Example Problem: Layout of a Horizontal Curve

A horizontal curve is to be designed on a two$-$lane rural highway with a design speed of $\backslash (50\backslash$mathrm$\{$mi$\}/\backslash$mathrm$\{$h$\}\backslash ).$ The curve has a central angle $\backslash ((\backslash$Delta$)\backslash )$ of $\backslash (30^\{\backslash$circ$\}\backslash )$ and a radius $\backslash (($R$)\backslash )$ of $1200$ ft $.$ The curve begins at station $\backslash (10+\backslash )50($Point of Curve, PC$)$ and ends at the Point of Tangent $($PT$).$

You are required to calculate the following:

$1.$ Station of the Point of Tangent $($PT$)$

$2.$ Length of the curve $($L$)$

$3.$ Tangent distance $($T$)$

$4.$ Middle ordinate $($M$)$

$5.$ External distance $($E$)$

$6.$ Deflection angles and chord lengths for each station along the curve, starting with a partial station at $\backslash (10+50\backslash )$

Hint on the last part:

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|\}$

$\backslash$hline Station & Distance from PC $($ ft$\backslash ()\backslash )$ & Deflection Angle $(\backslash (\backslash$left$.\{\}^\{(\}\backslash$right$)\backslash )$ & Chord Length $($ ft$\backslash ()\backslash )\backslash \backslash$

$\backslash$hline $\backslash (11+00\backslash )$ & $50$ & $2\mathrm{.}39$ & $49\mathrm{.}99\backslash \backslash$

$\backslash$hline $\backslash (12+00\backslash )$ & $150$ & $7\mathrm{.}16$ & $149\mathrm{.}94\backslash \backslash$

$\backslash$hline $\backslash (13+00\backslash )$ & $250$ & $11\mathrm{.}93$ & $249\mathrm{.}55\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$