4.19 - Stopping Distances

Stopping distance = thinking + braking distance

The stopping distance is the total distance a vehicle travels from the moment a driver spots a hazard to when the vehicle comes to a complete stop:

• Thinking distance - The distance the vehicle travels during the driver's reaction time, between noticing the hazard and applying the brakes.
• Braking distance - The distance the vehicle travels once the brakes are applied, while slowing to a stop.

In an emergency stop, the driver applies the maximum braking force to stop in the shortest possible distance.

What increases thinking distance

• Higher speed - The faster the vehicle travels, the further it goes during the reaction time.
• Longer reaction time - Increased by tiredness, alcohol, drugs and distractions.

What increases braking distance

• Higher speed - A faster vehicle travels further before the braking force brings it to a stop.
• Greater mass - A heavier vehicle takes longer to stop under the same braking force.
• Worn or faulty brakes - These can't apply as much braking force.
• Poor road or tyre conditions - Wet or icy roads, dirt, or worn tyres reduce friction, making skidding more likely.

Braking transfers energy to the brakes

1. When the brake pedal is pushed, the brake pads press against the wheels.
2. The contact causes friction, so work is done between the brakes and the wheels.
3. This work transfers energy from the kinetic energy store of the moving car to the thermal energy store of the brakes, causing them to heat up.

Faster cars need a greater braking force

• The faster a car travels, the more kinetic energy it has, so the more work the brakes must do to stop it.
• To stop within a given distance, a faster car needs a greater braking force, which results in a larger deceleration.

Risks of very large decelerations

• The brakes can overheat and lose effectiveness.
• The tyres can lose grip and cause the car to skid.

Braking distance and work done by the brakes

To stop a car, the work done by the braking force must equal the kinetic energy of the car:

Where:

• $m$ = Mass of the car, in kilograms (kg)
• $v$ = Speed of the car, in metres per second (m/s)
• $F$ = Braking force, in newtons (N)
• $d$ = Braking distance, in metres (m)

During an emergency stop the braking force $F$ is at its maximum, so the braking distance $d$ depends directly on kinetic energy:

• Doubling the mass doubles the kinetic energy, doubling the braking distance.
• Speed is squared ($v^2$), so doubling the speed quadruples the kinetic energy, increasing the braking distance four-fold.

Worked example - Total stopping distance

A car travelling at 20 m/s makes an emergency stop to avoid a hazard. The braking force is 8,000 N. Estimate the total stopping distance. Take the driver's reaction time as 0.5 s and the mass of the car as 1,200 kg.

How speed affects stopping distance

Thinking distance increases linearly with speed

• Because reaction time is roughly constant, distance travelled is directly proportional to speed ($d=v\times t$).
• Doubling the speed doubles the thinking distance.
• A graph of thinking distance against speed is a straight line.

Braking distance increases with the square of speed

• Braking distance depends on kinetic energy ($\frac{1}{2}m{v}^2$).
• Doubling the speed increases the braking distance four-fold (2² = 4); trebling it increases the braking distance nine-fold (3² = 9).
• A graph of braking distance against speed curves upwards.

Total stopping distance

• Total stopping distance combines a linear increase and a squared increase.
• At low speeds, thinking distance makes up the larger proportion of stopping distance.
• At high speeds, braking distance dominates.

Worked example - Comparing stopping distances from a graph

The graph shows stopping distance against speed for two cars, A and B. Compare their stopping distances at 30 m/s.

Typical stopping distances for a family car

• Braking distance increases much faster than thinking distance as speed increases, so total stopping distance more than quadruples between 30 mph and 70 mph.
• To avoid collisions, drivers must leave a gap of at least the stopping distance behind the vehicle in front.