Vehicle Body 6DOF Three Axles

R2026b

Three-axle vehicle tractor body with translational and rotational motion

Libraries:
Vehicle Dynamics Blockset / Vehicle Body

Description

The Vehicle Body 6DOF Three Axles block implements a six degrees-of-freedom (DOF) rigid three-axle vehicle body model that calculates longitudinal, lateral, vertical, pitch, roll, and yaw motion. Use the block to model three-axle vehicles like a tractor. 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.

Connect the block to virtual sensors, suspension systems, or external systems like body control actuators. Use the Vehicle Body 6DOF Three Axles 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, Fh_x, Fh_y, and Fh_z, in the vehicle-fixed frame
Rear hitch moments	`Mh`	Hitch moment at the rear hitch location, Mh_x, Mh_y, and Mh_z, 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:

Tractor front
Cab overhead
Tractor frame left and frame right
Cab left and cab right
Tractor rear

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
Tractor 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
Cab 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
Tractor frame 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
Tractor frame 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
Cab 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
Cab 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
Tractor 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 Three Axles 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 center of gravity of the sprung mass.

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 to be constant.

$\begin{array}{l} {\bar{F}}_{b} = [\begin{matrix} F_{x} \\ F_{y} \\ F_{z} \end{matrix}] = m ({\dot{\bar{V}}}_{b} + \bar{ω} \times {\bar{V}}_{b}) \\ {\bar{M}}_{b} = [\begin{matrix} L \\ M \\ N \end{matrix}] = I \dot{\bar{ω}} + \bar{ω} \times (I \bar{ω}) \\ I = [\begin{matrix} I_{x x} & - I_{x y} & - I_{x z} \\ - I_{y x} & I_{y y} & - I_{y z} \\ - I_{z x} & - I_{z y} & I_{z z} \end{matrix}] \end{array}$

To determine the relationship between the vehicle-fixed angular velocity vector, [p q r]^T, and the rate of change of the Euler angles, $[\begin{matrix} \dot{ϕ} & \dot{θ} & \dot{ψ} \end{matrix}]^{T}$ , the block resolves the Euler rates into the vehicle-fixed frame.

$[\begin{matrix} p \\ q \\ r \end{matrix}] = [\begin{matrix} \dot{ϕ} \\ 0 \\ 0 \end{matrix}] + [\begin{matrix} 1 & 0 & 0 \\ 0 & \cos ϕ & \sin ϕ \\ 0 & - \sin ϕ & \cos ϕ \end{matrix}] [\begin{matrix} 0 \\ \dot{θ} \\ 0 \end{matrix}] + [\begin{matrix} 1 & 0 & 0 \\ 0 & \cos ϕ & \sin ϕ \\ 0 & - \sin ϕ & \cos ϕ \end{matrix}] [\begin{matrix} \cos θ & 0 & - \sin θ \\ 0 & 1 & 0 \\ \sin θ & 0 & \cos θ \end{matrix}] [\begin{matrix} 0 \\ 0 \\ \dot{ψ} \end{matrix}] \equiv J^{- 1} [\begin{matrix} \dot{ϕ} \\ \dot{θ} \\ \dot{ψ} \end{matrix}]$

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

$[\begin{matrix} \dot{ϕ} \\ \dot{θ} \\ \dot{ψ} \end{matrix}] = J [\begin{matrix} p \\ q \\ r \end{matrix}] = [\begin{matrix} 1 & (\sin ϕ \tan θ) & (\cos ϕ \tan θ) \\ 0 & \cos ϕ & - \sin ϕ \\ 0 & \frac{\sin ϕ}{\cos θ} & \frac{\cos ϕ}{\cos θ} \end{matrix}] [\begin{matrix} p \\ q \\ r \end{matrix}]$

