Trailer Body 3DOF

Trailer body with longitudinal, lateral, and yaw motion

  • Library:
  • Vehicle Dynamics Blockset / Vehicle Body

Description

The Trailer Body 3DOF block implements a rigid two-axle or three-axle trailer body model to calculate longitudinal, lateral, and yaw motion. Configure the block for a single or dual track. The block accounts for axle and hitch reaction forces due to the trailer 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 tracks.

Vehicle Track SettingImplementation

Single 2-axle

Trailer with a single track and two axles.

  • Forces act along the center line of the axles.

  • No lateral load transfer.

Dual 2-axle

Trailer with a dual track and two axles. Forces act at the axle hard-point locations.

Single 3-axle

Trailer with a single track and three axles.

  • Forces act along the center line of the axles.

  • No lateral load transfer.

Dual 3-axle (default)

Trailer with a dual track and three axles. Forces act at the axle hard-point locations.

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

Axle Forces SettingImplementation

External longitudinal velocity

  • The block assumes that the external longitudinal velocity is in a quasi-steady state, and 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 PortDescription

Front wheel steering

WhlAngF

Front wheel angle, δF

Middle wheel steeringWhlAngM

Middle wheel angle, δM

Rear wheel steeringWhlAngR

Rear wheel angle, δR

External wind

WindXYZ

Wind speed, WX, WY, and WZ, in an inertial reference frame

External frictionMu

Friction coefficient

External forcesFExt

External force on the vehicle center of gravity (CG), Fx, Fy, and Fz, in the vehicle-fixed frame

External moments

MExt

External moment about the vehicle CG, Mx, My, and Mz, in the vehicle-fixed frame

Hitch forcesFh

Hitch force applied to the body at the hitch location, Fhx, Fhy, and Fhz, in the vehicle-fixed frame

Hitch momentsMh

Hitch moment at the hitch location, Mhx, Mhy, and Mhz, 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.

CalculationDescription

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 — Three Axles

Single Track — Two Axles

Dual Track — Three Axles

Dual Track — Two Axles

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 the tractor CG above the axle plane along the vehicle-fixed z-axis

d

Lateral distance from the geometric centerline to the center of mass along the vehicle-fixed y-axis

hh

Height of the hitch above the axle plane along the vehicle-fixed z-axis

dh

Longitudinal distance of the hitch from the normal projection point of tractor CG onto the common axle plane

wf, wm, wr

Front, middle, and rear track width, respectively

Drag

This table summarizes the block implementation for the drag calculation.

CalculationDescription

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 forces or External longitudinal velocity.

Parameter SettingsDescription
Mapped Corner StiffnessInclude Relaxation Length Dynamics

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.

Ports

Input

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Front wheel steering angles, δF, in rad.

Vehicle Track Setting

Variable

Signal Dimension

Single 2-axle

Single 3-axle

δF

Scalar – 1

Dual 2-axle

Dual 3-axle

δF=[δflδfr]  or  [δflδfr]

Array – [1x2] or [2x1]

Dependencies

To enable this port, under Input signals, select Front wheel steering.

Middle wheel steering angles, δM, in rad.

Vehicle Track Setting

Variable

Signal Dimension

Single 3-axleδM

Scalar – 1

Dual 3-axle

δM=[δmlδmr]  or  [δmlδmr]

Array – [1x2] or [2x1]

Dependencies

To enable this port:

  • Set Vehicle track to Single 3-axle or Dual 3-axle.

  • To enable this port, under Input signals, select Middle wheel steering.

Rear wheel steering angles, δR, in rad.

Vehicle Track Setting

Variable

Signal Dimension

Single 2-axle

Single 3-axle

δR

Scalar – 1

Dual 2-axle

Dual 3-axle

δR=[δrlδrr]  or  [δrlδrr]

Array – [1x2] or [2x1]

Dependencies

To enable this port, under Input signals, select Rear wheel steering.

