## 24 Dynamics Of Vehicle Motion

Tractive force is the force between the vehicle's tires and the road (and parallel to the road) supplied by the electric motor in an EV and by the combination of electric motor and IC engine in an HEV to overcome the road load. The dynamic equation of motion in the tangential direction is given by

where km is the rotational inertia coefficient to compensate for the apparent increase in the vehicle's mass due to the onboard rotating mass. The typical values of km are between 1.08 and 1.1, and it is dimensionless. The acceleration of the vehicle is dvXT/dt.

Dynamic equations can be represented in the state space format for simulation of an EV or HEV system. The motion described by Equation 2.5 is the fundamental equation required for dynamic simulation of the vehicle system. One of the state variables of the vehicle dynamical system is vxT. The second equation needed for modeling and simulation is the velocity equation, where either s or xF can be used as the state variable. The slope of the roadway B will be an input to the simulation model, which may be given in terms of the tangential roadway distance as B=B(s) or in terms of the horizontal distance as B=B(xF). If B is given in terms of s, then the second state variable equation is 