Main Content

Trailer Body 6DOF

Trailer body with translational and rotational motion

  • Library:
  • Vehicle Dynamics Blockset / Vehicle Body

  • Trailer Body 6DOF block

Description

The Trailer Body 6DOF block implements a rigid two-axle or three-axle trailer body model that calculates longitudinal, lateral, vertical, pitch, roll, and yaw motion. The block accounts for body mass, inertia, aerodynamic drag, road incline, and weight distribution between the axle hard-point locations due to suspension and external forces and moments.

Use the Inertial Loads parameters to analyze the trailer dynamics under different loading conditions. To specify the number of trailer axles, use the Number of axles parameter.

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

Parameter

Input PortDescription
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

Inertial Loads

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

  • Front end

  • Overhead

  • Front left and front right

  • Rear left and rear right

  • Rear end

For each of the loads, you can specify the mass, location, and inertia.

The illustrations provide the load locations and vehicle parameter dimensions. The table provides the corresponding location parameter sign settings.

Top down and side views of trailer showing load locations

This table summarizes the parameter settings that specify the load locations indicated by the dots. For the location, the block uses this distance vector:

  • Front axle to load, along the vehicle-fixed x-axis

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

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

Load

Parameter

Example Location

Front end

Distance vector from front axle, z1R

  • z1R(1,1)<0 — Forward of the front axle

  • z1R(1,2)>0 — Right of the vehicle centerline

  • z1R(1,3)>0 — Above the front axle suspension hardpoint

Overhead

Distance vector from front axle, z2R

  • z2R(1,1)>0 — Rear of the front axle

  • z2R(1,2)<0 — Left of the vehicle centerline

  • z2R(1,3)>0 — Above the front axle suspension hardpoint

Front left

Distance vector from front axle, z3R

  • z3R(1,1)>0 — Rear of the front axle

  • z3R(1,2)<0 — Left of the vehicle centerline

  • z3R(1,3)>0 — Above the front axle suspension hardpoint

Front right

Distance vector from front axle, z4R

  • z4R(1,1)>0 — Rear of the front axle

  • z4R(1,2)>0 — Right of the vehicle centerline

  • z4R(1,3)>0 — Above the front axle suspension hardpoint

Rear left

Distance vector from front axle, z5R

  • z5R(1,1)>0 — Rear of the front axle

  • z5R(1,2)<0 — Left of the vehicle centerline

  • z5R(1,3)>0 — Above the front axle suspension hardpoint

Rear right

Distance vector from front axle, z6R

  • z6R(1,1)>0 — Rear of the front axle

  • z6R(1,2)>0 — Right of the vehicle centerline

  • z6R(1,3)>0 — Above the front axle suspension hardpoint

Rear end

Distance vector from front axle, z7R

  • z7R(1,1)>0 — Rear of the front axle

  • z7R(1,2)>0 — Right of the vehicle centerline

  • z7R(1,3)>0 — Above the front axle suspension hardpoint

Equations of Motion

To determine the vehicle motion, the block implements calculations for the rigid body vehicle dynamics, wind drag, inertial loads, and coordinate transformations. The body-fixed and vehicle-fixed coordinate systems are the same.

The block considers the rotation of a body-fixed coordinate frame about a flat earth-fixed inertial reference frame. The origin of the body-fixed coordinate frame is the vehicle center of gravity of the body.

The block uses this equation to calculate the translational motion of the body-fixed coordinate frame, where the applied forces [Fx Fy Fz]T are in the body-fixed frame, and the mass of the body, m, is assumed to be constant.

F¯b=[FxFyFz]=m(V¯˙b+ω¯×V¯b)M¯b=[LMN]=Iω¯˙+ω¯×(Iω¯)I=[IxxIxyIxzIyxIyyIyzIzxIzyIzz]

To determine the relationship between the body-fixed angular velocity vector, [p q r]T, and the rate of change of the Euler angles, [ϕ˙θ˙ψ˙]T, the block resolves the Euler rates into the body-fixed frame.

