Vehicle Body 6DOF

6DOF rigid vehicle body to calculate translational and rotational motion

  • Library:
  • Vehicle Dynamics Blockset / Vehicle Body

Description

The Vehicle Body 6DOF block implements a six degrees-of-freedom (DOF) rigid two-axle vehicle body model to calculate longitudinal, lateral, vertical, pitch, roll, and yaw motion. The block accounts for body mass, inertia, aerodynamic drag, road incline, and weight distribution between the axles due to suspension and external forces and moments. Use the Inertial Loads parameters to analyze the vehicle dynamics under different loading conditions.

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

Inertial Loads

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

  • Front powertrain

  • Front and rear row passengers

  • Overhead cargo

  • Rear cargo

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

The dots in this illustration indicate example load locations. The table provides the corresponding location parameter sign settings.

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

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

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

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

Load

Parameter

Example Location

Front

Distance vector from front axle, z1R

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

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

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

Overhead

Distance vector from front axle, z2R

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

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

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

Row 1, left side

Distance vector from front axle, z3R

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

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

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

Row 1, right side

Distance vector from front axle, z4R

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

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

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

Row 2, left side

Distance vector from front axle, z5R

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

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

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

Row 2, right side

Distance vector from front axle, z6R

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

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

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

Rear

Distance vector from front axle, z7R

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

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

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

Equations of Motion

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

The Vehicle Body 6DOF 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 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]+[FRLxFRLyFRLz]+[FRRxFRRyFRRz]M¯b=[MxMyMz]=[MdxMdyMdz]+[MextxMextyMextz]+[MFLxMFLyMFLz]+[MFRxMFRyMFRz]+[MRLxMRLyMRLz]+[MRRxMRRyMRRz]+M¯F

CalculationImplementation

Load masses and inertias

Block uses 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

Block uses 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+b)Mdp=12TRCpmAfPabs(w¯)2(a+b)Mdy=12TRCymAfPabs(w¯)2(a+b)

External forces, Fin, and moments, Min

External forces and moments are input via ports FExt and MExt.

Suspension forces and moments

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

  • FFL, MFL — Front left

  • FFR, MFR — Front right

  • FRL, MRL — Rear left

  • FRR, MRR — Rear right

The equations use these variables.

x,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 front left hardpoint along the vehicle-fixed x-, y-, and z-axes

FFRx, FFRy, FFRz

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

FRLx, FRLy, FRLz

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

FRRx, FRRy, FRRz

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

MFx, FFy, FFz

Suspension moments applied to vehicle CM about the vehicle-fixed x-, y-, and z-axes

Fextx, Fexty, Fextz

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

Fdx, Fdy, Fdz

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

Mextx, Mexty, Mextz

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

Mdx, Mdy, Mdz

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

I

Vehicle body moments of inertia

a, b

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

h

Height of vehicle CM above the axle plane

wF, wR

Front and rear track widths

γ

Road grade angle

Cd

Air drag coefficient acting along vehicle-fixed x-axis

Cs

Air drag coefficient acting along vehicle-fixed y-axis

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

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

Cpm

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

Cym

Air drag yaw moment acting about 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 applied to the vehicle at the hardpoint location, in N. Signal dimensions are [3x4].

FSusp=[FxFLFxFRFxRLFxRRFyFLFyFRFyRLFyRRFzFLFzFRFzRLFzRR]

Array ElementAxleTrackForce Axis
FSusp(1,1)FrontLeftVehicle-fixed x-axis (longitudinal)
FSusp(1,2)FrontRight
FSusp(1,3)RearLeft
FSusp(1,4)RearRight
FSusp(2,1)FrontLeftVehicle-fixed y-axis (lateral)
FSusp(2,2)FrontRight
FSusp(2,3)RearLeft
FSusp(2,4)RearRight
FSusp(3,1)FrontLeftVehicle-fixed z-axis (vertical)
FSusp(3,2)FrontRight
FSusp(3,3)RearLeft
FSusp(3,4)RearRight

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

MSusp=[MxFLMxFRMxRLMxRRMyFLMyFRMyRLMyRRMzFLMzFRMzRLMzRR]

