Capstan law motion planning in funicular railways

An algorithm to compute suitable laws of motion for the capstan of funicular railways is presented. The aim is to reduce, by these computed capstan laws of motion, the car oscillations that occur during the start stop transients. By the proposed algorithm, once the mathematical model and the equation of motion are defined, the desired car's law is imposed and the equations are solved, computing the law of motion of the capstan and then the law of motion of the other car. A computed example is given by considering the data of an existing funicular railway. These first computed results show that the railroad car's oscillations, that occur during the start and stop transients, can be significantly reduced in some operating conditions. A very simple braking law has been tested: it was supposed a constant deceleration within 12 seconds; it could be possible that, by adopting more suitable deceleration laws, better results can be achieved in all operating conditions.