Magic Formula Tire Force and Torque

Apply steady-state tire force and torque by using Magic Formula tire equations

Since R2021b

• 

Libraries:
Simscape / Multibody / Forces and Torques

Description

The Magic Formula Tire Force and Torque block implements the combined slip steady-state Magic Formula model and can optionally include turn slip effects [1]. You can use the block for tires that have square-like cross-sections, such as the tires of passenger cars, trucks, and off-road vehicles.

The block calculates only the tire force and torque. To model the geometry and inertia properties of the tire, you must use a solid block, such as the Cylindrical Solid block. The Magic Formula tire model assumes that tires are disks, as shown in the diagram.

The follower frame is at the center of the tire and rotates with the tire. The contact frame is at the contact point between the tire and the contact surface. The tire block has two methods to compute the location and orientation of the contact frame. For scenarios that require only single-point contact, use the closest point method. For driving conditions that require multiple-point contacts, use the weighted penetration method. For more information, see Contact Frame Method.

The image shows the contact and follower frames of the tire at zero configuration.

The yaw, camber, and spin angles correspond to a y-x-z sequence rotation about the follower frame of the tire.

To specify the properties of a tire model, generate a scalar structure array by using the simscape.multibody.tirread function and enter the array in the Tire Parameters parameter. The structure array must include all the necessary tire parameters, while any extra parameters are ignored in the tire modeling. For the list of required parameters, see Required Tire Parameters. The block uses the ISO sign conventions.

To specify the side of the vehicle to which a tire is mounted, use the Tire Side parameter. Specifying the wrong side can lead to unexpected simulation results. To correctly orient the tires on a vehicle, you must align the z-axes of the follower frames with the blue arrows shown in the diagram.

The signal output by the con port indicates whether the tire and the contact surface have a valid contact. If the tire and the surface are not in contact or the contact is not valid, all sensed outputs, such as the tire force, tire torque, and slip angle, become zero.

Ports

Geometry

B — Base geometry

geometry

Base geometry that represents the surface that the tire contacts. The contact surface can move or be fixed relative to the world frame. You must connect this port to an Infinite Plane or Grid Surface block.

Frame

F — Follower frame

frame

Follower frame that represents the tire. The frame origin is located at the center of the tire.

Input

lmux — Scaling factor of longitudinal friction coefficient, unitless

physical signal

Physical signal port that accepts the scaling factor of the longitudinal friction coefficient of the tire.

Dependencies

To enable this port, under Scaling Coefficients, set LMUX to Provided by Input.

lmuy — Scaling factor of lateral friction coefficient, unitless

physical signal

Physical signal port that accepts the scaling factor of the lateral friction coefficient of the tire.

Dependencies

To enable this port, under Scaling Coefficients, set LMUY to Provided by Input.

Output

con — Contact signal, unitless

physical signal

Physical signal output port that provides a signal to determine whether the tire and contact surface have a valid contact. When they are in contact and the contact is valid, the signal equals 1, otherwise the signal equals 0.

If the follower frame is below the contact surface, the tire and the surface have an invalid contact and the block does not apply force and torque to the tire.

Dependencies

To enable this port, under Sensing, select Contact Signal.

Force/Torque

ft — Tire force, N

physical signal

Physical signal output port that provides the magic formula tire force that is applied to the contact frame of the block. The output contains three parts:

• F_x is the longitudinal force tangential to the contact surface at the contact point.

• F_y is the lateral force which is orthogonal to the plane defined by F_x and F_z.

• F_z is the normal force that is normal to the contact surface at the contact point.

The block resolves the force in the follower frame of the tire if you set the Resolution Frame parameter to Follower.

Dependencies

To enable this port, under Sensing > Force/Torque, select Tire Force.

tt — Tire torque, N*m

physical signal

Physical signal output port that provides the magic formula tire torque that is applied to the contact frame of the block. The output contains three parts:

• M_x is the overturning moment.

• M_y is the rolling resistance moment.

• M_z is the aligning torque.

The block resolves the torque in the follower frame of the tire if you set the Resolution Frame parameter to Follower.

Dependencies

To enable this port, under Sensing > Force/Torque, select Tire Torque.

t — Pneumatic trail, m

physical signal

Physical signal output port that provides the distance from the contact point to the point of the resultant lateral force. The value has a unit of length.

You can use the pneumatic trail to compute the aligning torque, M_z.

