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Automotive and vehicle dynamics
Brake mean effective pressure
Engine torque divided by displacement, expressed as a pressure.
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- Automotive and vehicle dynamics
- Result
- BMEP [MPa]
Te is the brake torque in N·m, Vd the swept displacement in litres and nr the number of crankshaft revolutions per power stroke cycle: 2 for a four-stroke engine and 1 for a two-stroke engine. The work per cycle is 2π nr Te, and dividing it by the volume swept gives a pressure. The result is in MPa (1 MPa = 10 bar), and is a measure of how hard the engine works, independent of its size.
Engine torque divided by displacement, expressed as a pressure. It shows how hard the engine works its cylinders, independent of engine size. n_r is 2 for a four-stroke and 1 for a two-stroke.
Calculator
- BMEP in bar18.85 bar
- Torque per litre of displacement150 N·m/L
- Work per cycle, 2π nr Te3,770 J
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.
- A 2.0 L engine making 300 N·m has a BMEP of 1.885 MPa (18.85 bar). Naturally aspirated petrol engines are typically 8 to 13 bar, turbocharged petrol 15 to 25 bar and heavy diesels above 20 bar.
- BMEP depends only on torque and displacement, not on speed. It is the right measure to compare engine loading, whereas power also depends on how fast the engine turns.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (MPa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Vd Swept displacement | 0.5 to 8 L | 0.4712 | 7.54 | 7.069 | +10% | −9.09 % |
| Te Engine torque | 10 to 1,000 N·m | 0.06283 | 6.283 | 6.22 | +10% | +10 % |
| nr Crankshaft revolutions per power cycle | 1 to 2 | 0.9425 | 1.885 | 0.9425 | +1 | +50 % |
Sweep of Engine torque
| Engine torque (N·m) | Brake mean effective pressure (MPa) |
|---|---|
| 10 | 0.06283 |
| 133.8 | 0.8404 |
| 257.5 | 1.618 |
| 381.3 | 2.395 |
| 505 | 3.173 |
| 628.8 | 3.951 |
| 752.5 | 4.728 |
| 876.3 | 5.506 |
| 1,000 | 6.283 |
Sweep one variable
Variables and how each one contributes
Brake mean effective pressure
What the equation gives you. Everything else feeds it.
Engine torque
The brake (shaft) torque of the engine, in N·m. Directly proportional: the same displacement producing more torque has a higher BMEP. Raising it by 10 % (to 330) moves the result by +10 %, from 1.885 to 2.073 MPa.
Swept displacement
The total swept displacement of the engine, in litres. Inversely proportional: for the same torque, a bigger engine works at a lower pressure. Raising it by 10 % (to 2.2) moves the result by −9.09 %, from 1.885 to 1.714 MPa.
Crankshaft revolutions per power cycle
The crankshaft revolutions per power cycle: 2 for a four-stroke engine, 1 for a two-stroke. A four-stroke engine (2) has half as many power strokes per revolution as a two-stroke (1), so the same torque and displacement give twice the BMEP. Lowering it by 1 (to 1) moves the result by −50 %, from 1.885 to 0.9425 MPa.
Worked example with the values above
- Work per cycle: 2π nr Te = 2π × 2 × 300 = 3,770 J.
- Displacement in m³: Vd = 2 L = 0.002 m³.
- BMEP = 3,770 / 0.002 = 1,885,000 Pa = 1.885 MPa (18.85 bar).
Assumptions and limits
- The torque is the brake torque at the output shaft, so friction and pumping losses are already deducted.
- The displacement is the total swept volume. nr = 2 for a four-stroke engine and 1 for a two-stroke engine.
Common mistakes
- Using the two-stroke factor (nr = 1) for a four-stroke engine. This halves the BMEP.
- Entering the displacement in cm³ or m³ instead of litres.
Statistics and uncertainty
BMEP is a ratio of two measured quantities, so a 2 % torque error and a 0.5 % displacement error give about 2 % in BMEP. A bigger uncertainty is the torque measurement itself, which is affected by dynamometer calibration, temperature and correction factors, so published figures from different test standards can differ by several per cent.
Where it is used
- Comparing the loading of petrol, diesel and turbocharged engines of different sizes.
- Checking the likely torque of a design from its displacement and a target BMEP.
Maths you need
- Work and pressure: work = pressure × volume
- Torque and work: work per revolution = 2π T