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Design of Transport Infrastructure February (Alignment Calculations)
Instructions
- This item of coursework is worth 22% of the module
· Please read the instructions carefully.
- You are strongly advised to use diagrams to illustrate your
- Marks will be awarded for appropriate methods and correct
· Answers to all questions should be correct to the nearest millimetre.
| Question: | Q1 | Q2 | Q3 | Q4 | Q5 | ||||||||||
| Variable: | Φ | R | q | g1 | g2 | hsum | R | q | Lstr | W | h | Φ | V | q1 | q2 |
| Units: | ° | m | m/s3 | % | % | M | m | m/s3 | m | m | m | ° | km/h | m/s3 | m/s3 |
| 46 | 990 | 0.6 | 2.5% | -4.9% | 43.5 | 815 | 0.51 | 815 | 37 | 7.6 | 48 | 75 | 0.340 | 0.510 | |
1 Horizontal Alignment
Two straight sections of road are to be linked by a circular arc with symmetrical clothoid transition curves between the straight and curved sections.
Deflection angle between the two straight sections Φ
Radius of the circular arc R
Rate of gain of radial acceleration q
Design speed of the road 100kph
- What is the length of the circular arc?
- What is the minimum distance between the intersection point of the tangents and the alignment?
[16 marks]
2 Vertical Alignment
A parabolic vertical summit curve between two gradients has been designed in accordance with desirable minimum standards given in TD9.
| Approach gradient
Departure gradient Summit level Chainage of the vertical intersection point Design speed |
g1
g2 hsum 2513.615 m 120kph |
|
|
a) b) |
What is the chainage and level at each end of the curve? Between what chainages is the level greater than 42m? |
[16 marks] |
| 3 | Horizontal Alignment |
An existing road with a design speed of 85 km/h passes from one tangent through a right-hand circular arc onto a second tangent, and then through a left hand circular arc onto a third tangent which is parallel to the first. The circular arcs are joined to the straights by clothoid transition curves.
Radius of both circular arcs R
Rate of gain of radial acceleration on all transitions q
Length of straight between the two curves Lstr
Length of both circular arcs 250 m
- What is the perpendicular distance between the parallel straight sections?
- Using the same tangents and Intersection Points, the arc radii are increased to 2500m and the transition curves upgraded to a design speed of 120 km/h. How long is the straight section between the two curves after this redesign?
[20 marks]
4 Vertical Alignment Design
A road must be designed to cross some railway tracks. The approaches are both flat, with no horizontal curvature and are at the same level. The vertical alignment comprises a level approach at ground level, a sag curve, a single crest curve over the railway, and a sag curve returning to ground level. The maximum permitted gradient is 6%, and lengths of this gradient may be used between the crest and sag curves if required. The railway tracks are at ground level and are [W] metres wide. The road alignment must be at least [h]metres above ground level over this entire width.
Width of the railway tracks W
Clearance (height) between rail tracks and alignment h
- Design the shortest combination of vertical curves using the desirable minimum standards from TD9 for a design speed of 60kph. Give your answers in a table with the following headings:
| Element description
(hog, sag or gradient) |
Length (m) | K value or
Gradient (%) |
Start Level (m) | End Level (m) |
| Sag curve | 0 | |||
- Show how much shorter the alignment could be made if the crest curve is redesigned to one step below desirable minimum K value, but all the other constraints remain the same. Tabulate your answer as in section (a), and state the difference in length due to the
[26 marks]
5 Horizontal Alignment
NB show your method of calculating in order to gain full marks.
Two straight sections of road are to be linked by a wholly transitional curve comprising two clothoid spiral curves with differing rates of gain of radial acceleration.
Deflection angle between the two straight sections of road Φ
Design Speed V Rate of gain of radial acceleration for entry transition curve q1 Rate of gain of radial acceleration for exit transition curve q2
Answers required (give your answer to the nearest mm):
- What is the value of the point radius where the two transition curves meet?
- What is the distance between the horizontal intersection point where the two straight sections of road intersect, and the centre of the circle of which the point radius mentioned in part (a) above is a part?
[22 marks]
Dementia (Case study)
Audrey (aged 71) and Edward (aged 74) are a couple who have been married
for nearly fifty years and have a very close relationship. They have lived in the
same home for over 35 of those years and enjoy where they live – although in
recent years there have been many changes in the area, with new subdivisions
being made, many new buildings along with new roads and changes to existing
street configurations.
Dr Susan Saunders has been their general practitioner for the past ten years. Dr
Saunders notes that over that time they have attended routine appointments
together and have enjoyed generally good health, although Audrey has some
mild arthritis in her hips and fingers. Today, Edward has made an appointment
to see Dr Saunders without Audrey present. He tells Dr Saunders that he is
worried about Audrey’s memory. During the last month, Audrey has misplaced
her car keys three times (although on each occasion she did find them a short
time later). Having recently watched a documentary about dementia, Edward is
very worried that Audrey might have dementia. He has thus been watching her
closely for any other possible signs of dementia, and a couple of events have
added to his concerns.
Edward explains that last week Audrey walked into their lounge room, and
completely forgot what she had gone in there for. She retraced her steps
however, and remembered she was going into the lounge room to get her
reading glasses. Edward added that during a recent cleaning spree, they had
rearranged the items in the kitchen cupboards. A couple of days later when
making a cup of tea, Audrey forgot that the cups had been moved, and she went
to the wrong cupboard to get them. Although she immediately realised what she
had done, laughed about it, and quickly went to the correct cupboard, this
incident just added to his concerns.
Dr Saunders asks if they have noticed other changes. For example, has Audrey
had any new health issues? Is she managing her daily activities and chores?
Edward confirms that Audrey has not had any recent illnesses or medication
changes, is still participating in all her regular activities including driving her car,
going out with their friends to play golf and, as usual, continues to share all the
cooking, gardening, and housework duties with Edward. She has also been very
busy planning and organising a trip to Europe to see friends in Germany and
Croatia. Edward tells Dr Saunders that Audrey has always enjoyed organising
their holidays away and on this occasion she seems to be managing it well.
Edward also tells the doctor about one odd incident that happened about six
months ago – he tells the doctor that Audrey was driving home from a friend’s
house and became disoriented and could not remember how to get home on this
usually familiar route. He said that Audrey pulled over and rang him on her
mobile phone to tell him that she could not remember the way home, but after
they spoke for a couple of minutes she suddenly said that she had just
remembered the route and would be home shortly. She then made it safely
home without further incident. Otherwise, apart from the memory issues
mentioned earlier, Edward says there have been no other concerns or issues
worrying them.
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