Skip to main content

Engine performance parameters and efficiencies

Short answer

Indicated power is cylinder power, IP = pmi L A k N n/1000 kW; brake power is shaft output, BP = 2πNT/60000 kW; friction power FP = IP-BP. Mechanical efficiency ηm = BP/IP; indicated and brake thermal efficiencies are IP/(mf·CV) and BP/(mf·CV). Volumetric efficiency ηv = actual intake air volume / swept volume; relative efficiency ηrel = ηith/ηair-standard; bsfc = 3600 mf/BP kg/kWh.

Define the following for an internal combustion engine and give the formula for each: indicated power, brake power, friction power, mean effective pressure, mechanical efficiency, indicated and brake thermal efficiency, volumetric efficiency, relative efficiency and specific fuel consumption.

Let pmp_m be the mean effective pressure (Pa), LL the stroke (m), AA the piston area (m2^2), NN the speed (rev/s), k=1k = 1 for two-stroke and k=12k = \tfrac12 for four-stroke, nn the number of cylinders.

TermDefinitionFormula
Indicated power (IP)Power developed inside the cylinder on the piston, from the indicator diagramIP=pmiLA(kN)n1000IP = \dfrac{p_{mi} L A (kN) n}{1000} kW
Brake power (BP)Power available at the output shaft, measured by a dynamometerBP=2πNT1000BP = \dfrac{2\pi N T}{1000} kW
Friction power (FP)Power lost in friction, pumping and auxiliariesFP=IP−BPFP = IP - BP
Mean effective pressureHypothetical constant pressure which, acting on the piston over the whole power stroke, gives the same net work per cyclepm=work per cycleswept volumep_m = \dfrac{\text{work per cycle}}{\text{swept volume}}
Mechanical efficiencyFraction of indicated power delivered at the shaftηm=BP/IP=1−FP/IP\eta_m = BP/IP = 1 - FP/IP
Indicated thermal efficiencyIndicated work per energy in the fuelηith=IPm˙f⋅CV\eta_{ith} = \dfrac{IP}{\dot{m}_f \cdot CV}
Brake thermal efficiencyBrake work per energy in the fuelηbth=BPm˙f⋅CV=ηmηith\eta_{bth} = \dfrac{BP}{\dot{m}_f \cdot CV} = \eta_m \eta_{ith}
Volumetric efficiencyActual air drawn in (at ambient conditions) per swept volumeηv=V˙a,actualVs kN n\eta_v = \dfrac{\dot{V}_{a,actual}}{V_s\,kN\,n}
Relative (efficiency ratio)Indicated thermal efficiency per air-standard efficiencyηrel=ηith/ηair-std\eta_{rel} = \eta_{ith}/\eta_{air\text{-}std}
Specific fuel consumptionFuel used per unit power per hourbsfc=3600 m˙fBPbsfc = \dfrac{3600\,\dot{m}_f}{BP} kg/kWh

Notes:

  • m˙f\dot{m}_f is the fuel mass flow (kg/s) and CVCV the calorific value in kJ/kg.
  • Brake mean effective pressure: bmep=1000 BPLAkNnbmep = \dfrac{1000\,BP}{L A k N n} Pa (BP in kW). Using IP instead gives the indicated mean effective pressure pmip_{mi}.
  • A typical SI engine has ηm\eta_m = 80-90%, ηbth\eta_{bth} = 25-30%, bsfc = 0.27-0.35 kg/kWh; a diesel engine has ηbth\eta_{bth} = 30-40%, bsfc = 0.2-0.25 kg/kWh.

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Internal Combustion Engines chapter 8 questions →