Vehicle Body 6DOF

R2026b

Two-axle vehicle body with translational and rotational motion

• 

Vehicle Body 6DOF block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

Libraries:
Vehicle Dynamics Blockset / Vehicle Body

Description

The Vehicle Body 6DOF block implements a six degrees-of-freedom (DOF) rigid two-axle vehicle body model to calculate longitudinal, lateral, vertical, pitch, roll, and yaw motion. The block accounts for body dimensions, mass, inertia, aerodynamics, road incline and external forces and moments.

This block uses the Vehicle Dynamics Blockset™ Vehicle Coordinate System. The vehicle coordinate system axes (X_V, Y_V, Z_V) are fixed in a reference frame attached to the vehicle. The coordinate system conforms to SAE J670 standard with X-forward, Y-right, Z-down orientation with origin at the center of gravity of the sprung mass. Sign convention for steer angle is positive right.

Use the Inertial Loads parameters to analyze the vehicle dynamics under different loading conditions.

You can connect the block to virtual sensors, suspension system, or external systems like body control actuators. Use the Vehicle Body 6DOF block in ride and handling studies to model the effects of aerodynamics, passenger loading and suspension forces and moments.

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

Parameter	Input Port	Description
Rear hitch forces	Fh	Hitch force applied to the body at the rear hitch location, Fhx, Fhy, and Fhz, in the vehicle-fixed frame
Rear hitch moments	Mh	Hitch moment at the rear hitch location, Mhx, Mhy, and Mhz, about the vehicle-fixed frame

Inertial Loads

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

• Front powertrain

• Front and rear row passengers

• Overhead cargo

• Rear cargo

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

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

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

Load	Parameter	Example Location
Front	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 — Right of the vehicle centerline z2R(1,3)>0 — Above the front axle suspension hardpoint
Row 1, left side	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
Row 1, right side	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
Row 2, left side	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
Row 2, right side	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	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 solves the rigid body dynamics equations of motion.

The Vehicle Body 6DOF block considers the rotation of a vehicle-fixed coordinate frame about a flat earth-fixed inertial reference frame. The origin of the vehicle-fixed coordinate frame is the sprung mass center of gravity.

The block uses this equation to calculate the translational motion of the vehicle-fixed coordinate frame, where the applied forces [F_x F_y F_z]^T are in the vehicle-fixed frame, and the mass of the body, m, is assumed 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 vehicle-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 vehicle-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 aerodynamic, gravitational, external, and suspension forces.

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

Calculation	Implementation
Load masses and inertias	Block uses 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	Block uses direction cosine matrix (DCM) to transform the gravitational vector in the inertial-fixed frame to the vehicle-fixed frame.
Aerodynamic forces, Fa, and moments, Ma	To determine a relative airspeed, the block subtracts the wind velocity from the vehicle CG velocity. Using the relative airspeed, the block determines the aerodynamic forces. $$\begin{array}{l}\overline{w}=\sqrt{{(\dot{x}-w_x)}^2+{(\dot{y}-w_y)}^2+{(\dot{z}-w_z)}^2}\\ \\ F_{ax}=-\frac{1}{2TR}{C}_d{A}_f{P}_{abs}{(}^{\overline{w}}\\ F_{ay}=-\frac{1}{2TR}{C}_s{A}_f{P}_{abs}{(}^{\overline{w}}\\ F_{az}=-\frac{1}{2TR}{C}_l{A}_f{P}_{abs}{(}^{\overline{w}}\end{array}$$ The signs for the aerodynamic terms indicate a resistive force with respect to the components of the relative wind speed. In this convention, a positive lift coefficient increases downforce (pushing the vehicle to the ground) while a negative lift coefficient generates lift (raising the vehicle upwards). Using the relative airspeed, the block determines the aerodynamic moments. $$\begin{array}{l}{M}_{ar}=-\frac{1}{2TR}{C}_{rm}{A}_f{P}_{abs}{(}^{\overline{w}}(a+b)\\ M_{ap}=-\frac{1}{2TR}{C}_{pm}{A}_f{P}_{abs}{(}^{\overline{w}}(a+b)\\ M_{ay}=-\frac{1}{2TR}{C}_{ym}{A}_f{P}_{abs}{(}^{\overline{w}}(a+b)\end{array}$$
External forces, Fin, and moments, Min	External forces and moments are input via ports FExt and MExt.
Suspension forces and moments	Block assumes that the suspension forces and moments act on these hardpoint locations: FFL, MFL — Front left FFR, MFR — Front right FRL, MRL — Rear left FRR, MRR — Rear right

