---
title: "Engine performance parameters and efficiencies"
subject: "Internal Combustion Engines"
chapter: 8
key: "semester_6/internal_combustion_engines:engine-performance-parameters-definitions"
source: https://www.bctengineer.com/q/semester_6/internal_combustion_engines/engine-performance-parameters-definitions
site: BCT Engineering
---

# Engine performance parameters and efficiencies

Internal Combustion Engines · Chapter 8: Engine performance and testing of engines

- Asked in: year not given, 6 marks
- Video: [IC Engine Performance Parameters (Indicated Power, Brake Power, Friction Power & Efficiency)](https://www.youtube.com/watch?v=uLqdBl21Rk0) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/internal_combustion_engines/engine-performance-parameters-definitions
- Whole chapter: https://www.bctengineer.com/md/semester_6/internal_combustion_engines/chapter-8

## Question

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.

## 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.

## Answer

Let $p_m$ be the mean effective pressure (Pa), $L$ the stroke (m), $A$ the piston area (m$^2$), $N$ the speed (rev/s), $k = 1$ for two-stroke and $k = \tfrac12$ for four-stroke, $n$ the number of cylinders.

| Term | Definition | Formula |
|---|---|---|
| Indicated power (IP) | Power developed inside the cylinder on the piston, from the indicator diagram | $IP = \dfrac{p_{mi} L A (kN) n}{1000}$ kW |
| Brake power (BP) | Power available at the output shaft, measured by a dynamometer | $BP = \dfrac{2\pi N T}{1000}$ kW |
| Friction power (FP) | Power lost in friction, pumping and auxiliaries | $FP = IP - BP$ |
| Mean effective pressure | Hypothetical constant pressure which, acting on the piston over the whole power stroke, gives the same net work per cycle | $p_m = \dfrac{\text{work per cycle}}{\text{swept volume}}$ |
| Mechanical efficiency | Fraction of indicated power delivered at the shaft | $\eta_m = BP/IP = 1 - FP/IP$ |
| Indicated thermal efficiency | Indicated work per energy in the fuel | $\eta_{ith} = \dfrac{IP}{\dot{m}_f \cdot CV}$ |
| Brake thermal efficiency | Brake work per energy in the fuel | $\eta_{bth} = \dfrac{BP}{\dot{m}_f \cdot CV} = \eta_m \eta_{ith}$ |
| Volumetric efficiency | Actual air drawn in (at ambient conditions) per swept volume | $\eta_v = \dfrac{\dot{V}_{a,actual}}{V_s\,kN\,n}$ |
| Relative (efficiency ratio) | Indicated thermal efficiency per air-standard efficiency | $\eta_{rel} = \eta_{ith}/\eta_{air\text{-}std}$ |
| Specific fuel consumption | Fuel used per unit power per hour | $bsfc = \dfrac{3600\,\dot{m}_f}{BP}$ kg/kWh |

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

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is mechanical efficiency?
   A. IP/BP
   B. BP/IP = 1 - FP/IP
   C. FP/BP
   D. BP/fuel energy
   Answer: B. Mechanical efficiency is the fraction of indicated power delivered at the shaft. (Key point: Mechanical efficiency)

2. How is friction power obtained?
   A. FP = IP + BP
   B. FP = IP - BP
   C. FP = BP - IP
   D. FP = BP x efficiency
   Answer: B. Friction power (including pumping and auxiliaries) is the difference between indicated and brake power. (Key point: Friction power)

3. How is brake thermal efficiency related to the other efficiencies?
   A. eta_bth = eta_ith / eta_m
   B. eta_bth = eta_m x eta_ith
   C. eta_bth = eta_ith + eta_m
   D. eta_bth = eta_v x eta_m
   Answer: B. BP/(mf CV) = (BP/IP)(IP/(mf CV)) = eta_m x eta_ith. (Key point: Brake thermal efficiency relation)

4. What is the relative efficiency?
   A. Brake thermal efficiency per mechanical efficiency
   B. Indicated thermal efficiency per air-standard efficiency
   C. Actual air per swept volume
   D. Fuel per unit power per hour
   Answer: B. eta_rel = eta_ith / eta_air-standard; volumetric efficiency is air drawn per swept volume and sfc is fuel per power-hour. (Key point: Relative efficiency)

## Related in Internal Combustion Engines

- [Efficiency ratio and specific fuel consumption](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Arelative-efficiency-sfc-numerical) — Internal Combustion Engines, chapter 8
- [IP, BP and efficiencies of a petrol engine](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Aindicated-brake-power-efficiency-numerical) — Internal Combustion Engines, chapter 8
- [Willans line and friction power estimation](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Awillans-line-friction-power-methods) — Internal Combustion Engines, chapter 8
- [Volumetric efficiency from orifice air measurement](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Avolumetric-efficiency-orifice-air-consumption) — Internal Combustion Engines, chapter 8
- [Morse test for friction power](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Amorse-test-four-cylinder-numerical) — Internal Combustion Engines, chapter 8
- [Otto cycle efficiency and mean effective pressure](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Aotto-cycle-efficiency-numerical) — Internal Combustion Engines, chapter 1

## Related in other subjects

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- [Two-stroke motoring test with specific fuel consumption](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Amotoring-test-sfc) — Power Plant Equipment, chapter 5, asked 6×
- [Engine test: four-cylinder, 85% mechanical efficiency](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aengine-test-85-percent) — Power Plant Equipment, chapter 5, asked 5×
- [Turbojet thrust, efficiencies and fuel consumption](https://www.bctengineer.com/question.md?key=semester_7%2Fturbo_machines%3Aturbojet-thrust-efficiencies-numerical) — Turbo Machines, chapter 5