User:Anothersignalman/Railway Dynamics

This page stores various math functions for rail vehicle runtime estimates.

MACLINE estimates of speed at 100m intervals

$V^{2}=U^{2}+KS({\frac {P}{UM}}-{\frac {g}{G}}-A-BU-CU^{2})$

• V = Final speed (m/s)
• U = Initial speed (m/s)
• S = Distance (m)
• P = Power-at-rail for speed U (kW)
• M = Train mass (t)
• g = 9.8m/s²
• G = Compensated grade (1 in G, +ve=uphill / -ve=downhill)
• A, B & C = rolling resistance coefficients, assume 0.01, 0.0005, 0.00002.

Rolling resistance of trailing vehicles

$RR={\frac {3600GD-9800MS}{GMS}}$

• RR = rolling resistance (N/t)
• G = Grade
• D = Drawbar (kW)
• M = Trailing mass (t)
• S = Speed (km/h)