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Fit a Tire Model to Tire Data

This example uses:

Open Live Script
Step 7 of 8 in Get Started with the Extended Tire Features for Vehicle Dynamics Blockset

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

Manually set the nominal test conditions to match the test data supplied to fit the tire model.

tm.INFLPRES = 262000;
tm.NOMPRES = 262000;
tm.FNOMIN = 4300;

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=5×8 table
        Parameter        Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds           Parameter Description       
    _________________    _____________    ___________    __________    ____________    ____________    ____________    ___________________________________

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

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=9×8 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds             Parameter Description         
    _________    _____________    ___________    __________    ____________    ____________    ____________    _______________________________________

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

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.

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 [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4300, 5170, 6460. Axes object 2 with title Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2150, 4280, 5170, 6460. Axes object 3 with title Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4310, 5170, 6460.

View the diffTable variable to inspect which variables were optimized.

diffTable
diffTable=19×8 table
    Parameter    Initial Value    Final Value    Difference     % Difference    Lower Bounds    Upper Bounds                             Parameter Description                         
    _________    _____________    ___________    ___________    ____________    ____________    ____________    _______________________________________________________________________

     "PCX1"            1.579           1.5138      -0.065167           -4.1         -Inf            Inf         "Shape factor Cfx for longitudinal force"                              
     "PDX1"           1.0422           1.1786        0.13637           13.1         -Inf            Inf         "Longitudinal friction Mux at Fznom"                                   
     "PDX2"         -0.08285        -0.040475       0.042375          -51.1         -Inf            Inf         "Variation of friction Mux with load"                                  
     "PDX3"                0         0.070743       0.070743            Inf         -Inf            Inf         "Variation of friction Mux with camber"                                
     "PEX1"          0.11113          0.33671        0.22558            203         -Inf            Inf         "Longitudinal curvature Efx at Fznom"                                  
     "PEX2"           0.3143         -0.49929       -0.81359         -258.9         -Inf            Inf         "Variation of curvature Efx with load"                                 
     "PEX3"                0          0.16845        0.16845            Inf         -Inf            Inf         "Variation of curvature Efx with load squared"                         
     "PEX4"         0.001719        -0.098787       -0.10051        -5846.8         -Inf            Inf         "Factor in curvature Efx while driving"                                
     "PKX1"           21.687           46.607          24.92          114.9         -Inf            Inf         "Longitudinal slip stiffness Kfx/Fz at Fznom"                          
     "PKX2"           13.728      -0.00026746        -13.728           -100         -Inf            Inf         "Variation of slip stiffness Kfx/Fz with load"                         
     "PKX3"          -0.4098          0.10057        0.51037         -124.5         -Inf            Inf         "Exponent in slip stiffness Kfx/Fz with load"                          
     "PHX1"       0.00021615      -0.00098607     -0.0012022         -556.2         -Inf            Inf         "Horizontal shift Shx at Fznom"                                        
     "PHX2"        0.0011598       0.00048149    -0.00067831          -58.5         -Inf            Inf         "Variation of shift Shx with load"                                     
     "PVX1"       2.0283e-05         0.049022       0.049002     2.4159e+05         -Inf            Inf         "Vertical shift Svx/Fz at Fznom"                                       
     "PVX2"       0.00010568       -0.0070435     -0.0071492        -6764.9         -Inf            Inf         "Variation of shift Svx/Fz with load"                                  
     "PPX1"          -0.3485          -0.3485              0              0         -Inf            Inf         "Linear influence of inflation pressure on longitudinal slip stiffness"
      ⋮

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.

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 [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4300, 5160, 6460. Axes object 2 with title Inclination angle [rad] = 0, xlabel Slip angle [rad], ylabel Lateral force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4270, 5160, 6460. Axes object 3 with title Inclination angle [rad] = -0.105, xlabel Slip angle [rad], ylabel Lateral force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4300, 5160, 6450.

