Motorcycle Body Longitudinal In-Plane

Longitudinal in-plane motorcycle vehicle motion

Since R2021b

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Libraries:
Powertrain Blockset / Vehicle Dynamics
Vehicle Dynamics Blockset / Vehicle Body

Description

The Motorcycle Body Longitudinal In-Plane block implements a longitudinal in-plane motorcycle body model to calculate longitudinal, vertical, and pitch motion. The block accounts for:

• Mass of the frame, rear arm, front upper fork, front lower fork, front wheel, and rear wheel

• In-plane dynamic effects of the frame, front lower fork, front wheel, rear wheel, rear suspension, front suspension, rear wheel damper, rear arm, and chain

• External forces, external moments, and aerodynamic drag

• Road incline

• Weight distribution between the axles due to acceleration

Consider using this block to represent motorcycle motion in powertrain and fuel economy studies, for example, in studies with heavy breaking or acceleration or road profiles that contain larger vertical changes.

The block uses rigid-body vehicle motion, suspension system forces, and wind and drag forces to calculate the forces on the motorcycle frames. The block then determines the position and velocity of motorcycle at the front and rear contact patches.

Layout

To determine the rigid-body motorcycle motion, the block uses right-handed (RH) Cartesian reference frames systems attached to the motorcycle. i, j, and k are orthogonal unit vectors attached to the frames.

Frame	Variable in Figure	Description
Road	x, z	Road-fixed coordinate system. x is along road grade, and z points downward.
Motorcycle main frame iFrm – Forward along vector given by θfrm kFrm – Downward jFrm – Orthogonal to motorcycle plane	OFrm	Main frame origin
	GFrm	Center of mass (CM) of the main frame with respect to OFrm, along iFrm and kFrm, respectively
	GRdr	CM of the rider with respect to OFrm, along iFrm and kFrm, respectively
	ϴfrm	Main frame rotation about jFrm
Upper fork iFrkUp – Forward along vector given by θfrm kFrkUp – Downward jFrkUp – Orthogonal to motorcycle plane	OFrkUp	Upper fork origin
	GFrkUp	CM of the upper fork with respect to OFrkUp, along iFrkUp and kFrkUp, respectively
Lower fork iFrkLw – Forward along vector given by θfrm kFrkLw – Downward jFrkLw – Orthogonal to motorcycle plane	OFrkLw	Lower fork origin
	GFrkLw	CM of the lower fork with respect to OFrkLw, along iFrkLw and kFrkLw, respectively
Rear arm iArmRr – Forward along vector given by θra kArmRr – Downward jArmRr – Orthogonal to motorcycle plane	OArmRr	Rear arm origin
	GArmRr	CM of the rear arm with respect to OArmRr, along iArmRr and kArmRr, respectively
	ϴra	Rear arm rotation about jArmRr
Front wheel contact patch iCpF – Forward along vector given by road-fixed x- axis kCpF – Downward along vector given by road-fixed z- axis jCpF – Orthogonal to motorcycle plane	OCpF	Front wheel contact patch origin
Rear wheel contact patch iCpR – Forward along vector given by road-fixed x- axis kCpR – Downward along vector given by road-fixed z- axis jCpR – Orthogonal to motorcycle plane	OCpR	Rear wheel contact patch origin

Use the parameters in this table to specify the geometric layout of your motorcycle.

