Engine

Brake mean effective pressure differential

The brake mean effective pressure differential (BMEP_d) can be experimentally calculated if we know the engine power available at the crankshaft (brake horsepower, P) and the measured volumetric flow rate (Q_m) of the air entering the engine's intake system:

BMEPd = P Qm

(1)

If we want to estimate BMEP_d, we know it represents two engine characteristics: the indicated mean effective pressure differential ( IMEP_d ) and the friction mean effective pressure ( FMEP_d ).

The first one represents the actual gas pressure differential inside the engine and the other represents the losses due to bearing friction and windage, but also the power loss from the required devices to run the engine, such as oil, fuel and coolant pumps, fan or ignition system. Therefore, BMEP_d is also defined as:

BMEPd = IMEPd − FMEPd

(2)

Here are some typical values for different engines:

engine type	BMEPd* @ max power
2-stroke − diesel	8.3 bar
2-stroke − no tuning	8.8 bar
4-stroke − diesel	9.4 bar
4-stroke − Wankel** (turbocharged)	9.5 bar
2-stroke − tuned	9.6 bar
4-stroke − forced induction (crankshaft driven)	9.6 bar
4-stroke − Wankel**	9.9 bar
4-stroke − low CR	10.0 bar
4-stroke − forced induction (exhaust gas driven)	10.5 bar
4-stroke − typical	11.0 bar
4-stroke − high performance	12.0 bar
Dragster - Top Fuel	45.0 bar

*Note: Based on SAE J1349 air conditions.

**Note: Modern Wankel engines tend to have values closer to typical piston 4-stroke engines.

Brake specific fuel consumption

The brake specific fuel consumption (BSFC) is introduced here because it is closely related to the BMEP_d :

BSFC = ρatm AFR BMEPd

(3)

Where:

BSFC	= brake specific fuel consumption (kg/J or kg/s/W)
ρatm	= atmospheric air density (kg/m³)
AFR	= air fuel ratio
BMEPd	= brake mean effective pressure differential (Pa)

The air density is fixed by the environment and the AFR is fixed by the type of fuel used, so the only variable left is BMEP_d : The higher it is, the lower is the fuel consumption.

Brake mean effective pressure

With reciprocating engines, most values available for brake mean effective pressure do not represent the BMEP differential as defined previously. The brake mean effective pressure ( BMEP ) is the equivalent average pressure acting on the piston during the entire volume change in the cylinder. The difference is that they are found using the theoretical volumetric flow rate (Q_th) instead of the measured volumetric flow rate (Q_m), i.e. we assume that the volumetric efficiency is 100%. Equation (4) from the power page shows the relationship between the BMEP and the measured engine torque.

BMEP  = BMEPd VE

(4)

The BMEP is a combination of 2 independent engine characteristics. So when the BMEP of an engine increases, we don't know if it is because the engine can extract more power from the combustion (BMEP_d increase) or because the engine can draw more air (VE increase).

With a similar reasoning, equation (4) is also true for the relationship between FMEP and FMEP_d or between IMEP and IMEP_d such that equation (2) can also be rewritten this way:

BMEP = IMEP − FMEP

(5)

For other types of engine (like gas turbine for example), mean effective pressures cannot be evaluated as these engines don't have a reference displacement for evaluating the volumetric efficiency (VE). But mean effective pressure differential can be evaluated and compared with each other, no matter what is the engine type.