Vehicle Body 3DOF Three Axles

Three-axle vehicle body with longitudinal, lateral, and yaw motion

Since R2020a

Libraries:
Vehicle Dynamics Blockset / Vehicle Body

Description

The Vehicle Body 3DOF Three Axles block implements a rigid, three-axle vehicle body model to calculate longitudinal, lateral, and yaw motion. The block accounts for the axle and hitch reaction forces due to the vehicle body mass acceleration, aerodynamic drag, and steering.

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

Use the Vehicle track parameter to specify the number of wheels.

Vehicle Track Setting Implementation

Vehicle Track Setting	Implementation
`Single (bicycle)`	Forces act along the center line of the axles. No lateral load transfer.
`Dual`	Forces act at the axle hard-point locations.

Single (bicycle)

Forces act along the center line of the axles.
No lateral load transfer.

Dual

Forces act at the axle hard-point locations.

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

Axle Forces Setting Implementation

Axle Forces Setting	Implementation
`External longitudinal velocity`	The block assumes that the external longitudinal velocity is in a quasi-steady state, so the longitudinal acceleration is approximately zero. Because the motion is quasi-steady, the block calculates lateral forces using the tire slip angles and linear cornering stiffness. Consider this setting when you want to: Generate virtual sensor signal data. Conduct high-level software studies that are not impacted by driveline or nonlinear tire responses.
`External longitudinal forces`	The block uses the external longitudinal force to accelerate or brake the vehicle. The block calculates lateral forces using the tire slip angles and linear cornering stiffness. Consider this setting when you want to: Account for changes in the longitudinal velocity on the lateral and yaw motion. Specify the external longitudinal motion through a force instead of an external longitudinal velocity. Connect the block to tractive actuators, wheels, brakes, and hitches.
`External forces`	The block uses the external lateral and longitudinal forces to steer, accelerate, or brake the vehicle. The block does not use the steering input to calculate vehicle motion. Consider this setting when you need tire models with more accurate nonlinear combined lateral and longitudinal slip.

External longitudinal velocity

The block assumes that the external longitudinal velocity is in a quasi-steady state, so the longitudinal acceleration is approximately zero.
Because the motion is quasi-steady, the block calculates lateral forces using the tire slip angles and linear cornering stiffness.
Consider this setting when you want to:
- Generate virtual sensor signal data.
- Conduct high-level software studies that are not impacted by driveline or nonlinear tire responses.

External longitudinal forces

The block uses the external longitudinal force to accelerate or brake the vehicle.
The block calculates lateral forces using the tire slip angles and linear cornering stiffness.
Consider this setting when you want to:
- Account for changes in the longitudinal velocity on the lateral and yaw motion.
- Specify the external longitudinal motion through a force instead of an external longitudinal velocity.
- Connect the block to tractive actuators, wheels, brakes, and hitches.

External forces

The block uses the external lateral and longitudinal forces to steer, accelerate, or brake the vehicle.
The block does not use the steering input to calculate vehicle motion.
Consider this setting when you need tire models with more accurate nonlinear combined lateral and longitudinal slip.

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

Input Signals Pane Parameter	Input Port	Description
Front wheel steering	`WhlAngF`	Front wheel angle, δ_F
Middle wheel steering	`WhlAngM`	Middle wheel angle, δ_M
Rear wheel steering	`WhlAngR`	Rear wheel angle, δ_R
External wind	`WindXYZ`	Wind speed, W_X, W_Y, and W_Z, in an inertial reference frame
External friction	`Mu`	Friction coefficient
External forces	`FExt`	External force on the vehicle center of gravity (CG), F_x, F_y, and F_z, in the vehicle-fixed frame
External moments	`MExt`	External moment about the vehicle CG, M_x, M_y, and M_z, in the vehicle-fixed frame
Front hitch forces	`FhF`	Hitch force applied to the body at the front hitch location, FhF_x, FhF_y, and FhF_z, in the vehicle-fixed frame
Front hitch moments	`MhF`	Hitch moment at the front hitch location, MhF_x, MhF_y, and MhF_z, about the vehicle-fixed frame
Rear hitch forces	`FhR`	Hitch force applied to the body at the rear hitch location, FhR_x, FhR_y, and FhR_z, in the vehicle-fixed frame
Rear hitch moments	`MhR`	Hitch moment at the rear hitch location, MhR_x, MhR_y, and MhR_z, about the vehicle-fixed frame
Initial longitudinal position	`X_o`	Initial vehicle CG displacement along the earth-fixed X-axis
Initial yaw angle	`psi_o`	Initial rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)
Initial longitudinal velocity	`xdot_o`	Initial vehicle CG velocity along the vehicle-fixed x-axis
Initial yaw rate	`r_o`	Initial vehicle angular velocity about the vehicle-fixed z-axis (yaw rate)
Initial lateral position	`Y_o`	Initial vehicle CG displacement along the earth-fixed Y-axis
Air temperature	`AirTemp`	Ambient air temperature. Consider this option if you want to vary the temperature during run time.
Initial lateral velocity	`ydot_o`	Initial vehicle CG velocity along the vehicle-fixed y-axis

Theory

To determine the vehicle motion, the block solves the rigid body planar dynamics equations of motion.