Parameter			Variable in Figure
Initial conditions	Position	Rear contact patch longitudinal coordinate, CpRrX0	OCpR with respect to road-fixed coordinate system, along x
		Rear contact patch vertical coordinate, CpRrZ0	OCpR with respect to road-fixed coordinate system, along z
		Pitch angle of rear arm, ArmRrAng0	θra
		Pitch angle of main frame, FrmAng0	θFrm
		Fork length, FrkFrL0	df
Frame		Center of mass location, FrmCmPxz	GFrm with respect to OFrm, along iFrm and kFrm, respectively
		Length, FrmLen	FrmLen
Rider		Center of mass location, RdrCmPxz	GRdr with respect to OFrm, along iFrm and kFrm, respectively
Front Fork	Upper	Position, FrkUpCmPxz	GFrkUp with respect to OFrkUp, along iFrkUp and kFrkUp, respectively
		Offset, FrkOfs	FrkOfs
	Lower	Position, FrkLwCmPxz	GFrkLw with respect to OFrkLw, along iFrkLw and kFrkLw, respectively
Rear Arm		Position, ArmRrCmPxz	GArmRr with respect to OArmRr, along iArmRr and kArmRr, respectively
		Length, ArmRrLen	ArmRrLen
Wheels	Front	Radius, WhlFrR	WhlFrR
	Rear	Radius, WhlRrR	WhlRrR
Suspension	Front	Equilibrium length, FrkLwL0	df
	Rear	Equilibrium angle, ShkRrAng0	θFrm

Input Signals

You can use these block parameters to create additional input ports. This table summarizes the settings.

Input Signals Pane Parameter	Input Port	Description
External forces	FExt	External longitudinal and vertical forces applied at equivalent rider and motorcycle center of mass (CM).
External moments	MExt	External moment about equivalent rider and motorcycle CM, for example, moment due to rider physical motion.
External front wheel moment	MWhlF	External moment at the front wheel GWhlFr, for example, wheel motors and external intermittent friction-related disturbances.
External rear wheel moment	MWhlR	External moment at the rear wheel GWhlRr, for example, wheel motors and external intermittent friction-related disturbances.
Grade angle	Grade	Road grade angle.
Wind velocity	WindXYZ	Wind speed.
Ambient temperature	Temp	Ambient air temperature. Consider this option if you want to vary the temperature during run-time.

Suspension System

Use the Suspension type parameter to specify the type of suspension.

Setting	Description
Simple	Block models the suspension force and moment as a spring-damper system: Suspension force at the upper fork Suspension moment at the rear arm
User-defined	Input the suspension force and moment: FSuspF – Suspension force at the upper fork MSuspR – Suspension moment at the rear arm

Wind and Drag Forces

The block subtracts the wind speeds from the vehicle velocity components to obtain a net relative airspeed. To calculate the drag force and moments acting on the motorcycle, the block uses the net relative airspeed.

Use in 3D Environment

To co-simulate in the Unreal Engine^® and provide a motorcycle with the motion calculated by the Motorcycle Body Longitudinal In-Plane block:

1. Put the Simulation 3D Motorcycle block in your model.

2. Route these the Info bus port signals to the Simulation 3D Motorcycle input ports Translation and Rotation.

   • PosOrgInert

   • PosFwBdy

   • PosRwBdy

   • AngOrgInert

   

For more information about using the block in the 3D environment, see Longitudinal Motorcycle Braking Test.

Power Accounting

The block accounts for the power transferred, not transferred, and stored.

Bus Signal			Description
PwrInfo	PwrTrnsfrd — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	PwrFxExt	Mechanical power from longitudinal external force
		PwrFzExt	Mechanical power from vertical external force
		PwrMyExt	Mechanical power from external pitch moment
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrFxDrag	Mechanical power loss from longitudinal drag force
		PwrFzDrag	Mechanical power loss from vertical lift
		PwrMyDrag	Mechanical power loss from pitch moment drag
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrStoredGrvty	Rate change in gravitational potential energy
		PwrStoredxdot	Rate of change of longitudinal kinetic energy
		PwrStoredzdot	Rate of change of vertical kinetic energy
		PwrStoredq	Rate of change of rotational pitch kinetic energy
		PwrStoredFsFzSprng	Stored spring energy from front suspension
		PwrStoredFsRzSprng	Stored spring energy from rear suspension

Examples

Longitudinal Motorcycle Braking Test Reference Application

Simulate an in-plane motorcycle model undergoing a braking test. Use for motorcycle dynamics ride and handling analysis and chassis controls development.

