Exploring distance time graphs
Exploring distance time graphs

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Exploring distance time graphs

1.9.5 Video task: Planning specials

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JUDY EKINS
Even if you constructed a perfect timetable, there’s still a potential safety hazard if one train doesn’t run to time. So there’s a tried and tested procedure which overrides the timetable and ensures that only one train can be on any one section of the track. For instance, the single-track journey through Arley to Bewdley can only be undertaken if the driver possesses the relevant physical pass – or ‘token’ – that grants the driver sole permission to travel on that section. On reaching Bewdley, the driver gives up the token by looping it in its holder over the arm of the waiting signalman. The operations superintendent for the railway is John Hill. And on occasions he is also a signalman.
JOHN HILL
Right well, I’ve collected the token off the driver. As you see, this is the Arley–Bewdley North section, and this is the driver’s permission to be on that single-line section. The key token, as you can see, which now goes into the machine. I then tap out the code to the signalman at Arley to tell him the train has arrived here safely; he will acknowledge that. I’ve just tapped out the code for the train that we have waiting here, and, as again you see, I get the token for the Arley–Bewdley North section out, and this will now be given to the driver of the train that’s waiting here, allowing him to proceed up the single line to Arley. [Inaudible conversation between driver and man on platform]
JUDY EKINS
So the railway is operated very safely. But there’s still a need to pay the running costs, and therefore it also has to be commercial. With this in mind Keith Shaw provides the enquiry office with a list of all possible extra slots, which are available for excursions.
PAMELA WESTWOOD
You want to book a special excursion? What time of year? In May, yes. We do a restricted service in May. And you want the dining-car facilities, do you? From Bridgnorth to Kidderminster, there’s a train at 12.10, which arrives in Kidderminster at 1.15, and back from Kidderminster at 2.10, arriving in Bridgnorth at 3.15. We could put that train on for you at those times. Would you like me to send you some details?
JUDY EKINS
How do you identify spare slots for excursions between the regular service? Take that slot for a restaurant-car excursion that was suggested to the telephone caller. This is the timetable in force in May. The service outline here in pink is known as the A timetable North 1. How could a dining excursion be made to mesh with this timetable?
KEITH SHAW
If we wanted to leave Bridgnorth at about 12, we can see that we’d need to cross the service train at Bewdley at 12.55, so a train could leave, and if it was running non-stop, it would of course be a continuous line. Something between 12 and 12.10, the train could run to Bewdley, and in fact, if we got it exactly right, it could pass Bewdley nonstop, whilst the service train was standing there. We’d then need to look and see how we could work that train back to Bridgnorth, and it’s just possible to leave straight away, but in fact the first practical time to leave would be when the following service train gets to Kidderminster there, which from the graph you can see is 1.41. So we could leave, say, at 1.45, and the train could run non-stop to Bridgnorth. It’s got to get there before the 2.35 train departs; otherwise it will interfere with the normal service. This train is run for the benefit of our customers and the person who’s chartering the train, so they would be given some choices as to when they left, and it might be, for example, that they will wish to leave Bridgnorth at about, say, quarter past eleven, when they could cross the service train at Hampton Loade, because that’s another crossing point which is available. The train could leave Hampton Loade, and it then could stop at some attractive viewpoint; it could then join the original path and go on to Kidderminster in the original timetable. That would give a much more leisurely journey, and some of our charterers like that sort of facility.
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Activity: 25 Planning a special

A special train has been booked to take a party from Bridgnorth to Kidderminster. Use your distance-time graph to plan an extra train that will leave Bridgnorth at 11.13 am, cross the service train at Hampton Loade and wait there for 30 minutes. It is then to continue non-stop to Kidderminster, crossing with the service train at Bewdley.

  1. When should the train reach Bewdley?

  2. What should be its average speed between Hampton Loade and Bewdley?

  3. What time should it arrive at Kidderminster, assuming it maintains a constant speed from Hampton Loade?

Discussion

  1. To cross the service train without stopping, it should pass through Bewdley just after AN1 arrives at 12.56 am. Scheduling the cross at 12.57 would leave a little time for AN1 to arrive.

  2. If the train leaves Hampton Loade at 12.00 and passes through Bewdley at 12.57, it will have covered 12.8 km in 57minutes. Its average speed will be (12.8/57)×60=13.5 km per hour.

