Engee documentation

Tire (Magic Formula)

Page in progress.

Tyre model determined by the coefficients of the empirical formula of H.Paceika.

blockType: Engee1DMechanical.Vehicles.Tires.MagicFormula

tire magic formula

Path in the library:

/Physical Modeling/1D Mechanical/Tires & Vehicles/Tire (Magic Formula)

Description

The block Tire (Magic Formula) represents the longitudinal motion of a tyre given by the empirical formula of H. Paceika [1], which is based on four coefficients. It is possible to simulate the tyre dynamics under constant or variable road surface conditions.

The longitudinal direction of the tyre coincides with the direction of its movement on the road surface.

This block is a component based on the block Tire-Road Interaction (Magic Formula).

To increase the accuracy of the tyre model, properties such as pliability, inertia, rolling resistance and varying effective rolling radius can be defined. However, these properties increase the complexity of the tyre model and can slow down the simulation. When calculating the model in real time or when preparing the model for semi-natural simulation, the tyre pliability and inertia should be neglected.

Tyre model

In this block, the tyre is considered as a rigid wheel and tyre combination that is in contact with the road and subject to slippage. When torque drives the wheel axle, the tyre transmits the longitudinal force , to the road. The tyre transmits the resulting reaction in the form of force back to the wheel. This action rotates the wheel, creating longitudinal motion. If the pliability of the tyre is modelled, the tyre will also deform elastically under load. If the parameter Effective rolling radius model is set to . Load and velocity dependent (Magic Formula), the tyre radius will also change as a function of load and rotational speed.

The figure shows the forces acting on the tyre.

tire magic formula 1

Variables that define the tyre model:

  • - tyre rolling radius;

  • - longitudinal velocity of the wheel hub;

  • - longitudinal deformation of the tyre;

  • - angular velocity of the wheel;

  • - angular velocity of the contact point. If there is no longitudinal deformation of the tyre, ;

  • - longitudinal velocity of the tyre tread. Typically, tyre tread longitudinal velocity includes a component related to tyre rotation , and an additional component related to tyre deformation ;

  • - contact patch slip velocity. If there is no longitudinal elastic deformation of the tyre, ;

  • - is the wheel slip coefficient for a tyre without elastic deformation;

  • - is the threshold speed of the wheel hub;

  • - lower limit of the denominator of the slip coefficient;

  • - vertical load on the tyre;

  • - longitudinal force acting on the tyre at the point of contact;

  • - longitudinal stiffness of the tyre under deformation;

  • - longitudinal damping of the tyre during deformation;

  • - inertia of the wheel, such that the effective mass is equal to ;

  • - torque applied to the axle with the wheel.

Kinematics and reaction of the tyre

You can simulate rolling, sliding and deformation.

Rolling and sliding

The equation of translational motion of a non-sliding, non-deformable tyre is as follows: . Sliding of tyres leads to a change in longitudinal force .

The sliding velocity of the contact patch is . For a non-deforming tyre .

The unsmoothed value of the contact patch slip rate is equal to:

The block defines the denominator of the slip coefficient as:

where is the value of the parameter Lower boundary of slip denominator, VXLOW.

The value of changes smoothly to in transient regions:

,

.

The block determines the sliding coefficient according to:

where

  • - is the value of the parameters Minimum valid wheel slip, KPUMIN;

  • - the value of the parameters Maximum valid wheel slip, KPUMAX.

The value of changes smoothly in transient regions:

,

.

The block defines the smoothing threshold of the slip coefficient as:

For this equation, a locked, sliding wheel has . For perfect rolling .

Deformation

If Compliance is checked, the block treats the tyre as elastic. When the tyre deforms, the tyre’s contact point with the road rotates with an angular velocity , slightly different from the wheel speed , causing the contact patch to slip. The unit defines the deforming tyre as a progressive spring damper with stiffness and damping .

