Combined Slip Wheel CPI
Libraries:
Vehicle Dynamics Blockset /
Wheels and Tires
Description
The Combined Slip Wheel CPI block implements the longitudinal and lateral behavior of a wheel characterized by the Magic Formula[1][2] 6.2 that complies with the contact point interface (CPI) Tyre Data Exchange Format (TYDEX)[3] standard. You can import your own tire model or use a built-in tire model. Use the block in driveline and vehicle simulations where low-frequency tire-road interactions are required to determine vehicle acceleration, braking, and wheel-rolling resistance. The block is suitable for applications that require combined lateral slip, for example, in lateral motion and yaw stability studies.
Based on the wheel rotational velocity, longitudinal and lateral velocity, wheel camber angle, and inflation pressure, the block determines the vertical motion, forces, and moments in all six degrees of freedom (DOF). Use the vertical DOF to study tire-suspension resonances from road profiles or chassis motion.
If you install the Extended Tire Features for Vehicle Dynamics Blockset support package, these additional capabilities are available:
Plot generation — 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]
Import tire parameters — Use the
tireModel.getmethod to import tire parameter values defined in the Combined Slip Wheel CPI block to atireModelobject.Export tire parameters — Use the
setmethod to export tire parameter values from atireModelobject to the Combined Slip Wheel CPI block.Tire model conversion — Use the
convertmethod to convert a tire model of one of these types to a Magic Formula 6.2 tire model that you can import to the Combined Slip Wheel CPI block:Magic Formula 5.2
Fiala
Dugoff
Use the Tire type parameter to select the source of the tire data.
| Goal | Action |
|---|---|
Implement the Magic Formula 6.2 using empirical equations1, 2. The equations use fitting coefficients that correspond to the block parameters. | Update the block parameters with fitting coefficients from a file:
|
Select one of the Magic Formula 6.2 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:
|
Rotational Wheel Dynamics
The block calculates the inertial response of the wheel subject to:
Axle losses
Tire rolling resistance
Ground contact through the tire-road interface
To implement the Magic Formula 6.2, 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 |
|
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. |
CPI Tire Coordinate System
The block uses tire coordinate system axes (XT, YT, ZT) that are fixed in a reference frame attached to the tire. The origin is at the tire contact with the ground.
The CPI tire coordinate system is shown in red.
Note
The CPI tire coordinate system (red) is equivalent to the TYDEX wheel-axis coordinate system.
| Axis | Description |
|---|---|
| XT | XT and YT are parallel to the road plane. The intersection of the wheel plane and the road plane define the orientation of the XT axis. |
| YT | YT is the projection of the wheel spin axis on the ground. |
| ZT | ZT points upward. |
Examples
Braking Test Reference Application
Simulate a full vehicle dynamics model undergoing a braking test. Use for vehicle dynamics ride and handling analysis and chassis controls development, including the dynamic response to split-mu tests.
Ports
Input
Tire rotational velocity, ω, about wheel spin 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.
Axle longitudinal velocity, Vx, 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.
Axle lateral velocity, Vy, 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 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.
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.
Axle force applied to tire, Fext, 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.
Tire radial deflection, RadialDeflct, in m. This value will be used in all internal dependent Magic Formula 6.2 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.
Magic Formula 6.2 scale factor array. Array dimensions are 27 by
the number of wheels, N.
The Magic Formula 6.2 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 |
Tire inflation pressure, pi, 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 create this port, select Input tire pressure.
Output
Block data, returned as a bus signal containing these block values.
| Signal | Description | Units |
|---|---|---|
| Wheel angular velocity about wheel-fixed y-axis | rad/s |
| Longitudinal vehicle force along tire-fixed x-axis | N |
| Lateral vehicle force along tire-fixed y-axis | N |
| Vertical vehicle force along tire-fixed z-axis | N |
| Overturning moment about tire-fixed x-axis | N·m |
| Rolling resistance torque about tire-fixed y-axis | N·m |
Mz | Aligning moment about tire-fixed z-axis | N·m |
| Vehicle longitudinal velocity along tire-fixed x-axis | m/s |
| Vehicle lateral velocity along tire-fixed y-axis | m/s |
| Loaded effective radius | m |
| Longitudinal slip ratio | NA |
| Side slip angle | rad |
| Contact patch half length | m |
| Contact patch half width | m |
| Camber angle | rad |
| Tire angular velocity about the tire-fixed z-axis (yaw rate) | rad/s |
| Tire radial deflection | m |
| Vertical sidewall force on ground along tire-fixed z-axis | N |
| Tire inflation pressure | Pa |
| Loaded radius | m |
| Wheel torque | N·m |
Longitudinal force acting on axle, Fx, 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.
