December 5, 2016

Calibration of Pacejka’s "Magic Formula"

Industry: Automotive | Product: pSeven Core | Company: Force India Formula 1 Team


Pacejka’s “Magic Formula” relates forces acting on the tire to the tire’s kinematic characteristics. This expression contains a large number of coefficients, and for the formula to give useful predictions, the coefficients must be fitted (calibrated) using track data. The customer used to fit the coefficients with a workflow that involved a standard optimization algorithm applied to an Excel implementation of the Magic Formula. The calibration process used to take the impractically long time of 24 hours. The objective was to reduce this time to 1 hour.

Tyre model

Tyre test rig


DATADVANCE examined and optimized the customer’s fitting process:

  • Calibration was entirely performed in the more efficient pSeven Core environment
  • The original Excel implementation of Magic Formula was identified as a bottleneck and replaced with a fast C++ implementation
  • The original optimization algorithm was replaced with pSeven Core Generic Tool for Optimization


In the context of Formula 1 races, the accelerated calibration makes it possible to almost immediately assess the driving conditions and thus better prepare the vehicle for the race and to control it during the race.

Final 01

Final 02


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