Calculation Description

Calculation	Description
Dynamics	The block solves the rigid-body planar dynamics equations to determine the vehicle longitudinal motion. If you set Axle forces to `External longitudinal velocity`, the block assumes a quasi-steady state for the longitudinal acceleration.
External forces	External forces include both drag and external force inputs. The forces act on the vehicle CG. The block divides the normal forces by the nominal normal load to vary the effective friction parameters during weight and load transfer. The block maintains pitch and roll equilibrium.
Tire forces	The block uses the ratio of the local, longitudinal, and lateral velocities to determine the slip angles. The block uses the steering angles to transform the tire forces to the vehicle-fixed frame. If you set Axle forces to `External forces`, the block assumes that the externally provided forces are in the vehicle-fixed frame at the axle-wheel location.

Dynamics

The block solves the rigid-body planar dynamics equations to determine the vehicle longitudinal motion. If you set Axle forces to External longitudinal velocity, the block assumes a quasi-steady state for the longitudinal acceleration.

External forces

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

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

Tire forces

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

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

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

Single Track

Isometric view of vertical, longitudinal, and lateral forces acting at single track suspension locations

Dual Track

Isometric view of vertical, longitudinal, and lateral forces acting at dual track suspension locations

The illustrations use these variables.

a, b, c	Longitudinal 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 vehicle CG above the axle plane along the vehicle-fixed z-axis
d	Lateral distance from geometric centerline to center of mass along the vehicle-fixed y-axis
hh	Height of the hitch above the axle plane along the vehicle-fixed z-axis
dh	Longitudinal distance of the hitch from normal projection point of the vehicle CG onto the common axle plane
hl	Lateral distance from center of mass to hitch along the vehicle-fixed y-axis.
wf, wm, wr	Front, middle, and rear track width, respectively

Drag

This table summarizes the block implementation for the drag calculation.

Calculation	Description
Coordinate transformation	The block transforms the wind speeds from the inertial frame to the vehicle-fixed frame.
Drag forces	To determine a relative airspeed, the block subtracts the wind speed from the CG vehicle velocity. Using the relative airspeed, the block determines the drag forces.
Drag moments	Using the relative airspeed, the block determines the drag moments.

Lateral Corner Stiffness and Relaxation Dynamics

To enable the mapped corner stiffness and relaxation length dynamic parameters, set Axle forces to External longitudinal force or External longitudinal velocity.

Parameter Settings		Description
Mapped Corner Stiffness	Include Relaxation Length Dynamics	Description
`Off` (default)	`On` (default)	The block uses constant corner stiffness values. The slip angles include the relaxation length dynamic settings. The relaxation length approximates an effective corner stiffness force that is a function of wheel travel.
`On`	`On` (default)	The block uses lookup tables that are functions of the corner stiffness data and slip angles. The slip angles include the relaxation length dynamic settings. The relaxation length approximates an effective corner stiffness force that is a function of wheel travel.
`Off` (default)	`Off`	The block uses constant corner stiffness values.

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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WhlAngF — Front wheel steering angles
`scalar` | `array`

Front wheel steering angles, δ_F, in rad.

Vehicle Track Setting	Variable	Signal Dimension
`Single (bicycle)`	δ_F	Scalar – `1`
`Dual`	$δ_{F} = [\begin{matrix} δ_{f l} & δ_{f r} \end{matrix}] or [\begin{matrix} δ_{f l} \\ δ_{f r} \end{matrix}]$	Array – `[1x2]` or `[2x1]`

Dependencies

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

WhlAngM — Middle wheel steering angles
`scalar` | `array`

Middle wheel steering angles, δ_M, in rad.

Vehicle Track Setting	Variable	Signal Dimension
`Single (bicycle)`	δ_M	Scalar – `1`
`Dual`	$δ_{M} = [\begin{matrix} δ_{m l} & δ_{m r} \end{matrix}] or [\begin{matrix} δ_{m l} \\ δ_{m r} \end{matrix}]$	Array – `[1x2]` or `[2x1]`

Dependencies

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

WhlAngR — Rear wheel steering angles
`scalar` | `array`

Rear wheel steering angles, δ_R, in rad.