  3. From the graph or by calculation, the train should reach Kidderminster just after 1.16pm.

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JUDY EKINS
In situations like this, graphs are very useful. But for other purposes a table might be preferable.
JOHN HILL
The peak-season, summer timetable is Table C, with a train departing at every 45 minutes. This is a working timetable, Table C working timetable, showing light-engine movements, passenger-train movements and empty-stock movements. It is impossible to squeeze in another train that runs the whole length of the line from Kidderminster to Bridgnorth, but it is possible to run trains that will be doing shorter distances, for instance, Kidderminster to Bewdley. And to see how this is done, we need to go back to Keith’s graphs.
KEITH SHAW
This is our C Timetable; it’s the maximum possible service at the present time, drawn on a similar basis, using all the crossing points – Bewdley, Arley and Hampton Loade. If we wished to increase the service any further, we would need additional crossing points in between each of the existing ones, for example, at somewhere near Northwood Holt. This would enable us to double the frequency again, but we would need three more crossing points in order to do that.
JUDY EKINS
So what happens if you want to add in a special train to this service?
KEITH SHAW
Well, by definition, because we’ve got the maximum service over the whole line, we can’t add in a further train for the whole line. We could add a train between Bewdley and Kidderminster quite easily, and just about run a train between Bewdley and Arley and vice versa. And there are a number of these slots during the day which we could use.
JUDY EKINS
The long journey time between Bridgnorth and Hampton Loade prevents Keith from devising a more frequent service for the whole line. However, the single journeys from Arley to Bewdley and Bewdley to Kidderminster are shorter, and so it is possible to increase the frequency of the service over this top half of the line. At Christmas this greater flexibility is tested to the full, because the Severn Valley Railway has many thousands of customers queuing up at Kidderminster to make the journey to Arley, where Santa’s grotto is to be found. It’s an essential part of the railway’s effort to balance the books. It’s also very important to the children, and they have limited patience, so the more trains, the better.
SANTA (JOHN HILL)
I see, and have you been good enough to get these presents?
JUDY EKINS
The children’s wishes come first, of course. But finally, what would a railwayman dream of for Christmas?
SANTA
Ho, ho, ho, who’s next for Santa?
KEITH SHAW
Oh, hello, Santa.
SANTA
Oh, hello, Keith. What do you want for Christmas?
KEITH SHAW
Well, I wouldn’t mind a new signal box. Perhaps a coat of paint for the station. But what I’d really like is a passing loop at Northwood; do you think you could fix that?
SANTA
Well, we could have a try for Christmas.
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Figure 58
Figure 58 Position-time graph for two Santa Specials

Activity 26: Timetabling a Santa Special

At Christmas, Santa Special trains run between Kidderminster and Arley. The service runs every 30 minutes, leaving Kidderminster at 15 and 45 minutes past the hour.

Figure 58 shows the position-time graphs of two Santa Special trains. Between these trains two more trains run to complete the service.

Draw in the graph for the train that leaves Kidderminster at 11.15 am. It runs at exactly the same speed as the 10.45 and the 11.45 trains. Trains can cross just outside Kidderminster.

  1. When does it arrive at and depart from Bewdley?

  2. At what time will it reach Arley?

    Draw in the graph for the train that arrives at Kidderminster at 11.46 am.

  3. When does it arrive at and depart from Bewdley?

  4. At what a time does it leave Arley?

  5. Could another service be fitted in so that trains at 15-minute intervals?

Make a few notes to explain how you obtained your answer.

Discussion

Figure 59
Figure 59 Graphs of the Santa Specials

Figure 60 shows the graphs for all the Santa Specials between the given times. Notice that the graph for the 11.15 from Kidderminster is the same as the graph for the 10.45, only shifted along by thirty minutes. Similarly, the 11.46 arrival at Kidderminster has the same graph as the 11.16 arrival, but shifted forward by thirty minutes.

  1. The 11.15 from Kidderminster arrives at Bewdley at 11.25 am, and departs at 11.30 am.

  2. It will arrive at Arley at 11.42 am.

  3. The 11.46 arrival at Kidderminster arrives at Bewdley at 11.29 am and leaves Bewdley at 11.35 am.

  4. It leaves Arley at 11.14 am.

  5. To run a fifteen-minute service, extra trains would have to leave Kidderminster at 11.00am (and 11.30am). But these trains would have to cross the 11.05 (and 11.35) trains from Bewdley. Since there is no crossing place between Bewdley and Kidderminster, the extra trains cannot run.

MU120_3

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