Mean effective pressure: Difference between revisions

Mean effective pressure
Mean effective pressure
Common symbols	p
SI unit	Pascal (Pa)
In SI base units	1 kg⋅m−1⋅s−2
Derivations from; other quantities	p = W·V−1
Dimension

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The mean effective pressure (MEP) is a quantity relating to the operation of a reciprocating engine and is a measure of an engine's capacity to do work that is independent of engine displacement.^[1] Despite having the dimension of pressure, MEP cannot be measured.^[2] When quoted as an indicated mean effective pressure (IMEP), it may be thought of as the average pressure acting on a piston during the different portions of its cycle. When friction losses are subtracted from the IMEP, the result is the brake mean effective pressure (BMEP).

Derivation

Let:

P

= power output in watt;

p_{\text{me}}

= mean effective pressure in megapascal;

V_{\text{d}}

= displacement volume in cubic centimetre;

i

= number of cycles per revolution (for a 4-stroke engine,

i=0.5

, for a 2-stroke engine,

i=1

);^{[Note 1]}

n

= number of revolutions per second;

\omega =

angular velocity, i.e.

\omega =2\pi n

;

M

= torque in newton-metre.

Then, BMEP may be used to determine an engine's power output as follows:

P=i\cdot n\cdot V_{\text{d}}\cdot p_{\text{me}}

Since we know that power is:

P=\omega \cdot M=2\pi \cdot n\cdot M

We now see that, BMEP is a measure of expressing torque per displacement:

P=i\cdot n\cdot V_{\text{d}}\cdot p_{\text{me}}=2\pi \cdot n\cdot M

And thus, the equation for BMEP in terms of torque is:

p_{\text{me}}={{M\cdot 2\pi } \over {V_{\text{d}}\cdot i}}.

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, 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.^[2]

Brake mean effective pressure (BMEP) is calculated from measured dynamometer torque. Net indicated mean effective pressure (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.^[3]

Examples

MEP from torque and displacement

A four-stroke engine produces 159 N·m of torque, and displaces 2000 cm³

$i=0.5$
$M=159\,{\text{N}}{\cdot }{\text{m}}$
$V_{\text{d}}=2000\,{\text{cm}}^{3}$

p_{\text{me}}={2\pi }\cdot {0.5^{-1}}{{159\,{\text{N}}{\cdot }{\text{m}}} \over {2000\,{\text{cm}}^{3}}}={2\pi }\cdot {0.5^{-1}}{{15900\,{\text{N}}{\cancel {\cdot {\text{cm}}}}} \over {2000\,{\text{cm}}^{{\cancel {3}}2}}}\approx 100\,N\cdot cm^{-2}=1\,{\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: $P=i\cdot n\cdot V_{\text{d}}\cdot p_{\text{me}}$
In our example, the engine puts out 159 N·m of torque at 3600 min⁻¹ (=60 s⁻¹):

$i=0.5$
$n=60\,{\text{s}}^{-1}$
$V_{\text{d}}=2000\,{\text{cm}}^{3}$
$p_{\text{me}}=1\,{\text{MPa}}$

Thus:

P={2000\,cm^{3}\cdot 1\,N\cdot cm^{-2}\cdot 60\,s^{-1}\cdot 0.5}=60,000\,N\cdot m\cdot s^{-1}=60,000\,{\text{W}}=60\,{\text{kW}}

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 72 kW at 5400 min⁻¹ = 90 s⁻¹, and its BMEP is 0.80 MPa, we get the following equation:

$i=0.5$
$n=90\,{\text{s}}^{-1}$
$V_{\text{d}}=2000\,{\text{cm}}^{3}$
$p_{\text{me}}=0.80\,{\text{MPa}}$

Then:

