# Trailer Body 6DOF

Trailer body with translational and rotational motion

• Library:
• Vehicle Dynamics Blockset / Vehicle Body

• ## Description

The Trailer Body 6DOF block implements a rigid two-axle or three-axle trailer body model that calculates longitudinal, lateral, vertical, pitch, roll, and yaw motion. The block accounts for body mass, inertia, aerodynamic drag, road incline, and weight distribution between the axle hard-point locations due to suspension and external forces and moments.

Use the Inertial Loads parameters to analyze the trailer dynamics under different loading conditions. To specify the number of trailer axles, use the Number of axles parameter.

To create additional input ports, under Input signals, select these block parameters.

Parameter

Input PortDescription
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

• Front end

• Front left and front right

• Rear left and rear right

• Rear end

For each of the loads, you can specify the mass, location, and inertia.

The illustrations provide the load locations and vehicle parameter dimensions. The table provides the corresponding location parameter sign settings. This table summarizes the parameter settings that specify the load locations indicated by the dots. For the location, the block uses this distance vector:

• Front axle to load, along the vehicle-fixed x-axis

• Vehicle centerline to load, along the vehicle-fixed y-axis

• Front axle to load, along the vehicle-fixed z-axis

Parameter

Example Location

Front end

Distance vector from front axle, z1R

• `z1R(1,1)<0` — Forward of the front axle

• `z1R(1,2)>0` — Right of the vehicle centerline

• `z1R(1,3)>0` — Above the front axle suspension hardpoint

Distance vector from front axle, z2R

• `z2R(1,1)>0` — Rear of the front axle

• `z2R(1,2)<0` — Left of the vehicle centerline

• `z2R(1,3)>0` — Above the front axle suspension hardpoint

Front left

Distance vector from front axle, z3R

• `z3R(1,1)>0` — Rear of the front axle

• `z3R(1,2)<0` — Left of the vehicle centerline

• `z3R(1,3)>0` — Above the front axle suspension hardpoint

Front right

Distance vector from front axle, z4R

• `z4R(1,1)>0` — Rear of the front axle

• `z4R(1,2)>0` — Right of the vehicle centerline

• `z4R(1,3)>0` — Above the front axle suspension hardpoint

Rear left

Distance vector from front axle, z5R

• `z5R(1,1)>0` — Rear of the front axle

• `z5R(1,2)<0` — Left of the vehicle centerline

• `z5R(1,3)>0` — Above the front axle suspension hardpoint

Rear right

Distance vector from front axle, z6R

• `z6R(1,1)>0` — Rear of the front axle

• `z6R(1,2)>0` — Right of the vehicle centerline

• `z6R(1,3)>0` — Above the front axle suspension hardpoint

Rear end

Distance vector from front axle, z7R

• `z7R(1,1)>0` — Rear of the front axle

• `z7R(1,2)>0` — Right of the vehicle centerline

• `z7R(1,3)>0` — Above the front axle suspension hardpoint

### Equations of Motion

To determine the vehicle motion, the block implements calculations for the rigid body vehicle dynamics, wind drag, inertial loads, and coordinate transformations. The body-fixed and vehicle-fixed coordinate systems are the same.

The block considers the rotation of a body-fixed coordinate frame about a flat earth-fixed inertial reference frame. The origin of the body-fixed coordinate frame is the vehicle center of gravity of the body.

The block uses this equation to calculate the translational motion of the body-fixed coordinate frame, where the applied forces [Fx Fy Fz]T are in the body-fixed frame, and the mass of the body, m, is assumed to be constant.

`$\begin{array}{l}{\overline{F}}_{b}=\left[\begin{array}{c}{F}_{x}\\ {F}_{y}\\ {F}_{z}\end{array}\right]=m\left({\stackrel{˙}{\overline{V}}}_{b}+\overline{\omega }×{\overline{V}}_{b}\right)\\ \\ {\overline{M}}_{b}=\left[\begin{array}{c}L\\ M\\ N\end{array}\right]=I\stackrel{˙}{\overline{\omega }}+\overline{\omega }×\left(I\overline{\omega }\right)\\ \\ I=\left[\begin{array}{ccc}{I}_{xx}& -{I}_{xy}& -{I}_{xz}\\ -{I}_{yx}& {I}_{yy}& -{I}_{yz}\\ -{I}_{zx}& -{I}_{zy}& {I}_{zz}\end{array}\right]\end{array}$`

To determine the relationship between the body-fixed angular velocity vector, [p q r]T, and the rate of change of the Euler angles, $\left[\begin{array}{ccc}\stackrel{˙}{\varphi }\text{ }\text{\hspace{0.17em}}& \stackrel{˙}{\theta }\text{\hspace{0.17em}}\text{ }\text{ }& \stackrel{˙}{\psi }\end{array}{\right]}^{T}$, the block resolves the Euler rates into the body-fixed frame.

