Problem $5(12$ pts$)$

a$)$ Design a horizontal curve with a central angle of $50$ degrees and a degree of curve of $5$

degrees. Assuming a PI station of $213+00\mathrm{.}75.$ Determine the stations of the PC and PT$.(2$

pts$)$

b$)$ Provide the total deflection angles and the total chords to the first and second whole

points on the curve and to the PT$.(4$ pts$)$

c$)$ Assuming a right deflection angle and an azimuth of the PCPI line of $40$ degrees. Given

$x$ and $Y$ state plane coordinates of $45,000$ and $35,000$ for the $PC,$ determine the

coordinates of the second whole station on the curve. $(2$ pts$)$

d$)$ Assume a $4-$lane highway with $12-$ft lanes, a normal crown rate of $2\mathrm{.}5\%,$ a travel speed of

$45mph$ and a superelevation rate of $4\%,$ compute the lengths of superelevation runoff

and tangent runout necessary to achieve full superelevation on the curve. $(2$ pts$)$

e$)$ Provide the plot $($station and elevation above the centerline$)$ of the transition sections to

full super$-$elevation on the centerline curve $(2$ pts$).$