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# Stopping Sight Distance Concept & Solved Problems

Stopping sight distance is the minimum distance required for the driver to stop a vehicle moving at design speed, without colliding with an obstruction. Stopping sight distance comprises two parts, namely, lag distance and braking distance. Detailed information on stopping sight distance will be covered in this blog.

### Sight Distance

Before getting into stopping sight distance it is essential to know about sight distance. Sight distance is the length of road visible for a driver at any given instant. It is essential to maintain appropriate sight distance in every cross-section of the road.

According to IRC, the eye level of the driver is 1.2 metres and the height of the obstruction is 0.15 metres. This is considered standard across all cases.

### Factors Affecting Stopping Sight Distance

As said, stopping sight distance is the minimum distance required for the driver to stop a vehicle moving at design speed, without colliding with an obstruction. It depends on five factors as mentioned below.

1. Design speed

2. Reaction time

3. Co-efficient of longitudinal friction

4. Longitudinal slope

5. The efficiency of the brakes

We will see all of these terms in detail while deriving the equation for stopping sight distance.

### Derivation for Stopping Sight Distance

Stopping sight distance has two parts, namely, lag distance and brake distance. Each of these terms is explained and the stopping sight distance formula is derived further.

#### 1) Lag Distance

Lag distance is the distance travelled by a vehicle during the reaction time of the driver.

Lag distance = Design speed * Reaction time

The reaction time of the driver is the time required by the driver to analyse the situation and apply the brake. It is based on PIEV theory, i.e., Perception, Intellection, Emotion, and Volition. It is generally taken as 2.5 seconds.

#### 2) Brake Distance

Brake distance is the distance travelled by the vehicle after the application of the brake and the instance of its stopping. It is dependent on the coefficient of longitudinal friction, the gradient of the road, and the efficiency of the brake.

The coefficient of longitudinal friction is the frictional resistance offered by the road. It is dependent on the design speed or the velocity of the vehicle.

 Design speed (in kmph) Coefficient of longitudinal friction (f) 20 to 30 0.4 30 to 40 0.38 40 to 50 0.37 50 to 65 0.36 65 to 80 0.35 80 to 100 0.34

Braking distance (Lbrake) in a levelled road is found by equating the kinetic energy of the vehicle with the frictional resistance offered by the road.

1/2 * m * v^2 = Ff * L(brake)

1/2 * m * v^2 = f * m*g * L

L = (v^2) / (2*g*f)

Similarly for road surfaces with rising gradients,

L = (v^2) / (2*g*(f+n)), where n is the slope in fraction

Similarly for road surfaces with falling gradients,

L = (v^2) / (2*g*(f-n)), where n is the slope in fraction

### Stopping Sight Distance Formula

Combining both lag distance and brake distance, we get, the stopping sight distance formula as,

SSD = v * t + ((v^2) / (2*g*(f ± n))),

To put it in a better way,

SSD = 0.278*v*t + ((v^2) / (254 * (f ± n))),

where,

v - design speed in kmph

t - reaction time of the driver (2.5 seconds)

The same is provided in a pictorial format for better understanding. Stopping Sight Distance Formula

Note:

SSD for 2 lane road is simply SSD. But, SSD for single lane roads with two-way traffic is twice the SSD, i.e., SSD = 2*SSD.

Based on stopping sight distance several other important factors could be found as mentioned below.

#### Head-on Collision Distance

It is the addition of two stopping distances based on the speeds of two different vehicles.

Head-on collision distance = SSD1 + SSD2

#### Head Light Distance

Headlight distance is the same as SSD.

#### Intermediate Sight Distance

This is essential when two-way traffic in a single lane road exists. It is essential to provide limited overtaking opportunities where Overtaking Sight Distance is not possible.

Intermediate Sight Distance = 2 * SSD

### Practise Problem

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