The Indicator Diagram & Mean Effective Pressure

Outside the engine, shaft torque is easy enough to measure with a torsion meter. Inside the cylinder, the work is done by hot combustion gas pushing the piston down, and that gas pressure rises and falls through the cycle in a way no external sensor sees directly. Engineers capture it with an indicator diagram: a transducer logs cylinder pressure against cylinder volume (or crank angle, converted to volume) over a full working cycle, tracing a closed p–V loop. The thermodynamic cycle fundamentals behind that loop are covered in the Material & Energy Balances course; this module focuses on what the loop tells us about engine performance.

The shape of that loop tells the engine's whole performance story at a glance. Compression lifts pressure along the upward (leftward) branch as the piston squeezes the air; combustion spikes pressure near the top at minimum volume; expansion drives pressure back down the rightward branch as the piston descends and delivers work; finally the exhaust and scavenge processes return the cylinder to its starting state. The enclosed area inside the loop is the net work delivered by the gas per cycle — literally the integral of pressure with respect to volume. A fat loop means more work; a thin or distorted one signals poor combustion, late timing, or leaking rings.

Comparing two engines by loop area is awkward because swept volumes differ, so naval architects flatten the loop into a single representative pressure. The indicated mean effective pressure pmi is defined as the loop's enclosed work divided by the cylinder's swept volume — physically, it is the average pressure that, acting at a constant value over the whole power stroke, would deliver the same work as the actual fluctuating pressure. A pmi of, say, 1.8 MPa means the cycle averages out to that steady push.

Because pmi is a pressure, multiplying it by the piston's bore area and the stroke length gives the mean force times distance — the work per power stroke. Multiply that by the number of power strokes per second and you have the indicated power: the rate at which the cylinder gas delivers mechanical work to the piston, before any of it is lost to the engine's own friction. This is the bridge between what combustion achieves inside the cylinder and the power figures used to size the ship's machinery.

The only term in the indicated-power formula that changes between engine families is the firing rate. A two-stroke fires once every revolution, so at N rpm it produces N/60 power strokes per second per cylinder. A four-stroke fires once every two revolutions, so it produces N/120. This is why the worked example's two-stroke at 120 rpm fires twice per second per cylinder, while a four-stroke research engine at 750 rpm fires 6.25 times per second — the four-stroke needs far higher speed to compete on firing frequency.

Note carefully what indicated power does and does not include. It measures the gas work reaching the piston — the pure thermodynamic deliverable of the cycle. It does not yet subtract the work the engine spends on itself: pumping air and exhaust, driving the valve train and fuel pumps, and overcoming ring and bearing friction. Those mechanical losses are the subject of the next lesson, where indicated power is converted into the brake power actually available at the engine's output flange.