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Understanding the mechanics of a road traffic accident

I do not intend to bore the reader to death so I will keep everything simple. What has to be understood are the fundamental laws upon which classic dynamics are based. They are in fact very simple and you almost certainly have heard of them before. At school you must have been taught about one Mr Newton, he had a profound and lasting effect on the sciences. His three ‘laws of motion’ run throughout the accident reconstruction world and if you can master them you have mastered the basics of accident reconstruction.

In detail they read:

1. a body will continue in its state of rest or uniform motion in a straight line unless acted on by an external impressed force.

2. rate of change of momentum is proportional to the applied force, and takes place in the direction of that force.

3. whenever a force acts on an object an equal and opposite force always acts on a different object.

In each of these laws Newton refers to ‘force’. One might therefore reasonably assume that it has some considerable relevance. But what is ‘force’? Defining ‘force’ using an equation it will be expressed as F = ma. ‘F’ is the symbol for ‘force, ‘m’ for mass and ‘a’ for acceleration. Mass is essentially a variation on the weight of a vehicle, or in Newton’s case an object and acceleration its speed as either a positive or a negative figure, i.e. increasing speed or reducing it.

The purest in reconstruction will tell you this is a very, very basic view of a complicated subject and they would be right, but if you understand this you will get your mind round a lot more than you might think possible. If we look again at each of these ‘laws’ how can we demonstrate the meaning in relation to road traffic accidents?

Try these examples:

A body will continue in its state of rest or uniform motion in a straight line unless acted on by an external impressed force. When the driver applies steering or braking he is applying a force to the vehicle which alters its course, when 2 cars collide they alter course because the speed of each knocks the other from its original course as happens with snooker balls in a game of snooker.

Rate of change of momentum is proportional to the applied force, and takes place in the direction of that force. If two cars of the same weight collide at the same speed and at 90’ to each other they are each knocked from their original course away from the each other to a common angle of 45 degrees. The change of momentum is proportionate to the force applied. This again can be seen on the snooker table when the snooker balls collide.

Whenever a force acts on an object an equal and opposite force always acts on a different object. This is more difficult to express as ‘force’ can not be seen only the result of it. It can however be felt, try putting your hands together infront of you and pushing. You will feel pressure at your hands and the muscles in your arms creating that pressure. But you will also feel the pressure of those muscles working across your chest. This is not a very good example but perhaps gives you a clue about forces acting on each other. Again the snooker ball principle is an excellent example.

If you can understand the principles of Mr Newton’s laws of motion you are well on the way to understanding much of the mechanics of road traffic accidents.

You will hear talk of ‘momentum’, Newton mentions it, it is not a lot different in our terms than force although again the purest would offer a more complicated explanation. Again it is expressed as a formulae, momentum = m*v. Momentum is expressed as ‘p’ because ‘m’ is used already for mass, and ‘v’ is velocity, for our purposes speed expressed as an equation. Simply put momentum is the weight of a vehicle multiplied by its speed. Be warned, do not make the calculations yourself without understanding the mathematics of it all, but understand the principles.

your weight is 70k

The formulae is simply p = m*v, so

You, p = 0*70 = 70

Train p = 1000 * 55,880 = 55,880,000

Needless to say you will be wiped out by the train and have no effect on it whatsoever. Why? because you have no weight or speed in the direction of the train. Bear this in mind throughout as you will find it of untold value in understanding what is going on when you look at the circumstances of road traffic accidents.

An alternative example would be the office collision, as you walk through the office should you bump into someone who weighs considerably more than you or indeed a person of similar or less weight who is running, you will be bowled over by their higher force or momentum. The combinations are infinite in that a heavy person standing still could be knocked over by a much lighter person who is running at great speed just as a heavy person travelling at a similar speed to someone of less weight will knock that lighter person down. The combination is one of multiplying weight and speed but in units that are compatible mathematically.

A common mistake that is made when people talk of head on collisions is that they tend to combine speeds, i.e. if 2 cars approach each other in opposite directions, at say 40 m.p.h. and 30 m.p.h. people assume the impact speed is 70 m.p.h. Our friend Mr Newton resolves this for us and puts it into context. A major difference when we talk about force and momentum is that of direction, so for each vehicle we have both plus and minus speeds.

A car doing 40 m.p.h. in a westerly direction has no speed in the easterly direction, it is the same in which ever direction the vehicles are travelling. The result is that mathematically one vehicle has a plus speed in its direction of travel and a negative value in the direction of the other car. It is therefore possible to work out from the result of a collision the speeds of each vehicle. For your part what you need to remember is that the closing speed of approach may well be the 2 speeds added together but at collision the speed will never be greater than the fastest of the 2 vehicles i.e. in this case 40 m.p.h. and will almost certainly be lower.