North American Railroad
Curved Track Speed Equation


Federal Railroad Administration – Track Compliance Manual Chapter 6 (1 January 2002) (330~ kb PDF)
Comparison of Upgrades Needed to Recognize Difference in Curve Speeds (LINK)

The Equation:

Vmax = SQRT[ (Ea + Eu) / (0.0007 * D) ]


Vmax = Maximum allowable operating speed in MPH
Ea = Amount of super-elevation of outside rail over inside rail on a curve in inches. Limited to 6” usually in the US, and often lower to reduce wear on inner rail from heavy freights.
Eu = Unbalanced Elevation in Inches. Restricted to 3” in USA, though up to 7” has been granted to the Acelas by waiver. European systems can have up to 11.8” of this to permit tilting HSR.
D = Degree of curvature in degrees per 100 feet.