[pqr]=[ϕ˙00]+[1000cosϕsinϕ0sinϕcosϕ][0θ˙0]+[1000cosϕsinϕ0sinϕcosϕ][cosθ0sinθ010sinθ0cosθ][00ψ˙]J1[ϕ˙θ˙ψ˙]

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

[ϕ˙θ˙ψ˙]=J[pqr]=[1(sinϕtanθ)(cosϕtanθ)0cosϕsinϕ0sinϕcosθcosϕcosθ][pqr]

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

F¯b=[FxFyFz]=[FdxFdyFdz]+[FgxFgyFgz]+[FextxFextyFextz]+[FFLxFFLyFFLz]+[FFRxFFRyFFRz]+[FMLxFMLyFMLz]+[FMRxFMRyFMRz]+[FRLxFRLyFRLz]+[FRRxFRRyFRRz]M¯b=[MxMyMz]=[MdxMdyMdz]+[MextxMextyMextz]+[MFLxMFLyMFLz]+[MFRxMFRyMFRz]+[MMLxMMLyMMLz]+[MMRxMMRyMMRz]+[MRLxMRLyMRLz]+[MRRxMRRyMRRz]+M¯F

CalculationImplementation

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.

Jij=Iij+m(|R|2δijRiRj)

Gravitational forces, Fg

The block uses the direction cosine matrix (DCM) to transform the gravitational vector in the inertial-fixed frame to the body-fixed frame.

Drag forces, Fd, and moments, Md

To determine a relative airspeed, the block subtracts the wind speed from the vehicle center of mass (CM) velocity. Using the relative airspeed, the block determines the drag forces.

w¯=(x˙bwx)2+(x˙ywx)2+(wz)2Fdx=12TRCdAfPabs(w¯)2Fdy=12TRCsAfPabs(w¯)2Fdz=12TRClAfPabs(w¯)2

Using the relative airspeed, the block determines the drag moments.

Mdr=12TRCrmAfPabs(w¯)2(a+c)Mdp=12TRCpmAfPabs(w¯)2(a+c)Mdy=12TRCymAfPabs(w¯)2(a+c)

External forces, Fin, and moments, Min

The external forces and moments are input via ports FExt and MExt.

Suspension forces and moments

The block assumes that the suspension forces and moments act on these hardpoint locations:

  • FFL, MFL — Front left

  • FFR, MFR — Front right

  • FML, MML — Middle left

  • FMR, MMR — Middle right

  • FRL, MRL — Rear left

  • FRR, MRR — Rear right

The equations use these variables.

x,x˙,x¨

Vehicle CM displacement, velocity, and acceleration along the vehicle-fixed x-axis

y,y˙,y¨

Vehicle CM displacement, velocity, and acceleration along the vehicle-fixed y-axis

z,z˙,z¨

Vehicle CM displacement, velocity, and acceleration along the vehicle-fixed z-axis

φ

Rotation of the vehicle-fixed frame about the earth-fixed X-axis (roll)

θ

Rotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)

ψ

Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)

FFLx, FFLy, FFLz

Suspension forces applied to the front left hardpoint along the vehicle-fixed x-, y-, and z-axes

FFRx, FFRy, FFRz

Suspension forces applied to the front right hardpoint along the vehicle-fixed x-, y-, and z-axes

FMLx, FMLy, FMLz

Suspension forces applied to the middle left hardpoint along the vehicle-fixed x-, y-, and z-axes

FMRx, FMRy, FMRz

Suspension forces applied to the middle right hardpoint along the vehicle-fixed x-, y-, and z-axes

FRLx, FRLy, FRLz

Suspension forces applied to the rear left hardpoint along the vehicle-fixed x-, y-, and z-axes

FRRx, FRRy, FRRz

Suspension forces applied to the rear right hardpoint along the vehicle-fixed x-, y-, and z-axes

MFLx, MFLy, MFLz

Suspension moment applied to the front left hardpoint about the vehicle-fixed x-, y-, and z-axes

MFRx, MFRy, MFRz

Suspension moment applied to the front right hardpoint about the vehicle-fixed x-, y-, and z-axes