`$\left[\begin{array}{c}p\\ q\\ r\end{array}\right]=\left[\begin{array}{c}\stackrel{˙}{\varphi }\\ 0\\ 0\end{array}\right]+\left[\begin{array}{ccc}1& 0& 0\\ 0& \mathrm{cos}\varphi & \mathrm{sin}\varphi \\ 0& -\mathrm{sin}\varphi & \mathrm{cos}\varphi \end{array}\right]\left[\begin{array}{c}0\\ \stackrel{˙}{\theta }\\ 0\end{array}\right]+\left[\begin{array}{ccc}1& 0& 0\\ 0& \mathrm{cos}\varphi & \mathrm{sin}\varphi \\ 0& -\mathrm{sin}\varphi & \mathrm{cos}\varphi \end{array}\right]\left[\begin{array}{ccc}\mathrm{cos}\theta & 0& -\mathrm{sin}\theta \\ 0& 1& 0\\ \mathrm{sin}\theta & 0& \mathrm{cos}\theta \end{array}\right]\left[\begin{array}{c}0\\ 0\\ \stackrel{˙}{\psi }\end{array}\right]\equiv {J}^{-1}\left[\begin{array}{c}\stackrel{˙}{\varphi }\\ \stackrel{˙}{\theta }\\ \stackrel{˙}{\psi }\end{array}\right]$`

Inverting J gives the required relationship to determine the Euler rate vector.

`$\left[\begin{array}{c}\stackrel{˙}{\varphi }\\ \stackrel{˙}{\theta }\\ \stackrel{˙}{\psi }\end{array}\right]=J\left[\begin{array}{c}p\\ q\\ r\end{array}\right]\text{\hspace{0.17em}}=\left[\begin{array}{ccc}1& \left(\mathrm{sin}\varphi \mathrm{tan}\theta \right)& \left(\mathrm{cos}\varphi \mathrm{tan}\theta \right)\\ 0& \mathrm{cos}\varphi & -\mathrm{sin}\varphi \\ 0& \frac{\mathrm{sin}\varphi }{\mathrm{cos}\theta }& \frac{\mathrm{cos}\varphi }{\mathrm{cos}\theta }\end{array}\right]\left[\begin{array}{c}p\\ q\\ r\end{array}\right]$`

The applied forces and moments are the sum of the drag, gravitational, external, and suspension forces.

`$\begin{array}{l}{\overline{F}}_{b}=\left[\begin{array}{c}{F}_{x}\\ {F}_{y}\\ {F}_{z}\end{array}\right]=\left[\begin{array}{c}{F}_{d}{}_{{}_{x}}\\ {F}_{d}{}_{{}_{y}}\\ {F}_{d}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{F}_{g}{}_{{}_{x}}\\ {F}_{g}{}_{{}_{y}}\\ {F}_{g}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{F}_{ext}{}_{{}_{x}}\\ {F}_{ext}{}_{{}_{y}}\\ {F}_{ext}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{F}_{FL}{}_{{}_{x}}\\ {F}_{FL}{}_{{}_{y}}\\ {F}_{FL}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{F}_{FR}{}_{{}_{x}}\\ {F}_{FR}{}_{{}_{y}}\\ {F}_{FR}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{F}_{ML}{}_{{}_{x}}\\ {F}_{ML}{}_{{}_{y}}\\ {F}_{ML}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{F}_{MR}{}_{{}_{x}}\\ {F}_{MR}{}_{{}_{y}}\\ {F}_{MR}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{F}_{RL}{}_{{}_{x}}\\ {F}_{RL}{}_{{}_{y}}\\ {F}_{RL}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{F}_{RR}{}_{{}_{x}}\\ {F}_{RR}{}_{{}_{y}}\\ {F}_{RR}{}_{{}_{z}}\end{array}\right]\\ \\ {\overline{M}}_{b}=\left[\begin{array}{c}{M}_{x}\\ {M}_{y}\\ {M}_{z}\end{array}\right]=\left[\begin{array}{c}{M}_{d}{}_{{}_{x}}\\ {M}_{d}{}_{{}_{y}}\\ {M}_{d}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{M}_{ext}{}_{{}_{x}}\\ {M}_{ext}{}_{{}_{y}}\\ {M}_{ext}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{M}_{FL}{}_{{}_{x}}\\ {M}_{FL}{}_{{}_{y}}\\ {M}_{FL}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{M}_{FR}{}_{{}_{x}}\\ {M}_{FR}{}_{{}_{y}}\\ {M}_{FR}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{M}_{ML}{}_{{}_{x}}\\ {M}_{ML}{}_{{}_{y}}\\ {M}_{ML}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{M}_{MR}{}_{{}_{x}}\\ {M}_{MR}{}_{{}_{y}}\\ {M}_{MR}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{M}_{RL}{}_{{}_{x}}\\ {M}_{RL}{}_{{}_{y}}\\ {M}_{RL}{}_{{}_{z}}\end{array}\right]+\left[\begin{array}{c}{M}_{RR}{}_{{}_{x}}\\ {M}_{RR}{}_{{}_{y}}\\ {M}_{RR}{}_{{}_{z}}\end{array}\right]+{\overline{M}}_{F}\end{array}$`

CalculationImplementation

The block uses the parallel axis theorem to resolve the individual load masses and inertias with the vehicle mass and inertia.

`${J}_{ij}={I}_{ij}+m\left({|R|}^{2}{\delta }_{ij}-{R}_{i}{R}_{j}\right)$`

Gravitational forces, Fg

The block uses the direction cosine matrix (DCM) to transform the gravitational vector in the inertial-fixed frame to the body-fixed frame.

Drag forces, Fd, and moments, Md

To determine a relative airspeed, the block subtracts the wind speed from the vehicle center of mass (CM) velocity. Using the relative airspeed, the block determines the drag forces.

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

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

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

External forces, Fin, and moments, Min

The external forces and moments are input via ports FExt and MExt.

Suspension forces and moments

The block assumes that the suspension forces and moments act on these hardpoint locations:

• FFL, MFL — Front left

• FFR, MFR — Front right

• FML, MML — Middle left

• FMR, MMR — Middle right

• FRL, MRL — Rear left

• FRR, MRR — Rear right

The equations use these variables.

