Combined Slip Wheel 2DOF

Combined slip 2DOF wheel with disc, drum, or mapped brake

Libraries:
Vehicle Dynamics Blockset / Wheels and Tires

Description

Combined Slip Wheel 2DOF incorporates two degrees of freedom (DOF's) of wheel motion, and 6 DOF's of tire forcing, in combined longitudinal and lateral slip conditions.

Wheel motion: Rotation about spin axis, and vertical displacement.
Tire forces and moments: Fx, Fy, and Fz; Mx, My, and Mz.

It models the tire using the Magic Formula.^{[1] and [2]} Set the Magic Formula coefficients by either importing your own file (in MF 6.X format), or selecting one of the built-in tire models.

Use this block in simulations like the following.

Vehicle braking and acceleration, including rolling resistance.
Vehicle ride motions, including effects of suspension modes.
Maneuvers with combined lateral and longitudinal slip, such as lateral vehicle motion and yaw stability.

If you install the Extended Tire Features for Vehicle Dynamics Blockset support package, you can click the Plot steady state force, moment response button to generate these plots:

Lateral force [N] vs Slip angle [rad]
Self-aligning moment [Nm] vs Slip angle [rad]
Longitudinal force [N] vs Longitudinal slip []
Longitudinal force [N] vs Lateral force [N]

With the support package, you can also import tire parameter values defined in the Combined Slip Wheel 2DOF block to a tireModel object or export tire parameter values from a tireModel object to the Combined Slip Wheel 2DOF block. For more information, see tireModel.get and set.

Use the Tire type parameter to select the source of the tire data.

Goal Action

Goal	Action
Import your own external file containing Magic Formula coefficients, and use them to drive the empirical equations modeling the tire^{1 and 2}. The file you import can be a .mat, .tir, or .txt type, and must contain parameter names corresponding to those in the tire block.	Update the block parameters with fitting coefficients from a file: Set Tire type to `External file`. On the Wheel and Tire Parameters > External tire source pane, select Select file. Select the tire coefficient file. Select Update mask values from file. In the dialog box that prompts you for confirmation, click OK. The block updates the parameters. Select Apply.
Select one of the Magic Formula built-in tire models to drive the empirical equations modeling the tire ^{1 and 2}.	Update the applicable block parameters with values from a built-in tire model: Set Tire type to the tire that you want to implement. Options include: `Light passenger car 205/60R15` `Light passenger car 245/60R16` `Mid-size passenger car 235/45R18` `Performance car 225/40R19` `SUV 265/50R20` `Light truck 275/65R18` `Commercial truck 295/75R22.5` Select Update block with applicable tire values. On the Tire Parameters tab, the block updates the applicable parameters, including Tire nominal section width, Rim radius, and Tire mass. Select Apply.

Import your own external file containing Magic Formula coefficients, and use them to drive the empirical equations modeling the tire^{1 and 2}. The file you import can be a .mat, .tir, or .txt type, and must contain parameter names corresponding to those in the tire block.

Update the block parameters with fitting coefficients from a file:

Set Tire type to External file.
On the Wheel and Tire Parameters > External tire source pane, select Select file.
Select the tire coefficient file.
Select Update mask values from file. In the dialog box that prompts you for confirmation, click OK. The block updates the parameters.
Select Apply.

Select one of the Magic Formula built-in tire models to drive the empirical equations modeling the tire ^{1 and
2}.

Update the applicable block parameters with values from a built-in tire model:

Set Tire type to the tire that you want to implement. Options include:
- Light passenger car 205/60R15
- Light passenger car 245/60R16
- Mid-size passenger car 235/45R18
- Performance car 225/40R19
- SUV 265/50R20
- Light truck 275/65R18
- Commercial truck 295/75R22.5
Select Update block with applicable tire values. On the Tire Parameters tab, the block updates the applicable parameters, including Tire nominal section width, Rim radius, and Tire mass.
Select Apply.

Use the Brake Type parameter to select the brake.

Action	Brake Type Setting
No braking	`None`
Implement brake that converts the brake cylinder pressure into a braking force	`Disc`
Implement simplex drum brake that converts the applied force and brake geometry into a net braking torque	`Drum`
Implement lookup table that is a function of the wheel speed and applied brake pressure	`Mapped`

Rotational Wheel Dynamics

The block calculates the inertial response of the wheel subject to:

Axle losses
Brake and drive torque
Tire rolling resistance
Ground contact through the tire-road interface

To implement the Magic Formula, the block uses these equations from the cited references:

Calculation	Equations
Longitudinal force	Tire and Vehicle Dynamics² equations 4.E9 through 4.E57
Lateral force - pure sideslip	Tire and Vehicle Dynamics² equations 4.E19 through 4.E30
Lateral force - combined slip	Tire and Vehicle Dynamics² equations 4.E58 through 4.E67
Vertical dynamics	Tire and Vehicle Dynamics² equations 4.E68, 4.E1, 4.E2a, and 4.E2b
Overturning couple	Tire and Vehicle Dynamics² equation 4.E69
Rolling resistance	An improved Magic Formula/Swift tyre model that can handle inflation pressure changes¹ equation 6.1.2 Tire and Vehicle Dynamics² equation 4.E70
Aligning moment	Tire and Vehicle Dynamics² equation 4.E31 through 4.E49
Aligning torque - combined slip	Tire and Vehicle Dynamics² equation 4.E71 through 4.E78 If you clear Include turn slip, the block sets some of these equations to 1.

The input torque is the summation of the applied axle torque, braking torque, and moment arising from the combined tire torque.

$T_{i} = T_{a} - T_{b} + T_{d}$

For the moment arising from the combined tire torque, the block implements tractive wheel forces and rolling resistance with first-order dynamics. The rolling resistance has a time constant parameterized in terms of a relaxation length.

$T_{d} (s) = \frac{1}{\frac{L_{e}}{| ω | R_{e}} s + 1} (F_{x} R_{e} + M_{y})$

Braking torque is based on an idealized dry clutch friction model (if brakes are selected). Depending on the lockup condition, the block implements these friction and dynamic models:

If	Lockup Condition	Friction Model	Dynamic Model
$\begin{array}{l} ω \neq 0 \\ or \\ T_{S} < \| T_{i} + T_{f} - ω b \| \end{array}$	Unlocked	$\begin{array}{l} T_{f} = T_{k}, \\ where \\ T_{k} = F_{c} R_{e f f} μ_{k} \tanh [4 (- ω_{d})] \\ T_{s} = F_{c} R_{e f f} μ_{s} \\ R_{e f f} = \frac{2 (R_{o}^{3} - R_{i}^{3})}{3 (R_{o}^{2} - R_{i}^{2})} \end{array}$	$\dot{ω} J = - ω b + T_{i} + T_{o}$
$\begin{array}{l} ω = 0 \\ and \\ T_{S} \geq \| T_{i} + T_{f} - ω b \| \end{array}$	Locked	$T_{f} = T_{s}$	$ω = 0$

The equations use these variables.

ω	Wheel angular velocity
a	Velocity independent force component
b	Linear velocity force component
c	Quadratic velocity force component
L_e	Tire relaxation length
J	Moment of inertia
M_y	Rolling resistance torque
T_a	Applied axle torque about wheel spin axis
T_b	Braking torque
T_d	Combined tire torque
T_f	Frictional torque
T_i	Net input torque
T_k	Kinetic frictional torque
T_o	Net output torque
T_s	Static frictional torque
F_c	Applied clutch force
F_x	Longitudinal force developed by the tire road interface due to slip
R_eff	Effective clutch radius
R_o	Annular disk outer radius
R_i	Annular disk inner radius
R_e	Effective tire radius while under load and for a given pressure
V_x	Longitudinal axle velocity
F_z	Vehicle normal force
ɑ	Tire pressure exponent
β	Normal force exponent
p_i	Tire pressure
μ_s	Coefficient of static friction
μ_k	Coefficient of kinetic friction

Tire and Wheel Coordinate Systems

To resolve the forces and moments, the block uses the Z-Up orientation of the tire and wheel coordinate systems.

Tire coordinate system axes (X_T, Y_T, Z_T) are fixed in a reference frame attached to the tire. The origin is at the tire contact with the ground.
Wheel coordinate system axes (X_W, Y_W, Z_W) are fixed in a reference frame attached to the wheel. The origin is at the wheel center.

Z-Up Orientation¹

Z-Up tire and wheel coordinate systems showing wheel plane and road plane

Brakes

Disc

If you specify the Brake Type parameter as Disc, the block implements a disc brake. This figure shows the side and front views of a disc brake.

Front and side view of disc brake, showing pad, disc, and caliper

A disc brake converts brake cylinder pressure from the brake cylinder into force. The disc brake applies the force at the brake pad mean radius.

The block uses these equations to calculate brake torque for the disc brake.

$T = {\begin{matrix} \frac{μ P π B_{a}^{2} R_{m} N_{p a d s}}{4} when N \neq 0 \\ \frac{μ_{s t a t i c} P π B_{a}^{2} R_{m} N_{p a d s}}{4} when N = 0 \end{matrix}$

$R m = \frac{R o + R i}{2}$

The equations use these variables.

Variable	Value
T	Brake torque
P	Applied brake pressure
N	Wheel speed
N_pads	Number of brake pads in disc brake assembly
μ_static	Disc pad-rotor coefficient of static friction
μ	Disc pad-rotor coefficient of kinetic friction
B_a	Brake actuator bore diameter
R_m	Mean radius of brake pad force application on brake rotor
R_o	Outer radius of brake pad
R_i	Inner radius of brake pad

Drum

If you specify the Brake Type parameter as Drum, the block implements a static (steady-state) simplex drum brake. A simplex drum brake consists of a single two-sided hydraulic actuator and two brake shoes. The brake shoes do not share a common hinge pin.

The simplex drum brake model uses the applied force and brake geometry to calculate a net torque for each brake shoe. The drum model assumes that the actuators and shoe geometry are symmetrical for both sides, allowing a single set of geometry and friction parameters to be used for both shoes.

The block implements equations that are derived from these equations in Fundamentals of Machine Elements.

$\begin{array}{l} T_{r s h o e} = (\frac{π μ c r (\cos θ_{2} - \cos θ_{1}) B_{a}^{2}}{2 μ (2 r (\cos θ_{2} - \cos θ_{1}) + a (\cos^{2} θ_{2} - \cos^{2} θ_{1})) + a (2 θ_{1} - 2 θ_{2} + \sin 2 θ_{2} - \sin 2 θ_{1})}) P \\ T_{l s h o e} = (\frac{π μ c r (\cos θ_{2} - \cos θ_{1}) B_{a}^{2}}{- 2 μ (2 r (\cos θ_{2} - \cos θ_{1}) + a (\cos^{2} θ_{2} - \cos^{2} θ_{1})) + a (2 θ_{1} - 2 θ_{2} + \sin 2 θ_{2} - \sin 2 θ_{1})}) P \end{array}$

$T = {\begin{matrix} T_{r s h o e} + T_{l s h o e} when N \neq 0 \\ (T_{r s h o e} + T_{l s h o e}) \frac{μ_{s t a t i c}}{μ} when N = 0 \end{matrix}$

Side view of drum brake

The equations use these variables.

Variable	Value
T	Brake torque
P	Applied brake pressure
N	Wheel speed
μ_static	Disc pad-rotor coefficient of static friction
μ	Disc pad-rotor coefficient of kinetic friction
T_rshoe	Right shoe brake torque
T_lshoe	Left shoe brake torque
a	Distance from drum center to shoe hinge pin center
c	Distance from shoe hinge pin center to brake actuator connection on brake shoe
r	Drum internal radius
B_a	Brake actuator bore diameter
Θ₁	Angle from shoe hinge pin center to start of brake pad material on shoe
Θ₂	Angle from shoe hinge pin center to end of brake pad material on shoe

Mapped

If you specify the Brake Type parameter as Mapped, the block uses a lookup table to determine the brake torque.

$T = {\begin{matrix} f_{b r a k e} (P, N) when N \neq 0 \\ (\frac{μ_{s t a t i c}}{μ}) f_{b r a k e} (P, N) when N = 0 \end{matrix}$

The equations use these variables.

Variable	Value
T	Brake torque
$f_{b r a k e}^{} (P, N)$	Brake torque lookup table
P	Applied brake pressure
N	Wheel speed
μ_static	Friction coefficient of drum pad-face interface under static conditions
μ	Friction coefficient of disc pad-rotor interface

The lookup table for the brake torque, $f_{b r a k e}^{} (P, N)$ , is a function of applied brake pressure and wheel speed, where:

T is brake torque, in N·m.
P is applied brake pressure, in bar.
N is wheel speed, in rpm.

Plot of brake torque as a function of wheel speed and applied brake pressure

Examples

Scene Interrogation with Camera and Ray Tracing Reference Application

Interrogate a 3D Unreal Engine^® scene with a vehicle dynamics model by using a camera and ray tracing reference application project.

Open Script

Ports

Input

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BrkPrs — Brake pressure
scalar | N-by-`1` vector

Brake pressure, in Pa.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Dependencies

To enable this port, set the Brake Type parameter, to one of these types:

Disc
Drum
Mapped

AxlTrq — Axle torque
scalar | N-by-`1` vector

Axle torque, T_a, about wheel spin axis, in N·m.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Vx — Longitudinal velocity
scalar | N-by-`1` vector

Axle longitudinal velocity, V_x, along tire-fixed x-axis, in m/s.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Vy — Lateral velocity
scalar | N-by-`1` vector

Axle lateral velocity, V_y, along tire-fixed y-axis, in m/s.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Camber — Inclination angle
scalar | N-by-`1` vector

Camber angle, ɣ, or inclination angle, ε, in rad.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

YawRate — Tire angular velocity
scalar | N-by-`1` vector

Tire angular velocity, r, about the tire-fixed z-axis (yaw rate), in rad/s.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Prs — Tire inflation pressure
scalar | N-by-`1` vector

Tire inflation pressure, p_i, in Pa.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Gnd — Ground displacement
scalar | N-by-`1` vector

Ground displacement along tire-fixed z-axis, in m. Positive input produces wheel lift.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Fext — Axle force applied to tire
scalar | N-by-`1` vector

Axle force applied to tire, F_ext, along vehicle-fixed z-axis (positive input compresses the tire), in N.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Dependencies

To enable this parameter, set Vertical Motion to None or Magic Formula.

RadialDeflct — Tire radial deflection
scalar | N-by-`1` vector

Tire radial deflection, RadialDeflct, in m. This value will be used in all internal dependent magic formula equations that rely on deflection.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Dependencies

To enable this port, set Vertical Motion to External Deflection.

ScaleFctrs — Scale factors
`27`-by-`N` array

Magic Formula scale factor array. Array dimensions are 27 by the number of wheels, N.

The Magic Formula equations use scale factors to account for static or simulation run-time variations. Nominally, most are set to 1.

Array Element	Variable	Scale Factor
`ScaleFctrs(1,1)`	`lam_Fzo`	Nominal load
`ScaleFctrs(2,1)`	`lam_mux`	Longitudinal peak friction coefficient
`ScaleFctrs(3,1)`	`lam_muy`	Lateral peak friction coefficient
`ScaleFctrs(4,1)`	`lam_muV`	Slip speed, Vs, decaying friction
`ScaleFctrs(5,1)`	`lam_Kxkappa`	Brake slip stiffness
`ScaleFctrs(6,1)`	`lam_Kyalpha`	Cornering stiffness
`ScaleFctrs(7,1)`	`lam_Cx`	Longitudinal shape factor
`ScaleFctrs(8,1)`	`lam_Cy`	Lateral shape factor
`ScaleFctrs(9,1)`	`lam_Ex`	Longitudinal curvature factor
`ScaleFctrs(10,1)`	`lam_Ey`	Lateral curvature factor
`ScaleFctrs(11,1)`	`lam_Hx`	Longitudinal horizontal shift
`ScaleFctrs(12,1)`	`lam_Hy`	Lateral horizontal shift
`ScaleFctrs(13,1)`	`lam_Vx`	Longitudinal vertical shift
`ScaleFctrs(14,1)`	`lam_Vy`	Lateral vertical shift
`ScaleFctrs(15,1)`	`lam_Kygamma`	Camber force stiffness
`ScaleFctrs(16,1)`	`lam_Kzgamma`	Camber torque stiffness
`ScaleFctrs(17,1)`	`lam_t`	Pneumatic trail (effecting aligning torque stiffness)
`ScaleFctrs(18,1)`	`lam_Mr`	Residual torque
`ScaleFctrs(19,1)`	`lam_xalpha`	Alpha influence on Fx (kappa)
`ScaleFctrs(20,1)`	`lam_ykappa`	Kappa influence on Fy (alpha)
`ScaleFctrs(21,1)`	`lam_Vykappa`	Induced ply steer Fy
`ScaleFctrs(22,1)`	`lam_s`	Moment arm of Fx
`ScaleFctrs(23,1)`	`lam_Cz`	Radial tire stiffness
`ScaleFctrs(24,1)`	`lam_Mx`	Overturning couple stiffness
`ScaleFctrs(25,1)`	`lam_VMx`	Overturning couple vertical shift
`ScaleFctrs(26,1)`	`lam_My`	Rolling resistance moment
`ScaleFctrs(27,1)`	`lam_Mphi`	Parking torque Mz

Output

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Info — Block data
bus

Block data, returned as a bus signal containing these block values.

Signal	Description	Units
`AxlTrq`	Axle torque about wheel-fixed y-axis	N·m
`Omega`	Wheel angular velocity about wheel-fixed y-axis	rad/s
`Fx`	Longitudinal vehicle force along tire-fixed x-axis	N
`Fy`	Lateral vehicle force along tire-fixed y-axis	N
`Fz`	Vertical vehicle force along tire-fixed z-axis	N
`Mx`	Overturning moment about tire-fixed x-axis	N·m
`My`	Rolling resistance torque about tire-fixed y-axis	N·m
`Mz`	Aligning moment about tire-fixed z-axis	N·m
`Vx`	Vehicle longitudinal velocity along tire-fixed x-axis	m/s
`Vy`	Vehicle lateral velocity along tire-fixed y-axis	m/s
`Re`	Loaded effective radius	m
`Kappa`	Longitudinal slip ratio	NA
`Alpha`	Side slip angle	rad
`a`	Contact patch half length	m
`b`	Contact patch half width	m
`RL`	Loaded radius	m
`RadialDeflct`	Tire radial deflection	m
`WhlTrq`	Wheel torque	N·m
`Gamma`	Camber angle	rad
`psidot`	Tire angular velocity about the tire-fixed z-axis (yaw rate)	rad/s
`BrkTrq`	Brake torque about vehicle-fixed y-axis	N·m
`BrkPrs`	Brake pressure	Pa
`z`	Axle vertical displacement along tire-fixed z-axis	m
`zdot`	Axle vertical velocity along tire-fixed z-axis	m/s
`Gnd`	Ground displacement along tire-fixed z-axis (positive input produces wheel lift)	m
`GndFz`	Vertical sidewall force on ground along tire-fixed z-axis	N
`Prs`	Tire inflation pressure	Pa

Omega — Wheel angular velocity
scalar | N-by-`1` vector

Wheel angular velocity, ω, about wheel-fixed y-axis, in rad/s.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Fx — Longitudinal axle force
scalar | N-by-`1` vector

Longitudinal force acting on axle, F_x, along tire-fixed x-axis, in N. Positive force acts to move the vehicle forward.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Fy — Lateral axle force
scalar | N-by-`1` vector

Lateral force acting on axle, F_y, along tire-fixed y-axis, in N.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Fz — Vertical axle force
scalar | N-by-`1` vector

Vertical force acting on axle, F_z, along tire-fixed z-axis, in N.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Mx — Overturning moment
scalar | N-by-`1` vector

Longitudinal moment acting on axle, M_x, about tire-fixed x-axis, in N·m.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

My — Rolling resistive moment
scalar | N-by-`1` vector

Lateral moment acting on axle, M_y, about tire-fixed y-axis, in N·m.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Mz — Aligning moment
scalar | N-by-`1` vector

Vertical moment acting on axle, M_z, about tire-fixed z-axis, in N·m.

Vector is the number of wheels, N, by 1. If you provide a scalar value, the block assumes that number of wheels is one.

Parameters

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Tire Options

Tire type — Select type
`External file` (default) | `Light passenger car 205/60R15` | `Light passenger car 245/60R16` | `Mid-size passenger car 235/45R18` | `Performance car 225/40R19` | `SUV 265/50R20` | `Light truck 275/65R18` | `Commercial truck 295/75R22.5`

Use the Tire type parameter to select the source of the tire data.

Goal Action

Goal	Action
Import your own external file containing Magic Formula coefficients, and use them to drive the empirical equations modeling the tire^{1 and 2}. The file you import can be a .mat, .tir, or .txt type, and must contain parameter names corresponding to those in the tire block.	Update the block parameters with fitting coefficients from a file: Set Tire type to `External file`. On the Wheel and Tire Parameters > External tire source pane, select Select file. Select the tire coefficient file. Select Update mask values from file. In the dialog box that prompts you for confirmation, click OK. The block updates the parameters. Select Apply.
Select one of the Magic Formula built-in tire models to drive the empirical equations modeling the tire ^{1 and 2}.	Update the applicable block parameters with values from a built-in tire model: Set Tire type to the tire that you want to implement. Options include: `Light passenger car 205/60R15` `Light passenger car 245/60R16` `Mid-size passenger car 235/45R18` `Performance car 225/40R19` `SUV 265/50R20` `Light truck 275/65R18` `Commercial truck 295/75R22.5` Select Update block with applicable tire values. On the Tire Parameters tab, the block updates the applicable parameters, including Tire nominal section width, Rim radius, and Tire mass. Select Apply.

Update the block parameters with fitting coefficients from a file:

Set Tire type to External file.
On the Wheel and Tire Parameters > External tire source pane, select Select file.
Select the tire coefficient file.
Select Update mask values from file. In the dialog box that prompts you for confirmation, click OK. The block updates the parameters.
Select Apply.

Select one of the Magic Formula built-in tire models to drive the empirical equations modeling the tire ^{1 and
2}.

Update the applicable block parameters with values from a built-in tire model:

Set Tire type to the tire that you want to implement. Options include:
- Light passenger car 205/60R15
- Light passenger car 245/60R16
- Mid-size passenger car 235/45R18
- Performance car 225/40R19
- SUV 265/50R20
- Light truck 275/65R18
- Commercial truck 295/75R22.5
Select Update block with applicable tire values. On the Tire Parameters tab, the block updates the applicable parameters, including Tire nominal section width, Rim radius, and Tire mass.
Select Apply.

Vertical Motion — Vertical motion model
`Magic Formula` (default) | `None` | `External deflection`

Type of vertical motion. By default, the block uses the Magic Formula to calculate the vertical motion of the tire.

Ply steer — Include ply steer
`on` (default) | `off`

Select to include ply steer in the Magic Formula equations.

By default, the blocks include ply steer and turn slip in the Magic Formula equations. The equations are fit to flat-belt test data and predict a number of tire effects, including ply steer and turn slip. Consider removing the effects if your:

Test data does not include ply steer or turn slip data.
Analysis does not require ply steer or turn slip effects.

If you clear Ply steer, the block internally sets these parameters to 0:

Vertical shift of overturning moment, QSX1
Combined slip Fx shift factor reduction, RHX1
Efy curvature constant camber dependency, PEY3
SHY horizontal shift at FZNOM, PHY1
SHY variation with load, PHY2
Svy/Fz vertical shift at FZNOM, PVY1
Svy/Fz variation with load, PVY2
Fy shift reduction with slip angle, RBY3
Slip ratio side force Svyk/Muy*Fz at FZNOM, RVY1
Side force Svyk/Muy*Fz variation with load, RVY2
Bpt slope variation with camber, QBZ4
Dpt peak trail variation with camber, QDZ3
Dmr peak residual torque, QDZ6
Dmr peak residual torque variation with load, QDZ7
Ept variation with sign of alpha-t, QEZ4
Sht horizontal trail shift at FZNOM, QHZ1
Sht variation with load, QHZ2
Nominal value of s/R0: effect of Fx on Mz, SSZ1

Turn slip — Include turn slip
`on` (default) | `off`

Select to include ply steer in Magic Formula equations.

Test data does not include ply steer or turn slip data.
Analysis does not require ply steer or turn slip effects.

If you clear Turn slip, the block internally:

Sets the Magic Formula turn slip equations to 1. Specifically, equations 4.E77, 4.E79, 4.E81, 4.E83, 4.E84, 4.E92, 4.E102, 4.E101, and 4.E105².
Uses Magic Formula terms that effect horizontal shift.
Uses Magic Formula small turn slip values in 4.E27².

Brake type — Brake type
`None` | `Disc` | `Drum` | `Mapped`

Use the Brake Type parameter to select the brake.

Action	Brake Type Setting
No braking	`None`
Implement brake that converts the brake cylinder pressure into a braking force	`Disc`
Implement simplex drum brake that converts the applied force and brake geometry into a net braking torque	`Drum`
Implement lookup table that is a function of the wheel speed and applied brake pressure	`Mapped`

Plotting

Install Extended Tire Features — Option to install Extended Tire Features for Vehicle Dynamics Blockset™ support package
button

Click Install Extended Tire Features to install the Extended Tire Features for Vehicle Dynamics Blockset support package. With the support package, you can plot steady-state force and moment tire responses from the Combined Slip Wheel 2DOF Block Parameters dialog box.

Plot steady state force, moment response — Option to plot steady-state force and moment tire responses
button

Click Plot steady state force, moment response to generate these plots:

Lateral force [N] vs Slip angle [rad]
Self-aligning moment [Nm] vs Slip angle [rad]
Longitudinal force [N] vs Longitudinal slip []
Longitudinal force [N] vs Lateral force [N]

Dependencies

To enable this parameter, click Install Extended Tire Features.

Brake

Static friction coefficient, mu_static — Static friction coefficient
`0.3` (default) | scalar | N-by-`1` vector

Static friction coefficient, specified as a scalar or N-by-1 vector, dimensionless. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other brake parameters.

N is the number of wheels and must match the input signal dimensions.

Dependencies

To enable this parameter, set Brake Type to Disc, Drum, or Mapped.

Kinetic friction coefficient, mu_kinetic — Kinetic friction
`0.2` (default) | scalar | N-by-`1` vector

Kinematic friction coefficient, specified as a scalar or N-by-1 vector, dimensionless. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other brake parameters.

N is the number of wheels and must match the input signal dimensions.

Dependencies

To enable this parameter, set Brake Type to Disc, Drum, or Mapped.

Disc

Disc brake actuator bore, disc_abore — Bore distance
`0.05` (default) | scalar | N-by-`1` vector

Disc brake actuator bore, specified as a scalar or N-by-1 vector, in m. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other brake parameters.

N is the number of wheels and must match the input signal dimensions.

Dependencies

To enable this parameter, set Brake Type to Disc.

Brake pad mean radius, Rm — Radius
`0.177` (default) | scalar | N-by-`1` vector

Brake pad mean radius, specified as a scalar or N-by-1 vector, in m. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other brake parameters.

N is the number of wheels and must match the input signal dimensions.

Dependencies

To enable this parameter, set Brake Type to Disc.

Number of brake pads, num_pads — Number of brake pads
`2` (default) | scalar | N-by-`1` vector

Number of brake pads, specified as a scalar or N-by-1 vector, dimensionless. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other brake parameters.

N is the number of wheels and must match the input signal dimensions.

Dependencies

To enable this parameter, set Brake Type to Disc.

Drum

Drum brake actuator bore, disc_abore — Bore distance
`0.0508` (default) | scalar | N-by-`1` vector

Drum brake actuator bore, specified as a scalar or N-by-1 vector, in m. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other brake parameters.

N is the number of wheels and must match the input signal dimensions.

Dependencies

To enable this parameter, set Brake Type to Drum.

Shoe pin to drum center distance, drum_a — Shoe pin to drum center distance
`0.123` (default) | scalar

Shoe pin to drum center distance, in m.

Dependencies

To enable this parameter, set Brake Type to Drum.

Shoe pin center to force application point distance, drum_c — Shoe pin center to force application point distance
`0.212` (default) | scalar

Shoe pin center to force application point distance, in m.

Dependencies

To enable this parameter, set Brake Type to Drum.

Drum internal radius, drum_r — Drum internal radius
`0.15` (default) | scalar

Drum internal radius, in m.

Dependencies

To enable this parameter, set Brake Type to Drum.

Shoe pin to pad start angle, drum_theta1 — Shoe pin to pad start angle
`0` (default) | scalar

Shoe pin to pad start angle, in deg.

Dependencies

To enable this parameter, set Brake Type to Drum.

Shoe pin to pad end angle, drum_theta2 — Shoe pin to pad end angle
`126` (default) | scalar

Shoe pin to pad end angle, in deg.

Dependencies

To enable this parameter, set Brake Type to Drum.