MMLx, MMLy, MMLz

Suspension moment applied to the middle left hardpoint about the vehicle-fixed x-, y-, and z-axes

MMRx, MMRy, MMRz

Suspension moment applied to the middle right hardpoint about the vehicle-fixed x-, y-, and z-axes

MRLx, MRLy, MRLz

Suspension moment applied to the rear left hardpoint about the vehicle-fixed x-, y-, and z-axes

MRRx, MRRy, MRRz

Suspension moment applied to the rear right hardpoint about the vehicle-fixed x-, y-, and z-axes

Fextx, Fexty, Fextz

External forces applied to the vehicle CM along the vehicle-fixed x-, y-, and z-axes

Fdx, Fdy, Fdz

Drag forces applied to the vehicle CM along the vehicle-fixed x-, y-, and z-axes

Mextx, Mexty, Mextz

External moment about the vehicle CM about the vehicle-fixed x-, y-, and z-axes

Mdx, Mdy, Mdz

Drag moment about the vehicle CM about the vehicle-fixed x-, y-, and z-axes

I

Vehicle body moments of inertia

a, b, c

Distance of the front, middle, and rear axles, respectively, from the normal projection point of the vehicle CM onto the common axle plane

h

Height of the vehicle CM above the axle plane

d

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

hh

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 the vehicle CM onto the common axle plane

hl

Lateral distance from center of mass to the hitch along the vehicle-fixed y-axis.

wF, wM, wR

Front, middle, and rear track widths, respectively

Cd

Air drag coefficient acting along the vehicle-fixed x-axis

Cs

Air drag coefficient acting along the vehicle-fixed y-axis

ClAir drag coefficient acting along the vehicle-fixed z-axis
Crm

Air drag roll moment acting about the vehicle-fixed x-axis

Cpm

Air drag pitch moment acting about the vehicle-fixed y-axis

Cym

Air drag yaw moment acting about the vehicle-fixed z-axis

Af

Frontal area

RAtmospheric specific gas constant
TEnvironmental air temperature
PabsEnvironmental absolute pressure
wx, wy, wz

Wind speed along the vehicle-fixed x-, y-, and z-axes

Wx, Wy, Wz

Wind speed along inertial X-, Y-, and Z-axes

Ports

Input

expand all

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

Number of axles Setting

Variable

Signal Dimension

2

FSusp=[FFLxFFRxFRLxFRRxFFLyFFRyFRLyFRRyFFLzFFRzFRLzFRRz]

Array – 3-by-4

3

FSusp=[FFLxFFRxFMLxFMRxFRLxFRRxFFLyFFRyFMLyFMRyFRLyFRRyFFLzFFRzFMLzFMRzFRLzFRRz]

Array – 3-by-6

The arrays use these variables.

FFLx, FFLy, FFLz

Suspension forces applied to front left hardpoint along the vehicle-fixed x-, y-, and z-axes

FFRx, FFRy, FFRz

Suspension forces applied to front right hardpoint along the vehicle-fixed x-, y-, and z-axes

FMLx, FMLy, FMLz

Suspension forces applied to middle left hardpoint along the vehicle-fixed x-, y-, and z-axes

FMRx, FMRy, FMRz

Suspension forces applied to middle right hardpoint along the vehicle-fixed x-, y-, and z-axes

FRLx, FRLy, FRLz

Suspension forces applied to rear left hardpoint along the vehicle-fixed x-, y-, and z-axes

FRRx, FRRy, FRRz

Suspension forces applied to rear right hardpoint along the vehicle-fixed x-, y-, and z-axes

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

Number of axles Setting

Variable

Signal Dimension

2

MSusp=[MFLxMFRxMRLxMRRxMFLyMFRyMRLyMRRyMFLzMFRzMRLzMRRz]

Array – 3-by-4

3

MSusp=[MFLxMFRxMMLxMMRxMRLxMRRxMFLyMFRzMMLyMMRyMRLyMRRyMFLzMFRzMMLzMMRzMRLzMRRz]

Array – 3-by-6

The arrays use these variables.