P={2000\,cm^{3}\cdot 0.80\,N\cdot cm^{-2}\cdot 90\,s^{-1}\cdot 0.5}=72,000\,N\cdot m\cdot s^{-1}=72\,{\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, $p_{me}$ ) - Mean effective pressure calculated from measured brake torque.
Indicated mean effective pressure (IMEP, $p_{mi}$ ) - Mean effective pressure calculated from in-cylinder pressure over the complete engine cycle (720° in a four-stroke, 360° in a two-stroke). IMEP may be determined by planimetering the area in an engine's pV-diagram. Since naturally aspirated four-stroke engines must perform pumping work to suck the charge into the cylinder, and to remove the exhaust from the cylinder, IMEP may be split into the high-pressure, gross mean effective pressure (GMEP, $p_{mg}$ ) and the pumping mean effective pressure (PMEP, $p_{miGW}$ ). In naturally aspirated engines, PMEP is negative, and in super- or turbocharged engines, it is usually positive. IMEP may be derived from PMEP and GMEP: $p_{mi}=p_{mg}-p_{miGW}$ .^[3]
Friction mean effective pressure (FMEP, $p_{mr}$ ) - Theoretical mean effective pressure required to overcome engine friction, can be thought of as mean effective pressure lost due to friction: $p_{mr}=p_{mi}-p_{me}$ . FMEP rises with an increase in engine speed.^[4]

BMEP typical values

BMEP typical values^[5]
Engine type	Typical max. BMEP
Motorbike engine	1.2 MPa (174.0 lbf/in²)
Race car engine (NA Formula 1)	1.6 MPa (232.1 lbf/in²)
Passenger car engine (naturally aspirated Otto)	1.3 MPa (188.5 lbf/in²)
Passenger car engine (turbocharged Otto)	2.2 MPa (319.1 lbf/in²)
Passenger car engine (turbocharged Diesel)	2.0 MPa (290.1 lbf/in²)
Lorry engine (turbocharged Diesel)	2.4 MPa (348.1 lbf/in²)
High-speed industrial Diesel engine	2.8 MPa (406.1 lbf/in²)
Medium-speed industrial Diesel engine	2.5 MPa (362.6 lbf/in²)
Low-speed two-stroke Diesel engine	1.5 MPa (217.6 lbf/in²)

Notes and references

Notes

^ Wankel engines are four-stroke engines, so $i=0.5$ ; the displacement $V_{\text{d}}$ is derived from the chamber volume $V_{\text{c}}$ by multiplying it with the number of rotary pistons $i$ and 2: $V_{\text{d}}=2V_{\text{c}}i$ (see Wolf-Dieter Bensinger: Rotationskolben-Verbrennungsmotoren, Springer, Berlin/Heidelberg/New York 1973, ISBN 978-3-642-52174-4, p. 66)

References

^ Heywood, J. B., "Internal Combustion Engine Fundamentals", McGraw-Hill Inc., 1988, p. 50
^ ^a ^b Schreiner, Klaus (2011-05-25). Basiswissen Verbrennungsmotor (in German). Wiesbaden: Vieweg+Teubner Verlag. p. 41. ISBN 978-3-8348-1279-7.
^ ^a ^b Ulrich Spicher: Kapitel 3 · Kenngrößen – table 3.16: Effektiver Mitteldruck heutiger Motoren, in Richard van Basshuysen, Fred Schäfer (eds.): Handbuch Verbrennungsmotor – Grundlagen · Komponenten · Systeme · Perspektiven, 8th edition, Springer, Wiesbaden 2017, ISBN 978-3-658-10901-1, DOI 10.1007/978-3-658-10902-8_3, p. 24
^ Ulrich Spicher: Kapitel 3 · Kenngrößen – table 3.16: Effektiver Mitteldruck heutiger Motoren, in Richard van Basshuysen, Fred Schäfer (eds.): Handbuch Verbrennungsmotor – Grundlagen · Komponenten · Systeme · Perspektiven, 8th edition, Springer, Wiesbaden 2017, ISBN 978-3-658-10901-1, DOI 10.1007/978-3-658-10902-8_3, p. 26, formula 3.48
^ Ulrich Spicher: Kapitel 3 · Kenngrößen – table 3.16: Effektiver Mitteldruck heutiger Motoren, in Richard van Basshuysen, Fred Schäfer (eds.): Handbuch Verbrennungsmotor – Grundlagen · Komponenten · Systeme · Perspektiven, 8th edition, Springer, Wiesbaden 2017, ISBN 978-3-658-10901-1, DOI 10.1007/978-3-658-10902-8_3, p. 27

External links

Brake Mean Effective Pressure (bmep), Power and Torque, Factory Pipe
All About Mean Effective Pressure, Harleyc.com

