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Bicycle Model

Implement a single track 3DOF rigid vehicle body to calculate longitudinal, lateral, and yaw motion

Description

The Bicycle Model block implements a rigid two-axle 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.

BlockImplementation

Bicycle Model - Velocity Input

  • Block assumes that the external longitudinal velocity is quasi-steady state so the longitudinal acceleration is approximately zero.

  • Since the motion is quasi-steady, the block calculates only lateral forces using the tire slip angles and linear cornering stiffness.

Bicycle Model - Force Input

  • Block uses the external longitudinal force to accelerate or brake the vehicle.

  • Block calculates lateral forces using the tire slip angles and linear cornering stiffness.

To calculate the normal forces on the front and rear axles, the block uses rigid-body vehicle motion, suspension system forces, and wind and drag forces. The block resolves the force and moment components on the rigid vehicle body frame.

Ports

Input

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Front wheel angle, in rad.

Longitudinal force on the front axle, FxF, along vehicle-fixed x-axis, in N.

Bicycle Model - Force Input block input port.

Longitudinal force on the rear axle, FxR, along vehicle-fixed x-axis, in N.

Bicycle Model - Force Input block input port.

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

Bicycle Model - Velocity Input block input port.

Output

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Bus signal containing these block values.

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

Computed

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

Computed

m

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

Computed

m/s

YdotVehicle CG velocity along the earth-fixed Y-axis

Computed

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

Computed

rad
FrntAxlDispXFront wheel displacement along the earth-fixed X-axis

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

m
VelXdotHitch offset velocity from axle plane along the earth-fixed X-axis

Computed

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

Computed

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

Computed

m
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 CG velocity along the vehicle-fixed x-axis

Computed

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

Computed

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

Body slip angle, β

β=VyVx

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

rad/s
DCM

Direction cosine matrix

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Hitch force applied to body at the hitch location along the vehicle-fixed x-axis

Input

N
Fy

Hitch force applied to body at the hitch location along the vehicle-fixed y-axis

Input

N
Fz

Hitch force applied to body at the hitch location along the vehicle-fixed z-axis

Input

N
FrntAxlFx

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

Computed

N
Fy

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

Computed

N
Fz

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

Computed

N
RearAxlFx

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

Computed

N
Fy

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

Computed

N
Fz

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

ComputedN
TiresFrntTireFx

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

ComputedN
Fy

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

ComputedN
Fz

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

ComputedN
RearTireFxFx

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

ComputedN
Fy

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

ComputedN
Fz

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

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Computed

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

Front left wheel steering angle

Computed

rad
WhlAngFR

Front right wheel steering angle

Computed

rad
RearAxlDispxRear wheel displacement along the vehicle-fixed x-axis

Computed

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

Computed

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

Computed

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

Computed

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

Rear left wheel steering angle

Computed

rad
WhlAngRR

Rear right wheel steering angle

Computed

rad
HitchDispxHitch offset from axle plane along the vehicle-fixed x-axis

Input

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

Input

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

Input

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

Computed

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

Computed

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

Computed

m/s
PwrExtApplied external power

Computed

W
HitchPower loss due to hitch

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-axis0m/s
AngBeta

Body slip angle, β

β=VyVx

Computed

rad

SignalDescriptionValueUnits
PwrInfoPwrTrnsfrdPwrFxExtExternally applied longitudinal force power

Computed

W
PwrFyExtExternally applied lateral force power

Computed

W
PwrMzExtExternally applied roll moment power

Computed

W
PwrFwFxLongitudinal force applied at the front axle power

Computed

W
PwrFwFyLateral force applied at the front axle power

Computed

W
PwrFwRxLongitudinal force applied at the rear axle power

Computed

W
PwrFwRyLateral force applied at the rear axle power

Computed

W
PwrNotTrnsfrdPwrFxDragLongitudinal drag force power

Computed

W
PwrFyDragLateral drag force power

Computed

W
PwrMzDragDrag pitch moment power

Computed

W
PwrStoredPwrStoredGrvtyRate change in gravitational potential energy

Computed

W
PwrStoredxdotRate of change of longitudinal kinetic energy

Computed

W
PwrStoredydotRate of change of lateral kinetic energy

Computed

W
PwrStoredrRate of change of rotational yaw kinetic energy

Computed

W

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

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

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

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

Parameters

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Longitudinal

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

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

Vehicle mass, m, in kg.

Horizontal distance a from the vehicle CG to the front wheel axle, in m.

Horizontal distance b from the vehicle CG to the rear wheel axle, in m.

Height of vehicle CG above the axles, h, in m.

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

Dependencies

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

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

Dependencies

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

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

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

Dependencies

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

Lateral

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

Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Clear Mapped corner stiffness.

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

Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Clear Mapped corner stiffness.

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

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

Yaw

Yaw polar inertia, in kg*m^2.

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

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

Aerodynamic

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

Air drag coefficient, Cd. The value is dimensionless.

Air lift coefficient, Cl. The value is dimensionless.

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

Relative wind angle vector, βw, in rad.

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

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

Environment

Environmental absolute pressure, Pabs, in Pa.

Environmental absolute temperature, T, in K.

Dependencies

To enable this parameter, clear Air temperature.

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

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

Dependencies

For the Vehicle Body 3DOF Single Track or Vehicle Body 3DOF Dual Track blocks, to enable this parameter:

  1. Set Axle forces to one of these options:

    • External longitudinal velocity

    • External longitudinal forces

  2. Clear External Friction.

Simulation

Longitudinal velocity tolerance, in m/s.

Nominal normal force, in N.

Dependencies

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

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.

Introduced in R2018a