---
title: "Efficiency ratio and specific fuel consumption"
subject: "Internal Combustion Engines"
chapter: 8
key: "semester_6/internal_combustion_engines:relative-efficiency-sfc-numerical"
source: https://www.bctengineer.com/q/semester_6/internal_combustion_engines/relative-efficiency-sfc-numerical
site: BCT Engineering
---

# Efficiency ratio and specific fuel consumption

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

- Asked in: year not given, 6 marks
- Video: [The Best Way To Compare Engine Efficiency - BSFC](https://www.youtube.com/watch?v=jagNsS9MxFQ) — Engineering Explained
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/internal_combustion_engines/relative-efficiency-sfc-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_6/internal_combustion_engines/chapter-8

## Question

A single-cylinder four-stroke petrol engine with a compression ratio of 7 has an indicated power of 22 kW and a brake power of 18 kW. It uses 6.2 kg/h of fuel of calorific value 44 000 kJ/kg. Calculate the mechanical efficiency, indicated and brake thermal efficiencies, the relative efficiency with respect to the air-standard Otto cycle ($\gamma = 1.4$), and the brake and indicated specific fuel consumption.

## Short answer

ηm =81.8%, ηith =29.0%, ηbth =23.8%. Air-standard Otto efficiency 1-1/7^0.4 =54.1%, so relative efficiency ηrel =53.7%. bsfc =0.344 kg/kWh, isfc =0.282 kg/kWh.

## Answer

#### Fuel energy
$$
Q_f = \dot{m}_f \times CV = \frac{6.2}{3600} \times 44\,000 = 75.78\ \text{kW}
$$

#### Efficiencies
$$
\begin{aligned}
\eta_m &= \frac{BP}{IP} = \frac{18}{22} = 0.818 \\
\eta_{ith} &= \frac{IP}{Q_f} = \frac{22}{75.78} = 0.290 \\
\eta_{bth} &= \frac{BP}{Q_f} = \frac{18}{75.78} = 0.2375
\end{aligned}
$$

#### Air-standard efficiency and relative efficiency
$$
\begin{aligned}
\eta_{Otto} &= 1 - \frac{1}{r^{\gamma-1}} = 1 - 7^{-0.4} = 0.541 \\
\eta_{rel} &= \frac{\eta_{ith}}{\eta_{Otto}} = \frac{0.290}{0.541} = 0.537
\end{aligned}
$$

The relative efficiency of 53.7% shows how well the real engine approaches the ideal cycle: the rest is lost to the real-gas properties, heat loss, finite burning time and incomplete combustion. Typical values are 50-60% for SI engines.

#### Specific fuel consumption
$$
bsfc = \frac{6.2}{18} = 0.344\ \text{kg/kWh}, \qquad isfc = \frac{6.2}{22} = 0.282\ \text{kg/kWh}
$$

**Answer:** $\eta_m$ = 81.8%, $\eta_{ith}$ = 29.0%, $\eta_{bth}$ = 23.8%, $\eta_{rel}$ = 53.7%, bsfc = 0.344 kg/kWh, isfc = 0.282 kg/kWh.

## Check yourself

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

1. What is the air-standard Otto efficiency for r = 7, gamma = 1.4?
   A. 54.1%
   B. 35%
   C. 70%
   D. 25%
   Answer: A. eta = 1 - 7^-0.4 = 0.541. (Key point: Otto efficiency)

2. How is the relative efficiency calculated and what is its value?
   A. eta_ith / eta_Otto = 0.290/0.541 = 53.7%
   B. eta_bth / eta_Otto
   C. eta_Otto / eta_ith
   D. eta_m x eta_Otto
   Answer: A. Relative efficiency uses indicated thermal efficiency: 0.290/0.541 = 0.537. (Key point: Relative efficiency)

3. What are indicated and brake thermal efficiencies?
   A. 29.0% and 23.8%
   B. 23.8% and 29.0%
   C. 81.8% and 29%
   D. 54% and 29%
   Answer: A. Fuel energy is 75.78 kW; 22/75.78 = 0.290 and 18/75.78 = 0.2375. (Key point: Thermal efficiencies)

4. How is bsfc calculated and what is it?
   A. Fuel kg/h divided by BP = 0.344 kg/kWh
   B. Fuel divided by IP = 0.344
   C. BP divided by fuel
   D. Fuel x BP
   Answer: A. bsfc = 6.2/18 = 0.344 kg/kWh; isfc uses IP: 6.2/22 = 0.282. (Key point: Specific fuel consumption)

## Related in Internal Combustion Engines

- [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
- [Heat balance sheet of a diesel engine](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Adiesel-engine-heat-balance-numerical) — Internal Combustion Engines, chapter 8
- [Calorific value of fuel by Dulong's formula](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Acalorific-value-dulong-formula-numerical) — Internal Combustion Engines, chapter 3
- [Two-stroke and four-stroke engine comparison](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Atwo-stroke-versus-four-stroke-engine) — Internal Combustion Engines, chapter 2
- [Valve timing diagram of four-stroke engine](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Avalve-timing-diagram-four-stroke) — Internal Combustion Engines, chapter 4
- [Four-stroke SI engine working and components](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Afour-stroke-si-engine-working-components) — Internal Combustion Engines, chapter 2

## Related in other subjects

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- [Diesel engine 75 kW: fuel consumption and efficiencies](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Adiesel-75kw-fuel-consumption) — Power Plant Equipment, chapter 5
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