A horizontal curve is being designed through mountainous terrain for a four$-$lane road with lanes that are $3\mathrm{.}75$ m wide. Due to geometrical constraints, the radius of the curve is chosen as $420$ m $.$ The curve's central angle is $25.$ The Posted Speed limit on the road is $80K\frac{m}{h}r.$ The station of the end of circular curve is $400+00.$ The inside edge of the curve is the east bound traffic. East bound is a $2\mathrm{.}5\%$ uphill slope. Use Table $3\mathrm{.}2\mathrm{.}1$ from the Transportation Association of Canada $($TAC$)$ to determine the coefficient of side $($lateral$)$ friction.

Calculate the following:

a$)$ Degree of curvature

b$)$ Superelevation on the curve

c$)$ Length of the curve.

d$)$ The clearance on the inside edge to satisfy sufficient sight distance

e$)$ Length of spiral curve connecting the circular curve to the tangent.

f$)$ Plot a sketch $($plan$,$ elevation and cross$-$section$($s$))$ to show how the superelevation will be gradually introduced to the roadway through rotation around road centreline. Assume the normal cross$-$fall is $2\%.$ Show the stations TS$,$ SC$,$ start of tangent runout and the start of lowering inside edge.