Critical speed tyre marks.

The method of driving fast around a bend is perhaps the best way to start this subject as it explains the bit before you enter ‘critical speed’. If you are a Formula One fan or have seen police traffic patrol cars as they speed to an emergency around a bend you may have wondered why they tend to use the full width of the road. On a left hand bend the best view is obtained from the right hand, (offside), kerb line so the closer you can get to it the better the view you get of oncoming traffic. On exiting the bend, about the point of the apex of the bend or as the view opens up, you move back towards the correct side of the road. Likewise on a right hand bend the opposite should happen, tucked into the left hand, (nearside) kerb on the way into the bend and moving out towards the crown on exit the best view is obtained.

You need to be careful before you try it as you need to ensure the increased view you gain allows you the distance to get back where you should be if there is something coming the other way. Fail to do so and have an accident and not only will you find yourself before the Magistrates from whom you will not receive a lot of sympathy but you are likely to go down at the subsequent Civil Hearing. An unwritten rule for such driving is that the extremes of expert driving are usually paramount to dangerous driving, if it works great if it does not then driver be ware, you will get no support from anyone.

The view is not the only advantage as the speed at which you can get round the bend safely will be increased, sometimes substantially. There is one motorway bend I know well around which you can only do about 100 m.p.h. if you stay in any one lane, use the above technique and all three lanes and 170 m.p.h. although not comfortable is achievable. Why is this possible? Because you are effectively straightening out the bend, increasing the radius of the circle you are describing. So where does ‘critical speed’ come into things. The words are chosen very carefully as the critical bit is the point at which the sideways forces, (sometimes referred to as side ways ‘g’), exceed the ability of the tyre to grip the road, (the coefficient of friction), and the car starts to yaw, (turn round).

The calculations I am about to detail are formulated to determine the speed at which a vehicle can negotiate the given radius and be at that critical point, any faster and it will break away. The same calculation can be used to determine the critical point of the bend however as most roads have deviations in the kerb lines and central white lines it is often necessary to carry out the same process for each to obtain a full picture. It is also often the case that a good line through the bend needs to be calculated as well, i.e. what speed could be achieved as with my motorway.

Critical speed tyre marks are the result of tyres that are rotating but are not travelling in the direction of that rotation and are therefore dragging across the road surface as they rotate. These are useful to the reconstruction expert as he can determine the speed at which a vehicle would need to travel to describe the circle that these marks form. The pattern these marks make is very distinctive and is usually referred to as striated.

Understanding motion in a circle is necessary in dealing with critical speed marks, the formulae is derived to establish a relationship between velocity, acceleration and the radius of the circle being described. The formulae is then applied to the vehicle to establish the limit of friction at the tyre/road interface.

To describe the relevant forces involved in circular motion, imagine you are swinging a ball that is attached to a piece of string around your head. The string is represented by the cord, ‘r’and the course of the ball the outer circle between points ‘a’ and ‘b’. The reality as the ball rotates is that it is subjected to centripetal force which prevents it from following the course it would naturally, remember Newton, straight lines and external forces. The ball will naturally want to go off in a straight line away from you but is confined by the string, the course the ball would take if it could is called the vector and the vector is constantly changing as the ball rotates. What we are interested in is the point ‘a’ to ‘b’ on the circle and there is a formulae to help us.

You will of course note that if we draw a straight line between points ‘a’ and ‘b’ we create a triangle below the line leaving us with an area under the circle and above the straight line. The straight line between ‘a’ and ‘b’ is called a chord and one of the requirements is that this chord is a minimum of 15m long in practice. The mid point on the chord to the height of the circle is the mid ordinate, a series of formulae crunching leads us to a formulae to produce the radius of the circle:

r = radius c = chord M = Mid ordinate

                                               r = (sq.)c + M
                                                       ----- ----
                                                         8M 2

The figure determined in the above formulae is then entered into one of two further formulae dependent upon the angle of the road surface.

A level road surface: v = (sq.) mugr

3+ degree positive camber v = (sq.) gr(mu + tan0)
---------------
(1 - mutan0)

With two alternative calculations of inclines either up or down hill of 6 degree or more.

When skidding on a banked track those forces alter as below:

Both positive and negative values apply here and by using a combination of the tan, sin and cos of the angles involved allowances can be made for the banking.

When cornering on a banked track the situation is a little simpler:

Critical speed determines the relationship between velocity, acceleration rate and the radius of the circle described by a vehicle. When a vehicle is being driven at a speed too high for the circular path intended and the centripetal force required for that path just exceeds the maximum frictional force between the tyres and the road surface, the vehicle is said to be in ‘critical speed’ state.

While the vehicle is in this state, striated scuff marks are usually left on the road surface by the tyres. These marks are easily distinguishable and provide an indication that the vehicle was in a critical speed condition. They also show the path that the vehicle followed and the vehicles attitude along the path. If we are able to find the radius of the path that the vehicle has followed and the coefficient of friction relative to the road surface, then the speed of the vehicle can be calculated.

Courtesy of the West Midlands Accident Investigation Training School. 1986.

A comparatively complex system which is perhaps best left to the expert however an insight will at least aid you in determining the need for such an expert.