Analysis of vehicles complex displacement in the process of investigation of vehicle crash

Annotation. Nowadays, the vehicle crashes are the main problem concerned with automobilization growth, apart traffic management issues. The process of investigation of vehicle crash is an important task. There is very often the necessity to determine the vehicle crash mechanical device at each of its stages in order to determine the extent of responsibility of its participants, in the process of investigation of vehicle crash. However, it is not always possible due to the absence or efficiency of track conditions, on which the modern analysis models are currently based. The acquisition of general and inclusive model for vehicle displacement in the vehicle crash is the main task nowadays. The proposed model makes it possible to predict the vehicle displacement based on complex array of variables, at each mechanism’s stage during the compound motion based on the fundamental principles of engineering (theoretical) mechanics.

We'll regard that both bodies (objects) have planes of material balance, which move in a common fixed plane. Impact momentum are located in the same plane.
Vectors ri×ni, Ȧi ɢ ȍi are perpendicular to the motion plane [5].  (1) where: h 1 and h 2 are level arms of impulses. The level arms of impulses are defined through the coordinates of the impact point, while h 1 is expressed by coordinates of the impact point of body (object) 1 into the system of relative coordinates at point C 1 , and h 2 -into the system of relative coordinates at point ɋ 2 [6][7]. We will take the moments of body inertia (momentas) as for rectangular solid in connection with axis which is perpendicular to the common fixed plane.°°°°® Since the bodies (objects) move translationally before the interaction, then U 1 = V 1 ; U 2 = V 2 , where: U 1 , U 2 are body (object) velocities before impact [8,9].

°°®
Let's find the speed projection components of velocities at the responding standards. n U n U (7) We'll find an impact pulse where: İ is the recovery factor.
Determine the center-of-mass velocities after impact: Since the bodies (objects) were moving forward before the impact, then Ȧ 1z = Ȧ 2z = 0. Determine rotational speeds (rates) of the bodies (objects) after impact Let's consider the determined dependencies using a particular example. The vehicle «GAZ 322133» with 5 passengers in it and «Mercedes Benz 280 GE» as well as a «Freightliner GL120 COLUMBIA» with «Schwarzmüller KIS 3/E» full-trailer parked on the carriageway in a vehicle crash on the carriageway of Magistralniy proezd in Kursk. As a result of this vehicle crash, the passengers of public taxi bus died on accident scene because of received bodily injury, and the driver of public taxi bus was taken to health care center in Kursk with injuries of various degrees of severity (Figure 2-3). As a result of vehicles' damage survey was determined that the initial contact was between the right forebody section of the vehicle «GAZ 322133» and the left hand rear part of «Schwarzmüller KIS 3/E» full -trailer (the overlap area was 0.2 meters), with that the vehicle «GAZ 322133» tXUQHG DURXQG DW DERXW Û UDGian) and made the recontact with «Mercedes Benz 280 GE». Besides, according to the responses of electronic speedometer of the vehicle «GAZ 322133», was determined that the vehicle, at the moment of the contact, outpaced 80 km/h (Figure 4). The expert was faced with the problem of determining the turnaround time of the vehicle «GAZ 322133» in order to determine whether the driver of the vehicle «Mercedes Benz 280 GE» had a technical capability to prevent recontact .
The fonts for analysis are presented in table 1. The analytical force model is presented in Figure 5. Thereinafter, we calculate, according to the model represented above, and obtain the following values in table 2. Let's consider the further displacement of the first body. We will assume that it performs a plane motion. Let's write down equations of the displacement (motion) [4][5][6]10]. As stated above, the taper angle of the vehicle «GAZ 322133» towards the contact point iV DERXW Û 21 radian). On the basis of this condition, using the third equation, we obtain that the turnaround time to recontact is 0,68 second. Now we will determine the distance on which the vehicle back axle will be displaced during this time in order to compare with the actual position of the vehicle at the accident site. To do this, we will define the level arm of banking in simplified form ( Figure 6). It is h 1 = 3,4 meters. The distance dependence along the bow of displacement can be expressed through [11]: Therefore we determine the distance L 1 , which in this case will compose to 0,7 meters ZKHQ WKH DQJOH FKDQJHV IURP Û WR Û that is confirmed by the vehicle «GAZ 322133» final location on the roadway, stated in the case information of concerned accident ( Figure 2).
Thus, the usage of proposed model allows to approach differentially to analysis of different situations, which connected with the complex displacement of vehicles as a result of their impact. The proposed method makes it possible to expand the array of design conditions of vehicles' displacement by vehicle crash through the infusion of additional font for analysis, for example, such as the wheels position relatively to the slip plain in the process of unsteered displacement, its rotation or blocking with consideration of different balance wheel and its influence on forecasting the explored displacement, as well as taking into different emergency responses (loss of part of the supporting wheels by impact, downdraught displacement or displacement as a result of blocking one of the support points, etc.).