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

$\begin{array}{l} {\bar{F}}_{b} = [\begin{matrix} F_{x} \\ F_{y} \\ F_{z} \end{matrix}] = [\begin{matrix} F_{d}_{_{x}} \\ F_{d}_{_{y}} \\ F_{d}_{_{z}} \end{matrix}] + [\begin{matrix} F_{g}_{_{x}} \\ F_{g}_{_{y}} \\ F_{g}_{_{z}} \end{matrix}] + [\begin{matrix} F_{e x t}_{_{x}} \\ F_{e x t}_{_{y}} \\ F_{e x t}_{_{z}} \end{matrix}] + [\begin{matrix} F_{F L}_{_{x}} \\ F_{F L}_{_{y}} \\ F_{F L}_{_{z}} \end{matrix}] + [\begin{matrix} F_{F R}_{_{x}} \\ F_{F R}_{_{y}} \\ F_{F R}_{_{z}} \end{matrix}] + [\begin{matrix} F_{M L}_{_{x}} \\ F_{M L}_{_{y}} \\ F_{M L}_{_{z}} \end{matrix}] + [\begin{matrix} F_{M R}_{_{x}} \\ F_{M R}_{_{y}} \\ F_{M R}_{_{z}} \end{matrix}] + [\begin{matrix} F_{R L}_{_{x}} \\ F_{R L}_{_{y}} \\ F_{R L}_{_{z}} \end{matrix}] + [\begin{matrix} F_{R R}_{_{x}} \\ F_{R R}_{_{y}} \\ F_{R R}_{_{z}} \end{matrix}] \\ {\bar{M}}_{b} = [\begin{matrix} M_{x} \\ M_{y} \\ M_{z} \end{matrix}] = [\begin{matrix} M_{d}_{_{x}} \\ M_{d}_{_{y}} \\ M_{d}_{_{z}} \end{matrix}] + [\begin{matrix} M_{e x t}_{_{x}} \\ M_{e x t}_{_{y}} \\ M_{e x t}_{_{z}} \end{matrix}] + [\begin{matrix} M_{F L}_{_{x}} \\ M_{F L}_{_{y}} \\ M_{F L}_{_{z}} \end{matrix}] + [\begin{matrix} M_{F R}_{_{x}} \\ M_{F R}_{_{y}} \\ M_{F R}_{_{z}} \end{matrix}] + [\begin{matrix} M_{M L}_{_{x}} \\ M_{M L}_{_{y}} \\ M_{M L}_{_{z}} \end{matrix}] + [\begin{matrix} M_{M R}_{_{x}} \\ M_{M R}_{_{y}} \\ M_{M R}_{_{z}} \end{matrix}] + [\begin{matrix} M_{R L}_{_{x}} \\ M_{R L}_{_{y}} \\ M_{R L}_{_{z}} \end{matrix}] + [\begin{matrix} M_{R R}_{_{x}} \\ M_{R R}_{_{y}} \\ M_{R R}_{_{z}} \end{matrix}] + {\bar{M}}_{F} \end{array}$