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

Dependencies

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

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

Vehicle Track Setting

Axle Forces Setting

Description

Variable

Signal Dimension

Single 2-axle

Single 3-axle

External longitudinal forces

Longitudinal force on the front wheel

FwF=Fxf

Scalar – 1

External forces

Longitudinal and lateral forces on the front wheel

FwF=[FxfFyf]  or [FxfFyf]

Array – [1x2] or [2x1]

Dual 2-axle

Dual 3-axle

External longitudinal forces

Longitudinal force on the front wheels

FwF=[FxflFxfr] or [FxflFxfr]

Array – [1x2] or [2x1]

External forces

Longitudinal and lateral forces on the front wheels

FwF=[FxflFxfrFyflFyfr]

Array – [2x2]

Dependencies

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

  • External longitudinal forces

  • External forces

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

Vehicle Track Setting

Axle Forces Setting

Description

Variable

Signal Dimension

Single 3-axle

External longitudinal forces

Longitudinal force on the middle wheel

FwM=Fxr

Scalar – 1

External forces

Longitudinal and lateral forces on the middle wheel

FwM=[FxmFym]  or [FxmFym]

Array – [1x2] or [2x1]

Dual 3-axle

External longitudinal forces

Longitudinal force on the middle wheels

FwM=[FxmlFxmr] or [FxmlFxmr]

Array – [1x2] or [2x1]

External forces

Longitudinal and lateral forces on the middle wheels

FwM=[FxmlFxmrFymlFymr]

Array – [2x2]

Dependencies

To enable this port, set:

  • Vehicle track to Single 3-axle or Dual 3-axle.

  • Axle forces to External longitudinal forces or External forces.

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

Vehicle Track Setting

Axle Forces Setting

Description

Variable

Signal Dimension

Single 2-axle

Single 3-axle

External longitudinal forces

Longitudinal force on the rear wheel

FwR=Fxr

Scalar – 1

External forces

Longitudinal and lateral forces on the rear wheel

FwR=[FxrFyr]  or [FxrFyr]

Array – [1x2] or [2x1]

Dual 2-axle

Dual 3-axle

External longitudinal forces

Longitudinal force on the rear wheels

FwR=[FxrlFxrr] or [FxrlFxrr]

Array – [1x2] or [2x1]

External forces

Longitudinal and lateral forces on the rear wheels

FwR=[FxrlFxrrFyrlFyrr]

Array – [2x2]

Dependencies

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

  • External longitudinal forces

  • External forces

External forces applied to the vehicle CG, Fxext, Fyext, Fzext, in vehicle-fixed frame, in N. The signal vector dimensions are [1x3] or [3x1].

Dependencies

To enable this port, under Input signals, select External forces.

External moment about the vehicle CG, Mx, My, Mz, in the vehicle-fixed frame, in N·m. The signal vector dimensions are [1x3] or [3x1].

Dependencies

To enable this port, under Input signals, select External moments.

Hitch force applied to the body at the hitch location, Fhx, Fhy, Fhz, in the vehicle-fixed frame, in N. The signal array dimensions are [1x3] or [3x1].

Dependencies

To enable this port, under Input signals, select Hitch forces.

Hitch moment at the hitch location, Mhx, Mhy, Mhz, about the vehicle-fixed frame, in N·m. The signal array dimensions are [1x3] or [3x1].

Dependencies

To enable this port, under Input signals, select Hitch moments.

Wind speed, Wx, Wy, Wz, along the inertial X-, Y-, and Z-axes, in m/s. The signal vector dimensions are [1x3] or [3x1].

Dependencies

To enable this port, under Input signals, select External wind.

Tire friction coefficient, μ. The value is dimensionless.

Vehicle Track Setting

Description

Variable

Signal Dimension

Single 2-axle

Friction coefficient on the wheels

Mu=[μfμr] or [μfμr]

Array – [1x2] or [2x1]

Dual 2-axle

Friction coefficient on the wheels

Mu=[μflμfrμrlμrr]

Array – [2x2]

Single 3-axle

Friction coefficient on the wheels

Mu=[μfμmμr] or [μfμmμr]

Array – [1x3] or [3x1]

Dual 3-axle

Friction coefficient on the wheels

Mu=[μflμfrμmlμmrμrlμrr]

Array – [3x2]

Dependencies

To enable this port, under Input signals, select External friction.

Ambient air temperature, in K.

Dependencies

To enable this port, under Input signals, select Air temperature.

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

Dependencies

To enable this port, under Input signals, select Initial longitudinal position.

