Module 3: Geometric design of highways

Lecture 17 Vertical alignment I

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Length of the summit curve

The important design aspect of the summit curve is the determination of the length of the curve which is parabolic. As noted earlier, the length of the curve is guided by the sight distance consideration. That is, a driver should be able to stop his vehicle safely if there is an obstruction on the other side of the road. Equation of the parabola is given by $y=ax^2$, where $a=\frac{N}{2L}$, where N is the deviation angle and $L$ is the length of the In deriving the length of the curve, two situations can arise depending on the uphill and downhill gradients when the length of the curve is greater than the sight distance and the length of the curve is greater than the sight distance.

Let$L$ is the length of the summit curve, $S$ is the SSD/ISD/OSD, $N$ is the deviation angle, $h_1$ driver's eye height (1.2 m), and $h_2$ the height of the obstruction, then the length of the summit curve can be derived for the following two cases. The length of the summit curve can be derived from the simple geometry as shown below: