Library / Automotive and vehicle dynamics / VEH-09
Automotive and vehicle dynamics
Brake thermal efficiency
The fraction of the fuel energy that appears as useful shaft power.
- Ref
- VEH-09
- Rev
- v1
- Field
- Automotive and vehicle dynamics
- Result
- ηb [%]
Pb is the brake (shaft) power in kW, ṁf the fuel mass flow in kg/h and HL the lower heating value of the fuel in MJ/kg: about 43 for petrol and 42.5 for diesel. The fuel energy rate is ṁf HL (converted to kW), and ηb is the share of it that reaches the shaft. The result is shown as a percentage. BSFC, the fuel used per unit of energy, is shown as a derived row in g/kWh.
The fraction of the fuel energy that appears as useful shaft power. Brake specific fuel consumption (BSFC) is the same information expressed as fuel used per unit of energy delivered.
Calculator
- Brake specific fuel consumption, BSFC240 g/kWh
- Fuel energy input, ṁf HL286.7 kW
- Energy lost as heat and exhaust (input − Pb)186.7 kW
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With 100 kW from 24 kg/h of fuel, the engine converts 34.88 % of the fuel energy into shaft power, which is typical of a good petrol engine. Modern diesels reach 40 to 45 % at best load and large ship engines over 50 %.
- The remaining 65.12 % leaves as exhaust heat and coolant heat. BSFC and efficiency are the same quantity: ηb = 3600 / (BSFC × HL) with BSFC in g/kWh and HL in kJ/g, so a lower BSFC means a higher efficiency.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (%) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ṁf Fuel mass flow rate | 1 to 150 kg/h | 5.581 | 837.2 | 831.6 | +10% | −9.09 % |
| Pb Brake shaft power | 5 to 500 kW | 1.744 | 174.4 | 172.7 | +10% | +10 % |
| HL Lower heating value of the fuel | 30 to 50 MJ/kg | 30 | 50 | 20 | +10% | −9.09 % |
Sweep of Fuel mass flow rate
| Fuel mass flow rate (kg/h) | Brake thermal efficiency (%) |
|---|---|
| 1 | 837.2 |
| 19.63 | 42.66 |
| 38.25 | 21.89 |
| 56.88 | 14.72 |
| 75.5 | 11.09 |
| 94.13 | 8.895 |
| 112.8 | 7.425 |
| 131.4 | 6.373 |
| 150 | 5.581 |
Sweep one variable
Variables and how each one contributes
Brake thermal efficiency
What the equation gives you. Everything else feeds it.
Brake shaft power
The brake (shaft) power the engine delivers, in kW. Directly proportional: more output power for the same fuel flow means higher efficiency. Raising it by 10 % (to 110) moves the result by +10 %, from 34.88 to 38.37 %.
Fuel mass flow rate
The fuel mass flow rate, in kg/h. Inversely proportional: burning more fuel for the same power means lower efficiency. Raising it by 10 % (to 26.4) moves the result by −9.09 %, from 34.88 to 31.71 %.
Lower heating value of the fuel
The lower heating value of the fuel, in MJ/kg: about 43 for petrol and 42.5 for diesel. Inversely proportional: with a more energetic fuel the same flow carries more energy, so the same power means lower efficiency. Raising it by 10 % (to 47.3) moves the result by −9.09 %, from 34.88 to 31.71 %.
Worked example with the values above
- Fuel energy rate: ṁf HL = (24 / 3600) × 43 MJ/s × 1000 = 286.7 kW.
- Efficiency: ηb = Pb / 286.7 = 100 / 286.7 = 0.3488.
- As a percentage: 34.88 %. BSFC = 240 g/kWh.
Assumptions and limits
- Steady operation at one operating point, with Pb and ṁf measured at the same time.
- The lower heating value is used, as is usual for engines, so the water vapour in the exhaust is assumed not to condense.
Common mistakes
- Mixing the heating value in MJ/kg with the fuel flow in g/s or kg/s without converting.
- Using the higher heating value in one place and the lower value in another when comparing engines.
Statistics and uncertainty
Both the power and the fuel flow come from instruments, typically accurate to 1 to 2 % each, and the heating value is known to about 1 %, so the efficiency is good to about 2 to 3 %. It also varies strongly with the operating point: efficiency is best at high load and falls off sharply at light load, so a single figure is only meaningful at a stated speed and torque.
Where it is used
- Rating the efficiency of petrol and diesel engines at a given operating point.
- Converting a fuel flow measurement into BSFC, and estimating fuel use for a given power.
Maths you need
- Efficiency: useful output divided by input
- Unit conversion: kg/h to kg/s, MJ to kW