Decomposition Analysis of an Automotive Powertrain Design ...

C roll = 0.05 (1. + 0.01 V). (3)
In either case, at a given tire pressure, C roll is a function of velocity. The resistance force due to
the grade is,
F grade = M g sin α, (4)
and aerodynamic resistance is modeled as the pressure drag based on the frontal area of the
vehicle, the vehicle drag coefficient, and dynamic pressure due to the velocity of the vehicle,
F aero = 0.5 C d A ρ air (V) 2 , (5)
where the frontal area is given by
A = 0.9 H a S w. (6)
The normal forces at the wheels are determined by taking moments about each wheel,
F nd = (L nd M g cos α - M dV/dt H cg - Mg sin α H cg - F aero H a ) / L w (7)
F nnd = (L d M g cos α + M dV/dt H cg + Mg sin α H cg + F aero H a ) / L w . (8)
Defining static weight distribution factors,
W d = L nd cos α / L w (9)
W nd = Ld cos α / L w (10)
and the dynamic axle weight,
∆W d = (M dV/dt H cg + Mg sin α H cg + F aero H a ) / L w (11)
the normal reactions can be simplified,
F nd = W d M g - ∆W d (front wheel drive) (12)
= W d M g + ∆W d (rear wheel drive)
F nnd = W nd M g + ∆W d (front wheel drive) (13)
= W nd M g - ∆W d (rear wheel drive)
The relationship between the powertrain and the driving force at the wheels, F d , is developed next,
followed by detailed explicit models of each of the powertrain components.