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. $J_{i j} = I_{i j} + m ({\| R \|}^{2} δ_{i j} - R_{i} R_{j})$
Gravitational forces, F_g	The block uses the direction cosine matrix (DCM) to transform the gravitational vector in the inertial-fixed frame to the vehicle-fixed frame.
Aerodynamic forces, F_a, and moments, M_a	To determine a relative airspeed, the block subtracts the wind speed from the vehicle CG velocity. Using the relative airspeed, the block determines the aerodynamic forces. $\begin{array}{l} \bar{w} = \sqrt{{(\dot{x} - w_{x})}^{2} + {(\dot{y} - w_{y})}^{2} + {(\dot{z} - w_{z})}^{2}} \\ F_{a x} = - \frac{1}{2 T R} C_{d} A_{f} P_{a b s} (^{\bar{w}) 2} \\ F_{a y} = - \frac{1}{2 T R} C_{s} A_{f} P_{a b s} (^{\bar{w}) 2} \\ F_{a z} = - \frac{1}{2 T R} C_{l} A_{f} P_{a b s} (^{\bar{w}) 2} \end{array}$ 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. $\begin{array}{l} M_{a r} = - \frac{1}{2 T R} C_{r m} A_{f} P_{a b s} (^{\bar{w}) 2} (a + c) \\ M_{a p} = - \frac{1}{2 T R} C_{p m} A_{f} P_{a b s} (^{\bar{w}) 2} (a + c) \\ M_{a y} = - \frac{1}{2 T R} C_{y m} A_{f} P_{a b s} (^{\bar{w}) 2} (a + c) \end{array}$
External forces, F_in, and moments, M_in	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: F_FL, M_FL — Front left F_FR, M_FR — Front right F_ML, M_ML — Middle left F_MR, M_MR — Middle right F_RL, M_RL — Rear left F_RR, M_RR — 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)
F_FLx, F_FLy, F_FLz	Suspension forces applied to the front left hardpoint along the vehicle-fixed x-, y-, and z-axes
F_FRx, F_FRy, F_FRz	Suspension forces applied to the front right hardpoint along the vehicle-fixed x-, y-, and z-axes
F_MLx, F_MLy, F_MLz	Suspension forces applied to the middle left hardpoint along the vehicle-fixed x-, y-, and z-axes
F_MRx, F_MRy, F_MRz	Suspension forces applied to the middle right hardpoint along the vehicle-fixed x-, y-, and z-axes
F_RLx, F_RLy, F_RLz	Suspension forces applied to the rear left hardpoint along the vehicle-fixed x-, y-, and z-axes
F_RRx, F_RRy, F_RRz	Suspension forces applied to the rear right hardpoint along the vehicle-fixed x-, y-, and z-axes
M_FLx, M_FLy, M_FLz	Suspension moment applied to the front left hardpoint about the vehicle-fixed x-, y-, and z-axes
M_FRx, M_FRy, M_FRz	Suspension moment applied to the front right hardpoint about the vehicle-fixed x-, y-, and z-axes
M_MLx, M_MLy, M_MLz	Suspension moment applied to the middle left hardpoint about the vehicle-fixed x-, y-, and z-axes
M_MRx, M_MRy, M_MRz	Suspension moment applied to the middle right hardpoint about the vehicle-fixed x-, y-, and z-axes
M_RLx, M_RLy, M_RLz	Suspension moment applied to the rear left hardpoint about the vehicle-fixed x-, y-, and z-axes
M_RRx, M_RRy, M_RRz	Suspension moment applied to the rear right hardpoint about the vehicle-fixed x-, y-, and z-axes
F_extx, F_exty, F_extz	External forces applied to the vehicle CG along the vehicle-fixed x-, y-, and z-axes
F_dx, F_dy, F_dz	Aerodynamic forces applied to the vehicle CG along the vehicle-fixed x-, y-, and z-axes
M_extx, M_exty, M_extz	External moments applied to the vehicle CG about the vehicle-fixed x-, y-, and z-axes
M_dx, M_dy, M_dz	Aerodynamic moments applied to the vehicle CG 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 CG onto the common axle plane
h	Height of the vehicle CG above the axle plane
d	Lateral distance from the geometric centerline to the center of mass along the vehicle-fixed y-axis
hh_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 CG 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
w_F, w_M, w_R	Front, middle, and rear track widths, respectively
C_d	Aerodynamic drag force coefficient acting along the vehicle-fixed x-axis
C_s	Aerodynamic side force coefficient acting along the vehicle-fixed y-axis
C_l	Aerodynamic lift force coefficient acting along the vehicle-fixed z-axis
C_rm	Aerodynamic roll moment coefficient acting about the vehicle-fixed x-axis
C_pm	Aerodynamic pitch moment coefficient acting about the vehicle-fixed y-axis
C_ym	Aerodynamic yaw moment coefficient acting about the vehicle-fixed z-axis
A_f	Frontal area
R	Atmospheric specific gas constant
T	Environmental air temperature
P_abs	Environmental absolute pressure
w_x, w_y, w_z	Wind velocity along the vehicle-fixed x-, y-, and z-axes
W_x, W_y, W_z	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

Ports

Input

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FSusp — Suspension forces on vehicle
`3-by-6` array

Suspension longitudinal, lateral, and vertical suspension forces applied to the vehicle at the hardpoint location, in N, specified as a 3-by-6 array.

$F S u s p = [\begin{matrix} F_{F L x} & F_{F R x} & F_{M L x} & F_{M R x} & F_{R L x} & F_{R R x} \\ F_{F L y} & F_{F R y} & F_{M L y} & F_{M R y} & F_{R L y} & F_{R R y} \\ F_{F L z} & F_{F R z} & F_{M L z} & F_{M R z} & F_{R L z} & F_{R R z} \end{matrix}]$

Array Element	Axle	Track	Force Axis
`FSusp(1,1)`	Front	Left	Vehicle-fixed x-axis (longitudinal)
`FSusp(1,2)`	Front	Right
`FSusp(1,3)`	Middle	Left
`FSusp(1,4)`	Middle	Right
`FSusp(1,5)`	Rear	Left
`FSusp(1,6)`	Rear	Right
`FSusp(2,1)`	Front	Left	Vehicle-fixed y-axis (lateral)
`FSusp(2,2)`	Front	Right
`FSusp(2,3)`	Middle	Left
`FSusp(2,4)`	Middle	Right
`FSusp(2,5)`	Rear	Left
`FSusp(2,6)`	Rear	Right
`FSusp(3,1)`	Front	Left	Vehicle-fixed z-axis (vertical)
`FSusp(3,2)`	Front	Right
`FSusp(3,3)`	Middle	Left
`FSusp(3,4)`	Middle	Right
`FSusp(3,5)`	Rear	Left
`FSusp(3,6)`	Rear	Right

MSusp — Suspension moment on vehicle
`3-by-6` array

Suspension longitudinal, lateral, and vertical suspension moments applied about the vehicle at the hardpoint location, in N, specified as a 3-by-6 array.

