# Vehicle Body 3DOF

3DOF rigid vehicle body to calculate longitudinal, lateral, and yaw motion

• Library:
• Vehicle Dynamics Blockset / Vehicle Body

• ## Description

The Vehicle Body 3DOF block implements a rigid two-axle vehicle body model to calculate longitudinal, lateral, and yaw motion. The block accounts for body mass and aerodynamic drag between the axles due to acceleration and steering.

Use this block in vehicle dynamics and automated driving studies to model nonholonomic vehicle motion when vehicle pitch, roll, and vertical motion are not significant.

In the Vehicle Dynamics Blockset™ library, there are two types of Vehicle Body 3DOF blocks that model longitudinal, lateral, and yaw motion.

BlockVehicle Track SettingImplementation

Vehicle Body 3DOF Single Track `Single (bicycle)`

• Forces act along the center line at the front and rear axles.

Vehicle Body 3DOF Dual Track `Dual`

Forces act at the four vehicle corners or hard points.

Use the Axle forces parameter to specify the type of force.

Axle Forces SettingImplementation

```External longitudinal velocity```

• The block assumes that the external longitudinal velocity is in a quasi-steady state, so the longitudinal acceleration is approximately zero.

• Because the motion is quasi-steady, the block calculates lateral forces using the tire slip angles and linear cornering stiffness.

• Consider this setting when you want to:

• Generate virtual sensor signal data.

• Conduct high-level software studies that are not impacted by driveline or nonlinear tire responses.

```External longitudinal forces```

• The block uses the external longitudinal force to accelerate or brake the vehicle.

• The block calculates lateral forces using the tire slip angles and linear cornering stiffness.

• Consider this setting when you want to:

• Account for changes in the longitudinal velocity on the lateral and yaw motion.

• Specify the external longitudinal motion through a force instead of an external longitudinal velocity.

• Connect the block to tractive actuators, wheels, brakes, and hitches.

`External forces`

• The block uses the external lateral and longitudinal forces to steer, accelerate, or brake the vehicle.

• The block does not use the steering input to calculate vehicle motion.

• Consider this setting when you need tire models with more accurate nonlinear combined lateral and longitudinal slip.

You can use these block parameters to create additional input ports. This table summarizes the settings.

Input Signals Pane Parameter

Input PortDescription

Front wheel steering

`WhlAngF`

Front wheel angle, δF

External wind

`WindXYZ`

Wind speed, WX, WY, WZ, in the inertial reference frame

External forces`FExt`

External force on vehicle center of gravity (CG), Fx, Fy, Fz, in the vehicle-fixed frame

Rear wheel steering`WhlAngR`

Rear wheel angle, δR

External friction`Mu`

Friction coefficient

External moments

`MExt`

External moment about vehicle CG, Mx, My, Mz, in vehicle-fixed frame

Hitch forces`Fh`

Hitch force applied to the body at the hitch location, Fhx, Fhy, and Fhz, in the vehicle-fixed frame

Hitch moments`Mh`

Hitch moment at the hitch location, Mhx, Mhy, and Mhz, about the vehicle-fixed frame

Initial longitudinal position

`X_o`

Initial vehicle CG displacement along the earth-fixed X-axis, in m

Initial lateral position

`Y_o`

Initial vehicle CG displacement along the earth-fixed Y-axis, in m

Initial longitudinal velocity

`xdot_o`

Initial vehicle CG velocity along the vehicle-fixed x-axis, in m/s

Initial lateral velocity

`ydot_o`

Initial vehicle CG velocity along the vehicle-fixed y-axis, in m/s

Initial yaw angle

`psi_o`

Initial rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw), in rad

Initial yaw rate

`r_o`

Initial vehicle angular velocity about the vehicle-fixed z-axis (yaw rate), in rad/s

Air temperature

`AirTemp`

Ambient air temperature. Considering this option if you want to vary the temperature during run-time.

### Theory

The Vehicle Body 3DOF block implements a rigid two-axle vehicle body model to calculate longitudinal, lateral, and yaw motion. The block accounts for body mass, aerodynamic drag, and weight distribution between the axles due to acceleration and steering. To determine the vehicle motion, the block implements these equations for the single track, dual track, and drag calculations.

Single Track

CalculationDescription

Dynamics

The block uses these equations to calculate the rigid body planar dynamics.

`$\begin{array}{l}\stackrel{¨}{y}=-\stackrel{˙}{x}r+\frac{{F}_{yf}+{F}_{yr}+{F}_{yext}}{m}\\ \stackrel{˙}{r}=\frac{a{F}_{yf}-b{F}_{yr}+{M}_{zext}}{{I}_{zz}}\\ r=\stackrel{˙}{\psi }\end{array}$`

If you set Axle forces to either ```External longitudinal forces``` or `External forces`, the block uses this equation for the longitudinal acceleration.

`$\stackrel{¨}{x}=\stackrel{˙}{y}r+\frac{{F}_{xf}+{F}_{xr}+{F}_{xext}}{m}$`

If you set Axle forces to ```External longitudinal velocity```, the block assumes a quasi-steady state for the longitudinal acceleration.

`$\stackrel{¨}{x}=0$`

External forces

External forces include both drag and external force inputs. The forces act on the vehicle CG.

If you set Axle forces to `External longitudinal forces`, the block uses these equations.

If you set Axle forces to ```External longitudinal velocity```, the block uses these equations.

`$\begin{array}{l}{F}_{xft}=0\\ {F}_{yft}=-{C}_{yf}{\alpha }_{f}{\mu }_{f}\frac{{F}_{zf}}{{F}_{znom}}\\ {F}_{xrt}=0\\ {F}_{yrt}=-{C}_{yr}{\alpha }_{r}{\mu }_{r}\frac{{F}_{zr}}{{F}_{znom}}\end{array}$`

The block divides the normal forces by the nominal normal load to vary the effective friction parameters during weight and load transfer. The block uses these equations to maintain pitch and roll equilibrium.

`$\begin{array}{l}{F}_{zf}=\frac{bmg-\left(\stackrel{¨}{x}-\stackrel{˙}{y}r\right)mh+h{F}_{xext}+b{F}_{zext}-{M}_{yext}}{a+b}\\ {F}_{zr}=\frac{amg+\left(\stackrel{¨}{x}-\stackrel{˙}{y}r\right)mh-h{F}_{xext}+a{F}_{zext}+{M}_{yext}}{a+b}\end{array}$`

Tire forces

The block uses the ratio of the local and longitudinal and lateral velocities to determine the slip angles.

`$\begin{array}{l}{\alpha }_{f}=atan\left(\frac{\stackrel{˙}{y}+ar}{\stackrel{˙}{x}}\right)-{\delta }_{f}\\ {\alpha }_{r}=atan\left(\frac{\stackrel{˙}{y}-br}{\stackrel{˙}{x}}\right)-{\delta }_{r}\end{array}$`

To determine the tire forces, the block uses the slip angles.

