Road transport and safetyCalculating stopping distances

It is important to be able to estimate how the stopping distance for a vehicle varies with different speeds.

The diagram shows some typical stopping distances for an average car in normal conditions.

Some typical stopping distances

Travelling at 20 mph (32 km/h):

• thinking distance = 6 m
• braking distance = 6 m
• total stopping distance = 12 m

Travelling at 40 mph (64 km/h):

• thinking distance = 12 m
• braking distance = 24 m
• total stopping distance = 36 m

Travelling at 70 mph (112 km/h):

• thinking distance = 21 m
• braking distance = 75 m
• total stopping distance = 96 m

It is important to note that:

• thinking distance is proportional to the starting speed. This means that it increases proportionally as speed increases - i.e., if starting speed doubles, thinking distance also doubles;
• braking distance increases by a factor of four each time the starting speed doubles.

For example, if a car doubles its speed from 30 mph to 60 mph, the thinking distance will double from 9 m to 18 m and the braking distance will increase by a factor of four from 14 m to 56 m.

Example: Thinking distance calculation

A car travels at 12 m/s.

The driver has a reaction time of 0.5 s and sees a cat run into the road ahead.

What is the thinking distance as the driver reacts?

Answer

During the reaction time, the car travels at constant speed because the brakes have not been applied.

Distance = speed × time.

Speed = 12 m/s.

Time = 0.5 s.

d = 12 × 0.5.

d = 6 m.

The thinking distance at 12 m/s is 6 m.

Example: Stopping distance calculation

For a car travelling at 12 m/s the thinking distance is 6 m and the braking distance is found to be 32 m.

Calculate the stopping distance.

Answer

Stopping distance = thinking distance + braking distance.

Thinking distance = 6 m.

Braking distance = 32 m.

Stopping distance = 6 + 32.

Stopping distance = 38 m.

For a car travelling at 12 m/s the stopping distance is 38 m.