Knowledge / Ship systems

Diesel indicator diagrams: indicated power, brake power and diagnostic limits

Read pressure–volume work, IMEP and shaft power together, with a six-cylinder calculation and checks on crank-angle reference, cycle definition and measurement uncertainty.

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A diesel indicator diagram describes what the gas in a cylinder does during a cycle. It can reveal an uneven contribution between cylinders or a change in combustion, but it does not directly measure useful shaft output. Reading it well requires three boundaries: the part of the cycle integrated, the mechanical output being compared and the measurement chain that produced the curve. These boundaries matter aboard ship because a plausible pressure trace can still yield a misleading power estimate.

Read work from the pressure–volume loop

Cylinder pressure acts on the piston while cylinder volume changes. The indicated work for a selected closed cycle is Wᵢ = ∮ p dV. Pressure in pascals multiplied by volume change in cubic metres gives joules. Expansion contributes positive work with this sign convention; compression contributes negative work. The enclosed area, including its direction, matters. A tall narrow pressure peak is therefore not equivalent to a large positive cycle-work area. Kistler’s measurement overview distinguishes peak pressure from indicated mean effective pressure and explains the pressure–volume basis of piston work.

A pressure–crank-angle plot is often more convenient for seeing timing, whereas a pressure–volume plot makes the work interpretation visible. Moving between them requires the cylinder geometry and a consistent crank-angle reference. Connecting sampled points on a screen does not establish that those inputs are correct. Keep the underlying sampling, geometry and reference information with the exported diagram so another reader can reproduce the calculation.

Define gross and net before comparing IMEP

Indicated mean effective pressure, IMEP, is indicated work divided by swept volume: IMEP = Wᵢ/Vd. It is an equivalent work-per-displacement quantity, not the average pressure shown by an ordinary gauge. For a four-stroke engine, a high-pressure compression/expansion loop and the full cycle do not represent the same accounting boundary. Xarin’s indication documentation distinguishes gross, pumping and net IMEP. State the integration interval and the sign convention for pumping work instead of treating every number labelled IMEP as interchangeable.

Gas exchange may consume net work, but the pressure conditions of a boosted engine can alter the sign and magnitude of the gas-exchange contribution. Avoid hard-coding a negative pumping value into every engine example. For a two-stroke engine, port and valve events also require an engine-appropriate cycle definition. When comparing cylinders or dates, use the same definition, geometry and software treatment throughout.

Convert cycle work into power with the correct cycle rate

For total engine swept volume Vd, mean IMEP pᵢ and rotational speed n in revolutions per second, indicated power is Pᵢ = pᵢ Vd n/k. Here k is two revolutions per cycle for a four-stroke engine and one for a two-stroke engine. MIT’s engine-operating notes give the corresponding mean-effective-pressure, displacement and cycle-rate relationship for brake output. The dimensional check is Pa × m³ × s⁻¹ = W. If individual cylinders have different IMEP, calculate and sum their contributions rather than assuming balance.

A frequent spreadsheet error combines revolutions per minute with a per-second formula. Another uses the swept volume of one cylinder while describing the result as total engine power. A third counts both the cylinder number and the already-total displacement. These are different errors, so one generic plausibility check may miss them. Write the displacement basis and cycle factor beside the numerical result.

Work through a hypothetical six-cylinder example

Assume six identical cylinders, each with bore 0.320 m and stroke 0.400 m. The swept volume per cylinder is π × 0.320² × 0.400/4 = 0.03217 m³. Total swept volume is 0.19302 m³. Take a four-stroke speed of 750 r/min, equal to 12.5 revolutions per second or 6.25 cycles per second per cylinder. Suppose every cylinder has a consistently evaluated net IMEP of 20.0 bar, equal to 2.00 × 10⁶ Pa.

Each cylinder then produces approximately 64.34 kJ of net indicated work per cycle and 402.1 kW of indicated power. The six-cylinder total is 2,412.7 kW. This number follows from the invented inputs; it is not a rating for an identified engine. Changing only the cycle factor to a two-stroke value would double the arithmetic result, but it would not describe a physical conversion of this engine. Cylinder charging, thermal loading and the actual operating envelope would all need their own model.

