Railroad Curve Superelevation, Unbalance, and Maximum Speed

Equilibrium elevation is the bank at which the resultant force sits square in the track and nothing pushes sideways on either rail. Below it the train leans out and loads the high rail; above it, at low speed, it leans in and loads the low rail. Freight railroads deliberately UNDERELEVATE for exactly that reason, because a curve elevated for 60 mph punishes a coal drag moving at 20, and the low-rail wear and the risk of a slow train stringlining are both real. That is why the operating rule is written on UNBALANCE rather than on elevation: actual elevation is set for the mixed traffic that uses the curve, and the maximum speed is whatever that elevation plus the allowed unbalance supports. A 4 degree curve carrying 4 in of actual elevation, with 3 in of allowable unbalance, is good for 50.0 mph. At that speed the curve wants 7.00 in of equilibrium elevation and has 4, so the train runs exactly 3 in underbalanced -- right at the limit. Send a freight through the same curve at 25 mph and the equilibrium elevation is only 1.75 in, so that train is 2.25 in OVER-elevated and leaning onto the low rail. Raise the elevation to 6 in and the passenger limit goes to 56.7 mph while the freight's over-elevation grows to 4.25 in, which is the trade in one line. Actual elevation is commonly capped near 6 in and unbalance near 3 in, and more than that requires specific approval for specific equipment. The classic relation for a circular curve at steady speed, nothing more. It does not design a curve: spiral transition length is what allows elevation to be run in and out and usually governs whether a given elevation is achievable at all, and elevation cannot be applied without adequate spirals. It does not evaluate rail wear, gauge widening, lubrication, or the curving performance of specific equipment, and it does not address vertical curves, curvature combined with grade, or the special rules for yards and turnouts. The FRA Track Safety Standards at 49 CFR 213, the railroad's own engineering instructions and timetable special instructions, and the track owner govern.

equilibrium E = 0.0007 x D x V squared (in, degrees of curve, mph); unbalance = equilibrium - actual; maximum speed = sqrt((actual + allowable unbalance) / (0.0007 x D)); elevation required for a target speed = equilibrium at target - allowable unbalance.

The classic equilibrium-elevation relation for a circular curve at steady speed, by name, with 49 CFR 213 (FRA Track Safety Standards) named as the source of the elevation and unbalance limits. The caps are entered rather than reproduced. The railroad's engineering instructions and timetable special instructions, and the track owner, govern.

49 CFR 213 is US federal regulation and public domain; the elevation relation is standard track engineering arithmetic on the user's own curve.

Estimate. AHJ and licensed professional govern.

Field names used by the API: degree_of_curve, speed_mph, actual_elevation_in, allowable_unbalance_in, max_elevation_in, target_speed_mph, equilibrium_in, unbalance_in, max_speed_mph, required_elevation_in

• The rule is written on unbalance actual elevation serves mixed traffic; speed follows elevation plus the allowed unbalance49 CFR 213
• Caps are entered, not shipped actual elevation commonly capped near 6 in and unbalance near 3 in, with more only by specific approval for specific equipment49 CFR 213 and railroad instructions
• Spirals govern achievability elevation cannot be applied without adequate transition length to run it in and outrailroad engineering instructions