*3.1. Vehicle Dynamics*

Simulations aimed at the calculation of the fuel economy and assessment of the powertrain operation usually replicate vehicles moving through driving cycles that model real-world driving conditions. Cycle schedules do not include the driving trajectory, and, thus, when modeling, the vehicle motion is considered linear. Furthermore, there were additional assumptions that were made in this work to derive the vehicle dynamics model. The tire slip is neglected due to the assumption that the maximum adhesion coefficient is high, and thus, a sufficient tractive force is exerted with a small slip. The model also neglects the dynamics of wheel vertical forces and variations of the wheel radii. Given these assumptions, the model of the vehicle linear motion can be presented as the dynamics of a single lumped mass:

$$\dot{\upsilon} = \frac{T\_w/r\_w - F\_f - F\_{air} - F\_\alpha}{m\_\upsilon + n \cdot T\_w/r\_w^2},\tag{1}$$

where *v* is the vehicle velocity; *mv* is the vehicle mass; *Tw* is the torque at the driving wheels; *rw* is the wheel radius; I*<sup>w</sup>* is the wheel inertia; *n* is the number of wheels on the vehicle (including the trailer's wheels); and *Fair*, *Ff* , and *F*<sup>α</sup> are the resistance forces.

The rolling resistance force is calculated using the following formula: *Ff* = *mv*·*g*· *f*, where *g* is the acceleration due to gravity and *f* is the dimensionless coefficient of tire-rolling resistance. When identifying the model parameters from the coast-down test results, it was found that the function *<sup>f</sup>*(*v*) was satisfactorily approximated using the known quadratic expression: *<sup>f</sup>* <sup>=</sup> *<sup>f</sup>*<sup>0</sup> <sup>+</sup> *kv*·*v*<sup>2</sup> [30], where *f*<sup>0</sup> is the rolling resistance coefficient at near-zero velocity and *kv* is the factor of the velocity-dependent growth of the rolling resistance. The rolling resistance force calculated with these formulae was assumed to be equal (i.e., averaged) for all the tires of the vehicle.

A well-known empirical formula is used for calculating the aerodynamic resistance force:

$$F\_w = 0.5 \cdot \mathbb{C}\_x \cdot A \cdot \rho \cdot v^2,\tag{2}$$

where *Cx* is the air drag coefficient of the vehicle, *A* is the vehicle frontal area, and ρ is the air density.

The grade resistance force *F*β is a projection of the vehicle gravity force vector onto the road plane, which is calculated as follows: *F*<sup>β</sup> = *mv*·*g*·*sin*(β), where β is the road inclination angle (positive for an ascending slope).