The equations use these variables.

$$x,\dot{x},\ddot{x}$$	Vehicle CG displacement, velocity, and acceleration along the vehicle-fixed x-axis
$$y,\dot{y},\ddot{y}$$	Vehicle CG displacement, velocity, and acceleration along the vehicle-fixed y-axis
$$z,\dot{z},\ddot{z}$$	Vehicle CG 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 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
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
MFx, FFy, FFz	Suspension moments applied to vehicle CG about the vehicle-fixed x-, y-, and z-axes
Fextx, Fexty, Fextz	External forces applied to vehicle CG along the vehicle-fixed x-, y-, and z-axes
Fax, Fay, Faz	Aerodynamic forces applied to vehicle CG along the vehicle-fixed x-, y-, and z-axes
Mextx, Mexty, Mextz	External moments applied to vehicle CG about the vehicle-fixed x-, y-, and z-axes
Max, May, Maz	Aerodynamic moments applied to vehicle CG about the vehicle-fixed x-, y-, and z-axes
I	Sprung mass moments of inertia
a, b	Distance of front and rear wheels, respectively, from the normal projection point of vehicle CG onto the common axle plane
d	Lateral distance from the geometric centerline to the center of mass along the vehicle-fixed y-axis
h	Height of vehicle CG above the axle plane
hh	Height of the hitch above the axle plane along the vehicle-fixed z-axis
dh	Longitudinal distance of the hitch from the normal projection point of tractor CG onto the common axle plane
hl	Lateral distance from center of mass to hitch along the vehicle-fixed y-axis.
wF, wR	Front and rear track widths
Cd	Aerodynamic drag coefficient acting along vehicle-fixed x-axis
Cs	Aerodynamic side coefficient acting along vehicle-fixed y-axis
Cl	Aerodynamic lift coefficient acting along vehicle-fixed z-axis
Crm	Aerodynamic roll coefficient acting about vehicle-fixed x-axis
Cpm	Aerodynamic pitch coefficient acting about the vehicle-fixed y-axis
Cym	Aerodynamic yaw coefficient acting about vehicle-fixed z-axis
Af	Frontal area
R	Atmospheric specific gas constant
T	Environmental air temperature
Pabs	Environmental absolute pressure
wx, wy, wz	Wind velocity along the vehicle-fixed x-, y-, and z-axes
Wx, Wy, Wz	Wind velocity 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 vehicle

array

Suspension longitudinal, lateral, and vertical suspension forces applied to the vehicle at the hardpoint location, in N. Signal dimensions are [3x4].

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

Array Element	Axle	Wheel	Force Axis
FSusp(1,1)	Front	Left	Vehicle-fixed x-axis (longitudinal)
FSusp(1,2)	Front	Right
FSusp(1,3)	Rear	Left
FSusp(1,4)	Rear	Right
FSusp(2,1)	Front	Left	Vehicle-fixed y-axis (lateral)
FSusp(2,2)	Front	Right
FSusp(2,3)	Rear	Left
FSusp(2,4)	Rear	Right
FSusp(3,1)	Front	Left	Vehicle-fixed z-axis (vertical)
FSusp(3,2)	Front	Right
FSusp(3,3)	Rear	Left
FSusp(3,4)	Rear	Right

MSusp — Suspension moment on vehicle

array

Suspension longitudinal, lateral, and vertical suspension moments applied about the vehicle at the hardpoint location, in N·m. Signal dimensions are [3x4].

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

Array Element	Axle	Wheel	Moment Axis
MSusp(1,1)	Front	Left	Vehicle-fixed x-axis (longitudinal)
MSusp(1,2)	Front	Right
MSusp(1,3)	Rear	Left
MSusp(1,4)	Rear	Right
MSusp(2,1)	Front	Left	Vehicle-fixed y-axis (lateral)
MSusp(2,2)	Front	Right
MSusp(2,3)	Rear	Left
MSusp(2,4)	Rear	Right
MSusp(3,1)	Front	Left	Vehicle-fixed z-axis (vertical)
MSusp(3,2)	Front	Right
MSusp(3,3)	Rear	Left
MSusp(3,4)	Rear	Right

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)

Fh — Hitch force on the body

array

Hitch force applied to the body at the hitch location, Fh_x, Fh_y, Fh_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.

