Design speed from setback on 650 m curve

Data

$R=650$ m, $L=300$ m, setback $m=25$ m from the centre of the carriageway, sight distance = intermediate sight distance (ISD = 2 × SSD, IRC). The sight line is measured along the road centre line ($n=0$); $t=2.5$ s, $f=0.35$.

Step 1: sight distance provided by the setback

Try $S>L$ (usual for a short curve with a large setback):

$$\frac{\alpha}{2}=\frac{L}{2R}=\frac{300}{2(650)}=0.23077\ \text{rad}=13.222^\circ$$ $$m=R\left(1-\cos\frac{\alpha}{2}\right)+\frac{S-L}{2}\sin\frac{\alpha}{2}$$ $$25=17.231+\frac{S-300}{2}(0.2287)\Rightarrow S=367.9\ \text{m}$$

$S>L$, so the case is valid. ISD $=S=367.9$ m.

Step 2: SSD and design speed

$$SSD=\frac{ISD}{2}=184.0\ \text{m}$$ $$184.0=0.278V(2.5)+\frac{V^2}{254(0.35)}=0.695V+\frac{V^2}{88.9}$$

Solving: $V=100.7$ km/h.

Answer: design speed for the curve is about 101 km/h.