Engine Formulas

Engine Formulas



Cylinder Swept Volume (Vc):



where:

Vc= cylinder swept volume [cm3 (cc) or L]

Ac = cylinder area [cm2 or cm2/100]

dc = cylinder diameter [cm or cm/10]

L = stroke length (the distance between the TDC and BDC) [cm or cm/10]



BDC = Bottom Dead Center

TDC = Top Dead Center



* Increase the diameter or the stroke length will increase the cylinder volume, the ratio between the cylinder diameter/cylinder stroke called “bore/stroke” ratio.

- “bore/stroke” >1 is called over square engine, and is used in automotive engines

- “bore/stroke” =1 is called square engine

- “bore/stoke” <1 is called= under square engine, and is used in tractor engine





Engine Swept Volume (Ve):



where:

Ve = engine swept volume [cm3 (cc) or L]

n = number of cylinders

Vc = cylinder swept volume [cm3 (cc) or L]

Ac = cylinder area [cm2 or cm2/100]

dc = cylinder diameter [cm or cm/10]



* The units of cylinder swept volume is measured in (cm3, cubic centimeter (cc), or liter)

- Ve for small engines, 4 cylinder engines is (750 cc:1300 cc)

- Ve for big engine, 8 cylinder engines is (1600 cc:2500 cc)





Compression Ratio (r):



where:

r = compression ratio

Vs = cylinder swept volume (combustion chamber volume) [cc, L, or m3]

Vc = cylinder volume [cc, L, or m3]



* Increase the compression ratio increase engine power

- r (gasoline engine) = 7:12, the upper limit is engine pre ignition

- r (diesel engine) = 10:18, the upper limit is the stresses on engine parts





Engine Volumetric Efficiency (hv):



where:

hV = volumetric efficiency

Vair = volume of air taken into cylinder [cc, L, or m3]

Vc = cylinder swept volume [cc, L, or m3]



* Increase the engine volumetric efficiency increase engine power

- Engine of normal aspiration has a volumetric efficiency of 80% to 90%

- Engine volumetric efficiency can be increased by using:

(turbo and supper charger can increase the volumetric efficiency by 50%)







Engine Indicated Torque (Ti):



where:

Ti = engine indicated torque [Nm]

imep = indicated mean effective pressure [N/m2]

Ac = cylinder area [m2]

L = stroke length [m]

z = 1 (for 2 stroke engines), 2 (for 4 stroke engines)

n = number of cylinders

θ = crank shaft angle [1/s]





Engine Indicated Power (Pi):



,

where:

imep = is the indicated mean effective pressure [N/m2]

Ac = cylinder area [m2]

L = stroke length [m]

n = number of cylinders

N = engine speed [rpm]

z = 1 (for 2 stroke engines), 2 (for 4 stroke engines)

Vc = cylinder swept volume [m3]

Ve = engine swept volume [m3]

Ti = engine indicated torque [Nm]

ω = engine angular speed [1/s]





Engine Mechanical Efficiency (hm):





where:

hm = mechanical efficiency

Pb = engine brake power [kW]

Pi = engine indicated power [kW]

Pf = engine friction power [kW]





Engine Specific Fuel Consumption (SFC):



where:

SFC = specific fuel consumption [(kg/h)/kW, kg/(3600 s x kW), kg/(3600 kJ)]

FC = fuel consumption [kg/h]

Pb = brake power [kW]





Engine Thermal Efficiency (hth):





where:

hth = thermal efficiency

Pb = brake power [kW]

FC = fuel consumption [kg/h = (fuel consumption in L/h) x (ρ in kg/L)]

CV = calorific value of kilogram fuel [kJ/kg]

ρ = relative density of fuel [kg/L]