Tiddler steam engine

[Wankel-3] Wankel engines are four-stroke engines, so $i=0.5$ ; the displacement $V_{\text{d}}$ is derived from the chamber volume $V_{\text{c}}$ by multiplying it with the number of rotary pistons $i$ and 2: $V_{\text{d}}=2V_{\text{c}}i$ (see Wolf-Dieter Bensinger: Rotationskolben-Verbrennungsmotoren, Springer, Berlin/Heidelberg/New York 1973, ISBN 978-3-642-52174-4, p. 66)

[1] Heywood, J. B., "Internal Combustion Engine Fundamentals", McGraw-Hill Inc., 1988, p. 50

[Schreiner_2011_p._41-2] Schreiner, Klaus (2011-05-25). Basiswissen Verbrennungsmotor (in German). Wiesbaden: Vieweg+Teubner Verlag. p. 41. ISBN 978-3-8348-1279-7.

[Spicher_2017_24-4] Ulrich Spicher: Kapitel 3 · Kenngrößen – table 3.16: Effektiver Mitteldruck heutiger Motoren, in Richard van Basshuysen, Fred Schäfer (eds.): Handbuch Verbrennungsmotor – Grundlagen · Komponenten · Systeme · Perspektiven, 8th edition, Springer, Wiesbaden 2017, ISBN 978-3-658-10901-1, DOI 10.1007/978-3-658-10902-8_3, p. 24

[5] Ulrich Spicher: Kapitel 3 · Kenngrößen – table 3.16: Effektiver Mitteldruck heutiger Motoren, in Richard van Basshuysen, Fred Schäfer (eds.): Handbuch Verbrennungsmotor – Grundlagen · Komponenten · Systeme · Perspektiven, 8th edition, Springer, Wiesbaden 2017, ISBN 978-3-658-10901-1, DOI 10.1007/978-3-658-10902-8_3, p. 26, formula 3.48

[6] Ulrich Spicher: Kapitel 3 · Kenngrößen – table 3.16: Effektiver Mitteldruck heutiger Motoren, in Richard van Basshuysen, Fred Schäfer (eds.): Handbuch Verbrennungsmotor – Grundlagen · Komponenten · Systeme · Perspektiven, 8th edition, Springer, Wiesbaden 2017, ISBN 978-3-658-10901-1, DOI 10.1007/978-3-658-10902-8_3, p. 27

[1]

[2]

[Note 1]

[3]

[4]

[5]

