Module 3: Geometric design of highways

Lecture 18 Vertical alignment II

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Safety criteria

Length of the valley curve for headlight distance may be determined for two conditions: (1) length of the valley curve greater than stopping sight distance and (2) length of the valley curve less than the stopping sight distance.

Case 1 Length of valley curve greater than stopping sight distance ($L>S$)

The total length of valley curve $L$ is greater than the stopping sight distance SSD. The sight distance available will be minimum when the vehicle is in the lowest point in the valley. This is because the beginning of the curve will have infinite radius and the bottom of the curve will have minimum radius which is a property of the transition curve. The case is shown in figure 1.

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

From the geometry of the figure, we have:

$$h_1+S\tan\alpha = aS^2$$

$$= \frac{NS^2}{2L}$$

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

where $N$ is the deviation angle in radians, $h_1$ is the height of headlight beam, $\alpha$ is the head beam inclination in degrees and $S$ is the sight distance. The inclination $\alpha$ is $\approx$ 1 degree.