Vehicle Body 3DOF Longitudinal

3DOF rigid vehicle body to calculate longitudinal, vertical, and pitch motion

• 

×

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

Description

The Vehicle Body 3DOF Longitudinal block implements a three degrees-of-freedom (3DOF) rigid vehicle body model with configurable axle stiffness to calculate longitudinal, vertical, and pitch motion. The block accounts for body mass, aerodynamic drag, road incline, and weight distribution between the axles due to acceleration and the road profile.

You can specify the type of axle attachment to the vehicle:

• Grade angle — Vertical axle displacement from road surface to axles remains constant. The block uses tabular stiffness and damping parameters to model the suspension forces acting between the vehicle body and axles.

• Axle displacement — Axles have input-provided vertical displacement and velocity with respect to the road grade. The block uses tabular stiffness and damping parameters to model the suspension forces acting between the vehicle body and axle.

• External suspension — Axles have externally applied forces for coupling the vehicle body to custom suspension models.

If the weight transfer from vertical and pitch motions are not negligible, consider using this block to represent vehicle 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 normal forces on the front and rear axles. The block resolves the force components and moments on the rigid vehicle body frame:

$$\begin{array}{l}{F}_x=F_{wF}+F_{wR}-F_{d,x}-F_{sx,F}-F_{sx,R}+F_{g,x}\\ F_z=F_{d,z}-F_{sz,F}-F_{sz,R}+F_{g,z}\\ M_y=a{F}_{sz,F}-b{F}_{sz,R}+h\left(F_{wF}+F_{wR}+F_{sx,F}+F_{sx,R}\right)-M_{d,y}\end{array}$$

Rigid-Body Vehicle Motion

The vehicle axles are parallel and form a plane. The longitudinal direction lies in this plane and is perpendicular to the axles. If the vehicle is traveling on an inclined slope, the normal direction is not parallel to gravity but is always perpendicular to the axle-longitudinal plane.

The block uses the net effect of all the forces and torques acting on it to determine the vehicle motion. The longitudinal tire forces push the vehicle forward or backward. The weight of the vehicle acts through its center of gravity (CG). Depending on the inclined angle, the weight pulls the vehicle to the ground and either forward or backward. Whether the vehicle travels forward or backward, aerodynamic drag slows it down. For simplicity, the drag is assumed to act through the CG.

The Vehicle Body 3DOF Longitudinal implements these equations.

$$\begin{array}{l}\ddot{x}=\frac{F_x}{m}-qz\\ \ddot{z}=\frac{F_z}{m}-qx\\ \dot{q}=\frac{M_y}{I_{yy}}\\ \dot{\theta }=q\end{array}$$

Suspension System Forces

If you configure the block with the Ground interaction type parameter Grade angle or Axle displacement, velocity, the block uses nonlinear stiffness and damping parameters to model the suspension system.

The front and rear axle suspension forces are given by:

$$\begin{array}{l}F{s}_F=N_F\left[F{k}_F+F{b}_F\right]\\ F{s}_R=N_R\left[F{k}_R+F{b}_R\right]\end{array}$$

The block uses lookup tables to implement the front and rear suspension stiffness. To account for kinematic and material nonlinearities, including collisions with end-stops, the tables are functions of the stroke.

$$\begin{array}{l}F{k}_F=f(d{Z}_F)\\ F{k}_R=f(d{Z}_R)\end{array}$$

The block uses lookup tables to implement the front and rear suspension damping. To account for nonlinearities, compression, and rebound, the tables are functions of the stroke rate.

$$\begin{array}{l}F{b}_F=f(d{\dot{Z}}_F)\\ F{b}_R=f(d{\dot{Z}}_R)\end{array}$$

The stroke is the difference in the vehicle vertical and axle positions. The stroke rate is the difference in the vertical and axle velocities.

$$\begin{array}{l}d{Z}_F=Z_F-{\overline{Z}}_F\\ d{Z}_R=Z_R-{\overline{Z}}_R\\ d{\dot{Z}}_F={\dot{Z}}_F-{\dot{\overline{Z}}}_F\\ d{\dot{Z}}_R={\dot{Z}}_R-{\dot{\overline{Z}}}_R\end{array}$$

When the Ground interaction type parameter is Grade angle, the axle vertical positions ($${\overline{Z}}_F,{\overline{Z}}_R$$) and velocities ($${\dot{\overline{Z}}}_F,{\dot{\overline{Z}}}_R$$) are set to 0.

