Trailer Body 6DOF

Trailer body with translational and rotational motion

Since R2020b

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Libraries:
Vehicle Dynamics Blockset / Vehicle Body

Description

The Trailer Body 6DOF block implements a rigid one-axle, 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 Port	Description
Front hitch forces	FhF	Hitch force applied to the body at the front hitch location, FhFx, FhFy, and FhFz, in the vehicle-fixed frame
Front hitch moments	MhF	Hitch moment at the front hitch location, MhFx, MhFy, and MhFz, about the vehicle-fixed frame
Rear hitch forces	FhR	Hitch force applied to the body at the rear hitch location, FhRx, FhRy, and FhRz, in the vehicle-fixed frame
Rear hitch moments	MhR	Hitch moment at the rear hitch location, MhRx, MhRy, and MhRz, about the vehicle-fixed frame

Inertial Loads

To analyze the vehicle dynamics under different loading conditions, use the Inertial Loads parameters. You can specify these loads:

• Front end

• Overhead

• 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

Load	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
Overhead	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 [F_x F_y F_z]^T are in the body-fixed frame, and the mass of the body, m, is assumed to be constant.

$$\begin{array}{l}{\overline{F}}_b=\left[\begin{array}{c}{F}_x\\ F_y\\ F_z\end{array}\right]=m\left({\dot{\overline{V}}}_b+\overline{\omega }\times {\overline{V}}_b\right)\\ \\ {\overline{M}}_b=\left[\begin{array}{c}L\\ M\\ N\end{array}\right]=I\dot{\overline{\omega }}+\overline{\omega }\times (I\overline{\omega })\\ \\ I=\left[\begin{array}{ccc}{I}_{xx}& -I_{xy}& -I_{xz}\\ -I_{yx}& I_{yy}& -I_{yz}\\ -I_{zx}& -I_{zy}& I_{zz}\end{array}\right]\end{array}$$

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

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

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

$$\left[\begin{array}{c}\dot{\varphi }\\ \dot{\theta }\\ \dot{\psi }\end{array}\right]=J\left[\begin{array}{c}p\\ q\\ r\end{array}\right]=\left[\begin{array}{ccc}1& (\sin \varphi \tan \theta )& (\cos \varphi \tan \theta )\\ 0& \cos \varphi & -\sin \varphi \\ 0& \frac{\sin \varphi }{\cos \theta }& \frac{\cos \varphi }{\cos \theta }\end{array}\right]\left[\begin{array}{c}p\\ q\\ r\end{array}\right]$$

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

$$\begin{array}{l}{\overline{F}}_b=\left[\begin{array}{c}{F}_x\\ F_y\\ F_z\end{array}\right]=\left[\begin{array}{c}{F}_d{}_{{}_x}\\ F_d{}_{{}_y}\\ F_d{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{F}_g{}_{{}_x}\\ F_g{}_{{}_y}\\ F_g{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{F}_{ext}{}_{{}_x}\\ F_{ext}{}_{{}_y}\\ F_{ext}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{F}_{FL}{}_{{}_x}\\ F_{FL}{}_{{}_y}\\ F_{FL}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{F}_{FR}{}_{{}_x}\\ F_{FR}{}_{{}_y}\\ F_{FR}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{F}_{ML}{}_{{}_x}\\ F_{ML}{}_{{}_y}\\ F_{ML}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{F}_{MR}{}_{{}_x}\\ F_{MR}{}_{{}_y}\\ F_{MR}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{F}_{RL}{}_{{}_x}\\ F_{RL}{}_{{}_y}\\ F_{RL}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{F}_{RR}{}_{{}_x}\\ F_{RR}{}_{{}_y}\\ F_{RR}{}_{{}_z}\end{array}\right]\\ \\ {\overline{M}}_b=\left[\begin{array}{c}{M}_x\\ M_y\\ M_z\end{array}\right]=\left[\begin{array}{c}{M}_d{}_{{}_x}\\ M_d{}_{{}_y}\\ M_d{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{M}_{ext}{}_{{}_x}\\ M_{ext}{}_{{}_y}\\ M_{ext}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{M}_{FL}{}_{{}_x}\\ M_{FL}{}_{{}_y}\\ M_{FL}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{M}_{FR}{}_{{}_x}\\ M_{FR}{}_{{}_y}\\ M_{FR}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{M}_{ML}{}_{{}_x}\\ M_{ML}{}_{{}_y}\\ M_{ML}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{M}_{MR}{}_{{}_x}\\ M_{MR}{}_{{}_y}\\ M_{MR}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{M}_{RL}{}_{{}_x}\\ M_{RL}{}_{{}_y}\\ M_{RL}{}_{{}_z}\end{array}\right]+\left[\begin{array}{c}{M}_{RR}{}_{{}_x}\\ M_{RR}{}_{{}_y}\\ M_{RR}{}_{{}_z}\end{array}\right]+{\overline{M}}_F\end{array}$$

