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 oneaxle, twoaxle or threeaxle 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 Setting  Implementation 

 Trailer with a single track and one axle.

 Trailer with a dual track and one axle. Forces act at the axle hardpoint locations. 
 Trailer with a single track and two axles.

 Trailer with a dual track and two axles. Forces act at the axle hardpoint locations. 
 Trailer with a single track and three axles.

 Trailer with a dual track and three axles. Forces act at the axle hardpoint locations. 
Use the Axle forces parameter to specify the type of force.
Axle Forces Setting  Implementation 







To create additional input ports, under Input signals, select these block parameters.
Input Signals Pane Parameter  Input Port  Description 

Front wheel steering 
 Front wheel angle, δ_{F} 
Middle wheel steering  WhlAngM  Middle wheel angle, δ_{M} 
Rear wheel steering  WhlAngR  Rear wheel angle, δ_{R} 
External wind 
 Wind speed, W_{X}, W_{Y}, and W_{Z}, in an inertial reference frame 
External friction  Mu  Friction coefficient 
External forces  FExt  External force on the vehicle center of gravity (CG), F_{x}, F_{y}, and F_{z}, in the vehiclefixed frame 
External moments 
 External moment about the vehicle CG, M_{x}, M_{y}, and M_{z}, in the vehiclefixed frame 
Front hitch forces  FhF  Hitch force applied to the body at the front hitch location, FhF_{x}, FhF_{y}, and FhF_{z}, in the vehiclefixed frame 
Front hitch moments  MhF  Hitch moment at the front hitch location, MhF_{x}, MhF_{y}, and MhF_{z}, about the vehiclefixed frame 
Rear hitch forces  FhR  Hitch force applied to the body at the rear hitch location, FhR_{x}, FhR_{y}, and FhR_{z}, in the vehiclefixed frame 
Rear hitch moments  MhR  Hitch moment at the rear hitch location, MhR_{x}, MhR_{y}, and MhR_{z}, about the vehiclefixed frame 
Initial longitudinal position 
 Initial vehicle CG displacement along the earthfixed Xaxis 
Initial yaw angle 
 Initial rotation of the vehiclefixed frame about the earthfixed Zaxis (yaw) 
Initial longitudinal velocity 
 Initial vehicle CG velocity along the vehiclefixed xaxis 
Initial yaw rate 
 Initial vehicle angular velocity about the vehiclefixed zaxis (yaw rate) 
Initial lateral position 
 Initial vehicle CG displacement along the earthfixed Yaxis 
Air temperature  AirTemp  Ambient air temperature. Consider this option if you want to vary the temperature during run time. 
Initial lateral velocity 
 Initial vehicle CG velocity along the vehiclefixed yaxis 
Theory
To determine the vehicle motion, the block solves the rigid body planar dynamics equations of motion.
Calculation  Description 

Dynamics  The block solves the rigidbody
planar dynamics equations to determine the vehicle
longitudinal motion. If you set Axle
forces to 
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 vehiclefixed frame. If you set Axle
forces to 
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 vehiclefixed zaxis 
d  Lateral distance from the geometric centerline to the center of mass along the vehiclefixed yaxis 
hh_f, hh_r  Height of the front and rear hitch, respectively, above the axle plane along the vehiclefixed zaxis 
dh_f, dh_r  Longitudinal distance of the front and rear hitch, respectively, from the normal projection point of tractor CG onto the common axle plane 
wf, wm, wr  Front, middle, and rear track width, respectively 
This table summarizes the block implementation for the drag calculation.
Calculation  Description 

Coordinate transformation  The block transforms the wind speeds from the inertial frame to the vehiclefixed 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. 
To enable the mapped corner stiffness and relaxation length dynamic
parameters, set Axle forces to External
longitudinal forces
or External longitudinal
velocity
.
Parameter Settings  Description  

Mapped Corner Stiffness  Include Relaxation Length Dynamics  

 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. 

 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. 

 The block uses constant corner stiffness values. 
Ports
Input
WhlAngF
— Front wheel steering angles
scalar
 array
Front wheel steering angles, δ_{F}, in rad.
Vehicle Track Setting  Variable  Signal Dimension 

 δ_{F}  Scalar –


$${\delta}_{F}=[\begin{array}{cc}{\delta}_{fl}& {\delta}_{fr}\end{array}]\text{or}\left[\begin{array}{c}{\delta}_{fl}\\ {\delta}_{fr}\end{array}\right]$$  Array – 
Dependencies
To enable this port, under Input signals, select Front wheel steering.
WhlAngM
— Middle wheel steering angles
scalar
 array
Middle wheel steering angles, δ_{M}, in rad.
Vehicle Track Setting  Variable  Signal Dimension 

Single 3axle  δ_{M}  Scalar –

Dual 3axle 
$${\delta}_{M}=[\begin{array}{cc}{\delta}_{ml}& {\delta}_{mr}\end{array}]\text{or}\left[\begin{array}{c}{\delta}_{ml}\\ {\delta}_{mr}\end{array}\right]$$  Array – 
Dependencies
To enable this port:
Set Vehicle track to
Single 3axle
orDual 3axle
.To enable this port, under Input signals, select Middle wheel steering.
WhlAngR
— Rear wheel steering angles
scalar
 array
Rear wheel steering angles, δ_{R}, in rad.
Vehicle Track Setting  Variable  Signal Dimension 

 δ_{R}  Scalar –


$${\delta}_{R}=[\begin{array}{cc}{\delta}_{rl}& {\delta}_{rr}\end{array}]\text{or}\left[\begin{array}{c}{\delta}_{rl}\\ {\delta}_{rr}\end{array}\right]$$  Array – 
Dependencies
To enable this port, under Input signals, select Rear wheel steering.
xdotin
— Longitudinal velocity
scalar
Vehicle CG velocity along the vehiclefixed xaxis, in m/s.
Dependencies
To enable this port, set Axle forces to
External longitudinal
velocity
.
FwF
— Total force on the front wheels
scalar
 array
Force on the front wheels, Fw_{F}, along the vehiclefixed axis, in N.
Vehicle Track Setting  Axle Forces Setting  Description  Variable  Signal Dimension 

 External longitudinal
forces  Longitudinal force on the front wheel 
$$FwF=F{x}_{f}$$
 Scalar –