`$\begin{array}{l}{F}_{xf}={F}_{xft}\mathrm{cos}\left({\delta }_{f}\right)-{F}_{yft}\mathrm{sin}\left({\delta }_{f}\right)\\ {F}_{yf}=-{F}_{xft}\mathrm{sin}\left({\delta }_{f}\right)+{F}_{yft}\mathrm{cos}\left({\delta }_{f}\right)\\ {F}_{xr}={F}_{xrt}\mathrm{cos}\left({\delta }_{r}\right)-{F}_{yrt}\mathrm{sin}\left({\delta }_{r}\right)\\ {F}_{yr}=-{F}_{xrt}\mathrm{sin}\left({\delta }_{r}\right)+{F}_{yrt}\mathrm{cos}\left({\delta }_{r}\right)\end{array}$`

If you set Axle forces to ```External forces```, the block sets the tire forces equal to the external input force.

`$\begin{array}{l}{F}_{xf}={F}_{xft}={F}_{xfinput}\\ {F}_{yf}={F}_{yft}={F}_{yfinput}\\ {F}_{xr}={F}_{xrt}={F}_{xrinput}\\ {F}_{yr}={F}_{yrt}={F}_{yrinput}\end{array}$`

Dual Track CalculationDescription

Dynamics

The block uses these equations to calculate the rigid body planar dynamics.

`$\begin{array}{l}\stackrel{¨}{x}=\stackrel{˙}{y}r+\frac{{F}_{xfl}+{F}_{xfr}+{F}_{xrl}+{F}_{xrr}+{F}_{xext}}{m}\\ \stackrel{¨}{y}=-\stackrel{˙}{x}r+\frac{{F}_{yfl}+{F}_{yfr}+{F}_{yrl}+{F}_{yrr+}{F}_{yext}}{m}\\ \stackrel{˙}{r}=\frac{a\left({F}_{yfl}+{F}_{yfr}\right)-b\left({F}_{yrl}+{F}_{yrr}\right)+\frac{{w}_{f}\left({F}_{xfl}-{F}_{xfr}\right)}{2}+\frac{{w}_{r}\left({F}_{xrl}-{F}_{xrr}\right)}{2}+{M}_{zext}}{{I}_{zz}}\\ r=\stackrel{˙}{\psi }\end{array}$`

If you set Axle forces to ```External longitudinal velocity```, the block assumes a quasi-steady state for the longitudinal acceleration.

`$\stackrel{¨}{x}=0$`

External forces

External forces include both drag and external force inputs. The forces act on the vehicle CG.

If you set Axle forces to ```External longitudinal forces```, the block uses these equations.

`$\begin{array}{l}{F}_{xflt}={F}_{xflinput}\\ {F}_{yflt}=-{C}_{yfl}{\alpha }_{fl}{\mu }_{fl}\frac{{F}_{zfl}}{2{F}_{znom}}\\ {F}_{xfrt}={F}_{xlrinput}\\ {F}_{yfrt}=-{C}_{yfr}{\alpha }_{fr}{\mu }_{fr}\frac{{F}_{zfr}}{2{F}_{znom}}\\ {F}_{xrlt}={F}_{xrlinput}\\ {F}_{yrlt}=-{C}_{yrl}{\alpha }_{rl}{\mu }_{rl}\frac{{F}_{zrl}}{2{F}_{znom}}\\ {F}_{xrrt}={F}_{xrrinput}\\ {F}_{yrrt}=-{C}_{yrr}{\alpha }_{rr}{\mu }_{rr}\frac{{F}_{zrr}}{2{F}_{znom}}\end{array}$`

If you set Axle forces to ```External longitudinal velocity```, the block uses these equations.

`$\begin{array}{l}{F}_{xflt}=0\\ {F}_{yflt}=-{C}_{yfl}{\alpha }_{fl}{\mu }_{fl}\frac{{F}_{zfl}}{2{F}_{znom}}\\ {F}_{xfrt}=0\\ {F}_{yfrt}=-{C}_{yfr}{\alpha }_{fr}{\mu }_{fr}\frac{{F}_{zfr}}{2{F}_{znom}}\\ {F}_{xrlt}=0\\ {F}_{yrlt}=-{C}_{yrl}{\alpha }_{rl}{\mu }_{rl}\frac{{F}_{zrl}}{2{F}_{znom}}\\ {F}_{xrrt}=0\\ {F}_{yrrt}=-{C}_{yrr}{\alpha }_{rr}{\mu }_{rr}\frac{{F}_{zrr}}{2{F}_{znom}}\end{array}$`

The block divides the normal forces by the nominal normal load to vary the effective friction parameters during weight and load transfer. The block uses these equations to maintain pitch and roll equilibrium.

`$\begin{array}{l}{F}_{zf}=\frac{bmg-\left(\stackrel{¨}{x}-\stackrel{˙}{y}r\right)mh+h{F}_{xext}+b{F}_{zext}-{M}_{yext}}{a+b}\\ {F}_{zr}=\frac{amg+\left(\stackrel{¨}{x}-\stackrel{˙}{y}r\right)mh-h{F}_{xext}+a{F}_{zext}+{M}_{yext}}{\left(a+b\right)}\\ {F}_{zfl}={F}_{zf}+\left(mh\left(\stackrel{¨}{y}+\stackrel{˙}{x}r\right)-h{F}_{yext}-{M}_{xext}\right)\frac{2}{{w}_{f}}\\ {F}_{zfr}={F}_{zf}+\left(-mh\left(\stackrel{¨}{y}+\stackrel{˙}{x}r\right)+h{F}_{yext}+{M}_{xext}\right)\frac{2}{{w}_{f}}\\ {F}_{zrl}={F}_{zr}+\left(mh\left(\stackrel{¨}{y}+\stackrel{˙}{x}r\right)-h{F}_{yext}-{M}_{xext}\right)\frac{2}{{w}_{r}}\\ {F}_{zrr}={F}_{zr}+\left(-mh\left(\stackrel{¨}{y}+\stackrel{˙}{x}r\right)+h{F}_{yext}+{M}_{xext}\right)\frac{2}{{w}_{r}}\end{array}$`

Tire forces

The block uses the ratio of the local and longitudinal and lateral velocities to determine the slip angles.

`$\begin{array}{l}{\alpha }_{fl}=atan\left(\frac{\stackrel{˙}{y}+ar}{\stackrel{˙}{x}+r\frac{{w}_{f}}{2}}\right)-{\delta }_{fl}\\ {\alpha }_{fr}=atan\left(\frac{\stackrel{˙}{y}+ar}{\stackrel{˙}{x}-r\frac{{w}_{f}}{2}}\right)-{\delta }_{fr}\\ {\alpha }_{rl}=atan\left(\frac{\stackrel{˙}{y}-ar}{\stackrel{˙}{x}+r\frac{{w}_{r}}{2}}\right)-{\delta }_{rl}\\ {\alpha }_{rr}=atan\left(\frac{\stackrel{˙}{y}-ar}{\stackrel{˙}{x}-r\frac{{w}_{r}}{2}}\right)-{\delta }_{rr}\end{array}$`

The block uses the steering angles to transform the tire forces to the vehicle-fixed frame.

