# Mean effective pressure

The mean effective pressure is a quantity relating to the operation of a reciprocating engine and is a valuable measure of an engine's capacity to do work that is independent of engine displacement.[1] When quoted as an indicated mean effective pressure or imep (defined below), it may be thought of as the average pressure over a cycle in the combustion chamber of the engine.

## Derivation

Let,

$W$ = work per cycle in joule
$P$ = power output in watt
$p_{mep}$ = mean effective pressure in pascal
$V_d$ = displacement volume in cubic metre
$n_c$ = number of revolutions per cycle (for a 4-stroke engine $n_c = 2$)
$N$ = number of revolutions per second
$T$ = torque in newton-metre

The power produced by the engine is equal to the work done per operating cycle times the number of operating cycles per second. If N is the number of revolutions per second, and $n_c$ is the number of revolutions per cycle, the number of cycles per second is just their ratio. We can write

$W = {P n_c \over N}$

By definition:

$W = p_{mep} V_d$

so that

$p_{mep} = {P n_c \over V_d N}$

Since the torque T is related to the angular speed (which is just N 2 π) and power produced by

$P = T N {2 \pi}$

Then the equation for mep in terms of torque becomes,

$p_{mep} = {T n_c \over V_d} {2 \pi}$

Notice that speed has dropped out of the equation and the only variables are the torque and displacement volume. Since the range of maximum brake mean effective pressures for good engine designs is well established, we now have an engine displacement independent measure of the torque producing capacity of an engine design (a specific torque of sorts). This is useful for comparing engines of different displacements. Mean effective pressure is also useful for initial design calculations; that is, given a torque, we can use standard mep values to estimate the required engine displacement. However, it is important to remember that mean effective pressure does not reflect the actual pressures inside an individual combustion chamber—although the two are certainly related—and serves only as a convenient measure of performance.

Brake Mean Effective Pressure or bmep is, as usual, calculated from measured dynamometer torque. Indicated mean effective pressure or imep is calculated using the indicated power; i.e., the pressure volume integral in the work per cycle equation. Sometimes the term fmep (friction mean effective pressure) is used as an indicator of the mean effective pressure lost to friction (or friction torque) and is just the difference between imep and bmep.

## Types of mean effective pressures

Mean effective pressure (MEP) is defined by the location measurement and method of calculation, some commonly used MEPs are given here.

• Brake mean effective pressure (BMEP) - Mean effective pressure calculated from brake power
• Indicated mean effective pressure (IMEP) - Mean effective pressure calculated from in cylinder pressure, average in cylinder pressure over engine cycle (720° in a 4 stroke, 360° in a 2 stroke).
• Friction mean effective pressure (FMEP) - Theoretical mean effective pressure required to over come engine friction, can be thought of as mean effective pressure lost due to friction. BMEP = IMEP - FMEP

## BMEP typical values

• Naturally aspirated spark-ignition engines : Maximum BMEP in the range 8.5 to 10.5 bar (850 to 1050 kPa; 125 to 150 lbf/in2), at the engine speed where maximum torque is obtained. At rated power, bmep values are typically 10 to 15% lower.[2]
• Boosted spark ignition engines : Maximum BMEP in the 12.5 to 17 bar range (1.25 to 1.7 MPa; 180 to 250 lbf/in2).[3]
• Naturally aspirated four-stroke diesels: Maximum BMEP in the 7 to 9 bar range (700 to 900 kPa; 100 to 130 lbf/in2).[4]
• Boosted automotive four-stroke diesels : Maximum BMEP in the 14 to 18 bar (1.4 to 1.8 MPa; 200 to 269 lbf/in2) range.
• Two-stroke diesels have comparable values, but very large low speed diesels like the Wärtsilä-Sulzer RTA96-C can run at BMEPs of up to 19 bar (1.9 MPa; 275 lbf/in2).
• Ultra boosted engines such as the engine used in the Koenigsegg Agera can run at BMEPs as high as 28 bar (32 bar for the Agera R)[5]
• Top Fuel dragster engines: 80–100 bar (8.0-10 MPa)

For example, a four-stroke motor producing 160 N·m from 2 litres of displacement has a bmep of (4π)(160 N·m)/(0.002 m³) = 1,005,000 N/m2 =1,005 kPa (10.05 bar). If the same engine produces 76 kW at 5400 rpm (90 Hz), its torque is 134 N·m and its bmep is 8.42 bar (842 kPa). As piston engines always have their maximum torque at a lower rotating speed than the maximum output, the BMEP is lower at full power.

It may be of interest to consider the, 0.13 cc displacement, high speed uniflow steam engine "Tiddler", built by model engineer Geoff Wolfe. It appears to manage a full load output of 20w@5,300 rpm . Reciprocating steam engines have $n_c=1$ just like 2-strokes, so the engine's BMEP can be calculated as just under 129 bar.