Mh — Hitch moment about body

array

Hitch moment at the hitch location, Mh_x, Mh_y, Mh_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 — Bus signal

bus

Bus signal containing these block values.

Signal						Description	Value	Units
InertFrm	Cg	Disp	X			Vehicle CG displacement along the earth-fixed X-axis	Computed relative to the road grade.	m
			Y			Vehicle CG displacement along the earth-fixed Y-axis	Computed relative to the road grade.	m
			Z			Vehicle CG displacement along the earth-fixed Z-axis	Computed relative to the road grade.	m
		Vel	Xdot			Vehicle CG velocity along the earth-fixed X-axis	Computed relative to the road grade.	m/s
			Ydot			Vehicle CG velocity along the earth-fixed Y-axis	Computed relative to the road grade.	m/s
			Zdot			Vehicle CG velocity along the earth-fixed Z-axis	Computed relative to the road grade.	m/s
		Ang	phi			Rotation of the vehicle-fixed frame about the earth-fixed X-axis (roll)	Computed relative to the grade angle.	rad
			theta			Rotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)	Computed relative to the grade angle.	rad
			psi			Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)	Computed relative to the grade angle.	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
	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 axle plane along the earth-fixed X-axis	Computed	m
			Y			Hitch offset from axle plane along the earth-fixed Y-axis	Computed	m
			Z			Hitch offset from axle plane along the earth-fixed Z-axis	Computed	m
		Vel	Xdot			Hitch 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			Vehicle chassis offset from axle plane along the earth-fixed X-axis	Computed	m
			Y			Vehicle chassis offset from center plane along the earth-fixed Y-axis	Computed	m
			Z			Vehicle chassis offset from axle plane along the earth-fixed Z-axis	Computed	m
		Vel	Xdot			Vehicle chassis offset velocity along the earth-fixed X-axis	Computed	m/s
			Ydot			Vehicle chassis offset velocity along the earth-fixed Y-axis	Computed	m/s
			Zdot			Vehicle chassis offset velocity along the earth-fixed Z-axis	Computed	m/s
BdyFrm	Cg	Vel	xdot			Vehicle CG velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot			Vehicle CG velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot			Vehicle CG velocity along the vehicle-fixed z-axis	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 CG acceleration along the vehicle-fixed x-axis	Computed	gn
			ay			Vehicle CG acceleration along the vehicle-fixed y-axis	Computed	gn
			az			Vehicle CG acceleration along the vehicle-fixed z-axis	Computed	gn
			xddot			Vehicle CG acceleration along the vehicle-fixed x-axis	Computed	m/s^2
			yddot			Vehicle CG acceleration along the vehicle-fixed y-axis	Computed	m/s^2
			zddot			Vehicle CG acceleration along the vehicle-fixed z-axis	Computed	m/s^2
		DCM	Direction cosine matrix				Computed	rad
	Forces	Body	Fx			Net force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			Net force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			Net force on vehicle CG along the vehicle-fixed z-axis	Computed	N
		Ext	Fx			External force on vehicle CG along the vehicle-fixed x-axis	Input	N
			Fy			External force on vehicle CG along the vehicle-fixed x-axis	Input	N
			Fz			External force on vehicle CG along the vehicle-fixed x-axis	Input	N
		FrntAxl	Fx			Front axle force, along the vehicle-fixed x-axis	Computed	N
			Fy			Front axle force, along the vehicle-fixed y-axis	Computed	N
			Fz			Front axle force, along the vehicle-fixed z-axis	Computed	N
		RearAxl	Fx			Rear axle force, along the vehicle-fixed x-axis	Computed	N
			Fy			Rear axle force, along the vehicle-fixed y-axis	Computed	N
			Fz			Rear axle force, along the vehicle-fixed z-axis	Computed	N
		Hitch	Fx			Hitch force applied to body at the hitch location along the vehicle-fixed x-axis	Computed	N
			Fy			Hitch force applied to body at the hitch location along the vehicle-fixed y-axis	Computed	N
			Fz			Hitch force applied to 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
			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			Aerodynamic drag force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			Aerodynamic side force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			Aerodynamic lift force on vehicle CG along the vehicle-fixed z-axis	Computed	N
		Grvty	Fx			Gravity force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy			Gravity force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz			Gravity force on vehicle CG along the vehicle-fixed z-axis	Computed	N
	Moments	Body	Mx			Body moment on vehicle CG about the vehicle-fixed x-axis	Computed	N·m
			My			Body moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			Mz			Body moment on vehicle CG about the vehicle-fixed z-axis	Computed	N·m
		Drag	Mx			Aerodynamic roll moment on vehicle CG about the vehicle-fixed x-axis	Computed	N·m
			My			Aerodynamic pitch moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			Mz			Aerodynamic yaw moment on vehicle CG about the vehicle-fixed z-axis	Computed	N·m
		Ext	Mx			External moment on vehicle CG about the vehicle-fixed x-axis	Computed	N·m
			My			External moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			Mz			External moment on vehicle CG about the vehicle-fixed z-axis	Computed	N·m
		Hitch	Mx			Hitch moment at the hitch location about vehicle-fixed x-axis	Computed	N·m
			My			Hitch moment at the hitch location about vehicle-fixed y-axis	Computed	N·m
			Mz			Hitch moment at the hitch location about vehicle-fixed z-axis	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
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		Vehicle chassis offset from axle plane along the vehicle-fixed x-axis	Input	m
			y		Vehicle chassis offset from center plane along the vehicle-fixed y-axis	Input	m
			z		Vehicle chassis offset from axle plane along the vehicle-fixed z-axis	Input	m
	Vel		xdot		Vehicle chassis offset velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Vehicle chassis offset velocity along the vehicle-fixed y-axis	Computed	m/s
			zdot		Vehicle chassis offset velocity along the vehicle-fixed z-axis	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 CG 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 CG 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 CG position along inertial-fixed X-, Y-, Z-axes, respectively, in m, returned as a vector.

