Engee documentation

Longitudinal Vehicle

An abstract vehicle with perfect brakes and tires.

blockType: Engee1DMechanical.Vehicles.Longitudinal

longitudinal vehicle

Path in the library:

/Physical Modeling/1D Mechanical/Tires & Vehicles/Longitudinal Vehicle

Description

Block Longitudinal Vehicle It is an abstract vehicle limited by longitudinal movement. You can parameterize any vehicle or select predefined parameterizations. The unit includes optional non-slip tires and perfect brakes.

This block can be used as a simpler alternative to the block Vehicle Body. Block Longitudinal Vehicle It requires less information for parameterization and is more suitable for the early design stage.

The following variables are used in the block equations:

  • — parameter Vehicle mass.

  • — the longitudinal speed at the output port VehSpd.

  • — the sum of the longitudinal forces.

  • — the radius of the tire, equivalent to the parameter Tire rolling radius.

  • , and — the driving force of the vehicle, the braking force and the force of resistance to the movement of the vehicle, respectively. In the balance of power equation and they counteract the movement of the vehicle.

  • — the torque on the axle.

  • — the input braking force coming through the Brake port.

  • — the speed of rotation of the axis.

  • — an arbitrary constant that regulates the speed range in which the block suppresses the force .

  • — rolling resistance of the tire.

  • — air resistance force.

  • — the slope angle of the road coming through the port Angle, NG or PG.

  • — an arbitrary constant that regulates the speed range in which the block suppresses forces and .

Parameterization

For all parameter settings Parameterization type the unit calculates the velocity equations of the longitudinal vehicle as

where

and

The block considers the direction of movement to be positive in the balance of forces equation. The block solves this equation using the following substitutions:

You can set for the parameter Parameterization type meaning Road-load or Regular parameter set to simulate an arbitrary vehicle. You can also select one of the three predefined parameterizations, which are set to Typical small car, Typical medium-sized car and Typical large sports utility vehicle.

standard set of parameters

If for the parameter Parameterization type the value is set Regular parameter set, you can specify the parameters Tire rolling coefficient, Air drag coefficient and Vehicle frontal area, which the block converts into coefficients of resistance to movement.

The block calculates the rolling resistance of the tire as

where — parameter Tire rolling coefficient.

The unit calculates the air resistance as

where — parameter Air drag coefficient, — parameter Vehicle frontal area in m2, and — density of dry air. The block assumes that kg/m3 at pressure 1 atmosphere.

resistance to movement

If set for the parameter Parameterization type meaning Road-load The block uses the standard model of motion resistance and calculates the basic physical dependencies using the formula

where , and — coefficients of resistance to movement.

Each coefficient of motion resistance corresponds to its own units of measurement . There are no standard units for these coefficients, however, certain units may be used in some texts. Select the correct units of measurement when parameterizing these coefficients.

The block uses these coefficients to calculate values in basic physical relationships, such as

and

Here — the wind speed coming through the Wind port.

prespectively defined parameterizations

For the parameter Parameterization type Three predefined values can be set: Typical small car, Typical medium-sized car and Typical large sports utility vehicle. The values correspond to industry averages, not specific vehicles. You can start with one of these predefined values, and then adjust them by setting the parameter Parameterization type meaning Road-load or Regular parameter set and using the relevant information from the tables.

Regular parameter set
Parameterization type Vehicle mass Tire rolling radius Tire rolling coefficient Air drag coefficient Vehicle frontal area

Typical small car

1100 kg

0.3 m

0.013

0.3

0.9*1.65*1.45 = 2.153 m2

Typical medium-sized car

1800 kg

0.3 m

0.0136

0.31

0.9*1.75*1.5 = 2.36 m2

Typical large sports utility vehicle

2600 kg

0.4 m

0.014

0.36

0.9*1.88*1.85 = 3.13 m2

Note that each pre-defined parameterization assumes for the method of resistance to movement.

Road-load
Parameterization type A B C

Typical small car

140.3 N

0 N/(m/s)

0.3824 N·s2/m2

Typical medium-sized car

240.1 N

0 N/(m/s)

0.4336 N·s2/m2

Typical large sports utility vehicle

357.1 N

0 N/(m/s)

0.6671 N·s2/m2

The equation for the parameter Vehicle frontal area corresponds to the coefficient 0.9 multiplied by the product of the width and height of the vehicle.

