The ballast pick-up problem in high speed trains

Abstract

When a high speed train overpasses a critical speed produces a wind speed close to the track large enough to start the motion of the ballast elements, eventually leading to the rolling of the stones and, if they get enough energy, they can jump and then initiate a saltation-like chain reaction. In this contribution a mathematical model of the initiation of the motion is presented. The dynamics of the stone is formulated taking into account both gravity and aerodynamic forces. These aerodynamic forces are the result of the train-generated-gust impinging on the stones. Although they are intrinsically non steady, under some conditions a cuasi-steady aerodynamic model can be employed. Conditions for the start of the motion are obtained in terms of the Tachikawa number (a kind of Froude number). The aerodynamic characteristics are included in terms of the zero aerodynamic moment line of the stone, and the aerodynamic moment coefficient.