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  Module 3: Geometric design of highways
Lecture 17 Vertical alignment I
  

Case a. Length of summit curve greater than sight distance($L>S$)

Figure 1: Length of summit curve ($L>S$)
\begin{figure}\centerline{\epsfig{file=../../../figeps/g18-summit-curve-details,width=8cm}}\end{figure}
The situation when the sight distance is less than the length of the curve is shown in figure 1.
$\displaystyle y$ $\textstyle =$ $\displaystyle ax^2$  
$\displaystyle a$ $\textstyle =$ $\displaystyle \frac{N}{2L}$  
$\displaystyle h_1$ $\textstyle =$ $\displaystyle aS_1^2$  
$\displaystyle h_2$ $\textstyle =$ $\displaystyle aS_2^2$  
$\displaystyle S_1$ $\textstyle =$ $\displaystyle \sqrt{\frac{h_1}{a}}$  
$\displaystyle S_2$ $\textstyle =$ $\displaystyle \sqrt{\frac{h_2}{a}}$  
$\displaystyle S_1+S_2$ $\textstyle =$ $\displaystyle \sqrt{\frac{h_1}{a}}+\sqrt{\frac{h_2}{a}}$  
$\displaystyle S^2$ $\textstyle =$ $\displaystyle \left(\frac{1}{\sqrt{a}}\right)^2 \left(\sqrt{h_1}+\sqrt{h_2}\right)^2$  
$\displaystyle S^2$ $\textstyle =$ $\displaystyle \frac{2L}{N}\left(\sqrt{h_1}+\sqrt{h_2}\right)^2$  
$\displaystyle L$ $\textstyle =$ $\displaystyle \frac{NS^2}{2\left(\sqrt{h_1}+\sqrt{h_2}\right)^2}$ (1)