MFLx, MFLy, MFLz

Suspension moment applied to front left hardpoint about the vehicle-fixed x-, y-, and z-axes

MFRx, MFRy, MFRz

Suspension moment applied to front right hardpoint about the vehicle-fixed x-, y-, and z-axes

MMLx, MMLy, MMLz

Suspension moment applied to middle left hardpoint about the vehicle-fixed x-, y-, and z-axes

MMRx, MMRy, MMRz

Suspension moment applied to middle right hardpoint about the vehicle-fixed x-, y-, and z-axes

MRLx, MRLy, MRLz

Suspension moment applied to rear left hardpoint about the vehicle-fixed x-, y-, and z-axes

MRRx, MRRy, MRRz

Suspension moment applied to rear right hardpoint about the vehicle-fixed x-, y-, and z-axes

External forces on the vehicle, in N, specified as a 1-by-3 or 3-by-1 vector.

FExt=Fext=[FextxFextyFextz]or[FextxFextyFextz]

Array ElementForce 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)

External moments acting on the vehicle, in N·m, specified as a 1-by-3 or 3-by-1 vector.

MExt=Mext=[MextxMextyMextz]or[MextxMextyMextz]

Array ElementForce 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)

Hitch force applied to the body at the hitch location, Fhx, Fhy, Fhz, 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.

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

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

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

Dependencies

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

Output

expand all

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

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

Computed

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

Computed

m

ZVehicle CM displacement along the earth-fixed Z-axis

Computed

m
VelXdotVehicle CM velocity along the earth-fixed X-axis

Computed

m/s

YdotVehicle CM velocity along the earth-fixed Y-axis

Computed

m/s
ZdotVehicle CM velocity along the earth-fixed Z-axis

Computed

m/s
AngphiRotation of the vehicle-fixed frame about the earth-fixed X-axis (roll)

Computed

rad
thetaRotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)

Computed

rad
psiRotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)

Computed

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

Computed

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

Computed

m
ZFront left axle displacement along the earth-fixed Z-axis

Computed

m
VelXdotFront left axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
ZdotFront left axle velocity along the earth-fixed Z-axis

Computed

m/s
RghtDispXFront right axle displacement along the earth-fixed X-axis

Computed

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

Computed

m
ZFront right axle displacement along the earth-fixed Z-axis

Computed

m
VelXdotFront right axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
ZdotFront right axle velocity along the earth-fixed Z-axis

Computed

m/s
MidlAxlLftDispXMiddle left axle displacement along the earth-fixed X-axis

Computed

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

Computed

m
ZMiddle left axle displacement along the earth-fixed Z-axis

Computed

m
VelXdotMiddle left axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
ZdotMiddle left axle velocity along the earth-fixed Z-axis

Computed

m/s
RghtDispXMiddle right axle displacement along the earth-fixed X-axis

Computed

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

Computed

m
ZMiddle right axle displacement along the earth-fixed Z-axis

Computed

m
VelXdotMiddle right axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
ZdotMiddle right axle velocity along the earth-fixed Z-axis

Computed

m/s
RearAxlLftDispXRear left axle displacement along the earth-fixed X-axis

Computed

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

Computed

m
ZRear left axle displacement along the earth-fixed Z-axis

Computed

m
VelXdotRear left axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
ZdotRear left axle velocity along the earth-fixed Z-axis

Computed

m/s
RghtDispXRear right axle displacement along the earth-fixed X-axis

Computed

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

Computed

m
ZRear right axle displacement along the earth-fixed Z-axis

Computed

m
VelXdotRear right axle velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
ZdotRear right axle velocity along the earth-fixed Z-axis

Computed

m/s
HitchDispXHitch offset from the axle plane along the earth-fixed X-axis

Computed

m
YHitch offset from the axle plane along the earth-fixed Y-axis

Computed

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

Computed

m
VelXdotHitch velocity along the earth-fixed X-axis

Computed

m/s
YdotHitch velocity along the earth-fixed Y-axis

Computed

m/s
ZdotHitch velocity along the earth-fixed Z-axis

Computed

m/s
GeomDispXTrailer offset from the axle plane along the earth-fixed X-axis

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

m/s
zdotVehicle CM velocity along the vehicle-fixed z-axisComputedm/s
AngVelpVehicle angular velocity about the vehicle-fixed x-axis (roll rate)

