Setback on curve 400 m radius, 1.9 m

Data

$R=400$ m (centre line), $L=200$ m, $n=1.9$ m (centre line of road to centre of inner lane). The sight line is taken along the centre of the inner lane, so its radius is $R-n=398.1$ m. The setback $m$ is measured from the centre line of the pavement to the obstruction line.

(a) Stopping sight distance S = 90 m ($S<L$)

Half the angle subtended by the sight distance:

$$\frac{\alpha}{2}=\frac{S}{2(R-n)}=\frac{90}{2(398.1)}=0.11304\ \text{rad}=6.477^\circ$$ $$m=R-(R-n)\cos\frac{\alpha}{2}=400-398.1\cos(6.477^\circ)=4.441\ \text{m}$$

(b) Overtaking sight distance S = 300 m ($S>L$)

For $S>L$ the angle is based on the curve length:

$$\frac{\alpha}{2}=\frac{L}{2(R-n)}=\frac{200}{2(398.1)}=0.25119\ \text{rad}=14.392^\circ$$ $$m=R-(R-n)\cos\frac{\alpha}{2}+\frac{S-L}{2}\sin\frac{\alpha}{2}=14.394+50\sin(14.392^\circ)=26.822\ \text{m}$$

Answer: setback from the centre line = 4.44 m for SSD = 90 m and 26.82 m for OSD = 300 m.