Module 3: Geometric design of highways

Lecture 16 Horizontal alignment III

1

2

3

4

5

6

7

8

9

10

Case (a) $L_s<L_c$

For single lane roads:

$$\alpha = \frac{s}{R}~~{\mathrm radians}$$

$$= \frac{180s}{\pi R}~~{\mathrm degrees}$$

$$\alpha/2 = \frac{180s}{2\pi R}~~{\mathrm degrees}$$ (1)

Therefore,

$$m=R-R\cos\left(\frac{\alpha}{2}\right)$$ (2)

Figure 1: Set-back for single lane roads ($L_s<L_c$)

For multi lane roads, if $d$ is the distance between centerline of the road and the centerline of the inner lane, then

$$m=R-(R-d)\cos\left(\frac{180s}{2\pi (R-d)}\right)$$ (3)

$$m=R-R\cos\left(\frac{\alpha}{2}\right)$$ (4)

Figure 2: Set-back for multi-lane roads ($L_s<L_c$)