Overturning vehicle

Generally a vehicle will overturn when the overturning movements of the vehicle become greater than the righting moments. To achieve this situation the centre of gravity must reach a point to the outside of the vehicles wheelbase. Modern motor cars are designed so that the limit of adhesion between the tyres and road surface interface is reached before there is any chance of a vehicle overturning. That is not to say that it does not occur indeed large vehicles, goods or passenger carrying and such vehicles as caravans are most susceptible to the feature.

The information needed to calculate the speed at which a vehicle will need to travel and in what circumstances to cause it to overturn is substantial and is again best left to the expert. So that the reader may access the potential of any file before them at an early stage the basics are detailed here:

Required data:

d = track, w = weight, v = velocity, w1 = weight inner wheels when level,

r = radius of path of centre of gravity.

The centre of gravity is all important in this calculation and of course there is a formulae to calculate its position in a vehicle. Generally speaking it will be in an area to the centre line of the vehicle towards the engine end of the vehicle, bearing in mind that some vehicles have their engine to the front and others to the rear. The height from the ground will be at about the same height as the centre of the engine.

When needed the following will place the centre of gravity in the vehicle.

weight on one axle * wheelbase
total vehicle weight

This will give you the distance of the centre of gravity from the opposite axle to that weighed. The centre of gravity laterally can be determined in the same manner but the weight supported by the wheels on one side of the vehicle should be weighed not an axle, the process is then the same. Determining the height of the centre of gravity in a vehicle is much more difficult, to do this the vehicle must be weighed, the weight on one axle must then be determined and then the weight on the same axle weighed when that axle is raised above the ground by a known distance.

Data needed:

wt = weight transfer not weight recorded, hcg = height above ground only when tyre radius added.

The information gained is entered via a number of formulae which would finally be expressed as

hcg = wheelbase * weight transfer = tyre rolling radius
weight of vehicle * tan angle raised

The information is then entered into the vehicle moments either anticlockwise or clockwise and finally into the equation:

v = (sq) gr (dw1 + hcgwtan0)
(hcgw - w1dtan0)

This equation is considered a coverall number crunching solution that will deal with both positive and negative cambers as well as neutral.

The method of obtaining those weights needed are well known to most police officers, they can be obtained using any local, approved weighbridge. The procedure is equally important the vehicle needing to be placed on the weighbridge correctly to reflect an accurate weight indication. Even more difficult is the process of lifting the vehicle to a known angle and gathering the weights needed. This process is not for the beginner and should not be undertaken lightly.