Mapped

Brake actuator pressure breakpoints, brake_p_bpt — Brake actuator pressure breakpoints
vector

Brake actuator pressure breakpoints, in bar.

Dependencies

To enable this parameter, set Brake Type to Mapped.

Wheel speed breakpoints, brake_n_bpt — Wheel speed breakpoints
vector

Wheel speed breakpoints, in rpm.

Dependencies

To enable this parameter, set Brake Type to Mapped.

Brake torque map, f_brake_t — Lookup table for brake torque
array

The lookup table for the brake torque, $f_{b r a k e}^{} (P, N)$ , is a function of applied brake pressure and wheel speed, where:

T is brake torque, in N·m.
P is applied brake pressure, in bar.
N is wheel speed, in rpm.

Plot showing brake torque as a function of wheel speed and applied brake pressure

Dependencies

To enable this parameter, set Brake Type to Mapped.

Simulation

Nominal pressure, NOMPRES — Pressure
scalar

Nominal pressure, NOMPRES, in Pa.

Maximum pressure, PRESMAX — Maximum pressure
scalar

Maximum pressure, PRESMAX, in Pa.

Minimum pressure, PRESMIN — Minimum pressure
scalar

Minimum pressure, PRESMIN, in Pa.

Nominal normal force, FNOMIN — Force
scalar

Nominal normal force, FNOMIN, in N.

Maximum normal force, FZMAX — Force
scalar

Maximum normal force, FZMAX, in N.

Minimum normal force, FZMIN — Force
scalar

Minimum normal force, FZMIN, in N.

Velocity tolerance used to handle low velocity situations, VXLOW — Tolerance
scalar

Velocity tolerance used to handle low velocity situations, VXLOW, in m/s.

Max allowable slip ratio (absolute), KPUMAX — Max allowable slip ratio
scalar

Max allowable slip ratio (absolute), KPUMAX, dimensionless.

Minimum allowable slip ratio (absolute), KPUMIN — Minimum allowable slip ratio
scalar

Minimum allowable slip ratio (absolute), KPUMIN, dimensionless.

Max allowable slip angle (absolute), ALPMAX — Max allowable slip angle
scalar

Max allowable slip angle (absolute), ALPMAX, in rad.

Minimum allowable slip angle (absolute), ALPMIN — Minimum allowable slip angle
scalar

Minimum allowable slip angle (absolute), ALPMIN, in rad.

Maximum allowable camber angle, CAMMAX — Maximum allowable camber angle
scalar

Maximum allowable camber angle CAMMAX, in rad.

Minimum allowable camber angle, CAMMIN — Minimum allowable camber angle
scalar

Minimum allowable camber angle, CAMMIN, in rad.

Nominal longitudinal speed, LONGVL — Speed
scalar

Nominal longitudinal speed, LONGVL, in m/s.

Initial wheel rotational velocity, omegao — Initial wheel rotational velocity
scalar | N-by-`1` vector

Initial wheel rotational velocity, specified as a scalar or N-by-1 vector, in rad/s. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other rotational parameters.

N is the number of wheels and must match the input signal dimensions.

Dimension

Tire unloaded radius, UNLOADED_RADIUS — Radius
`scalar`

Tire unloaded radius, UNLOADED_RADIUS, in m.

Tire nominal section width, WIDTH — Tire nominal section width
scalar

Tire nominal section width, WIDTH, in m.

Rim radius, RIM_RADIUS — Radius
`scalar`

Rim radius, RIM_RADIUS, in m.

Nominal aspect ratio, ASPECT_RATIO — Ratio
scalar

Nominal aspect ratio, ASPECT_RATIO, dimensionless.

Inertial and Damping

Tire mass, MASS — Mass
scalar | N-by-`1` vector

Tire mass, specified as a scalar or N-by-1 vector, in kg. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other inertial parameters.

N is the number of wheels and must match the input signal dimensions.

Dependencies

To enable this parameter, set Vertical Motion to Magic Formula.

Tire rotational inertia (rolling axis), IYY — Tire rotational inertia
scalar | N-by-`1` vector

Tire rotational inertia (rolling axis), specified as a scalar or N-by-1 vector, in kg·m². If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other rotational parameters.

N is the number of wheels and must match the input signal dimensions.

Rotational damping, br — Rotational damping
scalar | N-by-`1` vector

Rotational damping, specified as a scalar or N-by-1 vector, in N·m·s/rad. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other rotational parameters.

N is the number of wheels and must match the input signal dimensions.

Gravity, GRAVITY — Gravity
scalar

Gravity, GRAVITY, in m/s^2.

Dependencies

To enable this parameter, set Vertical Motion to Magic Formula.

Vertical

Initial tire displacement, zo — Displacement
scalar | N-by-`1` vector

Initial tire displacement, specified as a scalar or N-by-1 vector, in m. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other vertical parameters.

N is the number of wheels and must match the input signal dimensions.

Initial wheel vertical velocity (wheel fixed frame), zdoto — Velocity
scalar | N-by-`1` vector

Initial wheel vertical velocity, specified as a scalar or N-by-1 vector, in m/s. If you specify a scalar, the block uses that value for all wheels. If you specify a vector, you must specify vectors for the other vertical parameters.

N is the number of wheels and must match the input signal dimensions.

Effective rolling radius at low load stiffness, BREFF — Stiffness
scalar

Effective rolling radius at low load stiffness, BREFF, dimensionless.

Effective rolling radius peak value, DREFF — Radius
scalar

Effective rolling radius peak value, DREFF, dimensionless.

Effective rolling radius at high load stiffness, FREFF — Radius
`scalar`

Effective rolling radius at high load stiffness, FREFF, dimensionless.

Unloaded to nominal rolling radius ratio, Q_RE0 — Ratio
`scalar`

Unloaded to nominal rolling radius ratio, Q_RE0, dimensionless.

Radius rotational speed dependence, Q_V1 — Speed
`scalar`

Radius rotational speed dependence, Q_V1, dimensionless.

Stiffness rotational speed dependence, Q_V2 — Speed
`scalar`

Stiffness rotational speed dependence, Q_V2, dimensionless.

Linear load change with deflection, Q_FZ1 — Load change
`scalar`

Linear load change with deflection, Q_FZ1, dimensionless.

Quadratic load change with deflection, Q_FZ2 — Load change
`scalar`

Quadratic load change with deflection, Q_FZ2, dimensionless.

Linear load change with deflection and quadratic camber, Q_FZ3 — Load change
`scalar`

Linear load change with deflection and quadratic camber, Q_FZ3, dimensionless.

Load response to longitudinal force, Q_FCX — Force
`scalar`

Load response to longitudinal force, Q_FCX, dimensionless.

Load response to lateral force, Q_FCY — Force
`scalar`

Load response to lateral force, Q_FCY, dimensionless.

Vertical stiffness change due to lateral load dependency on lateral stiffness, Q_FCY2 — Stiffness
`scalar`

Vertical stiffness change due to lateral load dependency on lateral stiffness, Q_FCY2, dimensionless.

Stiffness response to pressure, PFZ1 — Stiffness
`0.7098` (default) | `scalar`

Stiffness response to pressure, PFZ1, dimensionless.

Vertical tire stiffness, VERTICAL_STIFFNESS — Stiffness
`scalar`

Vertical tire stiffness, VERTICAL_STIFFNESS, in N/m.

Vertical tire damping, VERTICAL_DAMPING — Damping
`scalar`

Vertical tire damping, VERTICAL_DAMPING, in N·s/m.

Rim bottoming out offset, BOTTOM_OFFST — Offset
`scalar`

Rim bottoming out offset, BOTTOM_OFFST, in m.

Bottoming out stiffness, BOTTOM_STIFF — Stiffness
`scalar`

Bottoming out stiffness, BOTTOM_STIFF, in N/m.

Linear load dependent camber angle effect on vertical stiffness, Q_CAM1 — Stiffness
scalar

Linear load dependent camber angle effect on vertical stiffness, Q_CAM1, dimensionless.

Quadratic load dependent camber angle effect on vertical stiffness, Q_CAM2 — Stiffness
scalar

Quadratic load dependent camber angle effect on vertical stiffness, Q_CAM2, dimensionless.

Linear reduction of stiffness with load and camber angle, Q_CAM3 — Stiffness
scalar

Linear reduction of stiffness with load and camber angle, Q_CAM3, dimensionless.

Constant camber and slip angle effect on vertical stiffness, Q_FYS1 — Stiffness
scalar

Constant camber and slip angle effect on vertical stiffness, Q_FYS1, dimensionless.

Linear camber and slip angle effect on vertical stiffness, Q_FYS2 — Stiffness
scalar

Linear camber and slip angle effect on vertical stiffness, Q_FYS2, dimensionless.

Quadratic camber and slip angle effect on vertical stiffness, Q_FYS3 — Stiffness
scalar

Quadratic camber and slip angle effect on vertical stiffness, Q_FYS3, dimensionless.

Structural

Longitudinal stiffness, LONGITUDINAL_STIFFNESS — Stiffness
scalar

Longitudinal stiffness, LONGITUDINAL_STIFFNESS, in N/m.

Lateral stiffness, LATERAL_STIFFNESS — Stiffness
scalar

Longitudinal stiffness, LATERAL_STIFFNESS, in N/m.

Linear vertical deflection influence on longitudinal stiffness, PCFX1 — Deflection influence
scalar

Linear vertical deflection influence on longitudinal stiffness, PCFX1, dimensionless.

Quadratic vertical deflection influence on longitudinal stiffness, PCFX2 — Deflection influence
scalar

Quadratic vertical deflection influence on longitudinal stiffness, PCFX2, dimensionless.

Pressure dependency on longitudinal stiffness, PCFX3 — Pressure dependency
scalar

Pressure dependency on longitudinal stiffness, PCFX3, dimensionless.