Lateral force acting on axle, Fy, 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.
Vertical force acting on axle, Fz, 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.
Longitudinal moment acting on axle, Mx, 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.
Lateral moment acting on axle, My, 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.
Vertical moment acting on axle, Mz, 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
Tire Options
Use the Tire type parameter to select the source of the tire data.
| Goal | Action |
|---|---|
Implement the Magic Formula 6.2 using empirical equations1, 2. The equations use fitting coefficients that correspond to the block parameters. | Update the block parameters with fitting coefficients from a file:
|
Select one of the Magic Formula 6.2 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:
|
Programmatic Use
To set the block
parameter value programmatically, use the set_param
function.
To get the block
parameter value programmatically, use the get_param
function.
| Parameter: | tireType |
| Values: | 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 |
| Data Types: | character vector |
Tire file .tir or object containing empirical data
to model tire longitudinal and lateral behavior with the Magic Formula
6.2. If you provide an .txt file, make sure the file
contains names that correspond to the block parameters.
Update the block parameters with fitting coefficients from a file:
Set Tire type to
External file.On the 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.
Programmatic Use
To set the block
parameter value programmatically, use the set_param
function.
To get the block
parameter value programmatically, use the get_param
function.
| Parameter: | tireParamSet |
| Values: | vdynPassCar.mat (default) | .tir | .txt |
| Data Types: | character vector |
Tire inflation pressure, p, in Pa.
Dependencies
To enable this parameter, clear Input tire pressure.
Programmatic Use
To set the block
parameter value programmatically, use the set_param
function.
To get the block
parameter value programmatically, use the get_param
function.
| Parameter: | TirePrs |
| Values: | scalar |
| Data Types: | double |
Select to include ply steer in the Magic Formula 6.2 equations.
By default, the blocks include ply steer and turn slip in the Magic Formula 6.2 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
Programmatic Use
To set the block parameter value
programmatically, use the set_param function.
To get the block parameter value
programmatically, use the get_param function.
| Parameter: | plySteer |
| Values: | on (default) | off |
| Data Types: | character vector |
Select to include ply steer in Magic Formula 6.2 equations.
By default, the blocks include ply steer and turn slip in the Magic Formula 6.2 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 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.
Programmatic Use
To set the block parameter value
programmatically, use the set_param function.
To get the block parameter value
programmatically, use the get_param function.
| Parameter: | turnslip |
| Values: | on (default) | off |
| Data Types: | character vector |
Plotting
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 CPI Block Parameters dialog box.
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.
Simulation
Dimension
Vertical
Linear load change with deflection and quadratic camber, Q_FZ3, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | Q_FZ3 |
| Values: | scalar |
| Data Types: | double |
Vertical stiffness change due to lateral load dependency on lateral stiffness, Q_FCY2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | Q_FCY2 |
| Values: | scalar |
| Data Types: | double |
Linear load dependent camber angle effect on vertical stiffness, Q_CAM1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | Q_CAM1 |
| Values: | scalar |
| Data Types: | double |
Quadratic load dependent camber angle effect on vertical stiffness, Q_CAM2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | Q_CAM2 |
| Values: | scalar |
| Data Types: | double |
Linear reduction of stiffness with load and camber angle, Q_CAM3, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | Q_CAM3 |
| Values: | scalar |
| Data Types: | double |
Constant camber and slip angle effect on vertical stiffness, Q_FYS1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | Q_FYS1 |
| Values: | scalar |
| Data Types: | double |
Linear camber and slip angle effect on vertical stiffness, Q_FYS2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | Q_FYS2 |
| Values: | scalar |
| Data Types: | double |
Quadratic camber and slip angle effect on vertical stiffness, Q_FYS3, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | Q_FYS3 |
| Values: | scalar |
| Data Types: | double |
Structural
Linear vertical deflection influence on longitudinal stiffness, PCFX1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PCFX1 |
| Values: | scalar |
| Data Types: | double |
Quadratic vertical deflection influence on longitudinal stiffness, PCFX2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PCFX2 |
| Values: | scalar |
| Data Types: | double |
Linear vertical deflection influence on lateral stiffness, PCFY1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PCFY1 |
| Values: | scalar |
| Data Types: | double |
Quadratic vertical deflection influence on lateral stiffness, PCFY2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PCFY2 |
| Values: | scalar |
| Data Types: | double |
Contact Patch
Longitudinal
Linear variation of longitudinal slip stiffness with tire pressure, PPX1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PPX1 |
| Values: | scalar |
| Data Types: | double |