External
forces  Longitudinal and lateral forces on the front wheel 
$$FwF=\left[\begin{array}{cc}F{x}_{f}& F{y}_{f}\end{array}\right]\text{or}\left[\begin{array}{c}F{x}_{f}\\ F{y}_{f}\end{array}\right]$$
 Array –  
 External longitudinal
forces  Longitudinal force on the front wheels 
$$FwF=\left[\begin{array}{cc}{F}_{xfl}& {F}_{xfr}\end{array}\right]\text{or}\left[\begin{array}{c}{F}_{xfl}\\ {F}_{xfr}\end{array}\right]$$
 Array – 
External
forces  Longitudinal and lateral forces on the front wheels 
$$FwF=\left[\begin{array}{cc}{F}_{xfl}& {F}_{xfr}\\ {F}_{yfl}& {F}_{yfr}\end{array}\right]$$
 Array –

Dependencies
To enable this port, set Axle forces to one of these options:
External longitudinal forces
External forces
FwM
— Total force on the middle wheels
scalar
 array
Force on the middle wheels, Fw_{M}, along the vehiclefixed axis, in N.
Vehicle Track Setting  Axle Forces Setting  Description  Variable  Signal Dimension 

 External longitudinal
forces  Longitudinal force on the middle wheel 
$$FwM=F{x}_{r}$$
 Scalar –

External
forces  Longitudinal and lateral forces on the middle wheel 
$$FwM=\left[\begin{array}{cc}F{x}_{m}& F{y}_{m}\end{array}\right]\text{or}\left[\begin{array}{c}F{x}_{m}\\ F{y}_{m}\end{array}\right]$$
 Array –  
 External longitudinal
forces  Longitudinal force on the middle wheels 
$$FwM=\left[\begin{array}{cc}{F}_{xml}& {F}_{xmr}\end{array}\right]\text{or}\left[\begin{array}{c}{F}_{xml}\\ {F}_{xmr}\end{array}\right]$$
 Array – 
External
forces  Longitudinal and lateral forces on the middle wheels 
$$FwM=\left[\begin{array}{cc}{F}_{xml}& {F}_{xmr}\\ {F}_{yml}& {F}_{ymr}\end{array}\right]$$
 Array –

Dependencies
To enable this port, set:
Vehicle track to
Single 3axle
orDual 3axle
.Axle forces to
External longitudinal forces
orExternal forces
.
FwR
— Total force on the rear wheels
scalar
 array
Force on the rear wheels, Fw_{R}, along the vehiclefixed axis, in N.
Vehicle Track Setting  Axle Forces Setting  Description  Variable  Signal Dimension 

 External longitudinal
forces  Longitudinal force on the rear wheel 
$$FwR=F{x}_{r}$$
 Scalar –

External
forces  Longitudinal and lateral forces on the rear wheel 
$$FwR=\left[\begin{array}{cc}F{x}_{r}& F{y}_{r}\end{array}\right]\text{or}\left[\begin{array}{c}F{x}_{r}\\ F{y}_{r}\end{array}\right]$$
 Array –  
 External longitudinal
forces  Longitudinal force on the rear wheels 
$$FwR=\left[\begin{array}{cc}{F}_{xrl}& {F}_{xrr}\end{array}\right]\text{or}\left[\begin{array}{c}{F}_{xrl}\\ {F}_{xrr}\end{array}\right]$$
 Array – 
External
forces  Longitudinal and lateral forces on the rear wheels 
$$FwR=\left[\begin{array}{cc}{F}_{xrl}& {F}_{xrr}\\ {F}_{yrl}& {F}_{yrr}\end{array}\right]$$
 Array –

Dependencies
To enable this port, set:
Vehicle track to
Single 3axle
,Single 2axle
,Dual 3axle
orDual 2axle
.Axle forces to
External longitudinal forces
orExternal forces
.
FExt
— External force on the vehicle CG
array
External forces applied to the vehicle CG,
F_{xext},
F_{yext},
F_{zext}, in
vehiclefixed frame, in N. The signal vector dimensions are
[1x3]
or [3x1]
.
Dependencies
To enable this port, under Input signals, select External forces.
MExt
— External moment about vehicle CG
array
External moment about the vehicle CG,
M_{x},
M_{y},
M_{z}, in the
vehiclefixed frame, in N·m. The signal vector dimensions are
[1x3]
or [3x1]
.
Dependencies
To enable this port, under Input signals, select External moments.
FhF
— Front hitch force on the body
array
Hitch force applied to the body at the front hitch location,
FhF_{x},
FhF_{y},
FhF_{z}, in the vehiclefixed frame, in
N, specified as a 1by3
or 3by1
array.
Dependencies
To enable this port, under Input signals, select Front hitch forces.
MhF
— Front hitch moment about body
array
Hitch moment at the front hitch location,
MhF_{x},
MhF_{y},
MhF_{z}, about the
vehiclefixed frame, in N·m, specified as a 1by3
or
3by1
array.
Dependencies
To enable this port, under Input signals, select Front hitch moments.
FhR
— Rear hitch force on the body
array
Hitch force applied to the body at the rear hitch location,
FhR_{x},
FhR_{y},
FhR_{z}, in the vehiclefixed frame, in
N, specified as a 1by3
or 3by1
array.
Dependencies
To enable this port, under Input signals, select Rear hitch forces.
MhR
— Rear hitch moment about body
array
Hitch moment at the rear hitch location,
MhR_{x},
MhR_{y},
MhR_{z}, about the
vehiclefixed frame, in N·m, specified as a 1by3
or
3by1
array.
Dependencies
To enable this port, under Input signals, select Rear hitch moments.
WindXYZ
— Wind speed
array
Wind speed, W_{x},
W_{y},
W_{z}, along the inertial
X, Y, and
Zaxes, in m/s. The signal vector dimensions
are 1by3
or 3by1
.
Dependencies
To enable this port, under Input signals, select External wind.
Mu
— Tire friction coefficient
array
Tire friction coefficient, μ. The value is dimensionless.
Vehicle Track Setting  Description  Variable  Signal Dimension 

Single 1axle  Friction coefficient on the wheels 
$$Mu={\mu}_{f}$$  Array – 
Dual 1axle  Friction coefficient on the wheels 
$$Mu=\left[\begin{array}{cc}{\mu}_{fl}& {\mu}_{fr}\end{array}\right]\text{or}\left[\begin{array}{c}{\mu}_{fl}\\ {\mu}_{fr}\end{array}\right]$$  Array – 
Single 2axle  Friction coefficient on the wheels 
$$Mu=\left[\begin{array}{cc}{\mu}_{f}& {\mu}_{r}\end{array}\right]\text{or}\left[\begin{array}{c}{\mu}_{f}\\ {\mu}_{r}\end{array}\right]$$  Array – 
Dual 2axle  Friction coefficient on the wheels 
$$Mu=\left[\begin{array}{cc}{\mu}_{fl}& {\mu}_{fr}\\ {\mu}_{rl}& {\mu}_{rr}\end{array}\right]$$  Array – 
Single 3axle  Friction coefficient on the wheels 
$$Mu=\left[\begin{array}{ccc}{\mu}_{f}& {\mu}_{m}& {\mu}_{r}\end{array}\right]\text{or}\left[\begin{array}{c}{\mu}_{f}\\ {\mu}_{m}\\ {\mu}_{r}\end{array}\right]$$  Array – 
Dual 3axle  Friction coefficient on the wheels 
$$Mu=\left[\begin{array}{cc}{\mu}_{fl}& {\mu}_{fr}\\ {\mu}_{ml}& {\mu}_{mr}\\ {\mu}_{rl}& {\mu}_{rr}\end{array}\right]$$  Array – 
Dependencies
To enable this port, under Input signals, select External friction.
AirTemp
— Ambient air temperature
scalar
Ambient air temperature, in K.
Dependencies
To enable this port, under Input signals, select Air temperature.
X_o
— Initial longitudinal position
scalar
Initial vehicle CG displacement along the earthfixed Xaxis, in m.
Dependencies
To enable this port, under Input signals, select Initial longitudinal position.
Y_o
— Initial lateral position
scalar
Initial vehicle CG displacement along the earthfixed Yaxis, in m.
Dependencies
To enable this port, under Input signals, select Initial lateral position.
xdot_o
— Initial longitudinal position
scalar
Initial vehicle CG velocity along the vehiclefixed xaxis, in m/s.
Dependencies
To enable this port:
Set Axle forces to one of these options:
External longitudinal forces
External forces
Under Input signals, select Initial longitudinal velocity
ydot_o
— Initial lateral position
scalar
Initial vehicle CG velocity along the vehiclefixed yaxis, in m/s.
Dependencies
To enable this port, under Input signals, select Initial lateral velocity.
psi_o
— Initial yaw angle
scalar
Rotation of the vehiclefixed frame about the earthfixed Zaxis (yaw), in rad.
Dependencies
To enable this port, under Input signals, select Initial yaw angle.
r_o
— Initial yaw rate
scalar
Vehicle angular velocity about the vehiclefixed zaxis (yaw rate), in rad/s.
Dependencies
To enable this port, under Input signals, select Initial yaw rate.
Output
Info
— Trailer data
bus
Trailer data, returned as a bus signal containing these block values.
Signal  Description  Value  Units  

InertFrm  Cg  Disp  X  Vehicle CG displacement along the earthfixed Xaxis  Computed  m  
Y  Vehicle CG displacement along the earthfixed Yaxis  Computed  m  
Z  Vehicle CG displacement along the earthfixed Zaxis  0  m  
Vel  Xdot  Vehicle CG velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Vehicle CG velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Vehicle CG velocity along the earthfixed Zaxis  0  m/s  
Ang  phi  Rotation of the vehiclefixed frame about the earthfixed Xaxis (roll)  0  rad  
theta  Rotation of the vehiclefixed frame about the earthfixed Yaxis (pitch)  0  rad  
psi  Rotation of the vehiclefixed frame about the earthfixed Zaxis (yaw)  Computed  rad  
FrntAxl  Lft  Disp  X  Front left wheel displacement along the earthfixed Xaxis  Computed  m  
Y  Front left wheel displacement along the earthfixed Yaxis  Computed  m  
Z  Front left wheel displacement along the earthfixed Zaxis  0  m  
Vel  Xdot  Front left wheel velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Front left wheel velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Front left wheel velocity along the earthfixed Zaxis  0  m/s  
Rght  Disp  X  Front right wheel displacement along the earthfixed Xaxis  Computed  m  
Y  Front right wheel displacement along the earthfixed Yaxis  Computed  m  
Z  Front right wheel displacement along the earthfixed Zaxis  0  m  
Vel  Xdot  Front right wheel velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Front right wheel velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Front right wheel velocity along the earthfixed Zaxis  0  m/s  
MidlAxl  Lft  Disp  X  Middle left wheel displacement along the earthfixed Xaxis  Computed  m  
Y  Middle left wheel displacement along the earthfixed Yaxis  Computed  m  
Z  Middle left wheel displacement along the earthfixed Zaxis  0  m  
Vel  Xdot  Middle left wheel velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Middle left wheel velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Middle left wheel velocity along the earthfixed Zaxis  0  m/s  
Rght  Disp  X  Middle right wheel displacement along the earthfixed Xaxis  Computed  m  
Y  Middle right wheel displacement along the earthfixed Yaxis  Computed  m  
Z  Middle right wheel displacement along the earthfixed Zaxis  0  m  
Vel  Xdot  Middle right wheel velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Middle right wheel velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Middle right wheel velocity along the earthfixed Zaxis  0  m/s  
RearAxl  Lft  Disp  X  Rear left wheel displacement along the earthfixed Xaxis  Computed  m  
Y  Rear left wheel displacement along the earthfixed Yaxis  Computed  m  
Z  Rear left wheel displacement along the earthfixed Zaxis  0  m  
Vel  Xdot  Rear left wheel velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Rear left wheel velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Rear left wheel velocity along the earthfixed Zaxis  0  m/s  
Rght  Disp  X  Rear right wheel displacement along the earthfixed Xaxis  Computed  m  
Y  Rear right wheel displacement along the earthfixed Yaxis  Computed  m  
Z  Rear right wheel displacement along the earthfixed Zaxis  0  m  
Vel  Xdot  Rear right wheel velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Rear right wheel velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Rear right wheel velocity along the earthfixed Zaxis  0  m/s  
Geom  Disp  X  Trailer body offset from the axle plane along the earthfixed Xaxis  Computed  m  
Y  Trailer body offset from the center plane along the earthfixed Yaxis  Computed  m  
Z  Trailer body offset from the axle plane along the earthfixed Zaxis  Computed  m  
Vel  Xdot  Trailer body offset velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Trailer body offset velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Trailer body offset velocity along the earthfixed Zaxis  Computed  m/s  
HitchF  Disp  X  Trailer front hitch offset from the axle plane along the earthfixed Xaxis  Computed  m  
Y  Trailer front hitch offset from the center plane along the earthfixed Yaxis  Computed  m  
Z  Trailer front hitch offset from the axle plane along the earthfixed Zaxis  Computed  m  
Vel  Xdot  Trailer front hitch offset velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Trailer front hitch offset velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Trailer front hitch offset velocity along the earthfixed Zaxis  Computed  m/s  
HitchR  Disp  X  Trailer rear hitch offset from the axle plane along the earthfixed Xaxis  Computed  m  
Y  Trailer rear hitch offset from the center plane along the earthfixed Yaxis  Computed  m  
Z  Trailer rear hitch offset from the axle plane along the earthfixed Zaxis  Computed  m  
Vel  Xdot  Trailer rear hitch offset velocity along the earthfixed Xaxis  Computed  m/s  
Ydot  Trailer rear hitch offset velocity along the earthfixed Yaxis  Computed  m/s  
Zdot  Trailer rear hitch offset velocity along the earthfixed Zaxis  Computed  m/s  
BdyFrm  Cg  Vel  xdot  Vehicle CG velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Vehicle CG velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Vehicle CG velocity along the vehiclefixed zaxis  0  m/s  
Ang  Beta  Body slip angle, β
$$\beta =\frac{{V}_{y}}{{V}_{x}}$$
 Computed  rad  
AngVel  p  Vehicle angular velocity about the vehiclefixed xaxis (roll rate)  0  rad/s  
q  Vehicle angular velocity about the vehiclefixed yaxis (pitch rate)  0  rad/s  
r  Vehicle angular velocity about the vehiclefixed zaxis (yaw rate)  Computed  rad/s  
Acc  ax  Vehicle CG acceleration along the vehiclefixed xaxis  Computed  gn  
ay  Vehicle CG acceleration along the vehiclefixed yaxis  Computed  gn  
az  Vehicle CG acceleration along the vehiclefixed zaxis  0  gn  
xddot  Vehicle CG acceleration along the vehiclefixed xaxis  Computed  m/s^2  
yddot  Vehicle CG acceleration along the vehiclefixed yaxis  Computed  m/s^2  
zddot  Vehicle CG acceleration along the vehiclefixed zaxis  0  m/s^2  
AngAcc  pdot  Vehicle angular acceleration about the vehiclefixed xaxis  0  rad/s  
qdot  Vehicle angular acceleration about the vehiclefixed yaxis  0  rad/s  
rdot  Vehicle angular acceleration about the vehiclefixed zaxis  Computed  rad/s  
Forces  Body  Fx  Net force on the vehicle CG along the vehiclefixed xaxis  Computed  N  
Fy  Net force on the vehicle CG along the vehiclefixed yaxis  Computed  N  
Fz  Net force on the vehicle CG along the vehiclefixed zaxis  0  N  
Ext  Fx  External force on the vehicle CG along the vehiclefixed xaxis  Computed  N  
Fy  External force on the vehicle CG along the vehiclefixed yaxis  Computed  N  
Fz  External force on the vehicle CG along the vehiclefixed zaxis  0  N  
HitchF  Fx  Hitch front force applied to the body at the hitch location along the vehiclefixed xaxis  Computed  N  
Fy  Hitch front force applied to the body at the hitch location along the vehiclefixed yaxis  Computed  N  
Fz  Hitch front force applied to the body at the hitch location along the vehiclefixed zaxis  Computed  N  
HitchR  Fx  Hitch rear force applied to the body at the hitch location along the vehiclefixed xaxis  Computed  N  
Fy  Hitch rear force applied to the body at the hitch location along the vehiclefixed yaxis  Computed  N  
Fz  Hitch rear force applied to the body at the hitch location along the vehiclefixed zaxis  Computed  N  
FrntAxl  Lft  Fx  Longitudinal force on the left front wheel along the vehiclefixed xaxis  Computed  N  
Fy  Lateral force on the left front wheel along the vehiclefixed yaxis  Computed  N  
Fz  Normal force on the left front wheel along the vehiclefixed zaxis  Computed  N  
Rght  Fx  Longitudinal force on the right front wheel along the vehiclefixed xaxis  Computed  N  
Fy  Lateral force on the right front wheel along the vehiclefixed yaxis  Computed  N  
Fz  Normal force on the right front wheel along the vehiclefixed zaxis  Computed  N  
MidlAxl  Lft  Fx  Longitudinal force on the left middle wheel along the vehiclefixed xaxis  Computed  N  
Fy  Lateral force on the left middle wheel along the vehiclefixed yaxis  Computed  N  
Fz  Normal force on the left middle wheel along the vehiclefixed zaxis  Computed  N  
Rght  Fx  Longitudinal force on the right middle wheel along the vehiclefixed xaxis  Computed  N  
Fy  Lateral force on the right middle wheel along the vehiclefixed yaxis  Computed  N  
Fz  Normal force on the right middle wheel along the vehiclefixed zaxis  Computed  N  
RearAxl  Lft  Fx  Longitudinal force on the left rear wheel along the vehiclefixed xaxis  Computed  N  
Fy  Lateral force on the left rear wheel along the vehiclefixed yaxis  Computed  N  
Fz  Normal force on the left rear wheel along the vehiclefixed zaxis  Computed  N  
Rght  Fx  Longitudinal force on the right rear wheel along the vehiclefixed xaxis  Computed  N  
Fy  Lateral force on the right rear wheel along the vehiclefixed yaxis  Computed  N  
Fz  Normal force on the right rear wheel along the vehiclefixed zaxis  Computed  N  
Tires  FrntTires  Lft  Fx  Front left tire force along the vehiclefixed xaxis  Computed  N  
Fy  Front left tire force along the vehiclefixed yaxis  Computed  N  
Fz  Front left tire force along the vehiclefixed zaxis  Computed  N  
Rght  Fx  Front right tire force along the vehiclefixed xaxis  Computed  N  
Fy  Front right tire force along the vehiclefixed yaxis  Computed  N  
Fz  Front right tire force along the vehiclefixed zaxis  Computed  N  
RearTires  Lft  Fx  Rear left tire force along the vehiclefixed xaxis  Computed  N  
Fy  Rear left tire force along the vehiclefixed yaxis  Computed  N  
Fz  Rear left tire force along the vehiclefixed zaxis  Computed  N  
Rght  Fx  Rear right tire force along the vehiclefixed xaxis  Computed  N  
Fy  Rear right tire force along the vehiclefixed yaxis  Computed  N  
Fz  Rear right tire force along the vehiclefixed zaxis  Computed  
Drag  Fx  Drag force on the vehicle CG along the vehiclefixed xaxis  Computed  N  
Fy  Drag force on the vehicle CG along the vehiclefixed yaxis  Computed  N  
Fz  Drag force on the vehicle CG along the vehiclefixed zaxis  Computed  N  
Grvty  Fx  Gravity force on the vehicle CG along the vehiclefixed xaxis  Computed  N  
Fy  Gravity force on the vehicle CG along the vehiclefixed yaxis  Computed  N  
Fz  Gravity force on the vehicle CG along the vehiclefixed zaxis  Computed  N  
Moments  Body  Mx  Body moment on the vehicle CG about the vehiclefixed xaxis  0  N·m  
My  Body moment on the vehicle CG about the vehiclefixed yaxis  Computed  N·m  
Mz  Body moment on the vehicle CG about the vehiclefixed zaxis  0  N·m  
Drag  Mx  Drag moment on the vehicle CG about the vehiclefixed xaxis  0  N·m  
My  Drag moment on the vehicle CG about the vehiclefixed yaxis  Computed  N·m  
Mz  Drag moment on the vehicle CG about the vehiclefixed zaxis  0  N·m  
Ext  Mx  External moment on the vehicle CG about the vehiclefixed xaxis  0  N·m  
My  External moment on the vehicle CG about the vehiclefixed yaxis  Computed  N·m  
Mz  External moment on the vehicle CG about the vehiclefixed zaxis  0  N·m  
HitchF  Mx  Hitch moment at the front hitch location about vehiclefixed xaxis  0  N·m  
My  Hitch moment at the front hitch location about vehiclefixed yaxis  Computed  N·m  
Mz  Hitch moment at the front hitch location about vehiclefixed zaxis  0  N·m  
HitchR  Mx  Hitch moment at the rear hitch location about vehiclefixed xaxis  0  N·m  
My  Hitch moment at the rear hitch location about vehiclefixed yaxis  Computed  N·m  
Mz  Hitch moment at the rear hitch location about vehiclefixed zaxis  0  N·m  
FrntAxl  Lft  Disp  x  Front left wheel displacement along the vehiclefixed xaxis  Computed  m  
y  Front left wheel displacement along the vehiclefixed yaxis  Computed  m  
z  Front left wheel displacement along the vehiclefixed zaxis  Computed  m  
Vel  xdot  Front left wheel velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Front left wheel velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Front left wheel velocity along the vehiclefixed zaxis  0  m/s  
Rght  Disp  x  Front right wheel displacement along the vehiclefixed xaxis  Computed  m  
y  Front right wheel displacement along the vehiclefixed yaxis  Computed  m  
z  Front right wheel displacement along the vehiclefixed zaxis  Computed  m  
Vel  xdot  Front right wheel velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Front right wheel velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Front right wheel velocity along the vehiclefixed zaxis  0  m/s  
Steer  WhlAngFL  Front left wheel steering angle  Computed  rad  
WhlAngFR  Front right wheel steering angle  Computed  rad  
MidlAxl  Lft  Disp  x  Middle left wheel displacement along the vehiclefixed xaxis  Computed  m  
y  Middle left wheel displacement along the vehiclefixed yaxis  Computed  m  
z  Middle left wheel displacement along the vehiclefixed zaxis  Computed  m  
Vel  xdot  Middle left wheel velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Middle left wheel velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Middle left wheel velocity along the vehiclefixed zaxis  0  m/s  
Rght  Disp  x  Middle right wheel displacement along the vehiclefixed xaxis  Computed  m  
y  Middle right wheel displacement along the vehiclefixed yaxis  Computed  m  
z  Middle right wheel displacement along the vehiclefixed zaxis  Computed  m  
Vel  xdot  Middle right wheel velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Middle right wheel velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Middle right wheel velocity along the vehiclefixed zaxis  0  m/s  
Steer  WhlAngRL  Middle left wheel steering angle  Computed  rad  
WhlAngRR  Middle right wheel steering angle  Computed  rad  
RearAxl  Lft  Disp  x  Rear left wheel displacement along the vehiclefixed xaxis  Computed  m  
y  Rear left wheel displacement along the vehiclefixed yaxis  Computed  m  
z  Rear left wheel displacement along the vehiclefixed zaxis  Computed  m  
Vel  xdot  Rear left wheel velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Rear left wheel velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Rear left wheel velocity along the vehiclefixed zaxis  0  m/s  
Rght  Disp  x  Rear right wheel displacement along the vehiclefixed xaxis  Computed  m  
y  Rear right wheel displacement along the vehiclefixed yaxis  Computed  m  
z  Rear right wheel displacement along the vehiclefixed zaxis  Computed  m  
Vel  xdot  Rear right wheel velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Rear right wheel velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Rear right wheel velocity along the vehiclefixed zaxis  0  m/s  
Steer  WhlAngRL  Rear left wheel steering angle  Computed  rad  
WhlAngRR  Rear right wheel steering angle  Computed  rad  
HitchF  Disp  x  Front hitch offset from axle plane along the vehiclefixed xaxis  Input  m  
y  Front hitch offset from center plane along the vehiclefixed yaxis  Input  m  
z  Front hitch offset from axle plane along the earthfixed zaxis  Input  m  
Vel  xdot  Front hitch offset velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Front hitch offset velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Front hitch offset velocity along the vehiclefixed zaxis  0  m/s  
HitchR  Disp  x  Rear hitch offset from axle plane along the vehiclefixed xaxis  Input  m  
y  Rear hitch offset from center plane along the vehiclefixed yaxis  Input  m  
z  Rear hitch offset from axle plane along the earthfixed zaxis  Input  m  
Vel  xdot  Rear hitch offset velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Rear hitch offset velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Rear hitch offset velocity along the vehiclefixed zaxis  0  m/s  
Pwr  Ext  Applied external power  Computed  W  
HitchF  Front hitch power  Computed  W  
HitchR  Rear hitch power  Computed  W  
Drag  Power loss due to drag  Computed  W  
Geom  Disp  x  Trailer offset from axle plane along the vehiclefixed xaxis  Input  m  
y  Trailer offset from center plane along the vehiclefixed yaxis  Input  m  
z  Trailer offset from axle plane along the vehiclefixed zaxis  Input  m  
Vel  xdot  Trailer offset velocity along the vehiclefixed xaxis  Computed  m/s  
ydot  Trailer offset velocity along the vehiclefixed yaxis  Computed  m/s  
zdot  Trailer offset velocity along the vehiclefixed zaxis  0  m/s  
Ang  Beta  Body slip angle, β
$$\beta =\frac{{V}_{y}}{{V}_{x}}$$
 Computed  rad 
Signal  Description  Value  Units  

PwrInfo  PwrTrnsfrd  PwrFxExt  Externally applied longitudinal force power  Computed  W  
PwrFyExt  Externally applied lateral force power  Computed  W  
PwrMzExt  Externally applied yaw moment power  Computed  W  
PwrFwFLx  Longitudinal force applied at the front left axle power  Computed  W  
PwrFwFLy  Lateral force applied at the front left axle power  Computed  W  
PwrFwFRx  Longitudinal force applied at the front right axle power  Computed  W  
PwrFwFRy  Lateral force applied at the front right axle power  Computed  W  
PwrFwMLx  Longitudinal force applied at the middle left axle power  Computed  W  
PwrFwMLy  Lateral force applied at the middle left axle power  Computed  W  
PwrFwMRx  Longitudinal force applied at the middle right axle power  Computed  W  
PwrFwMRy  Lateral force applied at the middle right axle power  Computed  W  
PwrFwRLx  Longitudinal force applied at the rear left axle power  Computed  W  
PwrFwRLy  Lateral force applied at the rear left axle power  Computed  W  
PwrFwRRx  Longitudinal force applied at the rear right axle power  Computed  W  
PwrFwRRy  Lateral force applied at the rear right axle power  Computed  W  
PwrNotTrnsfrd  PwrFxDrag  Longitudinal drag force power  Computed  W  
PwrFyDrag  Lateral drag force power  Computed  W  
PwrMzDrag  Drag pitch moment power  Computed  W  
PwrStored  PwrStoredGrvty  Rate change in gravitational potential energy  Computed  W  
PwrStoredxdot  Rate of change of longitudinal kinetic energy  Computed  W  
PwrStoredydot  Rate of change of lateral kinetic energy  Computed  W  
PwrStoredr  Rate of change of rotational yaw kinetic energy  Computed  W 
xdot
— Trailer longitudinal velocity
scalar
Trailer CG velocity along the vehiclefixed xaxis, in m/s.
ydot
— Trailer lateral velocity
scalar
Trailer CG velocity along the vehiclefixed yaxis, in m/s.
psi
— Yaw
scalar
Rotation of the vehiclefixed frame about the earthfixed Zaxis (yaw), in rad.
r
— Yaw rate
scalar
Vehicle angular velocity, r, about the vehiclefixed zaxis (yaw rate), in rad/s.
FzF
— Normal force on the front wheels
scalar
 array
Normal force on the front wheels, Fz_{F}, along the vehiclefixed zaxis, in N.
Vehicle Track Setting  Description  Variable  Signal Dimension 

