Four-wheel car dynamics#

The Four-wheel car dynamics block simulates a vehicle driven in longitudinal motion by forces:

Then the general equation of the vehicle force (1):

(1)#\[F_{total}=m\cdot a = F_{T,f}+F_{T,r}+F_{D}+F_{R}+F_{W} \]

The forces of the front and rear axle \(F_{T,f}\), \(F_{T,r}\) , are set to the first two ports on the right side.

The force of resistance to tire movement is calculated by the formula (2):

(2)#\[F_{R}=C_{R}\cdot F_{N,i}, \]

where

\(C_{R}\) - rolling coefficient;

\(F_{N,i}\) - force acting on either the front or rear transmission axle and equal to (3):

\[L_{101}\cdot F_{N,f}=m\cdot g \cdot cos\theta \cdot CG_{r} - m\cdot a \cdot CG_{h}-m\cdot g \cdot sin\theta \cdot CG_{h}; \]

(3)#\[L_{101}\cdot F_{N,r}=m\cdot g \cdot cos\theta \cdot CG_{f} + m\cdot a \cdot CG_{h}+m\cdot g \cdot sin\theta \cdot CG_{h}. \]

\(L_{101}\) - wheelbase length, [m];

\(F_{N,f}\), \(F_{N,r}\) - forces acting on the front and rear axles of the vehicle transmission, respectively, [N];

\(CG_{h}\) - height of mass center, [m]

\(CG_{f}\), \(CG_{r}\) - distances from the rear and front axle to the center of mass, [m].

The aerodynamic resistance force is calculated by the formula (4):

(4)#\[F_{D}=\frac{1}{2}\cdot \rho \cdot A \cdot C_{D} \cdot V^2, \]

where

\(\rho\) - air density, [kg/m\(^3\)];

А - frontal area of electric vehicle, [m\(^2\)];

\(C_{D}\) - aerodynamic resistance coefficient;

V - longitudinal speed of the vehicle, [m/s].

The gravity force is calculated by the formula (5):

(5)#\[F_{W}=m\cdot g \cdot sin\theta, \]

where

g - free fall acceleration, [m\(^2\)/s];

\(\theta\) - tilt angle, [deg];

m - mass of transport, [kg].

1. Properties#

Property	Default value	Description	Units of measurement
Wheelbase length	2.7	-	m
Height of mass center	0.4	-	m
Distance from rear axle to center of mass	1.4	-	m
Distance from front axle to center of mass	1.3	-	m
Free fall acceleration	9.81	-	m/s\(^2\)
Car mass	1540.0	-	kg
Frontal area	2.4	-	m\(^2\)
Air density	1.2	-	kg/m\(^3\)
Braking coefficient	0.27	-	-
Rolling coefficient	0.009	-	-
Velocity threshold	1e-4	-	m/s
Account wheel inertia	Off	-	-
Wheel inertia, available when selecting `Account wheel inertia` - `On`	0.3	-	kg\(\cdot m^2\)
Wheel radius, available when selecting `Account wheel inertia` - `On`	0.32	-	m

Parameters	Input/Output	Description	Units of measurement	Port type
Force on the front axle	Input	-	N	Translational motion
Force on the rear axle	Input	-	N	Translational motion
Vertical deviation angle	Input	-	rad	Automation
Displacement	Output	-	m	Automation
Overall resistive force	Output	-	N	Automation
Speed	Output	-	km/h	Automation

In order to see the connection capabilities of the block, you need to go to page Description of block ports