This fact sheet provides a mathematical explanation of impact speeds and stopping distances using miles per hour. For kph, the following conversions are relevant:
10mph = 16kph; 20mph = 32kph; 30mph = 48kph; 40mph = 64kph; 50mph = 81kph; 60mph = 97kph; 70mph = 113kph; 80mph = 129kph; 90mph = 145kph.

The travelling speed of a vehicle prior to spotting a hazard and attempting to brake, and the consequential stopping distance, is the critical factor in avoiding a crash and the potential for death and injury at any speed of collision.

The following example demonstrates how an increase in speed prevents a vehicle from stopping in time or even reducing its speed to any significant degree. A vehicle travelling at a speed limit of 20mph at the onset of an incident would stop in time to avoid a child running out three car-lengths in front. The same vehicle initially breaking this limit at 25mph would still be travelling at 18 mph at the three car lenghts marker.  A pedestrian hit at 18 mph by a 1 ton car  would be likely to suffer death or serious injury. To imagine the effect this is roughly the same as a child falling out backwards and head first from an upstairs window. We say backwards and head first to demonstrate the lack of control a child has in a road crash, and the potential not only for that child to be hit severely on their head and upper body but also be run over and consequently crushed by a vehicle.

To see this analogy visually at a range of speeds and showing falls from a range of heights of buildings, click here.

It can take much longer than drivers imagine for collision speeds to reduce once a hazard has been noticed, as this document goes on to explain. The logical conclusion of this document, explained below through a process of mathematics, is that wherever there is a risk of pedestrians, particularly children, being hit by a vehicle, there must be a speed limit of no more than 20 mph, with actual speeds travelled being lower as necessary according to the conditions, to give the greatest chance of stopping in time, rather than colliding at any speed. Even running in to a lamp post at 5mph is not to be recommended: colliding with, or running over, a person at any speed is unacceptable and can result in death or injury.

Stopping distance 

Stopping distance is made up of two components: the thinking distance and the braking distance.  For a given driver, vehicle and road conditions the thinking distance depends on the driver's reaction time and initial speed.  The braking distance depends on the initial Kinetic Energy of the vehicle and is proportional to the square of the initial speed.

If the initial speed in mph is 'U' (in mph), and the total stopping distance in feet is 'D' (in feet) then the following relationship is approximately correct: D = U + 0.05xUxU.

The first factor, 'U', accounts for the thinking distance and is based on a reaction time of 0.67 seconds. This assumes that the driver is alert and well rested and not influenced by drugs or alcohol. Some research suggests that a reaction time of 1.5 seconds is more appropriate, which would increase the thinking distances by a factor of 2.25. Consequently the figures given must be regarded as minimal.

The second factor, dependent on 'U' squared, accounts for the draking distance.

We thus get the following values for dtopping distances (similar to those published in the UK Highway Code) shown below first as a table:

and now as a graph:

 The dramatic nature of increase in stopping distance with increase in initial speed is apparent from the graph above. What should be particularly noted is the trebling of stopping distance when speed is increased from 20mph to 40 mph; roughly an increase of 5.25  average car lengths. This trebling in stopping distance between 20mph and 40mph is a crucial factor in the causation of crashes, or their avoidance.

Collision speed

Of crucial importance in the consequences of any crash is the collision speed. The collision speed depends on the Thinking Distance and the amount of kinetic energy that can be lost in the distance remaining to impact.

Clearly, if the distance to impact is less than the thinking distance then there is no time for any braking to take place and no loss in speed; so thinking distance is a critical factor. The fact that kinetic energy depends on the square of speed determines the way in which speed is lost during the braking process. If the initial speed is 'U' (in mph), the distance to impact is 'P' (in feet) and the collision speed is 'V' (in mph) then the following formula applies for any P>U: VxV = UxU - 20(P-U)

Now shown as a table, to show calculations:

Discussion and example

These figures and graphs tell a clear story: higher speed is disproportionately more risky. We can highlight the nature of the risk with the specific example cited in the introduction above. Consider a vehicle travelling at 30mph. A crash would be avoided altogether if a stopping distance of 75 feet, or 5 car lengths, were clear. However if that vehicle were to have been travelling at 36 mph at the onset of the incident, a crash would have been unavoidable and the vehicle would still have had a considerable residual speed at impact.

Using:           VxV = UxU - 20(P-U)         with U = 36 and P = 75, gives:   V = 22.72 mph

That is: the residual speed would be 22.72mph. To state it again:

 A vehicle travelling at 30mph at the onset of an incident would stop in 75 feet, or about 5 car lengths.

 The same vehicle initially travelling at 36mph would still be travelling at 22.72 mph at the 75 foot distance.

The parameters used in the above equations could be challenged on the grounds that modern vehicles with disc brakes and ABS and stability control have shorter braking distances. However it is also the case that typical thinking distances may be underestimated in government stopping distance charts. Whatever the parameters used, the basic principles and relationships between speed and stopping distance and collision speed are unaffected. In all circumstances higher speed incurs higher risk of a crash, disproportionately higher residual speed and more serious consequences.

Five car lengths clear, the stopping distance at 30 mph is too much to expect in a built-up area with many vehicles, cyclists and pedestrians, especially children and the elderly, in close proximity to the road. Three car lengths, the estimated stopping distance at just over 20 mph, might be the most that could reasonably be expected.

 It is very easy, and quick, for a modern vehicle to accelerate from 20 mph to higher speeds.  Indeed car manufacturers pride themselves on the acceleration capabilities of their products. However this acceleration capability leads too readily to a vehicle exceeding even a 30 mph speed limit. Encouragement to use all gears and to change up to a higher gear at the earliest opportunity results in the over-use of acceleration to achieve a speed at which the higher gear can be engaged. Examination of vehicle handbooks reveals that a number of cars are designed to use fourth gear above 30 mph. A result of this driving behaviour is that most vehicles are naturally driven above 30 mph. Arguments that the use of lower gears incurs higher fuel consumption are largely specious; most engines are designed to run at maximal efficiency at around 2000-2500 revs/min which implies the use of a lower gear below 30 mph.

To campaign for slower speed limits and slower driving, go to our campaign page Slower speeds save lives