Fit a Tire Model to Tire Data

R2026b

This example uses:

Open Live Script

Use the fit method to fit tire model parameters to tire data. The fit method optimizes parameter values of a tire model to match the tire model response to the target tire data as closely as possible.

First, import tire data. Then, choose a model as the seed for fitting a new tire model parameter set. You can import an existing tire model or create a new tire model from default parameters for the seed model. Finally, fit the tire model parameter sets by specifying the fitType argument of the fit method. For more information on the fit types available, see fitType.

This example requires the Extended Tire Features for Vehicle Dynamics Blockset™ support package. See Install Support Package.

Note that using a built-in tire model as a seed model is not supported.

Import Tire Data

Build a string array from the TYDEX filenames that contain the tire data.

tirepath = pwd;
tydexdir = dir(fullfile(tirepath,"data_tydex_files","*.tdx"));
tydexstr = join([{tydexdir.folder}',{tydexdir.name}'],filesep);

Import the tire data into an array of tireData objects from the files specified in the string array tydexstr. The length of the tireData objects array is the same length as the input string array. Data from each file is stored in a tireData object. For more information on tire data permitted, see Example Tire Data.

td = tireData(tydexstr);

Use the mean function to preprocess the Fz data channel to remove noise and variation.

td = mean(td, "Fz");

Create tireModel Object

Create a Magic Formula 6.2 tire model type with default parameters to use as the seed model. Then, name the new model. 

tm = tireModel.new("MF");
tm.Name = "New Fitted Model";

Set Dimensions, Nominal Test Conditions, and Model Limits

Set the nominal test conditions for FNOMIN, LONGVL, NOMPRES, and INFLPRES.

tm = fit(tm,td,"Nominal");

Manually set the size of the tire tested.

tm.TireSize = "245/45R18";

Specify the fitType as Dimensions to automatically set the dimensional properties of the tire to match the test data supplied to the model.

[tm, diffTable] = fit(tm, td, "Dimensions");

View the diffTable variable to inspect which variables were revised.

diffTable
diffTable = 5×9 table
        Parameter        Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds           Parameter Description             Status   
    _________________    _____________    ___________    __________    ____________    ____________    ____________    ___________________________________    ___________

    "UNLOADED_RADIUS"       0.3135          0.33454       0.021045          6.7             0              Inf         "Free tire radius"                     "Optimized"
    "WIDTH"                  0.205            0.235           0.03         14.6             0              Inf         "Nominal section width of the tire"    "Optimized"
    "ASPECT_RATIO"             0.6             0.45          -0.15          -25             0              Inf         "Nominal aspect ratio"                 "Optimized"
    "RIM_RADIUS"            0.1905           0.2286         0.0381           20             0              Inf         "Nominal rim radius"                   "Optimized"
    "RIM_WIDTH"              0.152           0.2032         0.0512         33.7             0              Inf         "Rim width"                            "Optimized"

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Specify the fitType as Limits to automatically set the model limits to match the test data supplied to fit the model. Keep the FZMIN parameter value constant when these limits are applied by setting the FixedParameters argument to FZMIN.

[tm, diffTable] = fit(tm, td, "Limits", FixedParameters="FZMIN");

View the diffTable variable to inspect which variables were revised.

diffTable
diffTable = 9×9 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds             Parameter Description               Status   
    _________    _____________    ___________    __________    ____________    ____________    ____________    _______________________________________    ___________

