Design of Horizontal and Vertical Alignments

Horizontal Alignment

This work is to be carried out individually. Each person will work with different data. Your calculations and answers will therefore be different from everyone else. Where the question shows a variable name, please take your value from the table below. Start your  answer to each question by stating your individual data, so that these can be checked.

Answers using the wrong data will not be marked, and will score zero.

• Your work should be handwritten, neat and clear.

• You are strongly advised to use diagrams to illustrate your calculations.

• Marks will be awarded for appropriate methods and correct solutions.

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

Radius of the circular arc

Rate of gain of radial acceleration

Design speed of the road 100kph

a) What is the length of the circular arc?

b) What is the minimum distance between the intersection point of the tangents and the alignment?

A parabolic vertical summit curve between two gradients has been designed in accordance with desirable minimum standards given in TD9.

Summit level hsum  Chainage of the vertical intersection point 2513.615 Design speed 120kph

a) What is the chainage and level at each end of the curve?

b) Between what chainages is the level greater than 42m?

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

Rate of gain of radial acceleration on all transitions

Length of straight between the two curves Lst

Length of both circular arcs 250

a) What is the perpendicular distance between the parallel straight sections?

b) 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?

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.

Clearance (height) between rail tracks and alignment h

a) 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:

b) 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 redesign