Sight distance with obstruction on curve

Sight distance available

Assumptions: two-lane road, 7.0 m wide (lane 3.5 m); $R=300$ m refers to the road centre line; the driver is at the centre of the inner lane, so the obstruction is $m=10+1.75=11.75$ m from the driver's path, and the path radius is $R_i=300-1.75=298.25$ m.

Assuming $S<L$ (500 m):

$$\cos\theta=1-\frac{m}{R_i}=1-\frac{11.75}{298.25}=0.9606\Rightarrow\theta=16.14^\circ=0.2816\ \text{rad}$$ $$S=2R_i\theta=2(298.25)(0.2816)=168.0\ \text{m}$$

$S<L$, so the assumption is valid. Sight distance available = 168 m.

Required overtaking sight distance at V = 50 km/h (IRC)

Speed of the overtaken vehicle $v_b=V-16=34$ km/h $=9.44$ m/s; reaction time $t=2$ s; $a=3.6$ km/h/s $=1.0$ m/s²; speed of the overtaking and opposing vehicles $v=50/3.6=13.89$ m/s.

• $d_1=v_bt=9.44\times2=18.9$ m
• Spacing $s=0.7v_b+6=0.7(9.44)+6=12.6$ m ($v_b$ in m/s); overtaking time $T=\sqrt{4s/a}=\sqrt{4(12.61)/1.0}=7.10$ s
• $d_2=v_bT+2s=9.44(7.10)+2(12.61)=92.3$ m
• $d_3=vT=13.89(7.10)=98.6$ m (opposing vehicle at design speed)

$$OSD=d_1+d_2+d_3=18.9+92.3+98.6=209.8\ \text{m}$$

Check

Available (168 m) < required OSD (about 210 m), so the curve does not meet the overtaking sight distance requirement. Overtaking must be prohibited on this curve (centre line marking and signs), or the obstruction must be cleared. The available distance does exceed the SSD at 50 km/h (62.9 m, $f=0.35$), so stopping is safe.