Stopping Distances and Kinetic Energy

How Fast Can You Stop?

Remember the adverts for 30mph in urban areas?  You may recall the statistics that referred to a chance of fatality at 35mph and 40mph.  Do these still hold true?
If a vehicle is travelling at 30mph and at a point A is subjected to maximum braking it will stop at point B.

If we repeat the experiment at 35mph the vehicle cannot stop in the same distance and will go beyond point B.  Perfectly logical so far.  Logic may also suggest that the speed is descending in a linear fashion and this time the vehicle will pass point B at 5mph.  Taking this to 40mph, we may expect to pass point B at 10mph.

Unfortunately, this is where logic lets us down, the mph on the speedometer is only a human representation of what makes us move which is actually energy.  Kinetic energy, to be precise, gives us a reading on the speedometer.  If you remember from school:

Kinetic Energy = ½ X mass X speed2

So let’s take a car and carry out this experiment.  As the vehicle and the conditions are the same every time, we can effectively ignore the ½ X mass part of the equation.  The differing speeds past point B can be said to be caused by speed alone.

At 30mph our kinetic energy will be 30 X 30 = 900.  We can lose this completely at point B and stop.

At 35mph our kinetic energy will be 35 X 35 = 1225.  This is an increase of 1/3 for a small 5mph increase in speed.  We can lose a maximum of 900 unitis of energy at point B so pass it with the remaining (1225 – 900) 325 units of energy.  To work out the speed relating to this simply take the square root.  This means that from 35mph at point A, you will now pass point B at 18mph.

Taking this to 40mph at point A, we have an energy level of 40 X 40 = 1600.  Lose the maximum 900 at point B and you have 700 units of kinetic energy remaining.  This represents 26mph.

Translating this to a motorway situation, and emergency stop from 70mph may just stop you before a collision.  If you were doing 100mph instead the collision speed would be 71mph!

Doubling the driving speed quadruples the braking distance.

It takes nearly TWICE as far to stop at 70mph as it does to stop at 50mph!

An easy way to calculate stopping distances (in feet) follows:

Thinking distance in ft = speed in mph
Braking distance in ft = speed in mph squared, divided by 20 (so divide by 2 and knock the 0 off).  Add the two together for overall stopping distance.

So:

30 mph = 30 ft thinking, 45 ft braking = 75 ft
40 mph = 40 ft thinking, 80 ft braking = 120 ft
50 mph = 50 ft thinking, 125 ft braking = 175 ft
60 mph = 60 ft thinking, 180 ft braking = 240 ft
70 mph = 70 ft thinking, 245 ft braking = 315 ft

Another way to remember (And you can do this in your head) is that thinking distance is the same as the speed, ie at 70 thinking distance is 70 as we all now, to calculate the stopping distance is this, just multiply the speed increments going up by .5

30 x 2.5  = 75
40 x 3     = 120
50 x 3.5  = 175
60 x 4     = 240
70 x 4.5  = 315

So to calculate overall stopping distance from 70mph would be 4.5 x 70 = 315.

According to the National Safety Council, your chance of dying in a crash doubles for every 10 mph that you travel above 50 mph. This is because of the increase of kinetic energy as your vehicle gains speed.

Kinetic energy, or energy of motion, is the energy that an object, such as your vehicle, has when it moves. As you increase your speed, the amount of kinetic energy also increases – exponentially.

Always remember – when you double your speed, the amount of kinetic energy quadruples. Thus if you were traveling at 30 mph and then decided to accelerate to 60 mph, the amount of energy in a crash would be four times greater! Here are some quick facts about energy and speed:

A vehicle’s kinetic energy doubles when its weight doubles.
When the weight of a vehicle doubles, it needs about twice the distance to stop.
A vehicle’s energy of motion is proportional to the square of its increased speed.
For example:

When the speed of a vehicle doubles, it needs about four times the distance to stop.
When the speed of a vehicle triples, it needs about nine times the distance to stop.