$M S u s p = [\begin{matrix} M_{F L x} & M_{F R x} & M_{M L x} & M_{M R x} & M_{R L x} & M_{R R x} \\ M_{F L y} & M_{F R z} & M_{M L y} & M_{M R y} & M_{R L y} & M_{R R y} \\ M_{F L z} & M_{F R z} & M_{M L z} & M_{M R z} & M_{R L z} & M_{R R z} \end{matrix}]$

Array Element	Axle	Track	Moment Axis
`MSusp(1,1)`	Front	Left	Vehicle-fixed x-axis (longitudinal)
`MSusp(1,2)`	Front	Right
`MSusp(1,3)`	Middle	Left
`MSusp(1,4)`	Middle	Right
`MSusp(1,5)`	Rear	Left
`MSusp(1,6)`	Rear	Right
`MSusp(2,1)`	Front	Left	Vehicle-fixed y-axis (lateral)
`MSusp(2,2)`	Front	Right
`MSusp(2,3)`	Middle	Left
`MSusp(2,4)`	Middle	Right
`MSusp(2,5)`	Rear	Left
`MSusp(2,6)`	Rear	Right
`MSusp(3,1)`	Front	Left	Vehicle-fixed z-axis (vertical)
`MSusp(3,2)`	Front	Right
`MSusp(3,3)`	Middle	Left
`MSusp(3,4)`	Middle	Right
`MSusp(3,5)`	Rear	Left
`MSusp(3,6)`	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.

$FExt = F_{e x t} = [\begin{matrix} F_{e x t_{x}} & F_{e x t_{y}} & F_{e x t_{z}} \end{matrix}] o r [\begin{matrix} F_{e x t_{x}} \\ F_{e x t_{y}} \\ F_{e x t_{z}} \end{matrix}]$

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.

$MExt = M_{e x t} = [\begin{matrix} M_{e x t_{x}} & M_{e x t_{y}} & M_{e x t_{z}} \end{matrix}] o r [\begin{matrix} M_{e x t_{x}} \\ M_{e x t_{y}} \\ M_{e x t_{z}} \end{matrix}]$

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

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Info — Vehicle body information
bus

