Car Performance Formulas- أداء السيارة  Car Performance Formulas- أداء السيارة المعادلات الحسابية للسيارات Automotive Mathematical Formulas   Car Performance Formulas-  أداء السيارة    Air Resistance (Air Drag) (AR): where:             AR = air resistance [N]             ρ = air density [kg/m3] ≈ 1.202 kg/m3, at sea level and at 15o C             Af = car frontal area [m2] ≈ 1.2 : 3.2 m2, for small and mid size cars             Cd = coefficient of aerodynamics resistance (drag coefficient) ≈ 0.2 : 0.5 for cars             v = car relative velocity [km/h]             vcar = car velocity [km/h] (vcar = v, at stand still wind, vwind = 0)             vwind = wind velocity [km/h]   * ( + ), (+) with head wind, the wind velocity opposite the car velocity direction (against) .             (-) with tail wind, the wind velocity in the same direction as the car velocity (with).       Rolling Resistance (RR): where:             RR = rolling resistance [N]             fr = coefficient of rolling resistance ≈ 0.015 : 0.02 (hard surface) 0.2 : 0.3 (sand)             w = car weight [N] ≈ 10000 : 24000 N, for small and mid size cars             m = car mass [kg] ≈ 1000 : 2400 kg, for small and mid size cars             g = acceleration due to gravity = 9.81 [m/s2]       Gradient Resistance (GR): where:             GR = gradient resistance [N]             w = car weight [N] = mg [kg m/s2, (N)]             θ = gradient angle < 2.3o (highways), 5.7 : 6.9o (local roads), ≈ 11.5o (max. grad)             S = gradient percentage [%] S < 4% (highways), <10% : 12% (local roads), ≈ 20% (maximum gradient)             G = gradient ratio [1: n = 1/n]                 <1:25 (1/25) highways, < 1:8 (1/8) local roads, 1:5 (1/5) maximum grad.   * ( + ), (+) with the car going up hill (ascending). {resistance effort}             (-) with the car going down hill (descending). {tractive effort}     Inertia Resistance (IR): where:             IR = inertia resistance [N]         m = car mass + equivalent mass of rotating parts [kg] a = car acceleration [m/s2], (from 0 to 100 km/h in: 6 s (4.63 m/s2), 18 s (1.543 m/s2)) mcar = car mass [kg] meq = equivalent mass of rotating parts [kg]                    = [ Iw (1/rw)2 + Ip hf (if /rw)2 + Ie ht (if ig / rw)2]                         where:                                     Iw = polar moment of inertia of wheels and axles ≈ 2.7 [kg m2]                                     Ip = polar moment of inertia of propeller shaft ≈ 0.05 [kg m2] Ie = polar moment of inertia of engine ≈ 0.2 [kg/m2] + polar moment   of inertia of flywheel and clutch ≈ 0.5 [kg m2] hf = mechanical efficiency of final drive ht = mechanical efficiency of transmission system (hg x hf) ig = gearbox reduction ratio [ig1 or ig2 or ………….] if = final drive reduction ratio rw = tire radius [m]   * ( + ), (+) with the car in acceleration. {tractive resistance}             (-) with the car in deceleration. {tractive effort}     Total Resistance (TR): where:             TR = total resistance [N]             RR = rolling resistance [N]             AR = air resistance [N]             GR = gradient resistance [N]             IR = inertia resistance [N]     Car Velocity (v): where:             v = car velocity [km/h]             rw = rolling radius of the tire [m]             Nw = tire rotational speed [rpm]             Ne = engine rotation speed [rev/s, (rpm)]             ig = gearbox reduction ratio             if = final drive reduction ratio     Wheel torque (Tw): where             Tw = wheel torque [Nm]             Te = engine torque [Nm]             ig = gearbox reduction ratio             if = final drive reduction ratio             ht = total transmission efficiency             Pw = wheel power [kW]             Pe = engine power [kW]     Wheel Power (Pw): where:             Pw = wheel power [kW]             Tw = wheel torque [Nm]             Nw = wheel rotational speed [rev/s, (rpm)]             Ne = engine rotational speed [rev/s, (rpm)]             ht = total transmission efficiency               Car Tractive Effort (TE): where:             TE = tractive effort [N]             Tw = wheel torque [Nm]             Te = engine torque [Nm]             Pw = wheel power [kW]             Pe = engine power [kW]             v = car velocity [km/h]             ig = gearbox reduction ratio             if = final drive reduction ratio             v = car velocity [km/h]     Surplus Effort (SE): where:             SE = surplus effort [N]             TE = tractive effort [N]             TR = total resistance [N]   * At maximum car speed, SE = 0   