Vehicle Body 1DOF Longitudinal

Two-axle vehicle in forward and reverse motion

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

Description

The Vehicle Body 1DOF Longitudinal block implements a one degree-of-freedom (1DOF) rigid vehicle body with constant mass undergoing longitudinal (that is, forward and reverse) motion. Use the block:

• In powertrain and fuel economy studies to represent the vehicle inertial and drag loads when weight transfer from vertical and pitch motions are negligible.

• To determine the engine torque and power required for the vehicle to follow a specified drive cycle.

You can select block options to create input ports for external forces, moments, air temperature, and wind speed.

Block Option Setting	External Input Ports	Description
External forces	FExt	External force applied to vehicle CG in the vehicle-fixed frame.
External moments	MExt	External moment about vehicle CG in the vehicle-fixed frame.
Air temperature	AirTemp	Ambient air temperature. Consider this option if you want to vary the temperature during run-time.
Wind X,Y,Z	WindXYZ	Wind speed along earth-fixed X-, Y-, and Z-axes. If you do not select this option, the block implements input port WindX — Longitudinal wind speed along the earth-fixed X-axis.

Vehicle Body Model

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). The grade angle changes the direction of the resolved gravitational force acting on the vehicle CG. Similarly, the block resolves the resistive aerodynamic drag force on the vehicle CM.

The Vehicle Body 1DOF Longitudinal block implements these equations.

$$\begin{array}{l}{F}_b=m\ddot{x}\\ \\ F_b=F_{xF}+F_{xR}-F_{d,x}+F_{ext,x}-mg\sin \gamma \end{array}$$

Zero normal acceleration and zero pitch torque determine the normal force on each front and rear axles.

$$\begin{array}{l}{F}_{zF}=\frac{-M_{ext,y}-M_{d,y}+ b\left(F_{d,z}+F_{ext,z}+ mg\cos \gamma \right)-h\left(-F_{ext,x}+F_{d,x}+ mg\sin \gamma +m\ddot{x}\right)}{N_F(a+b)}\\ \\ F_{zR}=\frac{M_{ext,y}+M_{d,y}+ a\left(F_{d,z}+F_{ext,z}+ mg\cos \gamma \right)+h\left(-F_{ext,x}+F_{d,x}+ mg\sin \gamma +m\ddot{x}\right)}{N_R(a+b)}\end{array}$$

The wheel normal forces satisfy this equation.

$$N_F{F}_{zF}+N_R{F}_{zR}-F_{ext,z}=mg\cos \gamma$$

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.

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

By default, to calculate the wind speed along the vehicle-fixed x-axis, the block uses the longitudinal wind speed along the earth-fixed X-axis. If you select WindX,Y,Z, the block uses the wind speed along the earth-fixed X-, Y-, Z-axes.

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 force power	$P_{FxExt}=F_{xExt}\dot{x}$
		PwrFwFx	Longitudinal force power applied at the front axle	$P_{FwFx}=F_{wF}\dot{x}$
		PwrFwRx	Longitudinal force power 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	PwrFxDrag	Drag force power	$P_d=-\frac{0.5C_d{A}_f{P}_{abs}{\left({\dot{x}}^2-w_x\right)}^2}{287.058T}\dot{x}$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	wrStoredGrvty	Rate change in gravitational potential energy	$P_g=-mg\dot{Z}$
		PwrStoredxdot	Rate in change of longitudinal kinetic energy	$P_{\dot{x}}=m\ddot{x}\dot{x}$

The equations use these variables.