If the checkbox Compliance, then , and there is no longitudinal deformation of the tyre at any time in the simulation, then .

Tyre and wheel dynamics

This block consists of several subcomponents. An equivalent block diagram is shown below.

tire magic formula

The block simulates transient and steady-state modes as well as start and stop. The blocks Translational Spring and Translational Damper are equivalent to the stiffness and damping of the tyre, respectively.

Block Tire-Road Interaction (Magic Formula) represents the longitudinal force on the tyre as a function of and using H.Paceika’s empirical formula, where is the independent slip variable and is the input signal at port N.

The block Wheel and Axle is the rolling radius of the tyre . The inertia value is the effective inertia . The characteristic function of the tyre defines the longitudinal force . Together with the drive shaft torque applied to the wheel axle, determines the angular and longitudinal motion of the wheel.

If the tyre deformation is not modelled, the block does not consider the subcomponents Translational Spring and Translational Damper in the equivalent circuit, and the contact variables revert to wheel variables. In this case the tyre effectively has infinite stiffness and the P port of the Wheel and Axle block connects directly to the C port of the Force Sensor block .

If a different rolling resistance model is specified in the Rolling Resistance block than the Pressure and velocity dependent (Magic Formula) rolling resistance model, the equivalent circuit will not use block Force Sensor and port T of block Rolling Resistance. If Compliance is unchecked, the P port of Wheel and Axle is connected directly to the C port of Force Sensor or the T port of Tire-Road Interaction (Magic Formula).

Effective rolling radius

This block defines the effective rolling radius, taking into account its increase or decrease due to centrifugal forces, such that

where

  • - is the effective rolling radius;

  • - the increase in the free radius of the tyre due to centrifugal forces;

  • - vertical load on the tyre;

  • - parameter value Tire nominal vertical load, FNOMIN;

  • - parameter value Vertical stiffness;

  • - wheel rotation speed;

  • - parameter value Low load stiffness effective rolling radius, BREFF;

  • - parameter value Peak value of effective rolling radius, DREFF;

  • - parameter value High load stiffness effective rolling radius, FREFF;

  • - parameter value Ratio of nominal tire radius with non-rolling free tire radius, Q_RE0;

  • - parameter value Tire radius increase with speed, Q_V1.

Assumptions and limitations

  • The block assumes longitudinal movement only and does not take into account camber, cornering or lateral movement.

  • Tyre pliability assumes a time delay in the response of the tyre to forces acting on it. Simulation with time delay improves model accuracy but increases simulation time.

Ports

Input

# N — normal force, N
scalar

Details

Input port related to the normal force acting on the tyre, in N. The normal force is positive if it acts on the tyre in a downward direction, pressing it against the road surface.

Data types

Float64.
Complex numbers support

No

# M — vector of coefficients of the empirical formula
vector

Details

Input port specifying the coefficients of H.Paceika’s empirical formula.

Provide the coefficients as a vector .

Dependencies

To use this port, set the parameters Parameterize by to Physical signal Magic Formula coefficients.

Data types

Float64.
Complex numbers support

No

Conserving

# A — axis
`rotational mechanics

Details

A mechanical rotational port associated with an axis.

Program usage name

axle_flange

# H — hub
translational mechanics

Details

A mechanical progressive port connected to the hub of a wheel.

Program usage name

hub_flange

Output

# S — slip
scalar

Details

output port related to the slip coefficient, , between the tyre and the road.

Data types

Float64.
Complex numbers support

No

Parameters

Main

# Parameterize by — parameterization method
Peak longitudinal force and corresponding slip | Constant Magic Formula coefficients | Load-dependent Magic Formula coefficients | Physical signal Magic Formula coefficients

Details

Select how the block parameterises the bus using an empirical formula:

  • Peak longitudinal force and corresponding slip - parameterization of the empirical formula using the physical characteristics of the tyre.

  • Constant Magic Formula coefficients - set the parameters defining the constant coefficients , , and as scalars.