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 vehicle, the block uses the net relative airspeed:

$$\begin{array}{l}{F}_{d,x}=\frac{1}{2TR}{C}_d{A}_f{P}_{abs}{(}^{\dot{x}}\\ F_{d,z}=\frac{1}{2TR}{C}_l{A}_f{P}_{abs}{(}^{\dot{x}}\\ M_{d,y}=\frac{1}{2TR}{C}_{pm}{A}_f{P}_{abs}{(}^{\dot{x}}(a+b)\end{array}$$

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Equations
PwrInfo	PwrTrnsfrd — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	PwrFxExt	Externally applied longitudinal force power	$P_{FxExt}=F_{xExt}\dot{x}$
		PwrFzExt	Externally applied longitudinal force power	$P_{FzExt}=F_{zExt}\dot{z}$
		PwrMyExt	Externally applied pitch moment power	$P_{MzExt}=M_{zExt}\dot{\theta }$
		PwrFwFx	Longitudinal force applied at the front axle	$P_{FwFx}=F_{wF}\dot{x}$
		PwrFwRx	Longitudinal force applied at the rear axle	$P_{FwRx}=F_{wR}\dot{x}$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrFsF	Internal power transferred between suspension and vehicle body at the front axle	$$P_{Fs,F}=-P_{FwFx}+P_{FsbF}+P_{Fsk,F}+F_{xF}{\dot{x}}_F+F_{zF}{\dot{z}}_F$$
		PwrFsR	Internal power transferred between suspension and vehicle body at the rear axle	$P_{Fs,R}=-P_{FwRx}+P_{Fsb,R}+P_{Fsk,R}+F_{xF}{\dot{x}}_F+F_{zF}{\dot{z}}_F$
		PwrFxDrag	Longitudinal drag force power	$P_{d,x}=F_{d,x}\dot{x}$
		PwrFzDrag	Vertical drag force power	$P_{d,z}=F_{d,z}\dot{z}$
		PwrMyDrag	Drag pitch moment power	$P_{d,My}=M_{d,y}\dot{\theta }$
		PwrFsb	Total suspension damping power	$P_{Fsb}={\displaystyle \sum }_{i=F,R}^{}{F}_{sb,i}{\dot{z}}_i$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrStoredGrvty	Rate change in gravitational potential energy	$P_g=-mg\dot{Z}$
		PwrStoredxdot	Rate of change of longitudinal kinetic energy	$P_{\dot{x}}=m\ddot{x}\dot{x}$
		PwrStoredzdot	Rate of change of longitudinal kinetic energy	$P_{\dot{z}}=m\ddot{z}\dot{z}$
		PwrStoredq	Rate of change of rotational pitch kinetic energy	$P_{\dot{\theta }}=I_{yy}\ddot{\theta }\dot{\theta }$
		PwrStoredFsFzSprng	Stored spring energy from front suspension	$P_{FskF}=F_{sk,F}{\dot{z}}_F$
		PwrStoredFsRzSprng	Stored spring energy from rear suspension	$P_{FskF}=F_{sk,R}{\dot{z}}_R$

The equations use these variables.