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

Dependencies

To enable this port, under Input signals, select Initial lateral position.

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

Dependencies

To enable this port:

  1. Set Axle forces to one of these options:

    • External longitudinal forces

    • External forces

  2. Under Input signals, select Initial longitudinal velocity

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

Dependencies

To enable this port, under Input signals, select Initial lateral velocity.

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

Dependencies

To enable this port, under Input signals, select Initial yaw angle.

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

Dependencies

To enable this port, under Input signals, select Initial yaw rate.

Output

expand all

Trailer data, returned as a bus signal containing these block values.

SignalDescriptionValueUnits
InertFrmCgDispXVehicle CG displacement along the earth-fixed X-axis

Computed

m
YVehicle CG displacement along the earth-fixed Y-axis

Computed

m

ZVehicle CG displacement along the earth-fixed Z-axis0m
VelXdotVehicle CG velocity along the earth-fixed X-axis

Computed

m/s

YdotVehicle CG velocity along the earth-fixed Y-axis

Computed

m/s
ZdotVehicle CG velocity along the earth-fixed Z-axis0m/s
AngphiRotation of the vehicle-fixed frame about the earth-fixed X-axis (roll)0rad
thetaRotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)0rad
psiRotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)

Computed

rad
FrntAxlLftDispXFront left wheel displacement along the earth-fixed X-axis

Computed

m
YFront left wheel displacement along the earth-fixed Y-axis

Computed

m
ZFront left wheel displacement along the earth-fixed Z-axis0m
VelXdotFront left wheel velocity along the earth-fixed X-axis

Computed

m/s
YdotFront left wheel velocity along the earth-fixed Y-axis

Computed

m/s
ZdotFront left wheel velocity along the earth-fixed Z-axis0m/s
RghtDispXFront right wheel displacement along the earth-fixed X-axis

Computed

m
YFront right wheel displacement along the earth-fixed Y-axis

Computed

m
ZFront right wheel displacement along the earth-fixed Z-axis0m
VelXdotFront right wheel velocity along the earth-fixed X-axis

Computed

m/s
YdotFront right wheel velocity along the earth-fixed Y-axis

Computed

m/s
ZdotFront right wheel velocity along the earth-fixed Z-axis0m/s
MidlAxlLftDispXMiddle left wheel displacement along the earth-fixed X-axis

Computed

m
YMiddle left wheel displacement along the earth-fixed Y-axis

Computed

m
ZMiddle left wheel displacement along the earth-fixed Z-axis0m
VelXdotMiddle left wheel velocity along the earth-fixed X-axis

Computed

m/s
YdotMiddle left wheel velocity along the earth-fixed Y-axis

Computed

m/s
ZdotMiddle left wheel velocity along the earth-fixed Z-axis0m/s
RghtDispXMiddle right wheel displacement along the earth-fixed X-axis

Computed

m
YMiddle right wheel displacement along the earth-fixed Y-axis

Computed

m
ZMiddle right wheel displacement along the earth-fixed Z-axis0m
VelXdotMiddle right wheel velocity along the earth-fixed X-axis

Computed

m/s
YdotMiddle right wheel velocity along the earth-fixed Y-axis

Computed

m/s
ZdotMiddle right wheel velocity along the earth-fixed Z-axis0m/s
RearAxlLftDispXRear left wheel displacement along the earth-fixed X-axis

Computed

m
YRear left wheel displacement along the earth-fixed Y-axis

Computed

m
ZRear left wheel displacement along the earth-fixed Z-axis0m
VelXdotRear left wheel velocity along the earth-fixed X-axis

Computed

m/s
YdotRear left wheel velocity along the earth-fixed Y-axis

Computed

m/s
ZdotRear left wheel velocity along the earth-fixed Z-axis0m/s
RghtDispXRear right wheel displacement along the earth-fixed X-axis

Computed

m
YRear right wheel displacement along the earth-fixed Y-axis

Computed

m
ZRear right wheel displacement along the earth-fixed Z-axis0m
VelXdotRear right wheel velocity along the earth-fixed X-axis

Computed

m/s
YdotRear right wheel velocity along the earth-fixed Y-axis

Computed

m/s
ZdotRear right wheel velocity along the earth-fixed Z-axis0m/s
GeomDispXTrailer body offset from the axle plane along the earth-fixed X-axis