 $x,\stackrel{˙}{x},\stackrel{¨}{x}$ Vehicle CM displacement, velocity, and acceleration along the vehicle-fixed x-axis $y,\stackrel{˙}{y},\stackrel{¨}{y}$ Vehicle CM displacement, velocity, and acceleration along the vehicle-fixed y-axis $z,\stackrel{˙}{z},\stackrel{¨}{z}$ Vehicle CM displacement, velocity, and acceleration along the vehicle-fixed z-axis φ Rotation of the vehicle-fixed frame about the earth-fixed X-axis (roll) θ Rotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch) ψ Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw) FFLx, FFLy, FFLz Suspension forces applied to the front left hardpoint along the vehicle-fixed x-, y-, and z-axes FFRx, FFRy, FFRz Suspension forces applied to the front right hardpoint along the vehicle-fixed x-, y-, and z-axes FMLx, FMLy, FMLz Suspension forces applied to the middle left hardpoint along the vehicle-fixed x-, y-, and z-axes FMRx, FMRy, FMRz Suspension forces applied to the middle right hardpoint along the vehicle-fixed x-, y-, and z-axes FRLx, FRLy, FRLz Suspension forces applied to the rear left hardpoint along the vehicle-fixed x-, y-, and z-axes FRRx, FRRy, FRRz Suspension forces applied to the rear right hardpoint along the vehicle-fixed x-, y-, and z-axes MFLx, MFLy, MFLz Suspension moment applied to the front left hardpoint about the vehicle-fixed x-, y-, and z-axes MFRx, MFRy, MFRz Suspension moment applied to the front right hardpoint about the vehicle-fixed x-, y-, and z-axes MMLx, MMLy, MMLz Suspension moment applied to the middle left hardpoint about the vehicle-fixed x-, y-, and z-axes MMRx, MMRy, MMRz Suspension moment applied to the middle right hardpoint about the vehicle-fixed x-, y-, and z-axes MRLx, MRLy, MRLz Suspension moment applied to the rear left hardpoint about the vehicle-fixed x-, y-, and z-axes MRRx, MRRy, MRRz Suspension moment applied to the rear right hardpoint about the vehicle-fixed x-, y-, and z-axes Fextx, Fexty, Fextz External forces applied to the vehicle CM along the vehicle-fixed x-, y-, and z-axes Fdx, Fdy, Fdz Drag forces applied to the vehicle CM along the vehicle-fixed x-, y-, and z-axes Mextx, Mexty, Mextz External moment about the vehicle CM about the vehicle-fixed x-, y-, and z-axes Mdx, Mdy, Mdz Drag moment about the vehicle CM about the vehicle-fixed x-, y-, and z-axes I Vehicle body moments of inertia a, b, c Distance of the front, middle, and rear axles, respectively, from the normal projection point of the vehicle CM onto the common axle plane h Height of the vehicle CM 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 the vehicle CM onto the common axle plane hl Lateral distance from center of mass to the hitch along the vehicle-fixed y-axis. wF, wM, wR Front, middle, and rear track widths, respectively Cd Air drag coefficient acting along the vehicle-fixed x-axis Cs Air drag coefficient acting along the vehicle-fixed y-axis Cl Air drag coefficient acting along the 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

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Suspension longitudinal, lateral, and vertical suspension forces, `FSusp`, applied to the trailer at the hardpoint location, in N, specified as a `3-by-4` or `3-by-6` array, depending on the Number of axles parameter.

Number of axles Setting

Variable

Signal Dimension

`2`

`$FSusp=\left[\begin{array}{cccc}{F}_{FLx}& {F}_{FRx}& {F}_{RLx}& {F}_{RRx}\\ {F}_{FLy}& {F}_{FRy}& {F}_{RLy}& {F}_{RRy}\\ {F}_{FLz}& {F}_{FRz}& {F}_{RLz}& {F}_{RRz}\end{array}\right]$`

Array – `3-by-4`

`3`

`$FSusp=\left[\begin{array}{cccccc}{F}_{FLx}& {F}_{FRx}& {F}_{MLx}& {F}_{MRx}& {F}_{RLx}& {F}_{RRx}\\ {F}_{FLy}& {F}_{FRy}& {F}_{MLy}& {F}_{MRy}& {F}_{RLy}& {F}_{RRy}\\ {F}_{FLz}& {F}_{FRz}& {F}_{MLz}& {F}_{MRz}& {F}_{RLz}& {F}_{RRz}\end{array}\right]$`

Array – `3-by-6`

The arrays use these variables.

 FFLx, FFLy, FFLz Suspension forces applied to front left hardpoint along the vehicle-fixed x-, y-, and z-axes FFRx, FFRy, FFRz Suspension forces applied to front right hardpoint along the vehicle-fixed x-, y-, and z-axes FMLx, FMLy, FMLz Suspension forces applied to middle left hardpoint along the vehicle-fixed x-, y-, and z-axes FMRx, FMRy, FMRz Suspension forces applied to middle right hardpoint along the vehicle-fixed x-, y-, and z-axes FRLx, FRLy, FRLz Suspension forces applied to rear left hardpoint along the vehicle-fixed x-, y-, and z-axes FRRx, FRRy, FRRz Suspension forces applied to rear right hardpoint along the vehicle-fixed x-, y-, and z-axes

Suspension longitudinal, lateral, and vertical suspension moments, `MSusp`, applied about the vehicle at the hardpoint location, in N·m, specified as a `3-by-4` or `3-by-6` array, depending on the Number of axles parameter.

