Vehicle Body Total Road Load

Vehicle motion using coast-down testing coefficients

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.

$F_{r o a d} = a + b \dot{x} + c {\dot{x}}^{2} + m g \sin (θ)$

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.

$F_{t o t a l} = m \ddot{x} + F_{r o a d}$

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.

$\begin{array}{l} P_{t o t a l} = F_{t o t a l} \dot{x} \\ P_{r o a d} = F_{r o a d} \dot{x} \end{array}$

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	P_FxExt	$P_{F x E x t} = F_{t o t a l} \dot{x}$
	`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	$P_{d} = - (a + b \dot{x} + c {\dot{x}}^{2}) \dot{x}$
	`PwrStored` — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	`wrStoredGrvty`	Rate change in gravitational potential energy	P_g	$P_{g} = - m g \dot{Z}$
		`PwrStoredxdot`	Rate in change of longitudinal kinetic energy	P_xdot	$P_{\dot{x}} = m \ddot{x} \dot{x}$

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
F_total	Total force acting on vehicle
F_road	Resistive road load due to losses and gravitational load
P_total	Total tractive input power
P_road	Total power due to losses and gravitational load
$\dot{Z}$	Vehicle vertical velocity along the vehicle-fixed `z`-axis

Ports

Input

expand all

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

expand all

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
	`Pwr`	`Drag`		Power loss due to drag	Computed	W
`PwrInfo`	`PwrTrnsfrd`	`PwrFxExt`		Externally applied force power	P_FxExt	W
	`PwrNotTrnsfrd`	`PwrFxDrag`		Drag force power	P_D	W
	`PwrStored`	`wrStoredGrvty`		Rate change in gravitational potential energy	P_g	W
	`PwrStored`	`PwrStoredxdot`		Rate in change of longitudinal kinetic energy	P_xdot	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

expand all

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

Input Mode	Creates Ports
`Kinematic`	`xdot` `xddot`
`Force`	`Force`
`Power`	`Power`

Kinematic

xdot

xddot

Force

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

Vehicle Body Total Road Load

Description

Dynamics

Power Accounting

Ports

Input

xdot — Vehicle longitudinal velocity scalar

Dependencies

xddot — Vehicle longitudinal acceleration scalar

Dependencies

PwrTot — Tractive input power scalar

Dependencies

ForceTot — Tractive input force scalar

Dependencies

Grade — Road grade angle scalar

Output

Info — Bus signal bus

xdot — Vehicle longitudinal velocity scalar

Dependencies

ForceTot — Tractive input force scalar

Dependencies

Parameters

Input Mode — Specify input mode Kinematic (default) | Force | Power

Dependencies

Mass — Vehicle body mass 1200 (default) | scalar

Rolling resistance coefficient, a — Rolling 196 (default) | scalar

Rolling and driveline resistance coefficient, b — Rolling and driveline 2.232 (default) | scalar

Aerodynamic drag coefficient, c — Drag 0.389 (default) | scalar

Gravitational acceleration, g — Gravity 9.81 (default) | scalar

Initial position, x_o — Position 0 (default) | scalar

Initial velocity, xdot_o — Velocity 0 (default) | scalar

References

Extended Capabilities

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

Version History

See Also

xdot — Vehicle longitudinal velocity
`scalar`

xddot — Vehicle longitudinal acceleration
`scalar`

PwrTot — Tractive input power
`scalar`

ForceTot — Tractive input force
`scalar`

Grade — Road grade angle
`scalar`

Info — Bus signal
bus

xdot — Vehicle longitudinal velocity
`scalar`

ForceTot — Tractive input force
`scalar`

Input Mode — Specify input mode
`Kinematic` (default) | `Force` | `Power`

Mass — Vehicle body mass
`1200` (default) | `scalar`

Rolling resistance coefficient, a — Rolling
`196` (default) | `scalar`

Rolling and driveline resistance coefficient, b — Rolling and driveline
`2.232` (default) | `scalar`

Aerodynamic drag coefficient, c — Drag
`0.389` (default) | `scalar`

Gravitational acceleration, g — Gravity
`9.81` (default) | `scalar`

Initial position, x_o — Position
`0` (default) | `scalar`

Initial velocity, xdot_o — Velocity
`0` (default) | `scalar`

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