Calculation	Implementation
Load masses and inertias	The block uses the parallel axis theorem to resolve the individual load masses and inertias with the vehicle mass and inertia. $$J_{ij}=I_{ij}+m({\left|R\right|}^2{\delta }_{ij}-R_i{R}_j)$$
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. $$\begin{array}{l}\overline{w}=\sqrt{{(\dot{x}-w_x)}^2+{(\dot{y}-w_y)}^2+{(w_z)}^2}\\ \\ F_{dx}=-\frac{1}{2TR}{C}_d{A}_f{P}_{abs}{(}^{\overline{w}}\\ F_{dy}=-\frac{1}{2TR}{C}_s{A}_f{P}_{abs}{(}^{\overline{w}}\\ F_{dz}=-\frac{1}{2TR}{C}_l{A}_f{P}_{abs}{(}^{\overline{w}}\end{array}$$ Using the relative airspeed, the block determines the drag moments. $$\begin{array}{l}{M}_{dr}=-\frac{1}{2TR}{C}_{rm}{A}_f{P}_{abs}{(}^{\overline{w}}(a+c)\\ M_{dp}=-\frac{1}{2TR}{C}_{pm}{A}_f{P}_{abs}{(}^{\overline{w}}(a+c)\\ M_{dy}=-\frac{1}{2TR}{C}_{ym}{A}_f{P}_{abs}{(}^{\overline{w}}(a+c)\end{array}$$
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.

$$x,\dot{x},\ddot{x}$$	Vehicle CM displacement, velocity, and acceleration along the vehicle-fixed x-axis
$$y,\dot{y},\ddot{y}$$	Vehicle CM displacement, velocity, and acceleration along the vehicle-fixed y-axis
$$z,\dot{z},\ddot{z}$$	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_f, hh_r	Height of the front and rear hitches, respectively, above the axle plane along the vehicle-fixed z-axis
dh_f, dh_r	Longitudinal distance of the front and rear hitches, respectively, from the normal projection point of the vehicle CM onto the common axle plane
hl_f, hl_r	Lateral distance from center of mass to the front and rear hitches, respectively, 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

Examples

Three-Axle Tractor Towing a Three-Axle Trailer

Simulates three-axle tractor towing a three-axle trailer for commercial trucking applications. Implements hitch subsystem, sinusoidal wave steering or braking test, and axle torque applied to tractor rear wheels.

• Open Model

Two-Axle Tractor Towing a Two-Axle Trailer

Simulate a two-axle tractor towing a two-axle trailer for a commercial trucking application. Model implements a hitch subsystem, sinusoidal wave steering input, and an axle torque applied to the rear wheels of the tractor.

• Open Model

Ports

Input

FSusp — Suspension forces on trailer

3-by-4 array (default) | 3-by-2 array | 3-by-6 array

Suspension longitudinal, lateral, and vertical suspension forces, FSusp, applied to the trailer at the hardpoint location, in N, specified as a 3-by-2, 3-by-4, or 3-by-6 array, depending on the Number of axles parameter.

Number of axles Setting	Variable	Signal Dimension
1	$$FSusp=\left[\begin{array}{cc}{F}_{FLx}& F_{FRx}\\ F_{FLy}& F_{FRy}\\ F_{FLz}& F_{FRz}\end{array}\right]$$	Array – 3-by-2
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

MSusp — Suspension moments on trailer

3-by-4 array (default) | 3-by-2 array | 3-by-6 array

Suspension longitudinal, lateral, and vertical suspension moments, MSusp, applied about the vehicle at the hardpoint location, in N·m, specified as a 3-by-2, 3-by-4, or 3-by-6 array, depending on the Number of axles parameter.