  • Load-dependent Magic Formula coefficients - set the parameters defining the load-dependent coefficients , , , , , and as vectors, one parameter for each coefficient.

  • Physical signal Magic Formula coefficients - set the coefficients of the empirical formula through the M port as a four-element vector .

Values

Peak longitudinal force and corresponding slip | Constant Magic Formula coefficients | Load-dependent Magic Formula coefficients | Physical signal Magic Formula coefficients
Default value

Peak longitudinal force and corresponding slip
Program usage name

friction_model
Evaluatable

Yes

# Rated vertical load — rated load force
N | kN | lb | mN | dyn | lbf

Details

Rated vertical load force .

Dependencies

To use this parameter, set the Parameterize by parameters to . Peak longitudinal force and corresponding slip.

Units

N | kN | lb | mN | dyn | lbf
Default value

3000.0 N
Program usage name

F_vertical_load
Evaluatable

Yes

# Peak longitudinal force at rated load — maximum longitudinal force at rated load
N | kN | lb | mN | dyn | lbf

Details

Maximum longitudinal force , which the tyre exerts on the wheel when the vertical load is equal to its nominal value .

Dependencies

To use this parameter, set the parameters Parameterize by to . Peak longitudinal force and corresponding slip.

Units

N | kN | lb | mN | dyn | lbf
Default value

3500.0 N
Program usage name

F_longitudinal_load
Evaluatable

Yes

# Slip at peak force at rated load (percent) — slip coefficient in per cent at maximum longitudinal force and rated load

Details

Slip coefficient , expressed as a percentage (%) when the longitudinal force is equal to the maximum value , and the vertical load is equal to the nominal value .

Dependencies

To use this parameter, set the parameters Parameterize by to Peak longitudinal force and corresponding slip.

Default value

10.0
Program usage name

percent_slip
Evaluatable

Yes

# Magic Formula B coefficient — constant factor B in the empirical formula

Details

Coefficient in the empirical formula, independent of load.

Dependencies

To use this parameter, set the parameter Parameterize by to the value of Constant Magic Formula coefficients.

Default value

10.0
Program usage name

coefficient_B
Evaluatable

Yes

# Magic Formula C coefficient — constant coefficient C in the empirical formula

Details

Coefficient in the empirical formula, independent of load.

Dependencies

To use this parameter, set the parameter Parameterize by to the value of Constant Magic Formula coefficients.

Default value

1.9
Program usage name

coefficient_C
Evaluatable

Yes

# Magic Formula D coefficient — constant factor D in the empirical formula

Details

Coefficient in the empirical formula, independent of load.

Dependencies

To use this parameter, set the parameter Parameterize by to the value of Constant Magic Formula coefficients.

Default value

1.0
Program usage name

coefficient_D
Evaluatable

Yes

# Magic Formula E coefficient — constant coefficient E in the empirical formula

Details

Coefficient in the empirical formula, independent of load.

Dependencies

To use this parameter, set the parameter Parameterize by to the value of Load-dependent Magic Formula coefficients.

Default value

0.97
Program usage name

coefficient_E
Evaluatable

Yes

# Tire nominal vertical load, FNOMIN — nominal normal force
N | kN | lb | mN | dyn | lbf

Details

Nominal normal force on the tyre.

FNOMIN is the identifier of the TIR file.

Dependencies

To use this parameter, set the Resistance model parameters to Pressure and velocity dependent (Magic Formula).

Units

N | kN | lb | mN | dyn | lbf
Default value

4000.0 N
Program usage name

F_vertical_nominal
Evaluatable

Yes

# Magic Formula C-coefficient parameter, p_Cx1 — C coefficient in the empirical formula

Details

Load-dependent coefficient in the empirical formula.

Dependencies

To use this parameter, set the parameter Parameterize by to the value of Load-dependent Magic Formula coefficients.

