Railway Civil Engineering, High-Speed Track Alignment & EN 13803
Railway Equilibrium Cant, Cant Deficiency & Curve Speed Formula
Calculate Standard-Gauge Railway Equilibrium Cant (11.8 * V_kmh^2) / R_m, Uncompensated Cant Deficiency I (mm), Passenger Lateral Acceleration (I / 1500)*9.81, and Maximum Permitted Curve Speed.
Balance fast passenger trains and slow heavy freight on shared-corridor railway curves!
On standard-gauge railway track (1,435 mm rail gauge; ~1,500 mm railhead contact-center spacing), raising the outer rail by Equilibrium Cant E_eq = (11.8 * V_kmh^2) / R_m (in mm) cancels 100% of lateral centrifugal acceleration at speed V! However, tracks cannot install 250+ mm of cant because stopped or slow heavy freight trains would overload the inner rail ("cant excess")! Track engineers therefore install moderate physical cant E_inst (e.g., 110 mm) and allow passenger trains to run with controlled Cant Deficiency I = E_eq - E_inst, exposing passengers to Unbalanced Track-Plane Lateral Acceleration a_lat = (I / 1500) * 9.81 m/s^2 and setting Maximum Permitted Curve Speed V_max = SQRT(((E_inst + I_max) * R_m) / 11.8)!
Verify on a Mixed-Traffic Intercity Curve—Passenger_Speed V = 160 km/h (B2), Curve_Radius R = 1,600 m (B3), Installed_Outer_Rail_Cant E_inst = 110 mm (B4), and Conventional_Cant_Deficiency_Limit I_max = 100 mm (B5): Equilibrium Cant is (11.8 * 25,600) / 1,600 = 188.80 mm (E2); Operating Cant Deficiency is 188.80 - 110.00 = 78.80 mm (E3); Unbalanced Lateral Acceleration is (78.80 / 1,500) * 9.81 = 0.5154 m/s^2 (E4); and Maximum Permitted Conventional Speed on this curve is SQRT(((110 + 100) * 1,600) / 11.8) = 168.74 km/h (E5)!
| EN 13803 Track Curve Metric (V=160 km/h, R=1,600 m, Cant=110 mm, Imax=100 mm) | Formula | Verified Output |
|---|---|---|
| Equilibrium Cant E_eq (mm) | (11.8 * Speed_kmh^2) / Radius_m | 188.80 mm |
| Operating Cant Deficiency I (mm) | Equilibrium_Cant - Installed_Cant | 78.80 mm |
| Unbalanced Lateral Accel (m/s^2) | (Cant_Deficiency / 1500) * 9.81 | 0.5154 m/s^2 |
| Max Permitted Speed V_max (km/h) | SQRT(((Cant + I_max) * R_m) / 11.8) | 168.74 km/h (213.13 @ Tilting) |
Maximum Permitted Railway Curve Speed Formula
Validate Train_Speed > 0, Curve_Radius >= 100 m, Installed_Cant in [0, 200] mm, and Max_Deficiency I_max in [0, 300] mm!
=LET(v_tr, B2, rd_m, B3, cn_i, B4, df_m, B5, IF(OR(v_tr <= 0, rd_m < 100, cn_i < 0, cn_i > 200, df_m < 0, df_m > 300, cn_i + df_m <= 0), "Invalid Railway Curve Input", ROUND(SQRT(((cn_i + df_m) * rd_m) / 11.8), 2)))Active-Tilting Pendolino Rolling-Stock Upgrade Check (Set I_max = 225 mm)
Deploy active-tilting passenger trainsets certified for B5 = 225 mm cant deficiency without Relaying a single meter of track: Max Permitted Curve Speed E5 jumps from 168.74 km/h to 213.13 km/h!
=IF(ISTEXT(E5), E5, ROUND((E3 / 1500) * 9.81, 4))Try the example
Use the original values or change them to test your understanding.