Ports

Conserving

# Axle — wheel rotation
rotational mechanics

Details

A non-directional port connected to the axle connection to the wheel hub. Connect this port to a transmission system, such as a gearbox.

Program usage name

axle_flange

Input

# Brake — longitudinal braking force, N
scalar

Details

The physical signal input port connected to the brakes. The brake port ignores negative values.

Dependencies

To use this port, check the box next to the option Show brake force inport.

Data types

Float64
Complex numbers support

No

# Wind — longitudinal wind speed, m/s
scalar

Details

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

Dependencies

To use this port, check the box next to the option Show wind speed inport.

Data types

Float64
Complex numbers support

No

# PG — percentage slope of the road, dimensionless
scalar

Details

The input port of the physical signal associated with the percentage slope of the road. The percentage slope of the road, equal to 100, is equivalent to the angle glad.

Dependencies

To use this port, check the box next to the option Show road slope inport, and for the parameter Slope input type set the value Percent grade.

Data types

Float64
Complex numbers support

No

# NG — normalized road slope, dimensionless
scalar

Details

The input port of the physical signal associated with the normalized slope of the road. The normalized slope of the road, equal to 1, is equivalent to the angle glad.

Dependencies

To use this port, check the box next to the option Show road slope inport, and for the parameter Slope input type set the value Normalized grade.

Data types

Float64
Complex numbers support

No

# Angle — Road slope, glad
scalar

Details

The input port of the physical signal associated with the slope of the road is in rad. This value represents the angle of inclination of the road relative to the horizontal surface when 0 and 100% slope at .

Dependencies

To use this port, check the box next to the option Show road slope inport, and for the parameter Slope input type set the value Incline angle.

Data types

Float64
Complex numbers support

No

Output

# VehSpd — vehicle speed, m/s
scalar

Details

The output port of the physical signal associated with the longitudinal velocity of the vehicle.

Data types

Float64
Complex numbers support

No

# G — longitudinal overload G, dimensionless
scalar

Details

The output port of the physical signal related to the longitudinal acceleration ratio vehicle acceleration to free fall .

Dependencies

To use this port, check the box next to the option Show G outport.

Data types

Float64
Complex numbers support

No

Parameters

Vehicle

# Parameterization type — choosing vehicle parameterization
Road-load | Regular parameter set | Typical small car | Typical medium-sized car | Typical large sports utility vehicle

Details

The possibility of vehicle parameterization. You can parameterize any vehicle by selecting the value Regular parameter set or Road-load, or choose one of three typical vehicle body specifications. For more information, see Parameterization.

Values

Road-load | Regular parameter set | Typical small car | Typical medium-sized car | Typical large sports utility vehicle
Default value

Regular parameter set
Program usage name

parameterization
Evaluatable

Yes

# Vehicle mass — inertial mass
kg | mg | g | t | lbm | oz | slug

Details

The effective mass of the vehicle.

Dependencies

To use this parameter, set for the parameter Parameterization type meaning Regular parameter set or Road-load.

Units

kg | mg | g | t | lbm | oz | slug
Default value

1200.0 kg
Program usage name

m
Evaluatable

Yes

# Tire rolling radius — rolling radius of the tire
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The distance from the center of the wheel to the outer surface of the tire, taking into account the gravity of the vehicle.

Dependencies

To use this parameter, set for the parameter Parameterization type meaning Regular parameter set or Road-load.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.3 m
Program usage name

tire_radius
Evaluatable

Yes

# Tire rolling coefficient — rolling coefficient of the tire

Details

The dimensionless coefficient of rolling resistance of the tire. The block uses this value to calculate according to the formula . Here’s the variable represents this parameter.

Dependencies

To use this parameter, set for the parameter Parameterization type meaning Regular parameter set.

Default value

0.0136
Program usage name

rolling_resistance_coefficient
Evaluatable

Yes

# Air drag coefficient — coefficient of aerodynamic drag of the vehicle

Details

The dimensionless coefficient of aerodynamic drag of the vehicle. The block uses this value to calculate according to the formula , where represents this parameter.

Dependencies

To use this parameter, set for the parameter Parameterization type meaning Regular parameter set.

Default value

0.31
Program usage name

C_d
Evaluatable

Yes

# Vehicle frontal area — frontal surface area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The effective surface area of the vehicle exposed to air resistance. A low-precision heuristic formula can be used to determine this value at the initial design stage.: .