Fxf, Fxr	Longitudinal forces on each wheel at the front and rear ground contact points, respectively
Fzf, Fzr	Normal load forces on each wheel at the front and rear ground contact points, respectively
FwF, FwR	Longitudinal force on front and rear axles along vehicle-fixed x-axis
FxExt, FwR	External force along the vehicle-fixed x-axis
Fd,x, Fd,z	Longitudinal and normal drag force on vehicle CG
Md,y	Torque due to drag on vehicle about the vehicle-fixed y-axis
Fd	Aerodynamic drag force
Vx	Velocity of the vehicle. When Vx > 0, the vehicle moves forward. When Vx < 0, the vehicle moves backward.
Nf, Nr	Number of wheels on front and rear axle, respectively
$\gamma$	Angle of road grade
m	Vehicle body mass
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
Cd	Frontal air drag coefficient
Af	Frontal area
Pabs	Absolute pressure
ρ	Mass density of air
x, $$\dot{x}$$, $$\ddot{x}$$	Vehicle longitudinal position, velocity, and acceleration along the vehicle-fixed x-axis
wx	Wind speed along the vehicle-fixed x-axis
$$\dot{Z}$$	Vehicle vertical velocity along the vehicle-fixed z-axis

Limitations

The Vehicle Body 1DOF Longitudinal block lets you model only longitudinal dynamics, parallel to the ground and oriented along the direction of motion. The vehicle is assumed to be in pitch and normal equilibrium. The block does not model pitch or vertical movement. To model a vehicle with three degrees-of-freedom (DOF), use the Vehicle Body 3DOF Longitudinal.

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 front axle

scalar

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

FwR — Total longitudinal force on 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.

WindX — Longitudinal wind speed

scalar

Longitudinal wind speed, W_w, along earth-fixed X-axis, in m/s.

Dependencies

To enable this port, clear Wind X,Y,Z components.

WindXYZ — Wind speed

array

Wind speed, W_w, W_wY, W_wZ along inertial X-, Y-, and Z-axes, in m/s. Signal vector dimensions are [1x3] or [3x1].

Dependencies

To enable this port, select Wind X,Y,Z components.

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.

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 (input - grade angle)	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	0	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	0	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)	0	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	0	gn
	Forces	Body	Fx		Net force on vehicle CG along the vehicle-fixed x-axis	0	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	0	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	0	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	0	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		Net moment on vehicle CG about the vehicle-fixed x-axis	0	N·m
			My		Net moment on vehicle CG about the vehicle-fixed y-axis	0	N·m
			Mz		Net 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	Computed	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	Computed	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 force power	Computed	W
		PwrFwFx			Longitudinal force power applied at the front axle	Computed	W
		PwrFwRx			Longitudinal force power applied at the rear axle	Computed	W
	PwrNotTrnsfrd	PwrFxDrag			Drag force power	Computed	W
	PwrStored	wrStoredGrvty			Rate change in gravitational potential energy	Computed	W
		PwrStoredxdot			Rate in change of longitudinal kinetic energy	Computed	W

xdot — Vehicle body longitudinal velocity

scalar

Vehicle body longitudinal velocity along the vehicle-fixed reference frame x-axis, in m/s.

FzF — Front axle normal force

scalar

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

FzR — Rear axle normal force

scalar

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

Parameters

Options

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.

Wind X,Y,Z components — WindXYZ input port

off (default) | on

Specify to create input port WindXYZ.

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

1500 (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

.35 (default) | scalar

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

Longitudinal drag coefficient, Cd — Drag

.3 (default) | scalar

Air drag coefficient, C_d. The value is dimensionless.

Longitudinal lift coefficient, Cl — Lift

0 (default) | scalar

Air lift coefficient, C_l. The value is dimensionless.

Longitudinal drag pitch moment, Cpm — Pitch drag

0 (default) | scalar

Pitch drag moment coefficient, C_pm. The value is dimensionless.

Frontal area, Af — Area

4 (default) | scalar

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

Initial position, x_o — Position

0 (default) | scalar

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

Initial velocity, xdot_o — Velocity

0 (default) | scalar

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

Environment

Absolute air pressure, Pabs — Pressure

101325 (default) | scalar

Environmental air absolute pressure, P_abs, in Pa.

Air temperature, T — 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) | scalar

Gravitational acceleration, g, in m/s².

Extended Capabilities

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

Version History

Introduced in R2017a