Banked Curve Angle
Worked example: 25 m/s on a 150 m curve → 23.02° — press Try an example to run it live, then adjust anything.
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Grade 12Grade 12 Physics
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Banked Curve Angle explained
Tilt a roadway and the surface's normal force gains an inward horizontal component; set the tilt so that component alone supplies mv²/r and the turn works even on ice, since mass cancels and tan θ = v²/rg. A 150 m curve designed for 25 m/s needs arctan(625 ⁄ (150 × 9.80665)) ≈ 23°. Railways call the same idea cant, and the maths dates to the 1830s when engineers first had trains fast enough to overturn.
Real tracks push it hard: Daytona banks 31°, Talladega 33°, and Bristol's short oval 28°, letting stock cars corner at speeds friction alone could never hold. The design is speed-specific — go slower than the design speed and the car tends to slide down the bank, go faster and friction has to make up the difference, which is why highway ramps combine a modest 4–8% superelevation with a posted advisory speed rather than relying on banking alone.
Banked Curve Angle formula
- = Bank angle (°)
- = Design speed (m/s)
- = Curve radius (m)
Missing one of these? Work it out first, then come back
- Bank angle — Torque with a Lever Arm (τ = rF sin θ), Angular Velocity (ω = θ/t)
- Design speed — Speed, Distance & Time, Kinetic Energy
- Curve radius — Maximum Speed on a Flat Curve, Centripetal Acceleration (a = v²/r)