`$\begin{array}{l}{F}_{xf}={F}_{xft}\mathrm{cos}\left({\delta }_{f}\right)-{F}_{yft}\mathrm{sin}\left({\delta }_{f}\right)\\ {F}_{yf}=-{F}_{xft}\mathrm{sin}\left({\delta }_{f}\right)+{F}_{yft}\mathrm{cos}\left({\delta }_{f}\right)\\ {F}_{xr}={F}_{xrt}\mathrm{cos}\left({\delta }_{r}\right)-{F}_{yrt}\mathrm{sin}\left({\delta }_{r}\right)\\ {F}_{yr}=-{F}_{xrt}\mathrm{sin}\left({\delta }_{r}\right)+{F}_{yrt}\mathrm{cos}\left({\delta }_{r}\right)\end{array}$`

If you set Axle forces to ```External forces```, the block uses these equations. The blocks assumes that the externally provided forces are in the vehicle-fixed frame at the axle-wheel location.

`$\begin{array}{l}{F}_{xf}={F}_{xft}={F}_{xfinput}\\ {F}_{yf}={F}_{yft}={F}_{yfinput}\\ {F}_{xr}={F}_{xrt}={F}_{xrinput}\\ {F}_{yr}={F}_{yrt}={F}_{yrinput}\end{array}$`

Drag

CalculationDescription

Coordinate transformation

The block transforms the wind speeds from the inertial frame to the vehicle-fixed frame.

`$\begin{array}{l}{w}_{x}={W}_{x}\mathrm{cos}\left(\psi \right)+{W}_{y}\mathrm{sin}\left(\psi \right)\\ {w}_{y}={W}_{y}\mathrm{cos}\left(\psi \right)-{W}_{x}\mathrm{sin}\left(\psi \right)\\ {w}_{z}={W}_{z}\end{array}$`

Drag forces

To determine a relative airspeed, the block subtracts the wind speed from the CG vehicle velocity. Using the relative airspeed, the block determines the drag forces.

`$\begin{array}{l}\overline{w}=\sqrt{{\left(\stackrel{˙}{x}-{w}_{x}\right)}^{2}+{\left(\stackrel{˙}{x}-{w}_{x}\right)}^{2}+{\left({w}_{z}\right)}^{2}}\\ \\ {F}_{dx}=-\frac{1}{2TR}{C}_{d}{A}_{f}{P}_{abs}{\left(}^{\overline{w}}\\ {F}_{dy}=-\frac{1}{2TR}{C}_{s}{A}_{f}{P}_{abs}{\left(}^{\overline{w}}\\ {F}_{dz}=-\frac{1}{2TR}{C}_{l}{A}_{f}{P}_{abs}{\left(}^{\overline{w}}\end{array}$`

Drag moments

Using the relative airspeed, the block determines the drag moments.

`$\begin{array}{l}{M}_{dr}=-\frac{1}{2TR}{C}_{rm}{A}_{f}{P}_{abs}{\left(}^{\overline{w}}\left(a+b\right)\\ {M}_{dp}=-\frac{1}{2TR}{C}_{pm}{A}_{f}{P}_{abs}{\left(}^{\overline{w}}\left(a+b\right)\\ {M}_{dy}=-\frac{1}{2TR}{C}_{ym}{A}_{f}{P}_{abs}{\left(}^{\overline{w}}\left(a+b\right)\end{array}$`

Lateral Corner Stiffness and Relaxation Dynamics

DescriptionImplementation

Constant values.

The block uses constant stiffness values for Cyf and Cyr.

Lookup tables as a function of corner stiffness data and slip angles.

The block uses lookup tables that are functions of the corner stiffness data and slip angles.

`$\begin{array}{l}C{y}_{f}=f\left({\alpha }_{f},C{y}_{fdata}\right)\\ C{y}_{r}=f\left({\alpha }_{r},C{y}_{rdata}\right)\end{array}$`

Lookup tables as a function of corner stiffness data and slip angles.

Slip angles include the relaxation length dynamic settings.

The block uses lookup tables that are functions of the corner stiffness data and slip angles. The slip angles include the relaxation length dynamic settings. The relaxation length approximates an effective corner stiffness force that is a function of wheel travel.

`$\begin{array}{l}C{y}_{f}=f\left({\alpha }_{f\sigma },C{y}_{fdata}\right)\\ C{y}_{r}=f\left({\alpha }_{r\sigma },C{y}_{rdata}\right)\\ \\ {\alpha }_{f\sigma }=\frac{1}{s}\left[\frac{\left({\alpha }_{f}-{\alpha }_{f\sigma }\right){v}_{wf}}{{\alpha }_{f}}\right]\\ \\ {\alpha }_{r\sigma }=\frac{1}{s}\left[\frac{\left({\alpha }_{r}-{\alpha }_{r\sigma }\right){v}_{wr}}{{\alpha }_{r}}\right]\end{array}$`

The equations use these variables.

