Eng. Filippo Begani
In this article we will discuss a case study of an accident between two cars and the verification of compatibility between the accelerometer data of a Black Box and the dynamic data of the accident.
Two vehicles A and B came into contact in the vicinity of a road intersection, resulting in the damage depicted in the figures below.
Figure 1 - damage to vehicles on the left Vehicle A, on the right Vehicle B
The following image shows a plan of the state of the site where the directions of travel of the vehicles involved in the accident are shown.
Figure 2 - direction of travel of vehicles, in red is the direction of travel of vehicle A, in blue that of vehicle B
The position relative to the impact, based on the deformations, is as shown below where the cars are positioned with the deformation planes coinciding at the position of maximum interpenetration.
Figure 3 - Position relative to the collision as reconstructed from the damage on the vehicles
The following image shows the plan drawn up on the basis of the relative position previously identified, on the basis of the traces found on the road surface and the quiet positions as surveyed.
Figure 4 - Location of the impact point as reconstructed from the damage on the ground traces (yellow trace relates to the right front wheel of vehicle A which was blocked in the collision).
The energy values found on the basis of the deformed profile of the two vehicles are 40 and 35 km/h. for vehicle A and vehicle B respectively.
The calculation of the impact velocity was carried out through the conservation of momentum considering known pre- and post-impact directions of movement. With respect to a reference system characterised by the horizontal X-axis and the vertical Y-axis, the directions of arrival and exit from the impact of the vehicles are as follows.
Vehicle A
- Pre-collision angle 14.51°.
- Post-impact angle 19.95°.
Vehicle B
- Pre-Collision Angle 167.38°
- Post-impact angle 29.1°
The post-collision speed of the vehicles was estimated from the distance travelled and the rotations made by the vehicles in the post-collision phase, derived from the position of rest and the point of impact, as shown in the table below:
Vehicle A
- Distance travelled: 7.33 m
- Rotation: -31.07
Vehicle B
- Distance travelled: 6.46 m
- Rotation: 124.46°.
The vehicles were schematised as rigid systems with three degrees of freedom, subjected to braking forces and associated torques. To determine the translation and rotation speeds after impact, a step-by-step integration of the laws of roto-translational motion was carried out for braked vehicles: where m is the mass of the vehicle, Iz is the moment of inertia with respect to the axis orthogonal to the plane of the roadway, Ff and Cf are respectively the braking force and torque (N-m) applied to the vehicle, v and omega are instead the translation speed and angular velocity of the vehicle (in m/s and rad/s respectively), t is the time in seconds. The braking force values assumed and the calculated linear and angular velocity values are shown below:
Vehicle A
Speed parameters:
- Angle speed: 14.51°
- Clockwise rotation: No
- Wheel angle: 10°
Braking parameters:
- Coefficient of friction: 0.7
- percentage locking front left front wheel: 20
- percentage locking front right wheel: 100
- percentage locking rear right wheel: 1
- percentage locking rear left wheel: 1
Results
- Travel speed Km/h: 23.85
- Rotational speed rad/s: 1.6
Vehicle B
Speed parameters:
- Speed angle: 167.38°
- Clockwise rotation: Yes
- Wheel inclination: 7.07°
Braking parameters:
- Coefficient of friction: 0.7
- percentage locking front left front wheel: 100
- percentage locking front right wheel: 20
- percentage locking rear right wheel: 1
- percentage locking rear left wheel: 1
Results
- Travel speed Km/h: 23.84
- Rotational speed rad/s: -4.5
In order to take into account the uncertainty in the exit speeds of the vehicles and the physical parameters such as angles of arrival and exit from the collision of the vehicles, masses, etc., a simulation of the accident was carried out using the MonteCarlo method. The method consists of simulating an ‘n’ number of times (‘n’=100,000 in this case) the collision, using in each simulation statistically derived parameter values within their plausible range of variation. Of the ‘n’ solutions found, only those are then considered which satisfy, within certain tolerances, certain imposed constraints. In this case, the post-crash speeds of the vehicles, the direction of the PDOF (resultant of the contact forces between the vehicles) and the kinetic energy dissipated in deformation were assumed as constraints.