Number of axles Setting

Variable

Signal Dimension

`2`

`$MSusp=\left[\begin{array}{cccc}{M}_{FLx}& {M}_{FRx}& {M}_{RLx}& {M}_{RRx}\\ {M}_{FLy}& {M}_{FRy}& {M}_{RLy}& {M}_{RRy}\\ {M}_{FLz}& {M}_{FRz}& {M}_{RLz}& {M}_{RRz}\end{array}\right]$`

Array – `3-by-4`

`3`

`$MSusp=\left[\begin{array}{cccccc}{M}_{FLx}& {M}_{FRx}& {M}_{MLx}& {M}_{MRx}& {M}_{RLx}& {M}_{RRx}\\ {M}_{FLy}& {M}_{FRz}& {M}_{MLy}& {M}_{MRy}& {M}_{RLy}& {M}_{RRy}\\ {M}_{FLz}& {M}_{FRz}& {M}_{MLz}& {M}_{MRz}& {M}_{RLz}& {M}_{RRz}\end{array}\right]$`

Array – `3-by-6`

The arrays use these variables.

 MFLx, MFLy, MFLz Suspension moment applied to front left hardpoint about the vehicle-fixed x-, y-, and z-axes MFRx, MFRy, MFRz Suspension moment applied to front right hardpoint about the vehicle-fixed x-, y-, and z-axes MMLx, MMLy, MMLz Suspension moment applied to middle left hardpoint about the vehicle-fixed x-, y-, and z-axes MMRx, MMRy, MMRz Suspension moment applied to middle right hardpoint about the vehicle-fixed x-, y-, and z-axes MRLx, MRLy, MRLz Suspension moment applied to rear left hardpoint about the vehicle-fixed x-, y-, and z-axes MRRx, MRRy, MRRz Suspension moment applied to rear right hardpoint about the vehicle-fixed x-, y-, and z-axes

External forces on the vehicle, in N, specified as a `1-by-3` or `3-by-1` vector.

`$\text{FExt}={F}_{ext}=\left[\begin{array}{ccc}{F}_{ex{t}_{x}}& {F}_{ex{t}_{y}}& {F}_{ex{t}_{z}}\end{array}\right]or\left[\begin{array}{c}{F}_{ex{t}_{x}}\\ {F}_{ex{t}_{y}}\\ {F}_{ex{t}_{z}}\end{array}\right]$`

Array ElementForce Axis

`FExt(1,1)`

Vehicle-fixed x-axis (longitudinal)

`FExt(1,2)` or `FExt(2,1)`

Vehicle-fixed y-axis (lateral)

`FExt(1,3)` or `FExt(3,1)`

Vehicle-fixed z-axis (vertical)

External moments acting on the vehicle, in N·m, specified as a `1-by-3` or `3-by-1` vector.

`$\text{MExt}={M}_{ext}=\left[\begin{array}{ccc}{M}_{ex{t}_{x}}& {M}_{ex{t}_{y}}& {M}_{ex{t}_{z}}\end{array}\right]or\left[\begin{array}{c}{M}_{ex{t}_{x}}\\ {M}_{ex{t}_{y}}\\ {M}_{ex{t}_{z}}\end{array}\right]$`

Array ElementForce Axis
`MExt(1,1)`Vehicle-fixed x-axis (longitudinal)

`MExt(1,2)` or `MExt(2,1)`

Vehicle-fixed y-axis (lateral)

`MExt(1,3)` or `MExt(3,1)`

Vehicle-fixed z-axis (vertical)

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, specified as a `1-by-3` or `3-by-1` array.

Ambient air temperature, Tair, in K, specified as a scalar.

#### Dependencies

To enable this port, under Environment, select Air temperature.

### Output

expand all

Trailer body information, returned as a bug signal containing the following values.

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

Computed

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

Computed

m

`Z`Vehicle CM displacement along the earth-fixed Z-axis

Computed

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

Computed

m/s

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

Computed

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

Computed

m/s
`Ang``phi`Rotation of the vehicle-fixed frame about the earth-fixed X-axis (roll)

Computed

`theta`Rotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)

Computed

`psi`Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)

Computed

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

Computed

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

Computed

m
`Z`Front left axle displacement along the earth-fixed Z-axis

Computed

m
`Vel``Xdot`Front left axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
`Zdot`Front left axle velocity along the earth-fixed Z-axis

Computed

m/s
`Rght``Disp``X`Front right axle displacement along the earth-fixed X-axis

Computed

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

Computed

m
`Z`Front right axle displacement along the earth-fixed Z-axis

Computed

m
`Vel``Xdot`Front right axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
`Zdot`Front right axle velocity along the earth-fixed Z-axis

Computed

m/s
`MidlAxl``Lft``Disp``X`Middle left axle displacement along the earth-fixed X-axis

Computed

m
`Y`Middle left axle displacement along the earth-fixed Y-axis

Computed

m
`Z`Middle left axle displacement along the earth-fixed Z-axis

Computed

m
`Vel``Xdot`Middle left axle velocity along the earth-fixed X-axis

Computed

m/s
`Ydot`Middle left axle velocity along the earth-fixed Y-axis

Computed

m/s
`Zdot`Middle left axle velocity along the earth-fixed Z-axis

Computed

m/s
`Rght``Disp``X`Middle right axle displacement along the earth-fixed X-axis

Computed

m
`Y`Middle right axle displacement along the earth-fixed Y-axis

Computed

m
`Z`Middle right axle displacement along the earth-fixed Z-axis

Computed

m
`Vel``Xdot`Middle right axle velocity along the earth-fixed X-axis

Computed

m/s
`Ydot`Middle right axle velocity along the earth-fixed Y-axis

Computed

m/s
`Zdot`Middle right axle velocity along the earth-fixed Z-axis

Computed

m/s
`RearAxl``Lft``Disp``X`Rear left axle displacement along the earth-fixed X-axis