Dependencies

To enable this port, under Sensing > Force/Torque, select Pneumatic Trail.

Slip

kappa — Longitudinal slip, unitless

physical signal

Physical signal output port that provides the ratio of the longitudinal slip velocity to the longitudinal speed of the tire.

Dependencies

To enable this port, under Sensing > Slip, select Longitudinal Slip.

kappas — Saturated longitudinal slip, unitless

physical signal

Physical signal output port that provides the longitudinal slip saturated to always be within the limits defined by the KPUMIN and KPUMAX parameters.

Dependencies

To enable this port, under Sensing > Slip, select Saturated Longitudinal Slip.

alpha — Slip angle, rad

physical signal

Physical signal output port that provides the angle of the right triangle made by the lateral slip velocity, V_sy and the longitudinal speed, V_x. The value has a unit of angle.

Dependencies

To enable this port, under Sensing > Slip, select Slip Angle.

alphas — Saturated slip angle, rad

physical signal

Physical signal output port that provides the slip angle saturated to always be within the limits defined by the ALPMIN and ALPMAX parameters. The value has a unit of angle.

Dependencies

To enable this port, under Sensing > Slip, select Saturated Slip Angle.

phit — Turn slip, rad/m

physical signal

Physical signal output port that provides the ratio of the tire yaw velocity to the magnitude of the tire velocity in the xy-plane of the contact frame. The value has a unit of angle/length.

Turn slip is useful when modeling low speed cornering, such as parking maneuvers.

Dependencies

To enable this port, under Sensing > Slip, select Turn Slip.

Linear Velocity

vx — Relative longitudinal velocity, m/s

physical signal

Physical signal output port that provides the component of the relative velocity between the follower frame and the contact point on the base geometry along the x-direction of the contact frame. The value has a unit of length/time.

Dependencies

To enable this port, under Sensing > Linear Velocity, select Relative Longitudinal Velocity.

vy — Relative lateral velocity, m/s

physical signal

Physical signal output port that provides the component of the relative velocity between the follower frame and the contact point on the base geometry along the y-direction of the contact frame. The value has a unit of length/time.

Dependencies

To enable this port, under Sensing > Linear Velocity, select Relative Lateral Velocity.

vsx — Longitudinal slip velocity, m/s

physical signal

Physical signal output port that provides the component of the relative velocity between the slip point on the tire and the coincident point on the base geometry along the x-direction of the contact frame. The value has a unit of length/time.

Dependencies

To enable this port, under Sensing > Linear Velocity, select Longitudinal Slip Velocity.

vsy — Lateral slip velocity, m/s

physical signal

Physical signal output port that provides the component of the relative velocity between the slip point on the tire and the coincident point on the base geometry along the y-direction of the contact frame. The value has a unit of length/time.

Dependencies

To enable this port, under Sensing > Linear Velocity, select Lateral Slip Velocity.

Yaw

psid — Yaw velocity, rad/s

physical signal

Physical signal output port that provides the first derivative of the yaw angle. The value has a unit of angle/time.

Dependencies

To enable this port, under Sensing > Yaw, select Velocity.

Camber

gamma — Camber angle, rad

physical signal

Physical signal output port that provides the camber angle of the tire. The value has a unit of angle.

Dependencies

To enable this port, under Sensing > Camber, select Angle.

gammas — Saturated camber angle, rad

physical signal

Physical signal output port that provides the camber angle of the tire saturated to always be within the limits defined by the CAMMIN and CAMMAX parameters. The value has a unit of angle.

Dependencies

To enable this port, under Sensing > Camber, select Angle.

gammad — Camber velocity, rad/s

physical signal

Physical signal output port that provides the first derivative of the camber angle. The value has a unit of angle/time.

Dependencies

To enable this port, under Sensing > Camber, select Velocity.

Spin

omega — Spin velocity, rad

physical signal

Physical signal output port that provides the first derivative of the spin angle. The value has a unit of angle/time.

Dependencies

To enable this port, under Sensing > Spin, select Velocity.

Tire Radius

romega — Free radius, m

physical signal

Physical signal output port that provides the free radius of the tire. The radius increases as the tire rotates faster. The value has a unit of length.

Dependencies

To enable this port, under Sensing > Tire Radius, select Free Radius.

rl — Loaded radius, m

physical signal

Physical signal output port that provides the distance from the center of the tire to the contact point between the tire and the contact surface. The value has a unit of length.

