# Mathematics and Railway Signalling

May 19th, 2015
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Railway signalling makes use of a limited number of simple mathematical equations including the equations of motion.One of the requirements of signalling is to keep trains separated so that each train has a length of track in front of it that is clear of other trains, enabling it to brake to rest clear of the train in front.

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Mathematics and Railway SignallingRailway signalling makes use of a limited number of simple mathematical equations including the equations of motion.One of the requirements of signalling is to keep trains separated so that each train has a length of track in front of it that is clear of other trains, enabling it to brake to rest clear of the train in front. This leads to a line capacity issue in the design of the signalling to enable the requisite number of trains to transit the section of the line. The inverse of the number of trains per hour is called the headway. 5 trains per hour, regularly spaced, equates to a headway of 12 minutes. In practice for a specified headway of 12 minutes the signalling would be designed to give a headway of 8 or 9 minutes, to maintain flexibility.The headway is actually defined as the time between following trains such that the second train runs under clear signals (Green). This is illustrated in Figure 1. The lowest section of the figure indicates the lamps that will be illuminated on a signal, as seen by a driver approaching it (from the left). The distances involved start with an approach distance to the first signal to allow fo

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