Quadratic variation of longitudinal slip stiffness with tire pressure, PPX2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PPX2 |
| Values: | scalar |
| Data Types: | double |
Linear variation of peak longitudinal friction with tire pressure, PPX3, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PPX3 |
| Values: | scalar |
| Data Types: | double |
Quadratic variation of peak longitudinal friction with tire pressure, PPX4, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PPX4 |
| Values: | scalar |
| Data Types: | double |
Combined slip longitudinal force, Fx, slope factor reduction, RBX1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RBX1 |
| Values: | scalar |
| Data Types: | double |
Slip ratio longitudinal force, Fx, slope reduction variation, RBX2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RBX2 |
| Values: | scalar |
| Data Types: | double |
Camber influence on combined slip longitudinal force, Fx, stiffness, RBX3, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RBX3 |
| Values: | scalar |
| Data Types: | double |
Shape factor for combined slip longitudinal force, Fx, reduction, RCX1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RCX1 |
| Values: | scalar |
| Data Types: | double |
Combined longitudinal force, Fx, curvature factor with load, REX2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | REX2 |
| Values: | scalar |
| Data Types: | double |
Combined slip longitudinal force, Fx, shift factor reduction, RHX1, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RHX1 |
| Values: | scalar |
| Data Types: | double |
Overturning
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.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QSX1 |
| Values: | scalar |
| Data Types: | double |
Overturning moment, Mx, combined lateral force load and camber, QSX4, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QSX4 |
| Values: | scalar |
| Data Types: | double |
Overturning moment, Mx, load effect due to lateral force and camber, QSX5, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QSX5 |
| Values: | scalar |
| Data Types: | double |
Overturning moment, Mx, due to B-factor of lateral force and load, QSX9, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QSX9 |
| Values: | scalar |
| Data Types: | double |
Overturning moment, Mx, due to vertical force and camber, QSX10, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QSX10 |
| Values: | scalar |
| Data Types: | double |
Overturning moment, Mx, due to B-factor of vertical force and camber, QSX11, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QSX11 |
| Values: | scalar |
| Data Types: | double |
Overturning moment, Mx, due to lateral force with camber, QSX14, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QSX14 |
| Values: | scalar |
| Data Types: | double |
Lateral
Lateral curvature, Efy, constant camber dependency, PEY3, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PEY3 |
| Values: | scalar |
| Data Types: | double |
Maximum lateral force stiffness, KFy, to nominal force, FZNOM, ratio, PKY1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PKY1 |
| Values: | scalar |
| Data Types: | double |
Load at maximum lateral force stiffness, KFy, to nominal force, FZNOM, ratio, PKY2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PKY2 |
| Values: | scalar |
| Data Types: | double |
Lateral force stiffness, KFy, to nominal force, FZNOM, stiffness variation with camber, PKY3, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PKY3 |
| Values: | scalar |
| Data Types: | double |
Horizontal shift, SHY, at nominal force, FZNOM, PHY1, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PHY1 |
| Values: | scalar |
| Data Types: | double |
Horizontal shift, SHY, variation with load, PHY2, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PHY2 |
| Values: | scalar |
| Data Types: | double |
Vertical shift, Svy, at nominal force, FZNOM, PVY1, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PVY1 |
| Values: | scalar |
| Data Types: | double |
Vertical shift, Svy, variation with load, PVY2, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PVY2 |
| Values: | scalar |
| Data Types: | double |
Cornering stiffness variation with inflation pressure induced nominal load dependency, PPY2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PPY2 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, 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.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RBY3 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, combined stiffness variation from camber, RBY4, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RBY4 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, combined reduction shift factor with load, RHY2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RHY2 |
| Values: | scalar |
| Data Types: | double |
Slip ratio side force at nominal force, FZNOM, RVY1, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RVY1 |
| Values: | scalar |
| Data Types: | double |
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.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | RVY2 |
| Values: | scalar |
| Data Types: | double |
Rolling
Aligning
Trail slope factor for trail Bpt at nominal force, FZNOM, QBZ1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QBZ1 |
| Values: | scalar |
| Data Types: | double |
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.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QBZ4 |
| Values: | scalar |
| Data Types: | double |
Peak trail, Dpt, variation with camber, QDZ3, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QDZ3 |
| Values: | scalar |
| Data Types: | double |