Linear vertical deflection influence on lateral stiffness, PCFY1 — Deflection influence
scalar

Linear vertical deflection influence on lateral stiffness, PCFY1, dimensionless.

Quadratic vertical deflection influence on lateral stiffness, PCFY2 — Deflection influence
scalar

Quadratic vertical deflection influence on lateral stiffness, PCFY2, dimensionless.

Pressure dependency on longitudinal stiffness, PCFY3 — Pressure dependency
scalar

Pressure dependency on longitudinal stiffness, PCFY3, dimensionless.

Contact Patch

Contact length square root term, Q_RA1 — Length term
scalar

Contact length square root term, Q_RA1, dimensionless.

Contact length linear term, Q_RA2 — Length term
scalar

Contact length linear term, Q_RA2, dimensionless.

Contact width root term, Q_RB1 — Width term
scalar

Contact width root term, Q_RB1, dimensionless.

Contact width linear term, Q_RB2 — Width term
scalar

Contact width linear term, Q_RB2, dimensionless.

Longitudinal

Cfx shape factor, PCX1 — Shape factor
scalar

Shape factor, C_fx, PCX1, dimensionless.

Longitudinal friction at nominal normal load, PDX1 — Friction
scalar

Longitudinal friction at nominal normal load, PDX1, dimensionless.

Frictional variation with load, PDX2 — Friction variation
scalar

Frictional variation with load, PDX2, dimensionless.

Frictional variation with camber, PDX3 — Friction variation
scalar

Frictional variation with camber, PDX3, in 1/rad^2.

Longitudinal curvature at nominal normal load, PEX1 — Curvature
scalar

Longitudinal curvature at nominal normal load, PEX1, dimensionless.

Variation of curvature factor with load, PEX2 — Curvature variation
scalar

Variation of curvature factor with load, PEX2, dimensionless.

Variation of curvature factor with square of load, PEX3 — Curvature variation
scalar

Variation of curvature factor with square of load, PEX3, dimensionless.

Longitudinal curvature factor with slip, PEX4 — Curvature
scalar

Longitudinal curvature factor with slip, PEX4, dimensionless.

Longitudinal slip stiffness at nominal normal load, PKX1 — Stiffness
scalar

Longitudinal slip stiffness at nominal normal load, PKX1, dimensionless.

Variation of slip stiffness with load, PKX2 — Stiffness variation
scalar

Variation of slip stiffness with load, PKX2, dimensionless.

Slip stiffness exponent factor, PKX3 — Slip stiffness
scalar

Slip stiffness exponent factor, PKX3, dimensionless.

Horizontal shift in slip ratio at nominal normal load, PHX1 — Slip ratio shift
scalar

Horizontal shift in slip ratio at nominal normal load, PHX1, dimensionless.

Variation of horizontal slip ratio with load, PHX2 — Slip variation
scalar

Variation of horizontal slip ratio with load, PHX2, dimensionless.

Vertical shift in load at nominal normal load, PVX1 — Load shift
scalar

Vertical shift in load at nominal normal load, PVX1, dimensionless.

Variation of vertical shift with load, PVX2 — Load variation
scalar

Variation of vertical shift with load, PVX2, dimensionless.

Linear variation of longitudinal slip stiffness with tire pressure, PPX1 — Stiffness variation
scalar

Linear variation of longitudinal slip stiffness with tire pressure, PPX1, dimensionless.

Quadratic variation of longitudinal slip stiffness with tire pressure, PPX2 — Stiffness variation
scalar

Quadratic variation of longitudinal slip stiffness with tire pressure, PPX2, dimensionless.

Linear variation of peak longitudinal friction with tire pressure, PPX3 — Friction variation
scalar

Linear variation of peak longitudinal friction with tire pressure, PPX3, dimensionless.

Quadratic variation of peak longitudinal friction with tire pressure, PPX4 — Friction variation
scalar

Quadratic variation of peak longitudinal friction with tire pressure, PPX4, dimensionless.

Combined slip Fx slope factor reduction, RBX1 — Combined slip longitudinal force slope factor reduction
scalar

Combined slip longitudinal force, F_x, slope factor reduction, RBX1, dimensionless.

Slip ratio Fx slope reduction variation, RBX2 — Slip ratio longitudinal force slope reduction variation
scalar

Slip ratio longitudinal force, F_x, slope reduction variation, RBX2, dimensionless.

Camber influence on combined slip Fx stiffness, RBX3 — Camber influence on combined slip longitudinal force stiffness
scalar

Camber influence on combined slip longitudinal force, F_x, stiffness, RBX3, dimensionless.

Shape factor for combined slip Fx reduction, RCX1 — Shape factor for combined slip longitudinal force reduction
scalar

Shape factor for combined slip longitudinal force, F_x, reduction, RCX1, dimensionless.

Combined Fx curvature factor, REX1 — Combined longitudinal force curvature factor
scalar

Combined longitudinal force, F_x, curvature factor, REX1, dimensionless.

Combined Fx curvature factor with load, REX2 — Combined longitudinal force curvature factor
scalar

Combined longitudinal force, F_x, curvature factor with load, REX2, dimensionless.

Combined slip Fx shift factor reduction, RHX1 — Combined slip longitudinal force slip factor
scalar

Combined slip longitudinal force, F_x, shift factor reduction, RHX1, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Overturning

Vertical shift of overturning moment, QSX1 — Overturning moment
scalar

Vertical shift of overturning moment, QSX1, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Overturning moment due to camber, QSX2 — Overturning moment due to camber
scalar

Overturning moment due to camber, QSX2, dimensionless.

Overturning moment due to Fy, QSX3 — Overturning moment due to lateral force
scalar

Overturning moment due to lateral force, QSX3, dimensionless.

Mx combined lateral force load and camber, QSX4 — Overturning moment
scalar

Overturning moment, M_x, combined lateral force load and camber, QSX4, dimensionless.

Mx load effect due to lateral force and camber, QSX5 — Overturning moment
scalar

Overturning moment, M_x, load effect due to lateral force and camber, QSX5, dimensionless.

Mx load effect due to B-factor, QSX6 — Overturning moment
scalar

Overturning moment, M_x, load effect due to B-factor, QSX6, dimensionless.

Mx due to camber and load, QSX7 — Overturning moment
scalar

Overturning moment, M_x, due to camber and load, QSX7, dimensionless.

Mx due to lateral force and load, QSX8 — Overturning moment
scalar

Overturning moment, M_x, due to lateral force and load, QSX8, dimensionless.

Mx due to B-factor of lateral force and load, QSX9 — Overturning moment
scalar

Overturning moment, M_x, due to B-factor of lateral force and load, QSX9, dimensionless.

Mx due to vertical force and camber, QSX10 — Overturning moment
scalar

Overturning moment, M_x, due to vertical force and camber, QSX10, dimensionless.

Mx due to B-factor of vertical force and camber, QSX11 — Overturning moment
scalar

Overturning moment, M_x, due to B-factor of vertical force and camber, QSX11, dimensionless.

Mx due to squared camber, QSX12 — Overturning moment
scalar

Overturning moment, M_x, due to squared camber, QSX12, dimensionless.

Mx due to lateral force, QSX13 — Overturning moment
scalar

Overturning moment, M_x, due to lateral force, QSX13, dimensionless.

Mx due to lateral force with camber, QSX14 — Overturning moment
scalar

Overturning moment, M_x, due to lateral force with camber, QSX14, dimensionless.

Mx due to inflation pressure, PPMX1 — Overturning moment due to pressure
scalar

Overturning moment, M_x, due to inflation pressure, PPMX1, dimensionless.

Lateral

Cfy shape factor for lateral force, PCY1 — Lateral force shape factor
scalar

Shape factor for lateral force, C_fy, PCY1, dimensionless.

Lateral friction muy, PDY1 — Lateral friction
scalar

Lateral friction, μ_y, PDY1, dimensionless.

Lateral friction variation of muy with load, PDY2 — Lateral friction variation
scalar

Variation of lateral friction, μ_y, with load, PDY2, dimensionless.

Lateral friction variation of muy with squared camber, PDY3 — Lateral friction variation
scalar

Variation of lateral friction, μ_y, with squared camber, PDY3, dimensionless.

Efy lateral curvature at nominal force FZNOM, PEY1 — Lateral curvature at nominal force
scalar

Lateral curvature, Ef_y, at nominal force, F_ZNOM, PEY1, dimensionless.

Efy curvature variation with load, PEY2 — Lateral curvature variation
scalar

Lateral curvature, Ef_y, variation with load, PEY2, dimensionless.

Efy curvature constant camber dependency, PEY3 — Lateral curvature constant
scalar

Lateral curvature, Ef_y, constant camber dependency, PEY3, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Efy curvature variation with camber, PEY4 — Lateral curvature variation
scalar

Lateral curvature, Ef_y, variation with camber, PEY4, dimensionless.

Efy curvature variation with camber squared, PEY5 — Lateral curvature variation
scalar

Lateral curvature, Ef_y, variation with camber squared, PEY5, dimensionless.

Maximum KFy/FZNOM stiffness, PKY1 — Maximum stiffness
scalar

Maximum lateral force stiffness, KF_y, to nominal force, F_ZNOM, ratio, PKY1, dimensionless.

Load at maximum KFy/FZNOM stiffness, PKY2 — Load
scalar

Load at maximum lateral force stiffness, KF_y, to nominal force, F_ZNOM, ratio, PKY2, dimensionless.

KFy/FZNOM stiffness variation with camber, PKY3 — Stiffness variation
scalar

Lateral force stiffness, KF_y, to nominal force, F_ZNOM, stiffness variation with camber, PKY3, dimensionless.

KFy curvature, PKY4 — Lateral force stiffness curvature
scalar

Lateral force stiffness, KF_y curvature, PKY4, dimensionless.

