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
Stiffness
Stretches the curve along slip. Higher B reaches the same peak at less slip.
Shape
C > 1 peaks then drops. Larger C → meaner fall toward sliding force.
Curvature
Rounding at the peak. Near 1 is broad; negative is sharp.
Peak friction
Scales D. Surface presets write μ together with B, C, E.
Peak force
Result: μ × Fz. Height of the curve. Does not move peak slip.
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
Magic Formula
Slip angle (deg)
Friction ellipse · combined operating point