Vehicle Track Setting	Variable	Signal Dimension
`Single (bicycle)`	δ_R	Scalar – `1`
`Dual`	$δ_{R} = [\begin{matrix} δ_{r l} & δ_{r r} \end{matrix}] or [\begin{matrix} δ_{r l} \\ δ_{r r} \end{matrix}]$	Array – `[1x2]` or `[2x1]`

Dependencies

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

xdotin — Longitudinal velocity
`scalar`

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

Dependencies

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

FwF — Total force on the front wheels
`scalar` | `array`

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

Vehicle Track Setting	Axle Forces Setting	Description	Variable	Signal Dimension
`Single (bicycle)`	`External longitudinal forces`	Longitudinal force on the front wheel	$F w F = F x_{f}$	Scalar – `1`
`Single (bicycle)`	`External forces`	Longitudinal and lateral forces on the front wheel	$F w F = [\begin{matrix} F x_{f} & F y_{f} \end{matrix}] or [\begin{matrix} F x_{f} \\ F y_{f} \end{matrix}]$	Array – `[1x2]` or `[2x1]`
`Dual`	`External longitudinal forces`	Longitudinal force on the front wheels	$F w F = [\begin{matrix} F_{x f l} & F_{x f r} \end{matrix}] or [\begin{matrix} F_{x f l} \\ F_{x f r} \end{matrix}]$	Array – `[1x2]` or `[2x1]`
`Dual`	`External forces`	Longitudinal and lateral forces on the front wheels	$F w F = [\begin{matrix} F_{x f l} & F_{x f r} \\ F_{y f l} & F_{y f r} \end{matrix}]$	Array – `[2x2]`

Dependencies

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

External longitudinal forces
External forces

FwM — Total force on the middle wheels
`scalar` | `array`

Force on the middle wheels, Fw_M, along the vehicle-fixed axis, in N.

Vehicle Track Setting	Axle Forces Setting	Description	Variable	Signal Dimension
`Single (bicycle)`	`External longitudinal forces`	Longitudinal force on the middle wheel	$F w M = F x_{r}$	Scalar – `1`
`Single (bicycle)`	`External forces`	Longitudinal and lateral forces on the middle wheel	$F w M = [\begin{matrix} F x_{m} & F y_{m} \end{matrix}] or [\begin{matrix} F x_{m} \\ F y_{m} \end{matrix}]$	Array – `[1x2]` or `[2x1]`
`Dual`	`External longitudinal forces`	Longitudinal force on the middle wheels	$F w M = [\begin{matrix} F_{x m l} & F_{x m r} \end{matrix}] or [\begin{matrix} F_{x m l} \\ F_{x m r} \end{matrix}]$	Array – `[1x2]` or `[2x1]`
`Dual`	`External forces`	Longitudinal and lateral forces on the middle wheels	$F w M = [\begin{matrix} F_{x m l} & F_{x m r} \\ F_{y m l} & F_{y m r} \end{matrix}]$	Array – `[2x2]`

Dependencies

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

External longitudinal forces
External forces

FwR — Total force on the rear wheels
`scalar` | `array`

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

Vehicle Track Setting	Axle Forces Setting	Description	Variable	Signal Dimension
`Single (bicycle)`	`External longitudinal forces`	Longitudinal force on the rear wheel	$F w R = F x_{r}$	Scalar – `1`
`Single (bicycle)`	`External forces`	Longitudinal and lateral forces on the rear wheel	$F w R = [\begin{matrix} F x_{r} & F y_{r} \end{matrix}] or [\begin{matrix} F x_{r} \\ F y_{r} \end{matrix}]$	Array – `[1x2]` or `[2x1]`
`Dual`	`External longitudinal forces`	Longitudinal force on the rear wheels	$F w R = [\begin{matrix} F_{x r l} & F_{x r r} \end{matrix}] or [\begin{matrix} F_{x r l} \\ F_{x r r} \end{matrix}]$	Array – `[1x2]` or `[2x1]`
`Dual`	`External forces`	Longitudinal and lateral forces on the rear wheels	$F w R = [\begin{matrix} F_{x r l} & F_{x r r} \\ F_{y r l} & F_{y r r} \end{matrix}]$	Array – `[2x2]`

Dependencies

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

External longitudinal forces
External forces

FExt — External force on vehicle CG
`array`

External forces applied to the vehicle CG, F_xext, F_yext, F_zext, in vehicle-fixed frame, in N. The signal array dimensions are [1x3] or [3x1].

Dependencies

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

MExt — External moment about vehicle CG
`array`

External moment about the vehicle CG, M_x, M_y, M_z, in the vehicle-fixed frame, in N·m. The signal array dimensions are [1x3] or [3x1].

Dependencies

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

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 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 Hitch moments.

WindXYZ — Wind speed
`array`

Wind speed, W_x, W_y, W_z along the inertial X-, Y-, and Z-axes, in m/s. The signal array dimensions are [1x3] or [3x1].

Dependencies

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

Mu — Tire friction coefficient
`array`

Tire friction coefficient, μ, dimensionless.