 $x,\stackrel{˙}{x},\stackrel{¨}{x}$ Vehicle CG displacement, velocity, and acceleration, along the vehicle-fixed x-axis $y,\stackrel{˙}{y},\stackrel{¨}{y}$ Vehicle CG displacement, velocity, and acceleration, along the vehicle-fixed y-axis ψ Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw) r,$\stackrel{˙}{\Psi }$ Vehicle angular velocity, about the vehicle-fixed z-axis (yaw rate) Fxf, Fxr Longitudinal forces applied to front and rear wheels, along the vehicle-fixed x-axis Fyf, Fyr Lateral forces applied to front and rear wheels, along vehicle-fixed y-axis Fxext, Fyext, Fzext External forces applied to vehicle CG, along the vehicle-fixed x-, y-, and z-axes Fdx, Fdy, Fdz Drag forces applied to vehicle CG, along the vehicle-fixed x-, y-, and z-axes Fxinput, Fyinput, Fzinput Input forces applied to vehicle CG, along the vehicle-fixed x-, y-, and z-axes Mxext, Myext, Mzext External moment about vehicle CG, about the vehicle-fixed x-, y-, and z-axes Mdx, Mdy, Mdz Drag moment about vehicle CG, about the vehicle-fixed x-, y-, and z-axes Mxinput, Myinput, Mzinput Input moment about vehicle CG, about the vehicle-fixed x-, y-, and z-axes Izz Vehicle body moment of inertia about the vehicle-fixed z-axis Fxft, Fxrt Longitudinal tire force applied to front and rear wheels, along the vehicle-fixed x-axis Fyft, Fyft Lateral tire force applied to front and rear wheels, along vehicle-fixed y-axis Fxfl, Fxfr Longitudinal force applied to front left and front right wheels, along the vehicle-fixed x-axis Fyfl, Fyfr Lateral force applied to front left and front right wheels, along the vehicle-fixed y-axis Fxrl, Fxrr Longitudinal force applied to rear left and rear right wheels, along the vehicle-fixed x-axis Fyrl, Fyrr Lateral force applied to rear left and rear right wheels, along the vehicle-fixed y-axis Fxflt, Fxfrt Longitudinal tire force applied to front left and front right wheels, along the vehicle-fixed x-axis Fyflt, Fyfrt Lateral force tire applied to front left and front right wheels, along the vehicle-fixed y-axis Fxrlt, Fxrrt Longitudinal tire force applied to rear left and rear right wheels, along the vehicle-fixed x-axis Fyrlt, Fyrrt Lateral force applied to rear left and rear right wheels, along the vehicle-fixed y-axis Fzf,Fzr Normal force applied to front and rear wheels, along vehicle-fixed z-axis Fznom Nominal normal force applied to axles, along the vehicle-fixed z-axis Fzfl,Fzfr Normal force applied to front left and right wheels, along vehicle-fixed z-axis Fzrl,Fzrr Normal force applied to rear left and right wheels, along vehicle-fixed z-axis m Vehicle body mass a, b Distance of front and rear wheels, respectively, from the normal projection point of vehicle CG onto the common axle plane h Height of vehicle CG above the axle plane d Lateral distance from the geometric centerline to the center of mass along the vehicle-fixed y-axis hh Height of the hitch above the axle plane along the vehicle-fixed z-axis dh Longitudinal distance of the hitch from the normal projection point of tractor CG onto the common axle plane hl Lateral distance from center of mass to hitch along the vehicle-fixed y-axis. αf, αr Front and rear wheel slip angles αfl, αfr Front left and right wheel slip angles αrl, αrr Rear left and right wheel slip angles δf, δr Front and rear wheel steering angles δrl, δrr Rear left and right wheel steering angles δfl, δfr Front left and right wheel steering angles wf, wr Front and rear track widths Cyf, Cyr Front and rear wheel cornering stiffness Cyfdata, Cyrdata Front and rear wheel cornering stiffness data σf, σr Front and rear wheel relaxation length αfσ, αrσ Front and rear wheel slip angles that include relaxation length vwf, vwr Magnitude of front and rear wheel hardpoint velocity μf, μr Front and rear wheel friction coefficient μfl, μfr Front left and right wheel friction coefficient μrl, μrr Rear left and right wheel friction coefficient Cd Air drag coefficient acting along vehicle-fixed x-axis Cs Air drag coefficient acting along vehicle-fixed y-axis Cl Air drag coefficient acting along vehicle-fixed z-axis Crm Air drag roll moment acting about the vehicle-fixed x-axis Cpm Air drag pitch moment acting about the vehicle-fixed y-axis Cym Air drag yaw moment acting about the vehicle-fixed z-axis Af Frontal area R Atmospheric specific gas constant T Environmental air temperature Pabs Environmental absolute pressure wx, wy, wz Wind speed, along the vehicle-fixed x-, y-, and z-axes Wx, Wy, Wz Wind speed, along inertial X-, Y-, and Z-axes

## Ports

### Input

expand all

Front wheel steering angles, δF, in rad.

Vehicle Track Setting

Variable

Signal Dimension

```Single (bicycle)```δF

Scalar – `1`

`Dual`

Array – `[1x2]` or `[2x1]`

#### Dependencies

To enable this port, on the Input signals pane, select Front wheel steering.

Rear wheel steering angles, δR, in rad.

Vehicle Track Setting

Variable

Signal Dimension

```Single (bicycle)```δR

Scalar – `1`

`Dual`

Array – `[1x2]` or `[2x1]`

#### Dependencies

To enable this port, on the Input signals pane, select Rear wheel steering.

Vehicle CG velocity along the vehicle-fixed x-axis, in m/s.

#### Dependencies

To enable this port, set Axle forces to ```External longitudinal velocity```.

Force on the front wheels, FwF, along the vehicle-fixed axis, in N.

Vehicle Track Setting

Axle Forces Setting

Description

Variable

Signal Dimension

```Single (bicycle)``````External longitudinal forces```

Longitudinal force on the front wheel

`$FwF=F{x}_{f}$`

Scalar – `1`

```External forces```

Longitudinal and lateral forces on the front wheel

Array – `[1x2]` or `[2x1]`

`Dual````External longitudinal forces```

Longitudinal force on the front wheels

Array – `[1x2]` or `[2x1]`

```External forces```

Longitudinal and lateral forces on the front wheels

`$FwF=\left[\begin{array}{cc}{F}_{xfl}& {F}_{xfr}\\ {F}_{yfl}& {F}_{yfr}\end{array}\right]$`

Array – `[2x2]`

#### Dependencies

To enable this port, set Axle forces to one of these options:

• `External longitudinal forces`

• `External forces`

Force on the rear wheels, FwR, along the vehicle-fixed axis, in N.

Vehicle Track Setting

Axle Forces Setting

Description

Variable

Signal Dimension

```Single (bicycle)``````External longitudinal forces```

Longitudinal force on the rear wheel

`$FwR=F{x}_{r}$`

Scalar – `1`

```External forces```

Longitudinal and lateral forces on the rear wheel

Array – `[1x2]` or `[2x1]`

`Dual````External longitudinal forces```

Longitudinal force on the rear wheels

Array – `[1x2]` or `[2x1]`

```External forces```

Longitudinal and lateral forces on the rear wheels

`$FwR=\left[\begin{array}{cc}{F}_{xrl}& {F}_{xrr}\\ {F}_{yrl}& {F}_{yrr}\end{array}\right]$`

Array – `[2x2]`

#### Dependencies

To enable this port, set Axle forces to one of these options:

• `External longitudinal forces`

• `External forces`

External forces applied to vehicle CG, Fxext, Fyext, Fzext, in vehicle-fixed frame, in N. Signal vector dimensions are `[1x3]` or `[3x1]`.

#### Dependencies

To enable this port, on the Input signals pane, select External forces.

External moment about vehicle CG, Mx, My, Mz, in the vehicle-fixed frame, in N·m. Signal vector dimensions are `[1x3]` or `[3x1]`.

#### Dependencies

To enable this port, on the Input signals pane, select External moments.

Hitch force applied to the body at the hitch location, Fhx, Fhy, Fhz, in the vehicle-fixed frame, in N, specified as a `1-by-3` or `3-by-1` array.

#### Dependencies

To enable this port, under Input signals, select Hitch forces.

Hitch moment at the hitch location, Mhx, Mhy, Mhz, about the vehicle-fixed frame, in N·m, specified as a `1-by-3` or `3-by-1` array.

#### Dependencies

To enable this port, under Input signals, select Hitch moments.