Fx	Longitudinal force on vehicle
Fz	Normal force on vehicle
My	Torque on vehicle about the vehicle-fixed y-axis
FwF, FwR	Longitudinal force on front and rear axles along vehicle-fixed x-axis
Fd,x, Fd,z	Longitudinal and normal drag force on vehicle CG
Fsx,F, Fsx,R	Longitudinal suspension force on front and rear axles
Fsz,F, Fsz,R	Normal suspension force on front and rear axles
Fg,x,Fg,z	Longitudinal and normal gravitational force on vehicle along the vehicle-fixed frame
Md,y	Torque due to drag on vehicle about the vehicle-fixed y-axis
a,b	Distance of front and rear axles, respectively, from the normal projection point of vehicle CG onto the common axle plane
h	Height of vehicle CG above the axle plane along vehicle-fixed z-axis
FsF, FsR	Front and rear axle suspension force along vehicle-fixed z-axis
ZwF, ZwR	Front and rear vehicle normal position along earth-fixed z-axis
Θ	Vehicle pitch angle about the vehicle-fixed y-axis
m	Vehicle body mass
NF, NR	Number of front and rear wheels
Iyy	Vehicle body moment of inertia about the vehicle-fixed y-axis
x, $$\dot{x}$$, $$\ddot{x}$$	Vehicle longitudinal position, velocity, and acceleration along the vehicle-fixed x-axis
$$z\text{, }\dot{z}\text{, }\ddot{z}$$	Vehicle normal position, velocity, and acceleration along the vehicle-fixed z-axis
FkF, FkR	Front and rear wheel suspension stiffness force along vehicle-fixed z-axis
FbF, FbR	Front and rear wheel suspension damping force along vehicle-fixed z-axis
ZF, ZR	Front and rear vehicle vertical position along earth-fixed Z-axis
$${\dot{Z}}_F,{\dot{Z}}_R$$	Front and rear vehicle vertical velocity along vehicle-fixed z-axis
$${\overline{Z}}_F,{\overline{Z}}_R$$	Front and rear wheel axle vertical position along vehicle-fixed z-axis
$${\dot{\overline{Z}}}_F,{\dot{\overline{Z}}}_R$$	Front and rear wheel axle vertical velocity along earth-fixed z-axis
dZF, dZR	Front and rear axle suspension deflection along vehicle-fixed z-axis
$$d{\dot{Z}}_F,d{\dot{Z}}_R$$	Front and rear axle suspension deflection rate along vehicle-fixed z-axis
Cd	Frontal air drag coefficient acting along the vehicle-fixed x-axis
Cl	Lateral air drag coefficient acting along the vehicle-fixed z-axis
Cpm	Air drag pitch moment acting about the vehicle-fixed y-axis
Af	Frontal area
Pabs	Environmental absolute pressure
R	Atmospheric specific gas constant
T	Environmental air temperature
wx	Wind speed along the vehicle-fixed x-axis

Ports

Input

FExt — External force on vehicle CG

array

External forces applied to vehicle CG, F_xext, F_yext, F_zext, in vehicle-fixed frame, in N. Signal vector dimensions are [1x3] or [3x1].

Dependencies

To enable this port, select External forces.

MExt — External moment about vehicle CG

array

External moment about vehicle CG, M_x, M_y, M_z, in the vehicle-fixed frame, in N·m. Signal vector dimensions are [1x3] or [3x1].

Dependencies

To enable this port, select External moments.

FwF — Total longitudinal force on the front axle

scalar

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

FwR — Total longitudinal force on the rear axle

scalar

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

Grade — Road grade angle

scalar

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

FsF — Suspension force on front axle per wheel

vector

Suspension force on front axle, Fs_F, along the vehicle-fixed z-axis, in N.

Dependencies

To enable this port, for the Ground interaction type parameter, select External suspension.

FsR — Suspension force on rear axle per wheel

vector

Suspension force on rear axle, Fs_R, along the vehicle-fixed z-axis, in N.

Dependencies

To enable this port, for the Ground interaction type parameter, select External suspension.

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].

AirTemp — 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 enable this port, select Air temperature.

zF,R — Forward and rear axle positions

vector

Forward and rear axle positions along the vehicle-fixed z-axis, $${\overline{Z}}_F,{\overline{Z}}_R$$, in m.

Dependencies

To enable this port, for the Ground interaction type parameter, select Axle displacement, velocity.

zdotF,R — Forward and rear axle velocities

vector

Forward and rear axle velocities along the vehicle-fixed z-axis, $${\dot{\overline{Z}}}_F,{\dot{\overline{Z}}}_R$$, in m/s.

Dependencies

To enable this port, for the Ground interaction type parameter, select Axle displacement, velocity.

Output

Info — Bus signal

bus

Bus signal containing these block values.