View the diffTable variable to inspect which variables were optimized.

diffTable
diffTable=27×8 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds                 Parameter Description              
    _________    _____________    ___________    __________    ____________    ____________    ____________    ________________________________________________

     "PCY1"           1.338          1.4671         0.1291          9.6            -Inf            Inf         "Shape factor Cfy for lateral forces"           
     "PDY1"          0.8785           1.086        0.20754         23.6            -Inf            Inf         "Lateral friction Muy"                          
     "PDY2"        -0.06452        -0.12512      -0.060598         93.9            -Inf            Inf         "Variation of friction Muy with load"           
     "PDY3"               0          1.8336         1.8336          Inf            -Inf            Inf         "Variation of friction Muy with squared camber" 
     "PEY1"         -0.8057         -1.2623       -0.45663         56.7            -Inf            Inf         "Lateral curvature Efy at Fznom"                
     "PEY2"         -0.6046         -1.6085        -1.0039          166            -Inf            Inf         "Variation of curvature Efy with load"          
     "PEY3"         0.09854        0.040037      -0.058503        -59.4            -Inf            Inf         "Zero order camber dependency of curvature Efy" 
     "PEY4"          -6.697          -9.113         -2.416         36.1            -Inf            Inf         "Variation of curvature Efy with camber"        
     "PEY5"               0          38.025         38.025          Inf            -Inf            Inf         "Variation of curvature Efy with camber squared"
     "PKY1"         -15.324         -34.635        -19.311          126            -Inf            Inf         "Maximum value of stiffness Kfy/Fznom"          
     "PKY2"           1.715          1.9465        0.23153         13.5            -Inf            Inf         "Load at which Kfy reaches maximum value"       
     "PKY3"          0.3695           1.271         0.9015          244            -Inf            Inf         "Variation of Kfy/Fznom with camber"            
     "PKY4"          2.0005          1.5178       -0.48274        -24.1            -Inf            Inf         "Curvature of stiffness Kfy"                    
     "PKY5"               0         -27.426        -27.426         -Inf            -Inf            Inf         "Peak stiffness variation with camber squared"  
     "PKY6"         -0.8987         -1.1743       -0.27558         30.7            -Inf            Inf         "Fy camber stiffness factor"                    
     "PKY7"        -0.23303        -0.54366       -0.31063        133.3            -Inf            Inf         "Vertical load dependency of camber stiffness"  
      ⋮

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.

Figure contains 14 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 [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2150, 4320, 5190, 6500. Axes object 2 with title Slip angle [rad] = 0.035; Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2150, 4320, 5180, 6480. Axes object 3 with title Slip angle [rad] = 0.035; Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4300, 5160, 6460. Axes object 4 with title Slip angle [rad] = -0.035; Inclination angle [rad] = 0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4300, 5160, 6460. Axes object 5 with title Slip angle [rad] = -0.035; Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2150, 4310, 5180, 6480. Axes object 6 with title Slip angle [rad] = -0.035; Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2160, 4330, 5200, 6500. Axes object 7 with title Slip angle [rad] = -0.087; Inclination angle [rad] = 0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2150, 4310, 5160, 6470. Axes object 8 with title Slip angle [rad] = -0.087; Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2160, 4330, 5200, 6500. Axes object 9 with title Slip angle [rad] = -0.087; Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2150, 4340, 5200, 6510. Axes object 10 with title Slip angle [rad] = -0.088; Inclination angle [rad] = 0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 3 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 5210, 6500. Axes object 11 with title Slip angle [rad] = -0.088; Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 3 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2190, 5220. Axes object 12 with title Slip angle [rad] = -0.14; Inclination angle [rad] = 0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4320, 5170, 6480. Axes object 13 with title Slip angle [rad] = -0.14; Inclination angle [rad] = 0, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2160, 4330, 5190, 6490. Axes object 14 with title Slip angle [rad] = -0.14; Inclination angle [rad] = -0.105, xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2170, 4350, 5210, 6510.