Ve — Vehicle velocity in inertial reference frame

vector

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

Parameters

Block Options

Input Signals

Rear hitch forces — Create input port

off (default) | on

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	htchFMode
Values:	off (default) | on
Data Types:	character vector

Rear hitch moments — Create input port

off (default) | on

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	htchMMode
Values:	off (default) | on
Data Types:	character vector

Chassis

Vehicle mass, m — Mass

2000 (default) | scalar

Vehicle mass, m, in kg. This mass typically corresponds to a sprung mass.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	m
Values:	2000 (default) | scalar
Data Types:	double

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

1.4 (default) | scalar

Distance from vehicle CG to front axle, a, in m.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	a
Values:	1.4 (default) | scalar
Data Types:	double

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

1.6 (default) | scalar

Distance from vehicle CG to front axle, b, in m.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	b
Values:	1.6 (default) | scalar
Data Types:	double

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

0 (default) | scalar

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	d
Values:	0 (default) | scalar
Data Types:	double

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

0.35 (default) | scalar

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	h
Values:	0.35 (default) | scalar
Data Types:	double

Longitudinal distance from center of mass to hitch, dh — Longitudinal distance from CG to hitch

1 (default) | scalar

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

Dependencies

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	dh
Values:	1 (default) | scalar
Data Types:	double

Lateral distance from geometric centerline to hitch, hl — Lateral distance from centerline to hitch

0 (default) | scalar

Lateral distance from geometric centerline to hitch, hl, in m.

Dependencies

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	hl
Values:	0 (default) | scalar
Data Types:	double

Vertical distance from hitch to axle plane, hh — Distance from hitch to axle plane

0.1 (default) | scalar

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

Dependencies

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	hh
Values:	0.1 (default) | scalar
Data Types:	double

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Xe_o
Values:	[0,0,0] (default) | vector
Data Types:	double

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	xbdot_o
Values:	[0,0,0] (default) | vector
Data Types:	double

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(yaw)- axes, respectively, in rad.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	eul_o
Values:	[0,0,0] (default) | vector
Data Types:	double

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	p_o
Values:	[0,0,0] (default) | vector
Data Types:	double

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].

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Iveh
Values:	[430 0 0; 0 1900 0; 0 0 2100] (default) | array
Data Types:	double

Track widths [front,rear], w — Widths

[1.9,1.9] (default) | vector

Front and rear track width, in m. Dimensions are [1-by-2].

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	w
Values:	[1.9,1.9] (default) | vector
Data Types:	double

Inertial Loads

Front

Mass, z1m — Mass

0 (default) | scalar

Mass, z1m, in kg.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z1m
Values:	0 (default) | scalar
Data Types:	double

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 the vehicle-fixed x-axis
z1R(1,2)	Vehicle centerline to load, along the vehicle-fixed y-axis
z1R(1,3)	Front suspension hardpoint to load, along the vehicle-fixed z-axis

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z1R
Values:	[.25,.125,.15] (default) | vector
Data Types:	double

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 CG.

