Edited by Ing. Filippo Begani
In the general case where two media of mass m1 and m2 have an impact in which they dissipate an aliquot of their kinetic energy in deformations, characterised by a value
it is possible to determine the values of Relative Velocity and Velocity Variation according to the following equations:
On the other hand, in the case of a collision between a car and a two-wheeler in which the driver of the latter gets out of the way during the contact phase, it is necessary to make some assessments of the mass of the two-wheeler, which must be taken into account in the formulations used for calculating the impact velocity and/or the relative velocity and the velocity change. For the assessment of the velocity change between the vehicle and the motorbike as shown in the article by Cialdai et al. (2014) ‘Motorcycle-to-car impact: influence of the mass of the rider in the calculation of the relative impact velocity’ the influence of the mass of the motorbike driver and passenger is important. The rider and passenger of the motorbike have an influence in the plastic deformation of the vehicle even if they are not rigidly welded to the motorbike. In order to take account of this change in mass, a correction coefficient η is defined, given by:
Where:
mR is the mass of the motorbike driver;
mM is the mass of the motorbike itself
Thus, by considering the correction factor for the mass of the two-wheeler related to the percentage of the driver's and/or passenger's weight, it is also possible to alternatively define the common mass stated above.
The corrected common mass makes it possible to calculate the relative speed, which takes into account the change in the mass of the two-wheeler as a result of the driver and/or passenger being separated as follows
The same assessment of the mass must be carried out if the change in speed experienced by the vehicles in the collision is to be evaluated.
As far as the deformation energy value is concerned, here too some assessments must be made regarding the mass values to be used in its calculation.
As far as the two-wheeler is concerned, two hypotheses must be assessed:
If the energy value is assessed through a visual comparison with similar damage on similar vehicles, the EES value of the crash test considered and the mass of the two-wheeler used for the experimental test must be taken into account. The energy value is then equal to
If the energy value is assessed through the correlation between pitch shortening and the EES value, the mass of the motorbike and the driver and/or passenger reduced by the factor . the energy value will then be equal to
Example
Consider a collision between a car weighing 1120 kg and a motorbike weighing 200 kg. The driver of the motorbike weighs 60 kg. During the contact phase, the driver detaches from the two-wheeler, travelling a different post-collision trajectory from that travelled by the two-wheeler. From the analysis of the deformations present on the car it can be seen that the damage present is characterised by an EES value of 30 km/h to which corresponds, given a mass of 1120 kg, an energy value of 38.9 kJ.
In the case of the two-wheeled vehicle, an EES value of approximately 50 km/h was estimated by shortening the wheelbase. In this case, to determine the value of energy actually absorbed by the two-wheeler, the mass that contributed to the deformation must be calculated. Considering a driver mass of 60 kg and a vehicle mass of 200 kg, a parameter value of 0.23 is obtained.
The value of the ‘active’ mass during the impact phase is therefore 213.8 kg
The corresponding energy value is therefore approximately 20.6 kJ.
The corrected common mass associated with the impact with the car is then calculated, and considering the car's mass parameters of 1120 kg and the motorbike's active mass of 213.8 kg, a value of 180 kg is obtained
It is therefore possible to calculate the value of the relative velocity considering a total deformation energy value of 59.5 kJ, a corrected common mass of 180 kg and a value of ε, coefficient of restitution, which can be evaluated according to the indications contained in ‘Energy loss in vehicle collisions from permanent deformation: an extension of the “triangle method”’ 2013 of 0.1. In light of the above, the relative velocity is calculated as follows:
Knowing the value of the energy dissipated in the collision, the value of the coefficient of restitution of the impact, which was previously estimated at approximately 0.1, and the value of the masses of the vehicles involved in the accident (complete mass for the car and reduced mass for the driver of the two-wheeler), it is possible to evaluate the variation in speed undergone by the vehicles at the moment of the collision by considering the reduction factor of the masses of the two vehicles as unitary. Considering the mass reduction factor as unity means considering that the contact force passes through the centre of gravity of both vehicles and, given the formulation, maximising the change in speed undergone in the collision.
Considering the above values, the following speed variation values are obtained:
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