Array ElementAxleTrackMoment Axis
MSusp(1,1)FrontLeftVehicle-fixed x-axis (longitudinal)
MSusp(1,2)FrontRight
MSusp(1,3)RearLeft
MSusp(1,4)RearRight
MSusp(2,1)FrontLeftVehicle-fixed y-axis (lateral)
MSusp(2,2)FrontRight
MSusp(2,3)RearLeft
MSusp(2,4)RearRight
MSusp(3,1)FrontLeftVehicle-fixed z-axis (vertical)
MSusp(3,2)FrontRight
MSusp(3,3)RearLeft
MSusp(3,4)RearRight

External forces on vehicle, in N. Signal vector dimensions are [1x3] or [3x1].

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 vehicle, in N·m. Signal vector dimensions are [1x3] or [3x1].

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)

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

Ambient air temperature, Tair, in K.

Dependencies

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

Output Arguments

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Bus signal containing these block 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
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
GeomDispXVehicle chassis offset from axle plane along the earth-fixed X-axis

Computed

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

Computed

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

Computed

m
VelXdotVehicle chassis offset velocity along the earth-fixed X-axis

Computed

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

Computed

m/s
ZdotVehicle chassis 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 vehicle CM along the vehicle-fixed x-axis

Computed

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

Computed

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

Computed

N
FrntAxlLftFx

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

Computed

N
Fy

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

Computed

N
Fz

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

ComputedN
RghtFx

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

Computed

N
Fy

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

Computed

N
Fz

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

Computed

N
RearAxlLftFx

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

Computed

N
Fy

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

Computed

N
Fz

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

Computed

N
RghtFx

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

Computed

N
Fy

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

Computed

N
Fz

Normal force on rear right axle 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
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 vehicle CM along the vehicle-fixed x-axis

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

N·m
MzDrag moment on vehicle CM 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
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
PwrPwrExtApplied external power

Computed

W
DragPower loss due to drag

Computed

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

Input

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

Input

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

Input

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

Computed

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

Computed

m/s
zdotVehicle 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.

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

Direction cosine matrix, in rad.

Euler angles, φ, θ, and ψ, respectively, in rad.

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

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

Parameters

expand all

Chassis

Vehicle mass, m, in kg.

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

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

Lateral distance from geometric centerline to center of mass, d, in m, along the vehicle-fixed y. 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.

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

Initial position of 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(yaw)- axes, respectively, in rad.

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

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

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

Inertial Loads

Front

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 indicated by the dots.

Example Location

Sign

  • Forward of the front axle

  • Right of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z1R(1,1) < 0

  • z1R(1,2) > 0

  • z1R(1,3) > 0

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 indicated by the dot.

Example Location

Sign

  • Rear of the front axle

  • Left of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z2R(1,1) > 0

  • z2R(1,2) < 0

  • z2R(1,3) > 0

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

Row 1, left side

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 indicated by the dot.

Example Location

Sign

  • Rear of the front axle

  • Left of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z3R(1,1) > 0

  • z3R(1,2) < 0

  • z3R(1,3) > 0

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

Row 1, right side

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 indicated by the dot.

Example Location

Sign

  • Rear of the front axle

  • Right of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z4R(1,1) > 0

  • z4R(1,2) > 0

  • z4R(1,3) > 0

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

Row 2, left side

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 indicated by the dot.

Example Location

Sign

  • Rear of the front axle

  • Left of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z5R(1,1) > 0

  • z5R(1,2) < 0

  • z5R(1,3) > 0

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

Row 2, right side

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 indicated by the dot.

Example Location

Sign

  • Rear of the front axle

  • Right of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z6R(1,1) > 0

  • z6R(1,2) > 0

  • z6R(1,3) > 0

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

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 indicated by the dot.

Example Location

Sign

  • Rear of the front axle

  • Right of the vehicle centerline

  • Above the front axle suspension hardpoint

  • z7R(1,1) > 0

  • z7R(1,2) > 0

  • z7R(1,3) > 0

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.

Vehicle chassis 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 independent of the vehicle CG.

Vehicle chassis 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 independent of the vehicle CG.

Vehicle chassis 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 independent 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 deselecting 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 R2018a