Variation of peak stiffness with squared camber, PKY5 — Stiffness variation
scalar

Variation of peak stiffness with squared camber, PKY5, dimensionless.

Fy camber stiffness factor, PKY6 — Lateral force camber stiffness factor
scalar

Lateral force, F_y, camber stiffness factor, PKY6, dimensionless.

Camber stiffness vertical load dependency, PKY7 — Stiffness
scalar

Camber stiffness vertical load dependency, PKY7, dimensionless.

SHY horizontal shift at FZNOM, PHY1 — Horizontal shift at nominal force
scalar

Horizontal shift, S_HY, at nominal force, F_ZNOM, PHY1, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

SHY variation with load, PHY2 — Horizontal shift variation
scalar

Horizontal shift, S_HY, variation with load, PHY2, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Svy/Fz vertical shift at FZNOM, PVY1 — Vertical shift at nominal force
scalar

Vertical shift, S_vy, at nominal force, F_ZNOM, PVY1, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Svy/Fz variation with load, PVY2 — Vertical shift variation with load
scalar

Vertical shift, S_vy, variation with load, PVY2, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Svy/Fz variation with camber, PVY3 — Vertical shift variation with camber
scalar

Vertical shift, S_vy, variation with camber, PVY3, dimensionless.

Svy/Fz variation with load and camber, PVY4 — Vertical shift variation with load and camber
scalar

Vertical shift, S_vy, variation with load and camber, PVY4, dimensionless.

Cornering stiffness variation with inflation pressure, PPY1 — Stiffness variation with pressure
scalar

Cornering stiffness variation with inflation pressure, PPY1, dimensionless.

Cornering stiffness variation with inflation pressure induced nominal load dependency, PPY2 — Stiffness variation with pressure
scalar

Cornering stiffness variation with inflation pressure induced nominal load dependency, PPY2, dimensionless.

Linear inflation pressure on peak lateral friction, PPY3 — Pressure
scalar

Linear inflation pressure on peak lateral friction, PPY3, dimensionless.

Quadratic inflation pressure on peak lateral friction, PPY4 — Pressure
scalar

Quadratic inflation pressure on peak lateral friction, PPY4, dimensionless.

Inflation pressure effect on camber stiffness, PPY5 — Pressure
scalar

Inflation pressure effect on camber stiffness, PPY5, dimensionless.

Combined Fy reduction slope factor, RBY1 — Combined lateral force reduction slope factor
scalar

Combined lateral force, F_y, reduction slope factor, RBY1, dimensionless.

Fy slope reduction with slip angle, RBY2 — Lateral force slope reduction with slip angle
scalar

Lateral force, F_y, slope reduction with slip angle, RBY2, dimensionless.

Fy shift reduction with slip angle, RBY3 — Lateral force shift reduction with slip angle
scalar

Lateral force, F_y, shift reduction with slip angle, RBY3, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Fy combined stiffness variation from camber, RBY4 — Lateral force combined stiffness variation from camber
scalar

Lateral force, F_y, combined stiffness variation from camber, RBY4, dimensionless.

Fy combined reduction shape factor, RCY1 — Lateral force combined reduction shape factor
scalar

Lateral force, F_y, combined reduction shape factor, RCY1, dimensionless.

Fy combined curvature factor, REY1 — Lateral force combined curvature factor
scalar

Lateral force, F_y, combined curvature factor, REY1, dimensionless.

Fy combined curvature factor with load, REY2 — Lateral force combined curvature factor with load
scalar

Lateral force, F_y, combined curvature factor with load, REY2, dimensionless.

Fy combined reduction shift factor, RHY1 — Lateral force combined reduction shift factor
scalar

Lateral force, F_y, combined reduction shift factor, RHY1, dimensionless.

Fy combined reduction shift factor with load, RHY2 — Lateral force combined reduction shift factor with load
scalar

Lateral force, F_y, combined reduction shift factor with load, RHY2, dimensionless.

**Slip ratio side force Svyk/Muy*Fz at FZNOM, RVY1** — Slip ratio slide force at nominal force
scalar

Slip ratio side force at nominal force, F_ZNOM, RVY1, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

**Side force Svyk/Muy*Fz variation with load, RVY2** — Side force variation with load
scalar

Side force variation with load, RVY2, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

**Side force Svyk/Muy*Fz variation with camber, RVY3** — Side force variation with camber
scalar

Side force variation with camber, RVY3, dimensionless.

**Side force Svyk/Muy*Fz variation with slip angle, RVY4** — Side force variation with slip angle
scalar

Side force variation with slip angle, RVY4, dimensionless.

**Side force Svyk/Muy*Fz variation with slip ratio, RVY5** — Side force variation with slip ratio
scalar

Side force variation with slip ratio, RVY5, dimensionless.

**Side force Svyk/Muy*Fz variation with slip ratio arctangent, RVY6** — Side force variation with slip ratio arctangent
scalar

Side force variation with slip ratio arctangent, RVY6, dimensionless.

Rolling

Torque resistance coefficient, QSY1 — Torque resistance
scalar

Torque resistance coefficient, QSY1, dimensionless.

Torque resistance due to Fx, QSY2 — Torque resistance due to longitudinal force
scalar

Torque resistance due to longitudinal force, F_x, QSY2, dimensionless.

Torque resistance due to speed, QSY3 — Torque resistance due to speed
scalar

Torque resistance due to speed, QSY3, dimensionless.

Torque resistance due to speed^4, QSY4 — Torque resistance due to speed
scalar

Torque resistance due to speed^4, QSY4, dimensionless.

Torque resistance due to square of camber, QSY5 — Torque resistance due to camber
scalar

Torque resistance due to square of camber, QSY5, dimensionless.

Torque resistance due to square of camber and load, QSY6 — Torque resistance due to camber and load
scalar

Torque resistance due to square of camber and load, QSY6, dimensionless.

Torque resistance due to load, QSY7 — Torque resistance due to load
scalar

Torque resistance due to load, QSY7, dimensionless.

Torque resistance due to pressure, QSY8 — Torque resistance due to pressure
scalar

Torque resistance due to pressure, QSY8, dimensionless.

Aligning

Trail slope factor for trail Bpt at FZNOM, QBZ1 — Trail slope factor at nominal force
scalar

Trail slope factor for trail Bpt at nominal force, F_ZNOM, QBZ1, dimensionless.

Bpt slope variation with load, QBZ2 — Slope variation with load
scalar

Slope variation with load, QBZ2, dimensionless.

Bpt slope variation with square of load, QBZ3 — Slope variation with load
`0` (default) | scalar

Slope variation with square of load, QBZ3, dimensionless.

Bpt slope variation with camber, QBZ4 — Slope variation with camber
scalar

Slope variation with camber, QBZ4, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Bpt slope variation with absolute value of camber, QBZ5 — Slope variation with camber
scalar

Slope variation with absolute value of camber, QBZ5, dimensionless.

Bpt slope variation with square of camber, QBZ6 — Slope variation with camber
scalar

Slope variation with square of camber, QBZ6, dimensionless.

Br of Mzr slope scaling factor, QBZ9 — Slope scaling factor
scalar

Slope scaling factor, QBZ9, dimensionless.

Br of Mzr cornering stiffness factor, QBZ10 — Cornering stiffness factor
scalar

Br of Mzr cornering stiffness factor, QBZ10, dimensionless.

Cpt pneumatic trail shape factor, QCZ1 — Pneumatic trail shape factor
scalar

Pneumatic trail shape factor, C_pt, QCZ1, dimensionless.

Dpt peak trail, QDZ1 — Peak trail
scalar

Peak trail, D_pt, QDZ1, dimensionless.

Dpt peak trail variation with load, QDZ2 — Peak trail variation with load
scalar

Peak trail, D_pt, variation with load, QDZ2, dimensionless.

Dpt peak trail variation with camber, QDZ3 — Peak trail variation with camber
scalar

Peak trail, D_pt, variation with camber, QDZ3, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Dpt peak trail variation with square of camber, QDZ4 — Peak trail variation with camber
scalar

Peak trail, D_pt, variation with square of camber, QDZ4, dimensionless.

Dmr peak residual torque, QDZ6 — Peak residual torque
scalar

Peak residual torque, D_mr, QDZ6, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Dmr peak residual torque variation with load, QDZ7 — Peak residual torque variation with load
scalar

Peak residual torque, D_mr, variation with load, QDZ7, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Dmr peak residual torque variation with camber, QDZ8 — Peak residual torque variation with camber
scalar

Peak residual torque, D_mr, variation with camber, QDZ8, dimensionless.

Dmr peak residual torque variation with camber and load, QDZ9 — Peak residual torque variation with camber and load
scalar

Peak residual torque, D_mr, variation with camber and load, QDZ9, dimensionless.

Dmr peak residual torque variation with square of camber, QDZ10 — Peak residual torque variation with camber
scalar

Peak residual torque, D_mr, variation with square of camber, QDZ10, dimensionless.

Dmr peak residual torque variation with square of load, QDZ11 — Peak residual torque variation with load
scalar

Peak residual torque, D_mr, variation with square of load, QDZ11, dimensionless.

Ept trail curvature at FZNOM, QEZ1 — Trail curvature at nominal force
scalar

Trail curvature, E_pt, at nominal force, F_ZNOM, QEZ1, dimensionless.

Ept variation with load, QEZ2 — Trail curvature variation with load
scalar

Trail curvature, E_pt variation with load, QEZ2, dimensionless.

Ept variation with square of load, QEZ3 — Trail curvature variation with load
scalar

Trail curvature, E_pt variation with square of load, QEZ3, dimensionless.

Ept variation with sign of alpha-t, QEZ4 — Trail curvature variation
scalar

Trail curvature, E_pt variation with sign of alpha-t, QEZ4, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Ept variation with sign of alpha-t and camber, QEZ5 — Variation
scalar

Trail curvature, E_pt variation with sign of alpha-t and camber, QEZ5, dimensionless.