Dependencies

To use this parameter, set for the parameter Parameterization type meaning Regular parameter set.

Units

m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Default value

2.3 m^2
Program usage name

midsection_area
Evaluatable

Yes

# Gravitational acceleration — acceleration of free fall
m/s^2 | mm/s^2 | cm/s^2 | km/s^2 | in/s^2 | ft/s^2 | mi/s^2 | gn

Details

The gravitational constant acting on the mass of the vehicle, taking into account the rotation of the body. Here, the weight of the vehicle is equal to the mass of the vehicle multiplied by the acceleration of gravity. The unit applies this weight to the tire to calculate rolling resistance. The block also uses this value to determine the overload factor if next to the parameter Show G outport the flag is checked.

Units

m/s^2 | mm/s^2 | cm/s^2 | km/s^2 | in/s^2 | ft/s^2 | mi/s^2 | gn
Default value

9.81 m/s^2
Program usage name

g
Evaluatable

Yes

# Road-load coefficient A — ratio
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

Details

Coefficient of resistance to movement .

Dependencies

To use this parameter, set for the parameter Parameterization type meaning Road-load.

Units

N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf
Default value

120.0 N
Program usage name

coefficient_A_road_load
Evaluatable

Yes

# Road-load coefficient B — ratio
N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in

Details

Coefficient of resistance to movement .

Dependencies

To use this parameter, set for the parameter Parameterization type meaning Road-load.

Units

N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in
Default value

1.8 N*s/m
Program usage name

coefficient_B_road_load
Evaluatable

Yes

# Road-load coefficient C — ratio
N/(m/s)^2

Details

Coefficient of resistance to movement .

Dependencies

To use this parameter, set for the parameter Parameterization type meaning Road-load.

Units

N/(m/s)^2
Default value

0.389 N/(m/s)^2
Program usage name

coefficient_C_road_load
Evaluatable

Yes

Simulation

# Vehicle speed threshold — speed threshold before the vehicle starts moving
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

The minimum speed at which the block simulates the movement of a vehicle. Below the absolute value of this threshold value, the block smoothly switches to the zero state.

Units

m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn
Default value

0.3 m/s
Program usage name

v_threshold
Evaluatable

Yes

# Axle speed threshold — speed threshold for starting axis rotation
rad/s | deg/s | rad/min | deg/min | rpm | rps

Details

The minimum rotation speed at which the block simulates the rotation of the axis. Below the absolute value of this threshold value, the block smoothly switches to the zero state.

Units

rad/s | deg/s | rad/min | deg/min | rpm | rps
Default value

0.01 rad/s
Program usage name

w_threshold
Evaluatable

Yes

# Show brake force inport — perfect brake port

Details

The ability to display the Brake port.

Default value

true (switched on)
Program usage name

enable_brake_force
Evaluatable

Yes

# Show road slope inport — road slope port

Details

The ability to enable a port for entering data related to the slope of the road. If you check the box next to this parameter, the parameter is activated. Slope input type.

Default value

true (switched on)
Program usage name

enable_road_slope
Evaluatable

Yes

# Slope input type — type of slope measurement
Percent grade | Normalized grade | Incline angle

Details

The ability to enter the value of the slope of the road. The options imply the following definitions:

  • Percent grade — the block uses a percentage scale of bias, where 0 corresponds to a flat surface, and 100 equivalent to evasion .

  • Normalized grade — the block uses a normalized slope scale, where 0 corresponds to a flat surface, and 1 equivalent to evasion .

  • Incline angle — the block uses a tilt angle where 0 corresponds to a flat surface, and pi/4 equivalent to evasion .

Dependencies

To use this option, check the box next to the option Show road slope inport.

Values

Percent grade | Normalized grade | Incline angle
Default value

Percent grade
Program usage name

road_slope_input_type
Evaluatable

Yes

# Show wind speed inport — wind port

Details

The ability to display the Wind port.

Default value

true (switched on)
Program usage name

enable_wind_speed
Evaluatable

Yes

# Show G outport — overload factor output port

Details

The ability to display the G port. Recording the gravity acceleration value as a multiple of the parameter Gravitational acceleration.

Default value

false (switched off)
Program usage name

enable_overload_output
Evaluatable

Yes

Literature

  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.