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

Signal						Description	Value	Units
`InertFrm`	`Cg`	`Disp`	`X`			Vehicle CG displacement along the earth-fixed X-axis	Computed	m
			`Y`			Vehicle CG displacement along the earth-fixed Y-axis	Computed	m
			`Z`			Vehicle CG displacement along the earth-fixed Z-axis	Computed	m
		`Vel`	`Xdot`			Vehicle CG velocity along the earth-fixed X-axis	Computed	m/s
			`Ydot`			Vehicle CG velocity along the earth-fixed Y-axis	Computed	m/s
			`Zdot`			Vehicle CG velocity along the earth-fixed Z-axis	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
	`Hitch`	`Disp`	`X`			Hitch offset from the axle plane along the earth-fixed X-axis	Computed	m
			`Y`			Hitch offset from the axle plane along the earth-fixed Y-axis	Computed	m
			`Z`			Hitch offset from the axle plane along the earth-fixed Z-axis	Computed	m
		`Vel`	`Xdot`			Hitch velocity along the earth-fixed X-axis	Computed	m/s
			`Ydot`			Hitch velocity along the earth-fixed Y-axis	Computed	m/s
			`Zdot`			Hitch velocity along the earth-fixed Z-axis	Computed	m/s
	`Geom`	`Disp`	`X`			Vehicle chassis offset from the 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 the 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 the vehicle CG along the vehicle-fixed x-axis	Computed	N
			`Fy`			Net force on the vehicle CG along the vehicle-fixed y-axis	Computed	N
			`Fz`			Net force on the vehicle CG along the vehicle-fixed z-axis	Computed	N
		`Ext`	`Fx`			External force on the vehicle CG along the vehicle-fixed x-axis	Input	N
			`Fy`			External force on the vehicle CG along the vehicle-fixed x-axis	Input	N
			`Fz`			External force on the 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
		`MidlAxl`	`Fx`			Middle axle force, along the vehicle-fixed x-axis	Computed	N
			`Fy`			Middle axle force, along the vehicle-fixed y-axis	Computed	N
			`Fz`			Middle 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 the body at the hitch location along the vehicle-fixed x-axis	Computed	N
			`Fy`			Hitch force applied to the body at the hitch location along the vehicle-fixed y-axis	Computed	N
			`Fz`			Hitch force applied to the body at the hitch location along the vehicle-fixed z-axis	Computed	N
		`Tires`	`FrntTires`	`Lft`	`Fx`	Front left tire force along the vehicle-fixed x-axis	Computed	N
					`Fy`	Front left tire force along the vehicle-fixed y-axis	Computed	N
					`Fz`	Front left tire force along the vehicle-fixed z-axis	Computed	N
				`Rght`	`Fx`	Front right tire force along the vehicle-fixed x-axis	Computed	N
					`Fy`	Front right tire force along the vehicle-fixed y-axis	Computed	N
					`Fz`	Front right tire force along the vehicle-fixed z-axis	Computed	N
			`MidlTires`	`Lft`	`Fx`	Middle left tire force along the vehicle-fixed x-axis	Computed	N
					`Fy`	Middle left tire force along the vehicle-fixed y-axis	Computed	N
					`Fz`	Middle left tire force along the vehicle-fixed z-axis	Computed	N
				`Rght`	`Fx`	Middle right tire force along the vehicle-fixed x-axis	Computed	N
					`Fy`	Middle right tire force along the vehicle-fixed y-axis	Computed	N
					`Fz`	Middle right tire force along the vehicle-fixed z-axis	Computed	N
			`RearTires`	`Lft`	`Fx`	Rear left tire force along the vehicle-fixed x-axis	Computed	N
					`Fy`	Rear left tire force along the vehicle-fixed y-axis	Computed	N
					`Fz`	Rear left tire force along the vehicle-fixed z-axis	Computed	N
				`Rght`	`Fx`	Rear right tire force along the vehicle-fixed x-axis	Computed	N
					`Fy`	Rear right tire force along the vehicle-fixed y-axis	Computed	N
					`Fz`	Rear right tire force along the vehicle-fixed z-axis	Computed	N
		`Drag`	`Fx`			Drag force on the vehicle CG along the vehicle-fixed x-axis	Computed	N
			`Fy`			Aerodynamic side force on the vehicle CG along the vehicle-fixed y-axis	Computed	N
			`Fz`			Aerodynamic lift force on the vehicle CG along the vehicle-fixed z-axis	Computed	N
		`Grvty`	`Fx`			Gravity force on the vehicle CG along the vehicle-fixed x-axis	Computed	N
			`Fy`			Gravity force on the vehicle CG along the vehicle-fixed y-axis	Computed	N
			`Fz`			Gravity force on the vehicle CG along the vehicle-fixed z-axis	Computed	N
	`Moments`	`Body`	`Mx`			Body moment on the vehicle CG about the vehicle-fixed x-axis	Computed	N·m
			`My`			Body moment on the vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			`Mz`			Body moment on the vehicle CG about the vehicle-fixed z-axis	Computed	N·m
		`Drag`	`Mx`			Aerodynamic roll moment on the vehicle CG about the vehicle-fixed x-axis	Computed	N·m
			`My`			Aerodynamic pitch moment on the vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			`Mz`			Aerodynamic yaw moment on the vehicle CG about the vehicle-fixed z-axis	Computed	N·m
		`Ext`	`Mx`			External moment on the vehicle CG about the vehicle-fixed x-axis	Computed	N·m
			`My`			External moment on the vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			`Mz`			External moment on the vehicle CG about the vehicle-fixed z-axis	Computed	N·m
`Hitch`		`Mx`			Hitch moment at the hitch location about 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
`MidlAxl`	`Lft`	`Disp`	`x`		Middle left axle displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Middle left axle displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Middle left axle displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Middle left axle velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Middle left axle velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Middle left axle velocity along the vehicle-fixed z-axis	Computed	m/s
	`Rght`	`Disp`	`x`		Middle right axle displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Middle right axle displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Middle right axle displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Middle right axle velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Middle right axle velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Middle right axle velocity along the vehicle-fixed z-axis	Computed	m/s
`RearAxl`	`Lft`	`Disp`	`x`		Rear left axle displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Rear left axle displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Rear left axle displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Rear left axle velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Rear left axle velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Rear left axle velocity along the vehicle-fixed z-axis	Computed	m/s
	`Rght`	`Disp`	`x`		Rear right axle displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Rear right axle displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Rear right axle displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Rear right axle velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Rear right axle velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Rear right axle velocity along the vehicle-fixed z-axis	Computed	m/s
`Hitch`	`Disp`		`x`		Hitch offset from the 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 the 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
`Pwr`	`Drag`				Power loss due to drag	Computed	W
`Geom`	`Disp`		`x`		Vehicle chassis offset from the 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 the 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 $β = \frac{V_{y}}{V_{x}}$	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

expand all

Block Options

Input Signals

Rear hitch forces — Create hitch force input port
`off` (default) | `on`

Select to create an input port, Fh, for the 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 hitch moment input port
`off` (default) | `on`

Select to create an input port, Mh, for the 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 from center of mass to front axle
`1.4` (default) | `scalar`

Distance from the vehicle CG to the 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 middle axle, b — Distance from center of mass to middle axle
`1.6` (default) | `scalar`