Below are the values assumed for the simulation and their plausible range of variation. The values refer to the reference system shown in the figures above, with the origin of the axes centred at the point of impact.
Vehicle A
- Pre-impact angle 14.51°variation +/- 3°
- Post-impact angle 19.95°variation +/- 3°
- Linear speed Km/h: 24°variation +/- 5 Km/h
Vehicle B
- Pre-impact angle 167.38°variation +/- 3°
- Post-impact angle 29.1°variation +/- 3°
- Linear speed Km/h: 23.84°variation +/- 5 Km/h
By solving the equations, all combinations of the velocities of the two vehicles at the moment of impact that satisfy the conservation of momentum and the imposed constraints were obtained, as shown in the diagram below. The x-axis shows the values of the velocities of vehicle A and the corresponding values of the velocities of vehicle B, the corresponding value of the deformation energy absorbed by the vehicles and the corresponding value of the PDOF calculated with respect to the longitudinal axis of vehicle A are shown on the y-axis.
Figura 5 – Diagramma dei risultati
Taking into account the value of dissipated kinetic energy considered to be 140 kJ, the following pre-collision vehicle speed values are determined from the above graph
- Speed vehicle A (Km/h): 58
- Speed vehicle B (Km/h): 29
Vehicle B was equipped with a Black Box device which recorded the Crash event, reporting a speed of 54 km/h as the last detected speed and a peak acceleration of approximately 6.22 g as the peak acceleration.
Together with the numerical values indicated above, the speed trend from the accelerometer and the accelerometric values measured on three axes are also reported.
Figura 6 – Diagramma delle velocità secondo l’accelerometro
Analysing the data it is possible to notice some discrepancies and inconsistencies with the dynamics of the event that can be reconstructed in particular the following is highlighted
- the speed of Vehicle B, after an initial decrease due to the contact with Vehicle A, tends to increase dramatically up to values of 70 km/h that ARE NOT CONSISTENT with the dynamics of the post impact phase that sees the vehicle stop in the short space of 10-12m
- The speed of 54 km/h is NOT consistent with the type of curve that the driver of Vehicle B was about to take. In fact, considering an average trajectory of the car, as represented in the following image, we obtain a maximum speed value that should have held the vehicle at the limit of the drift of approximately 40 km/h.
Figura 7 – Traiettoria curvilinea caratterizzata da un raggio di 20 m
- The maximum peak acceleration suffered by the car in the collision is on the Y axis of 6.22G while on the X axis it is about 3G from which we obtain a value of the peak acceleration modulus NOT exceeding 7G. Therefore, given the triangular approximation of the acceleration trend, a value of 3.5G is considered for the average. Even in this case, considering an impact duration time of 0.2s, it can be seen that the variation in speed undergone by the impact is NOT greater than 25 km/h.
It is therefore evident that having undergone an impact that caused it to move backwards with respect to the point of contact, the value of acceleration that vehicle B would have undergone in the collision would determine a variation in speed that, starting from the speed value indicated in the report of 54 km/h would NOT have determined the vehicle's centre of gravity moving backwards.
As a result of the above, it is clear that there is NO compatibility between the speed values and the accelerometer values, and there is NO compatibility between what is indicated as the last speed detected and reported in the black box report and the geometry of the intersection. It should also be pointed out that if vehicle B had been travelling at 54 km/h at the time of the collision, it is evident that vehicle A, having had to rear-end it, would have had to keep a speed close to 80 km/h. These speed values would NOT BE COMPATIBLE WITH THE DAMAGES DETECTED ON THE VEHICLES.
For these reasons, the black box report is considered to be reliable and usable.
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