A Study of Three Tunnel Designs

Calculation of the amount of concreate needed to fill shaded part in each diagram

DESIGN 1:

Figure 1: Tunnel design 1

Solution:

DESIGN 2

Figure 2: Design 2

Solution:

DESIGN 3

Figure 3: Design 3

Solution:

The required cost to construct each tunnel with considering that the cost of 1 m3

of concrete is £120.

DESIGN 1

DESIGN 2

DESIGN 3

In selecting the best type of tunnel to construct a number of factors must be considered first. These are: the general concept of the existing preliminary design, studying the location geology, vertical alignment selection, presenting different tunnel arrangements and constructions, defining tunnel cross section, setting plans for ventilation and emergency shafts and finally conducting a cost estimation. Therefore the tunnel that is chosen should be the one that strike a balance between all the factors stated above. From the three designs given tunnel 2 is the most expensive to construct while tunnels 2 and 3 cost almost the price to construct. However, we chose tunnel 3 because this design has two tunnels, it is less costly to construct and has a relatively wider.

REFERENCE:

PIARC Committee on Road Tunnels (1995b): Road Safety in Road Tunnels.

Stork-Moore, I., Charters, D.: The Development of a Fire Safety Strategy for Fire Safety in Tunnels, Australian Underground Construction and Tunneling Association.

PROBLEM 2

a. Timetable for both departure time and arrival time for trains from London to Birmingham and from Birmingham to London.

TRAINS FROM BIRMINGHAM TO LONDON

From

To

Train No.