Distance from the vehicle CG to the middle 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`

Longitudinal distance from center of mass to rear axle, c — Distance from center of mass to rear axle
`1.8` (default) | `scalar`

Distance from the vehicle CG to the rear axle, c, 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:	`c`
Values:	`1.8` (default) \| `scalar`
Data Types:	`double`

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 CG, 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
`.35` (default) | `scalar`

Vertical distance from the vehicle CG to the 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:	`.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 the CG to the 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 center of mass to hitch, hl — Lateral distance from CG to hitch
`0` (default) | `scalar`

Lateral distance from the CG to the 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 the hitch to the 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:	`.1` (default) \| `scalar`
Data Types:	`double`

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.

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 — Initial 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 — Initial Euler 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.

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 — Initial rotation rate
`[0,0,0]` (default) | `vector`

Initial vehicle CG angular velocity about the vehicle-fixed x- (roll rate), y- (pitch rate), z-axes (yaw rate), 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
`[1.9,1.9,1.9]` (default) | `vector`

Front, middle, and rear track widths, wf, wm, and, wr, respectively, in m. Dimensions are 1-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:	`w`
Values:	`[1.9.1.9.1.9]` (default) \| `vector`
Data Types:	`double`

Inertial Loads

Tractor Front

Mass, z1m — Tractor front 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 — Tractor front distance from front axle
`[-.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.

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

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 — Tractor front 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.

$z 1 I = [\begin{matrix} I_{x x} & I_{x y} & I_{x z} \\ I_{y x} & I_{y y} & I_{y z} \\ I_{z x} & I_{z y} & I_{z z} \end{matrix}]$

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`

Cab Overhead

Mass, z2m — Cab overhead 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 — Cab overhead distance from front axle
`[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.

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

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 — Cab overhead 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.

$z 2 I = [\begin{matrix} I_{x x} & I_{x y} & I_{x z} \\ I_{y x} & I_{y y} & I_{y z} \\ I_{z x} & I_{z y} & I_{z z} \end{matrix}]$

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`

Tractor Frame Left

Mass, z3m — Tractor frame left 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 — Tractor frame left distance from front axle
`[.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.

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

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 — Tractor frame left 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.

$z 3 I = [\begin{matrix} I_{x x} & I_{x y} & I_{x z} \\ I_{y x} & I_{y y} & I_{y z} \\ I_{z x} & I_{z y} & I_{z z} \end{matrix}]$

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`

Tractor Frame Right

Mass, z4m — Tractor frame right 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 — Tractor frame right distance from front axle
`[.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.

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

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 — Tractor frame right 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.

$z 4 I = [\begin{matrix} I_{x x} & I_{x y} & I_{x z} \\ I_{y x} & I_{y y} & I_{y z} \\ I_{z x} & I_{z y} & I_{z z} \end{matrix}]$

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`

Cab Left

Mass, z5m — Cab left 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 — Cab left distance from front axle
`[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.

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

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 — Cab left 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.

$z 5 I = [\begin{matrix} I_{x x} & I_{x y} & I_{x z} \\ I_{y x} & I_{y y} & I_{y z} \\ I_{z x} & I_{z y} & I_{z z} \end{matrix}]$

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`

Cab Right

Mass, z6m — Cab right 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 — Cab right distance from front axle
`[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.

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 — Cab right 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.

$z 6 I = [\begin{matrix} I_{x x} & I_{x y} & I_{x z} \\ I_{y x} & I_{y y} & I_{y z} \\ I_{z x} & I_{z y} & I_{z z} \end{matrix}]$

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`

Tractor Rear

Mass, z7m — Tractor rear 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 — Tractor rear mass distance from front axle
`[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.

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 — Tractor rear 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.

$z 7 I = [\begin{matrix} I_{x x} & I_{x y} & I_{x z} \\ I_{y x} & I_{y y} & I_{y z} \\ I_{z x} & I_{z y} & I_{z z} \end{matrix}]$

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
`.6` (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:	`.6` (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 air 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) \| `double`
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` (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` (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 clearing 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:	`on` (default) \| `off`
Data Types:	`character vector`

