$3$

Horizontal Alignment

An existing road with a design speed of $85k\frac{m}{h}$ 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

Length of both circular arcs

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 $120k\frac{m}{h}.$ How long is the straight section between the two curves after this redesign?

Show diagram and calculation methods