Computed

m
YTrailer body offset from the center plane along the earth-fixed Y-axis

Computed

m
ZTrailer body offset from the axle plane along the earth-fixed Z-axis

Computed

m
VelXdotTrailer body offset velocity along the earth-fixed X-axis

Computed

m/s
YdotTrailer body offset velocity along the earth-fixed Y-axis

Computed

m/s
ZdotTrailer body offset velocity along the earth-fixed Z-axis

Computed

m/s
BdyFrmCgVelxdotVehicle CG velocity along the vehicle-fixed x-axis

Computed

m/s
ydotVehicle CG velocity along the vehicle-fixed y-axis

Computed

m/s
zdotVehicle CG velocity along the vehicle-fixed z-axis0m/s
AngBeta

Body slip angle, β

β=VyVx

Computed

rad
AngVelpVehicle angular velocity about the vehicle-fixed x-axis (roll rate)0rad/s
qVehicle angular velocity about the vehicle-fixed y-axis (pitch rate)0rad/s
rVehicle angular velocity about the vehicle-fixed z-axis (yaw rate)

Computed

rad/s
AccaxVehicle CG acceleration along the vehicle-fixed x-axis

Computed

gn
ayVehicle CG acceleration along the vehicle-fixed y-axis

Computed

gn
azVehicle CG acceleration along the vehicle-fixed z-axis0gn
xddotVehicle CG acceleration along the vehicle-fixed x-axis

Computed

m/s^2
yddotVehicle CG acceleration along the vehicle-fixed y-axis

Computed

m/s^2
zddotVehicle CG acceleration along the vehicle-fixed z-axis0m/s^2
AngAccpdotVehicle angular acceleration about the vehicle-fixed x-axis0rad/s
qdotVehicle angular acceleration about the vehicle-fixed y-axis0rad/s
rdotVehicle angular acceleration about the vehicle-fixed z-axis

Computed

rad/s
ForcesBodyFxNet force on the vehicle CG along the vehicle-fixed x-axis

Computed

N
FyNet force on the vehicle CG along the vehicle-fixed y-axis

Computed

N
FzNet force on the vehicle CG along the vehicle-fixed z-axis0N
ExtFxExternal force on the vehicle CG along the vehicle-fixed x-axis

Computed

N
FyExternal force on the vehicle CG along the vehicle-fixed y-axis

Computed

N
FzExternal force on the vehicle CG along the vehicle-fixed z-axis0N
HitchFx

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
FrntAxlLftFx

Longitudinal force on the left front wheel along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the left front wheel along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the left front wheel along the vehicle-fixed z-axis

Computed

N
RghtFx

Longitudinal force on the right front wheel along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the right front wheel along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the right front wheel along the vehicle-fixed z-axis

ComputedN
MidlAxlLftFx

Longitudinal force on the left middle wheel along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the left middle wheel along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the left middle wheel along the vehicle-fixed z-axis

Computed

N
RghtFx

Longitudinal force on the right middle wheel along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the right middle wheel along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the right middle wheel along the vehicle-fixed z-axis

ComputedN
RearAxlLftFx

Longitudinal force on the left rear wheel along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the left rear wheel along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the left rear wheel along the vehicle-fixed z-axis

ComputedN
RghtFx

Longitudinal force on the right rear wheel along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the right rear wheel along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the right rear wheel along the vehicle-fixed z-axis

ComputedN
TiresFrntTiresLftFx

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

ComputedN
Fy

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

ComputedN
Fz

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

ComputedN
RghtFx

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

ComputedN
Fy

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

ComputedN
Fz

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

ComputedN
RearTiresLftFx

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

ComputedN
Fy

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

ComputedN
Fz

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

ComputedN
RghtFx

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

ComputedN
Fy

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

ComputedN
Fz

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

Computed 
DragFxDrag force on the vehicle CG along the vehicle-fixed x-axis

Computed

N
FyDrag force on the vehicle CG along the vehicle-fixed y-axis

Computed

N
FzDrag force on the vehicle CG along the vehicle-fixed z-axis

Computed

N
GrvtyFxGravity force on the vehicle CG along the vehicle-fixed x-axis

Computed

N
FyGravity force on the vehicle CG along the vehicle-fixed y-axis

Computed

N
FzGravity force on the vehicle CG along the vehicle-fixed z-axis

Computed

N
MomentsBodyMxBody moment on the vehicle CG about the vehicle-fixed x-axis0N·m
MyBody moment on the vehicle CG about the vehicle-fixed y-axis