Signal					Description	Value	Units
InertFrm	Cg	Disp	X		Vehicle CG displacement along earth-fixed X-axis	Computed	m
			Y		Vehicle CG displacement along earth-fixed Y-axis	0	m
			Z		Vehicle CG displacement along earth-fixed Z-axis	Computed	m
		Vel	Xdot		Vehicle CG velocity along earth-fixed X-axis	Computed	m/s
			Ydot		Vehicle CG velocity along earth-fixed Y-axis	0	m/s
			Zdot		Vehicle CG velocity along earth-fixed Z-axis	Computed	m/s
		Ang	phi		Rotation of vehicle-fixed frame about the earth-fixed X-axis (roll)	0	rad
			theta		Rotation of vehicle-fixed frame about the earth-fixed Y-axis (pitch)	Computed	rad
			psi		Rotation of vehicle-fixed frame about the earth-fixed Z-axis (yaw)	0	rad
	FrntAxl	Disp	X		Front axle displacement along the earth-fixed X-axis	Computed	m
			Y		Front axle displacement along the earth-fixed Y-axis	0	m
			Z		Front axle displacement along the earth-fixed Z-axis	Computed	m
		Vel	Xdot		Front axle velocity along the earth-fixed X-axis	Computed	m/s
			Ydot		Front axle velocity along the earth-fixed Y-axis	0	m/s
			Zdot		Front axle velocity along the earth-fixed Z-axis	Computed	m/s
	RearAxl	Disp	X		Rear axle displacement along the earth-fixed X-axis	Computed	m
			Y		Rear axle displacement along the earth-fixed Y-axis	0	m
			Z		Rear axle displacement along the earth-fixed Z-axis	Computed	m
		Vel	Xdot		Rear axle velocity along the earth-fixed X-axis	Computed	m/s
			Ydot		Rear axle velocity along the earth-fixed Y-axis	0	m/s
			Zdot		Rear axle velocity along the earth-fixed Z-axis	Computed	m/s
BdyFrm	Cg	Disp	x		Vehicle CG displacement along the vehicle-fixed x-axis	Computed	m
			y		Vehicle CG displacement along the vehicle-fixed y-axis	0	m
			z		Vehicle CG displacement along the vehicle-fixed z-axis	Computed	m
		Vel	xdot		Vehicle CG velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Vehicle CG velocity along the vehicle-fixed y-axis	0	m/s
			zdot		Vehicle CG velocity along the vehicle-fixed z-axis	Computed	m/s
		AngVel	p		Vehicle angular velocity about the vehicle-fixed x-axis (roll rate)	0	rad/s
			q		Vehicle angular velocity about the vehicle-fixed y-axis (pitch rate)	Computed	rad/s
			r		Vehicle angular velocity about the vehicle-fixed z-axis (yaw rate)	0	rad/s
		Accel	ax		Vehicle CG acceleration along the vehicle-fixed x-axis	Computed	gn
			ay		Vehicle CG acceleration along the vehicle-fixed y-axis	0	gn
			az		Vehicle CG acceleration along the vehicle-fixed z-axis	Computed	gn
	Forces	Body	Fx		Net force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy		Net force on vehicle CG along the vehicle-fixed y-axis	0	N
			Fz		Net force on vehicle CG along the vehicle-fixed z-axis	Computed	N
		Ext	Fx		External force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy		External force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz		External force on vehicle CG along the vehicle-fixed z-axis	Computed	N
		FrntAxl	Fx		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	0	N
			Fz		Normal force on front axle, along the vehicle-fixed z-axis	Computed	N
		RearAxl	Fx		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	0	N
			Fz		Normal force on rear axle, along the vehicle-fixed z-axis	Computed	N
		Tires	FrntTire	Fx	Front tire force, along the vehicle-fixed x-axis	0	N
				Fy	Front tire force, along the vehicle-fixed y-axis	0	N
				Fz	Front tire force, along the vehicle-fixed z-axis	Computed	N
			RearTire	Fx	Rear tire force, along the vehicle-fixed x-axis	0	N
				Fy	Rear tire force, along the vehicle-fixed y-axis	0	N
				Fz	Rear tire force, along the vehicle-fixed z-axis	Computed	N
		Drag	Fx		Drag force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy		Drag force on vehicle CG along the vehicle-fixed y-axis	Computed	N
			Fz		Drag force on vehicle CG along the vehicle-fixed z-axis	Computed	N
		Grvty	Fx		Gravity force on vehicle CG along the vehicle-fixed x-axis	Computed	N
			Fy		Gravity force on vehicle CG along the vehicle-fixed y-axis	0	N
			Fz		Gravity force on vehicle CG along the vehicle-fixed z-axis	Computed	N
	Moments	Body	Mx		Body moment on vehicle CG about the vehicle-fixed x-axis	0	N·m
			My		Body moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			Mz		Body moment on vehicle CG about the vehicle-fixed z-axis	0	N·m
		Drag	Mx		Drag moment on vehicle CG about the vehicle-fixed x-axis	0	N·m
			My		Drag moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			Mz		Drag moment on vehicle CG about the vehicle-fixed z-axis	0	N·m
		Ext	Fx		External moment on vehicle CG about the vehicle-fixed x-axis	Computed	N·m
			Fy		External moment on vehicle CG about the vehicle-fixed y-axis	Computed	N·m
			Fz		External moment on vehicle CG about the vehicle-fixed z-axis	Computed	N·m
	FrntAxl	Disp	x		Front axle displacement along the vehicle-fixed x-axis	Computed	m
			y		Front axle displacement along the vehicle-fixed y-axis	0	m
			z		Front axle displacement along the vehicle-fixed z-axis	Computed	m
		Vel	xdot		Front axle velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Front axle velocity along the vehicle-fixed y-axis	0	m/s
			zdot		Front axle velocity along the vehicle-fixed z-axis	Computed	m/s
		Steer	WhlAngFL		Front left wheel steering angle	Computed	rad
			WhlAngFR		Front right wheel steering angle	Computed	rad
	RearAxl	Disp	x		Rear axle displacement along the vehicle-fixed x-axis	Computed	m
			y		Rear axle displacement along the vehicle-fixed y-axis	0	m
			z		Rear axle displacement along the vehicle-fixed z-axis	Computed	m
		Vel	xdot		Rear axle velocity along the vehicle-fixed x-axis	Computed	m/s
			ydot		Rear axle velocity along the vehicle-fixed y-axis	0	m/s
			zdot		Rear axle velocity along the vehicle-fixed z-axis	Computed	m/s
		Steer	WhlAngRL		Rear left wheel steering angle	Computed	rad
			WhlAngRR		Rear right wheel steering angle	Computed	rad
	Pwr	PwrExt			Applied external power	Computed	W
		Drag			Power loss due to drag	Computed	W
PwrInfo	PwrTrnsfrd	PwrFxExt			Externally applied longitudinal force power	Computed	W
		PwrFzExt			Externally applied longitudinal force power	Computed	W
		PwrMyExt			Externally applied pitch moment power	Computed	W
		PwrFwFx			Longitudinal force applied at the front axle	Computed	W
		PwrFwRx			Longitudinal force applied at the rear axle	Computed	W
	PwrNotTrnsfrd	PwrFsF			Internal power transferred between suspension and vehicle body at the front axle	Computed	W
		PwrFsR			Internal power transferred between suspension and vehicle body at the rear axle	Computed	W
		PwrFxDrag			Longitudinal drag force power	Computed	W
		PwrFzDrag			Vertical drag force power	Computed	W
		PwrMyDrag			Drag pitch moment power	Computed	W
		PwrFsb			Total suspension damping power	Computed	W
	PwrStored	PwrStoredGrvty			Rate change in gravitational potential energy	Computed	W
		PwrStoredxdot			Rate of change of longitudinal kinetic energy	Computed	W
		PwrStoredzdot			Rate of change of longitudinal kinetic energy	Computed	W
		PwrStoredq			Rate of change of rotational pitch kinetic energy	Computed	W
		PwrStoredFsFzSprng			Stored spring energy from front suspension	Computed	W
		PwrStoredFsRzSprng			Stored spring energy from rear suspension	Computed	W