    "PRESMIN"         10000        2.62e+05       2.52e+05         2520               0            Inf         "Minimum valid tire inflation pressure"    "Optimized"
    "PRESMAX"         1e+06        2.62e+05      -7.38e+05        -73.8               0            Inf         "Maximum valid tire inflation pressure"    "Optimized"
    "FZMAX"           12000            6526          -5474        -45.6               0            Inf         "Maximum allowed wheel load"               "Optimized"
    "KPUMIN"           -1.5         -0.4808         1.0192        -67.9            -Inf            Inf         "Minimum valid wheel slip"                 "Optimized"
    "KPUMAX"            1.5          0.4811        -1.0189        -67.9            -Inf            Inf         "Maximum valid wheel slip"                 "Optimized"
    "ALPMIN"        -0.7854         -0.3265         0.4589        -58.4            -Inf            Inf         "Minimum valid slip angle"                 "Optimized"
    "ALPMAX"         0.7854          0.3239        -0.4615        -58.8            -Inf            Inf         "Maximum valid slip angle"                 "Optimized"
    "CAMMIN"       -0.17453         -0.1052        0.06933        -39.7            -Inf            Inf         "Minimum valid camber angle"               "Optimized"
    "CAMMAX"        0.17453          0.1052       -0.06933        -39.7            -Inf            Inf         "Maximum valid camber angle"               "Optimized"

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Fit Different Parameter Sets

Follow these steps to fit different tire model parameter sets.

Note that this section provides steps for only some of the available parameter sets. You can use these steps to fit all of the available parameter options.

Fit Pure Fx Parameters

Extract the longitudinal data from the tire data.

longitudinal_data = td([td.TestMethod] == "Longitudinal");

Using the fit function, set the fitType argument to "Fx Pure", and set the PlotFit argument to true to plot the result.

For additional information available for a fit, see Output Arguments. 

[tm, diffTable]  = fit(tm,longitudinal_data,"Fx Pure",PlotFit=true);
Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

<stopping criteria details>

Figure contains 3 axes objects and another object of type uitabgroup. Axes object 1 with title Inclination angle [rad] = 0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 2 with title Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 3 with title Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior.

View the diffTable variable to inspect which variables were optimized.

diffTable
diffTable = 19×9 table
    Parameter    Initial Value    Final Value    Difference     % Difference    Lower Bounds    Upper Bounds                             Parameter Description                               Status   
    _________    _____________    ___________    ___________    ____________    ____________    ____________    _______________________________________________________________________    ___________

     "PCX1"            1.579            2.281        0.70198           44.5          -Inf             Inf       "Shape factor Cfx for longitudinal force"                                  "Optimized"
     "PDX1"           1.0422            1.176         0.1338           12.8          -Inf             Inf       "Longitudinal friction Mux at Fznom"                                       "Optimized"
     "PDX2"         -0.08285        -0.090486      -0.007636            9.2          -Inf             Inf       "Variation of friction Mux with load"                                      "Optimized"
     "PDX3"                0           0.0759         0.0759            Inf          -Inf             Inf       "Variation of friction Mux with camber"                                    "Optimized"
     "PEX1"          0.11113           2.9465         2.8354         2551.4          -Inf             Inf       "Longitudinal curvature Efx at Fznom"                                      "Optimized"
     "PEX2"           0.3143          -1.3555        -1.6698         -531.3          -Inf             Inf       "Variation of curvature Efx with load"                                     "Optimized"
     "PEX3"                0           1.6471         1.6471            Inf          -Inf             Inf       "Variation of curvature Efx with load squared"                             "Optimized"
     "PEX4"         0.001719       6.7147e-07     -0.0017183           -100          -0.5             0.5       "Factor in curvature Efx while driving"                                    "Optimized"
     "PKX1"           21.687           45.212         23.525          108.5          -Inf             Inf       "Longitudinal slip stiffness Kfx/Fz at Fznom"                              "Optimized"
     "PKX2"           13.728           21.341         7.6129           55.5          -Inf             Inf       "Variation of slip stiffness Kfx/Fz with load"                             "Optimized"
     "PKX3"          -0.4098         -0.22864        0.18116          -44.2          -Inf             Inf       "Exponent in slip stiffness Kfx/Fz with load"                              "Optimized"
     "PHX1"       0.00021615      -0.00089319     -0.0011093         -513.2          -Inf             Inf       "Horizontal shift Shx at Fznom"                                            "Optimized"
     "PHX2"        0.0011598       0.00067769    -0.00048211          -41.6          -Inf             Inf       "Variation of shift Shx with load"                                         "Optimized"
     "PVX1"       2.0283e-05         0.049391       0.049371     2.4341e+05          -Inf             Inf       "Vertical shift Svx/Fz at Fznom"                                           "Optimized"
     "PVX2"       0.00010568        -0.014012      -0.014118         -13359          -Inf             Inf       "Variation of shift Svx/Fz with load"                                      "Optimized"
     "PPX1"          -0.3485          -0.3485              0              0       -0.3485         -0.3485       "Linear influence of inflation pressure on longitudinal slip stiffness"    "Inert"    