Vehicle Track Setting	Variable	Signal Dimension
`Single (bicycle)`	$M u = [\begin{matrix} μ_{f} & μ_{m} & μ_{r} \end{matrix}] or [\begin{matrix} μ_{f} \\ μ_{m} \\ μ_{r} \end{matrix}]$	Array – `[1x3]` or `[3x1]`
`Dual`	$M u = [\begin{matrix} μ_{f l} & μ_{f r} \\ μ_{m l} & μ_{m r} \\ μ_{r l} & μ_{r r} \end{matrix}]$	Array – `[3x2]`

Dependencies

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

AirTemp — Ambient air temperature
`scalar`

Ambient air temperature, in K.

Dependencies

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

X_o — Initial longitudinal position
`scalar`

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

Dependencies

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

Y_o — Initial lateral position
`scalar`

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

Dependencies

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

xdot_o — Initial longitudinal position
`scalar`

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

Dependencies

To enable this port:

Set Axle forces to one of these options:
- External longitudinal forces
- External forces
On the Input signals pane, select Initial longitudinal velocity

ydot_o — Initial lateral position
`scalar`

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

Dependencies

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

psi_o — Initial yaw angle
`scalar`

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

Dependencies

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

r_o — Initial yaw rate
`scalar`

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

Dependencies

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

Output

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Info — Vehicle data
bus

Vehicle data, returned as a bus signal containing these block 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	`0`	m
		`Vel`	`Xdot`			Vehicle CG velocity along the earth-fixed X-axis	Computed	m/s
			`Ydot`			Vehicle CG velocity along the earth-fixed Y-axis	Computed	m/s
			`Zdot`			Vehicle CG velocity along the earth-fixed Z-axis	`0`	m/s
		`Ang`	`phi`			Rotation of the vehicle-fixed frame about the earth-fixed X-axis (roll)	`0`	rad
			`theta`			Rotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)	`0`	rad
			`psi`			Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)	Computed	rad
	`FrntAxl`	`Lft`	`Disp`	`X`		Front left wheel displacement along the earth-fixed X-axis	Computed	m
				`Y`		Front left wheel displacement along the earth-fixed Y-axis	Computed	m
				`Z`		Front left wheel displacement along the earth-fixed Z-axis	`0`	m
			`Vel`	`Xdot`		Front left wheel velocity along the earth-fixed X-axis	Computed	m/s
				`Ydot`		Front left wheel velocity along the earth-fixed Y-axis	Computed	m/s
				`Zdot`		Front left wheel velocity along the earth-fixed Z-axis	`0`	m/s
		`Rght`	`Disp`	`X`		Front right wheel displacement along the earth-fixed X-axis	Computed	m
				`Y`		Front right wheel displacement along the earth-fixed Y-axis	Computed	m
				`Z`		Front right wheel displacement along the earth-fixed Z-axis	`0`	m
			`Vel`	`Xdot`		Front right wheel velocity along the earth-fixed X-axis	Computed	m/s
				`Ydot`		Front right wheel velocity along the earth-fixed Y-axis	Computed	m/s
				`Zdot`		Front right wheel velocity along the earth-fixed Z-axis	`0`	m/s
	`MidlAxl`	`Lft`	`Disp`	`X`		Middle left wheel displacement along the earth-fixed X-axis	Computed	m
				`Y`		Middle left wheel displacement along the earth-fixed Y-axis	Computed	m
				`Z`		Middle left wheel displacement along the earth-fixed Z-axis	`0`	m
			`Vel`	`Xdot`		Middle left wheel velocity along the earth-fixed X-axis	Computed	m/s
				`Ydot`		Middle left wheel velocity along the earth-fixed Y-axis	Computed	m/s
				`Zdot`		Middle left wheel velocity along the earth-fixed Z-axis	`0`	m/s
		`Rght`	`Disp`	`X`		Middle right wheel displacement along the earth-fixed X-axis	Computed	m
				`Y`		Middle right wheel displacement along the earth-fixed Y-axis	Computed	m
				`Z`		Middle right wheel displacement along the earth-fixed Z-axis	`0`	m
			`Vel`	`Xdot`		Middle right wheel velocity along the earth-fixed X-axis	Computed	m/s
				`Ydot`		Middle right wheel velocity along the earth-fixed Y-axis	Computed	m/s
				`Zdot`		Middle right wheel velocity along the earth-fixed Z-axis	`0`	m/s
	`RearAxl`	`Lft`	`Disp`	`X`		Rear left wheel displacement along the earth-fixed X-axis	Computed	m
				`Y`		Rear left wheel displacement along the earth-fixed Y-axis	Computed	m
				`Z`		Rear left wheel displacement along the earth-fixed Z-axis	`0`	m
			`Vel`	`Xdot`		Rear left wheel velocity along the earth-fixed X-axis	Computed	m/s
				`Ydot`		Rear left wheel velocity along the earth-fixed Y-axis	Computed	m/s
				`Zdot`		Rear left wheel velocity along the earth-fixed Z-axis	`0`	m/s
		`Rght`	`Disp`	`X`		Rear right wheel displacement along the earth-fixed X-axis	Computed	m
				`Y`		Rear right wheel displacement along the earth-fixed Y-axis	Computed	m
				`Z`		Rear right wheel displacement along the earth-fixed Z-axis	`0`	m
			`Vel`	`Xdot`		Rear right wheel velocity along the earth-fixed X-axis	Computed	m/s
				`Ydot`		Rear right wheel velocity along the earth-fixed Y-axis	Computed	m/s
				`Zdot`		Rear right wheel velocity along the earth-fixed Z-axis	`0`	m/s
	`Hitch`	`Disp`	`X`			Trailer hitch offset from the axle plane along the earth-fixed X-axis	Computed	m
			`Y`			Trailer hitch offset from the center plane along the earth-fixed Y-axis	Computed	m
			`Z`			Trailer hitch offset from the axle plane along the earth-fixed Z-axis	Computed	m
		`Vel`	`Xdot`			Trailer hitch offset velocity along the earth-fixed X-axis	Computed	m/s
			`Ydot`			Trailer hitch offset velocity along the earth-fixed Y-axis	Computed	m/s
			`Zdot`			Trailer hitch offset 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	`0`	m/s
		`Ang`	`Beta`			Body slip angle, β $β = \frac{V_{y}}{V_{x}}$	Computed	rad
		`AngVel`	`p`			Vehicle angular velocity about the vehicle-fixed x-axis (roll rate)	`0`	rad/s
			`q`			Vehicle angular velocity about the vehicle-fixed y-axis (pitch rate)	`0`	rad/s
			`r`			Vehicle angular velocity about the vehicle-fixed z-axis (yaw rate)	Computed	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	`0`	gn
			`xddot`			Vehicle CG acceleration along the vehicle-fixed x-axis	Computed	m/s^2
			`yddot`			Vehicle CG acceleration along the vehicle-fixed y-axis	Computed	m/s^2
			`zddot`			Vehicle CG acceleration along the vehicle-fixed z-axis	`0`	m/s^2
		`AngAcc`	`pdot`			Vehicle angular acceleration about the vehicle-fixed x-axis	`0`	rad/s
			`qdot`			Vehicle angular acceleration about the vehicle-fixed y-axis	`0`	rad/s
			`rdot`			Vehicle angular acceleration about the vehicle-fixed z-axis	Computed	rad/s
	`Forces`	`Body`	`Fx`			Net force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			`Fy`			Net force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			`Fz`			Net force on vehicle CG along the vehicle-fixed z-axis	`0`	N
		`Ext`	`Fx`			External force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			`Fy`			External force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			`Fz`			External force on vehicle CG along the vehicle-fixed z-axis	`0`	N
		`Hitch`	`Fx`			Hitch force applied to body at the hitch location along the vehicle-fixed x-axis	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