Wind speed, Wx, Wy, Wz along inertial X-, Y-, and Z-axes, in m/s. Signal vector dimensions are `[1x3]` or `[3x1]`.

#### Dependencies

To enable this port, on the Input signals pane, select External wind.

Tire friction coefficient, μ. The value is dimensionless.

Vehicle Track Setting

Description

Variable

Signal Dimension

`Single (bicycle)`

Longitudinal force on the front wheel

Array – `[1x2]` or `[2x1]`

`Dual`

Longitudinal force on the front wheels

`$Mu=\left[\begin{array}{cc}{\mu }_{fl}& {\mu }_{fr}\\ {\mu }_{rl}& {\mu }_{rr}\end{array}\right]$`

Array – `[2x2]`

#### Dependencies

To enable this port, on the Input signals pane, select External friction.

Ambient air temperature, in K.

#### Dependencies

To enable this port, on the Input signals pane, select Air temperature.

Initial vehicle CG displacement along the earth-fixed X-axis, in m.

#### Dependencies

To enable this port, on the Input signals pane, select Initial longitudinal position.

Initial vehicle CG displacement along the earth-fixed Y-axis, in m.

#### Dependencies

To enable this port, on the Input signals pane, select Initial lateral position.

Initial vehicle CG velocity along the vehicle-fixed x-axis, in m/s.

#### Dependencies

To enable this port:

1. Set Axle forces to one of these options:

• ```External longitudinal forces```

• ```External forces```

2. On the Input signals pane, select Initial longitudinal velocity

Initial vehicle CG velocity along the vehicle-fixed y-axis, in m/s.

#### Dependencies

To enable this port, on the Input signals pane, select Initial lateral velocity.

Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw), in rad.

#### Dependencies

To enable this port, on the Input signals pane, select Initial yaw angle.

#### Dependencies

To enable this port, on the Input signals pane, select Initial yaw rate.

### Output

expand all

Bus signal containing these block values.

SignalDescriptionValueUnits
`InertFrm``Cg``Disp``X`Vehicle CG displacement along the earth-fixed X-axis

Computed

m
`Y`Vehicle CG displacement along the earth-fixed Y-axis

Computed

m

`Z`Vehicle CG displacement along the earth-fixed Z-axis`0`m
`Vel``Xdot`Vehicle CG velocity along the earth-fixed X-axis

Computed

m/s

`Ydot`Vehicle CG velocity along the earth-fixed Y-axis

Computed

m/s
`Zdot`Vehicle CG velocity along the earth-fixed Z-axis`0`m/s
`Ang``phi`Rotation of the vehicle-fixed frame about the earth-fixed X-axis (roll)`0`rad
`theta`Rotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)`0`rad
`psi`Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)

Computed

`FrntAxl``Lft``Disp``X`Front left wheel displacement along the earth-fixed X-axis

Computed

m
`Y`Front left wheel displacement along the earth-fixed Y-axis

Computed

m
`Z`Front left wheel displacement along the earth-fixed Z-axis`0`m
`Vel``Xdot`Front left wheel velocity along the earth-fixed X-axis

Computed

m/s
`Ydot`Front left wheel velocity along the earth-fixed Y-axis

Computed

m/s
`Zdot`Front left wheel velocity along the earth-fixed Z-axis`0`m/s
`Rght``Disp``X`Front right wheel displacement along the earth-fixed X-axis

Computed

m
`Y`Front right wheel displacement along the earth-fixed Y-axis

Computed

m
`Z`Front right wheel displacement along the earth-fixed Z-axis`0`m
`Vel``Xdot`Front right wheel velocity along the earth-fixed X-axis

Computed

m/s
`Ydot`Front right wheel velocity along the earth-fixed Y-axis

Computed

m/s
`Zdot`Front right wheel velocity along the earth-fixed Z-axis`0`m/s
`RearAxl``Lft``Disp``X`Rear left wheel displacement along the earth-fixed X-axis

Computed

m
`Y`Rear left wheel displacement along the earth-fixed Y-axis

Computed

m
`Z`Rear left wheel displacement along the earth-fixed Z-axis`0`m
`Vel``Xdot`Rear left wheel velocity along the earth-fixed X-axis

Computed

m/s
`Ydot`Rear left wheel velocity along the earth-fixed Y-axis

Computed

m/s
`Zdot`Rear left wheel velocity along the earth-fixed Z-axis`0`m/s
`Rght``Disp``X`Rear right wheel displacement along the earth-fixed X-axis

Computed

m
`Y`Rear right wheel displacement along the earth-fixed Y-axis

Computed

m
`Z`Rear right wheel displacement along the earth-fixed Z-axis`0`m
`Vel``Xdot`Rear right wheel velocity along the earth-fixed X-axis

Computed

m/s
`Ydot`Rear right wheel velocity along the earth-fixed Y-axis

Computed

m/s
`Zdot`Rear right wheel velocity along the earth-fixed Z-axis`0`m/s
`Hitch``Disp``X`Hitch offset from axle plane along the earth-fixed X-axis

Computed

m
`Y`Hitch offset from center plane along the earth-fixed Y-axis

Computed

m
`Z`Hitch offset from axle plane along the earth-fixed Z-axis

Computed

m
`Vel``Xdot`Hitch offset velocity from axle plane along the earth-fixed X-axis

Computed

m
`Ydot`Hitch offset velocity from center plane along the earth-fixed Y-axis

Computed

m
`Zdot`Hitch offset velocity from axle plane along the earth-fixed Z-axis

Computed

m
`Geom``Disp``X`Vehicle chassis offset from axle plane along the earth-fixed X-axis

Computed

m
`Y`Vehicle chassis offset from center plane along the earth-fixed Y-axis

Computed

m
`Z`Vehicle chassis offset from axle plane along the earth-fixed Z-axis

Computed

m
`Vel``Xdot`Vehicle chassis offset velocity along the earth-fixed X-axis

Computed

m/s
`Ydot`Vehicle chassis offset velocity along the earth-fixed Y-axis

Computed

m/s
`Zdot`Vehicle chassis offset velocity along the earth-fixed Z-axis

Computed

m/s
`BdyFrm``Cg``Vel``xdot`Vehicle CG velocity along the vehicle-fixed x-axis

Computed

m/s
`ydot`Vehicle CG velocity along the vehicle-fixed y-axis

Computed

m/s
`zdot`Vehicle CG velocity along the vehicle-fixed z-axis`0`m/s
`Ang``Beta`

Body slip angle, β

`$\beta =\frac{{V}_{y}}{{V}_{x}}$`

Computed

`AngVel``p`Vehicle angular velocity about the vehicle-fixed x-axis (roll rate)`0`rad/s
`q`Vehicle angular velocity about the vehicle-fixed y-axis (pitch rate)`0`rad/s
`r`Vehicle angular velocity about the vehicle-fixed z-axis (yaw rate)