View the diffTable variable to inspect which variables were optimized.

diffTable
diffTable=7×8 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds                  Parameter Description               
    _________    _____________    ___________    __________    ____________    ____________    ____________    __________________________________________________

     "RBX1"           13.046          26.396         13.35         102.3           -Inf            Inf         "Slope factor for combined slip Fx reduction"     
     "RBX2"            9.718          24.341        14.623         150.5           -Inf            Inf         "Variation of slope Fx reduction with kappa"      
     "RBX3"                0          237.52        237.52           Inf           -Inf            Inf         "Influence of camber on stiffness for Fx combined"
     "RCX1"           0.9995          1.0661      0.066593           6.7           -Inf            Inf         "Shape factor for combined slip Fx reduction"     
     "REX1"          -0.4403         0.14933       0.58963        -133.9           -Inf            Inf         "Curvature factor of combined Fx"                 
     "REX2"          -0.4663       -0.021368       0.44493         -95.4           -Inf            Inf         "Curvature factor of combined Fx with load"       
     "RHX1"       -9.968e-05        0.002952     0.0030516       -3061.4           -Inf            Inf         "Shift factor for combined slip Fx reduction"

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);
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.

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 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4300, 5160, 6460. Axes object 2 with title Inclination angle [rad] = 0, xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4270, 5160, 6460. Axes object 3 with title Inclination angle [rad] = -0.105, xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 5 objects of type line. One or more of the lines displays its values using only markers These objects represent Model behavior, 2140, 4300, 5160, 6450.

View the diffTable variable to inspect which variables were optimized.

diffTable
diffTable=11×8 table
    Parameter    Initial Value    Final Value    Difference    % Difference    Lower Bounds    Upper Bounds                  Parameter Description              
    _________    _____________    ___________    __________    ____________    ____________    ____________    _________________________________________________

     "QSX1"        -0.007764      -0.00036964     0.0073944        -95.2           -Inf            Inf         "Vertical shift of overturning moment"           
     "QSX2"           1.1915           106.04        104.85       8799.6           -Inf            Inf         "Camber induced overturning couple"              
     "QSX3"         0.013948        0.0061915    -0.0077565        -55.6           -Inf            Inf         "Fy induced overturning couple"                  
     "QSX4"            4.912           97.209        92.297         1879           -Inf            Inf         "Mixed load lateral force and camber on Mx"      
     "QSX5"             1.02           1.0939      0.073941          7.2           -Inf            Inf         "Load effect on Mx with lateral force and camber"
     "QSX6"            22.83            639.6        616.77       2701.6           -Inf            Inf         "B-factor of load with Mx"                       
     "QSX7"           0.7104            -8.33       -9.0404      -1272.6           -Inf            Inf         "Camber with load on Mx"                         
     "QSX8"        -0.023393        0.0016263      0.025019         -107           -Inf            Inf         "Lateral force with load on Mx"                  
     "QSX9"           0.6581           3.4757        2.8176        428.1           -Inf            Inf         "B-factor of lateral force with load on Mx"      
     "QSX10"          0.2824           79.587        79.305        28082           -Inf            Inf         "Vertical force with camber on Mx"               
     "QSX11"           5.349        0.0056543       -5.3433        -99.9           -Inf            Inf         "B-factor of vertical force with camber on Mx"

