Factors affecting braking distance 1

From seeing a hazard to stopping

An emergency stop has two stages. During the driver's reaction time, the vehicle continues to travel through the thinking distance. Once the brakes act, it travels through the braking distance before stopping:

$\text{stopping distance}=\text{thinking distance}+\text{braking distance}$

This lesson focuses on the second stage. Braking distance begins when the brakes start to slow the vehicle, not when the driver first sees the hazard.

How braking slows a vehicle

Applying the brakes creates forces that oppose the vehicle's motion. The brakes must act effectively at the wheels, and the tyres must grip the road so that a backward frictional force can act on the vehicle. This resultant force produces a deceleration.

A large deceleration brings the vehicle to rest over a shorter distance. If poor conditions reduce the available braking force, the magnitude of the deceleration is smaller, so the vehicle travels farther before stopping.

Wet and icy roads

Water between a tyre and the road reduces grip, so a wet road usually increases braking distance. The effect is worse if water prevents good contact between the tyre and the road. Ice provides very little friction, so the available braking force and deceleration can be much smaller; braking distance can therefore increase greatly.

These conditions have an important safety implication: a driver should reduce speed and leave a larger gap from the vehicle ahead. This provides more distance in which to stop and reduces the braking distance that will be needed if an emergency occurs.

The condition of the brakes and tyres

For this specification, poor vehicle condition is limited to the brakes and tyres.

Poorly maintained or worn brakes may produce a smaller braking force at the wheels. The vehicle then decelerates less and takes a greater distance to stop.

Tyres provide the contact with the road. Worn or damaged tyres may have less grip, particularly on a wet surface, so they are more likely to slide and cannot provide as large a frictional force. Brakes and tyres both need to be in good condition: effective brakes cannot stop a vehicle quickly if the tyres cannot transmit the required force to the road.

Why speed has such a large effect

Suppose similar braking conditions produce an approximately constant deceleration. The uniform-acceleration equation is

$v^2-u^2=2as$

where $u$ is the initial speed, $v$ is the final speed, $a$ is the acceleration and $s$ is the braking distance. At rest, $v=0$. Because the acceleration during braking is negative, using its magnitude $|a|$ gives

$s=\frac{u^2}{2|a|}$

If the braking conditions and therefore $|a|$ remain the same, braking distance is approximately proportional to the square of the initial speed:

$s\propto u^2$

Therefore, doubling speed gives about four times the braking distance, while tripling speed gives about nine times the braking distance. This explains why even a modest increase in speed can greatly reduce the safety margin before a hazard.

Data for How braking distance varies with speed under the same conditions

The graph is an idealised estimate, not a set of measured road results. Its upward curve represents the square relationship under unchanged braking conditions. Real braking distances vary because the road, weather, brakes and tyres alter the deceleration.

Estimating from information in a question

When a graph or table is supplied, first identify the speed and read the corresponding distance with its unit. To estimate between plotted values, interpolate carefully rather than assuming a straight-line relationship over the whole graph.

For comparisons under similar conditions, use the speed factor. If the new speed is $1.5$ times the original speed, the estimated braking-distance factor is $1.5^2=2.25$. If road or vehicle condition also changes, the square-speed comparison alone is not enough: poorer grip or weaker brakes will lengthen the distance further.

Core chain

Wet or icy road, poor brakes or poor tyres $\rightarrow$ less effective braking force or grip $\rightarrow$ smaller deceleration $\rightarrow$ longer braking distance.

Speed relationship

For approximately uniform deceleration:

$v^2-u^2=2as$

Stopping from speed $u$ gives

$s=\frac{u^2}{2|a|}$

Under the same braking conditions, $s\propto u^2$:

• twice the speed $\rightarrow$ about four times the braking distance;
• three times the speed $\rightarrow$ about nine times the braking distance.

Essential distinctions

• Thinking distance: travelled before the brakes act.
• Braking distance: travelled while the brakes slow the vehicle.
• Stopping distance: thinking distance plus braking distance.

Actual values depend on road and weather conditions and on the condition of the brakes and tyres. Reduce speed and increase the gap in adverse conditions.