Mean effective pressure

# Mean effective pressure

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Encyclopedia
The mean effective pressure is a quantity related to the operation of an reciprocating engine
Reciprocating engine
A reciprocating engine, also often known as a piston engine, is a heat engine that uses one or more reciprocating pistons to convert pressure into a rotating motion. This article describes the common features of all types...

and is a valuable measure of an engine's capacity to do work that is independent of engine displacement
Engine displacement
Engine displacement is the volume swept by all the pistons inside the cylinders of an internal combustion engine in a single movement from top dead centre to bottom dead centre . It is commonly specified in cubic centimeters , litres , or cubic inches...

. When quoted as an indicated mean effective pressure or imep (defined below), it may be thought of as the average pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

over a cycle in the combustion chamber of the engine.

## Derivation

Let,
= work per cycle in joule
= power output in watt
= mean effective pressure in pascal
= displacement volume in cubic metre
= number of revolutions per cycle (for a 4-stroke engine )
= number of revolutions per second
= torque in newton-metre

The power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...

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 is the number of revolutions per cycle, the number of cycles per second is just their ratio. We can write
By definition:
so that

Since the torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

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

Then the equation for mep in terms of torque becomes,

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
Dynamometer
A dynamometer or "dyno" for short, is a device for measuring force, moment of force , or power. For example, the power produced by an engine, motor or other rotating prime mover can be calculated by simultaneously measuring torque and rotational speed .A dynamometer can also be used to determine...

torque. Indicated mean effective pressure or imep is calculated using the indicated power
Horsepower
Horsepower is the name of several units of measurement of power. The most common definitions equal between 735.5 and 750 watts.Horsepower was originally defined to compare the output of steam engines with the power of draft horses in continuous operation. The unit was widely adopted to measure the...

; 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 torque

• Indicated mean effective pressure (IMEP) - Mean effective pressure calculated from in cylinder pressure, average in cylinder pressure over engine cycle, 720°.

• Friction mean effective pressure (FMEP) - Theoretical mean effective pressure required 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.
• 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).
• Naturally aspirated four-stroke diesels: Maximum BMEP in the 7 to 9 bar range (700 to 900 kPa; 100 to 130 lbf/in2).
• 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
Wärtsilä-Sulzer RTA96-C
The Wärtsilä RT-flex96C is a two-stroke turbocharged low-speed diesel engine designed by the Finnish manufacturer Wärtsilä. It is currently considered the largest reciprocating engine in the world, designed for large container ships, running on heavy fuel oil...

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
Koenigsegg Agera
The Koenigsegg Agera is a mid-engined sports car made by Swedish car manufacturer Koenigsegg as of 2011. It is a successor to the Koenigsegg CCX/CCXR...

can run at BMEPs as high as 28 bar
• 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 MPa (10.05 bar
Bar (unit)
The bar is a unit of pressure equal to 100 kilopascals, and roughly equal to the atmospheric pressure on Earth at sea level. Other units derived from the bar are the megabar , kilobar , decibar , centibar , and millibar...

). 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 just like 2-strokes, so the engine's BMEP can be calculated as just under 129 bar.