The "Magic Formula"

Historically the MF was developed as a model for road car tyres based on the idea that a combination of sine and arctan curves could represent the lateral force characteristics of a tyre. Over the years further coefficients have been added to model the tyre’s longitudinal and combined characteristics as well as it’s self aligning torque.
Due to the nature of the curves, it is not always possible to achieve a good fit to the stability rig racing tyre data. For this reason the degree of confidence range is normally also given with the coefficients.

The "Magic Formula" - White-Smoke

The actual curves will normally have offsets that arise from adding camber or physical features such as conicity and ply steer. For the longitudinal force this is due to rolling resistance.

The "Magic Formula" - White-Smoke

Typical tyre characteristics for longitudinal and lateral forces as well as self-aligning torque are shown in the charts.

The "Magic Formula" - White-SmokeThe "Magic Formula" - White-Smoke

Longitudinal Force as a Function of Longitudinal Slip Lateral Force and S.A.T. as a Function of Slip Angle

• Fx as a function of the longitudinal slip ratio k
• Fy as a function of the slip angle a
• Mz as a function of the slip angle a

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