Setback on six lane road, 500 m radius

Assumptions

Six-lane undivided carriageway, lane width $w=3.5$ m, $R=500$ m (road centre line), $L=100$ m, SSD $S=200$ m. No extra widening. The sight line is along the centre of the inner (kerb-side) lane, at $n=2(3.5)+1.75=8.75$ m from the centre line, so its radius is $R_i=500-8.75=491.25$ m.

Check S against L

$S=200$ m is greater than $L=100$ m, so the sight line extends beyond the curve along the straight tangent and the angle is based on the curve length:

$$\frac{\alpha}{2}=\frac{L}{2R_i}=\frac{100}{2(491.25)}=0.10178\ \text{rad}=5.832^\circ$$

Setback from the centre line

$$m=R-(R-n)\cos\frac{\alpha}{2}+\frac{S-L}{2}\sin\frac{\alpha}{2}$$ $$m=11.292+50\sin(5.832^\circ)=16.373\ \text{m}$$

(Clearance from the centre of the inner lane is $m_c=7.623$ m; the road edge is $3\times3.5=10.5$ m from the centre line.)

Answer: minimum setback from the centre line $\approx$ 16.37 m.