Sht horizontal trail shift at FZNOM, QHZ1 — Horizontal trail shift at nominal load
scalar

Horizontal trail shift, Sh_t, at nominal load, F_ZNOM, QHZ1, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Sht variation with load, QHZ2 — Horizontal trail shift variation with load
scalar

Horizontal trail shift, Sh_t, variation with load, QHZ2, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

Sht variation with camber, QHZ3 — Horizontal trail shift variation with camber
scalar

Horizontal trail shift, Sh_t, variation with camber, QHZ3, dimensionless.

Sht variation with load and camber, QHZ4 — Horizontal trail shift variation with load and camber
scalar

Horizontal trail shift, Sh_t, variation with load and camber, QHZ4, dimensionless.

Inflation pressure influence on trail length, PPZ1 — Pressure influence on trail length
scalar

Inflation pressure influence on trail length, PPZ1, dimensionless.

Inflation pressure influence on residual aligning torque, PPZ2 — Pressure influence on aligning torque
scalar

Inflation pressure influence on residual aligning torque, PPZ2, dimensionless.

Nominal value of s/R0: effect of Fx on Mz, SSZ1 — Effect of longitudinal force on aligning torque
scalar

Nominal value of s/R0: effect of longitudinal force, F_x, on aligning torque, M_z, SSZ1, dimensionless.

Dependencies

If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.

s/R0 variation with lateral to nominal force ratio, SSZ2 — Variation with lateral to nominal force ratio
scalar

Variation with lateral to nominal force ratio, SSZ2, dimensionless.

s/R0 variation with camber, SSZ3 — Variation with camber
scalar

Variation with camber, SSZ3, dimensionless.

s/R0 variation with camber and load, SSZ4 — Variation with camber and load
scalar

Variation with camber and load, SSZ4, dimensionless.

Turnslip

Fx peak reduction due to spin, PDXP1 — Longitudinal force peak reduction due to spin
scalar

Longitudinal force, F_x, peak reduction due to spin, PDXP1, dimensionless.

Fx peak reduction due to spin with varying load, PDXP2 — Longitudinal force peak reduction due to spin
scalar

Longitudinal force, F_x, peak reduction due to spin with varying load, PDXP2, dimensionless.

Fx peak reduction due to spin with slip ratio, PDXP3 — Longitudinal force peak reduction due to spin
scalar

Longitudinal force, F_x, peak reduction due to spin with slip ratio, PDXP3, dimensionless.

Cornering stiffness reduction due to spin, PKYP1 — Stiffness reduction due to spin
scalar

Cornering stiffness reduction due to spin, PKYP1, dimensionless.

Fy peak reduction due to spin, PDYP1 — Lateral force peak reduction due to spin
scalar

Lateral force, F_y, peak reduction due to spin, PDYP1, dimensionless.

Fy peak reduction due to spin with varying load, PDYP2 — Lateral force peak reduction due to spin
scalar

Lateral force, F_y, peak reduction due to spin with varying load, PDYP2, dimensionless.

Fy peak reduction due to spin with slip angle, PDYP3 — Lateral force peak reduction due to spin
scalar

Lateral force, F_y, peak reduction due to spin with slip angle, PDYP3, dimensionless.

Fy peak reduction due to square root of spin, PDYP4 — Lateral force peak reduction due to spin
scalar

Lateral force, F_y, peak reduction due to square root of spin, PDYP4, dimensionless.

Fy vs. slip angle response lateral shift limit, PHYP1 — Lateral force versus slip angle response
scalar

Lateral force, F_y, versus slip angle response lateral shift limit, PHYP1, dimensionless.

Fy vs. slip angle response max lateral shift limit, PHYP2 — Lateral force versus slip angle response
scalar

Lateral force, F_y, versus slip angle response max lateral shift limit, PHYP2, dimensionless.

Fy vs. slip angle response max lateral shift limit with load, PHYP3 — Lateral force versus slip angle response
scalar

Lateral force, F_y, versus slip angle response max lateral shift limit with load, PHYP3, dimensionless.

Fy vs. slip angle response lateral shift curvature factor, PHYP4 — Lateral force versus slip angle response
scalar

Lateral force, F_y, versus slip angle response lateral shift curvature factor, PHYP4, dimensionless.

Camber stiffness reduction due to spin, PECP1 — Camber stiffness reduction
scalar

Camber stiffness reduction due to spin, PECP1, dimensionless.

Camber stiffness reduction due to spin with load, PECP2 — Camber stiffness reduction
scalar

Camber stiffness reduction due to spin with load, PECP2, dimensionless.

Turn slip pneumatic trail reduction factor, QDTP1 — Turn slip pneumatic trail reduction factor
scalar

Turn slip pneumatic trail reduction factor, QDTP1, dimensionless.

Turn moment for constant turning and zero longitudinal speed, QCRP1 — Turn moment for constant turning
scalar

Turn moment for constant turning and zero longitudinal speed, QCRP1, dimensionless.

Turn slip moment increase with spin at 90deg slip angle, QCRP2 — Turn slip moment
scalar

Turn slip moment increase with spin at 90-degree slip angle, QCRP2, dimensionless.

Residual spin torque reduction from side slip, QBRP1 — Residual spin torque reduction
scalar

Residual spin torque reduction from side slip, QBRP1, dimensionless.

Turn slip moment peak magnitude, QDRP1 — Turn slip moment peak magnitude
scalar

Turn slip moment peak magnitude, QDRP1, dimensionless.

Turn slip moment curvature, QDRP2 — Turn slip moment curvature
scalar

Turn slip moment curvature, QDRP2, dimensionless.

References

[1] Besselink, Igo, Antoine J. M. Schmeitz, and Hans B. Pacejka, "An improved Magic Formula/Swift tyre model that can handle inflation pressure changes," Vehicle System Dynamics - International Journal of Vehicle Mechanics and Mobility 48, sup. 1 (2010): 337–52, https://doi.org/10.1080/00423111003748088.

[2] Pacejka, H. B. Tire and Vehicle Dynamics. 3rd ed. Oxford, United Kingdom: SAE and Butterworth-Heinemann, 2012.

[3] Schmid, Steven R., Bernard J. Hamrock, and Bo O. Jacobson. Fundamentals of Machine Elements, SI Version. 3rd ed. Boca Raton: CRC Press, 2014.

Extended Capabilities

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

Version History

Introduced in R2018a

expand all

R2024b: New Tire type option

Starting in R2024b, you can specify Tire type to use the new built-in tire model, Light passenger car 245/60R16.

R2024b: Renamed block parameters

Starting in R2024b, these parameters have been renamed.

Old Name	New Name
Wheel width	Tire nominal section width
Unloaded radius	Tire unloaded radius
Initial rotational velocity	Initial wheel rotational velocity
Wheel mass	Tire mass
Rotational inertia	Tire rotational inertia

R2024b: New Vertical Motion option

Starting in R2024b, specifying Vertical Motion as External Deflection enables the RadialDeflct port. Use this port to define the sidewall deflection when interfacing with a tire in cases where forces are not provided.

R2024b: New signals added to the Info port bus

Starting in R2024b, the Info port bus contains these new signals.

Signal	Description
`RadialDeflct`	Tire radial deflection
`RL`	Loaded radius
`WhlTrq`	Wheel torque

R2024a: Plot steady-state force and moment responses

If you have the Extended Tire Features for Vehicle Dynamics Blockset support package installed, you can use the new Plot steady state force, moment response button to generate plots.

R2023a: New Vertical Motion Parameter

Starting from R2023a, the Combined Slip Wheel 2DOF block includes the Vertical Motion parameter. By default, the Combined Slip Wheel 2DOF block uses the Magic Formula to calculate the vertical motion of the tire.

R2022b: Specify Brake and Tire Parameters for Each Wheel

Starting from R2022b, you can to use the Combined Slip Wheel 2DOF block to specify brake and tire characteristics for each wheel on your vehicle. Specifically, the block allows N-by-1 vectors for these parameters:

Static friction coefficient, mu_static
Kinetic friction coefficient, mu_kinetic
Disc brake actuator bore, disc_abore
Brake pad mean radius, Rm
Number of brake pads, num_pads
Drum brake actuator bore, disc_abore
Initial rotational velocity, omegao
Rotational damping, br
Wheel mass, MASS
Rotational inertia (rolling axis), IYY
Initial tire displacement, zo
Initial wheel vertical velocity (wheel fixed frame), zdoto

N is the number of wheels and must match the input signal dimensions.

R2022b: New Ply steer and Turn slip Parameters

Starting from R2022b, the Combined Slip Wheel 2DOF block includes Ply steer and Turn slip parameters. To remove ply steer and turn slip from the Magic Formula implementation of these blocks, clear the Ply steer and Turn slip parameters.