Computed

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

Computed

m
`Z`Rear left axle displacement along the earth-fixed Z-axis

Computed

m
`Vel``Xdot`Rear left axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
`Zdot`Rear left axle velocity along the earth-fixed Z-axis

Computed

m/s
`Rght``Disp``X`Rear right axle displacement along the earth-fixed X-axis

Computed

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

Computed

m
`Z`Rear right axle displacement along the earth-fixed Z-axis

Computed

m
`Vel``Xdot`Rear right axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
`Zdot`Rear right axle velocity along the earth-fixed Z-axis

Computed

m/s
`Hitch``Disp``X`Hitch offset from the axle plane along the earth-fixed X-axis

Computed

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

Computed

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

Computed

m
`Vel``Xdot`Hitch velocity along the earth-fixed X-axis

Computed

m/s
`Ydot`Hitch velocity along the earth-fixed Y-axis

Computed

m/s
`Zdot`Hitch velocity along the earth-fixed Z-axis

Computed

m/s
`Geom``Disp``X`Trailer offset from the axle plane along the earth-fixed X-axis

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

m/s
`zdot`Vehicle CM velocity along the vehicle-fixed z-axisComputedm/s
`AngVel``p`Vehicle angular velocity about the vehicle-fixed x-axis (roll rate)

Computed

`q`Vehicle angular velocity about the vehicle-fixed y-axis (pitch rate)

Computed

`r`Vehicle angular velocity about the vehicle-fixed z-axis (yaw rate)

Computed

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

Computed

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

Computed

gn
`az`Vehicle CM acceleration along the vehicle-fixed z-axis

Computed

gn
`xddot`Vehicle CM acceleration along the vehicle-fixed x-axis

Computed

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

Computed

m/s^2
`zddot`Vehicle CM acceleration along the vehicle-fixed z-axis

Computed

m/s^2
`DCM`

Direction cosine matrix

Computed

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

Computed

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

Computed

N
`Fz`Net force on the vehicle CM along the vehicle-fixed z-axis

Computed

N
`Ext``Fx`External force on the vehicle CM along the vehicle-fixed x-axis

Input

N
`Fy`External force on the vehicle CM along the vehicle-fixed x-axis

Input

N
`Fz`External force on the vehicle CM along the vehicle-fixed x-axis

Input

N
`FrntAxl``Lft``Fx`

Front left axle velocity along the earth-fixed Y-axis

Computed

N
`Fy`

Lateral force on the left side of the front axle left along the vehicle-fixed y-axis

Computed

N
`Fz`

Normal force on the left side of the front axle along the vehicle-fixed z-axis

ComputedN
`Rght``Fx`

Longitudinal force on the right side of the front axle along the vehicle-fixed x-axis

Computed

N
`Fy`

Lateral force on the right side of the front axle left along the vehicle-fixed y-axis

Computed

N
`Fz`

Normal force on the right side of the front axle along the vehicle-fixed z-axis

Computed

N
`MidlAxl``Lft``Fx`

Longitudinal force on the left side of the middle axle along the vehicle-fixed x-axis

Computed

N
`Fy`

Longitudinal force on the left side of the middle axle along the vehicle-fixed x-axis

Computed

N
`Fz`

Normal force on the left side of the middle axle along the vehicle-fixed z-axis

Computed

N
`Rght``Fx`

Longitudinal force on the right side of the middle axle along the vehicle-fixed x-axis

Computed

N
`Fy`

Lateral force on the right side of the middle axle left along the vehicle-fixed y-axis

Computed

N
`Fz`

Normal force on the right side of the middle axle along the vehicle-fixed z-axis

Computed

N
`RearAxl``Lft``Fx`

Longitudinal force on the left side of the rear axle along the vehicle-fixed x-axis

Computed

N
`Fy`

Lateral force on the left side of the rear axle left along the vehicle-fixed y-axis

Computed

N
`Fz`

Normal force on the left side of the rear axle along the vehicle-fixed z-axis

Computed

N
`Rght``Fx`

Longitudinal force on the right side of the rear axle along the vehicle-fixed x-axis

Computed

N
`Fy`

Lateral force on the right side of the rear axle left along the vehicle-fixed y-axis

Computed

N
`Fz`

Normal force on the right side of the rear axle along the vehicle-fixed z-axis

Computed

N
`Hitch``Fx`

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

Computed

N
`Fy`

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

Computed

N
`Fz`

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

Computed

N
`Tires``FrntTires``Lft``Fx`

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

Computed

N
`Fy`

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

Computed

N
`Fz`

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

Computed

N
`Rght``Fx`

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

Computed

N
`Fy`

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

Computed

N
`Fz`

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

Computed

N
`MidlTires``Lft``Fx`

Middle left tire force along the vehicle-fixed x-axis

Computed

N
`Fy`

Middle left tire force along the vehicle-fixed y-axis

Computed

N
`Fz`

Middle left tire force along the vehicle-fixed z-axis

Computed

N
`Rght``Fx`

Middle right tire force along the vehicle-fixed x-axis

Computed

N
`Fy`

Middle right tire force along the vehicle-fixed y-axis

Computed

N
`Fz`

Middle right tire force along the vehicle-fixed z-axis

Computed

N
`RearTires``Lft``Fx`

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

Computed

N
`Fy`

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

Computed

N
`Fz`

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

Computed

N
`Rght``Fx`

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

Computed

N
`Fy`

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

Computed

N
`Fz`

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

Computed

N
`Drag``Fx`Drag force on the vehicle CM along the vehicle-fixed x-axis

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

N
`Moments``Body``Mx`Body moment on the vehicle CM about the vehicle-fixed x-axis