Computed

rad/s
qVehicle angular velocity about the vehicle-fixed y-axis (pitch rate)

Computed

rad/s
rVehicle angular velocity about the vehicle-fixed z-axis (yaw rate)

Computed

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

Computed

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

Computed

gn
azVehicle CM acceleration along the vehicle-fixed z-axis

Computed

gn
xddotVehicle CM acceleration along the vehicle-fixed x-axis

Computed

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

Computed

m/s^2
zddotVehicle CM acceleration along the vehicle-fixed z-axis

Computed

m/s^2
DCM

Direction cosine matrix

Computed

rad
ForcesBodyFxNet force on the vehicle CM along the vehicle-fixed x-axis

Computed

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

Computed

N
FzNet force on the vehicle CM along the vehicle-fixed z-axis

Computed

N
ExtFxExternal force on the vehicle CM along the vehicle-fixed x-axis

Input

N
FyExternal force on the vehicle CM along the vehicle-fixed x-axis

Input

N
FzExternal force on the vehicle CM along the vehicle-fixed x-axis

Input

N
FrntAxlLftFx

Front left axle velocity along the earth-fixed Y-axis

Computed

N
Fy

Lateral force on the left side of the front axle left along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the left side of the front axle along the vehicle-fixed z-axis

ComputedN
RghtFx

Longitudinal force on the right side of the front axle along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the right side of the front axle left along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the right side of the front axle along the vehicle-fixed z-axis

Computed

N
MidlAxlLftFx

Longitudinal force on the left side of the middle axle along the vehicle-fixed x-axis

Computed

N
Fy

Longitudinal force on the left side of the middle axle along the vehicle-fixed x-axis

Computed

N
Fz

Normal force on the left side of the middle axle along the vehicle-fixed z-axis

Computed

N
RghtFx

Longitudinal force on the right side of the middle axle along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the right side of the middle axle left along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the right side of the middle axle along the vehicle-fixed z-axis

Computed

N
RearAxlLftFx

Longitudinal force on the left side of the rear axle along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the left side of the rear axle left along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the left side of the rear axle along the vehicle-fixed z-axis

Computed

N
RghtFx

Longitudinal force on the right side of the rear axle along the vehicle-fixed x-axis

Computed

N
Fy

Lateral force on the right side of the rear axle left along the vehicle-fixed y-axis

Computed

N
Fz

Normal force on the right side of the rear axle along the vehicle-fixed z-axis

Computed

N
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
TiresFrntTiresLftFx

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
RghtFx

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
MidlTiresLftFx

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
RghtFx

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
RearTiresLftFx

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
RghtFx

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
DragFxDrag force on the vehicle CM along the vehicle-fixed x-axis

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

N
MomentsBodyMxBody moment on the vehicle CM about the vehicle-fixed x-axis

Computed

N·m
MyBody moment on the vehicle CM about the vehicle-fixed y-axis

Computed

N·m
MzBody moment on the vehicle CM about the vehicle-fixed z-axis

Computed

N·m
DragMxDrag moment on the vehicle CM about the vehicle-fixed x-axis

Computed

N·m
MyDrag moment on the vehicle CM about the vehicle-fixed y-axis

Computed

N·m
MzDrag moment on the vehicle CM about the vehicle-fixed z-axis

Computed

N·m
ExtMxExternal moment on the vehicle CG about the vehicle-fixed x-axis

Computed

N·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-axis

Computed

N·m
HitchMxHitch moment at the hitch location about the vehicle-fixed x-axis

Computed

N·m
MyHitch moment at the hitch location about the vehicle-fixed y-axis

Computed

N·m
MzHitch moment at the hitch location about the vehicle-fixed z-axis

Computed

N·m
FrntAxlLftDispxFront left axle displacement along the vehicle-fixed x-axis

Computed

m
yFront left axle displacement along the vehicle-fixed y-axis

Computed

m
zFront left axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
zdotFront left axle velocity along the vehicle-fixed z-axis