xdot — Vehicle longitudinal velocity

scalar

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

FzF — Front axle normal force

scalar

Normal force on front axle, Fz_F, along the vehicle-fixed z-axis, in N.

FzR — Rear axle normal force

scalar

Normal force on rear axle, Fz_R, along the vehicle-fixed z-axis, in N.

Parameters

Options

Ground interaction type — Axle attachment to the vehicle

Grade angle (default) | Axle displacement, velocity | External suspension

Specify the type of axle attachment to the vehicle:

• Grade angle — Vertical axle displacement from road surface to axles remains constant. The block uses tabular stiffness and damping parameters to model the suspension forces acting between the vehicle body and axles.

• Axle displacement, velocity — Axles have input-provided vertical displacement and velocity with respect to the road grade. The block uses tabular stiffness and damping parameters to model the suspension forces acting between the vehicle body and axle.

• External suspension — Axles have externally applied forces for coupling the vehicle body to custom suspension models.

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.

Air temperature — AirTemp input port

off (default) | on

Specify to create input port AirTemp.

Longitudinal

Number of wheels on front axle, NF — Front wheel count

2 (default) | scalar

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

Number of wheels on rear axle, NR — Rear wheel count

2 (default) | scalar

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

Mass, m — Vehicle mass

1200 (default) | scalar

Vehicle mass, m, in kg.

Horizontal distance from CG to front axle, a — Front axle distance

1.4 (default) | scalar

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

Horizontal distance from CG to rear axle, b — Rear axle distance

1.8 (default) | scalar

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

CG height above axles, h — Height

0.35 (default) | scalar

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

Longitudinal drag coefficient, Cd — Drag

.3 (default) | scalar

Air drag coefficient, C_d. The value is dimensionless.

