (often pre-ignition before injection), the diagram shows:
- High pressure rise rate
- Pressure ringing/oscillation patterns
- High Pmax
- Risk of mechanical damage
Causes: combustion chamber hot spots, advanced timing, deposit accumulation, fuel additive issues.
Misfire
If a cylinder fails to ignite (fuel injected but combustion fails to start or develop), the diagram shows:
- Continuation of compression line through TDC
- Slight pressure peak from compression alone
- No significant Pmax rise
- IMEP near zero (or negative)
Causes: fuel injector failure, gas charge issues (in dual-fuel), insufficient combustion temperature.
Ignition delay too long
If ignition delay is excessive (fuel injected but ignition delayed), the diagram shows:
- Compression line continues longer than expected
- Combustion when it occurs is rapid (premixed combustion of accumulated fuel)
- Very high pressure rise rate
- Knock-like patterns
Causes: low cetane fuel, low charge temperature, injection too late.
Compression decay
A slow decline in Pcomp over hours/days indicates:
- Ring or liner wear (compression leak)
- Exhaust valve seat erosion
- Gradual deposit changes
Trends are visible in long-term IMEP and Pcomp plots.
Exhaust valve leakage
A slight pressure decay during compression (before TDC) suggests:
- Exhaust valve not seating fully
- Gas leakage through valve seat
- Low Pcomp results
Confirmation: cold compression test, valve seat inspection.
Cylinder cover gasket leak
If the cover gasket leaks, gas escapes but at relatively constant rate. The Pcomp is reduced; expansion pressure traces also reduced.
Diagnostic value
Daily monitoring
Engineers review indicator diagrams as part of daily engine condition monitoring. Routine display includes:
- PV diagram per cylinder
- Pcomp, Pmax, IMEP for each cylinder
- Cylinder-to-cylinder comparison
- Trend over time
Troubleshooting
When a problem arises (e.g. SFOC rise, exhaust temperature anomaly), indicator diagrams are the first diagnostic tool:
- Compare current diagram to baseline
- Look for asymmetric pattern (one cylinder different from others)
- Check ignition delay, peak pressure timing, expansion characteristics
- Identify root cause
Performance verification
After major maintenance:
- Indicator diagrams confirm restored performance
- New baseline established
- Ongoing monitoring resumes
Optimisation
Indicator diagrams support performance optimisation:
- Verify benefits of fuel adjustments
- Confirm timing changes have intended effect
- Compare different operating regimes
Modern indicator analysis
Software automation
Modern PMI software automates much of the analysis:
- Real-time IMEP calculation
- Cylinder balance trending
- Automatic alarm on parameter deviation
- Heat release calculation
- Comparison to baseline
Cloud analytics
Data uploaded to cloud systems supports:
- Fleet-wide performance comparison
- Predictive maintenance algorithms
- Optimisation recommendations
- Continuous improvement
Integration with other data
Indicator diagram data integrates with:
- Fuel consumption metrics
- Exhaust temperature
- Turbocharger performance
- Oil sample data
- Vibration monitoring
The combined picture provides comprehensive engine condition assessment.
Related Calculators
- Indicator Diagram Calculator
- Mean Indicated Pressure (IMEP) Calculator
- Polytropic Compression Calculator
- Heat Release Rate Calculator
- Indicated Power Calculator
See also
- Engine Performance Monitoring (PMI) on Marine Engines
- Cylinder Peak Pressure (Pmax) Analysis on Marine Engines
- Cylinder Compression Pressure (Pcomp) Analysis on Marine Engines
- Engine Power and BMEP Relationships
References
- Heywood, J. B. (2018). Internal Combustion Engine Fundamentals (2nd ed.). McGraw-Hill.
- MAN Energy Solutions. (2023). Indicator Diagram Analysis Manual. MAN Energy Solutions.
- WinGD. (2023). X-Series Performance Analysis Reference. Winterthur Gas & Diesel.
- Lamb, A. (2009). Marine Diesel Engine Performance Monitoring. SNAME.
- Lloyd’s Register. (2022). Cylinder Pressure Monitoring Best Practices.