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# Mean effective pressure

Mean effective pressure
Common symbols
p
SI unitPascal (Pa)
In SI base units1 kgm−1s−2
Derivations from
other quantities
p = W·V−1
Dimension${\displaystyle {\mathsf {L}}^{-1}{\mathsf {M}}{\mathsf {T}}^{-2}}$

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 acting on a piston during the different portions of its cycle.

## Derivation

Let:

${\displaystyle W}$ = work per cycle in joule;
${\displaystyle P}$ = power output in watt;
${\displaystyle p_{\text{me}}}$ = mean effective pressure in pascal;
${\displaystyle V_{\text{d}}}$ = displacement volume in cubic metre;
${\displaystyle n_{\text{c}}}$ = number of revolutions per power stroke (for a 4-stroke engine, ${\displaystyle n_{\text{c}}=2}$);[Note 1]
${\displaystyle N}$ = number of revolutions per second;
${\displaystyle T}$ = 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 ${\displaystyle n_{\text{c}}}$ is the number of revolutions per power stroke, the number of power strokes per second is just their ratio. We can write:

${\displaystyle P={W{N \over n_{\text{c}}}}.}$

Reordering to put work on the left:

${\displaystyle W={P{n_{\text{c}} \over N}}.}$

By definition:

${\displaystyle W=p_{\text{me}}V_{\text{d}},}$

so that

${\displaystyle p_{\text{me}}={Pn_{\text{c}} \over V_{\text{d}}N}.}$

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

${\displaystyle P={2\pi }TN,}$

then the equation for MEP in terms of torque is:

${\displaystyle p_{\text{me}}={2\pi }{n_{\text{c}}}{T \over V_{\text{d}}}.}$

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 a 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, standard MEP values can be used 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 (BMEP) is calculated from measured dynamometer torque. Net indicated mean effective pressure (IMEPn) 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 IMEPn and BMEP.

## Examples

MEP from torque and displacement

A four-stroke engine produces 160 N·m of torque, and displaces 2 dm3=0.002 m3:

• ${\displaystyle n_{\text{c}}=2}$
• ${\displaystyle T=160\,{\text{N}}{\cdot }{\text{m}}}$
• ${\displaystyle V_{\text{d}}=0.002\,{\text{m}}^{3}}$
${\displaystyle p_{\text{me}}={2\pi }{2}{{160\,{\text{N}}{\cdot }{\text{m}}} \over {0.002\,{\text{m}}^{3}}}={2\pi }{2}{{160\,{\text{N}}{\cancel {\cdot {\text{m}}}}} \over {0.002\,{\text{m}}^{{\cancel {3}}2}}}=1,005,310\,{\text{N}}{\cdot }{\text{m}}^{-2}=10.05\,{\text{bar}}=1.005\,{\text{MPa}}}$

We also get the megapascal figure if we use cubic centimetres for ${\displaystyle V_{\text{d}}}$:

• ${\displaystyle n_{\text{c}}=2}$
• ${\displaystyle T=160\,{\text{N}}{\cdot }{\text{m}}}$
• ${\displaystyle V_{\text{d}}=2000\,{\text{cm}}^{3}}$
${\displaystyle p_{\text{me}}={2\pi }{2}{{160\,{\text{N}}{\cdot }{\text{m}}} \over {2000\,{\text{cm}}^{3}}}={2\pi }{2}{{160\,{\text{N}}{\cancel {\cdot {\text{m}}}}} \over {2000\,{\text{cm}}^{{\cancel {3}}2}}}=1.005\,{\text{MPa}}}$
Power from MEP and crankshaft speed

If we know the crankshaft speed, we can also determine the engine's power output from the MEP figure: ${\displaystyle P={V_{\text{d}}\cdot p_{\text{me}}\cdot N \over n_{\text{c}}}}$
In our example, the engine puts out 160 N·m of torque at 3600 min−1:

• ${\displaystyle n_{\text{c}}=2}$
• ${\displaystyle N=3600\,{\text{min}}^{-1}=60\,{\text{s}}^{-1}}$
• ${\displaystyle V_{\text{d}}=2000\,{\text{cm}}^{3}}$
• ${\displaystyle p_{\text{me}}=1.005\,{\text{MPa}}}$

${\displaystyle {2000\cdot 1.005\cdot 60 \over 2}=60,300\,{\text{W}}}$

As piston engines usually have their maximum torque at a lower rotating speed than the maximum power output, the BMEP is lower at full power (at higher rotating speed). If the same engine is rated 76 kW at 5400 min−1 = 90 min−1, and its BMEP is 0.844 MPa, we get the following equation:

• ${\displaystyle n_{\text{c}}=2}$
• ${\displaystyle N=5400\,{\text{min}}^{-1}=90\,{\text{s}}^{-1}}$
• ${\displaystyle V_{\text{d}}=2000\,{\text{cm}}^{3}}$
• ${\displaystyle p_{\text{me}}=0.844\,{\text{MPa}}}$

