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# Vehicle Body

Two-axle vehicle with longitudinal dynamics and motion and adjustable mass, geometry, and drag properties

Tires & Vehicles

## Description

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.

### Ports

You specify the headwind speed VW (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 Vx and the front and rear normal forces (load on wheels) Fzf, Fzr 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.

## Dialog Box and Parameters

Mass

Mass m of the vehicle. The default is 1200.

From the drop-down list, choose units. The default is kilograms (kg).

Number of wheels per axle

Number n of equally-sized wheels on each axle, forward and rear. The default is 2.

Horizontal distance from CG to front axle

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 from CG to rear axle

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).

CG height above ground

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).

Frontal area

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).

Drag coefficient

The dimensionless aerodynamic drag coefficient Cd, for the purpose of computing the aerodynamic drag force on the vehicle. The default is 0.4.

Initial velocity

The initial value Vx(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).

## Vehicle Body Model

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

SymbolDescription and Unit
gGravitational acceleration = 9.81 m/s2
βIncline angle
mVehicle mass
hHeight of vehicle CG above the ground
a, bDistance of front and rear axles, respectively, from the normal projection point of vehicle CG onto the common axle plane
VxLongitudinal vehicle velocity
nNumber of wheels on each axle
Fxf, FxrLongitudinal forces on each wheel at the front and rear ground contact points, respectively
Fzf, FzrNormal load forces on the each wheel at the front and rear ground contact points, respectively
AEffective frontal vehicle cross-sectional area
CdAerodynamic drag coefficient
ρMass density of air = 1.2 kg/m3
FdAerodynamic drag force

### Vehicle Dynamics and Motion

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.

$\begin{array}{l}m{\stackrel{˙}{V}}_{\text{x}}={F}_{\text{x}}-\text{​}{F}_{\text{d}}-mg\cdot \mathrm{sin}\beta ,\\ {F}_{\text{x}}=n\left({F}_{\text{xf}}+{F}_{\text{xr}}\right),\\ {F}_{\text{d}}=\frac{1}{2}{C}_{\text{d}}\rho A\left({{V}_{\text{x}}-{V}_{\text{W}}\right)}^{2}\cdot \mathrm{sgn}\left({V}_{\text{x}}-{V}_{\text{W}}\right)\end{array}$

Zero normal acceleration and zero pitch torque determine the normal force on each front and rear wheel:

$\begin{array}{l}{F}_{\text{zf}}=\frac{-h\left({F}_{\text{d}}+mg\mathrm{sin}\beta +m{\stackrel{˙}{V}}_{\text{x}}\right)+b\cdot mg\mathrm{cos}\beta }{n\left(a+b\right)},\\ {F}_{\text{zr}}=\frac{+h\left({F}_{\text{d}}+mg\mathrm{sin}\beta +m{\stackrel{˙}{V}}_{\text{x}}\right)+a\cdot mg\mathrm{cos}\beta }{n\left(a+b\right)}\end{array}$

The wheel normal forces satisfy Fzf + Fzr = mg·cosβ/n.

## Limitations

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.

## Examples

These SimDriveline™ example models contain working examples of vehicle bodies: