Implement a single track 3DOF rigid vehicle body to calculate longitudinal, lateral, and yaw motion
The Bicycle Model block implements a rigid twoaxle single track vehicle body model to calculate longitudinal, lateral, and yaw motion. The block accounts for body mass, aerodynamic drag, and weight distribution between the axles due to acceleration and steering. There are two types of Bicycle Model blocks.
Block  Implementation 

Bicycle Model  Velocity Input 

Bicycle Model  Force Input 

To calculate the normal forces on the front and rear axles, the block uses rigidbody vehicle motion, suspension system forces, and wind and drag forces. The block resolves the force and moment components on the rigid vehicle body frame.
WhlAngF
— Wheel anglescalar
Front wheel angle, in rad.
FxF
— Force Input: Total longitudinal force on the front axlescalar
Longitudinal force on the front axle,
Fx_{F}, along
vehiclefixed x
axis, in N.
Bicycle Model  Force Input block input port.
FxR
— Force Input: Total longitudinal force on the rear axlescalar
Longitudinal force on the rear axle,
Fx_{R}, along
vehiclefixed x
axis, in N.
Bicycle Model  Force Input block input port.
xdotin
— Velocity Input: Longitudinal velocityscalar
Vehicle CG velocity along vehiclefixed xaxis, in m/s.
Bicycle Model  Velocity Input block input port.
Info
— Bus signalBus signal containing these block values.
Signal  Description  Value  Units  

InertFrm  Cg  Disp  X  Vehicle CG displacement along earthfixed
X axis  Computed  m  
Y  Vehicle CG displacement along earthfixed
Y axis  0  m  
Z  Vehicle CG displacement along earthfixed
Z axis  Computed  m  
Vel  Xdot  Vehicle CG velocity along earthfixed
X axis  Computed  m/s  
Ydot  Vehicle CG velocity along earthfixed
Y axis  0  m/s  
Zdot  Vehicle CG velocity along earthfixed
Z axis  Computed  m/s  
Ang  phi  Rotation of the vehiclefixed frame about earthfixed
X axis (roll)  0  rad  
theta  Rotation of the vehiclefixed frame about earthfixed
Y axis (pitch)  Computed  rad  
psi  Rotation of the vehiclefixed frame about earthfixed
Z axis (yaw)  0  rad  
FrntAxl  Disp  X  Front axle displacement along the earthfixed
X axis  Computed  m  
Y  Front axle displacement along the earthfixed
Y axis  0  m  
Z  Front axle displacement along the earthfixed
Z axis  Computed  m  
Vel  Xdot  Front axle velocity along the earthfixed
X axis  Computed  m/s  
Ydot  Front axle velocity along the earthfixed
Y axis  0  m/s  
Zdot  Front axle velocity along the earthfixed
Z axis  Computed  m/s  
RearAxl  Disp  X  Rear axle displacement along the earthfixed
X axis  Computed  m  
Y  Rear axle displacement along the earthfixed
Y axis  0  m  
Z  Rear axle displacement along the earthfixed
Z axis  Computed  m  
Vel  Xdot  Rear axle velocity along the earthfixed
X axis  Computed  m/s  
Ydot  Rear axle velocity along the earthfixed
Y axis  0  m/s  
Zdot  Rear axle velocity along the earthfixed
Z axis  Computed  m/s  
BdyFrm  Cg  Vel  xdot  Vehicle CG velocity along vehiclefixed
x axis  Computed  m/s  
ydot  Vehicle CG velocity along vehiclefixed
y axis  0  m/s  
zdot  Vehicle CG velocity along vehiclefixed
z axis  Computed  m/s  
AngVel  p  Vehicle angular velocity about the vehiclefixed
x axis (roll rate)  0  rad/s  
q  Vehicle angular velocity about the vehiclefixed yaxis (pitch rate)  Computed  rad/s  
r  Vehicle angular velocity about the vehiclefixed zaxis (yaw rate)  0  rad/s  
Acc  ax  Vehicle CG acceleration along vehiclefixed
x axis  Computed  gn  
ay  Vehicle CG acceleration along vehiclefixed
y axis  0  gn  
az  Vehicle CG acceleration along vehiclefixed
z axis  Computed  gn  
xddot  Vehicle CG acceleration along vehiclefixed
x axis  Computed  gn  
yddot  Vehicle CG acceleration along vehiclefixed
y axis  0  gn  
zddot  Vehicle CG acceleration along vehiclefixed
z axis  Computed  gn  
Forces  Body  Fx  Net force on vehicle CG along vehiclefixed
x axis  Computed  N  
Fy  Net force on vehicle CG along vehiclefixed
y axis  0  N  
Fz  Net force on vehicle CG along vehiclefixed
z axis  Computed  N  
FrntAxl  Fx  Longitudinal force on front axle, along the
vehiclefixed
 Computed  N  
Fy  Lateral force on front axle, along the
vehiclefixed
 0  N  
Fz  Normal force on front axle, along the
vehiclefixed
 Computed  N  
RearAxl  Fx  Longitudinal force on rear axle, along the
vehiclefixed
 Computed  N  
Fy  Lateral force on rear axle, along the
vehiclefixed
 0  N  
Fz  Normal force on rear axle, along the
vehiclefixed
 Computed  N  
Tires  FrntTire  Fx  Front tire force, along vehiclefixed
 0  N  
Fy  Front tire force, along vehiclefixed
 0  N  
Fz  Front tire force, along vehiclefixed
 Computed  N  
RearTire  Fx  Rear tire force, along vehiclefixed
 0  N  
Fy  Rear tire force, along vehiclefixed
 0  N  
Fz  Rear tire force, along vehiclefixed
 Computed  N  
Drag  Fx  Drag force on vehicle CG along vehiclefixed
x axis  Computed  N  
Fy  Drag force on vehicle CG along vehiclefixed
y axis  Computed  N  
Fz  Drag force on vehicle CG along vehiclefixed
z axis  Computed  N  
Grvty  Fx  Gravity force on vehicle CG along vehiclefixed
x axis  Computed  N  
Fy  Gravity force on vehicle CG along vehiclefixed
y axis  0  N  
Fz  Gravity force on vehicle CG along vehiclefixed
z axis  Computed  N  
Moments  Body  Mx  Body moment on vehicle CG about vehiclefixed
x axis  0  N·m  
My  Body moment on vehicle CG about vehiclefixed
y axis  Computed  N·m  
Mz  Body moment on vehicle CG about vehiclefixed
z axis  0  N·m  
Drag  Mx  Drag moment on vehicle CG about vehiclefixed
x axis  0  N·m  
My  Drag moment on vehicle CG about vehiclefixed
y axis  Computed  N·m  
Mz  Drag moment on vehicle CG about vehiclefixed
z axis  0  N·m  
FrntAxl  Disp  x  Front axle displacement along the vehiclefixed
x axis  Computed  m  
y  Front axle displacement along the vehiclefixed
y axis  0  m  
z  Front axle displacement along the vehiclefixed
z axis  Computed  m  
Vel  xdot  Front axle velocity along the vehiclefixed
x axis  Computed  m/s  
ydot  Front axle velocity along the vehiclefixed
y axis  0  m/s  
zdot  Front axle velocity along the vehiclefixed
z axis  Computed  m/s  
RearAxl  Disp  x  Rear axle displacement along the vehiclefixed
x axis  Computed  m  
y  Rear axle displacement along the vehiclefixed
y axis  0  m  
z  Rear axle displacement along the vehiclefixed
z axis  Computed  m  
Vel  xdot  Rear axle velocity along the vehiclefixed
x axis  Computed  m/s  
ydot  Rear axle velocity along the vehiclefixed
y axis  0  m/s  
zdot  Rear axle velocity along the vehiclefixed
z axis  Computed  m/s  
Pwr  PwrExt  Applied external power  Computed  W  
Drag  Power loss due to drag  Computed  W 
xdot
— Vehicle body longitudinal velocityscalar
Vehicle CG velocity along vehiclefixed x
axis, in
m/s.
ydot
— Vehicle body lateral velocityscalar
Vehicle CG velocity along vehiclefixed y
axis, in
m/s.
psi
— Yawscalar
Rotation of the vehiclefixed frame about earthfixed
Z
axis (yaw), in rad..
r
— Yaw ratescalar
Vehicle angular velocity, r
, about the
vehiclefixed z
axis (yaw rate), in rad/s.
Number of wheels on front axle, NF
— Front wheel count2
(default)  scalar
Number of wheels on front axle, N_{F}. The value is dimensionless.
Number of wheels on rear axle, NR
— Rear wheel count2
(default)  scalar
Number of wheels on rear axle, N_{R}. The value is dimensionless.
Vehicle mass, m
— Vehicle mass2000
(default)  scalar
Vehicle mass, m, in kg.
Longitudinal distance from center of mass to front axle, a
— Front axle distance1.4
(default)  scalar
Horizontal distance a from the vehicle CG to the front wheel axle, in m.
Longitudinal distance from center of mass to rear axle, b
— Rear axle distance1.6
(default)  scalar
Horizontal distance b from the vehicle CG to the rear wheel axle, in m.
Vertical distance from center of mass to axle plane, h
— Height0.35
(default)  scalar
Height of vehicle CG above the axles, h, in m.
Initial inertial frame longitudinal position, X_o
— Position0
(default)  scalar
Initial vehicle CG displacement along earthfixed Xaxis, in m.
Initial longitudinal velocity, xdot_o
— Velocity0
(default)  scalar
Initial vehicle CG velocity along vehiclefixed xaxis, in m/s.
For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter, set Axle forces to one of these options:
External longitudinal forces
External forces
Front tire corner stiffness, Cy_f
— Stiffness12e3
(default)  scalar
Front tire corner stiffness, Cy_{f}, in N/rad.
For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Clear Mapped corner stiffness.
Rear tire corner stiffness, Cy_r
— Stiffness11e3
(default)  scalar
Rear tire corner stiffness, Cy_{r}, in N/rad.
For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:
Set Axle forces to one of these options:
External longitudinal velocity
External longitudinal forces
Clear Mapped corner stiffness.
Initial inertial frame lateral displacement, Y_o
— Position0
(default)  scalar
Initial vehicle CG displacement along earthfixed Yaxis, in m.
Initial lateral velocity, ydot_o
— Velocity0
(default)  scalar
Initial vehicle CG velocity along vehiclefixed yaxis, in m/s.
Yaw polar inertia, Izz
— Inertia4000
(default)  scalar
Yaw polar inertia, in kg*m^2.
Initial yaw angle, psi_o
— Psi rotation0
(default)  scalar
Rotation of the vehiclefixed frame about earthfixed Zaxis (yaw), in rad.
Initial yaw rate, r_o
— Yaw rate0
(default)  scalar
Vehicle angular velocity about the vehiclefixed zaxis (yaw rate), in rad/s.
Longitudinal drag area, Af
— Effective vehicle crosssectional area2
(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
— Pressure101325
(default)  scalar
 scalar
Environmental absolute pressure, P_{abs}, in Pa.
Air temperature, Tair
— Temperature273
(default)  scalar
Environmental absolute temperature, T, in K.
To enable this parameter, clear Air temperature.
Gravitational acceleration, g
— Gravity9.81
(default)  scalar
Gravitational acceleration, g, in m/s^2.
Nominal friction scaling factor, mu
— Friction scale factor1
(default)  scalar
Nominal friction scale factor, μ. The value is dimensionless.
For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, 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 force5000
(default)  scalar
Nominal normal force, in N.
For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, 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 offset0
(default)  scalar
Vehicle chassis offset from axle plane along bodyfixed xaxis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independent of the vehicle CG.
Geometric lateral offset from center plane, latOff
— Lateral offset0
(default)  scalar
Vehicle chassis offset from center plane along bodyfixed yaxis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independent of the vehicle CG.
Geometric vertical offset from axle plane, vertOff
— Vertical offset0
(default)  scalar
Vehicle chassis offset from axle plane along bodyfixed zaxis, in m. When you use the 3D visualization engine, consider using the offset to locate the chassis independent of the vehicle CG.
Wrap Euler angles, wrapAng
— Selectionoff
(default)  on
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.
[1] Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers (SAE), 1992.
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