Mean Effective Pressure - Derivation

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 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 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 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.