Tire (Magic Formula)

The tire model determined by the coefficients of the empirical formula X.The boys.

blockType: Engee1DMechanical.Vehicles.Tires.MagicFormula

Path in the library:

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

Description

Block Tire (Magic Formula) it represents the longitudinal movement of the tire, given by the empirical formula X.PAC [1], which is based on four coefficients. It is possible to simulate tire dynamics under constant or variable road surface conditions.

The longitudinal direction of the tire 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 improve the accuracy of the tire model, you can set properties such as ductility, inertia, rolling resistance, and a variable effective rolling radius. However, these properties increase the complexity of the bus model and can slow down the simulation. When calculating the model in real time or when preparing the model for semi-natural modeling, the pliability and inertia of the tire should be neglected.

Bus Model

In this block, a tire is considered as a rigid combination of a wheel and a tire that is in contact with the road and is prone to slipping. When the torque drives the wheel axle, the tire transmits the longitudinal force. , on the road. The tire transmits the resulting reaction in the form of force back to the wheel. This action rotates the wheel, creating a longitudinal motion. If we simulate the pliability of a tire, it will also deform elastically under load. If for the parameter Effective rolling radius model the value is set Load and velocity dependent (Magic Formula), then the radius of the tire will also change depending on the load and rotation speed.

The figure shows the forces acting on the tire.

tire magic formula 1

Variables that determine the bus model:

— rolling radius of the tire;
— the longitudinal speed of the wheel hub;
— longitudinal deformation of the tire;
— angular velocity of the wheel;
— the angular velocity of the point of contact. If there is no longitudinal deformation of the tire, then ;
— the longitudinal speed of the tire tread. Typically, the longitudinal tread velocity of a tire includes a component related to tire rotation , and an additional component related to tire deformation ;
— the sliding speed of the contact spot. If there is no longitudinal elastic deformation of the tire, then ;
— wheel sliding coefficient for tires without elastic deformation;
— the threshold speed of the wheel hub;
— the lower bound of the denominator of the slip coefficient;
— vertical tire load;
— the longitudinal force acting on the tire at the point of contact;
— longitudinal stiffness of the tire during deformation;
— longitudinal damping of the tire during deformation;
— the inertia of the wheel, such that the effective mass is ;
— the torque applied to the axle with the wheel.

Kinematics and reaction of the tire

You can simulate rolling, sliding and deformation.

Pumping and sliding_

The equation of translational motion of a non-sliding, non-deformable tire looks like this: . The sliding of the tires leads to a change in the longitudinal force .

The sliding speed of the contact spot is . For a tire without deformation .

The non-smoothed value of the slip coefficient of the contact spot is:

The block defines the denominator of the slip coefficient as:

where — parameter value Lower boundary of slip denominator, VXLOW.

Meaning smoothly changes to in transition areas:

The unit determines the sliding coefficient according to:

where

— parameter value Minimum valid wheel slip, KPUMIN;
— parameter value Maximum valid wheel slip, KPUMAX.

Meaning it changes smoothly in transition areas:

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

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

The formation

If the check box is selected Compliance, then the block considers the tire as elastic. When the tire is deformed, the point of contact of the tire with the road rotates with angular velocity slightly different from the speed of the wheel , which causes the contact patch to slip. The block defines a deformable tire as a translational spring damper with rigidity and damping .

If the checkbox is not checked Compliance Then , and there is no longitudinal deformation of the tire at any time in the simulation, then .

Dynamics of tires and wheels

This block consists of several sub-components. The equivalent block diagram is shown below.

tire magic formula

The block simulates the transient and stationary modes, as well as the start and stop. Blocks Translational Spring and Translational Damper are equivalent to rigidity and damping tires, respectively.

Block Tire-Road Interaction (Magic Formula) represents the longitudinal force on the bus as a function and using the empirical formula X .Guys, where — an independent sliding variable, and — input signal on port N.

Block Wheel and Axle — this is the rolling radius of the tire . The inertia value is the effective inertia. . Characteristic function of the bus determines the longitudinal force . Together with the torque of the drive shaft applied to the wheel axis, determines the angular and longitudinal movement of the wheel.

If the tire deformation is not modeled, then the block does not take into account the sub-components. Translational Spring and Translational Damper in an equivalent circuit, and the contact variables are returned to the wheel variables. In this case, the tire actually has infinite stiffness, and the P port of the block Wheel and Axle connects directly to the C port of the unit Force Sensor.