Number of axles Setting	Variable	Signal Dimension
1	$$MSusp=\left[\begin{array}{cc}{M}_{FLx}& M_{FRx}\\ M_{FLy}& M_{FRy}\\ M_{FLz}& M_{FRz}\end{array}\right]$$	Array – 3-by-2
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

FExt — External forces acting on vehicle

vector

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 Element	Force 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)

MExt — External moments acting on vehicle

vector

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 Element	Force 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)

FhF — Front hitch force on the body

array

Hitch force applied to the body at the front hitch location, FhF_x, FhF_y, FhF_z, 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 Front hitch forces.

MhF — Front hitch moment about body

array

Hitch moment at the front hitch location, MhF_x, MhF_y, MhF_z, 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 Front hitch moments.

FhR — Rear hitch force on the body

array

Hitch force applied to the body at the rear hitch location, FhR_x, FhR_y, FhR_z, 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 Rear hitch forces.

MhR — Rear hitch moment about body

array

Hitch moment at the rear hitch location, MhR_x, MhR_y, MhR_z, 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 Rear hitch moments.

WindXYZ — Wind speed

array

Wind speed, W_x, W_y, W_z along inertial X-, Y-, and Z-axes, in m/s, specified as a 1-by-3 or 3-by-1 array.

AirTemp — Ambient air temperature

scalar

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

Dependencies

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

Output

Info — Trailer body information

bus

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

Signal						Description	Value	Units
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	rad
			theta			Rotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)	Computed	rad
			psi			Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)	Computed	rad
	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
	HitchF	Disp	X			Trailer front hitch offset from the axle plane along the earth-fixed X-axis	Computed	m
			Y			Trailer front hitch offset from the center plane along the earth-fixed Y-axis	Computed	m
			Z			Trailer front hitch offset from the axle plane along the earth-fixed Z-axis	Computed	m
		Vel	Xdot			Trailer front hitch offset velocity along the earth-fixed X-axis	Computed	m/s
			Ydot			Trailer front hitch offset velocity along the earth-fixed Y-axis	Computed	m/s
			Zdot			Trailer front hitch offset velocity along the earth-fixed Z-axis	Computed	m/s
	HitchR	Disp	X			Trailer rear hitch offset from the axle plane along the earth-fixed X-axis	Computed	m
			Y			Trailer rear hitch offset from the center plane along the earth-fixed Y-axis	Computed	m
			Z			Trailer rear 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-axis	Computed	m/s
		AngVel	p			Vehicle angular velocity about the vehicle-fixed x-axis (roll rate)	Computed	rad/s
			q			Vehicle angular velocity about the vehicle-fixed y-axis (pitch rate)	Computed	rad/s
			r			Vehicle angular velocity about the vehicle-fixed z-axis (yaw rate)	Computed	rad/s
		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	rad
	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	Computed	N
			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
		HitchF	Fx			Hitch front force applied to the body at the hitch location along the vehicle-fixed x-axis	Computed	N
			Fy			Hitch front force applied to the body at the hitch location along the vehicle-fixed y-axis	Computed	N
			Fz			Hitch front force applied to the body at the hitch location along the vehicle-fixed z-axis	Computed	N
		HitchR	Fx			Hitch rear force applied to the body at the hitch location along the vehicle-fixed x-axis	Computed	N
			Fy			Hitch rear force applied to the body at the hitch location along the vehicle-fixed y-axis	Computed	N
			Fz			Hitch rear 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
	HitchF	Mx			Hitch moment at the front hitch location about vehicle-fixed x-axis	Computed	N·m
		My			Hitch moment at the front hitch location about vehicle-fixed y-axis	Computed	N·m
		Mz			Hitch moment at the front hitch location about vehicle-fixed z-axis	Computed	N·m
	HitchR	Mx			Hitch moment at the rear hitch location about vehicle-fixed x-axis	Computed	N·m
		My			Hitch moment at the rear hitch location about vehicle-fixed y-axis	Computed	N·m
		Mz			Hitch moment at the rear hitch location about 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
HitchF	Disp		x		Front hitch offset from axle plane along the vehicle-fixed x-axis	Input
			y		Front hitch offset from center plane along the vehicle-fixed y-axis	Input
			z		Front hitch offset from axle plane along the earth-fixed z-axis	Input
	Vel		xdot		Front hitch offset velocity along the vehicle-fixed x-axis	Computed
			ydot		Front hitch offset velocity along the vehicle-fixed y-axis	Computed
			zdot		Front hitch offset velocity along the vehicle-fixed z-axis	0
HitchR	Disp		x		Rear hitch offset from axle plane along the vehicle-fixed x-axis	Input	m
			y		Rear hitch offset from center plane along the vehicle-fixed y-axis	Input	m
			z		Rear hitch offset from axle plane along the earth-fixed z-axis	Input	m
	Vel		xdot		Rear hitch offset velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Rear hitch offset velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Rear hitch offset velocity along the vehicle-fixed z-axis	0	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	rad

