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.
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.
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.
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.
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.
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.
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.
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.
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.
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 F_{X} reduction due to spin parameter |
PDXP2 | Peak F_{X} reduction due to spin with varying load parameter |
PDXP3 | Peak F_{X} reduction due to spin with kappa parameter |
PKYP1 | Cornering stiffness reduction due to spin |
PDYP1 | Peak F_{Y} reduction due to spin parameter |
PDYP2 | Peak F_{Y} reduction due to spin with varying load parameter |
PDYP3 | Peak F_{Y} reduction due to spin with alpha parameter |
PDYP4 | Peak F_{Y} reduction due to square root of spin parameter |
PHYP1 | F_{Y-alpha} curve lateral shift limitation |
PHYP2 | F_{Y-alpha} curve maximum lateral shift parameter |
PHYP3 | F_{Y-alpha} curve maximum lateral shift varying with load parameter |
PHYP4 | F_{Y-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 |
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/TorqueResolution 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 F_{x} shape factor |
LMUX | Scale factor of F_{x} peak friction coefficient |
LEX | Scale factor of F_{x} curvature factor |
LKX | Scale factor of slip stiffness |
LHX | Scale factor of F_{x} horizontal shift |
LVX | Scale factor of F_{x} vertical shift |
LCY | Scale factor of F_{y} shape factor |
LMUY | Scale factor of F_{y} peak friction coefficient |
LEY | Scale factor of F_{y} 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 F_{y} horizontal shift |
LVY | Scale factor of F_{y} 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 F_{x} |
LYKA | Scale factor of alpha influence on F_{x} |
LVYKA | Scale factor of kappa induced F_{y} |
LS | Scale factor of Moment arm of F_{x} |
LMX | Scale factor of overturning moment |
LVMX | Scale factor of M_{x} 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 C_{fx} for longitudinal force |
PDX1 | Longitudinal friction Mu_{x} at F_{znom} |
PDX2 | Variation of friction Mu_{x} with load |
PDX3 | Variation of friction Mu_{x} with camber |
PEX1 | Longitudinal curvature E_{fx} at F_{znom} |
PEX2 | Variation of curvature E_{fx} with load |
PEX3 | Variation of curvature E_{fx} with load squared |
PEX4 | Factor in curvature E_{fx} while driving |
PKX1 | Longitudinal slip stiffness K_{fx}/F_{z} at F_{znom} |
PKX2 | Variation of slip stiffness K_{fx}/F_{z} with load |
PKX3 | Exponent in slip stiffness K_{fx}/F_{z} with load |
PHX1 | Horizontal shift S_{hx} at F_{znom} |
PHX2 | Variation of shift S_{hx} with load |
PVX1 | Vertical shift S_{vx}/F_{z} at F_{znom} |
PVX2 | Variation of shift S_{vx}/F_{z} with load |
RBX1 | Slope factor for combined slip F_{x} reduction |
RBX2 | Variation of slope F_{x} reduction with kappa |
RBX3 | Influence of camber on stiffness for F_{x} combined |
RCX1 | Shape factor for combined slip F_{x} reduction |
REX1 | Curvature factor of combined F_{x} |
REX2 | Curvature factor of combined F_{x} with load |
RHX1 | Shift factor for combined slip F_{x} 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 | F_{y} induced overturning couple |
QSX4 | Mixed load lateral force and camber on M_{x} |
QSX5 | Load effect on M_{x} with lateral force and camber |
QSX6 | B-factor of load with M_{x} |
QSX7 | Camber with load on M_{x} |
QSX8 | Lateral force with load on M_{x} |
QSX9 | B-factor of lateral force with load on M_{x} |
QSX10 | Vertical force with camber on M_{x} |
QSX11 | B-factor of vertical force with camber on M_{x} |
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 C_{fy} for lateral forces |
