Wheel/rail dynamics simulation for optimising minimum grade lengths to high-speed railways

Based on the principle of no car vibrations interference when trains pass grade section from the end of front vertical curve to the start of latter vertical curve, using railway wheel/rail simulation NUCARS (TM) software, some dynamics simulation studies for minimum grade lengths on high speed railway lines were made. The dynamics simulation results show that, the minimum tangent lengths between vertical transition curves should be more than 0.43 V in meters (V is speed of train, km/h). So the minimum length is 800 meters when the vertical curve radius is 25000 meters, and 900 meters when radius is 30000 meters for the Chinese Dedicated Passenger Railway lines (PDLs) on which maximum speed is 350 km/h and ruling gradient is 12 parts per thousand.