References

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

Vehicle Body 6DOF Three Axles

Description

Inertial Loads

Equations of Motion

Examples

Three-Axle Tractor Towing a Three-Axle Trailer

Ports

Input

FSusp — Suspension forces on vehicle 3-by-6 array

MSusp — Suspension moment on vehicle 3-by-6 array

FExt — External forces acting on vehicle vector

MExt — External moments acting on vehicle vector

Fh — Hitch force on the body array

Dependencies

Mh — Hitch moment about body array

Dependencies

WindXYZ — Wind speed array

AirTemp — Ambient air temperature scalar

Dependencies

Output

Info — Vehicle body information bus

Vb — Vehicle velocity along vehicle-fixed frame vector

pqr — Vehicle angular velocity about vehicle-fixed frame vector

DCM — Direction cosine matrix array

Euler — Euler angles array

Xe — Vehicle position in inertial reference frame vector

Ve — Vehicle velocity in inertial reference frame vector

Parameters

Block Options

Input Signals

Rear hitch forces — Create hitch force input port off (default) | on

Programmatic Use

Rear hitch moments — Create hitch moment input port off (default) | on

Programmatic Use

Chassis

Vehicle mass, m — Mass 2000 (default) | scalar

Programmatic Use

Longitudinal distance from center of mass to front axle, a — Distance from center of mass to front axle 1.4 (default) | scalar

Programmatic Use

Longitudinal distance from center of mass to middle axle, b — Distance from center of mass to middle axle 1.6 (default) | scalar

Programmatic Use

Longitudinal distance from center of mass to rear axle, c — Distance from center of mass to rear axle 1.8 (default) | scalar

Programmatic Use

Lateral distance from geometric centerline to center of mass, d — Distance from geometric centerline to center of mass 0 (default) | scalar

Programmatic Use

Vertical distance from center of mass to axle plane, h — Distance .35 (default) | scalar

Programmatic Use

Longitudinal distance from center of mass to hitch, dh — Longitudinal distance from CG to hitch 1 (default) | scalar

Dependencies

Programmatic Use

Lateral distance from center of mass to hitch, hl — Lateral distance from CG to hitch 0 (default) | scalar

Dependencies

Programmatic Use

Vertical distance from hitch to axle plane, hh — Distance from hitch to axle plane 0.1 (default) | scalar

Dependencies

Programmatic Use

Initial position in the inertial frame [Xeo,Yeo,Zeo], Xe_o — Initial position [0,0,0] (default) | vector

Programmatic Use

Initial velocity in body axes [xdot_o,ydot_o,zdot_o], xbdot_o — Initial velocity [0,0,0] (default) | vector

Programmatic Use

Initial Euler orientation [roll, pitch, yaw], eul_o — Initial Euler rotation [0,0,0] (default) | vector

Programmatic Use

Initial body rotation rates [p,q,r], p_o — Initial rotation rate [0,0,0] (default) | vector

Programmatic Use

Chassis inertia tensor, Iveh — Inertia [430 0 0; 0 1900 0; 0 0 2100] (default) | array

Programmatic Use

Track widths [front,rear], w — Widths [1.9,1.9,1.9] (default) | vector

Programmatic Use

Inertial Loads

Tractor Front

Mass, z1m — Tractor front mass 0 (default) | scalar

Programmatic Use

Distance vector from front axle, z1R — Tractor front distance from front axle [-.25,.125,.15] (default) | vector

Programmatic Use

Inertia tensor, z1I — Tractor front inertia [1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0 (default) | array

Programmatic Use

Cab Overhead

Mass, z2m — Cab overhead mass 0 (default) | scalar

Programmatic Use

Distance vector from front axle, z2R — Cab overhead distance from front axle [1.4,0,.8] (default) | vector

FSusp — Suspension forces on vehicle
`3-by-6` array

MSusp — Suspension moment on vehicle
`3-by-6` array

FExt — External forces acting on vehicle
`vector`

MExt — External moments acting on vehicle
`vector`

Fh — Hitch force on the body
`array`

Mh — Hitch moment about body
`array`

WindXYZ — Wind speed
`array`

AirTemp — Ambient air temperature
`scalar`

Info — Vehicle body information
bus

Vb — Vehicle velocity along vehicle-fixed frame
`vector`

pqr — Vehicle angular velocity about vehicle-fixed frame
`vector`

DCM — Direction cosine matrix
`array`

Euler — Euler angles
`array`

Xe — Vehicle position in inertial reference frame
`vector`

Ve — Vehicle velocity in inertial reference frame
`vector`

Rear hitch forces — Create hitch force input port
`off` (default) | `on`

Rear hitch moments — Create hitch moment input port
`off` (default) | `on`

Vehicle mass, m — Mass
`2000` (default) | `scalar`

Longitudinal distance from center of mass to front axle, a — Distance from center of mass to front axle
`1.4` (default) | `scalar`

Longitudinal distance from center of mass to middle axle, b — Distance from center of mass to middle axle
`1.6` (default) | `scalar`

Longitudinal distance from center of mass to rear axle, c — Distance from center of mass to rear axle
`1.8` (default) | `scalar`