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z1I
Values:	[1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0 (default) | array
Data Types:	double

Overhead

Mass, z2m — Mass

0 (default) | scalar

Mass, z2m, in kg.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z2m
Values:	0 (default) | scalar
Data Types:	double

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 the vehicle-fixed x-axis
z2R(1,2)	Vehicle centerline to load, along the vehicle-fixed y-axis
z2R(1,3)	Front suspension hardpoint to load, along the vehicle-fixed z-axis

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z2R
Values:	[-1.4,0,.8] (default) | vector
Data Types:	double

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 CG.

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z2I
Values:	[1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0 (default) | array
Data Types:	double

Row 1, left side

Mass, z3m — Mass

0 (default) | scalar

Mass, z3m, in kg.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z3m
Values:	0 (default) | scalar
Data Types:	double

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 the vehicle-fixed x-axis
z3R(1,2)	Vehicle centerline to load, along the vehicle-fixed y-axis
z3R(1,3)	Front suspension hardpoint to load, along the vehicle-fixed z-axis

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z3R
Values:	[-.75,-.5,.4] (default) | vector
Data Types:	double

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 CG.

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z3I
Values:	[5,-.1,-2;-2,9,.1;-.1,.1,6].*0 (default) | array
Data Types:	double

Row 1, right side

Mass, z4m — Mass

0 (default) | scalar

Mass, z4m, in kg.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z4m
Values:	0 (default) | scalar
Data Types:	double

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 the vehicle-fixed x-axis
z4R(1,2)	Vehicle centerline to load, along the vehicle-fixed y-axis
z4R(1,3)	Front suspension hardpoint to load, along the vehicle-fixed z-axis

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z4R
Values:	[-.75,.5,.4] (default) | vector
Data Types:	double

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 CG.

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z4I
Values:	[5,-.1,-2;-2,9,.1;-.1,.1,6].*0 (default) | array
Data Types:	double

Row 2, left side

Mass, z5m — Mass

0 (default) | scalar

Mass, z5m, in kg.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z5m
Values:	0 (default) | scalar
Data Types:	double

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 the vehicle-fixed x-axis
z5R(1,2)	Vehicle centerline to load, along the vehicle-fixed y-axis
z5R(1,3)	Front suspension hardpoint to load, along the vehicle-fixed z-axis

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z5R
Values:	[-1.25,-.5,.4] (default) | vector
Data Types:	double

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 CG.

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z5I
Values:	[5,-.1,-2;-2,9,.1;-.1,.1,6].*0 (default) | array
Data Types:	double

Row 2, right side

Mass, z6m — Mass

0 (default) | scalar

Mass, z6m, in kg.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z6m
Values:	0 (default) | scalar
Data Types:	double

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 the vehicle-fixed x-axis
z6R(1,2)	Vehicle centerline to load, along the vehicle-fixed y-axis
z6R(1,3)	Front suspension hardpoint to load, along the vehicle-fixed z-axis

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z6R
Values:	[-1.25,.5,.4] (default) | vector
Data Types:	double

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 CG.

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z6I
Values:	[5,-.1,-2;-2,9,.1;-.1,.1,6].*0 (default) | array
Data Types:	double

Rear

Mass, z7m — Mass

0 (default) | scalar

Mass, z7m, in kg.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z7m
Values:	0 (default) | scalar
Data Types:	double

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 the vehicle-fixed x-axis
z7R(1,2)	Vehicle centerline to load, along the vehicle-fixed y-axis
z7R(1,3)	Front suspension hardpoint to load, along the vehicle-fixed z-axis

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z7R
Values:	[-2,0,.25] (default) | vector
Data Types:	double

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 CG.