Dependencies

To enable this port, under Sensing > Tire Radius, select Loaded Radius.

re — Effective rolling radius, m

physical signal

Physical signal output port that provides the distance from the follower frame to the slip point. The value has a unit of length.

Dependencies

To enable this port, under Sensing > Tire Radius, select Effective Rolling Radius.

rho — Radial deflection, m

physical signal

Physical signal output port that provides the difference between the free radius output from the romega port and the loaded radius output from the rl port. The value has a unit of length.

Dependencies

To enable this port, under Sensing > Tire Radius, select Radial Deflection.

Friction

mux — Longitudinal friction coefficient, unitless

physical signal

Physical signal output port that provides the longitudinal friction coefficient of the tire computed by the magic formula equations.

Dependencies

To enable this port, under Sensing > Friction, select Longitudinal Friction Coefficient.

muy — Lateral friction coefficient, unitless

physical signal

Physical signal output port that provides the lateral friction coefficient of the tire computed by the magic formula equations.

Dependencies

To enable this port, under Sensing > Friction, select Lateral Friction Coefficient.

Contact Frame

Rb — Base rotation, unitless

physical signal

Physical signal port that outputs a 3-by-3 rotation matrix that maps the vectors in the contact frame to vectors in the reference frame of the base geometry. The output signal is resolved in the reference frame associated with the base geometry.

Dependencies

To enable this port, in the Sensing > Contact Frame section, select Base Rotation.

pb — Base translation, m

physical signal

Physical signal port that outputs a 3-by-1 vector that contains the coordinates of the origin of the contact frame resolved in the reference frame of the base geometry.

Dependencies

To enable this port, in the Sensing > Contact Frame section, select Base Translation.

Rf — Follower rotation, unitless

physical signal

Physical signal port that outputs a 3-by-3 rotation matrix that maps vectors in the contact frame to vectors in the reference frame of the follower geometry. The output signal is resolved in the reference frame associated with the follower geometry.

Dependencies

To enable this port, in the Sensing > Contact Frame section, select Follower Rotation.

pf — Follower translation, m

physical signal

Physical signal port that outputs a 3-by-1 vector that contains the coordinates of the origin of the contact frame resolved in the reference frame of the follower geometry.

Dependencies

To enable this port, in the Sensing > Contact Frame section, select Follower Translation.

Parameters

Tire Side — Tire position during modeling

Left (default) | Right

Tire position during modeling, specified as either Left or Right. Set the parameter to the side of the vehicle to which the tire is mounted.

Tire Parameters — Parameters of tire

[] (default) | scalar structure array

Tire parameters, specified as a scalar structure array. Use the simscape.multibody.tirread function to generate the structure array from a TIR file. The structure array must include all the necessary tire parameters, while any extra parameters are ignored in the tire modeling. For the list of required parameters, see Required Tire Parameters.

Slip Mode — Slip mode

Combined (default) | Combined + Turn

Slip mode, specified as either Combined or Combined + Turn.

To model combined slip, select Combined. To model combined slip with turn slip effects, select Combined + Turn. When selecting this option, the tire parameters require the turn slip coefficients.

Turn Slip Coefficients

PDXP1	Peak FX reduction due to spin parameter
PDXP2	Peak FX reduction due to spin with varying load parameter
PDXP3	Peak FX reduction due to spin with kappa parameter
PKYP1	Cornering stiffness reduction due to spin
PDYP1	Peak FY reduction due to spin parameter
PDYP2	Peak FY reduction due to spin with varying load parameter
PDYP3	Peak FY reduction due to spin with alpha parameter
PDYP4	Peak FY reduction due to square root of spin parameter
PHYP1	FY-alpha curve lateral shift limitation
PHYP2	FY-alpha curve maximum lateral shift parameter
PHYP3	FY-alpha curve maximum lateral shift varying with load parameter
PHYP4	FY-alpha curve maximum lateral shift parameter
PECP1	Camber w.r.t. spin reduction factor parameter in camber stiffness
PECP2	Camber w.r.t. spin reduction factor varying with load parameter in camber stiffness
QDTP1	Pneumatic trail reduction factor due to turn slip parameter
QCRP1	Turning moment at constant turning and zero forward speed parameter
QCRP2	Turn slip moment (at alpha=90deg) parameter for increase with spin
QBRP1	Residual (spin) torque reduction factor parameter due to side slip
QDRP1	Turn slip moment peak magnitude parameter

[1]

Contact Frame Method — Method to use to compute location and orientation of contact frame

Closest Point (default) | Weighted Penetration

Method to use to compute the location and orientation of the contact frame, specified as:

• Closest Point: This method determines the contact point by locating the point on the contact surface that is closest to the center of the tire and lies in the plane of the tire. The contact normal vector is at the contact point and perpendicular to the contact patch at the contact point.