Peak residual torque, Dmr, QDZ6, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QDZ6 |
| Values: | scalar |
| Data Types: | double |
Peak residual torque, Dmr, variation with load, QDZ7, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QDZ7 |
| Values: | scalar |
| Data Types: | double |
Peak residual torque, Dmr, variation with camber and load, QDZ9, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QDZ9 |
| Values: | scalar |
| Data Types: | double |
Peak residual torque, Dmr, variation with square of camber, QDZ10, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QDZ10 |
| Values: | scalar |
| Data Types: | double |
Peak residual torque, Dmr, variation with square of load, QDZ11, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QDZ11 |
| Values: | scalar |
| Data Types: | double |
Trail curvature, Ept 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.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QEZ4 |
| Values: | scalar |
| Data Types: | double |
Trail curvature, Ept variation with sign of alpha-t and camber, QEZ5, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QEZ5 |
| Values: | scalar |
| Data Types: | double |
Horizontal trail shift, Sht, at nominal load, FZNOM, QHZ1, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QHZ1 |
| Values: | scalar |
| Data Types: | double |
Horizontal trail shift, Sht, variation with load, QHZ2, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QHZ2 |
| Values: | scalar |
| Data Types: | double |
Horizontal trail shift, Sht, variation with load and camber, QHZ4, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QHZ4 |
| Values: | scalar |
| Data Types: | double |
Inflation pressure influence on residual aligning torque, PPZ2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PPZ2 |
| Values: | scalar |
| Data Types: | double |
Nominal value of s/R0: effect of longitudinal force, Fx, on aligning torque, Mz, SSZ1, dimensionless.
Dependencies
If you clear Ply steer, the block internally sets this parameter to 0 in the Magic Formula equations.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | SSZ1 |
| Values: | scalar |
| Data Types: | double |
Turnslip
Longitudinal force, Fx, peak reduction due to spin with varying load, PDXP2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PDXP2 |
| Values: | scalar |
| Data Types: | double |
Longitudinal force, Fx, peak reduction due to spin with slip ratio, PDXP3, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PDXP3 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, peak reduction due to spin with varying load, PDYP2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PDYP2 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, peak reduction due to spin with slip angle, PDYP3, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PDYP3 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, peak reduction due to square root of spin, PDYP4, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PDYP4 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, versus slip angle response lateral shift limit, PHYP1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PHYP1 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, versus slip angle response max lateral shift limit, PHYP2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PHYP2 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, versus slip angle response max lateral shift limit with load, PHYP3, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PHYP3 |
| Values: | scalar |
| Data Types: | double |
Lateral force, Fy, versus slip angle response lateral shift curvature factor, PHYP4, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | PHYP4 |
| Values: | scalar |
| Data Types: | double |
Turn moment for constant turning and zero longitudinal speed, QCRP1, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QCRP1 |
| Values: | scalar |
| Data Types: | double |
Turn slip moment increase with spin at 90-degree slip angle, QCRP2, dimensionless.
Programmatic Use
To set the block parameter
value programmatically, use the set_param
function.
To get the block parameter
value programmatically, use the get_param function.
| Parameter: | QCRP2 |
| Values: | scalar |
| Data Types: | double |
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, Hans B. Tire and Vehicle Dynamics. 3rd ed. Oxford, United Kingdom: SAE and Butterworth-Heinemann, 2012.
[3] Bohm, F., and H. P. Willumeit, "Tyre Models for Vehicle Dynamic Analysis: Proceedings of the 2nd International Colloquium on Tyre Models for Vehicle Dynamics Analysis, Held at the Technical University of Berlin, Germany, February 20-21, 1997." Vehicle System Dynamics - International Journal of Vehicle Mechanics and Mobility 27, sup. 1, 343–45. https://doi.org/0.1080/00423119708969669.
[4] 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 R2021bStarting in R2024b, you can specify Tire type to use the new built-in
tire model, Light passenger car 245/60R16.
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 |
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.
Starting in R2024b, the Info port bus contains these new signals.
| Signal | Description |
|---|---|
RadialDeflct | Tire radial deflection |
RL | Loaded radius |
WhlTrq | Wheel torque |
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.
Starting from R2022b, the Combined Slip Wheel CPI 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.
See Also
Blocks
- Combined Slip Wheel 2DOF | Combined Slip Wheel STI | Fiala Wheel 2DOF | Longitudinal Wheel | Dugoff Wheel 2DOF
Functions
1 Reprinted with permission Copyright © 2008 SAE International. Further distribution of this material is not permitted without prior permission from SAE.
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