 Normal force on the front axle 
$$FzF=F{z}_{f}$$
 Scalar – 
 Normal force on the front wheels 
$$FzF=\left[\begin{array}{cc}F{z}_{fl}& F{z}_{fr}\end{array}\right]$$
 Array – 
FzM
— Normal force on the middle wheels
scalar
 array
Normal force on the middle wheels, Fz_{M}, along the vehiclefixed zaxis, in N.
Vehicle Track Setting  Description  Variable  Signal Dimension 

 Normal force on the middle axle 
$$FzM=F{z}_{m}$$
 Scalar – 
 Normal force on the right and left middle wheels 
$$FzM=\left[\begin{array}{cc}F{z}_{ml}& F{z}_{rl}\end{array}\right]$$
 Array – 
Dependencies
To enable this port, set Vehicle track to
Single 3axle
or Dual
3axle
.
FzR
— Normal force on the rear wheels
scalar
 array
Normal force on the rear wheels, Fz_{R}, along the vehiclefixed zaxis, in N.
Vehicle Track Setting  Description  Variable  Signal Dimension 

 Normal force on the rear wheel 
$$FzR=F{z}_{r}$$
 Scalar – 
 Normal force on the rear wheels 
$$FzR=\left[\begin{array}{cc}F{z}_{rl}& F{z}_{rr}\end{array}\right]$$
 Array – 
Fhz
— Normal component of hitch force on the body
scalar
Normal hitch force applied to the body at the hitch location, Fh_{z}, in the vehiclefixed frame zaxis, in N.
If you enable the Hitch forces parameter, the block offsets the normal hitch force, Fh_{z}, with the value of the Fh input port component along the vehiclefixed zaxis.
Parameters
Vehicle track
— Type of vehicle track
Dual 2axle
(default)  Single 1axle
 Dual 1axle
 Single 2axle
  Dual 3axle
Use the Vehicle track parameter to specify the number of tracks.
Vehicle Track Setting  Implementation 

 Trailer with a single track and one axle.

 Trailer with a dual track and one axle. Forces act at the axle hardpoint locations. 
 Trailer with a single track and two axles.

 Trailer with a dual track and two axles. Forces act at the axle hardpoint locations. 
 Trailer with a single track and three axles.

 Trailer with a dual track and three axles. Forces act at the axle hardpoint locations. 
Axle forces
— Type of axle force
External forces
(default)  External longitudinal velocity
 External longitudinal forces
Use the Axle forces parameter to specify the type of force.
Axle Forces Setting  Implementation 