Computed

m/s
RghtDispxFront right axle displacement along the vehicle-fixed x-axis

Computed

m
yFront right axle displacement along the vehicle-fixed y-axis

Computed

m
zFront right axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
zdotFront right axle velocity along the vehicle-fixed z-axis

Computed

m/s
MidlAxlLftDispxMiddle left axle displacement along the vehicle-fixed x-axis

Computed

m
yMiddle left axle displacement along the vehicle-fixed y-axis

Computed

m
zMiddle left axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
zdotMiddle left axle velocity along the vehicle-fixed z-axis

Computed

m/s
RghtDispxMiddle right axle displacement along the vehicle-fixed x-axis

Computed

m
yMiddle right axle displacement along the vehicle-fixed y-axis

Computed

m
zMiddle right axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
zdotMiddle right axle velocity along the vehicle-fixed z-axis

Computed

m/s
RearAxlLftDispxRear left axle displacement along the vehicle-fixed x-axis

Computed

m
yRear left axle displacement along the vehicle-fixed y-axis

Computed

m
zRear left axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
zdotRear left axle velocity along the vehicle-fixed z-axis

Computed

m/s
RghtDispxRear right axle displacement along the vehicle-fixed x-axis

Computed

m
yRear right axle displacement along the vehicle-fixed y-axis

Computed

m
zRear right axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

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

Computed

m/s
zdotRear right axle velocity along the vehicle-fixed z-axis

Computed

m/s
HitchDispxHitch offset from axle plane along the vehicle-fixed x-axis

Input

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

Input

m
zHitch offset from axle plane along the vehicle-fixed z-axis

Input

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

Computed

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

Computed

m/s
zdotHitch offset velocity along the vehicle-fixed z-axis

Computed

m/s
PwrPwrExtApplied external power

Computed

W
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 vehicle-fixed z-axis

Input

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

Computed

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

Computed

m/s
zdotTrailer chassis offset velocity along the vehicle-fixed z-axis

Computed

m/s
AngBeta

Body slip angle, β

β=VyVx

Computed

rad

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

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

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

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

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

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

Parameters

expand all

Block Options

Specify the number of axles on the trailer.

Input Signals

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

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

Chassis

Vehicle mass, m, in kg.

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

Side view of trailer showing longitudinal axle and hitch distances from CM

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

Side view of trailer showing longitudinal axle and hitch distances from CM

Dependencies

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

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

Side view of trailer showing longitudinal axle and hitch distances from CM

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

Top down view of track widths and CM offset from centerline.

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

Top down and side views of trailer showing load locations

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

Top down and side views of trailer showing load locations

Dependencies

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

Lateral distance from center of mass to hitch, hl, in m.

Top down and side views of trailer showing load locations

Dependencies

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

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

Top down and side views of trailer showing load locations

Dependencies

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

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

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

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

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

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

Front track width, in m.

Top down view of track widths and CM offset from centerline.

Middle track width, in m.

Top down view of track widths and CM offset from centerline.

Dependencies

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

Rear track width, in m.

Top down view of track widths and CM offset from centerline.

Inertial Loads

Front End

Mass, z1m, in kg.

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

Array ElementDescription
z1R(1,1)

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

z1R(1,2)

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

z1R(1,3)

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

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

Example Location

Sign

  • Forward of the front axle

  • Right of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z1R(1,1) < 0

  • z1R(1,2) > 0

  • z1R(1,3) > 0

Inertia tensor, z1I, in kg·m^2. Dimensions are [3-by-3].

z1I=[IxxIxyIxzIyxIyyIyzIzxIzyIzz]

The tensor uses a coordinate system with an origin at the load CM.

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

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

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

Overhead

Mass, z2m, in kg.

