Motomathics

Pacejka

Sine Magic Formula. F = D sin(C arctan(B x − E(B x − arctan(B x)))). Combined slip is similarity, not PAC2002.

Inputs

Fz defaults to a quarter of vehicle weight. Editing B, C, E, or μ marks the curve Custom.

Coefficients

  • B

    Stiffness

    Stretches the curve along slip. Higher B reaches the same peak at less slip.

  • C

    Shape

    C > 1 peaks then drops. Larger C → meaner fall toward sliding force.

  • E

    Curvature

    Rounding at the peak. Near 1 is broad; negative is sharp.

  • μ

    Peak friction

    Scales D. Surface presets write μ together with B, C, E.

  • D

    Peak force

    Result: μ × Fz. Height of the curve. Does not move peak slip.

  • K

    Origin slope

    Result: B C D. Cornering stiffness Cα, N per radian.

Fit order: D from μ and load, C from the slide/peak ratio, K from the small-slip slope, B = K / (C D), E last to round the peak. α and κ set the operating point (gold dot) and the combined-slip σ.

Results

D peak
3,844.2 N
Height of the curve · μ × Fz
K at origin
39,979.8 N
Cornering stiffness · B C D
Slip at peak
13.3°
Where the curve tops · needs C > 1
F at op. point
1,976.6 N
pure Fy(α)
Combined Fx
2,325 N
similarity
Combined Fy
1,863.8 N
σ 0.072

Magic Formula

Slip angle (deg)

Friction ellipse · combined operating point

+Fx+Fy3,8443,844