• Weighted Penetration: This method simplifies the computation due to the irregularities of the contact surface and computes an equivalent plane at each simulation time step to approximate the actual contact area. The contact point is the nearest point on this equivalent plane to the center of the tire. The contact normal vector is at the contact point and perpendicular to the equivalent plane. For more information, see the description of Custom Tire Force and Torque.

For both settings, the contact frame is at the contact point and the z-axis of the frame is aligned with the contact normal.

Scaling Coefficients

LMUX — Scaling factor of longitudinal friction coefficient

From Tire Parameters (default) | Provided by Input

Scaling factor for the longitudinal friction coefficient. Select From Tire Parameters to use the constant scaling factor provided by the TIR file, or select Provided by Input to use input signals as scaling factors.

LMUY — Scaling factor of lateral friction coefficient

From Tire Parameters (default) | Provided by Input

Scaling factor for the lateral friction coefficient. Select From Tire Parameters to use the constant scaling factor provided by the TIR file, or select Provided by Input to use input signals as scaling factors.

Sensing

Force/Torque

Resolution Frame — Frame to resolve measurements

Contact (default) | Follower

Frame used to resolve the calculated tire force and torque, specified as either Contact or Follower.

More About

Required Tire Parameters

Scaling Coefficients

LFZO	Scale factor of nominal (rated) load
LCX	Scale factor of Fx shape factor
LMUX	Scale factor of Fx peak friction coefficient
LEX	Scale factor of Fx curvature factor
LKX	Scale factor of slip stiffness
LHX	Scale factor of Fx horizontal shift
LVX	Scale factor of Fx vertical shift
LCY	Scale factor of Fy shape factor
LMUY	Scale factor of Fy peak friction coefficient
LEY	Scale factor of Fy curvature factor
LKY	Scale factor of cornering stiffness
LKYC	Scale factor of camber stiffness
LKZC	Scale factor of camber moment stiffness
LHY	Scale factor of Fy horizontal shift
LVY	Scale factor of Fy vertical shift
LTR	Scale factor of peak of pneumatic trail
LRES	Scale factor for offset of residual torque
LXAL	Scale factor of alpha influence on Fx
LYKA	Scale factor of alpha influence on Fx
LVYKA	Scale factor of kappa induced Fy
LS	Scale factor of Moment arm of Fx
LMX	Scale factor of overturning moment
LVMX	Scale factor of Mx vertical shift
LMY	Scale factor of rolling resistance torque
LMP	Scale factor of parking moment

Mode

TYRESIDE	Position of tire during measurements
LONGVL	Reference speed
VXLOW	Lower boundary velocity in slip calculation

Dimension

UNLOADED_RADIUS	Free tire radius
WIDTH	Nominal section width of the tire
ASPECT_RATIO	Nominal aspect ratio

Operating Conditions

INFLPRES	Tire inflation pressure
NOMPRES	Nominal pressure used in magic formula equations

Vertical

FNOMIN	Nominal wheel load
VERTICAL_STIFFNESS	Tire vertical stiffness
BREFF	Low load stiffness of effective rolling radius
DREFF	Peak value of effective rolling radius
FREFF	High load stiffness of effective rolling radius
Q_RE0	Ratio of free tire radius with nominal tire radius
Q_V1	Tire radius increase with speed
Q_V2	Vertical stiffness increase with speed
Q_FCY	Lateral force influence on vertical stiffness
Q_FCY2	Explicit load dependency for including the lateral force influence on vertical stiffness
Q_FZ2	Quadratic term in load vs. deflection
Q_CAM1	Linear load dependent camber angle influence on vertical stiffness
Q_CAM2	Quadratic load dependent camber angle influence on vertical stiffness
Q_CAM3	Linear load and camber angle dependent reduction on vertical stiffness
Q_FYS1	Combined camber angle and side slip angle effect on vertical stiffness (constant)
Q_FYS2	Combined camber angle and side slip angle linear effect on vertical stiffness
Q_FYS3	Combined camber angle and side slip angle quadratic effect on vertical stiffness
PFZ1	Pressure effect on vertical stiffness