		`FrntAxl`	`Lft`	`Fx`		Longitudinal force on left front wheel along the vehicle-fixed x-axis	Computed	N
				`Fy`		Lateral force on left front wheel along the vehicle-fixed y-axis	Computed	N
				`Fz`		Normal force on left front wheel along the vehicle-fixed z-axis	Computed	N
			`Rght`	`Fx`		Longitudinal force on right front wheel along the vehicle-fixed x-axis	Computed	N
				`Fy`		Lateral force on right front wheel along the vehicle-fixed y-axis	Computed	N
				`Fz`		Normal force on right front wheel along the vehicle-fixed z-axis	Computed	N
		`MidlAxl`	`Lft`	`Fx`		Longitudinal force on left middle wheel along the vehicle-fixed x-axis	Computed	N
				`Fy`		Lateral force on left middle wheel along the vehicle-fixed y-axis	Computed	N
				`Fz`		Normal force on left middle wheel along the vehicle-fixed z-axis	Computed	N
			`Rght`	`Fx`		Longitudinal force on right middle wheel along the vehicle-fixed x-axis	Computed	N
				`Fy`		Lateral force on right middle wheel along the vehicle-fixed y-axis	Computed	N
				`Fz`		Normal force on right middle wheel along the vehicle-fixed z-axis	Computed	N
		`RearAxl`	`Lft`	`Fx`		Longitudinal force on left rear wheel along the vehicle-fixed x-axis	Computed	N
				`Fy`		Lateral force on left rear wheel along the vehicle-fixed y-axis	Computed	N
				`Fz`		Normal force on left rear wheel along the vehicle-fixed z-axis	Computed	N
			`Rght`	`Fx`		Longitudinal force on right rear wheel along the vehicle-fixed x-axis	Computed	N
				`Fy`		Lateral force on right rear wheel along the vehicle-fixed y-axis	Computed	N
				`Fz`		Normal force on right rear wheel along the vehicle-fixed z-axis	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
		`Drag`	`Fx`			Drag force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			`Fy`			Drag force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			`Fz`			Drag force on vehicle CG along the vehicle-fixed z-axis	Computed	N
		`Grvty`	`Fx`			Gravity force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			`Fy`			Gravity force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			`Fz`			Gravity force on vehicle CG along the vehicle-fixed z-axis	Computed	N
	`Moments`	`Body`	`Mx`			Body moment on vehicle CG about the vehicle-fixed x-axis	`0`	N·m
			`My`			Body moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			`Mz`			Body moment on vehicle CG about the vehicle-fixed z-axis	`0`	N·m
`Drag`		`Mx`			Drag moment on vehicle CG about the vehicle-fixed x-axis	`0`	N·m
		`My`			Drag moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
		`Mz`			Drag moment on vehicle CG about the vehicle-fixed z-axis	`0`	N·m
`Ext`		`Mx`			External moment on vehicle CG about the vehicle-fixed x-axis	`0`	N·m
		`My`			External moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
		`Mz`			External moment on vehicle CG about the vehicle-fixed z-axis	`0`	N·m
`Hitch`		`Mx`			Hitch moment at the hitch location about vehicle-fixed x-axis	`0`	N·m
		`My`			Hitch moment at the hitch location about vehicle-fixed y-axis	Computed	N·m
		`Mz`			Hitch moment at the hitch location about vehicle-fixed z-axis	`0`	N·m
`FrntAxl`	`Lft`	`Disp`	`x`		Front left wheel displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Front left wheel displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Front left wheel displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Front left wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Front left wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Front left wheel velocity along the vehicle-fixed z-axis	`0`	m/s
	`Rght`	`Disp`	`x`		Front right wheel displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Front right wheel displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Front right wheel displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Front right wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Front right wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Front right wheel velocity along the vehicle-fixed z-axis	`0`	m/s
	`Steer`	`WhlAngFL`			Front left wheel steering angle	Computed	rad
	`Steer`	`WhlAngFR`			Front right wheel steering angle	Computed	rad
`MidlAxl`	`Lft`	`Disp`	`x`		Middle left wheel displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Middle left wheel displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Middle left wheel displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Middle left wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Middle left wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Middle left wheel velocity along the vehicle-fixed z-axis	`0`	m/s
	`Rght`	`Disp`	`x`		Middle right wheel displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Middle right wheel displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Middle right wheel displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Middle right wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Middle right wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Middle right wheel velocity along the vehicle-fixed z-axis	`0`	m/s
	`Steer`	`WhlAngRL`			Middle left wheel steering angle	Computed	rad
	`Steer`	`WhlAngRR`			Middle right wheel steering angle	Computed	rad
`RearAxl`	`Lft`	`Disp`	`x`		Rear left wheel displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Rear left wheel displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Rear left wheel displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Rear left wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Rear left wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Rear left wheel velocity along the vehicle-fixed z-axis	`0`	m/s
	`Rght`	`Disp`	`x`		Rear right wheel displacement along the vehicle-fixed x-axis	Computed	m
			`y`		Rear right wheel displacement along the vehicle-fixed y-axis	Computed	m
			`z`		Rear right wheel displacement along the vehicle-fixed z-axis	Computed	m
		`Vel`	`xdot`		Rear right wheel velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Rear right wheel velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Rear right wheel velocity along the vehicle-fixed z-axis	`0`	m/s
	`Steer`	`WhlAngRL`			Rear left wheel steering angle	Computed	rad
	`Steer`	`WhlAngRR`			Rear right wheel steering angle	Computed	rad
`Hitch`	`Disp`		`x`		Hitch offset from axle plane along the vehicle-fixed x-axis	Input	m
			`y`		Hitch offset from center plane along the vehicle-fixed y-axis	Input	m
			`z`		Hitch offset from axle plane along the earth-fixed z-axis	Input	m
	`Vel`		`xdot`		Hitch offset velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Hitch offset velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Hitch offset velocity along the vehicle-fixed z-axis	`0`	m/s
`Pwr`	`Ext`				Applied external power	Computed	W
	`Hitch`				Power loss due to hitch	Computed	W
	`Drag`				Power loss due to drag	Computed	W
`Geom`	`Disp`		`x`		Vehicle chassis offset from axle plane along the vehicle-fixed x-axis	Input	m
			`y`		Vehicle chassis offset from center plane along the vehicle-fixed y-axis	Input	m
			`z`		Vehicle chassis offset from axle plane along the earth-fixed z-axis	Input	m
	`Vel`		`xdot`		Vehicle chassis offset velocity along the vehicle-fixed x-axis	Computed	m/s
			`ydot`		Vehicle chassis offset velocity along the vehicle-fixed y-axis	Computed	m/s
			`zdot`		Vehicle chassis offset velocity along the vehicle-fixed z-axis	`0`	m/s
	`Ang`		`Beta`		Body slip angle, β $β = \frac{V_{y}}{V_{x}}$	Computed	rad