Default value

1.685
Program usage name

p_C_x
Evaluatable

Yes

# Magic Formula D-coefficient parameters, [p_Dx1 p_Dx2] — D coefficients in the empirical formula

Details

Load-dependent coefficients in the empirical formula.

Dependencies

To use this parameter, set the parameters Parameterize by to Load-dependent Magic Formula coefficients.

Default value

[1.21, -0.037]
Program usage name

p_D_x
Evaluatable

Yes

# Magic Formula E-coefficient parameters, [p_Ex1 p_Ex2 p_Ex3 p_Ex4] — E coefficients in the empirical formula

Details

Load-dependent coefficients in the empirical formula.

Dependencies

To use this parameter, set the parameters Parameterize by to Load-dependent Magic Formula coefficients.

Default value

[0.344, 0.095, -0.02, 0.0]
Program usage name

p_E_x
Evaluatable

Yes

# Magic Formula BCD-coefficient parameters, [p_Kx1 p_Kx2 p_Kx3] — K coefficients in the empirical formula

Details

Load-dependent coefficients in the empirical formula.

Dependencies

To use this parameter, set the parameters Parameterize by to Load-dependent Magic Formula coefficients.

Default value

[21.51, -0.163, 0.245]
Program usage name

p_K_x
Evaluatable

Yes

# Magic Formula H-coefficient parameters, [p_Hx1 p_Hx2] — H coefficients in the empirical formula

Details

Load-dependent coefficients in the empirical formula.

Dependencies

To use this parameter, set the parameters Parameterize by to Load-dependent Magic Formula coefficients.

Default value

[-0.002, 0.002]
Program usage name

p_H_x
Evaluatable

Yes

# Magic Formula V-coefficient parameters, [p_Vx1 p_Vx2] — V coefficients in the empirical formula

Details

Load-dependent coefficients in the empirical formula.

Dependencies

To use this parameter, set the parameters Parameterize by to Load-dependent Magic Formula coefficients.

Default value

[0.0, 0.0]
Program usage name

p_V_x
Evaluatable

Yes

Geometry

# Rolling radius — tyre radius under load
m | cm | ft | in | km | mi | mm | um | yd

Details

Tyre radius under load .

Dependencies

To use this parameters, set:

  • for the parameters Parameterize by to be set to. Load-dependent Magic Formula coefficients`and for the parameters Effective rolling radius model to be set. `Constant radius;

  • for the parameters Parameterize by the value of. Peak longitudinal force and corresponding slip, Constant Magic Formula coefficients or Physical signal Magic Formula coefficients.

Units

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

0.3 m
Program usage name

tire_radius
Evaluatable

Yes

# Effective rolling radius model — model for calculating the effective rolling radius
Constant radius | Load and velocity dependent (Magic Formula)

Details

Select the model for determining the rolling radius:

  • Constant radius - The rolling radius is constant;

  • Load and velocity dependent (Magic Formula) - the rolling radius depends on load and speed.

Dependencies

To use this parameter, set the parameters Parameterize by to . Load-dependent Magic Formula coefficients.

Values

Constant radius | Load and velocity dependent (Magic Formula)
Default value

Constant radius
Program usage name

rolling_radius_parameterization
Evaluatable

Yes

# Non-rolling free tire radius, R0 — tyre free radius
m | cm | ft | in | km | mi | mm | um | yd

Details

The value of the free rolling radius of the tyre associated with the empirical formula.

R0 is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameter to and the parameter to R0. Load-dependent Magic Formula coefficients, and set the parameters Effective rolling radius model to Load and velocity dependent (Magic Formula).

Units

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

0.3 m
Program usage name

free_tire_radius
Evaluatable

Yes

# Low load stiffness effective rolling radius, BREFF — Breff variable

Details

Effective rolling radius for low load stiffness.

BREFF is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameter to and the parameter to . Load-dependent Magic Formula coefficients, and set the parameters Effective rolling radius model to Load and velocity dependent (Magic Formula).

