Question

A single-lane unidirectional highway has a design speed of 65 km/h. The perception-brake-reaction time of drivers is 2.5 s and the average length of vehicles is 5 m. The coefficient of longitudinal, friction of the pavement is 0.4. The capacity of this road in terms of 'vehicle per hour per lane' is

• A. 710
• B. 750
• C. 680
• D. 1440

Answer 1

The correct option is A 710

Highway is single lane unidirectional as minimum clear spacing between vehicles = Stopping Sight distance(SSD).
$SSD=vt+\frac{v^2}{2gf}$
Design speed,
$v=65\times \frac{5}{18}=18.056m/s$
Perception break time,
$t=2.5s$
Coefficient of longitudinal friction,
$f=0.4$
$SSD=18.056\times 2.5+\frac{(18.056{)}^2}{2\times 9.81\times 0.4}=86.68m$
Average Centre to Centre distance between vehicles
$S=SSD+lengthofvehicle$
$=86.68+5=91.68m$
Capacity = speed $\times$ density
$=65\times \frac{1000}{91.679}=708.9Vehicle/hr$
The closest option is 710 (c)