Computed

N·m
MzBody moment on the vehicle CG about the vehicle-fixed z-axis0N·m
DragMxDrag moment on the vehicle CG about the vehicle-fixed x-axis0N·m
MyDrag moment on the vehicle CG about the vehicle-fixed y-axis

Computed

N·m
MzDrag moment on the vehicle CG about the vehicle-fixed z-axis0N·m
ExtMxExternal moment on the vehicle CG about the vehicle-fixed x-axis0N·m
MyExternal moment on the vehicle CG about the vehicle-fixed y-axis

Computed

N·m
MzExternal moment on the vehicle CG about the vehicle-fixed z-axis0N·m
HitchMxHitch moment at the hitch location about vehicle-fixed x-axis0N·m
MyHitch moment at the hitch location about vehicle-fixed y-axis

Computed

N·m
MzHitch moment at the hitch location about vehicle-fixed z-axis0N·m
FrntAxlLftDispxFront left wheel displacement along the vehicle-fixed x-axis

Computed

m
yFront left wheel displacement along the vehicle-fixed y-axisComputedm
zFront left wheel displacement along the vehicle-fixed z-axis

Computed

m
VelxdotFront left wheel velocity along the vehicle-fixed x-axis

Computed

m/s
ydotFront left wheel velocity along the vehicle-fixed y-axis

Computed

m/s
zdotFront left wheel velocity along the vehicle-fixed z-axis0m/s
RghtDispxFront right wheel displacement along the vehicle-fixed x-axis

Computed

m
yFront right wheel displacement along the vehicle-fixed y-axisComputedm
zFront right wheel displacement along the vehicle-fixed z-axis

Computed

m
VelxdotFront right wheel velocity along the vehicle-fixed x-axis

Computed

m/s
ydotFront right wheel velocity along the vehicle-fixed y-axis

Computed

m/s
zdotFront right wheel velocity along the vehicle-fixed z-axis0m/s
SteerWhlAngFL

Front left wheel steering angle

Computed

rad
WhlAngFR

Front right wheel steering angle

Computed

rad
MidlAxlLftDispxMiddle left wheel displacement along the vehicle-fixed x-axis

Computed

m
yMiddle left wheel displacement along the vehicle-fixed y-axisComputedm
zMiddle left wheel displacement along the vehicle-fixed z-axis

Computed

m
VelxdotMiddle left wheel velocity along the vehicle-fixed x-axis

Computed

m/s
ydotMiddle left wheel velocity along the vehicle-fixed y-axis

Computed

m/s
zdotMiddle left wheel velocity along the vehicle-fixed z-axis0m/s
RghtDispxMiddle right wheel displacement along the vehicle-fixed x-axis

Computed

m
yMiddle right wheel displacement along the vehicle-fixed y-axisComputedm
zMiddle right wheel displacement along the vehicle-fixed z-axis

Computed

m
VelxdotMiddle right wheel velocity along the vehicle-fixed x-axis

Computed

m/s
ydotMiddle right wheel velocity along the vehicle-fixed y-axis

Computed

m/s
zdotMiddle right wheel velocity along the vehicle-fixed z-axis0m/s
SteerWhlAngRL

Middle left wheel steering angle

Computed

rad
WhlAngRR

Middle right wheel steering angle

Computed

rad
RearAxlLftDispxRear left wheel displacement along the vehicle-fixed x-axis

Computed

m
yRear left wheel displacement along the vehicle-fixed y-axisComputedm
zRear left wheel displacement along the vehicle-fixed z-axis

Computed

m
VelxdotRear left wheel velocity along the vehicle-fixed x-axis

Computed

m/s
ydotRear left wheel velocity along the vehicle-fixed y-axis

Computed

m/s
zdotRear left wheel velocity along the vehicle-fixed z-axis0m/s
RghtDispxRear right wheel displacement along the vehicle-fixed x-axis