Default value

8.39
Program usage name

B_reff
Evaluatable

Yes

# Peak value of effective rolling radius, DREFF — variable Dreff

Details

Peak value of the effective rolling radius.

DREFF - TIR file identifier.

Dependencies

To use this parameter, set the Parameterize by parameter to and the parameter to . Load-dependent Magic Formula coefficients, and set the parameters Effective rolling radius model to Load and velocity dependent (Magic Formula).

Default value

0.26
Program usage name

D_reff
Evaluatable

Yes

# High load stiffness effective rolling radius, FREFF — variable Freff

Details

Effective rolling radius at high load stiffness.

FREFF is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameter to and the parameter to . Load-dependent Magic Formula coefficients, and set the parameters Effective rolling radius model to Load and velocity dependent (Magic Formula).

Default value

0.074
Program usage name

F_reff
Evaluatable

Yes

# Ratio of nominal tire radius with non-rolling free tire radius, Q_RE0 — variable qre0

Details

The ratio of the nominal tyre radius to the radius of the tyre without rolling.

Q_RE0 is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameters to and to . Load-dependent Magic Formula coefficients`and set the parameters Effective rolling radius model to `Load and velocity dependent (Magic Formula).

Default value

0.99
Program usage name

q_re0
Evaluatable

Yes

# Tire radius increase with speed, Q_V1 — variable qV1

Details

Increase in tyre radius as a function of speed.

Q_V1 - TIR file identifier.

Dependencies

To use this parameter, set the Parameterize by parameters to and to . Load-dependent Magic Formula coefficients, and set the parameters Effective rolling radius model to Load and velocity dependent (Magic Formula).

Default value

0.008
Program usage name

q_v1
Evaluatable

Yes

# Nominal hub longitudinal speed, LONGVL — nominal longitudinal speed of the hub
fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s

Details

Nominal longitudinal speed of the hub.

LONGVL - TIR file identifier.

Dependencies

To use this parameter, set the Parameterize by parameters to and to . Load-dependent Magic Formula coefficients`and set the parameters Effective rolling radius model to `Load and velocity dependent (Magic Formula).

Units

fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s
Default value

17.0 m/s
Program usage name

v_longitudinal_nominal
Evaluatable

Yes

# Vertical stiffness — vertical rigidity
N/m | lbf/ft | lbf/in

Details

The vertical stiffness of the tyre.

Dependencies

To use this parameter, set the Parameterize by parameters to and the parameters to . Load-dependent Magic Formula coefficients`and set the parameters Effective rolling radius model to . `Load and velocity dependent (Magic Formula).

Units

N/m | lbf/ft | lbf/in
Default value

500000.0 N/m
Program usage name

k_vertical
Evaluatable

Yes

Rolling Resistance

# Model rolling resistance — roll resistance

Details

Select this check box to take tyre rolling resistance into account in the simulation.

Default value

false (switched off)
Program usage name

enable_resistance
Evaluatable

Yes

# Resistance model — rolling resistance model
Constant coefficient | Pressure and velocity dependent (SAE J2452) | Pressure and velocity dependent (Magic Formula)

Details

A model for calculating rolling resistance:

  • Constant coefficient - Rolling resistance is taken into account by means of a constant coefficient.

  • Pressure and velocity dependent (SAE J2452) - The rolling resistance is determined in accordance with SAE J2452.

  • Pressure and velocity dependent (Magic Formula) - The rolling resistance is determined according to an empirical formula.

Dependencies

To use this parameter, select the check box Model rolling resistance.

Values

Constant coefficient | Pressure and velocity dependent (SAE J2452) | Pressure and velocity dependent (Magic Formula)
Default value

Constant coefficient
Program usage name

rolling_resistance_parameterization
Evaluatable

Yes

# Constant coefficient — proportionality constant

Details

A coefficient that establishes the proportionality between the normal force and the rolling resistance force. Parameters must be greater than zero.

