# Mean Effective Pressure (MEP)

### Introduction

The Mean Effective Pressure (MEP) is a theoretical parameter used to measure the performance of an internal combustion engine (ICE). Even if it contains the word “pressure” it’s not an actual pressure measurements within the engine cylinder.

The cylinder pressure in an ICE is continuously changing during the combustion cycle. For a better understanding of the pressure variation within the cylinder, read the article The pressure-volume (pV) diagram and how work is produced in an ICE.

### Formula

The mean effective pressure can be regarded as an average pressure in the cylinder for a complete engine cycle. By definition, mean effective pressure is the ratio between the work and engine displacement:

pme = W / Vd
(1)

where:
pme [Pa] – mean effective pressure
W [J] – work performed in a complete engine cycle
Vd [m3] – engine (cylinder) displacement

From equation (1) we can write the expression of the engine work as:

W = pme · Vd
(2)

There is also a direct relationship between the power of the engine and the work produced:

W = (nr · P) / ne
(3)

where:
nr [-] – number of crankshaft rotations for a complete engine cycle (for 4-stroke engine nr = 2)
P [W] – engine power
ne [rps] – engine speed

By making equation (2) equal to (3), we get the expression of the mean effective pressure function of power and engine speed:

pme = (nr · P) / (ne · Vd)
(4)

Power is the product between torque and speed:

P = ω · T = 2 · π · ne · T
(5)

By replacing (5) in (4), we get the expression of mean effective pressure function of engine torque:

pme = (2 · π · nr · T) / Vd
(6)

As you can see, from expression (6), the mean effective pressure is not influenced by the engine speed. Also, since the torque is divided by the engine capacity, the mean effective pressure parameter can be used to compare internal combustion engines of different displacements.

For an engine with multiple cylinders we have to take into account the total volumetric capacity. For nc being the number of cylinders, the expression of mean effective pressure becomes:

pme = (2 · π · nr · T) / (nc · Vd)
(7)

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### Types

Mean effective pressure is used for initial engine design calculations, with engine torque and MEP as inputs, the engine designer can calculate what is the required engine volumetric capacity. Remember that mean effective pressure is only a parameter to measure engine performance and does not reflect the actual pressures inside an individual combustion chamber.

There are different “flavors” of mean effective pressure:

• indicated mean effective pressure (IMEP)
• brake mean effective pressure (BMEP)
• friction mean effective pressure (FMEP)

Indicated mean effective pressure (IMEP) is the mean effective pressure calculated with indicated power (work). This parameter does not take into account the efficiency of the engine.

Brake mean effective pressure (BMEP) is the mean effective pressure calculated from the dynamometer power (torque). This is the actual output of the internal combustion engine, at the crankshaft. Brake mean effective pressure takes into account the engine efficiency.

Friction mean effective pressure (FMEP) is an indicator of the mean effective pressure of the engine lost through friction and it’s the difference between indicated mean effective pressure and brake mean effective pressure.

FMEP = IMEP – BMEP
(8)

If we know the friction mean effective pressure, from equation (7), we can calculate the friction torque Tf [Nm] as:

Tf = (nc · Vd · FMEP) / (2 · π · nr)
(9)

If we consider the mechanical efficiency of the engine η[-], we can write the brake mean effective pressure function of the indicate mean effective pressure:

BMEP = ηm · IMEP
(10)

from which we can rewrite the expression of the mechanical efficiency as:

ηm = 1 – (FMEP / IMEP)
(11)

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### Example

Let’s work through an example. For a 4-stroke internal combustion engine, with the following parameters:

S = 97 mm (piston stroke)
B = 85 mm (cylinder bore)
nr = 2 (number of crankshaft rotations for a complete engine cycle)
nc = 4 (number of cylinders)
Ti = 250 Nm (indicated torque)
Te = 230 Nm (effective torque)

calculate the indicated mean effective pressure (IMEP), brake mean effective pressure (BMEP), friction mean effective pressure (FMEP), friction torque (Tf) and mechanical efficiency (ηm).

Step 1. Calculate the surface of the piston

Sp = (π · B2) / 4 = 0.0056745 m2

Step 2. Calculate the volume (displacement) of a cylinder

Vd = Sp · S = 0.0005504 m3

Step 3. Calculate the indicated mean effective pressure

IMEP = (2 · π · nr · Ti) / (nc · Vd) = 1426889.7 Pa = 14.27 bar

Step 4. Calculate the brake mean effective pressure

BMEP = (2 · π · nr · Te) / (nc · Vd) = 1312738.6 Pa = 13.13 bar

Step 5. Calculate the friction mean effective pressure

FMEP = IMEP – BMEP = 114151.18 Pa = 1.14 bar

Step 6. Calculate the friction torque

Tf = (nc · Vd · FMEP) / (2 · π · nr) = 20 Nm

this could also be easily calculated by subtracting the effective torque from the indicated torque:

Tf = Ti – Te = 20 Nm

Step 7. Calculate the mechanical efficiency

ηm = 1 – (FMEP/IMEP) = 0.92 = 92 %

Some facts about brake mean effective torque (BMEP):

• for any internal combustion engine, the maximum BMEP is obtained at full load (for a particular engine speed)
• throttling the engine decreases the BMEP due to higher pumping losses
• for a fixed engine displacement, if we increase the BMEP, we produce more effective torque at the crankshaft
• for the same value of the BMEP, a 2-stroke internal combustion engine has nearly double torque, compared to a 4-stroke engine
• the higher the BMEP, the higher the mechanical and thermal stress on the engine components

You can also check your results using the calculator below.

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### Calculator

 nr [-] nc [-] B [mm] S [mm] Ti [Nm] Te [Nm] IMEP [bar] = BMEP [bar] = FMEP [bar] = Friction torque, Tf [Nm] = Mechanical efficiency, ηm [-] =

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