Departure

Arrival

Empty

Clean

Ticket Check

BIRNINGHAM

LONDON

A

7:00

7:49

7:55

8:07

8:26

BIRNINGHAM

LONDON

B

7:20

8:09

8:15

8:27

8:46

BIRNINGHAM

LONDON

C

7:40

8:29

8:35

8:47

9:06

BIRNINGHAM

LONDON

D

8:00

8:49

8:55

9:07

9:26

BIRNINGHAM

LONDON

E

8:20

9:09

9:15

9:27

9:46

BIRNINGHAM

LONDON

F

8:40

9:29

9:35

9:47

10:06

BIRNINGHAM

LONDON

G

9:00

9:49

9:55

10:07

10:26

BIRNINGHAM

LONDON

H

9:20

10:09

10:15

10:27

10:46

BIRNINGHAM

LONDON

I

9:40

10:29

10:35

10:47

11:06

BIRNINGHAM

LONDON

A

10:00

10:49

10:55

11:07

11:26

BIRNINGHAM

LONDON

B

10:20

11:09

11:15

11:27

11:46

BIRNINGHAM

LONDON

C

10:40

11:29

11:35

11:47

12:06

BIRNINGHAM

LONDON

D

11:00

11:49

11:55

12:07

12:26

BIRNINGHAM

LONDON

E

11:20

12:09

12:15

12:27

12:46

BIRNINGHAM

LONDON

F

11:40

12:29

12:35

12:47

13:06

BIRNINGHAM

LONDON

G

12:00

12:49

12:55

13:07

13:26

BIRNINGHAM

LONDON

H

12:20

13:09

13:15

13:27

13:46

BIRNINGHAM

LONDON

I

12:40

13:29

13:35

13:47

14:06

BIRNINGHAM

LONDON

A

13:00

13:49

13:55

14:07

14:26

BIRNINGHAM

LONDON

B

13:20

14:09

14:15

14:27

14:46

BIRNINGHAM

LONDON

C

13:40

14:29

14:35

14:47

15:06

BIRNINGHAM

LONDON

D

14:00

14:49

14:55

15:07

15:26

BIRNINGHAM

LONDON

E

14:20

15:09

15:15

15:27

15:46

BIRNINGHAM

LONDON

F

14:40

15:29

15:35

15:47

16:06

BIRNINGHAM

LONDON

G

15:00

15:49

15:55

16:07

16:26

BIRNINGHAM

LONDON

H

15:20

16:09

16:15

16:27

16:46

BIRNINGHAM

LONDON

I

15:40

16:29

16:35

16:47

17:06

BIRNINGHAM

LONDON

A

16:00

16:49

16:55

17:07

17:26

BIRNINGHAM

LONDON

B

16:20

17:09

17:15

17:27

17:46

BIRNINGHAM

LONDON

C

16:40

17:29

17:35

17:47

18:06

BIRNINGHAM

LONDON

D

17:00

17:49

17:55

18:07

18:26

BIRNINGHAM

LONDON

E

17:20

18:09

18:15

18:27

18:46

BIRNINGHAM

LONDON

F

17:40

18:29

18:35

18:47

19:06

BIRNINGHAM

LONDON

G

18:00

18:49

18:55

19:07

19:26

BIRNINGHAM

LONDON

H

18:20

19:09

19:15

19:27

19:46

BIRNINGHAM

LONDON

I

18:40

19:29

19:35

19:47

20:06

BIRNINGHAM

LONDON

A

19:00

19:49

19:55

20:07

20:26

BIRNINGHAM

LONDON

B

19:20

20:09

20:15

20:27

20:46

BIRNINGHAM

LONDON

C

19:40

20:29

20:35

20:47

21:06

BIRNINGHAM

LONDON

D

20:00

20:49

20:55

21:07

21:26

BIRNINGHAM

LONDON

E

20:20

21:09

21:15

21:27

21:46

BIRNINGHAM

LONDON

F

20:40

21:29

21:35

21:47

-

BIRNINGHAM

LONDON

G

21:00

21:49

21:55

22:07

-

BIRNINGHAM

LONDON

H

21:20

22:09

22:15

22:27

-

BIRNINGHAM

LONDON

I

21:40

22:29

22:35

22:47

-

BIRNINGHAM

LONDON

A

22:00

22:49

22:55

23:07

-

TRAIN FROM LONDOM TO BIRMINGHAM

From

To

Train No.

