Magic Formula Tyre Tool

version 1.3.6 (27 MB) by Tom Teasdale
MATLAB GUI for Magic Formula Tyre Modeling


Updated Sun, 18 Sep 2022 13:27:54 +0000

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Magic Formula Tyre Tool

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Screenshot Analysis Tab with Plots

  • Interactively fit Magic Formula tyre models to data
  • Automatically separate timeseries data into steady-state conditions
  • Compare model outputs visually against data
  • Load/Save models from/to .tir (Tyre Property File)
  • Export fitted models parameters as struct

This project uses the model functions provided by the Magic Formula Tyre Library. You can export the model parameters to use with said library to simulate tyre behavior in MATLAB or create models suitable for code-generation in Simulink.


This project originates in my work as a Formula Student member of UPBracing, where we required computationally efficient but precise tire models suitable for code-generation. Especially students in Formula Student / Formula SAE who want to model their tires for control and estimation algorithms or simply for the purpose of better understanding might benefit from this tool.

This project would not have been possible without the data provided by the Formula SAE Tire Test Consortium (FSAE TTC) and the Calspan Tire Testing Research Facility (TIRF). De-identified and obscured test data has been used in examples and images or recordings of the application, to conform to the license agreement. Special thanks to Dr. Edward M. Kasprzak for granting me permission to provide the used, de-identified and obscured data for demonstration purposes.


  • MATLAB Base (tested with R2021a)
  • Optimization Toolbox (for fitting)
  • Signal Processing Toolbox (for raw measurement import)


There are several ways:


The core workflows are summarized in this flowchart:

flowchart TD
  InputData[/Raw Test-Bench Data/];
  ParseData[Parse Measurements using\npredefined or custom Parser];
  ExtSim[Third-Party Simulation];
  Plot[Plot Model vs. Data\nto verify good fit];
  Fit[Fit Model to Data];
  MatSim[MATLAB Simulation];

  Start --> InputData;
  InputData --> |.mat / .csv / ...| ParseData;
  subgraph tool[ ]
    DecideNewOrLoad{Base Model\navailable?}
    NewMdl[Create New\nTyre model];
    LoadMdl[Load from\n.tir file];
    ParseData --> DecideNewOrLoad;
    DecideNewOrLoad --> |no| NewMdl;
    DecideNewOrLoad --> |yes| LoadMdl;
    NewMdl --> Fit;
    LoadMdl --> Fit;
    Fit --> Plot
  Plot --> Out1;
  Plot --> |struct| Out2;
  Out1 --> ExtSim;
  Out2 --> MatSim;
  ExtSim --> End
  MatSim --> End;

Import Test-Bench Data

To import test-bench data, you might have to create a custom parser which takes and arbitrary input file and converts it into an array of tydex.Measurement objects. Each measurement object contains data for only one steady-state condition. This means that only one variable is sweeped (= transient). In case of Formula SAE Tire Test Consortium Data, two parsers for Cornering and Drive/Brake MAT files in SI-units are already available.

Animation Data Import

Fit Model to Data

You can interactively fit your Magic Formula tire model to measured test-bench data. Interactively means, you can cancel the fitting process at any point. The last iteration will be saved and you can compare the fitted values to the current model values in a table. You can then choose to append these values to your model.

Animation Fitting

Animation Fitting

Manual Model Editing

You can manually edit the model values in the table. When using the Auto-Refresh feature, the plot updates automatically to reflect your changes. This helps to get an intuition on the effects of different parameter values.

Animation Manual Editing

Plot Model against Data

To make sure the fitting process yields a plausible result, you can compare the test-bench data to your fitted model. If the import process of the measurements worked correctly, you will be able to select steady-state values from the dropdowns and thereby filter the data. The Magic Formula tire model will then be supplied with the measured inputs for an exact comparison.

Animation Plotting

Known Issues

  • Currently only Fitting of Fx0, Fy0, Fx, Fy is supported
  • Only Magic Formula version 6.1.2 (62) is supported.
  • The FSAE TTC parsers might not always work. You might have to create your own parser.

Cite As

Tom Teasdale (2022). Magic Formula Tyre Tool (, GitHub. Retrieved .

MATLAB Release Compatibility
Created with R2021a
Compatible with R2021a and later releases
Platform Compatibility
Windows macOS Linux

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To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.