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 80 axes objects and another object of type uitabgroup. Axes object 1 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4320, 5190, 6500. Axes object 2 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4320, 5190, 6500. Axes object 3 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4320, 5190, 6500. Axes object 4 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4320, 5190, 6500. Axes object 5 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4320, 5180, 6480. Axes object 6 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4320, 5180, 6480. Axes object 7 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4320, 5180, 6480. Axes object 8 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4320, 5180, 6480. Axes object 9 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 10 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 11 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 12 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 13 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 14 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 15 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 16 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 17 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4310, 5180, 6480. Axes object 18 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4310, 5180, 6480. Axes object 19 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4310, 5180, 6480. Axes object 20 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4310, 5180, 6480. Axes object 21 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5200, 6500. Axes object 22 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5200, 6500. Axes object 23 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5200, 6500. Axes object 24 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5200, 6500. Axes object 25 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4310, 5160, 6470. Axes object 26 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4310, 5160, 6470. Axes object 27 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4310, 5160, 6470. Axes object 28 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4310, 5160, 6470. Axes object 29 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5200, 6500. Axes object 30 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5200, 6500. Axes object 31 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5200, 6500. Axes object 32 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5200, 6500. Axes object 33 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4340, 5200, 6510. Axes object 34 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4340, 5200, 6510. Axes object 35 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4340, 5200, 6510. Axes object 36 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4340, 5200, 6510. Axes object 37 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 4 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 5210, 6500. Axes object 38 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 4 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 5210, 6500. Axes object 39 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 4 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 5210, 6500. Axes object 40 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 4 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 5210, 6500. Axes object 41 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 4 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2190, 5220. Axes object 42 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 4 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2190, 5220. Axes object 43 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 4 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2190, 5220. Axes object 44 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 4 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2190, 5220. Axes object 45 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4320, 5170, 6480. Axes object 46 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4320, 5170, 6480. Axes object 47 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4320, 5170, 6480. Axes object 48 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4320, 5170, 6480. Axes object 49 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5190, 6490. Axes object 50 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5190, 6490. Axes object 51 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5190, 6490. Axes object 52 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5190, 6490. Axes object 53 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2170, 4350, 5210, 6510. Axes object 54 with title Lateral force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2170, 4350, 5210, 6510. Axes object 55 with title Self-aligning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2170, 4350, 5210, 6510. Axes object 56 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2170, 4350, 5210, 6510. Axes object 57 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5170, 6460. 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 Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5170, 6460. Axes object 61 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4280, 5170, 6460. Axes object 62 with xlabel Longitudinal slip [], ylabel Lateral force [N] contains an object of type text. Axes object 63 with xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains an object of type text. Axes object 64 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4280, 5170, 6460. Axes object 65 with title Longitudinal force [N] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4310, 5170, 6460. Axes object 66 with xlabel Longitudinal slip [], ylabel Lateral force [N] contains an object of type text. Axes object 67 with xlabel Longitudinal slip [], ylabel Self-aligning moment [Nm] contains an object of type text. Axes object 68 with title Overturning moment [Nm] vs Longitudinal slip [], xlabel Longitudinal slip [], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4310, 5170, 6460. Axes object 69 with title Lateral force [N] vs Slip angle [rad], xlabel Slip angle [rad], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 70 with title Self-aligning moment [Nm] vs Slip angle [rad], xlabel Slip angle [rad], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 71 with title Overturning moment [Nm] vs Slip angle [rad], xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6460. Axes object 72 with title Lateral force [N] vs Slip angle [rad], xlabel Slip angle [rad], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4270, 5160, 6460. Axes object 73 with title Self-aligning moment [Nm] vs Slip angle [rad], xlabel Slip angle [rad], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4270, 5160, 6460. Axes object 74 with title Overturning moment [Nm] vs Slip angle [rad], xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4270, 5160, 6460. Axes object 75 with title Lateral force [N] vs Slip angle [rad], xlabel Slip angle [rad], ylabel Lateral force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6450. Axes object 76 with title Self-aligning moment [Nm] vs Slip angle [rad], xlabel Slip angle [rad], ylabel Self-aligning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6450. Axes object 77 with title Overturning moment [Nm] vs Slip angle [rad], xlabel Slip angle [rad], ylabel Overturning moment [Nm] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4300, 5160, 6450. Axes object 78 with title Friction Plot Inclination angle [rad] = 0.105, xlabel Lateral force [N], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2140, 4310, 5180, 6480. Axes object 79 with title Friction Plot Inclination angle [rad] = 0, xlabel Lateral force [N], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2150, 4320, 5190, 6490. Axes object 80 with title Friction Plot Inclination angle [rad] = -0.105, xlabel Lateral force [N], ylabel Longitudinal force [N] contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent New Fitted Model, Magic Formula v6.2, 2160, 4330, 5200, 6490.

See Also

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Get Started with the Extended Tire Features for Vehicle Dynamics Blockset
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