• Open Script

Ports

Input

FCpF — Longitudinal and vertical forces at front wheel contact patch

vector

Longitudinal and vertical forces at front wheel contact patch O_CpF, along i_CpF and k_CpF, in N. Signal vector dimensions are [1x2] or [2x1].

FCpR — Longitudinal and vertical forces at rear wheel contact patch

vector

Longitudinal and vertical forces at rear wheel contact patch O_CpR, along i_CpR and k_CpR, in N. Signal vector dimensions are [1x2] or [2x1].

MDrvArmR — Drive chain moment at rear arm

scalar

Drive chain moment at rear arm O_ArmRr, about j_ArmRr, in N·m.

MDrvFrm — Drive chain moment at frame

scalar

Drive chain moment at the frame O_Frm, about j_Frm, in N·m.

FExt — External longitudinal and vertical forces at frame

vector

External longitudinal and vertical forces applied at equivalent rider and motorcycle center of mass (CM), along i_Frm and k_Frm, in N. Signal vector dimensions are [1x2] or [2x1].

Dependencies

To create this port, select External forces.

MExt — External moment about frame

scalar

External moment about equivalent rider and motorcycle CM, j_Frm, for example, moment due to rider physical motion, in N·m.

Dependencies

To create this port, select External moments.

MBrkF — Brake moment at front wheel

scalar

Brake moment at the front wheel G_WhlFr, about j_WhlFr, in N·m.

MBrkR — Brake moment at rear wheel

scalar

Brake moment at the rear wheel G_WhlRr, about j_WhlRr, in N·m.

MWhlF — External moment at front wheel

scalar

External moment at the front wheel G_WhlFr, in N·m.

Dependencies

To create this port, select External front wheel moment.

MWhlR — External moment at rear wheel

scalar

External moment at the rear wheel G_WhlRr, in N·m.

Dependencies

To create this port, select External rear wheel moment.

FSuspF — External suspension force at upper fork

scalar

External suspension force at upper fork O_FrkUp, along k_FrkUp, in N.

Dependencies

To create this port, set Suspension type to User-defined.

MSuspR — External suspension moment at rear arm

scalar

External suspension force at upper fork O_ArmRr, about j_ArmRr, in N·m.

Dependencies

To create this port, set Suspension type to User-defined.

Grade — Road grade angle

scalar

Road grade angle, $\gamma$, in deg.

Dependencies

To create this port, select Grade angle.

WindXYZ — Wind speed

array

Wind speed, W_X, W_Y, W_Z along earth-fixed X-, Y-, and Z-axes, in m/s. Signal vector dimensions are [1x3] or [3x1].

Dependencies

To create this port, select Wind velocity.

Temp — Ambient air temperature

scalar

Ambient air temperature, T_air, in K. Considering this option if you want to vary the temperature during run-time.