@@ Line 1: / Line 1: @@
+{{Short description|Measure of an engine's capacity to do work}}
 {{ Infobox physical quantity
 | name = Mean effective pressure
@@ Line 8: / Line 9: @@
 }}
-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]].{{sfnp|Heywood|1988|page=50}} 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.
+The '''mean effective pressure''' ('''MEP''') is a quantity relating to the operation of a [[reciprocating engine]] and is a measure of an engine's capacity to do work that is independent of [[engine displacement]].<ref>Heywood, J. B., "Internal Combustion Engine Fundamentals", McGraw-Hill Inc., 1988, p. 50</ref> Despite having the dimension of pressure, MEP cannot be measured.<ref name="Schreiner 2011 p. 41" /> When quoted as an ''indicated mean effective pressure'' (''IMEP''), it may be thought of as the average [[pressure]] acting on a [[piston]] during the different portions of its [[engine cycle|cycle]]. When friction losses are subtracted from the IMEP, the result is the brake mean effective pressure ('''BMEP''').
 ==Derivation==
 Let:
-:<math>W</math> = work per cycle in joule;
 :<math>P</math> = power output in watt;
-:<math>p_\text{me}</math> = mean effective pressure in pascal;
+:<math>p_\text{me}</math> = mean effective pressure in megapascal;
-:<math>V_\text{d}</math> = displacement volume in cubic metre;
+:<math>V_\text{d}</math> = displacement volume in cubic centimetre;
-:<math>n_\text{c}</math> = number of revolutions per power stroke (for a 4-stroke engine, <math>n_\text{c} =2</math>);<ref name="Wankel" group="Note">Note that Wankel engines are four-stroke engines, so <math>n_\text{c} =2</math>; the displacement <math>V_\text{d}</math> is derived from the chamber volume <math>V_\text{c}</math> by multiplying it with the number of rotary pistons <math>i</math> and 2: <math>V_\text{d} = 2 V_\text{c} i</math> (see Wolf-Dieter Bensinger: ''Rotationskolben-Verbrennungsmotoren'', Springer, Berlin/Heidelberg/New York 1973, {{ISBN|978-3-642-52174-4}}, p. 66)</ref>
+:<math>i</math> = number of cycles per revolution (for a 4-stroke engine, <math>i =0.5</math>, for a 2-stroke engine, <math>i =1</math>);<ref name="Wankel" group="Note">Wankel engines are four-stroke engines, so <math>i =0.5</math>; the displacement <math>V_\text{d}</math> is derived from the chamber volume <math>V_\text{c}</math> by multiplying it with the number of rotary pistons <math>i</math> and 2: <math>V_\text{d} = 2 V_\text{c} i</math> (see [[Wolf-Dieter Bensinger]]: ''Rotationskolben-Verbrennungsmotoren'', Springer, Berlin/Heidelberg/New York 1973, {{ISBN|978-3-642-52174-4}}, p. 66)</ref>
-:<math>N</math> = number of revolutions per second;
+:<math>n</math> = number of revolutions per second;
-:<math>T</math> = torque in newton-metre.
+:<math>\omega = </math> angular velocity, i.e. <math>\omega = 2 \pi n</math>;
+:<math>M</math> = torque in newton-metre.
+Then, BMEP may be used to determine an engine's power output as follows:
-The [[Power (physics)|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 <math>n_\text{c}</math> is the number of revolutions per power stroke, the number of power strokes per second is just their ratio. We can write:
-:<math>
-P = {W  {N \over n_\text{c}}}.
-</math>
-Reordering to put work on the left:
-:<math>
-W = {P {n_\text{c} \over N}}.
-</math>
-By definition:
 :<math>
-W = p_\text{me} V_\text{d},
+P=i \cdot n \cdot V_\text{d} \cdot p_\text{me}
-</math>
-so that
-:<math>
-p_\text{me} = {P n_\text{c} \over V_\text{d} N}.
 </math>
+Since we know that power is:
-Since the [[torque]] ''T'' is related to the angular speed (which is just ''N''·2π) and power produced,
-:<math>
+:<math>P = \omega \cdot M = 2 \pi \cdot n \cdot M</math>