Signal			Description	Value	Units
`PwrInfo`	`PwrTrnsfrd`	`PwrFxExt`	Externally applied longitudinal force power	Computed	W
		`PwrFyExt`	Externally applied lateral force power	Computed	W
		`PwrMzExt`	Externally applied yaw moment power	Computed	W
		`PwrFwFLx`	Longitudinal force applied at the front left axle power	Computed	W
		`PwrFwFLy`	Lateral force applied at the front left axle power	Computed	W
		`PwrFwFRx`	Longitudinal force applied at the front right axle power	Computed	W
		`PwrFwFRy`	Lateral force applied at the front right axle power	Computed	W
		`PwrFwMLx`	Longitudinal force applied at the middle left axle power	Computed	W
		`PwrFwMLy`	Lateral force applied at the middle left axle power	Computed	W
		`PwrFwMRx`	Longitudinal force applied at the middle right axle power	Computed	W
		`PwrFwMRy`	Lateral force applied at the middle right axle power	Computed	W
		`PwrFwRLx`	Longitudinal force applied at the rear left axle power	Computed	W
		`PwrFwRLy`	Lateral force applied at the rear left axle power	Computed	W
		`PwrFwRRx`	Longitudinal force applied at the rear right axle power	Computed	W
		`PwrFwRRy`	Lateral force applied at the rear right axle power	Computed	W
	`PwrNotTrnsfrd`	`PwrFxDrag`	Longitudinal drag force power	Computed	W
		`PwrFyDrag`	Lateral drag force power	Computed	W
		`PwrMzDrag`	Drag pitch moment power	Computed	W
	`PwrStored`	`PwrStoredGrvty`	Rate change in gravitational potential energy	Computed	W
		`PwrStoredxdot`	Rate of change of longitudinal kinetic energy	Computed	W
		`PwrStoredydot`	Rate of change of lateral kinetic energy	Computed	W
		`PwrStoredr`	Rate of change of rotational yaw kinetic energy	Computed	W

