Documentation |
Two-axle vehicle with longitudinal dynamics and motion and adjustable mass, geometry, and drag properties
The Vehicle Body block models a two-axle vehicle, with an equal number of equally sized wheels on each axle, moving forward or backward along its longitudinal axis.
The model includes the following vehicle properties.
Mass
Number of wheels on each axle
Position of the vehicle's center of gravity (CG) relative to the front and rear axles and to the ground
Effective frontal cross-sectional area
Aerodynamic drag coefficient
Initial longitudinal velocity
For model details, see Vehicle Body Model.
You specify the headwind speed V_{W} (in meters/second) and the road inclination angle β (in radians) through physical signal inputs at ports W and beta, respectively.
The block reports the longitudinal vehicle velocity V_{x} and the front and rear normal forces (load on wheels) F_{zf}, F_{zr} as physical signal outputs at ports V, NF, and NR, respectively.
The horizontal motion of the vehicle is represented by the translational conserving port H.
Mass m of the vehicle. The default is 1200.
From the drop-down list, choose units. The default is kilograms (kg).
Number n of equally-sized wheels on each axle, forward and rear. The default is 2.
Horizontal distance a from the vehicle's center of gravity to the vehicle's front wheel axle. The default is 1.4.
From the drop-down list, choose units. The default is meters (m).
Horizontal distance b from the vehicle's center of gravity to the vehicle's rear wheel axle. The default is 1.6.
From the drop-down list, choose units. The default is meters (m).
Height h of the vehicle's center of gravity from the ground. The default is 0.5.
From the drop-down list, choose units. The default is meters (m).
Effective cross-sectional area A presented by the vehicle in longitudinal motion, to computer the aerodynamic drag force on the vehicle. The default is 3.
From the drop-down list, choose units. The default is meters-squared (m^2).
The dimensionless aerodynamic drag coefficient C_{d}, for the purpose of computing the aerodynamic drag force on the vehicle. The default is 0.4.
The initial value V_{x}(0) of the vehicle's horizontal velocity. The default is 0.
From the drop-down list, choose units. The default is meters/second (m/s).
The vehicle axles are parallel and form a plane. The longitudinal x direction lies in this plane and perpendicular to the axles. If the vehicle is traveling on an incline slope β, the normal z direction is not parallel to gravity but is always perpendicular to the axle-longitudinal plane.
This figure and table define the vehicle motion model variables.
Vehicle Dynamics and Motion
Vehicle Model Variables
Symbol | Description and Unit |
---|---|
g | Gravitational acceleration = 9.81 m/s^{2} |
β | Incline angle |
m | Vehicle mass |
h | Height of vehicle CG above the ground |
a, b | Distance of front and rear axles, respectively, from the normal projection point of vehicle CG onto the common axle plane |
V_{x} | Longitudinal vehicle velocity |
V_{W} | Headwind speed |
n | Number of wheels on each axle |
F_{xf}, F_{xr} | Longitudinal forces on each wheel at the front and rear ground contact points, respectively |
F_{zf}, F_{zr} | Normal load forces on the each wheel at the front and rear ground contact points, respectively |
A | Effective frontal vehicle cross-sectional area |
C_{d} | Aerodynamic drag coefficient |
ρ | Mass density of air = 1.2 kg/m^{3} |
F_{d} | Aerodynamic drag force |
The vehicle motion is determined by the net effect of all the forces and torques acting on it. The longitudinal tire forces push the vehicle forward or backward. The weight mg of the vehicle acts through its center of gravity (CG). Depending on the incline angle, the weight pulls the vehicle to the ground and pulls it either backward or forward. Whether the vehicle travels forward or backward, aerodynamic drag slows it down. For simplicity, the drag is assumed to act through the CG.
$$\begin{array}{l}m{\dot{V}}_{\text{x}}={F}_{\text{x}}-\text{}{F}_{\text{d}}-mg\cdot \mathrm{sin}\beta ,\\ {F}_{\text{x}}=n({F}_{\text{xf}}+{F}_{\text{xr}}),\\ {F}_{\text{d}}=\frac{1}{2}{C}_{\text{d}}\rho A({{\displaystyle {V}_{\text{x}}-{V}_{\text{W}})}}^{2}\cdot \mathrm{sgn}({V}_{\text{x}}-{V}_{\text{W}})\end{array}$$
Zero normal acceleration and zero pitch torque determine the normal force on each front and rear wheel:
$$\begin{array}{l}{F}_{\text{zf}}=\frac{-h({F}_{\text{d}}+mg\mathrm{sin}\beta +m{\dot{V}}_{\text{x}})+b\cdot mg\mathrm{cos}\beta}{n(a+b)},\\ {F}_{\text{zr}}=\frac{+h({F}_{\text{d}}+mg\mathrm{sin}\beta +m{\dot{V}}_{\text{x}})+a\cdot mg\mathrm{cos}\beta}{n(a+b)}\end{array}$$
The wheel normal forces satisfy F_{zf} + F_{zr} = mg·cosβ/n.
The Vehicle Body block lets you model only longitudinal dynamics, parallel to the ground and oriented along the direction of motion. The vehicle is assumed to be in pitch and normal equilibrium. The block does not model pitch or vertical movement.