Computed

m
yRear right wheel displacement along the vehicle-fixed y-axisComputedm
zRear right wheel displacement along the vehicle-fixed z-axis

Computed

m
VelxdotRear right wheel velocity along the vehicle-fixed x-axis

Computed

m/s
ydotRear right wheel velocity along the vehicle-fixed y-axis

Computed

m/s
zdotRear right wheel velocity along the vehicle-fixed z-axis0m/s
SteerWhlAngRL

Rear left wheel steering angle

Computed

rad
WhlAngRR

Rear right wheel steering angle

Computed

rad
PwrPwrExtApplied external power

Computed

W
PwrHtchHitch power

Computed

 
DragPower loss due to drag

Computed

W
GeomDispxTrailer offset from axle plane along the vehicle-fixed x-axis

Input

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

Input

m
zTrailer offset from axle plane along the earth-fixed z-axis

Input

m
VelxdotTrailer offset velocity along the vehicle-fixed x-axis

Computed

m/s
ydotTrailer offset velocity along the vehicle-fixed y-axis

Computed

m/s
zdotTrailer offset velocity along the vehicle-fixed z-axis0m/s
AngBeta

Body slip angle, β

β=VyVx

Computed

rad

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

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

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

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

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

Vehicle Track Setting

Description

Variable

Signal Dimension

Single 2-axle

Single 3-axle

Normal force on the front axle

FzF=Fzf

Scalar – 1

Dual 2-axle

Dual 3-axle

Normal force on the front wheels

FzF=[FzflFzfr]

Array – [1x2]

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

Vehicle Track Setting

Description

Variable

Signal Dimension

Single 3-axle

Normal force on the middle axle

FzM=Fzm

Scalar – 1

Dual 3-axle

Normal force on the right and left middle wheels

FzM=[FzmlFzrl]

Array – [1x2]

Dependencies

To enable this port, set Vehicle track to Single 3-axle or Dual 3-axle.

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

Vehicle Track Setting

Description

Variable

Signal Dimension

Single 2-axle

Single 3-axle

Normal force on the rear wheel

FzR=Fzr

Scalar – 1

Dual 2-axle

Dual 3-axle

Normal force on the rear wheels

FzR=[FzrlFzrr]

Array – [1x2]

Normal hitch force applied to the body at the hitch location, Fhz, in the vehicle-fixed frame z-axis, in N.

If you enable the Hitch forces parameter, the block offsets the normal hitch force, Fhz, with the value of the Fh input port component along the vehicle-fixed z-axis.

Parameters

expand all

Options

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

Vehicle Track SettingImplementation

Single 2-axle

Trailer with a single track and two axles.

  • Forces act along the center line of the axles.

  • No lateral load transfer.

Dual 2-axle

Trailer with a dual track and two axles. Forces act at the axle hard-point locations.

Single 3-axle

Trailer with a single track and three axles.

  • Forces act along the center line of the axles.

  • No lateral load transfer.

Dual 3-axle (default)

Trailer with a dual track and three axles. Forces act at the axle hard-point locations.

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

Axle Forces SettingImplementation

External longitudinal velocity

  • The block assumes that the external longitudinal velocity is in a quasi-steady state, and 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

Select to create input port WhlAngF.

Select to create input port WhlAngM.

Dependencies

To enable this parameter, set Vehicle track to Single 3-axle or Dual 3-axle.

Select to create input port WhlAngR.

Select to create input port WindXYZ.

Select to create input port Mu.

Dependencies

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

  • External longitudinal forces

  • External forces

Select to create input port FExt.

Select to create input port MExt.

Select to create input port Fh.

Select to create input port Mh.

Select to create input port X_o.

Select to create input port psi_o.

Select to create input port xdot_o.

Dependencies

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

Select to create input port r_o.

Select to create input port Y_o.

Select to create input port AirTemp.

Select to create input port ydot_o.

Longitudinal

Number of wheels on the front axle, NF. The value is dimensionless.

Number of wheels on the middle axle, NM. The value is dimensionless.

Dependencies

To enable this parameter, set Vehicle track to Single 3-axle or Dual 3-axle.

Number of wheels on the rear axle, NR. The value is dimensionless.

Vehicle mass, m, in kg.