Dependencies

To create this port, select Ambient temperature.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal						Signal	Units
Geom				PosOrgInert		Main frame position along the earth-fixed axes	m
				PosFwBdy		Front wheel center position relative to initial vehicle-fixed wheel position, along the vehicle Z-down X-, Y-, and Z-axes	m
				PosRwBdy		Rear wheel center position relative to initial vehicle-fixed wheel position, along the vehicle Z-down X-, Y-, and Z-axes	m
				AngOrgInert		Main frame rotation about the earth-fixed axes	rad
Frame	Inert	Cg	Disp	X		Vehicle CM displacement along the earth-fixed X-axis	m
				Y		Vehicle CM displacement along the earth-fixed Y-axis	m
				Z		Vehicle CM displacement along the earth-fixed Z-axis	m
			Vel	Xdot		Vehicle CM velocity along the earth-fixed X-axis	m/s
				Ydot		Vehicle CM velocity along the earth-fixed Y-axis	m/s
				Zdot		Vehicle CM velocity along the earth-fixed Z-axis	m/s
			Ang	phi		Rotation of the vehicle-fixed frame about the earth-fixed X-axis (roll)	rad
				theta		Rotation of the vehicle-fixed frame about the earth-fixed Y-axis (pitch)	rad
				psi		Rotation of the vehicle-fixed frame about the earth-fixed Z-axis (yaw)	rad
	BdyFrm	Cg	Disp	x		Vehicle CM position along the road-fixed x-axis	m
				y		Vehicle CM position along the road-fixed y-axis	m
				z		Vehicle CM position along the road-fixed z-axis	m
			Vel	xdot		Vehicle CM velocity along the road-fixed x-axis	m/s
				ydot		Vehicle CM velocity along the road-fixed y-axis	m/s
				zdot		Vehicle CM velocity along the road-fixed z-axis	m/s
			AngVel	p		Vehicle angular velocity about the road-fixed x-axis (roll rate)	rad/s
				q		Vehicle angular velocity about the road-fixed y-axis (pitch rate)	rad/s
				r		Vehicle angular velocity about the road-fixed z-axis (yaw rate)	rad/s
			Acc	ax		Vehicle CM acceleration along the road-fixed x-axis	m/s2
				ay		Vehicle CM acceleration along the road-fixed y-axis	m/s2
				az		Vehicle CM acceleration along the road-fixed z-axis	m/s2
				xddot		Vehicle CM acceleration along the road-fixed x-axis	m/s2
				yddot		Vehicle CM acceleration along the road-fixed y-axis	m/s2
				zddot		Vehicle CM acceleration along the road-fixed z-axis	m/s2
			AngAcc	pdot		Vehicle angular acceleration about the road-fixed x-axis	rad/s2
				qdot		Vehicle angular acceleration about the road-fixed y-axis	rad/s2
				rdot		Vehicle angular acceleration about the road-fixed z-axis	rad/s2
		Forces	Ext	Fx		External force on vehicle CM along the road-fixed x-axis	N
				Fy		External force on vehicle CM along the road-fixed x-axis	N
				Fz		External force on vehicle CM along the road-fixed x-axis	N
			Drag	Fx		Drag force on vehicle CM along the road-fixed x-axis	N
				Fy		Drag force on vehicle CM along the road-fixed y-axis	N
				Fz		Drag force on vehicle CM along the road-fixed z-axis	N
			Grvty	Fx		Gravity force on vehicle CM along the road-fixed x-axis	N
				Fy		Gravity force on vehicle CM along the road-fixed y-axis	N
				Fz		Gravity force on vehicle CM along the road-fixed z-axis	N
		Moments	Drag	Mx		Drag moment on vehicle CM about the road-fixed x-axis	N·m
				My		Drag moment on vehicle CM about the road-fixed z-axis	N·m
				Mz		Drag moment on vehicle CM about the road-fixed z-axis	N·m