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Fit Pure Fy Parameters

Extract the lateral data from the tire data.

lateral_data = td([td.TestMethod] == "Lateral");

Using the fit function, set the fitType argument to "Fy Pure", and set the PlotFit argument to true to plot the result.

For additional information available for a fit, see Output Arguments. 

[tm, diffTable]  = fit(tm,lateral_data,"Fy Pure",PlotFit=true);
Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

<stopping criteria details>

Figure contains 3 axes objects and another object of type uitabgroup. Axes object 1 with title Inclination angle [rad] = 0.105, xlabel Slip angle [rad], ylabel Lateral force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 2 with title Inclination angle [rad] = 0, xlabel Slip angle [rad], ylabel Lateral force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 3 with title Inclination angle [rad] = -0.105, xlabel Slip angle [rad], ylabel Lateral force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior.

View the diffTable variable to inspect which variables were optimized.

diffTable
diffTable = 27×9 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds                 Parameter Description                    Status   
    _________    _____________    ___________    __________    ____________    ____________    ____________    ________________________________________________    ___________

     "PCY1"           1.338          1.4654        0.12737          9.5            0.5              10         "Shape factor Cfy for lateral forces"               "Optimized"
     "PDY1"          0.8785          1.0644        0.18589         21.2              0              10         "Lateral friction Muy"                              "Optimized"
     "PDY2"        -0.06452        -0.14967      -0.085146          132            -10              10         "Variation of friction Muy with load"               "Optimized"
     "PDY3"               0          2.2826         2.2826          Inf            -10              10         "Variation of friction Muy with squared camber"     "Optimized"
     "PEY1"         -0.8057         -1.8916        -1.0859        134.8            -10              10         "Lateral curvature Efy at Fznom"                    "Optimized"
     "PEY2"         -0.6046         -2.3599        -1.7553        290.3            -10              10         "Variation of curvature Efy with load"              "Optimized"
     "PEY3"         0.09854          0.0337       -0.06484        -65.8            -10              10         "Zero order camber dependency of curvature Efy"     "Optimized"
     "PEY4"          -6.697         -7.2404       -0.54336          8.1            -10              10         "Variation of curvature Efy with camber"            "Optimized"
     "PEY5"               0              10             10          Inf            -10              10         "Variation of curvature Efy with camber squared"    "Optimized"
     "PKY1"         -15.324          -26.95        -11.626         75.9            -75               0         "Maximum value of stiffness Kfy/Fznom"              "Optimized"
     "PKY2"           1.715          1.5321       -0.18287        -10.7            -10              10         "Load at which Kfy reaches maximum value"           "Optimized"
     "PKY3"          0.3695         0.55667        0.18717         50.7            -10              10         "Variation of Kfy/Fznom with camber"                "Optimized"
     "PKY4"          2.0005          1.5486       -0.45191        -22.6            -10              10         "Curvature of stiffness Kfy"                        "Optimized"
     "PKY5"               0             -10            -10         -Inf            -10              10         "Peak stiffness variation with camber squared"      "Optimized"
     "PKY6"         -0.8987         -1.1905       -0.29179         32.5            -10              10         "Fy camber stiffness factor"                        "Optimized"
     "PKY7"        -0.23303        -0.59235       -0.35932        154.2            -10              10         "Vertical load dependency of camber stiffness"      "Optimized"

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Fit Combined Fx Parameters

Extract the combined data from the tire data.

combined_data = td([td.TestMethod] == "Combined");

Using the fit function, set the fitType argument to "Fx Combined", and set the PlotFit argument to true to plot the result.

