Electric Vehicle Dynamics
The electric vehicle is modeled as a single model, which is directly connected to the mechanical drive shaft on the left side of the model. On the right side a system signal provides the speed of the vehicle in [km/h].
The first step in vehicle performance modelling is to write an electric force model. This is the force transmitted to the ground through the drive wheels, and propelling the vehicle forward. This force must overcome the road load and accelerate the vehicle.
For any mission profile, an electric road vehicle is subjected to forces that the onboard propulsion system has to overcome in order to propel or retard the vehicle. These forces are composed of several components. The effort to overcome these forces by transmitting power via the vehicle drive wheels and tyres to the ground is known as the total tractive effort or total tractive force.
The parameters for this model are entered into the vehicle model.
The rolling resistance is primarily due to the friction of the vehicle tires on the road and can be written as: \[F_{R} = C_r \cdot M_v \cdot g\]
The aerodynamic drag is due to the friction of the body of vehicle moving through the air. The formula for this component is: \[F_{v} = \frac{1}{2} \rho C_w A v^2 \]
Hill climbing is the third resistance that is applied. \[F_{\alpha} = M_v \cdot g \cdot sin(\alpha)\]
The power that the electric vehicle must develop at constant speed is expressed by the following equation: \[P = (F_R +F_v +F_{\alpha} ) \cdot v\] The torque that the electric vehicle must develop at constant speed is expressed by the following equation: \[T = (F_R +F_v +F_{\alpha} ) \cdot R\]
The parameters in the formulas above have to be entered in Caspoc. They relate to the parameters in Caspoc as follows:
| Parameter | Caspoc Parameter |
| Mv | Car Mass [Kg] |
| R | Wheel Diameter [m] |
| Cr | Rolling Coefficient |
| Cw | Drag Coefficient |
| A | Frontal Area[m^2] |
| ρ | Air Density[Kg/m3] |
| sin(α) | Road Grade[%] |
| v | Vehicle speed + wind speed[m/s] |
The parameters for any vehicle are displayed below.
| Parameters(10) | Default | Remark |
| Cw[DragCoefficient] | 0.25 | Drag coefficient Cw (around 0.3 to 0.4) |
| Cr(RollingCoefficient) | 0.01 | Rolling coefficient cr of the wheels [N/kg] |
| CarMass[Kg] | 1500 | Total mass of the car [Kg] |
| RoadGrade[%] | 0 | Grade of the road in [%] |
| AirDensity[Kg/m3] | 1.225 | Air density (average value) |
| FrontalArea[m^2] | 2.2 | Frontal area of the car in [m*m] |
| Vwind[m/s] | 0 | Headwind speed blowing towards the vevicle |
| WheelRadius[m] | 0.3 | Wheel radius (m) |
| slip[0..1] | 0.1 | Slip between the tire and road [0..1] |
| IntialSpeed[kmh] | 0 | Initial speed of the vehicle in kilometers per hour [kmh] |
The parameters slip and initial speed are optional.
There are four popular models for electric vehicles available that have the corrdct parameters. You can apply them directly in the simulation, without the need for changing parameters.
The other vehicles that can be used in the simulation are a bicycle, known as Hollandrad, a scooter, Tuk-Tuk and a truck.
A custom vehicle can be set up where all four wheels can be controlled independently.
For easy connection with the main drive shaft coming from the power train, special blocks are provided that allow a direct connection from the drive train shaft to the wheels.