Computed

`Acc``ax`Vehicle CG acceleration along the vehicle-fixed x-axis

Computed

gn
`ay`Vehicle CG acceleration along the vehicle-fixed y-axis

Computed

gn
`az`Vehicle CG acceleration along the vehicle-fixed z-axis`0`gn
`xddot`Vehicle CG acceleration along the vehicle-fixed x-axis

Computed

m/s^2
`yddot`Vehicle CG acceleration along the vehicle-fixed y-axis

Computed

m/s^2
`zddot`Vehicle CG acceleration along the vehicle-fixed z-axis`0`m/s^2
`AngAcc``pdot`Vehicle angular acceleration about the vehicle-fixed x-axis`0`rad/s
`qdot`Vehicle angular acceleration about the vehicle-fixed y-axis`0`rad/s
`rdot`Vehicle angular acceleration about the vehicle-fixed z-axis

Computed

`DCM`

Direction cosine matrix

Computed

`Forces``Body``Fx`Net force on vehicle CG along the vehicle-fixed x-axis

Computed

N
`Fy`Net force on vehicle CG along the vehicle-fixed y-axis

Computed

N
`Fz`Net force on vehicle CG along the vehicle-fixed z-axis`0`N
`Ext``Fx`External force on vehicle CG along the vehicle-fixed x-axis

Computed

N
`Fy`External force on vehicle CG along the vehicle-fixed y-axis

Computed

N
`Fz`External force on vehicle CG along the vehicle-fixed z-axis`0`N
`Hitch``Fx`

Hitch force applied to body at the hitch location along the vehicle-fixed x-axis

Input

N
`Fy`

Hitch force applied to body at the hitch location along the vehicle-fixed y-axis

Input

N
`Fz`

Hitch force applied to body at the hitch location along the vehicle-fixed z-axis

Input

N
`FrntAxl``Lft``Fx`

Longitudinal force on left front wheel, along the vehicle-fixed x-axis

Computed

N
`Fy`

Lateral force on left front wheel along the vehicle-fixed y-axis

Computed

N
`Fz`

Normal force on left front wheel, along the vehicle-fixed z-axis

Computed

N
`Rght``Fx`

Longitudinal force on right front wheel, along the vehicle-fixed x-axis

Computed

N
`Fy`

Lateral force on right front wheel along the vehicle-fixed y-axis

Computed

N
`Fz`

Normal force on right front wheel, along the vehicle-fixed z-axis

ComputedN
`RearAxl``Lft``Fx`

Longitudinal force on left rear wheel, along the vehicle-fixed x-axis

Computed

N
`Fy`

Lateral force on left rear wheel along the vehicle-fixed y-axis

Computed

N
`Fz`

Normal force on left rear wheel, along the vehicle-fixed z-axis

ComputedN
`Rght``Fx`

Longitudinal force on right rear wheel, along the vehicle-fixed x-axis

Computed

N
`Fy`

Lateral force on right rear wheel along the vehicle-fixed y-axis

Computed

N
`Fz`

Normal force on right rear wheel, along the vehicle-fixed z-axis

ComputedN
`Tires``FrntTires``Lft``Fx`

Front left tire force, along the vehicle-fixed x-axis

ComputedN
`Fy`

Front left tire force, along the vehicle-fixed y-axis

ComputedN
`Fz`

Front left tire force, along the vehicle-fixed z-axis

ComputedN
`Rght``Fx`

Front right tire force, along the vehicle-fixed x-axis

ComputedN
`Fy`

Front right tire force, along the vehicle-fixed y-axis

ComputedN
`Fz`

Front right tire force, along the vehicle-fixed z-axis

ComputedN
`RearTires``Lft``Fx`

Rear left tire force, along the vehicle-fixed x-axis

ComputedN
`Fy`

Rear left tire force, along the vehicle-fixed y-axis

ComputedN
`Fz`

Rear left tire force, along the vehicle-fixed z-axis

ComputedN
`Rght``Fx`

Rear right tire force, along the vehicle-fixed x-axis

ComputedN
`Fy`

Rear right tire force, along the vehicle-fixed y-axis

ComputedN
`Fz`

Rear right tire force, along the vehicle-fixed z-axis

Computed
`Drag``Fx`Drag force on vehicle CG along the vehicle-fixed x-axis

Computed

N
`Fy`Drag force on vehicle CG along the vehicle-fixed y-axis

Computed

N
`Fz`Drag force on vehicle CG along the vehicle-fixed z-axis

Computed

N
`Grvty``Fx`Gravity force on vehicle CG along the vehicle-fixed x-axis

Computed

N
`Fy`Gravity force on vehicle CG along the vehicle-fixed y-axis

Computed

N
`Fz`Gravity force on vehicle CG along the vehicle-fixed z-axis

Computed

N
`Moments``Body``Mx`Body moment on vehicle CG about the vehicle-fixed x-axis`0`N·m
`My`Body moment on vehicle CG about the vehicle-fixed y-axis

Computed

N·m
`Mz`Body moment on vehicle CG about the vehicle-fixed z-axis`0`N·m
`Drag``Mx`Drag moment on vehicle CG about the vehicle-fixed x-axis`0`N·m
`My`Drag moment on vehicle CG about the vehicle-fixed y-axis

Computed

N·m
`Mz`Drag moment on vehicle CG about the vehicle-fixed z-axis`0`N·m
`Ext``Mx`External moment on vehicle CG about the vehicle-fixed x-axis`0`N·m
`My`External moment on vehicle CG about the vehicle-fixed y-axis

Computed

N·m
`Mz`External moment on vehicle CG about the vehicle-fixed z-axis`0`N·m
`Hitch``Mx`Hitch moment at the hitch location about vehicle-fixed x-axis`0`N·m
`My`Hitch moment at the hitch location about vehicle-fixed y-axis

Computed

N·m
`Mz`Hitch moment at the hitch location about vehicle-fixed z-axis`0`N·m
`FrntAxl``Lft``Disp``x`Front left wheel displacement along the vehicle-fixed x-axis

Computed

m
`y`Front left wheel displacement along the vehicle-fixed y-axisComputedm
`z`Front left wheel displacement along the vehicle-fixed z-axis

Computed

m
`Vel``xdot`Front left wheel velocity along the vehicle-fixed x-axis

Computed

m/s
`ydot`Front left wheel velocity along the vehicle-fixed y-axis

Computed

m/s
`zdot`Front left wheel velocity along the vehicle-fixed z-axis`0`m/s
`Rght``Disp``x`Front right wheel displacement along the vehicle-fixed x-axis

Computed

m
`y`Front right wheel displacement along the vehicle-fixed y-axisComputedm
`z`Front right wheel displacement along the vehicle-fixed z-axis

Computed

m
`Vel``xdot`Front right wheel velocity along the vehicle-fixed x-axis

Computed

m/s
`ydot`Front right wheel velocity along the vehicle-fixed y-axis

Computed

m/s
`zdot`Front right wheel velocity along the vehicle-fixed z-axis`0`m/s
`Steer``WhlAngFL`