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

Array ElementDescription
z2R(1,1)

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

z2R(1,2)

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

z2R(1,3)

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

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

Example Location

Sign

  • Rear of the front axle

  • Left of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z2R(1,1) > 0

  • z2R(1,2) < 0

  • z2R(1,3) > 0

Inertia tensor, z2I, in kg·m^2. Dimensions are [3-by-3].

z2I=[IxxIxyIxzIyxIyyIyzIzxIzyIzz]

The tensor uses a coordinate system with an origin at the load CM.

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

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

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

Front Left

Mass, z3m, in kg.

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

Array ElementDescription
z3R(1,1)

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

z3R(1,2)

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

z3R(1,3)

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

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

Example Location

Sign

  • Rear of the front axle

  • Left of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z3R(1,1) > 0

  • z3R(1,2) < 0

  • z3R(1,3) > 0

Inertia tensor, z3I, in kg·m^2. Dimensions are [3-by-3].

z3I=[IxxIxyIxzIyxIyyIyzIzxIzyIzz]

The tensor uses a coordinate system with an origin at the load CM.

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

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

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

Front Right

Mass, z4m, in kg.

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

Array ElementDescription
z4R(1,1)

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

z4R(1,2)

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

z4R(1,3)

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

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

Example Location

Sign

  • Rear of the front axle

  • Right of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z4R(1,1) > 0

  • z4R(1,2) > 0

  • z4R(1,3) > 0

Inertia tensor, z4I, in kg·m^2. Dimensions are [3-by-3].

z4I=[IxxIxyIxzIyxIyyIyzIzxIzyIzz]

The tensor uses a coordinate system with an origin at the load CM.

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

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

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

Rear Left

Mass, z5m, in kg.

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

Array ElementDescription
z5R(1,1)

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

z5R(1,2)

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

z5R(1,3)

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

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

Example Location

Sign

  • Rear of the front axle

  • Left of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z5R(1,1) > 0

  • z5R(1,2) < 0

  • z5R(1,3) > 0

Inertia tensor, z5I, in kg·m^2. Dimensions are [3-by-3].

z5I=[IxxIxyIxzIyxIyyIyzIzxIzyIzz]

The tensor uses a coordinate system with an origin at the load CM.

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

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

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

Rear Right

Mass, z6m, in kg.

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

Array ElementDescription
z6R(1,1)

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

z6R(1,2)

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

z6R(1,3)

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

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

Example Location

Sign

  • Rear of the front axle

  • Right of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z6R(1,1) > 0

  • z6R(1,2) > 0

  • z6R(1,3) > 0

Inertia tensor, z6I, in kg·m^2. Dimensions are [3-by-3].

z6I=[IxxIxyIxzIyxIyyIyzIzxIzyIzz]

The tensor uses a coordinate system with an origin at the load CM.

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

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

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

Rear End

Mass, z7m, in kg.

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

Array ElementDescription
z7R(1,1)

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

z7R(1,2)

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

z7R(1,3)

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

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

Example Location

Sign

  • Rear of the front axle

  • Right of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z7R(1,1) > 0

  • z7R(1,2) > 0

  • z7R(1,3) > 0

Inertia tensor, z7I, in kg·m^2. Dimensions are [3-by-3].

z7I=[IxxIxyIxzIyxIyyIyzIzxIzyIzz]

The tensor uses a coordinate system with an origin at the load CM.

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

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

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

Aerodynamic

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

Air drag coefficient, Cd, dimensionless.

Air lift coefficient, Cl, dimensionless.

Longitudinal drag pitch moment coefficient, Cpm, dimensionless.

Relative wind angle vector, βw, in rad.

Side force coefficient vector coefficient, Cs, dimensionless.

Yaw moment coefficient vector coefficient, Cym, dimensionless.

Environment

Environmental air absolute pressure, Pabs, in Pa.

Ambient air temperature, Tair, in K.

Dependencies

To enable this parameter, clear Air temperature.

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

Simulation

Longitudinal velocity tolerance, xdottol, in m/s.

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

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

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

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

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

  • Track the total vehicle yaw rotation.

  • Avoid discontinuities in the vehicle state estimators.

References

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

Extended Capabilities

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

Introduced in R2020b