A train air brake force model: Locomotive automatic brake valve and brake pipe flow formulations

The goal of this study is to integrate an air brake model with efficient algorithms for train longitudinal force calculation that are based on trajectory coordinate formulations. The air brake model, developed in this investigation and presented in this paper and a companion paper, consists of the locomotive automatic brake valve, air brake pipe and car control unit (CCU). The proposed air brake force model accounts for the effect of the air flow in long train pipes as well as the effect of leakage and branch pipe flows. This model can be used to study the dynamic behavior of the air flow in the train pipe and its effect on the longitudinal train forces during brake application and release. The governing equations of the air pressure flow are developed using the general fluid continuity and momentum equations, simplified using the assumptions of one-dimensional isothermal flow. Using these assumptions, one obtains two coupled air velocity/pressure partial differential equations that depend on time and the...