Combined Slip Wheel 2DOF

Description

Rotational Wheel Dynamics

Tire and Wheel Coordinate Systems

Brakes

Examples

Scene Interrogation with Camera and Ray Tracing Reference Application

Ports

Input

BrkPrs — Brake pressure scalar | N-by-1 vector

Dependencies

AxlTrq — Axle torque scalar | N-by-1 vector

Vx — Longitudinal velocity scalar | N-by-1 vector

Vy — Lateral velocity scalar | N-by-1 vector

Camber — Inclination angle scalar | N-by-1 vector

YawRate — Tire angular velocity scalar | N-by-1 vector

Prs — Tire inflation pressure scalar | N-by-1 vector

Gnd — Ground displacement scalar | N-by-1 vector

Fext — Axle force applied to tire scalar | N-by-1 vector

Dependencies

RadialDeflct — Tire radial deflection scalar | N-by-1 vector

Dependencies

ScaleFctrs — Scale factors 27-by-N array

Output

Info — Block data bus

Omega — Wheel angular velocity scalar | N-by-1 vector

Fx — Longitudinal axle force scalar | N-by-1 vector

Fy — Lateral axle force scalar | N-by-1 vector

Fz — Vertical axle force scalar | N-by-1 vector

Mx — Overturning moment scalar | N-by-1 vector

My — Rolling resistive moment scalar | N-by-1 vector

Mz — Aligning moment scalar | N-by-1 vector

Parameters

Tire Options

Tire type — Select type External file (default) | Light passenger car 205/60R15 | Light passenger car 245/60R16 | Mid-size passenger car 235/45R18 | Performance car 225/40R19 | SUV 265/50R20 | Light truck 275/65R18 | Commercial truck 295/75R22.5

Vertical Motion — Vertical motion model Magic Formula (default) | None | External deflection

Ply steer — Include ply steer on (default) | off

Turn slip — Include turn slip on (default) | off

Brake type — Brake type None | Disc | Drum | Mapped

Plotting

Install Extended Tire Features — Option to install Extended Tire Features for Vehicle Dynamics Blockset™ support package button

Plot steady state force, moment response — Option to plot steady-state force and moment tire responses button

Dependencies

Brake

Static friction coefficient, mu_static — Static friction coefficient 0.3 (default) | scalar | N-by-1 vector

Dependencies

Kinetic friction coefficient, mu_kinetic — Kinetic friction 0.2 (default) | scalar | N-by-1 vector

Dependencies

Disc brake actuator bore, disc_abore — Bore distance 0.05 (default) | scalar | N-by-1 vector

Dependencies

Brake pad mean radius, Rm — Radius 0.177 (default) | scalar | N-by-1 vector

Dependencies

Number of brake pads, num_pads — Number of brake pads 2 (default) | scalar | N-by-1 vector

Dependencies

Drum brake actuator bore, disc_abore — Bore distance 0.0508 (default) | scalar | N-by-1 vector

Dependencies

Shoe pin to drum center distance, drum_a — Shoe pin to drum center distance 0.123 (default) | scalar

Dependencies

Shoe pin center to force application point distance, drum_c — Shoe pin center to force application point distance 0.212 (default) | scalar

Dependencies

Drum internal radius, drum_r — Drum internal radius 0.15 (default) | scalar

Dependencies

Shoe pin to pad start angle, drum_theta1 — Shoe pin to pad start angle 0 (default) | scalar

Dependencies

Shoe pin to pad end angle, drum_theta2 — Shoe pin to pad end angle 126 (default) | scalar

Dependencies

Brake actuator pressure breakpoints, brake_p_bpt — Brake actuator pressure breakpoints vector

Dependencies

Wheel speed breakpoints, brake_n_bpt — Wheel speed breakpoints vector

Dependencies

Brake torque map, f_brake_t — Lookup table for brake torque array

Dependencies

Simulation

Nominal pressure, NOMPRES — Pressure scalar

Maximum pressure, PRESMAX — Maximum pressure scalar

Minimum pressure, PRESMIN — Minimum pressure scalar

Nominal normal force, FNOMIN — Force scalar

Maximum normal force, FZMAX — Force scalar

Minimum normal force, FZMIN — Force scalar

Velocity tolerance used to handle low velocity situations, VXLOW — Tolerance scalar

BrkPrs — Brake pressure
scalar | N-by-`1` vector

AxlTrq — Axle torque
scalar | N-by-`1` vector

Vx — Longitudinal velocity
scalar | N-by-`1` vector

Vy — Lateral velocity
scalar | N-by-`1` vector

Camber — Inclination angle
scalar | N-by-`1` vector

YawRate — Tire angular velocity
scalar | N-by-`1` vector

Prs — Tire inflation pressure
scalar | N-by-`1` vector

Gnd — Ground displacement
scalar | N-by-`1` vector

Fext — Axle force applied to tire
scalar | N-by-`1` vector

RadialDeflct — Tire radial deflection
scalar | N-by-`1` vector

ScaleFctrs — Scale factors
`27`-by-`N` array

Info — Block data
bus

Omega — Wheel angular velocity
scalar | N-by-`1` vector

Fx — Longitudinal axle force
scalar | N-by-`1` vector

Fy — Lateral axle force
scalar | N-by-`1` vector

Fz — Vertical axle force
scalar | N-by-`1` vector

Mx — Overturning moment
scalar | N-by-`1` vector

My — Rolling resistive moment
scalar | N-by-`1` vector

Mz — Aligning moment
scalar | N-by-`1` vector

Tire type — Select type
`External file` (default) | `Light passenger car 205/60R15` | `Light passenger car 245/60R16` | `Mid-size passenger car 235/45R18` | `Performance car 225/40R19` | `SUV 265/50R20` | `Light truck 275/65R18` | `Commercial truck 295/75R22.5`

Vertical Motion — Vertical motion model
`Magic Formula` (default) | `None` | `External deflection`

Ply steer — Include ply steer
`on` (default) | `off`

Turn slip — Include turn slip
`on` (default) | `off`

Brake type — Brake type
`None` | `Disc` | `Drum` | `Mapped`

Install Extended Tire Features — Option to install Extended Tire Features for Vehicle Dynamics Blockset™ support package
button

Plot steady state force, moment response — Option to plot steady-state force and moment tire responses
button

Static friction coefficient, mu_static — Static friction coefficient
`0.3` (default) | scalar | N-by-`1` vector

Kinetic friction coefficient, mu_kinetic — Kinetic friction
`0.2` (default) | scalar | N-by-`1` vector

Disc brake actuator bore, disc_abore — Bore distance
`0.05` (default) | scalar | N-by-`1` vector

Brake pad mean radius, Rm — Radius
`0.177` (default) | scalar | N-by-`1` vector

Number of brake pads, num_pads — Number of brake pads
`2` (default) | scalar | N-by-`1` vector

Drum brake actuator bore, disc_abore — Bore distance
`0.0508` (default) | scalar | N-by-`1` vector

Shoe pin to drum center distance, drum_a — Shoe pin to drum center distance
`0.123` (default) | scalar

Shoe pin center to force application point distance, drum_c — Shoe pin center to force application point distance
`0.212` (default) | scalar

Drum internal radius, drum_r — Drum internal radius
`0.15` (default) | scalar

Shoe pin to pad start angle, drum_theta1 — Shoe pin to pad start angle
`0` (default) | scalar

Shoe pin to pad end angle, drum_theta2 — Shoe pin to pad end angle
`126` (default) | scalar

Brake actuator pressure breakpoints, brake_p_bpt — Brake actuator pressure breakpoints
vector

Wheel speed breakpoints, brake_n_bpt — Wheel speed breakpoints
vector

Brake torque map, f_brake_t — Lookup table for brake torque
array

Nominal pressure, NOMPRES — Pressure
scalar

Maximum pressure, PRESMAX — Maximum pressure
scalar

Minimum pressure, PRESMIN — Minimum pressure
scalar

Nominal normal force, FNOMIN — Force
scalar

Maximum normal force, FZMAX — Force
scalar

Minimum normal force, FZMIN — Force
scalar

Velocity tolerance used to handle low velocity situations, VXLOW — Tolerance
scalar

Max allowable slip ratio (absolute), KPUMAX — Max allowable slip ratio
scalar

Minimum allowable slip ratio (absolute), KPUMIN — Minimum allowable slip ratio
scalar

Max allowable slip angle (absolute), ALPMAX — Max allowable slip angle
scalar

Minimum allowable slip angle (absolute), ALPMIN — Minimum allowable slip angle
scalar

Maximum allowable camber angle, CAMMAX — Maximum allowable camber angle
scalar

Minimum allowable camber angle, CAMMIN — Minimum allowable camber angle
scalar

Nominal longitudinal speed, LONGVL — Speed
scalar

Initial wheel rotational velocity, omegao — Initial wheel rotational velocity
scalar | N-by-`1` vector

Tire unloaded radius, UNLOADED_RADIUS — Radius
`scalar`

Tire nominal section width, WIDTH — Tire nominal section width
scalar

Rim radius, RIM_RADIUS — Radius
`scalar`

Nominal aspect ratio, ASPECT_RATIO — Ratio
scalar

Tire mass, MASS — Mass
scalar | N-by-`1` vector

Tire rotational inertia (rolling axis), IYY — Tire rotational inertia
scalar | N-by-`1` vector

Rotational damping, br — Rotational damping
scalar | N-by-`1` vector

Gravity, GRAVITY — Gravity
scalar

Initial tire displacement, zo — Displacement
scalar | N-by-`1` vector

Initial wheel vertical velocity (wheel fixed frame), zdoto — Velocity
scalar | N-by-`1` vector

Effective rolling radius at low load stiffness, BREFF — Stiffness
scalar

Effective rolling radius peak value, DREFF — Radius
scalar

Effective rolling radius at high load stiffness, FREFF — Radius
`scalar`

Unloaded to nominal rolling radius ratio, Q_RE0 — Ratio
`scalar`

Radius rotational speed dependence, Q_V1 — Speed
`scalar`

Stiffness rotational speed dependence, Q_V2 — Speed
`scalar`

Linear load change with deflection, Q_FZ1 — Load change
`scalar`

Quadratic load change with deflection, Q_FZ2 — Load change
`scalar`

Linear load change with deflection and quadratic camber, Q_FZ3 — Load change
`scalar`

Load response to longitudinal force, Q_FCX — Force
`scalar`

Load response to lateral force, Q_FCY — Force
`scalar`

Vertical stiffness change due to lateral load dependency on lateral stiffness, Q_FCY2 — Stiffness
`scalar`

Stiffness response to pressure, PFZ1 — Stiffness
`0.7098` (default) | `scalar`

Vertical tire stiffness, VERTICAL_STIFFNESS — Stiffness
`scalar`

Vertical tire damping, VERTICAL_DAMPING — Damping
`scalar`