Exploring distance time graphs

1.9.1 Introduction

The main aim of this section is to show an application of distance-time graphs in the operation of a railway service.

You will need graph paper for this section.

This section uses the video ‘Single track minders? to illustrate how distance-time graphs are drawn and interpreted by the timetable planners of a small railway company, and shows the role of this graphical technique in planning a flexible service. Graphical representations of journeys have been used for over a century by travel organisations to plan timetables.Figure 52 shows a graphic produced by the Frenchman E. J. Marey in 1885 showing the schedule for trains between Paris and Lyon. The stations are listed along the vertical axis and are separated in proportion to their actual distance apart. The horizontal axis shows a time span of 24 hours from 6 am through midday (midi), midnight (minuit) until 6 am the following morning. Each sloping line represents a scheduled train, with the slope of the line representing the train?s average speed. The faster the train, the steeper the line is. The horizontal lines indicate the time the train is stopped at a station.

Trains travelling away from Paris are indicated by lines with negative slopes, and those travelling towards Paris by lines with positive slopes. The intersection of two lines indicates that two trains travelling in opposite directions are at the same place at the same time; these are the locations at which trains pass each other.

Marey?s graph shows clearly how important the Paris-Lyon route was, even in the 1880s, with eight trains leaving Paris every day. Even a fast train, however, took over nine hours to make the journey. By comparison Figure 53 shows the path of the modern high-speed TGV (Train à Grande Vitesse)service overlaid on the original 1880s schedule. The TGV makes the journey in under three hours. These distance-time graphs make a powerful statement of the continuing national importance of the Paris-Lyon link.

Distance-time graphs and timetables used to be drawn up by hand. Now computers do the detailed work associated with scheduling in large-scale public transport systems. However, distance-time graphs still find a place in planning and operating smaller services.

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