Applications of Mathematics-

Project Brief

The Liverpool City Region has announced a plan for £1 billion of new investment in the Merseyrail system of trains over the next 20 years. This money will be spent on new rolling stock and upgrading the rolling stock, track and signalling on the existing network.

As well as this, the Liverpool City Region and Merseyrail are looking to expand the network to bring better transport links to the region, including reducing congestion on the regions roads and improve the economic outlook of a number of small towns within the area.

You have been approached by the Liverpool City Region to complete a feasibility design for the expansion of the railway network.

Merseyrail wishes to extend the line around the centre of Liverpool, as a significant amount of the area (shown below with current stations highlighted) is without a railway link.

Suggestions

You should consider several things about the new route:

• Where should the extension serve?
• How many stations are suitable?
• Where should the stations be located?
• Which stations are routes would best meet the Liverpool City Region objectives of economic improvement, improved transport links, reduced congestion.
• How will the methods of construction affect the design?
• What is the environmental impact?
• How expensive is the route(s)?
• How efficient will the service be?
• Any other important factors to consider?

Design Calculations

Your project submission will include a map with the stations you wish to add clearly marked, and your final route between them shown clearly. The map you can use is on the VLE. So your first decision is where to put the new stations and what the route will be.

However, when deciding on where the stations will go, you need to take the Horizontal Alignment into consideration.

Horizontal Alignment

The horizontal alignment is the route taken on the plan. The horizontal alignment should consider where the railway should serve and the route between stations. It is important to ensure that any curves in the track can be navigated by the rolling stock. To do this any curves must be greater than 500m radius.

The horizontal alignment must be shown on your map - drawn to scale - and coordinates recorded on your design spreadsheet. The calculation can be worked out by using Pythagoras and Arc Length, which is covered in Lesson 7.1.

Construction Method

You also need to calculate how long it will take to build the project. Use the table below to calculate the construction programme (method). You can do several tasks at once, but the more people you use, the higher the overall costs.

You need to submit a proper list of the construction programme time as part of your work.

Bill of Quantities

The Bill of Quantities is a detailed statement on work, price and other information leading to an estimate how much your project will cost to construct. You should fill in and submit the below table for your project.

Environmental Impact Statement

Once you have designed your route, you will need to consider the impact your design will have on the environment. For your design, you will submit a written report (between 500 and 1,500 words) explaining the impact your design has on the environment and the features of your design that you have included to mitigate this impact.

Viva

The Viva takes place after submission of the project and you will be asked questions about the decisions made, and to explain sections of your work. This is your chance to show the project in more detail and really describe your decisions in detail.

Submission - You will submit

• One A4 printed map, indicating your additional stations and route of track between them.
• Detailed mathematics showing the calculations provided for your Horizontal Alignment
• Spreadsheet (printed) detailing the amount of time it will take to construct your design.
• Spreadsheet (printed) detailing how much your route will cost to produce.
• Written report indicating the impact of your design.

Attachment:- Assignment.rar