${\displaystyle {2000\cdot 0.844\cdot 90 \over 2}=75,960\,{\text{W}}\approx 76\,{\text{kW}}}$

## 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 measured brake torque.
• Gross indicated mean effective pressure (IMEPg) - Mean effective pressure calculated from in-cylinder pressure over compression and expansion portion of engine cycle (360° in a four-stroke, 180° in a two-stroke). Direct measurement requires cylinder pressure sensing equipment.
• Net indicated mean effective pressure (IMEPn) - Mean effective pressure calculated from in-cylinder pressure over the complete engine cycle (720° in a four-stroke, 360° in a two-stroke). Direct measurement requires cylinder pressure sensing equipment.
• Pumping mean effective pressure (PMEP) - Mean effective pressure from work moving air in and out of the cylinder, across the intake and exhaust valves. Calculated from in-cylinder pressure over intake and exhaust portions of engine cycle (360° in a four-stroke, 0° in a two-stroke). Direct measurement requires cylinder pressure sensing equipment. PMEP = IMEPg - IMEPn.
• Friction mean effective pressure (FMEP) - Theoretical mean effective pressure required to overcome engine friction, can be thought of as mean effective pressure lost due to friction. Friction mean effective pressure calculation requires accurate measurement of cylinder pressure and dynamometer brake torque. FMEP = IMEPn - BMEP.

## BMEP typical values

Petrol engines :

• Naturally aspirated spark-ignition engines : current VW petrol engines maximum MEP range (in bar and psi) from 11.6 to 13.3 bar (168 to 193 psi), 10.1 to 11.4 bar (146 to 165 psi) at maximum power.
• 28-cylinder Pratt & Whitney R-4360 Wasp Major with 115/145 Octane World War II avgas, 3,600 HP at 2,700 rpm and 17.2 bar (249.4 psi) BMEP.
• Napier Sabre 7, at peak HP, 3055 HP at 3850 rpm, 19.4 bar (281.3 psi) BMEP
• Rolls-Royce Merlin 130/131, at peak HP, 2030 HP at 2900 rpm, 23.1 bar (335 psi) BMEP
• Boosted spark ignition engines : current VW petrol engines maximum MEP range from 16.4 to 23.1 bar (238 to 335 psi), 15.3 to 19.3 bar (222 to 280 psi) at maximum power.
• High-boost engines such as the Koenigsegg Agera can run at BMEPs as high as 28 bar (32 bar for the Agera R)[2]
• Formula One engines : in 1986 the 1.5 L Williams-Honda FW11 Turbo produced 1,400 hp (1,044 kW) at 12,000 rpm[3] for 831 Nm of torque, a 69.6 bar (1,009 psi) BMEP. In 2006 the 2.4 L Toyota TF106 produced 740 hp (552 kW) at 19,000 rpm[4] for 277 Nm of torque, a 14.5 bar (210 psi) MEP.
• Top Fuel dragster engines: 80–100 bar (8.0–10 MPa; 1160–1450 psi)

Diesel engines :

• Naturally aspirated four-stroke diesels: current VW diesel engines have a 8.9 bar (129 psi) maximum MEP, 8 bar (120 psi) at max power.
• Boosted automotive four-stroke diesels : current VW diesel engines have a 17.7 to 31.9 bar (257 to 463 psi) maximum MEP, 14.5 to 26.8 bar (210 to 389 psi) at max power.
• 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).
• The Wärtsilä W31, the world's most efficient four-stroke diesel engine as of October 2015, has a mean effective pressure of 30.1 bar.[5]

## Notes and references

### Notes

1. ^ Note that Wankel engines are four-stroke engines, so ${\displaystyle n_{\text{c}}=2}$; the displacement ${\displaystyle V_{\text{d}}}$ is derived from the chamber volume ${\displaystyle V_{\text{c}}}$ by multiplying it with the number of rotary pistons ${\displaystyle i}$ and 2: ${\displaystyle V_{\text{d}}=2V_{\text{c}}i}$ (see Wolf-Dieter Bensinger: Rotationskolben-Verbrennungsmotoren, Springer, Berlin/Heidelberg/New York 1973, ISBN 978-3-642-52174-4, p. 66)

### References

1. ^ Heywood (1988), p. 50.
2. ^ Drive (26 February 2013). The 1140 hp Heart of a Hypercar - Inside Koenigsegg. Youtube.
3. ^ "F1 rules and stats 1980-1989". F1Technical. 1 Jan 2009.
4. ^ "Toyota TF106". F1Technical.
5. ^ "Wärtsilä 31" (PDF). Wärtsilä. 2016.
• Heywood, J. B., "Internal Combustion Engine Fundamentals", McGraw-Hill Inc., 1988
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