Inflation Pressure Range

PRESMIN	Minimum allowed inflation pressure
PRESMAX	Maximum allowed inflation pressure

Vertical Force Range

FZMIN	Minimum allowed wheel load
FZMAX	Maximum allowed wheel load

Long Slip Range

KPUMIN	Minimum valid wheel slip
KPUMAX	Maximum valid wheel slip

Slip Angle Range

ALPMIN	Minimum valid slip angle
ALPMAX	Maximum valid slip angle

Inclination Angle Range

CAMMIN	Minimum valid camber angle
CAMMAX	Maximum valid camber angle

Longitudinal Coefficients

PCX1	Shape factor Cfx for longitudinal force
PDX1	Longitudinal friction Mux at Fznom
PDX2	Variation of friction Mux with load
PDX3	Variation of friction Mux with camber
PEX1	Longitudinal curvature Efx at Fznom
PEX2	Variation of curvature Efx with load
PEX3	Variation of curvature Efx with load squared
PEX4	Factor in curvature Efx while driving
PKX1	Longitudinal slip stiffness Kfx/Fz at Fznom
PKX2	Variation of slip stiffness Kfx/Fz with load
PKX3	Exponent in slip stiffness Kfx/Fz with load
PHX1	Horizontal shift Shx at Fznom
PHX2	Variation of shift Shx with load
PVX1	Vertical shift Svx/Fz at Fznom
PVX2	Variation of shift Svx/Fz with load
RBX1	Slope factor for combined slip Fx reduction
RBX2	Variation of slope Fx reduction with kappa
RBX3	Influence of camber on stiffness for Fx combined
RCX1	Shape factor for combined slip Fx reduction
REX1	Curvature factor of combined Fx
REX2	Curvature factor of combined Fx with load
RHX1	Shift factor for combined slip Fx reduction
PPX1	Linear influence of inflation pressure on longitudinal slip stiffness
PPX2	Quadratic influence of inflation pressure on longitudinal slip stiffness
PPX3	Linear influence of inflation pressure on peak longitudinal friction
PPX4	Quadratic influence of inflation pressure on peak longitudinal friction

Overturning Coefficients

QSX1	Vertical shift of overturning moment
QSX2	Camber induced overturning couple
QSX3	Fy induced overturning couple
QSX4	Mixed load lateral force and camber on Mx
QSX5	Load effect on Mx with lateral force and camber
QSX6	B-factor of load with Mx
QSX7	Camber with load on Mx
QSX8	Lateral force with load on Mx
QSX9	B-factor of lateral force with load on Mx
QSX10	Vertical force with camber on Mx
QSX11	B-factor of vertical force with camber on Mx
QSX12	Camber squared induced overturning moment
QSX13	Lateral force induced overturning moment
QSX14	Lateral force induced overturning moment with camber
PPMX1	Influence of inflation pressure on overturning moment

Lateral Coefficients

PCY1	Shape factor Cfy for lateral forces
PDY1	Lateral friction Muy
PDY2	Variation of friction Muy with load
PDY3	Variation of friction Muy with squared camber
PEY1	Lateral curvature Efy at Fznom
PEY2	Variation of curvature Efy with load
PEY3	Zero order camber dependency of curvature Efy
PEY4	Variation of curvature Efy with camber
PEY5	Variation of curvature Efy with camber squared
PKY1	Maximum value of stiffness Kfy/Fznom
PKY2	Load at which Kfy reaches maximum value
PKY3	Variation of Kfy/Fznom with camber
PKY4	Curvature of stiffness Kfy
PKY5	Peak stiffness variation with camber squared
PKY6	Fy camber stiffness factor
PKY7	Vertical load dependency of camber stiffness factor
PHY1	Horizontal shift Shy at Fznom
PHY2	Variation of shift Shy with load
PVY1	Vertical shift in Svy/Fz at Fznom
PVY2	Variation of shift Svy/Fz with load
PVY3	Variation of shift Svy/Fz with camber
PVY4	Variation of shift Svy/Fz with camber and load
RBY1	Slope factor for combined Fy reduction
RBY2	Variation of slope Fy reduction with alpha
RBY3	Shift term for alpha in slope Fy reduction
RBY4	Influence of camber on stiffness of Fy combined
RCY1	Shape factor for combined Fy reduction
REY1	Curvature factor of combined Fy
REY2	Curvature factor of combined Fy with load
RHY1	Shift factor for combined Fy reduction
RHY2	Shift factor for combined Fy reduction with load
RVY1	Kappa induced side force Svyk/Muy*Fz at Fznom
RVY2	Variation of Svyk/Muy*Fz with load
RVY3	Variation of Svyk/Muy*Fz with camber
RVY4	Variation of Svyk/Muy*Fz with alpha
RVY5	Variation of Svyk/Muy*Fz with kappa
RVY6	Variation of Svyk/Muy*Fz with atan(kappa)
PPY1	Influence of inflation pressure on cornering stiffness
PPY2	Influence of inflation pressure on dependency of nominal tire load on cornering stiffness
PPY3	linear influence of inflation pressure on lateral peak friction
PPY4	Quadratic influence of inflation pressure on lateral peak friction
PPY5	Influence of inflation pressure on camber stiffness

