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version 4.0.0 (4.47 MB) by Marco Furlan
Contains the necessary functions to evaluate Magic Formula 5.2, 6.1 and 6.2 models from .tir files


Updated 17 Mar 2020

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MFeval (Magic Formula evaluation) has been created to provide a robust way to evaluate Magic Formul tyre models.
The toolbox contains the function with the same name (mfeval.m) used to evaluate tyre property files with the Magic Formula 5.2, 6.1 or 6.2 equations. A tyre property file (.tir) contains the magic formula parameters that define the tyre's force and moment characteristics.

Cite As

Marco Furlan (2020). MFeval (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (42)

Very nice package!


Thanks a lot for your sharing.

Firstly, thank you for providing this library; it is extremely useful. However, when I use the library in a iterator subsystem I get multiple errors due to the continuous formulation of the library (e.g. iterators need to be changed for sample time reasons, computation errors that need to be fixed with delays etc). Even though I did manage to do changes in order to make it work, the results are not the best. I would like to ask if there is a guideline for us to use in order to make it compatible with iterative subsystems?

MFeval offers the same functionality as other paid-for models but is open source with good documentation and support from the author. Take the time to learn how to implement MFeval into your project and have fun!!!

Biome Zhao

Great tool! Gracias Marco


Yize Yu

wenquan hao


Marco Furlan

Hi Mikhail,

Thanks for your comment, and for contributing to the development of MFeval.

You are right. In the line 1580:

% Evaluate Gyk with gamma = 0 and phit = 0
[~,Gyk_sub0] = obj.calculateFy(..., Fyo, muy)

I pass the vectors "Fyo" and "muy" that include camber effects, so technically is not correct. However, "Fyo" and "muy" are not used to calculate "Gyk_sub0" so the result is not affected by this typo.

Even though the result will be the same, I will change the order to evaluate "Fyo_sub0" before "Gyk_sub0" to pass the right inputs (Fyo_sub0 and muy_sub0) and to make it easier to understand.


Hi Marco. You done very useful job. Thank you so much. I have a question:
In Solver61.m. when calculating Mz:

% Evaluate Gyk with gamma = 0 and phit = 0
[~,Gyk_sub0] = obj.calculateFy(tirParams, postProInputs_sub0, internalParams_sub0, modes, starVar, incrVar, Fyo, muy);

gamma is included in Fyo and muy, but when you calculate Fyo and muy you don't set gamma in zero. It is right?

Marco Furlan

Release notes - Version 2.2.0:

◾ Road position implemented in STI
◾ Road velocity implemented in STI
◾ Some MATLAB Function blocks have been replaced with inbuilt Simulink blocks
◾ The switch case to select the dynamics mode in CPI is done upstream to avoid unnecessary calculations
◾ The passband frequency of the low pass filters has been increased to 100 Hz
◾ Simulink library names updated. This will brake the links from old models and needs to be updated

Raúl Peña

Marco Furlan

Hi Thomas,
Since version 2.0 mfeval is written in Object Oriented. The function readTIR is now a method of mfeval and should be called as:

params = mfeval.readTIR('ExampleFile.tir');


Thomas Dunn

I am getting an 'unexpected MATLAB expression' when trying to run the readTIR script. Do you know why this might be the case? The first line of readTIR.m is below, showing what I tried.

function tirParams = readTIR('front.tir')


I use this tool for its import feature to my own scripts, which works well and is really easy to use!

zhao px

Ronit Saha


very help thanks

Carlos Rayo

Nice job Marco, very helpful!

