Design of Transport Infrastructure February (Alignment Calculations)

• 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.

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
 

1. What is the length of the circular arc?
2. 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.
 
 

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
 

1. What is the perpendicular distance between the parallel straight sections?
2. 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

1. 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:

1. 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):

1. What is the value of the point radius where the two transition curves meet?
2. 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]