Computed

N·m
`My`Body moment on the vehicle CM about the vehicle-fixed y-axis

Computed

N·m
`Mz`Body moment on the vehicle CM about the vehicle-fixed z-axis

Computed

N·m
`Drag``Mx`Drag moment on the vehicle CM about the vehicle-fixed x-axis

Computed

N·m
`My`Drag moment on the vehicle CM about the vehicle-fixed y-axis

Computed

N·m
`Mz`Drag moment on the vehicle CM about the vehicle-fixed z-axis

Computed

N·m
`Ext``Mx`External moment on the vehicle CG about the vehicle-fixed x-axis

Computed

N·m
`My`External moment on the vehicle CG about the vehicle-fixed y-axis

Computed

N·m
`Mz`External moment on the vehicle CG about the vehicle-fixed z-axis

Computed

N·m
`Hitch``Mx`Hitch moment at the hitch location about the vehicle-fixed x-axis

Computed

N·m
`My`Hitch moment at the hitch location about the vehicle-fixed y-axis

Computed

N·m
`Mz`Hitch moment at the hitch location about the vehicle-fixed z-axis

Computed

N·m
`FrntAxl``Lft``Disp``x`Front left axle displacement along the vehicle-fixed x-axis

Computed

m
`y`Front left axle displacement along the vehicle-fixed y-axis

Computed

m
`z`Front left axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
`zdot`Front left axle velocity along the vehicle-fixed z-axis

Computed

m/s
`Rght``Disp``x`Front right axle displacement along the vehicle-fixed x-axis

Computed

m
`y`Front right axle displacement along the vehicle-fixed y-axis

Computed

m
`z`Front right axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
`zdot`Front right axle velocity along the vehicle-fixed z-axis

Computed

m/s
`MidlAxl``Lft``Disp``x`Middle left axle displacement along the vehicle-fixed x-axis

Computed

m
`y`Middle left axle displacement along the vehicle-fixed y-axis

Computed

m
`z`Middle left axle displacement along the vehicle-fixed z-axis

Computed

m
`Vel``xdot`Middle left axle velocity along the vehicle-fixed x-axis

Computed

m/s
`ydot`Middle left axle velocity along the vehicle-fixed y-axis

Computed

m/s
`zdot`Middle left axle velocity along the vehicle-fixed z-axis

Computed

m/s
`Rght``Disp``x`Middle right axle displacement along the vehicle-fixed x-axis

Computed

m
`y`Middle right axle displacement along the vehicle-fixed y-axis

Computed

m
`z`Middle right axle displacement along the vehicle-fixed z-axis

Computed

m
`Vel``xdot`Middle right axle velocity along the vehicle-fixed x-axis

Computed

m/s
`ydot`Middle right axle velocity along the vehicle-fixed y-axis

Computed

m/s
`zdot`Middle right axle velocity along the vehicle-fixed z-axis

Computed

m/s
`RearAxl``Lft``Disp``x`Rear left axle displacement along the vehicle-fixed x-axis

Computed

m
`y`Rear left axle displacement along the vehicle-fixed y-axis

Computed

m
`z`Rear left axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
`zdot`Rear left axle velocity along the vehicle-fixed z-axis

Computed

m/s
`Rght``Disp``x`Rear right axle displacement along the vehicle-fixed x-axis

Computed

m
`y`Rear right axle displacement along the vehicle-fixed y-axis

Computed

m
`z`Rear right axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
`zdot`Rear right axle velocity along the vehicle-fixed z-axis

Computed

m/s
`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 vehicle-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``PwrExt`Applied external power

Computed

W
`Drag`Power loss due to drag

Computed

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

Input

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

Input

m
`z`Trailer offset from axle plane along the vehicle-fixed z-axis

Input

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

Computed

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

Computed

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

Computed

m/s
`Ang``Beta`

Body slip angle, β

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

Computed

Vehicle CM velocity along the vehicle-fixed x-, y-, z-axes, respectively, in m/s, returned as a vector.

Vehicle CM angular velocity about the vehicle-fixed x- (roll rate), y- (pitch rate), z-axes (yaw rate), respectively, in rad/s, returned as a vector.

Direction cosine matrix, in rad, returned as an array.

Euler angles, φ, θ, and ψ, respectively, in rad, returned as an array.

Vehicle CM position along inertial-fixed X-, Y-, Z-axes, respectively, in m, returned as a vector.

Vehicle CM velocity along inertial-fixed X-, Y-, Z-axes, respectively, in m/s, returned as a vector.

## Parameters

expand all

### Block Options

Specify the number of axles on the trailer.

Input Signals

Select to create an input port, `Fh`, for the hitch forces.

Select to create an input port, `Mh`, for the hitch moments.

### Chassis

Vehicle mass, m, in kg.

Distance from the vehicle CM to the front axle, a, in m. Distance from the vehicle CM to the middle axle, b, in m. #### Dependencies

To enable this parameter, set Number of axles to `3`.

