Free · Physics models

Ideal Banked Curve and Coordinated Turn

Relate bank angle, radius and speed for friction-limited ground curves or level coordinated flight.

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An unbanked curve of radius 100 meters with friction coefficient 0.7 gives an ideal maximum speed sqrt(686.7), about 26.2 m/s.

Resolve vertical and radial forces; speed²=rg(tanθ±μ)/(1∓μtanθ). A level coordinated turn has radius=v²/(g tanθ).

Enter these known values and leave the other values blank.

Ground modes assume a point vehicle at the friction limit on a uniform bank; flight modes assume a steady, level coordinated turn without wind.
Captured friction presets are illustrative coefficients. Maximum and minimum signs represent opposite limiting friction directions; combinations without a real nonnegative speed are outside the model.
Tire load sensitivity, vehicle rollover, stall margin, wind and transient motion are omitted.
Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.

Ground modes assume a point vehicle at the friction limit on a uniform bank; flight modes assume a steady, level coordinated turn without wind.

Tire load sensitivity, vehicle rollover, stall margin, wind and transient motion are omitted.

Model requirements: Ground curve radius must be positive.