For additional information available for a fit, see Output Arguments. 

[tm, diffTable]  = fit(tm,combined_data,"Fx Combined",PlotFit=true);
Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

<stopping criteria details>

Figure contains 12 axes objects and another object of type uitabgroup. Axes object 1 with title Slip angle [rad] = 0.035; Inclination angle [rad] = 0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 2 with title Slip angle [rad] = 0.035; Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 3 with title Slip angle [rad] = 0.035; Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 4 with title Slip angle [rad] = -0.035; Inclination angle [rad] = 0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 5 with title Slip angle [rad] = -0.035; Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 6 with title Slip angle [rad] = -0.035; Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 7 with title Slip angle [rad] = -0.087; Inclination angle [rad] = 0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 8 with title Slip angle [rad] = -0.087; Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 9 with title Slip angle [rad] = -0.087; Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 10 with title Slip angle [rad] = -0.14; Inclination angle [rad] = 0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 11 with title Slip angle [rad] = -0.14; Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 12 with title Slip angle [rad] = -0.14; Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 9 objects of type scatter, line. These objects represent Model behavior.

View the diffTable variable to inspect which variables were optimized.

diffTable
diffTable = 7×9 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds                  Parameter Description                     Status   
    _________    _____________    ___________    __________    ____________    ____________    ____________    __________________________________________________    ___________

     "RBX1"           13.046              20         6.954          53.3              0              20        "Slope factor for combined slip Fx reduction"         "Optimized"
     "RBX2"            9.718              20        10.282         105.8              5              20        "Variation of slope Fx reduction with kappa"          "Optimized"
     "RBX3"                0              15            15           Inf              0              15        "Influence of camber on stiffness for Fx combined"    "Optimized"
     "RCX1"           0.9995            1.25        0.2505          25.1            0.5            1.25        "Shape factor for combined slip Fx reduction"         "Optimized"
     "REX1"          -0.4403          0.4931        0.9334          -212            -10              10        "Curvature factor of combined Fx"                     "Optimized"
     "REX2"          -0.4663      -0.0029995        0.4633         -99.4             -5               5        "Curvature factor of combined Fx with load"           "Optimized"
     "RHX1"       -9.968e-05       0.0028376     0.0029373       -2946.7          -0.01            0.01        "Shift factor for combined slip Fx reduction"         "Optimized"

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Fit Mx Parameters

Using the fit function, set the fitType argument to "Mx", use the combined data, and set the PlotFit argument to true to plot the result.

For additional information available for a fit, see Output Arguments. 

[tm, diffTable]  = fit(tm, lateral_data,"Mx",PlotFit=true);
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =  2.021817e-16.

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =  2.021817e-16.

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =  1.021120e-17.

Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

<stopping criteria details>

Figure contains 3 axes objects and another object of type uitabgroup. Axes object 1 with title Inclination angle [rad] = 0.105, xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 2 with title Inclination angle [rad] = 0, xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 9 objects of type scatter, line. These objects represent Model behavior. Axes object 3 with title Inclination angle [rad] = -0.105, xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 9 objects of type scatter, line. These objects represent Model behavior.