Dependencies

To use this parameter, select the check box Model rolling resistance, and set the parameters Resistance model to the value of Constant coefficient.

Default value

0.015
Program usage name

const_rolling_resistance_coefficient
Evaluatable

Yes

# Velocity threshold for rolling resistance — threshold speed for rolling resistance
fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s

Details

The speed at which the full rolling resistance force is transferred to the wheel hub. This parameter ensures that the force remains continuous as the direction of speed changes, which increases the numerical stability of the simulation. The parameters must be greater than zero.

Dependencies

To use this parameter, select the checkbox Model rolling resistance.

Units

fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s
Default value

0.001 m/s
Program usage name

v_threshold_resistance
Evaluatable

Yes

# Tire pressure — tyre pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Tyre inflation pressure. The parameters must be greater than zero.

Dependencies

To use this parameter, select the check box Model rolling resistance, and for the parameter Resistance model set the value to Pressure and velocity dependent (SAE J2452) or Pressure and velocity dependent (Magic Formula).

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

250000.0 Pa
Program usage name

p_tire
Evaluatable

Yes

# Alpha — exponent in the equation for tyre pressure

Details

The exponent in the equation for tyre pressure.

Dependencies

To use this parameter, tick the checkbox Model rolling resistance, and set the parameters Resistance model to Pressure and velocity dependent (SAE J2452).

Default value

-0.003
Program usage name

alpha
Evaluatable

Yes

# Beta — exponent in the equation for the normal force

Details

The exponent in the equation for normal force.

Dependencies

To use this parameter, select the checkbox Model rolling resistance, and set the parameters Resistance model to Pressure and velocity dependent (SAE J2452).

Default value

0.97
Program usage name

beta
Evaluatable

Yes

# Coefficient A — velocity-independent force component, A

Details

The velocity-independent force component in the model equation. The parameters must be greater than zero.

Dependencies

To use this parameter, select the checkbox Model rolling resistance, and set the Resistance model parameters to Pressure and velocity dependent (SAE J2452).

Default value

0.0084
Program usage name

coefficient_a
Evaluatable

Yes

# Coefficient B — velocity-dependent force component, B
s/m | s/ft

Details

The velocity-dependent force component of the model equation. The parameters must be greater than zero.

Dependencies

To use this parameter, select the Model rolling resistance checkbox and set the Resistance model parameters to Pressure and velocity dependent (SAE J2452).

Units

s/m | s/ft
Default value

0.00062 s/m
Program usage name

coefficient_b
Evaluatable

Yes

# Coefficient C — velocity-dependent force component, C
(s/m)^2 | (s/ft)^2

Details

A force component that depends on the square of the velocity in the model equation. The parameters must be greater than zero.

Dependencies

To use this parameter, select the checkbox Model rolling resistance, and set the parameter Resistance model to Pressure and velocity dependent (SAE J2452).

Units

(s/m)^2 | (s/ft)^2
Default value

0.00016 (s/m)^2
Program usage name

coefficient_c
Evaluatable

Yes

# Tire nominal pressure, NOMPRES — nominal tyre pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Nominal tyre pressure.

NOMPRES is the identifier of the TIR file.

Dependencies

To use this parameter, set the Resistance model parameters to Pressure and velocity dependent (Magic Formula).

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

240000.0 Pa
Program usage name

p_tire_nominal
Evaluatable

Yes

# Tire nominal vertical load for rolling resistance, FNOMIN — normal force
N | kN | lb | mN | dyn | lbf

Details

Nominal normal force on the tyre.

FNOMIN is the identifier of the TIR file.

Dependencies

To use this parameter, set the Resistance model parameters to Pressure and velocity dependent (Magic Formula).

Units

N | kN | lb | mN | dyn | lbf
Default value

4000.0 N
Program usage name

F_vertical_nominal_resistance
Evaluatable

Yes

# Hub nominal longitudinal velocity for rolling resistance, LONGVL — nominal longitudinal speed of the hub
fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s

Details

Nominal longitudinal speed of the hub.

