$4$

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

$w=34m$

$n=7\mathrm{.}9m$

Clearance $($height$)$ between rail tracks and alignment

a$)$ Design the shortest combination of vertical curves using the desirable minimum standards from CD$109-$ Highway Link Design for a design speed of $60$kph$.$ Give your answers in a table with the following headings:

$\backslash$table$[[\backslash$table$[[$Element description$],[($hog$,$ sag or gradient$)]],$Length $($m$),\backslash$table$[[$K value or$],[$Gradient $(\%)]],$Start Level $(m),$End Level $($m$)],[$Sag curve,,,$0,],[,,,,],[,,,,],[,,,,],[,,,,]]$

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 change in length due to the redesign.