View the diffTable variable to inspect which variables were optimized.

diffTable
diffTable = 12×9 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds                     Parameter Description                       Status   
    _________    _____________    ___________    __________    ____________    ____________    ____________    _______________________________________________________    ___________

     "QSX1"        -0.007764      -0.00042217    0.0073418        -94.6             -5               5         "Vertical shift of overturning moment"                     "Optimized"
     "QSX2"           1.1915           4.9934       3.8019        319.1             -5               5         "Camber induced overturning couple"                        "Optimized"
     "QSX3"         0.013948         0.026999     0.013051         93.6             -5               5         "Fy induced overturning couple"                            "Optimized"
     "QSX4"            4.912          0.82782      -4.0842        -83.1            -20              20         "Mixed load lateral force and camber on Mx"                "Optimized"
     "QSX5"             1.02          0.61971     -0.40029        -39.2             -5               5         "Load effect on Mx with lateral force and camber"          "Optimized"
     "QSX6"            22.83            1.922      -20.908        -91.6            -20              20         "B-factor of load with Mx"                                 "Optimized"
     "QSX7"           0.7104           3.3723       2.6619        374.7             -5               5         "Camber with load on Mx"                                   "Optimized"
     "QSX8"        -0.023393        -0.086316    -0.062923          269             -5               5         "Lateral force with load on Mx"                            "Optimized"
     "QSX9"           0.6581           1.3724       0.7143        108.5             -5               5         "B-factor of lateral force with load on Mx"                "Optimized"
     "QSX10"          0.2824           2.4326       2.1502        761.4             -5               5         "Vertical force with camber on Mx"                         "Optimized"
     "QSX11"           5.349           1.1623      -4.1867        -78.3              0              20         "B-factor of vertical force with camber on Mx"             "Optimized"
     "PPMX1"               0                0            0            0              0               0         "Influence of inflation pressure on overturning moment"    "Inert"    

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Continue Fitting Parameter Sets

Use the steps established in the preceding sections to continue fitting the model using the remaining fit types.

Plot Fitted Tire Model Response

After fitting all available fit types, use the plot method to plot the results and compare to the original default model.

plot([tm,tireModel.new("MF")],Data=td);