Distance from the vehicle CM to the middle axle, c, in m. Lateral distance from the geometric centerline to the CM, d, in m, along the vehicle-fixed y-axis. 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. Vertical distance from the vehicle CM to the axle plane, 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.

Lateral distance from center of mass to hitch, hl, 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 position of the vehicle in the inertial frame, Xeo, in m.

Initial vehicle CM velocity along the vehicle-fixed x, y-, and z-axes, respectively, in m/s.

Initial Euler rotation of the vehicle-fixed frame about the earth-fixed X- (roll), Y- (pitch), Z-axes (yaw), respectively, in rad.

Initial vehicle CM angular velocity about the vehicle-fixed x- (roll rate), y- (pitch rate), z-axes (yaw rate), respectively, in rad/s.

Vehicle inertia tensor, Iveh, in kg*m^2. Dimensions are `[3-by-3]`.

Front track width, in m. Middle track width, in m. #### Dependencies

To enable this parameter, set Number of axles to `3`.

Rear track width, in m. Front End

Mass, z1m, in kg.

Distance vector from front axle to load, z1R, in m. Dimensions are `1-by-3`.

Array ElementDescription
`z1R(1,1)`

Front suspension hardpoint to load, along vehicle-fixed x-axis

`z1R(1,2)`

Vehicle centerline to load, along vehicle-fixed y-axis

`z1R(1,3)`

Front suspension hardpoint to load, along vehicle-fixed z-axis

For example, this table summarizes the parameter settings that specify the load location.

Example Location

Sign

• Forward of the front axle

• Right of the vehicle centerline

• Above the front axle suspension hardpoint

• `z1R(1,1)` < 0

• `z1R(1,2)` > 0

• `z1R(1,3)` > 0

Inertia tensor, z1I, in kg·m^2. Dimensions are `[3-by-3]`.

`$z1I=\left[\begin{array}{ccc}{I}_{xx}& {I}_{xy}& {I}_{xz}\\ {I}_{yx}& {I}_{yy}& {I}_{yz}\\ {I}_{zx}& {I}_{zy}& {I}_{zz}\end{array}\right]$`

The tensor uses a coordinate system with an origin at the load CM.

• x-axis along the vehicle-fixed x-axis

• y-axis along the vehicle-fixed y-axis

• z-axis along the vehicle-fixed z-axis

Mass, z2m, in kg.

Distance vector from front axle to load, z2R, in m. Dimensions are `1-by-3`.

Array ElementDescription
`z2R(1,1)`

Front suspension hardpoint to load, along vehicle-fixed x-axis

`z2R(1,2)`

Vehicle centerline to load, along vehicle-fixed y-axis

`z2R(1,3)`

Front suspension hardpoint to load, along vehicle-fixed z-axis

For example, this table summarizes the parameter settings that specify the load location.

Example Location

Sign

• Rear of the front axle

• Left of the vehicle centerline

• Above the front axle suspension hardpoint

• `z2R(1,1)` > 0

• `z2R(1,2)` < 0

• `z2R(1,3)` > 0

Inertia tensor, z2I, in kg·m^2. Dimensions are `[3-by-3]`.

`$z2I=\left[\begin{array}{ccc}{I}_{xx}& {I}_{xy}& {I}_{xz}\\ {I}_{yx}& {I}_{yy}& {I}_{yz}\\ {I}_{zx}& {I}_{zy}& {I}_{zz}\end{array}\right]$`

The tensor uses a coordinate system with an origin at the load CM.

• x-axis along the vehicle-fixed x-axis

• y-axis along the vehicle-fixed y-axis

• z-axis along the vehicle-fixed z-axis

Front Left

Mass, z3m, in kg.

Distance vector from front axle to load, z3R, in m. Dimensions are `1-by-3`.

Array ElementDescription
`z3R(1,1)`

Front suspension hardpoint to load, along vehicle-fixed x-axis

`z3R(1,2)`

Vehicle centerline to load, along vehicle-fixed y-axis

`z3R(1,3)`

Front suspension hardpoint to load, along vehicle-fixed z-axis

For example, this table summarizes the parameter settings that specify the load location.

Example Location

Sign

• Rear of the front axle

• Left of the vehicle centerline

• Above the front axle suspension hardpoint

• `z3R(1,1)` > 0

• `z3R(1,2)` < 0

• `z3R(1,3)` > 0

Inertia tensor, z3I, in kg·m^2. Dimensions are `[3-by-3]`.

`$z3I=\left[\begin{array}{ccc}{I}_{xx}& {I}_{xy}& {I}_{xz}\\ {I}_{yx}& {I}_{yy}& {I}_{yz}\\ {I}_{zx}& {I}_{zy}& {I}_{zz}\end{array}\right]$`

The tensor uses a coordinate system with an origin at the load CM.

• x-axis along the vehicle-fixed x-axis

• y-axis along the vehicle-fixed y-axis

• z-axis along the vehicle-fixed z-axis

Front Right

Mass, z4m, in kg.

Distance vector from front axle to load, z4R, in m. Dimensions are `1-by-3`.

Array ElementDescription
`z4R(1,1)`

Front suspension hardpoint to load, along vehicle-fixed x-axis

`z4R(1,2)`

Vehicle centerline to load, along vehicle-fixed y-axis

`z4R(1,3)`

Front suspension hardpoint to load, along vehicle-fixed z-axis

For example, this table summarizes the parameter settings that specify the load location.

Example Location

Sign

• Rear of the front axle

• Right of the vehicle centerline

• Above the front axle suspension hardpoint

• `z4R(1,1)` > 0

• `z4R(1,2)` > 0

• `z4R(1,3)` > 0

Inertia tensor, z4I, in kg·m^2. Dimensions are `[3-by-3]`.