xdot — Vehicle longitudinal velocity
`scalar`

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

ydot — Vehicle lateral velocity
`scalar`

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

psi — Yaw
`scalar`

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

r — Yaw rate
`scalar`

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

FzF — Normal force on front wheels
`scalar` | `array`

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

Vehicle Track Setting	Description	Variable	Signal Dimension
`Single (bicycle)`	Normal force on front axle	$F z F = F z_{f}$	Scalar – `1`
`Dual`	Normal force on the right and left front wheels	$F z F = [\begin{matrix} F z_{f l} & F z_{f r} \end{matrix}]$	Array – `[1x2]`

Vehicle Track Setting

Description

Variable

Signal Dimension

Single (bicycle)

Normal force on front axle

$F z F = F z_{f}$

Scalar – 1

Dual

Normal force on the right and left front wheels

$F z F = [\begin{matrix} F z_{f l} & F z_{f r} \end{matrix}]$

Array – [1x2]

FzM — Normal force on middle wheels
`scalar` | `array`

Normal force on the middle wheels, Fz_M, along the vehicle-fixed z-axis, in N.

Vehicle Track Setting	Description	Variable	Signal Dimension
`Single (bicycle)`	Normal force on middle axle	$F z M = F z_{m}$	Scalar – `1`
`Dual`	Normal force on the right and left middle wheels	$F z M = [\begin{matrix} F z_{m l} & F z_{r l} \end{matrix}]$	Array – `[1x2]`

Vehicle Track Setting

Description

Variable

Signal Dimension

Single (bicycle)

Normal force on middle axle

$F z M = F z_{m}$

Scalar – 1

Dual

Normal force on the right and left middle wheels

$F z M = [\begin{matrix} F z_{m l} & F z_{r l} \end{matrix}]$

Array – [1x2]

FzR — Normal force on rear wheels
`scalar` | `array`

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

Vehicle Track Setting	Description	Variable	Signal Dimension
`Single (bicycle)`	Normal force on rear wheel	$F z R = F z_{r}$	Scalar – `1`
`Dual`	Normal force on the right and left rear wheels	$F z R = [\begin{matrix} F z_{r l} & F z_{r r} \end{matrix}]$	Array – `[1x2]`

Vehicle Track Setting

Description

Variable

Signal Dimension

Single (bicycle)

Normal force on rear wheel

$F z R = F z_{r}$

Scalar – 1

Dual

Normal force on the right and left rear wheels

$F z R = [\begin{matrix} F z_{r l} & F z_{r r} \end{matrix}]$

Array – [1x2]

Parameters

expand all

Options

Vehicle track — Number of vehicle wheels
`Dual` (default) | `Single (bicycle)`

Use the Vehicle track parameter to specify the number of wheels.