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

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

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	z7I
Values:	[1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0 (default) | array
Data Types:	double

Aerodynamic

Longitudinal drag area, Af — Area

2 (default) | scalar

Vehicle cross-sectional frontal area, A_f, to calculate the aerodynamic forces and moments on the vehicle, in m^2.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Af
Values:	2 (default) | scalar
Data Types:	double

Longitudinal drag coefficient, Cd — Drag

.3 (default) | scalar

Aerodynamic drag force coefficient, C_d, dimensionless.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Cd
Values:	.3 (default) | scalar
Data Types:	double

Longitudinal lift coefficient, Cl — Lift

.1 (default) | scalar

Aerodynamic lift force coefficient, C_l, dimensionless.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Cl
Values:	.1 (default) | scalar
Data Types:	double

Longitudinal drag pitch moment, Cpm — Pitch

.1 (default) | scalar

Aerodynamic pitch moment coefficient, C_pm, dimensionless.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Cpm
Values:	.1 (default) | scalar
Data Types:	double

Relative wind angle vector, beta_w — Wind angle

[0,0.1745,0.3491,0.5236,0.6981,0.8727,1.0472,1.2217,1.3963,1.5708] (default) | vector

Relative wind angle vector, β_w, in rad.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	beta_w
Values:	[0,0.1745,0.3491,0.5236,0.6981,0.8727,1.0472,1.2217,1.3963,1.5708] (default) | vector
Data Types:	double

Side force coefficient vector, Cs — Side

[0.1000,0.1000,0.1000,0.1000,0.1000,0.1000,0.1000,0.1000,0.1000,0.1000] (default) | vector

Aerodynamic side force coefficient vector, C_s, dimensionless.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Cs
Values:	[0.1000,0.1000,0.1000,0.1000,0.1000,0.1000,0.1000,0.1000,0.1000,0.1000] (default) | vector
Data Types:	double

Yaw moment coefficient vector, Cym — Yaw

[0,0,0.0667,0.1000,0.1333,0.1667,0.2000,0.2333,0.2667,0.3000] (default) | vector

Aerodynamic yaw moment coefficient vector, C_ym, dimensionless.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Cym
Values:	[0,0,0.0667,0.1000,0.1333,0.1667,0.2000,0.2333,0.2667,0.3000] (default) | vector
Data Types:	double

Environment

Absolute Pressure, Pabs — Pressure

101325 (default) | scalar

Environmental air absolute pressure, P_abs, in Pa.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Pabs
Values:	101325 (default) | scalar
Data Types:	double

Air temperature — AirTemp input port

off (default) | on

Specify to create input port AirTemp.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	extTamb
Values:	off (default) | on
Data Types:	character vector

Air temperature, Tair — Ambient air temperature

273 (default) | scalar

Ambient air temperature, T_air, in K.

Dependencies

To enable this parameter, clear Air temperature.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	Tair
Values:	273 (default) | scalar
Data Types:	double

Gravitational acceleration, g — Gravity

9.81 (default) | scalar

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	g
Values:	9.81 (default) | scalar
Data Types:	double

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.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	xdot_tol
Values:	.1 (default) | scalar
Data Types:	double

Geometric longitudinal offset from CG along body longitudinal axis, longOff — Longitudinal offset

0 (default) | scalar

Geometric longitudinal offset of the vehicle chassis from the CG along the body longitudinal axis, in m. When using the 3D visualization engine, use the offset to locate the chassis relative to the vehicle’s CG to ensure alignment with the mesh origin relative to the CG. You can also use it to report position and velocity information at any defined location.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	longOff
Values:	0 (default) | scalar
Data Types:	double

Geometric lateral offset from CG along body lateral axis, latOff — Lateral offset

0 (default) | scalar

Geometric lateral offset of the vehicle chassis from the CG along the body lateral axis, in m. When using the 3D visualization engine, use the offset to locate the chassis relative to the vehicle’s CG to ensure alignment with the mesh origin relative to the CG. You can also use it to report position and velocity information at any defined location.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	latOff
Values:	0 (default) | scalar
Data Types:	double

Geometric vertical offset from CG along body vertical axis, vertOff — Vertical offset

0.35 (default) | scalar

Geometric vertical offset of the vehicle chassis from the CG along the body vertical axis, in m. When using the 3D visualization engine, use the offset to locate the chassis relative to the vehicle’s CG to ensure alignment with the mesh origin relative to the CG. You can also use it to report position and velocity information at any defined location.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	vertOff
Values:	0.35 (default) | scalar
Data Types:	double

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 deselecting the parameter if you want to:

• Track the total vehicle yaw rotation.

• Avoid discontinuities in the vehicle state estimators.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

To get the block parameter value programmatically, use the get_param function.

Parameter:	wrapAng
Values:	off (default) | on
Data Types:	character vector

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 R2018a