Figure contains 72 axes objects and another object of type uitabgroup. Axes object 1 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4320, 5190, 6500, New Fitted Model, Magic Formula v6.2. Axes object 2 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4320, 5190, 6500, New Fitted Model, Magic Formula v6.2. Axes object 3 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4320, 5190, 6500, New Fitted Model, Magic Formula v6.2. Axes object 4 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4320, 5190, 6500, New Fitted Model, Magic Formula v6.2. Axes object 5 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4320, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 6 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4320, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 7 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4320, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 8 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4320, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 9 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 10 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 11 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 12 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 13 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 14 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 15 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 16 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 17 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4310, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 18 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4310, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 19 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4310, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 20 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4310, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 21 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5200, 6500, New Fitted Model, Magic Formula v6.2. Axes object 22 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5200, 6500, New Fitted Model, Magic Formula v6.2. Axes object 23 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5200, 6500, New Fitted Model, Magic Formula v6.2. Axes object 24 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5200, 6500, New Fitted Model, Magic Formula v6.2. Axes object 25 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4310, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 26 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4310, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 27 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4310, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 28 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4310, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 29 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5200, 6500, New Fitted Model, Magic Formula v6.2. Axes object 30 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5200, 6500, New Fitted Model, Magic Formula v6.2. Axes object 31 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5200, 6500, New Fitted Model, Magic Formula v6.2. Axes object 32 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5200, 6500, New Fitted Model, Magic Formula v6.2. Axes object 33 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2170, 4340, 5210, 6510, New Fitted Model, Magic Formula v6.2. Axes object 34 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2170, 4340, 5210, 6510, New Fitted Model, Magic Formula v6.2. Axes object 35 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2170, 4340, 5210, 6510, New Fitted Model, Magic Formula v6.2. Axes object 36 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2170, 4340, 5210, 6510, New Fitted Model, Magic Formula v6.2. Axes object 37 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4320, 5170, 6480, New Fitted Model, Magic Formula v6.2. Axes object 38 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4320, 5170, 6480, New Fitted Model, Magic Formula v6.2. Axes object 39 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4320, 5170, 6480, New Fitted Model, Magic Formula v6.2. Axes object 40 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4320, 5170, 6480, New Fitted Model, Magic Formula v6.2. Axes object 41 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5190, 6490, New Fitted Model, Magic Formula v6.2. Axes object 42 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5190, 6490, New Fitted Model, Magic Formula v6.2. Axes object 43 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5190, 6490, New Fitted Model, Magic Formula v6.2. Axes object 44 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5190, 6490, New Fitted Model, Magic Formula v6.2. Axes object 45 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2170, 4350, 5210, 6510, New Fitted Model, Magic Formula v6.2. Axes object 46 with title Fy vs kappa, xlabel Longitudinal slip [], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2170, 4350, 5210, 6510, New Fitted Model, Magic Formula v6.2. Axes object 47 with title Mz vs kappa, xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2170, 4350, 5210, 6510, New Fitted Model, Magic Formula v6.2. Axes object 48 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2170, 4350, 5210, 6510, New Fitted Model, Magic Formula v6.2. Axes object 49 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5170, 6460, New Fitted Model, Magic Formula v6.2. Axes object 50 with xlabel Longitudinal slip [], ylabel Lateral force [N] contains an object of type text. Axes object 51 with xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains an object of type text. Axes object 52 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5170, 6460, New Fitted Model, Magic Formula v6.2. Axes object 53 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4280, 5170, 6460, New Fitted Model, Magic Formula v6.2. Axes object 54 with xlabel Longitudinal slip [], ylabel Lateral force [N] contains an object of type text. Axes object 55 with xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains an object of type text. Axes object 56 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4280, 5170, 6460, New Fitted Model, Magic Formula v6.2. Axes object 57 with title Fx vs kappa, xlabel Longitudinal slip [], ylabel Longitudinal force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4310, 5170, 6460, New Fitted Model, Magic Formula v6.2. Axes object 58 with xlabel Longitudinal slip [], ylabel Lateral force [N] contains an object of type text. Axes object 59 with xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains an object of type text. Axes object 60 with title Mx vs kappa, xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4310, 5170, 6460, New Fitted Model, Magic Formula v6.2. Axes object 61 with title Fy vs alpha, xlabel Slip angle [rad], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 62 with title Mz vs alpha, xlabel Slip angle [rad], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 63 with title Mx vs alpha, xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 64 with title Fy vs alpha, xlabel Slip angle [rad], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4270, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 65 with title Mz vs alpha, xlabel Slip angle [rad], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4270, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 66 with title Mx vs alpha, xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4270, 5160, 6460, New Fitted Model, Magic Formula v6.2. Axes object 67 with title Fy vs alpha, xlabel Slip angle [rad], ylabel Lateral force [kN] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6450, New Fitted Model, Magic Formula v6.2. Axes object 68 with title Mz vs alpha, xlabel Slip angle [rad], ylabel Self-aligning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6450, New Fitted Model, Magic Formula v6.2. Axes object 69 with title Mx vs alpha, xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 20 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4300, 5160, 6450, New Fitted Model, Magic Formula v6.2. Axes object 70 with title Friction Plot gamma = 0.105, xlabel Lateral force [kN], ylabel Longitudinal force [kN] contains 68 objects of type line. One or more of the lines displays its values using only markers These objects represent 2140, 4310, 5180, 6480, New Fitted Model, Magic Formula v6.2. Axes object 71 with title Friction Plot gamma = 0, xlabel Lateral force [kN], ylabel Longitudinal force [kN] contains 68 objects of type line. One or more of the lines displays its values using only markers These objects represent 2150, 4320, 5190, 6490, New Fitted Model, Magic Formula v6.2. Axes object 72 with title Friction Plot gamma = -0.105, xlabel Lateral force [kN], ylabel Longitudinal force [kN] contains 68 objects of type line. One or more of the lines displays its values using only markers These objects represent 2160, 4330, 5200, 6490, New Fitted Model, Magic Formula v6.2.

See Also

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