Problem $15-$A:

A $\backslash (+2\backslash \%\backslash )$ grade transitions to a $\backslash (-1\backslash \%\backslash )$ grade with vertical curve whose PVI is at $\backslash ($ x$=\backslash )$ station $\backslash (535+24\mathrm{.}25\backslash )($hundreds $+$ ones$)$ and an elevation of $300$ feet above mean sea level $($amsl$).$ The design speed is $65$ mph$.$

Make a sketch of the curve and determine:

a$.$ The minimum length $\backslash ($ L $\backslash )$ of the vertical curve using the K$-$factor method

b$.$ The stations and elevations of the PVC and PVT

c$.$ The elevation of the curve every $100$ ft along the x $-$axis

d$.$ The elevation of the high point on the curve

Problem $15-$B:

An existing horizontal curve has a degree of curve $\backslash (\backslash$mathrm$\{$D$\}=120\backslash )$ and $\backslash (\backslash$mathrm$\{$e$\}=0\mathrm{.}08\backslash ).$ A structure is being proposed on land on the inside of curve. Assume the road is on level gradeand the coefficient of sliding friction is $0\mathrm{.}16.$

Make a sketch of the curve and determine:

a$.$ The radius of the curve

b$.$ The current maximum safe speed of the curve considering the force balance

c$.$ The minimum distance allowable between the proposed structure and the centerline of the curve such that the current maximum safe speed won't need to be reduced. Assume that we are designing the sightline for a comfortable stopping sight distance.