			Ext	Mx		External moment on vehicle CG about the road-fixed x-axis	N·m
				My		External moment on vehicle CG about the road-fixed y-axis	N·m
				Mz		External moment on vehicle CG about the road-fixed z-axis	N·m
		Pwr	PwrExt			Applied external power	W
			Drag			Power loss due to drag	W
	PwrInfo	Pwr Trnsfrd	PwrFxExt			Mechanical power from longitudinal external force	W
			PwrFzExt			Mechanical power from vertical external force	W
			PwrMyExt			Mechanical power from external pitch moment	W
		PwrNot Trnsfrd	PwrFxDrag			Mechanical power loss from longitudinal drag force	W
			PwrFzDrag			Mechanical power loss from vertical lift force	W
			PwrMyDrag			Mechanical power loss from pitch moment drag	W
		PwrStored	PwrStoredGrvty			Rate change in gravitational potential energy	W
			PwrStoredxdot			Rate of change of longitudinal kinetic energy	W
			PwrStoredzdot			Rate of change of vertical kinetic energy	W
			PwrStoredq			Rate of change of rotational pitch kinetic energy	W
	Genrl	Vel	xdot			Vehicle CM velocity along the road-fixed x-axis	m/s
			zdot			Vehicle CM velocity along the road-fixed z-axis	m/s
		Ang	thetafrm			Pitch angle of main frame	rad
		AngVel	thetafrmdot			Main frame rotational velocity	rad/s
		AngAcc	thetafrmddot			Main frame rotational acceleration	rad/s2
Whl	Genrl	Frnt	Cp	Disp	x	Front wheel contact patch position along the road-fixed x-axis	m
					z	Front wheel contact patch position along the road-fixed z-axis	m
				Vel	xdot	Front wheel contact patch velocity along the road-fixed x-axis	m/s
					zdot	Front wheel contact patch velocity along the road-fixed z-axis	m/s
				Acc	xddot	Front wheel contact patch acceleration along the road-fixed x-axis	m/s2
					zddot	Front wheel contact patch acceleration along the road-fixed z-axis	m/s2
			Axl	Vel	xdot	Front wheel axle velocity along the road-fixed x-axis	m/s
					zdot	Front wheel axle velocity along the road-fixed z-axis	m/s
		Rear	Cp	Disp	x	Rear wheel contact patch position along the road-fixed x-axis	m
					z	Rear wheel contact patch position along the road-fixed z-axis	m
				Vel	xdot	Rear wheel contact patch velocity along the road-fixed x-axis	m/s
					zdot	Rear wheel contact patch velocity along the road-fixed z-axis	m/s
				Acc	xddot	Rear wheel contact patch acceleration along the road-fixed x-axis	m/s2
					zddot	Rear wheel contact patch acceleration along the road-fixed z-axis	m/s2
			Axl	Vel	xdot	Rear wheel axle velocity along the road-fixed x-axis	m/s
					zdot	Rear wheel axle velocity along the road-fixed z-axis	m/s
RearArm	Genrl	Vel	xdot			Rear arm velocity along the road-fixed x-axis	m/s
			zdot			Rear arm velocity along the road-fixed z-axis	m/s
		Ang	thetara			Pitch angle of rear arm	rad
		AngVel	thetaradot			Rear arm rotational velocity	rad/s
		AngAcc	thetaraddot			Rear arm rotational acceleration	rad/s2
Fork	Genrl	Upr	Vel	xdot		Upper fork velocity along the road-fixed x-axis	m/s
				zdot		Upper fork velocity along the road-fixed z-axis	m/s
		Lwr	Disp	df		Fork length	m
			Vel	xdot		Lower fork velocity along the road-fixed x-axis	m/s
				zdot		Lower fork velocity along the road-fixed z-axis	m/s
				dfdot		Fork length velocity	m/s
			Acc	dfddot		Fork length acceleration	m/s2
Susp	Genrl	Rear	Moments	Mthetafrm		Rear suspension moment at frame	N·m
		Frnt	Forces	Fdf		Suspensive force at upper fork	N