Vb — Vehicle velocity along vehicle-fixed frame

vector

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

pqr — Vehicle angular velocity about vehicle-fixed frame

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.

DCM — Direction cosine matrix

array

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

Euler — Euler angles

array

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

Xe — Vehicle position in inertial reference frame

vector

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

Ve — Vehicle velocity in inertial reference frame

vector

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

Parameters

Block Options

Number of axles — Create hitch force input port

2 (default) | 1 | 3

Specify the number of axles on the trailer.

Input Signals

Front hitch forces — FhF input port

on (default) | off

Select to create input port Fh.

Front hitch moments — MhF input port

on (default) | off

Select to create input port Mh.

Rear hitch forces — FhR input port

off (default) | on

Select to create input port Fh.

Rear hitch moments — MhR input port

off (default) | on

Select to create input port Mh.

Chassis

Vehicle mass, m — Mass

2000 (default) | scalar

Vehicle mass, m, in kg.

Longitudinal distance from center of mass to front axle, a — Distance from center of mass to front axle

1.4 (default) | scalar

Distance from the vehicle CM to the front axle, a, in m.

Longitudinal distance from center of mass to middle axle, b — Distance from center of mass to middle axle

1.6 (default) | scalar

Distance from the vehicle CM to the middle axle, b, in m.

Dependencies

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

Longitudinal distance from center of mass to rear axle, c — Distance from center of mass to rear axle

1.9 (default) | scalar

Distance from the vehicle CM to the rear axle, c, in m.

Dependencies

To enable this parameter, set Number of axles to 2 or 3.

Lateral distance from geometric centerline to center of mass, d — Distance from geometric centerline to center of mass

0 (default) | scalar

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 center of mass to axle plane, h — Distance from center of mass to axle plane

.35 (default) | scalar

Vertical distance from the vehicle CM to the axle plane, h, in m.

Longitudinal distance from center of mass to front hitch, dh_f — Longitudinal distance from CM to hitch

1 (default) | scalar

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

Dependencies

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

Lateral distance from geometric centerline to front hitch, hl_f — Distance from centerline to front hitch

0 (default) | scalar

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

Dependencies

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

Vertical distance from front hitch to axle plane, hh_f — Distance from front hitch to axle plane

0.1 (default) | scalar

Vertical distance from front hitch to axle plane, hh_f, in m.

Dependencies

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

Longitudinal distance from center of mass to rear hitch, dh_r — Distance to front hitch

1 (default) | scalar

Longitudinal distance from the center of mass to the rear hitch, dh_r, in m.

Dependencies

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

Lateral distance from geometric centerline to rear hitch, hl_r — Distance from centerline to rear hitch

0 (default) | scalar

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

Dependencies

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

Vertical distance from rear hitch to axle plane, hh_r — Distance from rear hitch to axle plane

0.1 (default) | scalar

Vertical distance from the rear hitch to the axle plane, hh_r, in m.

Dependencies

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

Initial position in the inertial frame [Xeo,Yeo,Zeo], Xe_o — Initial position

[0,0,0] (default) | vector

Initial position of the vehicle in the inertial frame, Xe_o, in m.

Initial velocity in body axes [xdot_o,ydot_o,zdot_o], xbdot_o — Initial velocity

[0,0,0] (default) | vector

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

Initial Euler orientation [roll, pitch, yaw], eul_o — Rotation

[0,0,0] (default) | vector

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

Initial body rotation rates [p,q,r], p_o — Initial rotation rate

[0,0,0] (default) | vector

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

Chassis inertia tensor, Iveh — Inertia

[430 0 0; 0 1900 0; 0 0 2100] (default) | array

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

Front track width, w_f — Front track width

1.9 (default) | scalar

Front track width, in m.