-P = {2 \pi} T N,
-</math>
-then the equation for MEP in terms of torque is:
+We now see that, BMEP is a measure of expressing torque per displacement:
+:<math>P = i \cdot n \cdot V_\text{d} \cdot p_\text{me} = 2 \pi \cdot n \cdot M</math>
+And thus, the equation for BMEP in terms of torque is:
 :<math>
-p_\text{me} = {2 \pi} {n_\text{c}} {T \over V_\text{d}}.
+p_\text{me} = {{M \cdot 2 \pi} \over {V_\text{d} \cdot i}}.
 </math>
-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.
+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{{snd}} 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, mean effective pressure does not reflect the actual pressures inside an individual combustion chamber{{snd}} although the two are certainly related{{snd}} and serves only as a convenient measure of performance.<ref name="Schreiner 2011 p. 41">{{cite book | last=Schreiner | first=Klaus | title=Basiswissen Verbrennungsmotor | publisher=Vieweg+Teubner Verlag | publication-place=Wiesbaden | date=2011-05-25 | isbn=978-3-8348-1279-7 | language=de | page=41}}</ref>
-Brake mean effective pressure (BMEP) is calculated from measured [[dynamometer]] torque. Net indicated mean effective pressure (IMEP<sub>n</sub>) is calculated using the [[horsepower|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<sub>n</sub> and BMEP.
+Brake mean effective pressure (BMEP) is calculated from measured [[dynamometer]] torque. Net indicated mean effective pressure (IMEP) is calculated using the [[horsepower|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.<ref name="Spicher_2017_24" />
 == Examples ==
@@ Line 56: / Line 48: @@
 ;MEP from torque and displacement
-A four-stroke engine produces 160&nbsp;N·m of torque, and displaces 2&nbsp;dm<sup>3</sup>=0.002&nbsp;m<sup>3</sup>:
+A four-stroke engine produces 159&nbsp;N·m of torque, and displaces 2000&nbsp;cm<sup>3</sup>
-*<math>n_\text{c}=2</math>
+*<math>i=0.5</math>
-*<math>T=160 \, \text{N} {\cdot} \text{m}</math>
+*<math>M=159 \, \text{N} {\cdot} \text{m}</math>
-*<math>V_\text{d}=0.002 \, \text{m}^3</math>
-:<math>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}</math>
-We also get the megapascal figure if we use cubic centimetres for <math>V_\text{d}</math>:
-*<math>n_\text{c}=2</math>
-*<math>T=160 \, \text{N} {\cdot} \text{m}</math>
 *<math>V_\text{d}=2000 \, \text{cm}^3</math>
-:<math>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}</math>
+:<math>p_\text{me} = {2 \pi} \cdot {0.5^{-1}} {{159 \, \text{N} {\cdot} \text{m}} \over {2000 \, \text{cm}^3}} = {2 \pi} \cdot {0.5^{-1}} {{15900 \, \text{N} \cancel{\cdot \text{cm}}} \over {2000 \, \text{cm}^{{\cancel 3} 2}}} \approx 100 \, N \cdot cm^{-2} = 1 \, \text{MPa}</math>
 ;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: <math>P= {V_\text{d} \cdot p_\text{me} \cdot N \over n_\text{c}}</math><br />
+If we know the crankshaft speed, we can also determine the engine's power output from the MEP figure: <math>P=i \cdot n \cdot V_\text{d} \cdot p_\text{me}</math><br />
-In our example, the engine puts out 160&nbsp;N·m of torque at 3600&nbsp;min<sup>&minus;1</sup>:
+In our example, the engine puts out 159&nbsp;N·m of torque at 3600&nbsp;min<sup>&minus;1</sup> (=60&nbsp;s<sup>&minus;1</sup>):
-*<math>n_\text{c}=2</math>
+*<math>i=0.5</math>
-*<math>N= 3600 \, \text{min}^{-1} = 60 \, \text{s}^{-1}</math>
+*<math>n= 60 \, \text{s}^{-1}</math>
 *<math>V_\text{d}=2000 \, \text{cm}^3</math>
-*<math>p_\text{me}= 1.005 \, \text{MPa}</math>
+*<math>p_\text{me}= 1 \, \text{MPa}</math>
+Thus:
-<br />
-:<math>{2000 \cdot 1.005 \cdot 60 \over 2}= 60,300 \, \text{W}</math>
+:<math>P={2000 \, cm^{3} \cdot 1 \, N \cdot cm^{-2} \cdot 60 \, s^{-1} \cdot 0.5}= 60,000 \, N \cdot m \cdot s^{-1} = 60,000 \, \text{W} = 60 \, \text{kW}</math>
