Numerical analysis of freight wagon rolling dynamics on a classification hump

<jats:p>Accurate prediction of freely rolling freight-wagon speed is required to set retarder demand, maintain cut separation, and limit coupling energy in classification yards. This study develops a reproducible one-dimensional model of wagon motion along the first descending section of a classification hump. The governing equation combines the downslope gravitational component, equivalent mechanical resistance, aerodynamic drag based on signed relative air velocity, and rotating-mass inertia expressed through an effective mass. Three modelling levels are compared under identical initial conditions: gravity-only motion, constant mechanical resistance with rotating inertia, and the complete relative-wind formulation. Simulations cover a 60 m section, an initial speed of 0.50 m/s, wagon masses of 68 and 24 t, and track-aligned wind from a 12 m/s headwind to a 12 m/s tailwind. The gravity-only model overpredicts final speed by 7.8–19.7% for the loaded wagon and 3.2–41.3% for the empty wagon. For the loaded wagon, changing from headwind to tailwind raises final speed from 3.869 to 4.295 m/s and reduces travel time from 27.21 to 24.89 s. The time-stepping implementation agrees with the closed-form zero-drag solution to within 0.011%. A complete 24 factorial design identifies wind, gradient, and equivalent resistance as the dominant factors and reveals a substantial wind–mass interaction. A 3,500-run Monte Carlo analysis yields final-speed percentiles of 3.659, 4.074, and 4.403 m/s at P5, P50, and P95, respectively. The model is suitable for preliminary yard assessment and measurement planning; operational use requires yard-specific resistance calibration and independent field validation using separate calibration and validation datasets.</jats:p>