Indicated vs. Brake Work: IMEP & BMEP

The cylinder makes more work than the crankshaft delivers — and two pressures, IMEP and BMEP, measure each side of that gap.

Automotive EngineeringICE PerformanceFree preview
⏱️ About 18 min
Indicated vs. Brake Work: IMEP & BMEP — illustration
Decorative illustration.

Bolt a dynamometer to the crankshaft and you measure one number; fit a pressure sensor in the cylinder and you measure another, always higher. The difference is friction and pumping — the engine's tax on itself.

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The big idea: Indicated work (from cylinder pressure, IMEP) exceeds brake work (at the shaft, BMEP) by the friction and pumping losses; the ratio is mechanical efficiency, and IMEP/BMEP let you compare engines of any size on a pressure basis.
🎯 By the end, you'll be able to
  • Distinguish indicated, brake, and friction work
  • Define IMEP and BMEP and compute power from them
  • Compute mechanical efficiency
  • Explain why BMEP is a fair engine-comparison metric

Two power numbers, one gap

An engine's indicated power is the work the combustion gas does on the piston, found by integrating cylinder pressure over volume (the indicator diagram). The brake power is what actually comes out at the crankshaft — measured by a dynamometer — and it is always less, because the engine spends some of its indicated work overcoming its own internal friction (pistons, bearings, valve train) and pumping losses (drawing air in and pushing exhaust out). That difference is the friction power. So brake power = indicated power − friction power, and the ratio brake/indicated is the mechanical efficiency — typically 80–90% at full load, falling at light load where friction is a bigger slice of a smaller pie.

\[ P_b=P_i-P_f,\qquad \eta_m=\frac{P_b}{P_i},\qquad P=\frac{p_{\text{MEP}}\,V_d\,N}{n_R}\;\;(\times\tfrac{1}{60}\text{ for rpm}) \]
Brake power P_b = indicated P_i − friction P_f; mechanical efficiency η_m = P_b/P_i. Power follows from the relevant MEP, displaced volume V_d, engine speed N (rpm), and strokes per cycle n_R (2 for 2-stroke, 4 for 4-stroke).

MEP: the size-independent yardstick

Raw torque or power depends on engine size, so they're poor for comparison. Mean effective pressure (MEP) is the trick: it's the constant pressure that, acting over one power stroke, would produce the cycle's work. Because MEP is a pressure, it normalises away the displacement — a 2-litre engine and a 5-litre engine with the same BMEP are equally efficient at turning displacement into work. IMEP uses indicated work; BMEP uses brake work; the difference is the FMEP (friction MEP). Naturally-aspirated petrol engines run ~8–13 bar BMEP at full load; turbos push higher; diesels sit a little higher still. A high BMEP at a given speed means the engine is working its displacement hard.

Indicated work (IMEP)Brake (BMEP)Friction (FMEP)IMEP = BMEP + FMEP; η_m = BMEP/IMEP
Indicated (cylinder-pressure) work minus friction/pumping losses equals brake (shaft) work. IMEP > BMEP by FMEP; mechanical efficiency = BMEP/IMEP.
🔑 BMEP is the great equaliser

Two engines: a 1.5-litre turbo making 180 N·m, and a 3.0-litre naturally-aspirated making 300 N·m. Which works its displacement harder? Convert torque to BMEP and the smaller, torquier (forced-induction) engine usually wins. That is why BMEP — not raw torque — is how engineers judge whether an engine is stressed, efficient, or leaving performance on the table. It's also why a turbocharged engine can match a much larger naturally-aspirated one: forced induction raises BMEP, cramming more air (and fuel) into the same displaced volume.

📝 Worked example: A 4-stroke engine has indicated power 95 kW and brake power 80 kW. Find the friction power and the mechanical efficiency.
  1. Friction power P_f = P_i − P_b = 95 − 80 = 15 kW
  2. Mechanical efficiency η_m = P_b / P_i = 80 / 95 = 0.842 (84.2%)
✓ P_f = 15 kW; η_m ≈ 84%
✏️ Practice: A 4-stroke, 2.0-litre (V_d = 0.002 m³) engine runs at 4000 rpm with a BMEP of 10 bar (1.0×10⁶ Pa). Estimate the brake power using P = (BMEP·V_d·N)/(4·60) (the 4 for 4-stroke, 60 for rpm→rps).
W
Solution
  1. P = (1.0×10⁶ × 0.002 × 4000) / (4 × 60) = (8.0×10⁹ × 0.002... )
  2. = (1.0×10⁶ × 0.002 × 4000) / 240 = 8.0×10⁶ / 240 = 33,333 W ≈ 33.3 kW

Check your understanding

1. Mechanical efficiency at light throttle is usually lower than at full throttle because:
Friction (and pumping) losses don't shrink much with load, so at light load they consume a larger fraction of the smaller indicated output — η_m falls.
2. BMEP is a useful comparison metric because it:
MEP converts work per cycle to an equivalent pressure, cancelling displacement — so BMEP compares how hard engines of any size work their volume.
✅ Key takeaways
  • Indicated work (cylinder pressure, IMEP) > brake work (shaft, BMEP) by friction/pumping (FMEP)
  • Brake power = indicated − friction; mechanical efficiency η_m = brake/indicated (~80–90% full load, less at light load)
  • MEP normalises out displacement, so IMEP/BMEP compare engines of any size on a pressure basis
  • Forced induction raises BMEP, letting a small engine match a larger naturally-aspirated one
➡️ Power and MEP quantify the engine's output; the next lesson asks how well it breathes — volumetric efficiency — and how that, with the cycle, sets the overall thermal efficiency.