Engine formulas

source:thecartech.com

Cylinder Swept Volume (V_c):

where:

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

            A_c = cylinder area [cm² or cm²/100]

            d_c = 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 (V_e):

where:

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

            n = number of cylinders

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

A_c = cylinder area [cm² or cm²/100]

d_{c =}  cylinder diameter [cm or cm/10]

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

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

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

Compression Ratio (r):

where:

            r = compression ratio

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

            V_c = 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:

            h_V  = volumetric efficiency

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

            V_c = 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 (T_i):

where:

            T_i = engine indicated torque [Nm]

            imep = indicated mean effective pressure [N/m²]

            A_c = 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 (P_i):

,                       

where:

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

            A_c = 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)

            V_c = cylinder swept volume [m³]

            V_e = engine swept volume [m³]

            T_i = engine indicated torque [Nm]

            ω = engine angular speed [1/s]

Engine Mechanical Efficiency (h_m):

 

where:

            h_m = mechanical efficiency

            P_b = engine brake power [kW]

            P_i = engine indicated power [kW]

            P_f = 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]

            P_b = brake power [kW]

Engine Thermal Efficiency (_hth):

 

where:

            h_th = thermal efficiency

            P_b = 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]