Now compute two equal$-$tangent vertical curves, one from $BVC$ to $CVC$ and another from CVC to EVC, by the methods of Section $25\mathrm{.}4.$ Since both curves are tangent to the same line $AB$ at point $CVC,$ they will be tangent to each other and form a smooth curve.

Example $25\mathrm{.}4$

For the configuration of Figure $25\mathrm{.}6,$ compute and tabulate the notes necessary to stake the unequal$-$tangent vertical curve at full stations.

Solution

Calculate elevations of $BVC,$EVC,$A,B,$ and $CVC,$ and grade $AB$

$()BVC()AB$

These elevations are shown in Figure $25\mathrm{.}6.$

$2.$ In computing the first curve, the grade of $AB$ will be $g_2$ in the formulas, and for the second curve it will be $g_1.$ The rates of change of grade for the two curves are, by Equation $(25\mathrm{.}4)$

$r_1=\frac{0\mathrm{.}16-(-2\mathrm{.}00)}{4}=+0\mathrm{.}54\frac{\%}{s}$tation

$r_2=\frac{1\mathrm{.}60-0\mathrm{.}16}{6}=+0\mathrm{.}24\frac{\%}{s}$tation

Figure $25\mathrm{.}6$ Unequal$-$tangent vertical curve.

$770$ VERTICAL CURVES

TABLE $25\mathrm{.}3$ NOTES FOR CURVE OF EXAMPLE $25\mathrm{.}3$

$\backslash$table$[[$Station$,x($sta$),g_{1}x,r{x}^{\frac{2}{2}},\backslash$table$[[$Curve$],[$Elevation$]],\backslash$table$[[$First$],[$Difference$]],\backslash$table$[[$Second$],[$Difference$]]],[93+00($EVC$),6,0\mathrm{.}96,4\mathrm{.}32,752\mathrm{.}84,1\mathrm{.}48,],[92+00,5,0\mathrm{.}80,3\mathrm{.}00,751\mathrm{.}36,1\mathrm{.}24,0\mathrm{.}24],[91+00,4,0\mathrm{.}64,1\mathrm{.}92,750\mathrm{.}12,1\mathrm{.}00,0\mathrm{.}24],[90+00,3,0\mathrm{.}48,1\mathrm{.}08,749\mathrm{.}12,0\mathrm{.}76,0\mathrm{.}24],[89+00,2,0\mathrm{.}32,0\mathrm{.}48,748\mathrm{.}36,0\mathrm{.}52,0\mathrm{.}24],[88+00,1,0\mathrm{.}16,0\mathrm{.}12,747\mathrm{.}84,0\mathrm{.}28,0\mathrm{.}24],[87+00($CVC$),4,-8\mathrm{.}00,4\mathrm{.}32,747\mathrm{.}56,-0\mathrm{.}11,],[86+00,3,-6\mathrm{.}00,2\mathrm{.}43,747\mathrm{.}67,-0\mathrm{.}65,0\mathrm{.}54],[85+00,2,-4\mathrm{.}00,1\mathrm{.}08,748\mathrm{.}32,-1\mathrm{.}19,0\mathrm{.}54],[84+00,1,-2\mathrm{.}00,0\mathrm{.}27,749\mathrm{.}51,-1\mathrm{.}73,0\mathrm{.}54],[83+00($BVC$),0,0\mathrm{.}00,0\mathrm{.}00,751\mathrm{.}24,,]]$