## Mathematical Basis for Power Correction Factor

The power output for a given engine type is dependent largely on the air mass flow rate that it achieves. This will vary as the pressure, humidity, and temperature of the air it inducts changes.

The basis for the correction factors used to standardize power and volumetric efficien­cies is the equation for one-dimensional steady compressible flow through an orifice or a flow restriction of effective area (AE):

(Y+l)

_ AeP0 / 2y

 Vp0y

 V p0 )

A/RM y-1

The derivation of this equation assumes that the fluid is an ideal gas, with gas constant R,

Q

And the ratio of specific heats y = —— is a constant, P0 and T0 are the total pressure

Cv

And temperature upstream of the restriction, respectively, and P is the pressure at the throat of the restriction.

If, in the engine, — is assumed constant at wide open throttle, then for a given intake P0 . system and engine, the mass flow rate of dry air m varies as

M a P0

Thus, to compare power outputs from days with changing ambient conditions, the actual pressures and temperatures must be related to a set of standard conditions. Therefore, if we write mast(j = CF x ma (measured), then using the preceding relationship between mass airflow rate and pressure/temperature, the correction factor (CF) can be expressed as

 P Vf
 P Vf
 CF =
 Mastandard ma measured
 T,
 Measured Standard
 ^standard Pmeasured

Here is assumed to be the dry air pressure, the pressure of any water vapor needs to be subtracted from the actual measured air pressure. Then the preceding expression can be written as

 Measured

Because P

 Tm Ts

Psd

CF =

Pm — Pvm

Where

Psd = standard dry air absolute pressure

Pm = measured ambient air absolute pressure

Pvm = measured ambient water vapor partial pressure

Tm = measured ambient temperature

Ts = standard ambient temperature

The basic principle of the internal combustion engine is that the rapid burning of a combustible mixture produces a release of energy in the form of a pressure rise within the cylinder. This energy is harnessed by various means and is converted into rotary motion. The formulae presented here are those commonly used in the management of air and fuel and the measurement of power and torque. Before going any further, I will review some terms commonly used when discussing engine performance.

Swept Volume

At top dead center, the volume remaining above the piston is termed the clearance volume. The swept volume is defined as the volume above the piston at bottom dead center less the clearance volume.

Hence,

Swept volume = Total volume — Clearance volume

Compression Ratio

The compression ratio (CR) is the ratio of the volume between the piston and the cylinder head before and after compression.

 Swept volume Clearance volume
 + 1
 CR =
 Total + Clearance volume Clearance volume

Typical values for the compression ratio are 8:1 to 12:1 for spark ignition engines and up to 24:1 for compression ignition engines.

Brake Mean Effective Pressure

The calculated brake mean effective pressure (BMEP) is measured in bar, kilograms per square meter (kg/m2), or pounds per square inch (psi) as

Brake work output (Nm) per cylinder per cycle BMhr =

Swept volume per cylinder (m)

The brake mean effective pressure is a better measure of engine performance than power, kilowatts (kW), or brake horsepower (BHP) for comparative purposes because it does not depend on engine size (Table 13.2).

TABLE 13.2

_________________ TYPICAL BMEP___________________

Engine Peak Torque Peak Power

Type BMEP Bar BMEP Bar

Spark ignition N/A 8.2-12.0 6.5-11.0

Spark ignition T/C 12.5-19.0 9.0-16.0

Pumping Mean Effective Pressure

The pumping mean effective pressure (PMEP) is a measure of the work done in drawing a fresh mixture through the induction system into the cylinder and expelling the burned gases out of the cylinder and through the exhaust system.

Compression/Expansion Mean Effective Pressure

In effect, the compression/expansion mean effective pressure (CEMEP) is the same as the gross IMEP.

Friction Mean Effective Pressure

The friction mean effective pressure (FMEP) is a measure of rubbing friction work and accessory work:

IMEP gross = IMEP net + PMEP CEMEP = IMEP net + PMEP BMEP = IMEP gross — PMEP — FMEP

Brake Torque and Power

Power is the product of torque and angular velocity. Torque is a measure of the ability of an engine to do work, and power is the rate at which work is done

P(power) = T (torque) x w (engine speed)

Where

W = angular velocity in radians per second 2n radians = 360° of crankshaft rotation

_ 2?tNT _ T x N _ 60 _ 9550

When N is the engine speed in revolutions per minute. lkW= 1.3596 PS= 1.341 BHP

1 Nm (torque) = 0.7376 lbf/ft = 9.81 kgf./m and 1 lbf/ft = 1.3558 Nm

BMEP = 1200 xP V x N

When

T = torque (Nm)

V = capacity (liters)

P = power (kW)

N = engine speed, rev/min Also, the units of BMEP are in bar (1 bar = 100 KPa).

Motoring Mean Effective Pressure

The motoring mean effective pressure (MMEP) is determined from the torque required to motor an engine at a predetermined condition and can be calculated as

, „ , 1000 x Motoring torque (Nm) x Number of strokes

MMEP (bar) =——————— —- — —— —r———————

Capacity (cm)