Vehicle Track Setting Implementation

Vehicle Track Setting	Implementation
`Single (bicycle)`	Forces act along the center line of the axles. No lateral load transfer.
`Dual`	Forces act at the axle hard-point locations.

Single (bicycle)

Forces act along the center line of the axles.
No lateral load transfer.

Dual

Forces act at the axle hard-point locations.

Axle forces — Type of axle force
`External longitudinal velocity` (default) | `External longitudinal forces` | `External forces`

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

Axle Forces Setting Implementation

Axle Forces Setting	Implementation
`External longitudinal velocity`	The block assumes that the external longitudinal velocity is in a quasi-steady state, so the longitudinal acceleration is approximately zero. Because the motion is quasi-steady, the block calculates lateral forces using the tire slip angles and linear cornering stiffness. Consider this setting when you want to: Generate virtual sensor signal data. Conduct high-level software studies that are not impacted by driveline or nonlinear tire responses.
`External longitudinal forces`	The block uses the external longitudinal force to accelerate or brake the vehicle. The block calculates lateral forces using the tire slip angles and linear cornering stiffness. Consider this setting when you want to: Account for changes in the longitudinal velocity on the lateral and yaw motion. Specify the external longitudinal motion through a force instead of an external longitudinal velocity. Connect the block to tractive actuators, wheels, brakes, and hitches.
`External forces`	The block uses the external lateral and longitudinal forces to steer, accelerate, or brake the vehicle. The block does not use the steering input to calculate vehicle motion. Consider this setting when you need tire models with more accurate nonlinear combined lateral and longitudinal slip.

External longitudinal velocity

The block assumes that the external longitudinal velocity is in a quasi-steady state, so the longitudinal acceleration is approximately zero.
Because the motion is quasi-steady, the block calculates lateral forces using the tire slip angles and linear cornering stiffness.
Consider this setting when you want to:
- Generate virtual sensor signal data.
- Conduct high-level software studies that are not impacted by driveline or nonlinear tire responses.

External longitudinal forces

The block uses the external longitudinal force to accelerate or brake the vehicle.
The block calculates lateral forces using the tire slip angles and linear cornering stiffness.
Consider this setting when you want to:
- Account for changes in the longitudinal velocity on the lateral and yaw motion.
- Specify the external longitudinal motion through a force instead of an external longitudinal velocity.
- Connect the block to tractive actuators, wheels, brakes, and hitches.

External forces

The block uses the external lateral and longitudinal forces to steer, accelerate, or brake the vehicle.
The block does not use the steering input to calculate vehicle motion.
Consider this setting when you need tire models with more accurate nonlinear combined lateral and longitudinal slip.

Input Signals

Front wheel steering — `WhlAngF` input port
`on` (default) | `off`

Select to create input port WhlAngF.

Middle wheel steering — `WhlAngM` input port
`off` (default) | `on`

Select to create input port WhlAngM.

Rear wheel steering — `WhlAngR` input port
`off` (default) | `on`

Select to create input port WhlAngR.

External wind — `WindXYZ` input port
`off` (default) | `on`

Select to create input port WindXYZ.

External friction — `Mu` input port
`off` (default) | `on`

Select to create input port Mu.

Dependencies

To enable this parameter, set Axle forces to External longitudinal forces or External forces.

External forces — `FExt` input port
`off` (default) | `on`

Select to create input port FExt.

External moments — `MExt` input port
`off` (default) | `on`

Select to create input port MExt.

Hitch forces — `Fh` input port
`on` (default) | `off`

Select to create input port Fh.

Hitch moments — `Mh` input port
`on` (default) | `off`

Specify to create input port Mh.

Initial longitudinal position — `X_o` input port
`off` (default) | `on`

Specify to create input port X_o.

Initial yaw angle — `psi_o` input port
`off` (default) | `on`

Specify to create input port psi_o.

Initial longitudinal velocity — `xdot_o` input port
`off` (default) | `on`

Specify to create input port xdot_o.

Dependencies

To enable this parameter, set Axle forces to External longitudinal forces or External forces.

Initial yaw rate — `r_o` input port
`off` (default) | `on`

Specify to create input port r_o.

Initial lateral position — `Y_o` input port
`off` (default) | `on`

Specify to create input port Y_o.

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

Specify to create input port AirTemp.

Initial lateral velocity — `ydot_o` input port
`off` (default) | `on`

Specify to create input port ydot_o.

Longitudinal

Number of wheels on front axle, NF — Front wheel count
`2` (default) | `scalar`

Number of wheels on the front axle, N_F, dimensionless.

Number of wheels on middle axle, NM — Middle wheel count
`2` (default) | `scalar`

Number of wheels on the middle axle, N_M, dimensionless.

Number of wheels on rear axle, NR — Rear wheel count
`2` (default) | `scalar`

Number of wheels on the rear axle, N_R, dimensionless.