Module 2: Geometric design of highways

Lecture 13 Sight distance

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Stopping sight distance

Stopping sight distance (SSD) is the minimum sight distance available on a highway at any spot having sufficient length to enable the driver to stop a vehicle traveling at design speed, safely without collision with any other obstruction.

There is a term called safe stopping distance and is one of the important measures in traffic engineering. It is the distance a vehicle travels from the point at which a situation is first perceived to the time the deceleration is complete. Drivers must have adequate time if they are to suddenly respond to a situation. Thus in highway design, sight distance atleast equal to the safe stopping distance should be provided. The stopping sight distance is the sum of lag distance and the braking distance. Lag distance is the distance the vehicle traveled during the reaction time $t$ and is given by $vt$, where $v$ is the velocity in $m/sec^2$. Braking distance is the distance traveled by the vehicle during braking operation. For a level road this is obtained by equating the work done in stopping the vehicle and the kinetic energy of the vehicle. If $F$ is the maximum frictional force developed and the braking distance is $l$, then work done against friction in stopping the vehicle is $Fl=fWl$ where $W$ is the total weight of the vehicle. The kinetic energy at the design speed is

$$\frac{1}{2}mv^2 = \frac{1}{2}\frac{Wv^2}{g}$$

$$fWl = \frac{Wv^2}{2g}$$

$$l = \frac{v^2}{2gf}$$

Therefore, the SSD = lag distance + braking distance and given by:

$$SSD=vt+\frac{v^2}{2gf}$$ (1)

where v is the design speed in $m/sec^2$, $t$ is the reaction time in $sec$, $g$ is the acceleration due to gravity and $f$ is the coefficient of friction. The coefficient of friction $f$ is given below for various design speed.

Table 1: Coefficient of longitudinal friction

Speed, kmph	$<$30	40	50	60	$>$80
$f$	0.40	0.38	0.37	0.36	0.35

When there is an ascending gradient of say $+n$%, the component of gravity adds to braking action and hence braking distance is decreased. The component of gravity acting parallel to the surface which adds to the the braking force is equal to $W\sin\alpha \approx W\tan\alpha=Wn/100$. Equating kinetic energy and work done:

$$\left(fW+\frac{Wn}{100}\right)l = \frac{Wv^2}{2g}$$

$$l = \frac{v^2}{2g\left(f+\frac{n}{100}\right)}$$

Similarly the braking distance can be derived for a descending gradient. Therefore the general equation is given by Equation 2.

$$SSD=vt+\frac{v^2}{2g(f\pm0.01n)}$$ (2)