Frontal area, Af — Area

2 (default) | scalar

Effective vehicle cross-sectional area, A_f to calculate the aerodynamic drag force on the vehicle, in m^2.

Initial position, x_o — Position

0 (default) | scalar

Vehicle body longitudinal initial position along earth-fixed x-axis, x_o, in m.

Initial velocity, xdot_o — Velocity

0 (default) | scalar

Vehicle body longitudinal initial velocity along earth-fixed x-axis, $${\dot{x}}_0$$, in m/s.

Vertical

Longitudinal lift coefficient, Cl — Lift

.1 (default) | scalar

Lift coefficient, C_l. The value is dimensionless.

Initial vertical position, z_o — Position

-.35 (default) | scalar

Initial vertical CG position, z_o, along the vehicle-fixed z-axis, in m.

Initial vertical velocity, zdot_o — Velocity

0 (default) | scalar

Initial vertical CG velocity, zdot_o, along the vehicle-fixed z-axis, in m.

Pitch

Inertia, Iyy — About body y-axis

3500 (default) | scalar

Vehicle body moment of inertia about body z-axis.

Longitudinal drag pitch moment, Cpm — Drag coefficient

.1 (default) | scalar

Pitch drag moment coefficient. The value is dimensionless.

Initial pitch angle, theta_o — Pitch

0 (default) | scalar

Initial pitch angle about body z-axis, in rad.

Initial angular velocity, q_o — Pitch velocity

0 (default) | scalar

Initial vehicle body angular velocity about body z-axis, in rad/s.

Suspension

Front axle stiffness force data, FskF — Force

[-50, -1, 0, 2, 3, 52].*1.5e4 (default) | vector

Front axle stiffness force data, Fk_F, in N.

Dependencies

To enable this parameter, for the Ground interaction type parameter, select Grade angle or Axle displacement, velocity.

Front axle displacement data, dzsF — Displacement

[-5e-3, -1e-4, 0, .2, .2001, .2051] (default) | vector

Front axle displacement data, in m.

Dependencies

To enable this parameter, for the Ground interaction type parameter, select Grade angle or Axle displacement, velocity.

Front axle damping force data, FsbF — Damping force

[-10000 -100 -10 0 10 100 10000] (default) | vector

Front axle damping force, in N.

Dependencies

To enable this parameter, for the Ground interaction type parameter, select Grade angle or Axle displacement, velocity.

Front axle velocity data, dzdotsF — Velocity

[-10 -1 -.1 0 .1 1 10] (default) | vector

Front axle velocity data, in m/s.

Dependencies

To enable this parameter, for the Ground interaction type parameter, select Grade angle or Axle displacement, velocity.

Rear axle stiffness force data, FskR — Force

[-50, -1, 0, 2, 3, 52].*1e4 (default) | vector

Rear axle stiffness force data, in N.

Dependencies

To enable this parameter, for the Ground interaction type parameter, select Grade angle or Axle displacement, velocity.

Rear axle displacement data, dzsR — Displacement

[-5e-3, -1e-4, 0, .2, .2001, .2051] (default) | vector

Rear axle displacement data, in m.

Dependencies

To enable this parameter, for the Ground interaction type parameter, select Grade angle or Axle displacement, velocity.

Rear axle damping force data, FsbR — Damping force

[-10000 -100 -10 0 10 100 10000] (default) | vector

Rear axle damping force, in N.

Dependencies

To enable this parameter, for the Ground interaction type parameter, select Grade angle or Axle displacement, velocity.

Rear axle velocity data, dzdotsR — Velocity

[-10 -1 -.1 0 .1 1 10] (default) | vector

Rear axle velocity data, in m/s.

Dependencies

To enable this parameter, for the Ground interaction type parameter, select Grade angle or Axle displacement, velocity.

Environment

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 Air temperature.

Gravitational acceleration, g — Gravity

9.81 (default)

Gravitational acceleration, g, in m/s².

References

[1] Gillespie, Thomas. Fundamentals of Vehicle Dynamics. Warrendale, PA: Society of Automotive Engineers, 1992.

[2] Vehicle Dynamics Standards Committee. Vehicle Dynamics Terminology. SAE J670. Warrendale, PA: Society of Automotive Engineers, 2008.

[3] Technical Committee. Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary. ISO 8855:2011. Geneva, Switzerland: International Organization for Standardization, 2011.

Extended Capabilities

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

Version History

Introduced in R2017a