VCpF — Longitudinal, lateral, and vertical velocity at front wheel contact patch

vector

Longitudinal, lateral, and vertical velocity at front wheel contact patch O_CpF, along i_CpF and k_CpF, in m/s. Signal vector dimensions are [1x3] or [3x1]. The lateral component is set to 0.

PCpF — Longitudinal, lateral, and vertical position at front wheel contact patch

vector

Longitudinal, lateral, and vertical position at front wheel contact patch O_CpF, along i_CpF and k_CpF, in m. Signal vector dimensions are [1x3] or [3x1]. The lateral component is set to 0.

VCpR — Longitudinal, lateral, and vertical velocity at rear wheel contact patch

vector

Longitudinal, lateral, and vertical velocity at rear wheel contact patch O_CpR, along i_CpR and k_CpR, in m/s. Signal vector dimensions are [1x3] or [3x1]. The lateral component is set to 0.

PCpR — Longitudinal, lateral, and vertical position at rear wheel contact patch

vector

Longitudinal, lateral, and vertical position at rear wheel contact patch O_CpR, along i_CpR, and k_CpR, in m. Signal vector dimensions are [1x3] or [3x1]. The lateral component is set to 0.

ThetaFrm — Main frame pitch angle

scalar

Main frame pitch angle, ϴ_frm, in rad.

ThetaArmR — Rear arm pitch angle

scalar

Rear arm pitch angle, ϴ_ra, in rad.

Parameters

Options

Suspension type — Type of suspension

Simple (default) | User-defined

Use the Suspension type parameter to specify the type of suspension.

Setting	Description
Simple	Block models the suspension force and moment as a spring-damper system: Suspension force at the upper fork Suspension moment at the rear arm
User-defined	Input the suspension force and moment: FSuspF – Suspension force at the upper fork MSuspR – Suspension moment at the rear arm

Input signals

External forces — FExt input port

off (default) | on

Specify to create input port FExt.

External moments — MExt input port

off (default) | on

Specify to create input port MExt.

External front wheel moment — MWhlF input port

off (default) | on

Specify to create input port MWhlF. Consider using this port to input external moments such as wheel motors and external intermittent friction-related disturbances.

External rear wheel moment — MWhlR input port

off (default) | on

Specify to create input port MWhlR. Consider using this port to input external moments such as wheel motors and external intermittent friction-related disturbances.

Grade angle — Grade input port

on (default) | off

Specify to create input port Grade.

Wind velocity — WindXYZ input port

on (default) | off

Specify to create input port WindXYZ.

Ambient temperature — Temp input port

off (default) | on

Specify to create input port Temp.

Layout

Use the parameters in this table to specify the geometric layout of your motorcycle.

Parameter			Variable in Figure
Initial conditions	Position	Rear contact patch longitudinal coordinate, CpRrX0	OCpR with respect to road-fixed coordinate system, along x
		Rear contact patch vertical coordinate, CpRrZ0	OCpR with respect to road-fixed coordinate system, along z
		Pitch angle of rear arm, ArmRrAng0	θra
		Pitch angle of main frame, FrmAng0	θFrm
		Fork length, FrkFrL0	df
Frame		Center of mass location, FrmCmPxz	GFrm with respect to OFrm, along iFrm and kFrm, respectively
		Length, FrmLen	FrmLen
Rider		Center of mass location, RdrCmPxz	GRdr with respect to OFrm, along iFrm and kFrm, respectively
Front Fork	Upper	Position, FrkUpCmPxz	GFrkUp with respect to OFrkUp, along iFrkUp and kFrkUp, respectively
		Offset, FrkOfs	FrkOfs
	Lower	Position, FrkLwCmPxz	GFrkLw with respect to OFrkLw, along iFrkLw and kFrkLw, respectively
Rear Arm		Position, ArmRrCmPxz	GArmRr with respect to OArmRr, along iArmRr and kArmRr, respectively
		Length, ArmRrLen	ArmRrLen
Wheels	Front	Radius, WhlFrR	WhlFrR
	Rear	Radius, WhlRrR	WhlRrR
Suspension	Front	Equilibrium length, FrkLwL0	df
	Rear	Equilibrium angle, ShkRrAng0	θFrm

Frame

Center of mass location, FrmCmPxz — Frame location

[0.255, -0.02] (default) | vector

Center of mass location of the frame, G_Frm. Specified as a vector with respect to O_Frm, along i_Frm and k_Frm, respectively.

Mass, FrmMass — Frame mass

223 (default) | scalar

Frame mass, FrmMass, in kg.

Mass moment of inertia, FrmIyy — Frame inertia

26.2 (default) | scalar

Mass moment of inertia, FrmIyy, in kg·m².

Length, FrmLen — Frame length

0.730 (default) | scalar

Length of the frame, FrmLen, in m.

Rider

Center of mass location, RdrCmPxz — Rider location

[0.275, -0.61] (default) | vector

Center of mass location of the rider, G_Rdr. Specified as a vector with respect to O_Frm, along i_Frm and k_Frm, respectively.

Mass, RdrMass — Rider mass

78 (default) | scalar

Rider mass, RdrMass, in kg.

