Vehicle Body Total Road Load

Vehicle motion using coast-down testing coefficients

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

Description

The Vehicle Body Total Road Load block implements a one degree-of-freedom (1DOF) rigid vehicle model using coast-down testing coefficients. You can use this block in a vehicle model to represent the load that the driveline and chassis applies to a transmission or engine. It is suitable for system-level performance, component sizing, fuel economy, or drive cycle tracking studies. The block calculates the dynamic powertrain load with minimal parameterization or computational cost.

You can configure the block for kinematic, force, or total power input.

• Kinematic — Block uses the vehicle longitudinal velocity and acceleration to calculate the tractive force and power.

• Force — Block uses the tractive force to calculate the vehicle longitudinal displacement and velocity.

• Power — Block uses the engine or transmission power to calculate the vehicle longitudinal displacement and velocity.

Dynamics

To calculate the total road load acting on the vehicle, the block implements this equation.

$$F_{road}=a+b\dot{x}+c{\dot{x}}^2+mg\sin (\theta )$$

To determine the coefficients a, b, and c, you can use a test procedure similar to the one described in Road Load Measurement and Dynamometer Simulation Using Coastdown Techniques. You can also use Simulink^® Design Optimization™ to fit the coefficients to measured data (see Estimate Vehicle Drag Coefficients by Coast-Down Testing (Simulink Design Optimization)).

To calculate the vehicle motion, the block uses Newton’s law for rigid bodies.

$$F_{total}=m\ddot{x}+F_{road}$$

Total power input is a product of the total force and longitudinal velocity. Power due to road and gravitational forces is a product of the road force and longitudinal velocity.

$$\begin{array}{l}{P}_{total}=F_{total}\dot{x}\\ P_{road}=F_{road}\dot{x}\end{array}$$

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Variable	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	PFxExt	$P_{FxExt}=F_{total}\dot{x}$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrFxDrag	Drag force power	PD	$P_d=-(a+b\dot{x}+c{\dot{x}}^2)\dot{x}$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	wrStoredGrvty	Rate change in gravitational potential energy	Pg	$P_g=-mg\dot{Z}$
		PwrStoredxdot	Rate in change of longitudinal kinetic energy	Pxdot	$P_{\dot{x}}=m\ddot{x}\dot{x}$

The equations use these variables.

a	Steady-state rolling resistance coefficient
b	Viscous driveline and rolling resistance coefficient
c	Aerodynamic drag coefficient
g	Gravitational acceleration
x	Vehicle longitudinal displacement with respect to ground, in the vehicle-fixed frame
$$\dot{x}$$	Vehicle longitudinal velocity with respect to ground, in the vehicle-fixed frame
$$\ddot{x}$$	Vehicle longitudinal acceleration with respect to ground, vehicle-fixed frame
m	Vehicle body mass
Θ	Road grade angle
Ftotal	Total force acting on vehicle
Froad	Resistive road load due to losses and gravitational load
Ptotal	Total tractive input power
Proad	Total power due to losses and gravitational load
$$\dot{Z}$$	Vehicle vertical velocity along the vehicle-fixed z-axis

Ports

Input

xdot — Vehicle longitudinal velocity

scalar

Vehicle total longitudinal velocity, $$\dot{x}$$, in m/s.

Dependencies

To enable this port, for the Input Mode parameter, select Kinematic.

xddot — Vehicle longitudinal acceleration

scalar

Vehicle total longitudinal acceleration, $$\ddot{x}$$, in m/s^2.

Dependencies

To enable this port, for the Input Mode parameter, select Kinematic.

PwrTot — Tractive input power

scalar

Tractive input power, P_total, in W.

Dependencies

To enable this port, for the Input Mode parameter, select Power.

ForceTot — Tractive input force

scalar

Tractive input force, F_total, in N.

Dependencies

To enable this port, for the Input Mode parameter, select Force.

Grade — Road grade angle

scalar

Road grade angle, Θ, in deg.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

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
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
		Acc	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	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	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	0	N
			Fz	External force on vehicle CG along the vehicle-fixed z-axis	0	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	0	N
			Fz	Drag force on vehicle CG along the vehicle-fixed z-axis	0	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
	Pwr	PwrExt		Applied external power	Computed	W
		Drag		Power loss due to drag	Computed	W
PwrInfo	PwrTrnsfrd	PwrFxExt		Externally applied force power	PFxExt	W
	PwrNotTrnsfrd	PwrFxDrag		Drag force power	PD	W
	PwrStored	wrStoredGrvty		Rate change in gravitational potential energy	Pg	W
		PwrStoredxdot		Rate in change of longitudinal kinetic energy	Pxdot	W

xdot — Vehicle longitudinal velocity

scalar

Vehicle total longitudinal velocity, $$\dot{x}$$, in m/s.

Dependencies

To enable this port, for the Input Mode parameter, select Power or Force.

ForceTot — Tractive input force

scalar

Tractive input force, F_total, in N.

Dependencies

To enable this port, for the Input Mode parameter, select Kinematic.

Parameters

Input Mode — Specify input mode

Kinematic (default) | Force | Power

Specify the input type.

• Kinematic — Block uses the vehicle longitudinal velocity and acceleration to calculate the tractive force and power. Use this configuration for powertrain, driveline, and braking system design, or component sizing.

• Force — Block uses the tractive force to calculate the vehicle longitudinal displacement and velocity. Use this configuration for system-level performance, fuel economy, or drive cycle tracking studies.

• Power — Block uses the engine or transmission power to calculate the vehicle longitudinal displacement and velocity. Use this configuration for system-level performance, fuel economy, or drive cycle tracking studies.

Dependencies

This table summarizes the port and input mode configurations.

Input Mode	Creates Ports
Kinematic	xdot xddot
Force	Force
Power	Power

Mass — Vehicle body mass

1200 (default) | scalar

Vehicle body mass, m, in kg.

Rolling resistance coefficient, a — Rolling

196 (default) | scalar

Steady-state rolling resistance coefficient, a, in N.

Rolling and driveline resistance coefficient, b — Rolling and driveline

2.232 (default) | scalar

Viscous driveline and rolling resistance coefficient, b, in N*s/m.

Aerodynamic drag coefficient, c — Drag

0.389 (default) | scalar

Aerodynamic drag coefficient, c, in N·s^2/m.

Gravitational acceleration, g — Gravity

9.81 (default) | scalar

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

Initial position, x_o — Position

0 (default) | scalar

Vehicle longitudinal initial position, in m.

Initial velocity, xdot_o — Velocity

0 (default) | scalar

Vehicle longitudinal initial velocity with respect to ground, in m/s.

References

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

[2] Light Duty Vehicle Performance And Economy Measure Committee. Road Load Measurement and Dynamometer Simulation Using Coastdown Techniques. Standard J1263_201003. SAE International, March 2010.

Extended Capabilities

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

Version History

Introduced in R2017a