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

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

Dependencies

To enable this parameter, set Vehicle track to Single 3-axle or Dual 3-axle.

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

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

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

Dependencies

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

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

Dependencies

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

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

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

Dependencies

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

  • External longitudinal forces

  • External forces

Lateral

Enables mapped corner stiffness calculation.

Dependencies

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

  • External longitudinal velocity

  • External longitudinal forces

Enables relaxation length dynamics.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Clear Mapped corner stiffness.

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

Front track width, wf, in m.

Dependencies

To enable this parameter, set Vehicle track to Dual 2-axle or Dual 3-axle.

Middle track width, wm, in m.

Dependencies

To enable this parameter, set Vehicle track to Dual 3-axle.

Rear track width, wr, in m.

Dependencies

To enable this parameter, set Vehicle track to Dual 2-axle or Dual 3-axle.

Front tire corner stiffness, Cyf, in N/rad.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Clear Mapped corner stiffness.

Middle tire corner stiffness, Cym, in N/rad.

Dependencies

To enable this parameter:

  1. Set Vehicle track to one of these options:

    • Single 3-axle

    • Dual 3-axle

  2. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  3. Clear Mapped corner stiffness.

Rear tire corner stiffness, Cyr, in N/rad.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Clear Mapped corner stiffness.

Front tire relaxation length, σf, in m.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Do either of these:

    • Select Mapped corner stiffness.

    • Clear Mapped corner stiffness and select Include relaxation length dynamics.

Middle tire relaxation length, σm, in m.

Dependencies

To enable this parameter:

  1. Set Vehicle track to one of these options:

    • Single 3-axle

    • Dual 3-axle

  2. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  3. Do either of these:

    • Select Mapped corner stiffness.

    • Clear Mapped corner stiffness and select Include relaxation length dynamics.

Rear tire relaxation length, σr, in m.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Do either of these:

    • Select Mapped corner stiffness.

    • Clear Mapped corner stiffness and select Include relaxation length dynamics.

Front axle slip angle breakpoints, αfbrk, in rad.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Select Mapped corner stiffness.

Front axle corner data, Cyfdata, in N/rad.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Select Mapped corner stiffness.

Middle axle slip angle breakpoints, αmbrk, in rad.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Select Mapped corner stiffness.

Middle axle corner data, Cymdata, in N/rad.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Select Mapped corner stiffness.

Rear axle slip angle breakpoints, αrbrk, in rad.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Select Mapped corner stiffness.

Rear axle corner data, Cyrdata, in N/rad.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Select Mapped corner stiffness.

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

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

Yaw

Yaw polar inertia, in kg*m^2.

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

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

Aerodynamic

Effective vehicle cross-sectional area, Af, to calculate the aerodynamic drag force on the vehicle, in m2.

Air drag coefficient, Cd. The value is dimensionless.

Air lift coefficient, Cl. The value is dimensionless.

Longitudinal drag pitch moment coefficient, Cpm. The value is dimensionless.

Relative wind angle vector, βw, in rad.

Side force coefficient vector coefficient, Cs. The value is dimensionless.

Yaw moment coefficient vector coefficient, Cym. The value is dimensionless.

Environment

Environmental absolute pressure, Pabs, in Pa.

Environmental absolute temperature, T, in K.

Dependencies

To enable this parameter, clear Air temperature.

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

Nominal friction scale factor, μ. The value is dimensionless.

Dependencies

To enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Clear External Friction.

Simulation

Longitudinal velocity tolerance, in m/s.

Nominal normal force, in N.

Dependencies

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

  • External longitudinal velocity

  • External longitudinal forces

Vehicle chassis offset from the axle plane along the vehicle-fixed x-axis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independently of the vehicle CG.

Vehicle chassis offset from the center plane along the vehicle-fixed y-axis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independently of the vehicle CG.

Vehicle chassis offset from the axle plane along the vehicle-fixed z-axis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independently of the vehicle CG.

Wrap the Euler angles to the interval [-pi, pi]. For vehicle maneuvers that might undergo vehicle yaw rotations that are outside of this interval, consider clearing the parameter if you want to:

  • Track the total vehicle yaw rotation.

  • Avoid discontinuities in the vehicle state estimators.

References

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

Extended Capabilities

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

Introduced in R2020a