05_Notes on Sign Convention

Sign convention

SAE Tyre Axis System

Adopted from [1]

By steering the front tyres to the left, positive slip angle \(\alpha\) is produced. A lateral tyre force \(F_y \) in the negative y-direction is generated.
Therefore, with SAE convention, lateral tyre force curve \(F_y \) against the slip angle \(\alpha\) range in the 2nd and the 4th quadrants. The tyre cornering stiffness are \(C_F <0\) and \(C_R<0 \).

Pacejka defined the direction of the positive slip angle \(\alpha\) in the opposite direction to SAE, making the cornering stiffness \(C_F >0\) and \(C_R>0 \).

Adopted from [2]

References

[1] W. Milliken and D. Milliken, Race Car Vehicle Dynamics.
[2] H. Pacejka, Tire and Vehicle Dynamics.