-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&nbsp;kW at 5400&nbsp;min<sup>&minus;1</sup> = 90&nbsp;s<sup>&minus;1</sup>, and its BMEP is 0.844&nbsp;MPa, we get the following equation:
+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 72&nbsp;kW at 5400&nbsp;min<sup>&minus;1</sup> = 90&nbsp;s<sup>&minus;1</sup>, and its BMEP is 0.80&nbsp;MPa, we get the following equation:
-*<math>n_\text{c}=2</math>
+*<math>i=0.5</math>
-*<math>N= 5400 \, \text{min}^{-1} = 90 \, \text{s}^{-1}</math>
+*<math>n= 90 \, \text{s}^{-1}</math>
 *<math>V_\text{d}=2000 \, \text{cm}^3</math>
-*<math>p_\text{me}= 0.844 \, \text{MPa}</math>
+*<math>p_\text{me}= 0.80 \, \text{MPa}</math>
+Then:
-<br />
-:<math>{2000 \cdot 0.844 \cdot 90 \over 2}= 75,960 \, \text{W} \approx 76 \, \text{kW}</math>
+:<math>P={2000 \, cm^{3} \cdot 0.80 \, N \cdot cm^{-2} \cdot 90 \, s^{-1} \cdot 0.5}= 72,000 \, N \cdot m \cdot s^{-1} = 72 \, \text{kW}</math>
 ==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.
+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.
+* Brake mean effective pressure (BMEP, <math>p_{me}</math>) - Mean effective pressure calculated from measured brake torque.
+* Indicated mean effective pressure (IMEP, <math>p_{mi}</math>) - Mean effective pressure calculated from in-cylinder pressure over the complete engine cycle (720° in a four-stroke, 360° in a two-stroke). IMEP may be determined by planimetering the area in an engine's [[Pressure–volume diagram|pV-diagram]]. Since naturally aspirated four-stroke engines must perform pumping work to suck the charge into the cylinder, and to remove the exhaust from the cylinder, IMEP may be split into the high-pressure, gross mean effective pressure (GMEP, <math>p_{mg}</math>) and the pumping mean effective pressure (PMEP, <math>p_{miGW}</math>). In naturally aspirated engines, PMEP is negative, and in super- or turbocharged engines, it is usually positive. IMEP may be derived from PMEP and GMEP: <math>p_{mi} = p_{mg}-p_{miGW}</math>.<ref name="Spicher_2017_24">Ulrich Spicher: ''Kapitel 3 · Kenngrößen – table 3.16: Effektiver Mitteldruck heutiger Motoren'', in Richard van Basshuysen, Fred Schäfer (eds.): ''Handbuch Verbrennungsmotor – Grundlagen · Komponenten · Systeme · Perspektiven'', 8th edition, Springer, Wiesbaden 2017, ISBN 978-3-658-10901-1, DOI 10.1007/978-3-658-10902-8_3, p. 24</ref>
-* Gross indicated mean effective pressure (IMEP<sub>g</sub>) - 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.
+* Friction mean effective pressure (FMEP, <math>p_{mr}</math>) - Theoretical mean effective pressure required to overcome engine friction, can be thought of as mean effective pressure lost due to friction: <math>p_{mr}=p_{mi}-p_{me}</math>. FMEP rises with an increase in engine speed.<ref>Ulrich Spicher: ''Kapitel 3 · Kenngrößen – table 3.16: Effektiver Mitteldruck heutiger Motoren'', in Richard van Basshuysen, Fred Schäfer (eds.): ''Handbuch Verbrennungsmotor – Grundlagen · Komponenten · Systeme · Perspektiven'', 8th edition, Springer, Wiesbaden 2017, ISBN 978-3-658-10901-1, DOI 10.1007/978-3-658-10902-8_3, p. 26, formula 3.48</ref>
-* Net indicated mean effective pressure (IMEP<sub>n</sub>) - 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 = IMEP<sub>g</sub> - IMEP<sub>n</sub>.
-* 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 = IMEP<sub>n</sub> - BMEP.
 ==BMEP typical values==
+{|class=wikitable
-Petrol engines :
+|+BMEP typical values<ref>Ulrich Spicher: ''Kapitel 3 · Kenngrößen – table 3.16: Effektiver Mitteldruck heutiger Motoren'', in Richard van Basshuysen, Fred Schäfer (eds.): ''Handbuch Verbrennungsmotor – Grundlagen · Komponenten · Systeme · Perspektiven'', 8th edition, Springer, Wiesbaden 2017, ISBN 978-3-658-10901-1, DOI 10.1007/978-3-658-10902-8_3, p. 27</ref>