Front left wheel steering angle

Computed

`WhlAngFR`

Front right wheel steering angle

Computed

`RearAxl``Lft``Disp``x`Rear left wheel displacement along the vehicle-fixed x-axis

Computed

m
`y`Rear left wheel displacement along the vehicle-fixed y-axisComputedm
`z`Rear left wheel displacement along the vehicle-fixed z-axis

Computed

m
`Vel``xdot`Rear left wheel velocity along the vehicle-fixed x-axis

Computed

m/s
`ydot`Rear left wheel velocity along the vehicle-fixed y-axis

Computed

m/s
`zdot`Rear left wheel velocity along the vehicle-fixed z-axis`0`m/s
`Rght``Disp``x`Rear right wheel displacement along the vehicle-fixed x-axis

Computed

m
`y`Rear right wheel displacement along the vehicle-fixed y-axisComputedm
`z`Rear right wheel displacement along the vehicle-fixed z-axis

Computed

m
`Vel``xdot`Rear right wheel velocity along the vehicle-fixed x-axis

Computed

m/s
`ydot`Rear right wheel velocity along the vehicle-fixed y-axis

Computed

m/s
`zdot`Rear right wheel velocity along the vehicle-fixed z-axis`0`m/s
`Steer``WhlAngRL`

Rear left wheel steering angle

Computed

`WhlAngRR`

Rear right wheel steering angle

Computed

`Hitch``Disp``x`Hitch offset from axle plane along the vehicle-fixed x-axis

Input

m
`y`Hitch offset from center plane along the vehicle-fixed y-axis

Input

m
`z`Hitch offset from axle plane along the earth-fixed z-axis

Input

m
`Vel``xdot`Hitch offset velocity along the vehicle-fixed x-axis

Computed

m/s
`ydot`Hitch offset velocity along the vehicle-fixed y-axis

Computed

m/s
`zdot`Hitch offset velocity along the vehicle-fixed z-axis

Computed

m/s
`Pwr``Ext`Applied external power

Computed

W
`Hitch`Power loss due to hitch

Computed

W
`Drag`Power loss due to drag

Computed

W
`Geom``Disp``x`Vehicle chassis offset from axle plane along the vehicle-fixed x-axis

Input

m
`y`Vehicle chassis offset from center plane along the vehicle-fixed y-axis

Input

m
`z`Vehicle chassis offset from axle plane along the earth-fixed z-axis

Input

m
`Vel``xdot`Vehicle chassis offset velocity along the vehicle-fixed x-axis

Computed

m/s
`ydot`Vehicle chassis offset velocity along the vehicle-fixed y-axis

Computed

m/s
`zdot`Vehicle chassis offset velocity along the vehicle-fixed z-axis`0`m/s
`Beta``Beta`

Body slip angle, β

`$\beta =\frac{{V}_{y}}{{V}_{x}}$`

Computed

SignalDescriptionValueUnits
`PwrInfo``PwrTrnsfrd``PwrFxExt`Externally applied longitudinal force power

Computed

W
`PwrFyExt`Externally applied lateral force power

Computed

W
`PwrMzExt`Externally applied roll moment power

Computed

W
`PwrFwFLx`Longitudinal force applied at the front left axle power

Computed

W
`PwrFwFLy`Lateral force applied at the front left axle power

Computed

W
`PwrFwFRx`Longitudinal force applied at the front right axle power

Computed

W
`PwrFwFRy`Lateral force applied at the front right axle power

Computed

W
`PwrFwRLx`Longitudinal force applied at the rear left axle power

Computed

W
`PwrFwRLy`Lateral force applied at the rear left axle power

Computed

W
`PwrFwRRx`Longitudinal force applied at the rear right axle power

Computed

W
`PwrFwRRy`Lateral force applied at the rear right axle power

Computed

W
`PwrNotTrnsfrd``PwrFxDrag`Longitudinal drag force power

Computed

W
`PwrFyDrag`Lateral drag force power

Computed

W
`PwrMzDrag`Drag pitch moment power

Computed

W
`PwrStored``PwrStoredGrvty`Rate change in gravitational potential energy

Computed

W
`PwrStoredxdot`Rate of change of longitudinal kinetic energy

Computed

W
`PwrStoredydot`Rate of change of lateral kinetic energy

Computed

W
`PwrStoredr`Rate of change of rotational yaw kinetic energy

Computed

W

Vehicle CG velocity along the vehicle-fixed x-axis, in m/s.

Vehicle CG velocity along the vehicle-fixed y-axis, in m/s.

Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw), in rad.

Vehicle angular velocity, `r`, about the vehicle-fixed z-axis (yaw rate), in rad/s.

Normal force on front wheels, FzF, along the vehicle-fixed z-axis, in N.

Vehicle Track Setting

Description

Variable

Signal Dimension

`Single (bicycle)`

Normal force on front axle

`$FzF=F{z}_{f}$`

Scalar – `1`

`Dual`

Normal force on the front wheels

`$FzF=\left[\begin{array}{cc}F{z}_{fl}& F{z}_{fr}\end{array}\right]$`

Array – `[1x2]`

Normal force on rear wheels, FzR, along the vehicle-fixed z-axis, in N.

Vehicle Track Setting

Description

Variable

Signal Dimension

`Single (bicycle)`

Normal force on rear wheel

`$FzR=F{z}_{r}$`

Scalar – `1`

`Dual`

Normal force on the rear wheels

`$FzR=\left[\begin{array}{cc}F{z}_{rl}& F{z}_{rr}\end{array}\right]$`

Array – `[1x2]`

## Parameters

expand all

Options

In the Vehicle Dynamics Blockset library, there are two types of Vehicle Body 3DOF blocks that model longitudinal, lateral, and yaw motion.

BlockVehicle Track SettingImplementation

Vehicle Body 3DOF Single Track `Single (bicycle)`

• Forces act along the center line at the front and rear axles.

Vehicle Body 3DOF Dual Track `Dual`

Forces act at the four vehicle corners or hard points.

Use the Axle forces parameter to specify the type of force.

Axle Forces SettingImplementation

```External longitudinal velocity```

• The block assumes that the external longitudinal velocity is in a quasi-steady state, so the longitudinal acceleration is approximately zero.

• Because the motion is quasi-steady, the block calculates lateral forces using the tire slip angles and linear cornering stiffness.

• Consider this setting when you want to:

• Generate virtual sensor signal data.

• Conduct high-level software studies that are not impacted by driveline or nonlinear tire responses.

```External longitudinal forces```

• The block uses the external longitudinal force to accelerate or brake the vehicle.

• The block calculates lateral forces using the tire slip angles and linear cornering stiffness.

• Consider this setting when you want to:

• Account for changes in the longitudinal velocity on the lateral and yaw motion.

• Specify the external longitudinal motion through a force instead of an external longitudinal velocity.