Mass moment of inertia, RdrIyy — Rider inertia

26.2 (default) | scalar

Rider mass moment of inertia, RdrIyy, in kg·m².

Front Fork – Upper

Position, FrkUpCmPxz — Upper fork location

[0.023, -0.098] (default) | vector

Center of mass location of the upper fork, G_FrkUp. Specified as a vector with respect to O_FrkUp, along i_FrkUp and k_FrkUp, respectively.

Mass, FrkUpMass — Upper fork mass

8.8 (default) | scalar

Upper fork mass, FrkUpMass, in kg.

Mass moment of inertia, FrkUpIyy — Upper fork inertia

0.14 (default) | scalar

Upper fork mass moment of inertia, FrkUpIyy, in kg·m².

Offset, FrkOfs — Upper fork offset

0.034 (default) | scalar

Upper fork offset, FrkOfs, in m.

Front Fork – Lower

Position, FrkLwCmPxz — Lower fork location

[-0.029, -0.189] (default) | vector

Center of mass location of the lower fork, G_FrkLw. Specified as a vector with respect to O_FrkLw, along i_FrkLw and k_FrkLw, respectively.

Mass, FrkLwMass — Lower fork mass

7.0 (default) | scalar

Lower fork mass, FrkLwMass, in kg.

Mass moment of inertia, FrkLwIyy — Lower fork inertia

0.18 (default) | scalar

Lower fork mass moment of inertia, FrkLwIyy, in kg·m².

Rear Arm

Position, ArmRrCmPxz — Rear arm location

[0.275, -0.052] (default) | vector

Center of mass location of the rear arm, G_ArmRr. Specified as a vector with respect to O_ArmRr, along i_ArmRr and k_ArmRr, respectively.

Mass, ArmRrMass — Rear arm mass

10 (default) | scalar

Rear arm mass, ArmRrMass, in kg.

Mass moment of inertia, ArmRrIyy — Rear arm inertia

0.8 (default) | scalar

Rear arm mass moment of inertia, ArmRrIyy, in kg·m².

Length, ArmRrLen — Rear arm length

0.535 (default) | scalar

Rear arm length, ArmRrLen, in m.

Wheels – Front

Mass, WhlFrMass — Front wheel mass

12 (default) | scalar

Front wheel mass, WhlFrMass, in kg.

Radius, WhlFrR — Front wheel radius

0.3 (default) | scalar

Front wheel radius, WhlFrR, in m.

Wheels – Rear

Mass, WhlRrMass — Rear wheel mass

16.2 (default) | scalar

Rear wheel mass, WhlRrMass, in kg.

Radius, WhlRrR — Rear wheel radius

0.33 (default) | scalar

Rear wheel radius, WhlRrR, in m.

Suspension – Front

Stiffness, SuspFrK — Front suspension stiffness

25e3 (default) | scalar

Front suspension stiffness at O_FrkUp, along k_FrkUp, in N/m.

Damping, SuspFrC — Front suspension damping

1250 (default) | scalar

Front suspension damping, at O_FrkUp, along k_FrkUp, in N·s/m.

Equilibrium length, FrkLwL0 — Front suspension equilibrium length

0.473 (default) | scalar

Front suspension equilibrium length, d_f, in m.

Suspension – Rear

Stiffness, SuspRrK — Rear arm suspension stiffness

1500 (default) | scalar

Rear arm suspension stiffness at O_ArmRr, about j_ArmRr, in N/rad.

Damping, SuspRrC — Rear arm suspension damping

150 (default) | scalar

Rear arm suspension damping at O_ArmRr, about j_ArmRr, in N·s/rad.

Equilibrium angle, ShkRrAng0 — Rear suspension equilibrium angle

0 (default) | scalar

Rear suspension equilibrium angle, θ_Frm, in rad.

Aerodynamic

Longitudinal drag area, Af — Area

2 (default) | scalar

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

Longitudinal drag coefficient, Cd — Drag

.2 (default) | scalar

Air drag coefficient, C_d, dimensionless.

