Simplified Lateral & Longitudinal models

Many well known racing simulation games have based their tyre models on the "Magic Formula" by Hans Pacejka.

The Pacejka formula is an empirical model and can sometimes be an "overkill" for certain types of simulation. Some software houses code their own simplified models depending on the game application, or might employ staff with academic qualifications to implement models with the help of car or tyre manufacturers, to include very realistic tyre wear and temperature effects.

Some of the best simulation games have been: rFactor, Grand Prix Legends, iRacing, GTR 2, Virtual Grand Prix 3, netKar Pro, TORCS, Assetto Corsa. See a table at the end of the page with physics model comparisons.

One of the simplified models is explained by Brian Beckman in his Physics of Racing articles. He jokingly called it the "Magic Trick Formula". It yields good results when implemented in Excel and Simulink.

Please follow the link for the Car-In-Excel Simplified Tyre Model.

The following parameters have been implemented to match up with tyre data supplied by Avon for its small single seater tyre range. Note that the definition of longitudinal and lateral slip is different, hence why the coefficients are not so similar.

Fz: vertical force (Newtons), 0 to 5000 N typically

s: slip (parts per one), -1 to +1

Coefficient 1 = 31

Coefficient 2 = 1

Coefficient 3 = 9.625

Coefficient 4 = 2.375

Fz: vertical force (Newtons), 0 to 5000 N typically

s: slip (degrees), -20 to +20 typically

Coefficient 1 = 0.13

Coefficient 2 = 0.3

Coefficient 3 = 0.07

Coefficient 4 = 1.6

Below are the results of the formulae described above, for longitudinal and lateral data, validated against data from the Avon rig on a Formula 3000 front and rear tyre.

Below is a comparison of various physics aspects for some successful racing simulation games.