Middle track width, w_m — Middle track width

1.9 (default) | scalar

Middle track width, in m.

Dependencies

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

Rear track width, w_r — Rear track width

1.9 (default) | scalar

Rear track width, in m.

Dependencies

To enable this parameter, set Number of axles to 2 or 3.

Inertial Loads

Front End

Mass, z1m — Mass

0 (default) | scalar

Mass, z1m, in kg.

Distance vector from front axle, z1R — Distance

[-.25,.125,.15] (default) | vector

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

Array Element	Description
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 — Inertia

[1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0 (default) | array

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

Overhead

Mass, z2m — Mass

0 (default) | scalar

Mass, z2m, in kg.

Distance vector from front axle, z2R — Distance

[1.4,0,.8] (default) | vector

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

Array Element	Description
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 — Inertia

[1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0 (default) | array

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 — Mass

0 (default) | scalar

Mass, z3m, in kg.

Distance vector from front axle, z3R — Distance

[.75,-.5,.4] (default) | vector

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

Array Element	Description
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 — Inertia

[5,-.1,-2;-2,9,.1;-.1,.1,6].*0 (default) | array

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 — Mass

0 (default) | scalar

Mass, z4m, in kg.

Distance vector from front axle, z4R — Distance

[.75,.5,.4] (default) | vector

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

Array Element	Description
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 — Inertia

[5,-.1,-2;-2,9,.1;-.1,.1,6].*0 (default) | array

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 — Mass

0 (default) | scalar

Mass, z5m, in kg.

Distance vector from front axle, z5R — Distance

[1.25,-.5,.4] (default) | vector

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

Array Element	Description
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 — Inertia

[5,-.1,-2;-2,9,.1;-.1,.1,6].*0 (default) | array

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 — Mass

0 (default) | scalar

Mass, z6m, in kg.

Distance vector from front axle, z6R — Distance

[1.25,-.5,.4] (default) | vector

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

Array Element	Description
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 — Inertia

[5,-.1,-2;-2,9,.1;-.1,.1,6].*0 (default) | array

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 — Mass

0 (default) | scalar

Mass, z7m, in kg.

Distance vector from front axle, z7R — Distance

[2,0,.25] (default) | vector

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

Array Element	Description
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 — Inertia

[1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0 (default) | array

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

Longitudinal drag area, Af — Drag area

2 (default) | scalar

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

Longitudinal drag coefficient, Cd — Drag coefficient

.3 (default) | scalar

Air drag coefficient, C_d, dimensionless.

Longitudinal lift coefficient, Cl — Lift

.1 (default) | scalar

Air lift coefficient, C_l, dimensionless.

Longitudinal drag pitch moment, Cpm — Pitch drag

.1 (default) | scalar

Longitudinal drag pitch moment coefficient, C_pm, dimensionless.

Relative wind angle vector, beta_w — Wind angle

[0:0.001:0.01] (default) | vector

Relative wind angle vector, β_w, in rad.

Side force coefficient vector, Cs — Side force drag

[0:0.01:0.1] (default) | vector

Side force coefficient vector coefficient, C_s, dimensionless.

Yaw moment coefficient vector, Cym — Yaw moment drag

[0:0.001:0.01] (default) | vector

Yaw moment coefficient vector coefficient, C_ym, dimensionless.

Environment

Absolute air pressure, Pabs — Pressure

101325 (default) | scalar

Environmental air absolute pressure, P_abs, in Pa.

Air temperature, Tair — Ambient air temperature

273 (default) | scalar

Ambient air temperature, T_air, in K.

Dependencies

To enable this parameter, clear Air temperature.

Gravitational acceleration, g — Gravity

9.81 (default) | scalar

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

Simulation

Longitudinal velocity tolerance, xdot_tol — Tolerance

.1 (default) | scalar

Longitudinal velocity tolerance, xdot_tol, in m/s.

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

Geometric longitudinal offset from axle plane, longOff — Longitudinal offset

0 (default) | scalar

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.

Geometric lateral offset from center plane, latOff — Lateral offset

0 (default) | scalar

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.

Geometric vertical offset from axle plane, vertOff — Vertical offset

0 (default) | scalar

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 Euler angles, wrapAng — Selection

on (default) | off

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.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020b