Longitudinal lift coefficient, Cl — Lift

.1 (default) | scalar

Air lift coefficient, C_l, dimensionless.

Longitudinal drag pitch moment, Cpm — Pitch drag

.1 (default) | scalar

Longitudinal drag pitch moment coefficient, C_pm, dimensionless.

Pitch moment length, Lcpm — Pitch drag

2 (default) | scalar

Pitch moment length, Lcpm, in m.

Environment

Gravitational acceleration, g — Gravity

9.80665 (default) | scalar

Gravitational acceleration, g, in m/s².

Absolute air pressure, Pabs — Pressure

101325 (default) | scalar

Environmental air absolute pressure, P_abs, in Pa.

Air temperature, Tair — Ambient air temperature

273 (default) | scalar

Ambient air temperature, T_air, in K.

Dependencies

To enable this parameter, clear Ambient temperature.

Initial conditions

Position

Rear contact patch longitudinal coordinate, CpRrX0 — Longitudinal coordinate

0 (default) | scalar

Rear contact patch longitudinal coordinate, O_CpR, with respect to road-fixed coordinate system, along x, in m.

Rear contact patch vertical coordinate, CpRrZ0 — Vertical coordinate

0 (default) | scalar

Rear contact patch vertical coordinate, O_CpR, with respect to road-fixed coordinate system, along z, in m.

Pitch angle of rear arm, ArmRrAng0 — Rear arm angle

0.0590379 (default) | scalar

Pitch angle of rear arm, θ_ra, in rad.

Pitch angle of main frame, FrmAng0 — Angle length

0.377024 (default) | scalar

Pitch angle of main frame, θ_Frm, in rad.

Fork length, FrkFrL0 — Fork length

0.4262193 (default) | scalar

Fork length, d_f, in m.

Velocity

Longitudinal velocity of rear contact patch — Longitudinal velocity

0 (default) | scalar

Rear contact patch longitudinal coordinate, $${\dot{O}}_{CpR}$$, with respect to road-fixed coordinate system, along x, in m/s.

Vertical velocity of rear contact patch, CpRrVz0 — Vertical velocity

0 (default) | scalar

Vertical velocity of rear contact patch, $${\dot{O}}_{CpR}$$, with respect to road-fixed coordinate system, along z, in m/s.

Pitch rate of rear arm, ArmRrAngV0 — Pitch rate

0 (default) | scalar

Pitch rate of rear arm, $${\dot{\theta }}_{ra}$$, in rad/s.

Pitch rate of main frame, FrmAngV0 — Pitch rate

0 (default) | scalar

Pitch rate of main frame, $${\dot{\theta }}_{Frm}$$, in rad/s.

Lower fork deformation velocity, FrkLwV0 — Deformation velocity

0 (default) | scalar

Lower fork deformation velocity, $${\dot{d}}_f$$, in m/s.

Coordinate Offsets

Longitudinal offset, longOff — Longitudinal offset

0 (default) | scalar

Vehicle main frame offset along the earth-fixed X-axis, in m.

Lateral offset, latOff — Lateral offset

0 (default) | scalar

Vehicle main frame offset along the earth-fixed Y-axis, in m.

Vertical offset, vertOff — Vertical offset

0 (default) | scalar

Vehicle main frame offset along the earth-fixed Z-axis, in m.

Roll offset, pitchOff — Roll offset

0 (default) | scalar

Vehicle main frame offset about the earth-fixed X-axis, in rad.

Pitch offset, pitchOff — Pitch offset

0 (default) | scalar

Vehicle main frame offset about the earth-fixed Y-axis, in rad.

Yaw offset, pitchOff — Yaw offset

0 (default) | scalar

Vehicle main frame offset about the earth-fixed Z-axis, in rad.

References

[1] Giner, David Moreno. “Symbolic-Numeric Tools for the Analysis of Motorcycle Dynamics. Development of a Virtual Rider for Motorcycles Based on Model Predictive Control.” PhD diss., Universidad Miguel Hernández de Elche, 2016.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2021b