-* Naturally aspirated spark-ignition engines : current [[List of Volkswagen Group petrol engines|VW petrol engines]] maximum MEP range (in [[Bar (unit)|bar]] and [[Psi (unit)|psi]]) from {{cvt|11.6|to|13.3|bar|psi}}, {{cvt|10.1|to|11.4|bar|psi}} at maximum power.
+|-
-* 28-cylinder [[Pratt & Whitney R-4360 Wasp Major]] with [[Avgas#Grades|115/145]] [[Octane rating|Octane]] [[World War II]] avgas, 3,600 HP at 2,700 rpm and 17.2 bar (249.4&nbsp;psi) BMEP.
+!Engine type
-* [[Napier Sabre]] 7, at peak HP, 3055 HP at 3850&nbsp;rpm, 19.4 bar (281.3&nbsp;psi) BMEP
+!Typical max. BMEP
-* [[Rolls-Royce Merlin]] 130/131, at peak HP, 2030 HP at 2900&nbsp;rpm, 23.1 bar (335&nbsp;psi) BMEP
+|-
-* Boosted spark ignition engines : current [[List of Volkswagen Group petrol engines|VW petrol engines]] maximum MEP range from {{cvt|16.4|to|23.1|bar|psi}}, {{cvt|15.3|to|19.3|bar|psi}} at maximum power.
+|Motorbike engine
-* High-boost engines such as the [[Koenigsegg Agera]] can run at BMEPs as high as 28 bar (32 bar for the Agera R)<ref>{{cite video |author= Drive |title= The 1140 hp Heart of a Hypercar - Inside Koenigsegg |url= https://www.youtube.com/watch?v=NzVc13UF2s8 |date= 26 February 2013 |publisher= Youtube}}</ref>
+|{{cvt|1.2|MPa|lbf/in2|1|abbr=on}}
-* [[Formula One engines]] : in 1986 the 1.5&nbsp;L Williams-Honda FW11 Turbo produced {{cvt|1400|hp|kW|0}} at 12,000 rpm<ref>{{cite web |url= http://www.f1technical.net/articles/26 |title= F1 rules and stats 1980-1989 |work= F1Technical |date= 1 Jan 2009}}</ref> for {{#expr:1044000/(2*pi)/(12000/60)round0}} Nm of torque, a {{cvt|{{#expr:4*pi*8.31/1.5round1}}|bar|psi}} BMEP. In 2006 the 2.4&nbsp;L Toyota TF106 produced {{cvt|740|hp|kW|0}} at 19,000&nbsp;rpm<ref>{{cite web |url= http://www.f1technical.net/f1db/cars/897/toyota-tf106 |title= Toyota TF106 |work= F1Technical}}</ref> for {{#expr:552000/(2*pi)/(19000/60)round0}} Nm of torque, a {{cvt|{{#expr:4*pi*2.77/2.4round1}}|bar|psi}} MEP.
+|-
-* Top Fuel dragster engines: 80–100 bar (8.0–10 MPa; 1160–1450&nbsp;psi)
+|Race car engine (NA Formula 1)
+|{{cvt|1.6|MPa|lbf/in2|1|abbr=on}}
-Diesel engines :
+|-
-* Naturally aspirated four-stroke diesels: current [[List of Volkswagen Group diesel engines|VW diesel engines]] have a {{cvt|8.9|bar|psi}} maximum MEP, {{cvt|8|bar|psi}} at max power.
+|Passenger car engine (naturally aspirated Otto)
-* Boosted automotive four-stroke diesels : current [[List of Volkswagen Group diesel engines|VW diesel engines]] have a {{cvt|17.7|to|31.9|bar|psi}} maximum MEP, {{cvt|14.5|to|26.8|bar|psi}} at max power.
+|{{cvt|1.3|MPa|lbf/in2|1|abbr=on}}
-* 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&nbsp;lbf/in<sup>2</sup>).
+|-
-* 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.<ref>{{cite web |url= http://cdn.wartsila.com/docs/default-source/product-files/engines/ms-engine/brochure-o-e-w31.pdf |title= Wärtsilä 31 |publisher= Wärtsilä |date= 2016 }}</ref>
+|Passenger car engine (turbocharged Otto)
+|{{cvt|2.2|MPa|lbf/in2|1|abbr=on}}
+|-
+|Passenger car engine (turbocharged Diesel)
+|{{cvt|2.0|MPa|lbf/in2|1|abbr=on}}
+|-
+|Lorry engine (turbocharged Diesel)
+|{{cvt|2.4|MPa|lbf/in2|1|abbr=on}}
+|-
+|High-speed industrial Diesel engine
+|{{cvt|2.8|MPa|lbf/in2|1|abbr=on}}
+|-
+|Medium-speed industrial Diesel engine
+|{{cvt|2.5|MPa|lbf/in2|1|abbr=on}}
+|-
+|Low-speed two-stroke Diesel engine
+|{{cvt|1.5|MPa|lbf/in2|1|abbr=on}}
+|}
 ==See also==
@@ Line 131: / Line 131: @@
 {{Reflist}}
-*Heywood, J. B., "Internal Combustion Engine Fundamentals", McGraw-Hill Inc., 1988
 ==External links ==