• Connect the block to tractive actuators, wheels, brakes, and hitches.

`External forces`

• The block uses the external lateral and longitudinal forces to steer, accelerate, or brake the vehicle.

• The block does not use the steering input to calculate vehicle motion.

• Consider this setting when you need tire models with more accurate nonlinear combined lateral and longitudinal slip.

Input Signals

Specify to create input port `WhlAngF`.

Specify to create input port `WindXYZ`.

Specify to create input port `FExt`.

Specify to create input port `MExt`.

Specify to create input port `WhlAngR`.

Specify to create input port `Mu`.

Select to create input port `Fh`.

Specify to create input port `Mh`.

Specify to create input port `X_o`.

Specify to create input port `Y_o`.

Specify to create input port `xdot_o`.

Specify to create input port `ydot_o`.

Specify to create input port `psi_o`.

Specify to create input port `r_o`.

Specify to create input port `AirTemp`.

Longitudinal

Number of wheels on front axle, NF. The value is dimensionless.

Number of wheels on rear axle, NR. The value is dimensionless.

Vehicle mass, m, in kg.

Horizontal distance a from the vehicle CG to the front wheel axle, in m.

Horizontal distance b from the vehicle CG to the rear wheel axle, in m.

Height of vehicle CG above the axles, h, in m.

Longitudinal distance from center of mass to hitch, dh, in m.

#### Dependencies

To enable this parameter, on the Input signals pane, select Hitch forces or Hitch moments.

Vertical distance from hitch to axle plane, hh, in m.

#### Dependencies

To enable this parameter, on the Input signals pane, select Hitch forces or Hitch moments.

Initial vehicle CG displacement along earth-fixed X-axis, in m.

Initial vehicle CG velocity along vehicle-fixed x-axis, in m/s.

#### Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter, set Axle forces to one of these options:

• `External longitudinal forces`

• `External forces`

Lateral

Front tire corner stiffness, Cyf, in N/rad.

#### Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:

1. Set Axle forces to one of these options:

• `External longitudinal velocity`

• `External longitudinal forces`

2. Clear Mapped corner stiffness.

Rear tire corner stiffness, Cyr, in N/rad.

#### Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:

1. Set Axle forces to one of these options:

• `External longitudinal velocity`

• `External longitudinal forces`

2. Clear Mapped corner stiffness.

Initial vehicle CG displacement along earth-fixed Y-axis, in m.

Initial vehicle CG velocity along vehicle-fixed y-axis, in m/s.

Enables mapped corner stiffness calculation.

#### Dependencies

To enable this parameter, set Axle forces to one of these options:

• ```External longitudinal velocity```

• ```External longitudinal forces```

Enables relaxation length dynamics.

#### Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

• ```External longitudinal velocity```

• ```External longitudinal forces```

2. Clear Mapped corner stiffness.

Lateral distance from geometric centerline to center of mass, d, in m, along the vehicle-fixed y. Positive values indicate that the vehicle CM is to the right of the geometric centerline. Negative values indicate that the vehicle CM is to the left of the geometric centerline.

Lateral distance from geometric centerline to the hitch, hl, in m, along the vehicle-fixed y. Positive values indicate that the hitch is to the right of the geometric centerline. Negative values indicate that the hitch is to the left of the geometric centerline.

#### Dependencies

To enable this parameter, on the Input signals pane, select Hitch forces or Hitch moments.

Track width, w, in m.

#### Dependencies

To enable this parameter, set Vehicle track to `Dual`.

Front tire relaxation length, σf, in m.

#### Dependencies

To enable this parameter:

1. Set Vehicle track to one of these options:

• `Single 2-axle`

• `Dual 2-axle`

• `Single 3-axle`

• `Dual 3-axle`

2. Set Axle forces to one of these options:

• `External longitudinal velocity`

• `External longitudinal forces`

3. Do either of these:

• Select Mapped corner stiffness.

• Clear Mapped corner stiffness and select Include relaxation length dynamics.

Rear tire relaxation length, σr, in m.

#### Dependencies

To enable this parameter:

1. Set Vehicle track to one of these options:

• `Single 2-axle`

• `Dual 2-axle`

• `Single 3-axle`

• `Dual 3-axle`

2. Set Axle forces to one of these options:

• `External longitudinal velocity`

• `External longitudinal forces`

3. Do either of these:

• Select Mapped corner stiffness.

• Clear Mapped corner stiffness and select Include relaxation length dynamics.

Front axle slip angle breakpoints, αfbrk, in rad.

#### Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

• `External longitudinal velocity`

• `External longitudinal forces`

2. Select Mapped corner stiffness.

Front axle corner data, Cyfdata, in N/rad.

#### Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

• `External longitudinal velocity`

• `External longitudinal forces`

2. Select Mapped corner stiffness.

Rear axle slip angle breakpoints, αrbrk, in rad.

#### Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

• `External longitudinal velocity`

• `External longitudinal forces`

2. Select Mapped corner stiffness.

Rear axle corner data, Cyrdata, in N/rad.

#### Dependencies

To enable this parameter:

1. Set Axle forces to one of these options:

• `External longitudinal velocity`

• `External longitudinal forces`

2. Select Mapped corner stiffness.

Yaw

Yaw polar inertia, in kg*m^2.

Aerodynamic

Effective vehicle cross-sectional area, Af, to calculate the aerodynamic drag force on the vehicle, in m2.

Air drag coefficient, Cd. The value is dimensionless.

Air lift coefficient, Cl. The value is dimensionless.

Longitudinal drag pitch moment coefficient, Cpm. The value is dimensionless.

Relative wind angle vector, βw, in rad.

Side force coefficient vector coefficient, Cs. The value is dimensionless.

Yaw moment coefficient vector coefficient, Cym. The value is dimensionless.

Environment

Environmental absolute pressure, Pabs, in Pa.

Environmental absolute temperature, T, in K.

#### Dependencies

To enable this parameter, clear Air temperature.

Gravitational acceleration, g, in m/s^2.

Nominal friction scale factor, μ. The value is dimensionless.

#### Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:

1. Set Axle forces to one of these options:

• ```External longitudinal velocity```

• ```External longitudinal forces```

2. Clear External Friction.

Simulation

Longitudinal velocity tolerance, in m/s.

Nominal normal force, in N.

#### Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter, set Axle forces to one of these options:

• `External longitudinal velocity`

• `External longitudinal forces`

Vehicle chassis offset from axle plane along body-fixed x-axis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independent of the vehicle CG.

Vehicle chassis offset from center plane along body-fixed y-axis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independent of the vehicle CG.

Vehicle chassis offset from axle plane along body-fixed z-axis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independent of the vehicle CG.

Wrap the Euler angles to the interval `[-pi, pi]`. For vehicle maneuvers that might undergo vehicle yaw rotations that are outside of the interval, consider deselecting the parameter if you want to:

• Track the total vehicle yaw rotation.

• Avoid discontinuities in the vehicle state estimators.

 Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers (SAE), 1992.