Marco Furlan

Hello Gustavo,
Sorry for the delay, but I don't receive a notification when a new comment is posted here.
Modelling is a hard and complex task. First of all you will need good quality tyre data. This data is difficult and expensive to obtain. The data can be measured with a roller drum bench, with a flat belt machine (like Calspan TIRF), with a test trailer (like TNO) or with a wheel force transducer mounted in a real car.
It's very probable that you will have to post-process and crop somehow the data. E.g. separate FreeRolling tests to fit pure lateral Fy, Mz and Mx; use BrakeDrive data to fit Fx and combined forces and moments; use the Spring Rate tests to fit the loaded radius model, etc. You should basically use the right data for the right equation.
Once you are happy with the data you can use a MATLAB fitting function like lsqnonlin to find the correct MF6.1 parameters for your model (or TIR file).
x = lsqnonlin(fun,x0)
Where "x" are your optimized parameters packed in a structure and "fun" is your cost function. Your cost function should calculate the error of the model vs the data. For example error = FYmodel – Fydata (use mfeval in your cost function to calculate FYmodel)
You should later plot your model against the data to see if you have a good fitting. Check if the model is stable in all the operating conditions. It can happen that the operating conditions in your simulation are outside of the tested range, so be sure that the model is able to extrapolate in a stable way.

Finally remember that it’s important to follow a certain order when you are fitting a full Magic Formula model. For example, you can’t fit the Fy combined parameters before the Fy pure parameters.

This is a vague overview of the process, hope it helps.

Hi Marco,
Firstly I would like to congratulate you for the amazing job done
Do you have some tips to find all the Magic Formula coefficients so that I can create the TIR file?

Hi Marco,
thank you. I already worked with that paper, but couldn't make any progress on Mz with it. I'll inform you if we do!

Marco Furlan

Hi Jochen,
I'm still working on the turn slip model, in particular on parking efforts at very low speeds.
I haven't been able to reproduce TNO results yet, but I suggest you to read the following paper:

Lugaro, C., Schmeitz, A., Ogawa, T., Murakami, T. et al., "Development of a Parameter Identification Method for MF-Tyre/ MF-Swift Applied to Parking and Low Speed Manoeuvres," SAE Int. J. Passeng. Cars - Mech. Syst. 9(2):2016, doi:10.4271/2016-01-1645.

Hope it helps, as soon as I can validate parking efforts I will publish MFeval 1.5.
If you find something interesting I would be very interested to know.

Best regards,

Hi Marco, great tool! Thank you for publishing. I am working in a MF6.2 tool to parameterize tires with measurements, done on our inner drum test bench at the KIT. I also got issues with the Turnslip of Mz. Did you make any progress on that topic?

Remember to type "help mfeval" in the command window to see the documentation and learn how to use it.

Very Helpful.Thanks.

Thanks for sharing this amazing work!
With your approval, I will use it in my Bachelor Tesis developed with Adams Car (Formula Student model)



MF-Tyre 5.2 equations have been implemented for backward compatibility


MF-Tyre 6.2 equations have been implemented. In 6.2 the loaded radius model is improved with camber dependencies. See the documentation for more information


Slip stiffness (Kxk) is now output number 30
In STI vertical damping forces only actuate if the tire is in contact with the road
In STI the Slip Angle calculation has been updated to use the transformation matrix


Road friction can be passed as input to STI and CPI interfaces
Unnecessary zero crossing detection have been disabled
Fx and Fy filters moved to reside inside Switch dynamics mode
In Mz calculation, Gyk_sub0 is now calculated after Fyo_sub0


Road position implemented in STI
Road velocity implemented in STI
Some MATLAB Function blocks have been replaced with inbuilt Simulink blocks
The switch case to select the dynamics mode in CPI is done upstream to avoid unnecessary calculations


◾ Simulink Library updated to work with variable solvers.
◾ Simulink memory blocks have been replaced with low pass filters with a pass band frequency of 15 Hz
◾ coefficientCheck inputs have been updated to be compatible with MFit


Simulink Library updated to be more robust and consistent (STI interface depends on CPI interface)
All Simulink blocks and demos are saved in MATLAB 2017b
Advance user guide completed: including a demo showing how to fit a model

MATLAB Release Compatibility
Created with R2017b
Compatible with R2017b to any release
Platform Compatibility
Windows macOS Linux