Longitudinal Vehicle

Longitudinal motion abstract vehicle with ideal brakes and tires

Since R2021b

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Libraries:
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 non-slipping 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.

• ω₁ 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.

• v₁ 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

$${\displaystyle \sum F_x}=F_{drive}-F_{brake}-F_{resist}.$$

The block treats the drive direction as positive in the force balance equation. It solves this equation using these substitutions:

$${\displaystyle \sum F_x}=\underset{F_{drive}}{\underbrace{\frac{{\tau }_{axle}}{r_{tire}}}}-\underset{F_{brake}}{\underbrace{F_B\tanh \left(\frac{{\omega }_{axle}}{{\omega }_1}\right)}}-\underset{F_{resist}}{\underbrace{\left\{\left(F_{tire}\cos \theta +F_{air}\right)\tanh \left(\frac{v_x}{v_1}\right)+mg\sin \theta \right\}.}}$$

You can set Parameterization type to Road-load or Regular parameter set to simulate an arbitrary vehicle. You can also choose from three predefined parameterizations, Typical small car, Typical medium-sized car, and Typical large sports utility vehicle.

Regular parameter set

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 road-load 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 m², and ρ_A is the density of dry air. The block assumes ρ_A = 1.184 kg/m³ at 1 atmosphere.

Road-load

When you set Parameterization type to Road-load, the block applies the standard road-load 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 road-load coefficients.

Note

Each road-load 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.

Predefined Parameterizations

You can set Parameterization type to three predefined parameterizations: Typical small car, Typical medium-sized 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 Road-load 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	1100 kg	0.3 m	0.013	0.3	0.9*1.65*1.45 = 2.153 m^2
Typical medium-sized car	1800 kg	0.3 m	0.0136	0.31	0.9*1.75*1.5 = 2.36 m^2
Typical large sports utility vehicle	2600 kg	0.4 m	0.014	0.36	0.9*1.88*1.85 = 3.13 m^2

Note that each predefined parameterization assumes B = 0 for the road-load method.

Road-load

Parameterization type	A	B	C
Typical small car	140.3 N	0 N/(m/s)	0.3824 N*s^2/m^2
Typical medium-sized car	240.1 N	0 N/(m/s)	0.4336 N*s^2/m^2
Typical large sports utility vehicle	357.1 N	0 N/(m/s)	0.6671 N*s^2/m^2

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.

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

Brake — Longitudinal braking force, N

physical signal

Physical signal input port associated with the brakes. The brake port ignores negative values.

Dependencies

To enable this port, set Show brake force inport to On.

Angle — Road incline, rad

physical signal

Physical signal input port associated with the road incline, in radians. This value represents the angle of the road with respect to the horizontal surface at 0 and a 100% grade at pi/4.

Dependencies

To enable this port, set

• Show road slope inport to On

• Slope input type to Incline angle

NG — Normalized road grade, unitless

physical signal

Physical signal input port associated with the normalized road grade. A normalized road grade of 1 is equivalent to a π/4 radian angle.

Dependencies

To enable this port, set

• Show road slope inport to On

• Slope input type to Normalized grade

PG — Percent road grade, unitless

physical signal

Physical signal input port associated with the percent road grade. A percent road grade of 100 is equivalent to a π/4 radian angle.

Dependencies

To enable this port, set

• Show road slope inport to On

• Slope input type to Percent grade

Wind — Longitudinal wind speed, m/s

physical signal

Physical signal input port associated with the longitudinal wind speed. This value is the longitudinal component of the wind speed, where positive values represent a headwind and negative values represent a tailwind.

Dependencies

To enable this port, set Show wind speed inport to On.

Output

VehSpd — Vehicle speed, m/s

physical signal

Physical signal output port associated with the longitudinal velocity of the vehicle.

G — Longitudinal G force, unitless

physical signal

Physical signal port associated with the ratio of the longitudinal vehicle acceleration, a_x, to the gravitational acceleration, g.

Dependencies

To enable this port, set Show G outport to On.

Conserving

Axle — Wheel rotation

mechanical rotational

Mechanical rotational conserving port associated with the axle connection to the wheel hub. Connect this port to a gear system such as a reduction gear.

Parameters

Vehicle

Parameterization type — Vehicle parameterization selection

Regular parameter set (default) | Road-load | Typical small car | Typical medium-sized car | Typical large sports utility vehicle

Option to parameterize the longitudinal vehicle. You can parameterize an arbitrary vehicle by choosing Regular parameter set or Road-load, or select one of three typical vehicle body specifications. Refer to Parameterizations for more information.

