Longitudinal Vehicle
Longitudinal motion abstract vehicle with ideal brakes and tires
 Library:
Simscape / Driveline / Tires & Vehicles
Description
The Longitudinal Vehicle block represents an abstract vehicle confined to longitudinal motion. You can parameterize an arbitrary vehicle or choose from predefined parameterizations. The block includes optional nonslipping tires and ideal brakes.
You can use this block as a simpler alternative to the Vehicle Body block. The Longitudinal Vehicle block requires less information to parameterize and is more suitable for a nascent design.
The block equations use these variables:
m is the Vehicle mass parameter.
v_{x} is the longitudinal velocity output at the VehSpd port.
F_{x} is the sum of longitudinal forces.
r_{tire} is the radius of the tire and is equivalent to the Tire rolling radius parameter.
F_{drive}, F_{brake}, and F_{resist} are the driving force of the vehicle, the braking force, and the vehicle resistance force, respectively. F_{brake} and F_{resist} oppose the driving motion of the vehicle in the force balance equation.
τ_{axle} is the torque at the axle.
F_{B} is the brake force input from the Brake port.
ω_{axle} is the rotational speed of the axle.
ω_{1} is an arbitrary constant that adjusts the speed range in which the block suppresses F_{brake}.
F_{tire} is the tire rolling resistance.
F_{air} is the drag force due to air resistance.
θ is the road incline angle input from either the Angle, NG, or PG port.
v_{1} is an arbitrary constant that adjusts the speed range in which the block suppresses F_{air} and F_{tire}.
You can access a visualization of the vehicle properties by clicking the vehicle properties hyperlink in the source code. The figure shows the default block properties, where the first plot is the resisting force as a function of vehicle speed for different road grades, and the second plot is the resisting power for a given speed at different road grades.
Parameterizations
For all settings of the Parameterization type parameter, the block calculates the equations of longitudinal vehicle speed as
$$m\frac{d{v}_{x}}{dt}={\displaystyle \sum {F}_{x}},$$
where
$${v}_{x}={r}_{tire}{\omega}_{axle},$$
and
$$\sum {F}_{x}}={F}_{drive}{F}_{brake}{F}_{resist}.$$
The block treats the drive direction as positive in the force balance equation. It solves this equation using these substitutions:
$$\sum {F}_{x}}=\underset{{F}_{drive}}{\underbrace{\frac{{\tau}_{axle}}{{r}_{tire}}}}\underset{{F}_{brake}}{\underbrace{{F}_{B}\mathrm{tanh}\left(\frac{{\omega}_{axle}}{{\omega}_{1}}\right)}}\underset{{F}_{resist}}{\underbrace{\left\{\left({F}_{tire}\mathrm{cos}\theta +{F}_{air}\right)\mathrm{tanh}\left(\frac{{v}_{x}}{{v}_{1}}\right)+mg\mathrm{sin}\theta \right\}.}$$
You can set Parameterization type to
Roadload
or Regular parameter
set
to simulate an arbitrary vehicle. You can also choose from
three predefined parameterizations, Typical small car
,
Typical mediumsized car
, and Typical
large sports utility vehicle
.
When you set Parameterization type to Regular parameter
set
, you can specify the Tire rolling
coefficient, Air drag coefficient, and
Vehicle frontal area parameters of the vehicle, which
the block converts to roadload coefficients.
The block computes the tire rolling resistance as
$${F}_{tire}={C}_{R}mg,$$
where C_{R} is the Tire rolling coefficient parameter.
The block computes the air resistance as
$${F}_{air}=\frac{1}{2}{C}_{D}{A}_{f}{\rho}_{a}{\left({v}_{x}+{v}_{w}\right)}^{2},$$
where C_{D} is the Air drag coefficient parameter, A_{f} is the Vehicle frontal area parameter in m^{2}, and ρ_{A} is the density of dry air. The block assumes ρ_{A} = 1.184 kg/m^{3} at 1 atmosphere.
When you set Parameterization type to
Roadload
, the block applies the standard
roadload formulation and computes the core physics as:
$${F}_{RL}=\underset{{F}_{tire}}{\underbrace{{A}_{RL}+{B}_{RL}{v}_{x}}}+\underset{{F}_{air}}{\underbrace{{C}_{RL}{v}_{x}^{2}}},$$
where A_{RL}, B_{RL}, and C_{RL} are the roadload coefficients.
Note
Each roadload coefficient is specific to its associated units of v_{x}. There are no standard units for these coefficients; however, some texts may assume certain units. Select the correct units when you parameterize these coefficients.
The block uses these coefficients to solve for the values in the core physics as
$${F}_{tire}={A}_{RL}+{B}_{RL}{v}_{x},$$
and
$${F}_{air}={C}_{RL}{\left({v}_{x}+{v}_{w}\right)}^{2}.$$
Here, v_{w} is the wind speed from the Wind port.
You can set Parameterization type to three predefined
parameterizations: Typical small car
,
Typical mediumsized car
, and
Typical large sports utility vehicle
. The values
represent industry averages rather than specific vehicles. You can start with
one of these predefined parameterizations and later adjust these values by
setting Parameterization type to
Roadload
or Regular parameter
set
and using the pertinent information from the tables.
Regular parameter set
Parameterization type  Vehicle mass  Tire rolling radius  Tire rolling coefficient  Drag coefficient  Frontal Area 

Typical small car 



 0.9*1.65*1.45 = 
Typical mediumsized
car 



 0.9*1.75*1.5 = 
Typical large sports utility
vehicle 



 0.9*1.88*1.85 = 
Note that each predefined parameterization assumes B = 0 for the roadload method.
Roadload
Parameterization type  A  B  C 

Typical small car 



Typical mediumsized
car 



Typical large sports utility
vehicle 



Where the Vehicle frontal area equation corresponds to 0.9·vehicle width·vehicle height.
Variables
To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables and Initial Conditions for Blocks with Finite Moist Air Volume.
Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.
Ports
Input
Output
Conserving
Parameters
References
[1] Eriksson, Lars, and Lars Nielsen. Modeling and Control of Engines and Drivelines: Eriksson/Modeling and Control of Engines and Drivelines. Chichester, UK: John Wiley & Sons, Ltd, 2014. https://doi.org/10.1002/9781118536186.
[2] Heywood, John B. Internal Combustion Engine Fundamentals. Second edition. New York: McGrawHill Education, 2018.
[3] Society of Automotive Engineers: Light Duty Vehicle Performance and Economy Measure Committee. “Chassis Dynamometer Simulation of Road Load Using Coastdown Techniques. SAE J2264” SAE International. 2014. https://doi.org/10.4271/J2264_201401.
[4] Society of Automotive Engineers: Light Duty Vehicle Performance and Economy Measure Committee. “Road Load Measurement and Dynamometer Simulation Using Coastdown Techniques. SAE J1263” SAE International. 2010. https://doi.org/10.4271/J1263_201003.