MTB Tire Dynamics — Pacejka & FastBike Model

MTB Tire Dynamics Simulator

Pacejka Magic Tire Formula · FastBike Twisting Torque Polynomial

Dressel, A.; Sadauckas, J.

RESEARCH INTERACTIVE

Pick two presets Editing any slider returns to manual comparison

A → — B → —

Tire Configuration

Wheel Diameter

* 32" extrapolated beyond tested sizes

Nominal Tire Width2.35"

1.9"2.6"

Internal Rim Width25 mm

19 mm40 mm

Wider rim → squarer profile → wider contact

Tread Knob Level

Higher knobs: ↓ CS, ↓ μ, ↓ effective contact area

Loading Conditions

Inflation Pressure30 psi

15 psi50 psi

Normal Load F_z500 N

200 N1000 N

Camber Angle γ0°

−25°+25°

Pacejka B·C·D·E Coefficients

B — Stiffness

—

C — Shape

—

D — Peak (N)

—

E — Curvature

—

BCD (N/rad)

—

α_peak

—

FastBike Poly Coefficients

t₀ (trail m)

—

B_t

—

c₀ (offset)

—

c₁ (linear)

—

Derived Outputs

Eff. Width

—

Contact Area

—

Patch L × W

—

Peak F_y

—

Peak |M_z|

—

μ_y

—

CS (N/°)

—

Vert. Stiff.

—

Model Equations

Pacejka Lateral Force

Fy = D·sin(C·atan(B·α'−E·(B·α'−atan(B·α'))))

α' = α + SHy (camber shift)

FastBike M_z

Mz = −t(α)·Fy + c₀+c₁α+c₂α²

t(α) = t₀·cos(C_t·atan(B_t·α))

Pneumatic trail + poly residual

Lateral Force F_y vs Slip Angle α

Pacejka Magic Formula — current vs slick ref overlay

FIG. 6

Self-Aligning Moment M_z vs Slip Angle α

FastBike polynomial + pneumatic trail

FIG. 6

Contact Patch Footprint

Pressure, load & rim-width dependent — fixed mm scale

FIG. 5

Side by side Overlaid 0%

Pressure Sensitivity — F_y Envelope

Fy at p = 20·25·30·35·40 psi — current highlighted

FIG. 3