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 earth-fixed X-axis

Computed

m
YVehicle CG displacement along earth-fixed Y-axis0

m

ZVehicle CG displacement along earth-fixed Z-axis

Computed

m
VelXdotVehicle CG velocity along earth-fixed X-axis

Computed

m/s

YdotVehicle CG velocity along earth-fixed Y-axis0m/s
ZdotVehicle CG velocity along earth-fixed Z-axis

Computed

m/s
AngphiRotation of the vehicle-fixed frame about earth-fixed X-axis (roll)0rad
thetaRotation of the vehicle-fixed frame about earth-fixed Y-axis (pitch)

Computed

rad
psiRotation of the vehicle-fixed frame about earth-fixed Z-axis (yaw)0rad
FrntAxlDispXFront axle displacement along the earth-fixed X-axis

Computed

m
YFront axle displacement along the earth-fixed Y-axis0m
ZFront axle displacement along the earth-fixed Z-axis

Computed

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

Computed

m/s
YdotFront axle velocity along the earth-fixed Y-axis0m/s
ZdotFront axle velocity along the earth-fixed Z-axis

Computed

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

Computed

m
YRear axle displacement along the earth-fixed Y-axis0m
ZRear axle displacement along the earth-fixed Z-axis

Computed

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

Computed

m/s
YdotRear axle velocity along the earth-fixed Y-axis0m/s
ZdotRear axle velocity along the earth-fixed Z-axis

Computed

m/s
BdyFrmCgVelxdotVehicle CG velocity along vehicle-fixed x-axis

Computed

m/s
ydotVehicle CG velocity along vehicle-fixed y-axis0m/s
zdotVehicle CG velocity along vehicle-fixed z-axisComputedm/s
AngVelpVehicle angular velocity about the vehicle-fixed x-axis (roll rate)0rad/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)0rad/s
AccaxVehicle CG acceleration along vehicle-fixed x-axis

Computed

gn
ayVehicle CG acceleration along vehicle-fixed y-axis0gn
azVehicle CG acceleration along vehicle-fixed z-axis

Computed

gn
xddotVehicle CG acceleration along vehicle-fixed x-axis

Computed

gn
yddotVehicle CG acceleration along vehicle-fixed y-axis0gn
zddotVehicle CG acceleration along vehicle-fixed z-axis

Computed

gn
ForcesBodyFxNet force on vehicle CG along vehicle-fixed x-axis

Computed

N
FyNet force on vehicle CG along vehicle-fixed y-axis0N
FzNet force on vehicle CG along vehicle-fixed z-axis

Computed

N
FrntAxlFx

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

Computed

N
Fy

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

0N
Fz

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

ComputedN
RearAxlFx

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

Computed

N
Fy

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

0N
Fz

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

ComputedN
TiresFrntTireFx

Front tire force, along vehicle-fixed x-axis

0N
Fy

Front tire force, along vehicle-fixed y-axis

0N
Fz

Front tire force, along vehicle-fixed z-axis

ComputedN
RearTireFx

Rear tire force, along vehicle-fixed x-axis

0N
Fy

Rear tire force, along vehicle-fixed y-axis

0N
Fz

Rear tire force, along vehicle-fixed z-axis

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

Computed

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

Computed

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

Computed

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

Computed

N
FyGravity force on vehicle CG along vehicle-fixed y-axis0N
FzGravity force on vehicle CG along vehicle-fixed z-axis

Computed

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

Computed

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

Computed

N·m
MzDrag moment on vehicle CG about vehicle-fixed z-axis0N·m
FrntAxlDispxFront axle displacement along the vehicle-fixed x-axis

Computed

m
yFront axle displacement along the vehicle-fixed y-axis0m
zFront axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

m/s
ydotFront axle velocity along the vehicle-fixed y-axis0m/s
zdotFront axle velocity along the vehicle-fixed z-axis

Computed

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

Computed

m
yRear axle displacement along the vehicle-fixed y-axis0m
zRear axle displacement along the vehicle-fixed z-axis

Computed

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

Computed

m/s
ydotRear axle velocity along the vehicle-fixed y-axis0m/s
zdotRear axle velocity along the vehicle-fixed z-axis

Computed

m/s
PwrPwrExtApplied external power

Computed

W
DragPower loss due to drag

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.

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