PDY1 | Lateral friction Mu_{y} |
PDY2 | Variation of friction Mu_{y} with load |
PDY3 | Variation of friction Mu_{y} with squared camber |
PEY1 | Lateral curvature E_{fy} at F_{znom} |
PEY2 | Variation of curvature E_{fy} with load |
PEY3 | Zero order camber dependency of curvature E_{fy} |
PEY4 | Variation of curvature E_{fy} with camber |
PEY5 | Variation of curvature E_{fy} with camber squared |
PKY1 | Maximum value of stiffness K_{fy}/F_{znom} |
PKY2 | Load at which K_{fy} reaches maximum value |
PKY3 | Variation of K_{fy}/F_{znom} with camber |
PKY4 | Curvature of stiffness K_{fy} |
PKY5 | Peak stiffness variation with camber squared |
PKY6 | F_{y} camber stiffness factor |
PKY7 | Vertical load dependency of camber stiffness factor |
PHY1 | Horizontal shift S_{hy} at F_{znom} |
PHY2 | Variation of shift S_{hy} with load |
PVY1 | Vertical shift in S_{vy}/F_{z} at F_{znom} |
PVY2 | Variation of shift S_{vy}/F_{z} with load |
PVY3 | Variation of shift S_{vy}/F_{z} with camber |
PVY4 | Variation of shift S_{vy}/F_{z} with camber and load |
RBY1 | Slope factor for combined F_{y} reduction |
RBY2 | Variation of slope F_{y} reduction with alpha |
RBY3 | Shift term for alpha in slope F_{y} reduction |
RBY4 | Influence of camber on stiffness of F_{y} combined |
RCY1 | Shape factor for combined F_{y} reduction |
REY1 | Curvature factor of combined F_{y} |
REY2 | Curvature factor of combined F_{y} with load |
RHY1 | Shift factor for combined F_{y} reduction |
RHY2 | Shift factor for combined F_{y} reduction with load |
RVY1 | Kappa induced side force S_{vyk}/Mu_{y}*F_{z} at F_{znom} |
RVY2 | Variation of S_{vyk}/Mu_{y}*F_{z} with load |
RVY3 | Variation of S_{vyk}/Mu_{y}*F_{z} with camber |
RVY4 | Variation of S_{vyk}/Mu_{y}*F_{z} with alpha |
RVY5 | Variation of S_{vyk}/Mu_{y}*F_{z} with kappa |
RVY6 | Variation of S_{vyk}/Mu_{y}*F_{z} 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 F_{x} |
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 B_{pt} at F_{znom} |
QBZ2 | Variation of slope B_{pt} with load |
QBZ3 | Variation of slope B_{pt} with load squared |
QBZ4 | Variation of slope B_{pt} with camber |
QBZ5 | Variation of slope B_{pt} with absolute camber |
QBZ9 | Factor for scaling factors of slope factor B_{r} of M_{zr} |
QBZ10 | Factor for dimensionless cornering stiffness of B_{r} of M_{zr} |
QCZ1 | Shape factor C_{pt} for pneumatic trail |
QDZ1 | Peak trail D_{pt} = D_{pt}*(F_{z}/F_{znom}*R_{0}) |
QDZ2 | Variation of peak D_{pt} with load |
QDZ3 | Variation of peak D_{pt} with camber |
QDZ4 | Variation of peak D_{pt} with camber squared |
QDZ6 | Peak residual torque D_{mr} = D_{mr}/(F_{z}*R_{0}) |
QDZ7 | Variation of peak factor D_{mr} with load |
QDZ8 | Variation of peak factor D_{mr} with camber |
QDZ9 | Variation of peak factor D_{mr} with camber and load |
QDZ10 | Variation of peak factor D_{mr} with camber squared |
QDZ11 | Variation of Dmr with camber squared and load |
QEZ1 | Trail curvature E_{pt} at F_{znom} |
QEZ2 | Variation of curvature E_{pt} with load |
QEZ3 | Variation of curvature E_{pt} with load squared |
QEZ4 | Variation of curvature E_{pt} with sign of Alpha-t |
QEZ5 | Variation of E_{pt} with camber and sign Alpha-t |
QHZ1 | Trail horizontal shift Sh_{t} at F_{znom} |
QHZ2 | Variation of shift Sh_{t} with load |
QHZ3 | Variation of shift Sh_{t} with camber |
QHZ4 | Variation of shift Sh_{t} with camber and load |
SSZ1 | Nominal value of s/R_{0}: effect of F_{x} on M_{z} |
SSZ2 | Variation of distance s/R_{0} with F_{y} /F_{znom} |
SSZ3 | Variation of distance s/R_{0} with camber |
SSZ4 | Variation of distance s/R_{0} with load and camber |
PPZ1 | Effect of inflation pressure on length of pneumatic trail |
PPZ2 | Influence of inflation pressure on residual aligning torque |
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 R2021bR2024b: 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.
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