Departure

Arrival

Empty

Clean

Ticket Check

LONDON

BIRMINGHAM 

I

7:10

7:59

8:05

8:17

8:36

LONDON

BIRMINGHAM 

H

7:30

8:19

8:25

8:37

8:56

LONDON

BIRMINGHAM 

G

7:50

8:39

8:45

8:57

9:16

LONDON

BIRMINGHAM 

F

8:10

8:59

9:05

9:17

9:36

LONDON

BIRMINGHAM 

E

8:30

9:19

9:25

9:37

9:56

LONDON

BIRMINGHAM 

D

8:50

9:39

9:45

9:57

10:16

LONDON

BIRMINGHAM 

C

9:10

9:59

10:05

10:17

10:36

LONDON

BIRMINGHAM 

B

9:30

10:19

10:25

10:37

10:56

LONDON

BIRMINGHAM 

A

9:50

10:39

10:45

10:57

11:16

LONDON

BIRMINGHAM 

I

10:10

10:59

11:05

11:17

11:36

LONDON

BIRMINGHAM 

H

10:30

11:19

11:25

11:37

11:56

LONDON

BIRMINGHAM 

G

10:50

11:39

11:45

11:57

12:16

LONDON

BIRMINGHAM 

F

11:10

11:59

12:05

12:17

12:36

LONDON

BIRMINGHAM 

E

11:30

12:19

12:25

12:37

12:56

LONDON

BIRMINGHAM 

D

11:50

12:39

12:45

12:57

13:16

LONDON

BIRMINGHAM 

C

12:10

12:59

13:05

13:17

13:36

LONDON

BIRMINGHAM 

B

12:30

13:19

13:25

13:37

13:56

LONDON

BIRMINGHAM 

A

12:50

13:39

13:45

13:57

14:16

LONDON

BIRMINGHAM 

I

13:10

13:59

14:05

14:17

14:36

LONDON

BIRMINGHAM 

H

13:30

14:19

14:25

14:37

14:56

LONDON

BIRMINGHAM 

G

13:50

14:39

14:45

14:57

15:16

LONDON

BIRMINGHAM 

F

14:10

14:59

15:05

15:17

15:36

LONDON

BIRMINGHAM 

E

14:30

15:19

15:25

15:37

15:56

LONDON

BIRMINGHAM 

D

14:50

15:39

15:45

15:57

16:16

LONDON

BIRMINGHAM 

C

15:10

15:59

16:05

16:17

16:36

LONDON

BIRMINGHAM 

B

15:30

16:19

16:25

16:37

16:56

LONDON

BIRMINGHAM 

A

15:50

16:39

16:45

16:57

17:16

LONDON

BIRMINGHAM 

I

16:10

16:59

17:05

17:17

17:36

LONDON

BIRMINGHAM 

H

16:30

17:19

17:25

17:37

17:56

LONDON

BIRMINGHAM 

G

16:50

17:39

17:45

17:57

18:16

LONDON

BIRMINGHAM 

F

17:10

17:59

18:05

18:17

18:36

LONDON

BIRMINGHAM 

E

17:30

18:19

18:25

18:37

18:56

LONDON

BIRMINGHAM 

D

17:50

18:39

18:45

18:57

19:16

LONDON

BIRMINGHAM 

C

18:10

18:59

19:05

19:17

19:36

LONDON

BIRMINGHAM 

B

18:30

19:19

19:25

19:37

19:56

LONDON

BIRMINGHAM 

A

18:50

19:39

19:45

19:57

20:16

LONDON

BIRMINGHAM 

I

19:10

19:59

20:05

20:17

20:36

LONDON

BIRMINGHAM 

H

19:30

20:19

20:25

20:37

20:56

LONDON

BIRMINGHAM 

G

19:50

20:39

20:45

20:57

21:16

LONDON

BIRMINGHAM 

F

20:10

20:59

21:05

21:17

21:36

LONDON

BIRMINGHAM 

E

20:30

21:19

21:25

21:37

21:56

LONDON

BIRMINGHAM 

D

20:50

21:39

21:45

21:57

-

LONDON

BIRMINGHAM 

C

21:10

21:59

22:05

22:17

-

LONDON

BIRMINGHAM 

B

21:30

22:19

22:25

22:37

-

LONDON

BIRMINGHAM 

A

21:50

22:39

22:45

22:57

-

b. The two tables above shows the time of arrival and departure for trains from London to Birmingham. We come up with the tables above by considering the following factors:

- We should have two trains, one from Birmingham to London and the other from London to Birmingham.

- We should have 3 trains should leave in each hour. To achieve the above two conditions we chose nine trains to operate between the two cities.

- Each train should be allocated 49 minutes transit time, 12 minutes to empty the train and 19 minutes for ticket checks and passengers to board the train.

- The working hours for London station is from 0701h to 2200h while that for Birmingham is 0700h to 2200h

For example, the following link shows one of them which shows the time of leave and time of arrive of trains between Hanoi and Ho Chi Minh City and Vise versa.

http://www.mrlinhadventure.com/en/travel-information/transportation/156-train-timetables.aspx

Another form of Timetable is provided in this link: http://learnenglishteens.britishcouncil.org/skills/reading-skills-practice/train-timetable which refers to the time of leave and arrival of train between Oxford and London Paddington stations

PROBLEM 3

a. Length of the train that maximizes profits:

From the calculations as shown the best selection maximizes the profits is the one with the following length: one first class engine carriage, one standard engine carriage, no standard class carriage and nine first class carriage.

b. The arrangement obtained in a. above- one first class engine carriage, one standard engine carriage, no standard class carriage and nine first class carriage is not a perfect solution to real life situation. This is because it is impossible to get all the passengers travelling using first class ticket. Therefore the arrangement chosen should always strike a balance between the profit made and the kind of services offered to passengers. Since in a real life situation we have passengers travelling using either first class or standard class tickets. From the analysis in a. above we would recommend the arrangement to be as follows: one first class engine carriage, one standard engine carriage, six standard class carriage and three first class carriage. Since most of the passengers prefer traveling using standard class. This is supported by the research information given below:

Figure 4: London travel Watch (2010). Research into Passenger Attitudes to First Class Travel.

London travel Watch (2010). Research into Passenger Attitudes to First Class Travel. From: http://www.londontravelwatch.org.uk/documents/get_lob?id=2217&field=file

PROBLEM 4

a. Determining the equation that will model the size of the wheel against distance travelled.

Solution:

Let y be the size of the loss for the tyre to be scrapped. Therefore y=844-838=6mm.

In order for the tyre to get worn by 1 mm the train should travel a distance of 3,120,000 km. therefore the equation relating the distance travelled d and the size worn out x will be:

Therefore:

The equation relating size of the wheel and distance travelled will be:

Let w be the size of the wheel. Therefore:

 

Substituting i in ii we have:

This can be illustrated using the table below:

Size of the wheel w in mm

Distance travelled d in km.

844

0

843

3,120,000

842

6,240,000

841

9,360,000

840

12,480,000

839

15,600,000

838

18,720,000

Figure 5: Plot of size of the wheel against distance

The equation of line:

w=mx+c

m=    = -   

w = -    X + 844.....................equation iii

b. The distance between London and Birmingham on the proposed route of HS phase 1, is 225km work out how many journeys a single train can make before the tires need to be changed.

Solution:

Therefore the train will travel 83200 journeys before the wheel gets scrapped.