Compare against shaft power at the same boundary

Now assume independently measured brake power at the engine output shaft is 2,200 kW at the same speed and stable operating point. The difference from net indicated power is approximately 212.7 kW, and the ratio Pᵦ/Pᵢ is about 91.2%. With consistent definitions, this is an illustrative mechanical-efficiency comparison. It is not overall fuel-to-shaft efficiency, which also requires the fuel-energy input. Nor does the difference identify which bearing, ring pack or auxiliary consumes the loss.

Shaft power can be cross-checked from torque using P = 2πnT. At 750 r/min, 2,200 kW corresponds to approximately 28.01 kN·m. Electrical generator output is another boundary: generator and any intermediate drive losses separate it from engine brake output. Comparing electrical kW directly with indicated kW and naming the entire difference engine friction would mix those boundaries. Record which auxiliaries are mechanically driven, externally powered or excluded from the measurement.

Treat crank-angle reference as a measurement variable

Pressure must be assigned to the right piston position. A crank-angle offset changes how pressure is paired with dV and can bias the work integral. A Kistler technical paper’s publicly indexed introduction demonstrates sensitivity of IMEP and inferred energy balance to top-dead-centre allocation. Its numerical sensitivity example is not a universal tolerance for every marine engine. The useful general point is that accurate pressure amplitude alone cannot rescue an incorrectly phased trace.

Check whether the reference is measured at a particular shaft location, how individual-cylinder offsets are handled and whether the interpretation accounts for relevant deformation under load. Pressure-transducer sensitivity, thermal effects and the pressure passage can also affect the result. Averaging repeated cycles reduces some random variation; it does not remove a common calibration error or a fixed crank-angle offset. A smooth mean curve can therefore conceal a systematic problem.

Use invariance and sensitivity as calculation checks

For a genuinely closed volume cycle, adding one constant pressure offset C changes the integral by C∮dV, which is zero. That mathematical check is useful for testing an integration routine. It does not mean pressure referencing is irrelevant to every combustion result: absolute pressure, heat-release calculations, leakage models and imperfectly closed integration intervals can respond differently. Keep the precise claim attached to the closed-loop work calculation.

Holding other inputs fixed, a 1% change in IMEP produces a 1% change in the calculated indicated power. Because swept volume depends on bore squared, a small 1% bore error produces roughly a 2% volume and power error. These simple sensitivities help prioritize verification, but they are not a complete uncertainty budget. Correlated errors between cylinders, cycle variability and model assumptions require separate treatment; six cylinders do not automatically reduce a common sensor bias by the square root of six.

Separate a symptom from a diagnosis

Imagine one cylinder shows lower IMEP while its exhaust temperature rises. Late heat release is one possible explanation, but the pair of observations does not uniquely prove an injector fault. Changes in trapped air, sealing, combustion timing, measurement alignment or operating condition can produce overlapping symptoms. The diagram should organize competing explanations and the evidence needed to distinguish them. It should not become an automatic instruction to increase fuel delivery to that cylinder.

Compare repeatable readings at matched speed, load and relevant temperatures. Preserve both individual-cycle behaviour and the average where available. Examine whether the apparent imbalance survives a measurement-chain check, whether other independent signals agree and whether the engine’s approved limits constrain further investigation. An arithmetic balance of cylinder powers is useful, but equalizing numbers alone can conceal a real thermal or mechanical limit.

Make the record reproducible

A useful record identifies the engine and measurement location, date, operating state, bore and stroke basis, cylinder count, cycle type, pressure units, speed units, crank-angle reference, integration interval and software convention. Include the actual diagrams and the separately measured shaft-output boundary. If a corrected sensor factor changes a historical trend, retain the correction and its reason rather than silently replacing the old values.

The final interpretation should answer three specific questions: what work was calculated, how certain is the comparison and which fault hypotheses remain unresolved? This turns an indicator diagram into traceable engineering evidence. It also keeps a worked educational calculation in its proper role: explaining relationships, while equipment-specific limits and actions remain tied to the applicable engine documentation.

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