Module 3: Geometric design of highways

Lecture 18 Vertical alignment II

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Case 2 Length of valley curve less than stopping sight distance ($L<S$)

The length of the curve $L$ is less than SSD. In this case the minimum sight distance is from the beginning of the curve. The important points are the beginning of the curve and the bottom most part of the curve. If the vehicle is at the bottom of the curve, then its headlight beam will reach far beyond the endpoint of the curve whereas, if the vehicle is at the beginning of the curve, then the headlight beam will hit just outside the curve. Therefore, the length of the curve is derived by assuming the vehicle at the beginning of the curve . The case is shown in figure 1.

From the figure,

$$h_1+s\tan\alpha = \left(S-\frac{L}{2}\right)N$$

$$L = 2S-\frac{2h_1+2S\tan\alpha}{N}$$ (1)

Figure 1: Valley curve, case 2, $S>L$

Note that the above expression is approximate and is satisfactory because in practice, the gradients are very small and is acceptable for all practical purposes. We will not be able to know prior to which case to be adopted. Therefore both has to be calculated and the one which satisfies the condition is adopted.