Stopping Sight Distance with Numerical Calculation

Stopping sight distance is defined as the minimum sight distance required along the road for the driver in order to stop the vehicle at design speed, safely without colliding with the other vehicle.

It is also known as non-passing sigh distance. The stopping sight distance is not constant but it varies depending upon the situation.

Factors affecting stopping sight distance

Following are the factors affecting the stopping sight distance:-

1. Total reaction time:- It is the time taken from the instant the object is visible by the driver to the instant the brake is applied by the driver’s feet. The total reaction time is divided into two components- i) perception time ii) reaction time.

Perception time is the time required between the instant when the drivers see the object on the road and the instant of realization that brake reaction is required. The length of perception time depends upon the following factors:-

i) Distance to the object.

ii) Color, type, and size of the object

iii) Condition and location of the road

iv) Optical ability of the driver

v) Speed of vehicle

Brake reaction time is the time between the moment the foot is removed from the accelerator paddle and placed on the brake paddle and the time to actual brake action. The brake reaction time depends upon the skill of the driver, environmental factors, etc.

Total reaction time is calculated based on PIEV theory and varies with the situation as well as the velocity of the vehicle. The total reaction time of an average driver may vary from 0.5 seconds for simple situations to as much as 4 seconds for complex situations. On average total reaction time is taken as 2.5 sec. Total reaction time is inversely proportional to the speed of the vehicle.

2. Speed of vehicle:- Stopping distance is directly proportional to the initial speed of. vehicle. Higher the speed of vehicles higher the kinetic energy developed by it and a longer distance will be required to dissipate the energy and stop the vehicle.

3. Braking efficiency:- Braking efficiency is said to be 100% if the wheels are fully locked preventing them from rotations upon the application of the brake. The efficiency of brake depends upon the system of brake (hydraulic or pneumatic), age, maintenance care, wear, and tear, etc. To consider all the negative effects, the efficiency of the brake is considered about 75%.

4. Coefficient of friction:- In the process of stopping a vehicle the driver applies brakes consequently, depending upon the condition of road surface and tyres, the vehicle may skid over the surface of the brakes are applied suddenly. The numerical value of the coefficient of friction is inversely proportional to the speed of the vehicle.

5. Slope of the road surface:- While traveling along with the uphill grade the stopping distance will be less and when downhill it is high for gravity forces if other conditions are the same.

Expression for Stopping distance

Stopping distance is the sum of lag distance and braking distance.

SD = Lagging distance + Braking distance———(i)

Lagging distance:- The distance traveled by the vehicle during the total reaction time is known as lag distance. It is also known as reaction distance. Let ‘t be the total reaction time of the driver in seconds and v is the design speed in m/sec then Lagging distance = vt m —————(ii)

Braking distance: – The distance traveled by the vehicle after the application of brakes to the instant the vehicle comes to a dead stop is known as braking distance. The braking distance can be visualized depending upon the initial speed of the vehicle and friction developed between tyre and road.

Assuming a level road, the braking distance may be calculated by equating the work done in stopping the vehicle and the kinetic energy.

If F be the maximum frictional force developed and I, be the braking distance then, Work done in stopping the vehicle at initial = F x I = fwl —-(iii)

Where, f = coefficient of friction

w = total weight of the vehicle

Kinetic energy is developed by the vehicle at initial speed, vm/sec.

Substituting the value of lag distance in equation (i)

Numerical Example

Q) determine the safe stopping sight distance while traveling at speed of 60 kmph. Assuming perception and brake reaction time is 2.5 sec. and coefficient of friction varying from 0.40 at 20 kmph to 0.35 at 100 kmph.

Case:-

1. level Ground

2. Upward gradient of 3%

Solution:- Coefficient of friction,