`$z4I=\left[\begin{array}{ccc}{I}_{xx}& {I}_{xy}& {I}_{xz}\\ {I}_{yx}& {I}_{yy}& {I}_{yz}\\ {I}_{zx}& {I}_{zy}& {I}_{zz}\end{array}\right]$`

The tensor uses a coordinate system with an origin at the load CM.

• x-axis along the vehicle-fixed x-axis

• y-axis along the vehicle-fixed y-axis

• z-axis along the vehicle-fixed z-axis

Rear Left

Mass, z5m, in kg.

Distance vector from front axle to load, z5R, in m. Dimensions are `1-by-3`.

Array ElementDescription
`z5R(1,1)`

Front suspension hardpoint to load, along vehicle-fixed x-axis

`z5R(1,2)`

Vehicle centerline to load, along vehicle-fixed y-axis

`z5R(1,3)`

Front suspension hardpoint to load, along vehicle-fixed z-axis

For example, this table summarizes the parameter settings that specify the load location.

Example Location

Sign

• Rear of the front axle

• Left of the vehicle centerline

• Above the front axle suspension hardpoint

• `z5R(1,1)` > 0

• `z5R(1,2)` < 0

• `z5R(1,3)` > 0

Inertia tensor, z5I, in kg·m^2. Dimensions are `[3-by-3]`.

`$z5I=\left[\begin{array}{ccc}{I}_{xx}& {I}_{xy}& {I}_{xz}\\ {I}_{yx}& {I}_{yy}& {I}_{yz}\\ {I}_{zx}& {I}_{zy}& {I}_{zz}\end{array}\right]$`

The tensor uses a coordinate system with an origin at the load CM.

• x-axis along the vehicle-fixed x-axis

• y-axis along the vehicle-fixed y-axis

• z-axis along the vehicle-fixed z-axis

Rear Right

Mass, z6m, in kg.

Distance vector from front axle to load, z6R, in m. Dimensions are `1-by-3`.

Array ElementDescription
`z6R(1,1)`

Front suspension hardpoint to load, along vehicle-fixed x-axis

`z6R(1,2)`

Vehicle centerline to load, along vehicle-fixed y-axis

`z6R(1,3)`

Front suspension hardpoint to load, along vehicle-fixed z-axis

For example, this table summarizes the parameter settings that specify the load location.

Example Location

Sign

• Rear of the front axle

• Right of the vehicle centerline

• Above the front axle suspension hardpoint

• `z6R(1,1)` > 0

• `z6R(1,2)` > 0

• `z6R(1,3)` > 0

Inertia tensor, z6I, in kg·m^2. Dimensions are `[3-by-3]`.

`$z6I=\left[\begin{array}{ccc}{I}_{xx}& {I}_{xy}& {I}_{xz}\\ {I}_{yx}& {I}_{yy}& {I}_{yz}\\ {I}_{zx}& {I}_{zy}& {I}_{zz}\end{array}\right]$`

The tensor uses a coordinate system with an origin at the load CM.

• x-axis along the vehicle-fixed x-axis

• y-axis along the vehicle-fixed y-axis

• z-axis along the vehicle-fixed z-axis

Rear End

Mass, z7m, in kg.

Distance vector from front axle to load, z7R, in m. Dimensions are `1-by-3`.

Array ElementDescription
`z7R(1,1)`

Front suspension hardpoint to load, along vehicle-fixed x-axis

`z7R(1,2)`

Vehicle centerline to load, along vehicle-fixed y-axis

`z7R(1,3)`

Front suspension hardpoint to load, along vehicle-fixed z-axis

For example, this table summarizes the parameter settings that specify the load location.

Example Location

Sign

• Rear of the front axle

• Right of the vehicle centerline

• Above the front axle suspension hardpoint

• `z7R(1,1)` > 0

• `z7R(1,2)` > 0

• `z7R(1,3)` > 0

Inertia tensor, z7I, in kg·m^2. Dimensions are `[3-by-3]`.

`$z7I=\left[\begin{array}{ccc}{I}_{xx}& {I}_{xy}& {I}_{xz}\\ {I}_{yx}& {I}_{yy}& {I}_{yz}\\ {I}_{zx}& {I}_{zy}& {I}_{zz}\end{array}\right]$`

The tensor uses a coordinate system with an origin at the load CM.

• x-axis along the vehicle-fixed x-axis

• y-axis along the vehicle-fixed y-axis

• z-axis along the vehicle-fixed z-axis

### Aerodynamic

Effective vehicle cross-sectional area, Af to calculate the aerodynamic drag force on the vehicle, in m^2.

Air drag coefficient, Cd, dimensionless.

Air lift coefficient, Cl, dimensionless.

Longitudinal drag pitch moment coefficient, Cpm, dimensionless.

Relative wind angle vector, βw, in rad.

Side force coefficient vector coefficient, Cs, dimensionless.

Yaw moment coefficient vector coefficient, Cym, dimensionless.

### Environment

Environmental air absolute pressure, Pabs, in Pa.

Ambient air temperature, Tair, in K.

#### Dependencies

To enable this parameter, clear Air temperature.

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

### Simulation

Longitudinal velocity tolerance, xdottol, in m/s.

The block uses this parameter to avoid a division by zero when it calculates the body slip angle, β.

Trailer 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 independently of the vehicle CG.

Trailer 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 independently of the vehicle CG.

Trailer 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 independently 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 clearing 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.

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