LONGVL - TIR file identifier.

Dependencies

To use this parameter, set the Resistance model parameters to Pressure and velocity dependent (Magic Formula).

Units

fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s
Default value

16.0 m/s
Program usage name

v_longitudinal_nominal_resistance
Evaluatable

Yes

# Q-coefficient parameters [qsy1 qsy2 qsy3 qsy4 qsy5 qsy6 qsy7 qsy8] — Q-coefficients for the empirical formula

Details

Coefficients for the empirical formula .

qsy1,…​, qsy8 - TIR file identifier.

Dependencies

To use this parameter, set the Resistance model parameters to Pressure and velocity dependent (Magic Formula).

Default value

[0.0082, 0.0, 0.0014, 0.001, 0.0, 0.0, 1.08, -0.5]
Program usage name

scaling_factor_vector
Evaluatable

Yes

Dynamics

# Compliance — consideration of tyre pliability

Details

Whether tyre pliability consideration should be included:

  • if the check box Compliance is not selected, the unit neglects dynamic deformation.

  • if the check box Compliance is selected, the unit treats the tyre as a spring-damped system under load.

Default value

false (switched off)
Program usage name

enable_compliance
Evaluatable

Yes

# Inertia — inertia model

Details

Select this check box to take the tyre inertia into account.

Default value

false (switched off)
Program usage name

enable_inertia
Evaluatable

Yes

# Longitudinal stiffness — longitudinal rigidity
N/m | lbf/ft | lbf/in

Details

Longitudinal tyre stiffness .

Dependencies

To use this parameter, select the check box Compliance.

Units

N/m | lbf/ft | lbf/in
Default value

1.0e6 N/m
Program usage name

k_longitudinal
Evaluatable

Yes

# Longitudinal damping — longitudinal damping
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Longitudinal tyre damping .

Dependencies

To use this parameter, select the check box Compliance.

Units

kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)
Default value

1000.0 N/(m/s)
Program usage name

C_longitudinal
Evaluatable

Yes

# Tire inertia — tyre inertia value
g*cm^2 | kg*m^2 | lbm*ft^2 | lbm*in^2 | slug*ft^2 | slug*in^2

Details

Moment of inertia of the wheel.

Dependencies

To use this parameter, select the check box Inertia.

Units

g*cm^2 | kg*m^2 | lbm*ft^2 | lbm*in^2 | slug*ft^2 | slug*in^2
Default value

1.0 kg*m^2
Program usage name

I_tire
Evaluatable

Yes

# Initial velocity — initial rotation speed
rpm | deg/s | rad/s

Details

Initial angular velocity of the tyre .

Dependencies

To use this parameter, select the check box Inertia.

Units

rpm | deg/s | rad/s
Default value

0.0 rad/s
Program usage name

w_start
Evaluatable

Yes

Advanced

# Lower boundary of slip denominator, VXLOW — lower limit of the denominator of the slip coefficient
fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s

Details

Lower boundary of the slip factor denominator .

VXLOW - TIR file identifier.

Units

fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s
Default value

1.0 m/s
Program usage name

v_slip_threshold
Evaluatable

Yes

# Velocity threshold — tyre slip mode threshold
fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s

Details

Threshold speed , which the unit uses to transition between slip modes.

For details, see [Rolling and Sliding]. Rolling and Sliding for details.

Units

fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s
Default value

0.1 m/s
Program usage name

v_threshold
Evaluatable

Yes

# Minimum valid wheel slip, KPUMIN — minimum value of wheel slip coefficient

Details

The minimum permissible value of the wheel slip coefficient. A negative value means that the wheel slides in the opposite direction to the rotation.

Default value

-1.5
Program usage name

min_wheel_slip
Evaluatable

Yes

# Maximum valid wheel slip, KPUMAX — maximum value of wheel slip coefficient

Details

Maximum permissible value of the wheel slip coefficient.