Vehicle mass — Inertial mass

1200 kg (default) | positive scalar

Effective mass of the longitudinal vehicle.

Dependencies

To enable this parameter, set Parameterization type to Regular parameter set or Road-load.

Tire rolling radius — Rolling radius of tire

0.3 m (default) | positive scalar

Distance from the wheel center to the outside surface of the tire while resisting the force of the vehicle due to gravity.

Dependencies

To enable this parameter, set Parameterization type to Regular parameter set or Road-load.

Tire rolling coefficient — Rolling coefficient of tire

0.0136 (default) | nonnegative scalar

Dimensionless coefficient of the tire rolling resistance. The block uses this value to calculate F_tire as F_tire = C_Rmg. Here, the variable C_R represents this parameter.

Dependencies

To enable this parameter, set Parameterization type to Regular parameter set.

Air drag coefficient — Vehicular drag coefficient

0.31 (default) | nonnegative scalar

Dimensionless coefficient of vehicular drag. The block uses this value to compute F_air as F_air = 1/2·C_DA_fρ(v_x+v_w)², where C_D represents this parameter.

Dependencies

To enable this parameter, set Parameterization type to Regular parameter set.

Vehicle frontal area — Forward-facing surface area

2.3 m^2 (default) | positive scalar

Effective area of the vehicle that succumbs to drag. You can use a low-fidelity heuristic formula to find this measurement during early design: A_f = 0.9·height·width.

Dependencies

To enable this parameter, set Parameterization type to Regular parameter set.

Road-load coefficient A — A_RL coefficient

120 N (default) | positive scalar

Road-load coefficient A_RL.

Dependencies

To enable this parameter, set Parameterization type to Road-load.

Road-load coefficient B — B_RL coefficient

1.8 N/(m/s) (default) | positive scalar

Road-load coefficient B_RL.

Dependencies

To enable this parameter, set Parameterization type to Road-load.

Road-load coefficient C — C_RL coefficient

0.389 N*s^2/m^2 (default) | positive scalar

Road-load coefficient C_RL.

Dependencies

To enable this parameter, set Parameterization type to Road-load.

Gravitational acceleration — Acceleration due to gravity

9.81 m/s^2 (default) | positive scalar

Gravitational constant that acts on the mass of the vehicle as a function of the axle rotation. Here, vehicle weight = vehicle mass·gravitational acceleration. The block applies this weight to the tire to calculate the rolling resistance. The block also uses this value to determine the G-force multiple when you set Show G outport to On.

Simulation

Vehicle speed threshold — Tolerance for vehicle motion

0.3 m/s (default) | scalar

Minimum speed at which the block simulates vehicle motion. Below the absolute value of this threshold, the block smoothly transitions to zero.

Axle speed threshold — Tolerance for axle rotation

0.01 rad/s (default) | scalar

Minimum rotational speed at which the block simulates axle rotation. Below the absolute value of this threshold, the block smoothly transitions to zero.

Show brake force inport — Ideal brakes port

On (default) | Off

Option to display Brake port.

Show road slope inport — Road slope port

On (default) | Off

Option to enable a port to input data related to the road grade or slope. Setting this parameter to On enables the Slope input type parameter.

Slope input type — Type of slope measurement

Percent grade (default) | Normalized grade | Incline angle

Option to input road slope. The options use these definitions:

• Percent grade — The block uses a percent grade scale where 0 is flat and 100 is equivalent to a slope of π/4.

• Normalized grade — The block uses a normalized grade scale where 0 is flat and 1 is equivalent to a slope of π/4.

• Incline angle — The block uses an angle of incline where 0 is flat and pi/4 is equivalent to a slope of π/4.

Dependencies

To enable this parameter, set Show road slope inport to On.

Show wind speed inport — Wind port

On (default) | Off

Option to display the Wind port.

Show G outport — G-force outport

Off (default) | On

Option to display the G port. record G-force as a multiple of the Gravitational acceleration parameter.

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: McGraw-Hill 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.

Extended Capabilities

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

Version History

Introduced in R2021b

R2022b: Select slope input type

You can use the Slope input type to parameterize the road slope according to these parameters:

• Percent grade

• Normalized grade

• Incline angle

R2022b: View road-load forces visualization

You can access a visualization of the vehicle properties by clicking the vehicle properties hyperlink in the source code.