Front wheel steering
— WhlAngF
input port
off
(default)  on
Select to create input port WhlAngF
.
Middle wheel steering
— WhlAngM
input port
off
(default)  on
Select to create input port WhlAngM
.
Dependencies
To enable this parameter, set Vehicle track to
Single 3axle
or Dual
3axle
.
Rear wheel steering
— WhlAngR
input port
off
(default)  on
Select to create input port WhlAngR
.
Dependencies
To enable this parameter, set Vehicle track to
Single 2axle
, Dual
2axle
, Single 3axle
, or
Dual 3axle
.
External wind
— WindXYZ
input port
off
(default)  on
Select to create input port WindXYZ
.
External friction
— Mu
input port
off
(default)  on
Select to create input port Mu
.
Dependencies
To enable this parameter, set Axle forces to one of these options:
External longitudinal forces
External forces
External forces
— FExt
input port
off
(default)  on
Select to create input port FExt
.
External moments
— MExt
input port
off
(default)  on
Select to create input port MExt
.
Front hitch forces
— FhF
input port
on
(default)  off
Select to create input port Fh
.
Front hitch moments
— MhF
input port
on
(default)  off
Select to create input port Mh
.
Rear hitch forces
— FhR
input port
off
(default)  on
Select to create input port Fh
.
Rear hitch moments
— MhR
input port
off
(default)  on
Select to create input port Mh
.
Initial longitudinal position
— X_o
input port
off
(default)  on
Select to create input port X_o
.
Initial yaw angle
— psi_o
input port
off
(default)  on
Select to create input port psi_o
.
Initial longitudinal velocity
— xdot_o
input port
off
(default)  on
Select to create input port xdot_o
.
Dependencies
To enable this parameter, set Axle forces to
External longitudinal forces
or
External forces
.
Initial yaw rate
— r_o
input port
off
(default)  on
Select to create input port r_o
.
Initial lateral position
— Y_o
input port
off
(default)  on
Select to create input port Y_o
.
Air temperature
— AirTemp
input port
off
(default)  on
Select to create input port AirTemp
.
Initial lateral velocity
— ydot_o
input port
off
(default)  on
Select to create input port ydot_o
.
Number of wheels on front axle, NF
— Front wheel count
2
(default)  scalar
Number of wheels on the front axle, N_{F}. The value is dimensionless.
Number of wheels on middle axle, NM
— Middle wheel count
2
(default)  scalar
Number of wheels on the middle axle, N_{M}. The value is dimensionless.
Dependencies
To enable this parameter, set Vehicle track to
Single 3axle
or Dual
3axle
.
Number of wheels on rear axle, NR
— Rear wheel count
2
(default)  scalar
Number of wheels on the rear axle, N_{R}. The value is dimensionless.
To enable this parameter, set Vehicle track to
Single 2axle
, Single
3axle
, Dual 2axle
, or
Dual 3axle
.
Vehicle mass, m
— Vehicle mass
26000
(default)  scalar
Vehicle mass, m, in kg.
Longitudinal distance from center of mass to front axle, a
— Distance from CM to front axle
4
(default)  scalar
Distance from the vehicle CM to the front axle, a, in m.
Longitudinal distance from center of mass to middle axle, b
— Distance from CM to middle axle
4.5
(default)  scalar
Distance from vehicle CM to middle axle, b, in m.
Dependencies
To enable this parameter, set Vehicle track to
Single 3axle
or Dual
3axle
.
Longitudinal distance from center of mass to rear axle, c
— Distance from CM to rear axle
5
(default)  scalar
Distance from vehicle CM to the front axle, c, in m.
Dependencies
To enable this parameter, set Vehicle track to
Single 2axle
, Single
3axle
, Single 3axle
, or
Dual 3axle
.
Vertical distance from center of mass to axle plane, h
— Distance from CM to axle plane
2
(default)  scalar
Vertical distance from vehicle CM to the axle plane, h, in m.
Longitudinal distance from center of mass to front hitch, dh_f
— Distance to front hitch
7.5
(default)  scalar
Longitudinal distance from the center of mass to the front hitch, dh_f, in m.
Dependencies
To enable this parameter, on the Input signals pane, select Front hitch forces or Front hitch moments.
Vertical distance from front hitch to axle plane, hh_f
— Distance from front hitch to axle plane
0.6
(default)  scalar
Vertical distance from the front hitch to the axle plane, hh_f, in m.
Dependencies
To enable this parameter, on the Input signals pane, select Front hitch forces or Front hitch moments.
Longitudinal distance from center of mass to rear hitch, dh_r
— Distance to front hitch
7.5
(default)  scalar
Longitudinal distance from the center of mass to the rear hitch, dh_r, in m.
Dependencies
To enable this parameter, on the Input signals pane, select Rear hitch forces or Rear hitch moments.
Vertical distance from front hitch to axle plane, hh_r
— Distance from rear hitch to axle plane
0.6
(default)  scalar
Vertical distance from the rear hitch to the axle plane, hh_r, in m.
Dependencies
To enable this parameter, on the Input signals pane, select Rear hitch forces or Rear hitch moments.
Initial inertial frame longitudinal position, X_o
— Initial inertial X location
0
(default)  scalar
Initial vehicle CG displacement along the earthfixed Xaxis, in m.
Initial longitudinal velocity, xdot_o
— Initial velocity
0
(default)  scalar
Initial vehicle CG velocity along the vehiclefixed xaxis, in m/s.
Dependencies
To enable this parameter, set Axle forces to one of these options:
External longitudinal forces
External forces
Mapped corner stiffness
— Selection
off
(default)  on
Enables mapped corner stiffness calculation.
Dependencies
To enable this parameter, set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Include relaxation length dynamics
— Enable relaxation length dynamics
on
(default)  off
Enables relaxation length dynamics.
Dependencies
To enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Clear Mapped corner stiffness.
Lateral distance from geometric centerline to center of mass, d
— Distance from centerline to CM
0
(default)  scalar
Lateral distance from the geometric centerline to the center of mass, d, in m, along the vehiclefixed 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.
Lateral distance from geometric centerline to front hitch, hl_f
— Distance from centerline to front hitch
0
(default)  scalar
Lateral distance from the geometric centerline to the front hitch, hl_f, in m, along the vehiclefixed y. Positive values indicate that the trailer hitch is to the right of the geometric centerline. Negative values indicate that the trailer hitch is to the left of the geometric centerline.
Dependencies
To enable this parameter, on the Input signals pane, select Front hitch forces or Front hitch moments.
Lateral distance from geometric centerline to rear hitch, hl_r
— Distance from centerline to rear hitch
0
(default)  scalar
Lateral distance from the geometric centerline to the rear hitch, hl_r, in m, along the vehiclefixed y. Positive values indicate that the trailer hitch is to the right of the geometric centerline. Negative values indicate that the trailer hitch is to the left of the geometric centerline.
Dependencies
To enable this parameter, on the Input signals pane, select Rear hitch forces or Rear hitch moments.
Front track width, w_f
— Front track width
1.82
(default)  scalar
Front track width, wf, in m.
Dependencies
To enable this parameter, set Vehicle track to
Dual 2axle
, Dual
2axle
, or Dual
3axle
.
Middle track width, w_m
— Middle track width
1.82
(default)  scalar
Middle track width, wm, in m.
Dependencies
To enable this parameter, set Vehicle track to
Dual 3axle
.
Rear track width, w_r
— Rear track width
1.82
(default)  scalar
Rear track width, wr, in m.
Dependencies
To enable this parameter, set Vehicle track to
Dual 2axle
or Dual
3axle
.
Front axle tire corner stiffness, Cy_f
— Front axle tire stiffness
12.3
(default)  scalar
Front tire corner stiffness, Cy_{f}, in N/rad.
Dependencies
To enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Clear Mapped corner stiffness.
Middle axle tire corner stiffness, Cy_m
— Middle axle tire stiffness
11.3
(default)  scalar
Middle tire corner stiffness, Cy_{m}, in N/rad.
Dependencies
To enable this parameter:
Set Vehicle track to one of these options:
Single 3axle
Dual 3axle
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Clear Mapped corner stiffness.
Rear axle tire corner stiffness, Cy_r
— Rear axle tire stiffness
11.3
(default)  scalar
Rear tire corner stiffness, Cy_{r}, in N/rad.
Dependencies
To enable this parameter:
Set Vehicle track to one of these options:
Single 2axle
Dual 2axle
Single 3axle
Dual 3axle
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Clear Mapped corner stiffness.
Front tire(s) relaxation length, sigma_f
— Relaxation length
.1
(default)  scalar
Front tire relaxation length, σ_{f}, in m.
Dependencies
To enable this parameter:
Set Vehicle track to one of these options:
Single 2axle
Dual 2axle
Single 3axle
Dual 3axle
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Do either of these:
Select Mapped corner stiffness.
Clear Mapped corner stiffness and select Include relaxation length dynamics.
Middle tire(s) relaxation length, sigma_m
— Relaxation length
.1
(default)  scalar
Middle tire relaxation length, σ_{m}, in m.
Dependencies
To enable this parameter:
Set Vehicle track to one of these options:
Single 3axle
Dual 3axle
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Do either of these:
Select Mapped corner stiffness.
Clear Mapped corner stiffness and select Include relaxation length dynamics.
Rear tire(s) relaxation length, sigma_r
— Relaxation length
.1
(default)  scalar
Rear tire relaxation length, σ_{r}, in m.
Dependencies
To enable this parameter:
Set Vehicle track to one of these options:
Single 2axle
Dual 2axle
Single 3axle
Dual 3axle
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Do either of these:
Select Mapped corner stiffness.
Clear Mapped corner stiffness and select Include relaxation length dynamics.
Front axle slip angle breakpoints, alpha_f_brk
— Breakpoints
[.1 .1]
(default)  vector
Front axle slip angle breakpoints, α_{fbrk}, in rad.
Dependencies
To enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Select Mapped corner stiffness.
Front axle corner data, Cy_f_data
— Breakpoints
[9e3 9e3]
(default)  vector
Front axle corner data, Cy_{fdata}, in N/rad.
Dependencies
To enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Select Mapped corner stiffness.
Middle axle slip angle breakpoints, alpha_m_brk
— Breakpoints
[.1 .1]
(default)  vector
Middle axle slip angle breakpoints, α_{mbrk}, in rad.
Dependencies
To enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Select Mapped corner stiffness.
Middle axle corner data, Cy_m_data
— Breakpoints
[9e3 9e3]
(default)  vector
Middle axle corner data, Cy_{mdata}, in N/rad.
Dependencies
To enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Select Mapped corner stiffness.
Rear axle slip angle breakpoints, alpha_r_brk
— Breakpoints
[.1 .1]
(default)  vector
Rear axle slip angle breakpoints, α_{rbrk}, in rad.
Dependencies
To enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Select Mapped corner stiffness.
Rear axle corner data, Cy_r_data
— Data
[9e3 9e3]
(default)  vector
Rear axle corner data, Cy_{rdata}, in N/rad.
Dependencies
To enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Select Mapped corner stiffness.
Initial inertial frame lateral displacement, Y_o
— Position
0
(default)  scalar
Initial vehicle CG displacement along the earthfixed Yaxis, in m.
Initial lateral velocity, ydot_o
— Velocity
0
(default)  scalar
Initial vehicle CG velocity along the vehiclefixed yaxis, in m/s.
Yaw polar inertia, Izz
— Inertia
4000
(default)  scalar
Yaw polar inertia, in kg*m^2.
Initial yaw angle, psi_o
— Psi rotation
0
(default)  scalar
Rotation of the vehiclefixed frame about earthfixed Zaxis (yaw), in rad.
Initial yaw rate, r_o
— Yaw rate
0
(default)  scalar
Vehicle angular velocity about the vehiclefixed zaxis (yaw rate), in rad/s.
Longitudinal drag area, Af
— Effective vehicle crosssectional area
2
(default)  scalar
Effective vehicle crosssectional area, A_{f}, to calculate the aerodynamic drag force on the vehicle, in m^{2}.
Longitudinal drag coefficient, Cd
— Air drag coefficient
.3
(default)  scalar
Air drag coefficient, C_{d}. The value is dimensionless.
Longitudinal lift coefficient, Cl
— Air lift coefficient
.1
(default)  scalar
Air lift coefficient, C_{l}. The value is dimensionless.
Longitudinal drag pitch moment, Cpm
— Pitch drag
.1
(default)  scalar
Longitudinal drag pitch moment coefficient, C_{pm}. The value is dimensionless.
Relative wind angle vector, beta_w
— Wind angle
[0:0.01:0.3]
(default)  vector
Relative wind angle vector, β_{w}, in rad.
Side force coefficient vector, Cs
— Side force coefficient
[0:0.03:0.9]
(default)  vector
Side force coefficient vector coefficient, C_{s}. The value is dimensionless.
Yaw moment coefficient vector, Cym
— Yaw moment drag
[0:0.01:0.3]
(default)  vector
Yaw moment coefficient vector coefficient, C_{ym}. The value is dimensionless.
Absolute air pressure, Pabs
— Pressure
101325
(default)  scalar
Environmental absolute pressure, P_{abs}, in Pa.
Air temperature, Tair
— Temperature
273
(default)  scalar
Environmental absolute temperature, T, in K.
Dependencies
To enable this parameter, clear Air temperature.
Gravitational acceleration, g
— Gravity
9.81
(default)  scalar
Gravitational acceleration, g, in m/s^2.
Nominal friction scaling factor, mu
— Friction scale factor
1
(default)  scalar
Nominal friction scale factor, μ. The value is dimensionless.
Dependencies
To enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Clear External Friction.
Longitudinal velocity tolerance, xdot_tol
— Tolerance
.01
(default)  scalar
Longitudinal velocity tolerance, in m/s.
Nominal normal force, Fznom
— Normal force
5000
(default)  scalar
Nominal normal force, in N.
Dependencies
To enable this parameter, set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Geometric longitudinal offset from axle plane, longOff
— Longitudinal offset
0
(default)  scalar
Vehicle chassis offset from the axle plane along the vehiclefixed xaxis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independently of the vehicle CG.
Geometric lateral offset from center plane, latOff
— Lateral offset
0
(default)  scalar
Vehicle chassis offset from the center plane along the vehiclefixed yaxis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independently of the vehicle CG.
Geometric vertical offset from axle plane, vertOff
— Vertical offset
0
(default)  scalar
Vehicle chassis offset from the axle plane along the vehiclefixed zaxis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independently of the vehicle CG.
Wrap Euler angles, wrapAng
— Wrap the Euler angles to the interval [pi, pi]
off
(default)  on
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.
Model Examples
References
[1] Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers (SAE), 1992.
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