Default value

1.5
Program usage name

max_wheel_slip
Evaluatable

Yes

Scaling

# Enable scaling coefficients — rolling resistance scaling

Details

Select this check box to include scaling factors in the parameterization of the empirical formula.

Dependencies

To use this parameter, check this box:

  • for the parameter Parameterize by the value Load-dependent Magic Formula coefficients;

  • for the parameter Resistance model the value of Pressure and velocity dependent (Magic Formula).

Default value

false (switched off)
Program usage name

enable_scaling_factors
Evaluatable

Yes

# Scale factor of rolling resistance, LMY — rolling resistance

Details

Scaling factor rolling resistance.

LMY - TIR file identifier.

Dependencies

To use this parameter, set:

  • for the parameter Parameterize by the value Load-dependent Magic Formula coefficients;

  • for the parameter Resistance model the value of Pressure and velocity dependent (Magic Formula).

And select the checkbox Enable scaling coefficients.

Default value

1.0
Program usage name

lambda_M_y
Evaluatable

Yes

# Scale factor of Fx nominal vertical load, LFZO — rated vertical load Fx

Details

Scaling factor nominal vertical load .

LFZO is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameters to Load-dependent Magic Formula coefficients and tick the checkbox Enable scaling coefficients.

Default value

1.0
Program usage name

lambda_F_z0
Evaluatable

Yes

# Scale factor of Fx shape factor, LCX — shape factor Fx

Details

Scaling factor shape factor .

LCX is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameters to Load-dependent Magic Formula coefficients and tick the checkbox Enable scaling coefficients.

Default value

1.0
Program usage name

lambda_C_x
Evaluatable

Yes

# Scale factor of Fx peak friction coefficient, LMUX — peak coefficient of friction Fx

Details

Scaling factor peak friction coefficient .

LMUX is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameters to Load-dependent Magic Formula coefficients and tick the checkbox Enable scaling coefficients.

Default value

1.0
Program usage name

lambda_mu_x
Evaluatable

Yes

# Scale factor of Fx curvature factor, LEX — curvature coefficient Fx

Details

Scaling factor curvature coefficient .

LEX is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameters to Load-dependent Magic Formula coefficients and tick the checkbox Enable scaling coefficients.

Default value

1.0
Program usage name

lambda_E_x
Evaluatable

Yes

# Scale factor of Fx slip stiffness, LKX — sliding stiffness Fx

Details

Scaling factor sliding stiffness .

LKX is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameters to . Load-dependent Magic Formula coefficients and select the Enable scaling coefficients checkbox.

Default value

1.0
Program usage name

lambda_K_x
Evaluatable

Yes

# Scale factor of Fx horizontal shift, LHX — horizontal displacement Fx

Details

Scaling factor horizontal shift .

LHX is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameters to Load-dependent Magic Formula coefficients and tick the checkbox Enable scaling coefficients.

Default value

1.0
Program usage name

lambda_H_x
Evaluatable

Yes

# Scale factor of Fx vertical shift, LVX — vertical displacement Fx

Details

Scaling factor vertical shift .

LVX is the identifier of the TIR file.

Dependencies

To use this parameter, set the Parameterize by parameters to Load-dependent Magic Formula coefficients and tick the checkbox Enable scaling coefficients.

Default value

1.0
Program usage name

lambda_V_x
Evaluatable

Yes

Literature

  1. I.J.M. Besselink, A.J.C. Schmeitz, H. B. Pacejka, An Improved Magic Formula/Swift Tyre Model That Can Handle Inflation Pressure Changes, Vehicle System Dynamics 48, no. sup1 (December 2010): 337-52. https://doi.org/10.1080/00423111003748088.

  2. H.B. Pacejka, Tire and Vehicle Dynamics, Elsevier Science, 2005.