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

Effective rolling radius

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

where

— effective rolling radius;
— increase in the free radius of the tire under the action of centrifugal forces;
— vertical tire load;
— parameter value Tire nominal vertical load, FNOMIN;
— parameter value Vertical stiffness;
— the speed of rotation of the wheel;
— 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 only longitudinal movement and does not take into account camber, turn or lateral movement.
Tire compliance implies a temporary delay in the tire’s response to forces acting on it. Time-delayed simulation increases the accuracy of the model, but increases the 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 | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

Details

Rated vertical load force .

Dependencies

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

Units	`N` \| `nN` \| `uN` \| `mN` \| `kN` \| `MN` \| `GN` \| `dyn` \| `lbf` \| `kgf`
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 | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

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` \| `nN` \| `uN` \| `mN` \| `kN` \| `MN` \| `GN` \| `dyn` \| `lbf` \| `kgf`
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 | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

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` \| `nN` \| `uN` \| `mN` \| `kN` \| `MN` \| `GN` \| `dyn` \| `lbf` \| `kgf`
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 | um | mm | cm | km | in | ft | yd | mi | nmi

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` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
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 | um | mm | cm | km | in | ft | yd | mi | nmi

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` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0.3 m`
Program usage name	`free_tire_radius`
Evaluatable	Yes

# Low load stiffness effective rolling radius, BREFF — B_reff 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 D_reff

Details

Peak value of the effective rolling radius.

DREFF - TIR file identifier.

Dependencies

Default value	`0.26`
Program usage name	`D_reff`
Evaluatable	Yes

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

Details

Effective rolling radius at high load stiffness.

FREFF is the identifier of the TIR file.

Dependencies

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 q_re0

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 q_V1

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

Details

Nominal longitudinal speed of the hub.

LONGVL - TIR file identifier.

Dependencies

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	`17.0 m/s`
Program usage name	`v_longitudinal_nominal`
Evaluatable	Yes

# Vertical stiffness — vertical rigidity
N/m | mN/m | kN/m | MN/m | GN/m | kgf/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` \| `mN/m` \| `kN/m` \| `MN/m` \| `GN/m` \| `kgf/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
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 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	`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	`0.001 m/s`
Program usage name	`v_threshold_resistance`
Evaluatable	Yes

# Tire pressure — tyre pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

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` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
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 | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

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` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
Default value	`240000.0 Pa`
Program usage name	`p_tire_nominal`
Evaluatable	Yes

# Tire nominal vertical load for rolling resistance, FNOMIN — normal force
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

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` \| `nN` \| `uN` \| `mN` \| `kN` \| `MN` \| `GN` \| `dyn` \| `lbf` \| `kgf`
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
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

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	`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	`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 | mN/m | kN/m | MN/m | GN/m | kgf/m | lbf/ft | lbf/in

Details

Longitudinal tyre stiffness .

Dependencies

To use this parameter, select the check box Compliance.

Units	`N/m` \| `mN/m` \| `kN/m` \| `MN/m` \| `GN/m` \| `kgf/m` \| `lbf/ft` \| `lbf/in`
Default value	`1.0e6 N/m`
Program usage name	`k_longitudinal`
Evaluatable	Yes

# Longitudinal damping — longitudinal damping
N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in

Details

Longitudinal tyre damping .

Dependencies

To use this parameter, select the check box Compliance.

Units	`Ns/m` \| `kgfs/m` \| `lbfs/ft` \| `lbfs/in`
Default value	`1000.0 N*s/m`
Program usage name	`C_longitudinal`
Evaluatable	Yes

Details

Moment of inertia of the wheel.

Dependencies

To use this parameter, select the check box Inertia.

Units	`kgm^2` \| `gm^2` \| `kgcm^2` \| `gcm^2` \| `lbmin^2` \| `lbmft^2` \| `slugin^2` \| `slugft^2`
Default value	`1.0 kg*m^2`
Program usage name	`I_tire`
Evaluatable	Yes

Details

Initial angular velocity of the tyre .

Dependencies

To use this parameter, select the check box Inertia.

Units	`rad/s` \| `deg/s` \| `rad/min` \| `deg/min` \| `rpm` \| `rps`
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
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

Lower boundary of the slip factor denominator .

VXLOW - TIR file identifier.

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	`1.0 m/s`
Program usage name	`v_slip_threshold`
Evaluatable	Yes

# Velocity threshold — tyre slip mode threshold
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

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

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

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	`0.1 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 F_x

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 F_x

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 F_x

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 F_x

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 F_x

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 F_x

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 F_x

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

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