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Problem #$2$: Vertical Alignment

Given:

Sufficient information is shown in Figure $2$ to establish the tangents of a vertical profile $($i$.$e$.,$ vertical alignment$)$ with a design speed of $50mph.$ The vertical alignment is not related to the horizontal alignment in Figure $1.$ There is an existing bridge above the proposed profile between stations $244+70$ and $246+00.$ The low member is at a constant elevation of $1105\mathrm{.}50$ feet at the location where the proposed profile will pass underneath.

Find:

i$.$ For vertical curve #$1$

a$.$ Design a vertical curve that provides for the minimum stopping sight distance along the alignment, such that the length is a multiple of $50$ feet $($e$.$g$.,$ if you determine that the vertical length should be $241$ feet, in order to achieve minimum stopping sight distance, design vertical curve length should be $250$ feet$).$

b$.$ Determine the PVC and PVT stations and elevations based on the vertical curve length in part a$.$

c$.$ Determine the vertical clearance between the low$-$member of the bridge and vertical profile at the beginning and end stations of the structure $($i$.$e$.,$ stations $244+70$ and $246+00).$

ii$.$ For vertical curve #$2$ :

a$.$ Design a vertical curve that provides for the minimum stopping sight distance along the alignment, such that the length is a multiple of $50$ feet.

b$.$ Determine the PVC and PVT stations and elevations based on the vertical curve length in part a$.$

c$.$ Determine the high point stations and elevation of the vertical curve.