Vehicle Propulsion SystemsFormulaeNazarbayev UniversitySchool of EngineeringDepartment of Mechanical EngineeringVehicle Propulsion Systems(Formulae)Basic Conceptsmvdv(t) = Ft (t) − (Fa (t) + Fr (t) + Fg (t) + Fd (t))dt1· ρa · Af · cd (v, …) · v 22Fr (v, p, …) = cr (v, p, …) · mv · g · cos(α), v > 0Fa (v) =Fg (α) = mv · g · sin(α)Fg (α) ≈ mv · g · αInertial Forcesdωw (t)dtΘw dFm,w (t) = 2 · v(t)rw dtTm,w (t) = Θw ·mr,w =Tm,e (t) = Θe ·Θwrw2dγ ddωe (t) = Θe · (γ · ωw (t)) = Θe ·· v(t)dtdtrw dtFm.e (t) =γγ2 d· Tm,e (t) = Θe · 2 · v(t)rwrw dtmr,e =γ2· Θerw2mr = mr,w + mr,e =γ21·Θ+· Θewrw2rw2Top Speed PerformancePmax ≈13· ρa · Af · cd · vmax2Uphill DrivingPmax ≈ mv · vmin · g · sin(αmax )Acceleration Timeto ≈v02 · mvPmaxPage 1Vehicle Propulsion SystemsFormulaeCoasting Velocityαβ−1vc (t) = · tan tan· vc (0) − α · β · t , vc > 0αβMechanical Energy Demand in Driving CyclesZ1Ft (t) · v(t)dt·F̄trac =xtot t∈tracF̄trac ≈F̄tracX1·F̄i · v̄i · hxtot i∈tracnX1 X1··≈(F̄a,i + F̄r,1 ) · v̄i · h +−F̄i · v̄i · hxtot i=0xtoti∈trac/1·xtotnX(F̄a,i + F̄r,1 ) · v̄i · h , F̄diss ≥ 0i=0X1·−F̄i · v̄i · h , F̄circ ≥ 0xtoti∈trac/Ē = Ēdiss + ĒcircNo recuperation:F̄trac = F̄trac,a + F̄trac,r + F? … Purchase document to see full attachment
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