Rolling Coefficients

QSY1	Rolling resistance torque coefficient
QSY2	Rolling resistance torque depending on Fx
QSY3	Rolling resistance torque depending on speed
QSY4	Rolling resistance torque depending on speed^4
QSY5	Rolling resistance torque depending on camber squared
QSY6	Rolling resistance torque depending on load and camber squared
QSY7	Rolling resistance torque coefficient load dependency
QSY8	Rolling resistance torque coefficient pressure dependency

Aligning Coefficients

QBZ1	Trail slope factor for trail Bpt at Fznom
QBZ2	Variation of slope Bpt with load
QBZ3	Variation of slope Bpt with load squared
QBZ4	Variation of slope Bpt with camber
QBZ5	Variation of slope Bpt with absolute camber
QBZ9	Factor for scaling factors of slope factor Br of Mzr
QBZ10	Factor for dimensionless cornering stiffness of Br of Mzr
QCZ1	Shape factor Cpt for pneumatic trail
QDZ1	Peak trail Dpt = Dpt*(Fz/Fznom*R0)
QDZ2	Variation of peak Dpt with load
QDZ3	Variation of peak Dpt with camber
QDZ4	Variation of peak Dpt with camber squared
QDZ6	Peak residual torque Dmr = Dmr/(Fz*R0)
QDZ7	Variation of peak factor Dmr with load
QDZ8	Variation of peak factor Dmr with camber
QDZ9	Variation of peak factor Dmr with camber and load
QDZ10	Variation of peak factor Dmr with camber squared
QDZ11	Variation of Dmr with camber squared and load
QEZ1	Trail curvature Ept at Fznom
QEZ2	Variation of curvature Ept with load
QEZ3	Variation of curvature Ept with load squared
QEZ4	Variation of curvature Ept with sign of Alpha-t
QEZ5	Variation of Ept with camber and sign Alpha-t
QHZ1	Trail horizontal shift Sht at Fznom
QHZ2	Variation of shift Sht with load
QHZ3	Variation of shift Sht with camber
QHZ4	Variation of shift Sht with camber and load
SSZ1	Nominal value of s/R0: effect of Fx on Mz
SSZ2	Variation of distance s/R0 with Fy /Fznom
SSZ3	Variation of distance s/R0 with camber
SSZ4	Variation of distance s/R0 with load and camber
PPZ1	Effect of inflation pressure on length of pneumatic trail
PPZ2	Influence of inflation pressure on residual aligning torque

[1]

References

[1] Pacejka, Hans B., and Igo Besselink. Tire and Vehicle Dynamics. 3rd. Engineering Automotive Engineering. Amsterdam: Elsevier/Butterworth-Heinemann, 2012.

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

[3] van der Hofstad, R. H. M. T. “Study on improving the MF-Swift tyre model.” (2010).

Version History

Introduced in R2021b

R2024b: Compute contact frame

Use the closest point or the weighted penetration method to compute the location and orientation of the contact frame between the tire and the contact surface.

R2024b: Compute radial deflection

Use the rho port to output the radial deflection. The radial deflection is the difference between the tire free radius and the loaded radius.

R2023a: Base geometry supports the Grid Surface block

Use the Grid Surface block to represent the contact surface.