Lateral distance from geometric centerline to center of mass, d — Distance from geometric centerline to center of mass
`0` (default) | `scalar`

Vertical distance from center of mass to axle plane, h — Distance
`.35` (default) | `scalar`

Longitudinal distance from center of mass to hitch, dh — Longitudinal distance from CG to hitch
`1` (default) | `scalar`

Lateral distance from center of mass to hitch, hl — Lateral distance from CG to hitch
`0` (default) | `scalar`

Vertical distance from hitch to axle plane, hh — Distance from hitch to axle plane
`0.1` (default) | `scalar`

Initial position in the inertial frame [Xeo,Yeo,Zeo], Xe_o — Initial position
`[0,0,0]` (default) | `vector`

Initial velocity in body axes [xdot_o,ydot_o,zdot_o], xbdot_o — Initial velocity
`[0,0,0]` (default) | `vector`

Initial Euler orientation [roll, pitch, yaw], eul_o — Initial Euler rotation
`[0,0,0]` (default) | `vector`

Initial body rotation rates [p,q,r], p_o — Initial rotation rate
`[0,0,0]` (default) | `vector`

Chassis inertia tensor, Iveh — Inertia
`[430 0 0; 0 1900 0; 0 0 2100]` (default) | `array`

Track widths [front,rear], w — Widths
`[1.9,1.9,1.9]` (default) | `vector`

Mass, z1m — Tractor front mass
`0` (default) | `scalar`

Distance vector from front axle, z1R — Tractor front distance from front axle
`[-.25,.125,.15]` (default) | `vector`

Inertia tensor, z1I — Tractor front inertia
`[1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0` (default) | `array`

Mass, z2m — Cab overhead mass
`0` (default) | `scalar`

Distance vector from front axle, z2R — Cab overhead distance from front axle
`[1.4,0,.8]` (default) | `vector`

Inertia tensor, z2I — Cab overhead inertia
`[1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0` (default) | `array`

Mass, z3m — Tractor frame left mass
`0` (default) | `scalar`

Distance vector from front axle, z3R — Tractor frame left distance from front axle
`[.75,-.5,.4]` (default) | `vector`

Inertia tensor, z3I — Tractor frame left inertia
`[5,-.1,-2;-2,9,.1;-.1,.1,6].*0` (default) | `array`

Mass, z4m — Tractor frame right mass
`0` (default) | `scalar`

Distance vector from front axle, z4R — Tractor frame right distance from front axle
`[.75,.5,.4]` (default) | `vector`

Inertia tensor, z4I — Tractor frame right inertia
`[5,-.1,-2;-2,9,.1;-.1,.1,6].*0` (default) | `array`

Mass, z5m — Cab left mass
`0` (default) | `scalar`

Distance vector from front axle, z5R — Cab left distance from front axle
`[1.25,-.5,.4]` (default) | `vector`

Inertia tensor, z5I — Cab left inertia
`[5,-.1,-2;-2,9,.1;-.1,.1,6].*0` (default) | `array`

Mass, z6m — Cab right mass
`0` (default) | `scalar`

Distance vector from front axle, z6R — Cab right distance from front axle
`[1.25,.5,.4]` (default) | `vector`

Inertia tensor, z6I — Cab right inertia
`[5,-.1,-2;-2,9,.1;-.1,.1,6].*0` (default) | `array`

Mass, z7m — Tractor rear mass
`0` (default) | `scalar`

Distance vector from front axle, z7R — Tractor rear mass distance from front axle
`[2,0,.25]` (default) | `vector`

Inertia tensor, z7I — Tractor rear inertia
`[1.4,-.2,.1;-.2,1.4,.1;.1,.1,2.25].*0` (default) | `array`

Longitudinal drag area, Af — Area
`2` (default) | `scalar`

Longitudinal drag coefficient, Cd — Drag
`.6` (default) | `scalar`

Longitudinal lift coefficient, Cl — Lift
`.1` (default) | `scalar`

Longitudinal drag pitch moment, Cpm — Pitch
`.1` (default) | `scalar`

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`

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`

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`

Absolute air pressure, Pabs — Pressure
`101325` (default) | `scalar`

Air temperature — `AirTemp` input port
`off` (default) | `on`

Air temperature, Tair — Ambient air temperature
`273` (default) | `scalar`

Gravitational acceleration, g — Gravity
`9.81` (default) | `scalar`

Longitudinal velocity tolerance, xdot_tol — Tolerance
`.1` (default) | `scalar`

Geometric longitudinal offset from CG along body longitudinal axis, longOff — Longitudinal offset
`0` (default) | `scalar`

Geometric lateral offset from CG along body lateral axis, latOff — Lateral offset
`0` (default) | `scalar`