# Construction of a mathematical model of vehicles tangent collision during reconstruction of the circumstances of a road accident

## Authors

• Oleksii Saraiev Kharkiv National Automobile and Highway University, Ukraine
• Alexey Voropay Kharkiv National Automobile and Highway University, Ukraine
• Oleksandr Koriak Kharkiv National Automobile and Highway University, Ukraine
• Serhii Povaliaiev Kharkiv National Automobile and Highway University, Ukraine
• Andrey Sharapata Kharkiv National Automobile and Highway University, Ukraine

## Keywords:

vehicle, side impact, loss of stability, absence of braking, reconstruction of TA circumstances

## Abstract

This paper considers the task to clarify the circumstances of a traffic accident (TA) involving two vehicles as a result of their lateral tangential collision at low angles.

The aim of the study is to construct a mathematical model of a tangential collision of vehicles for the reconstruction of TA circumstances.

Owing to the combination of the law of conservation of momentum and the theory of impact using the coefficient of recovery, it was possible to construct a mathematical model that describes the development of such an accident and makes it possible to determine the main parameters of the movement of vehicles after and before the collision. An answer is given regarding the possibility of losing the directional stability of the vehicle and its movement in the lateral direction because of a collision.

Based on the mathematical model, the basic parameters of vehicles motion after their side collision at angles of 5–15° were analytically determined, when there are no slip marks on the road surface.

A numerical experiment was conducted on the example of a specific accident. The findings make it possible to argue about the possibility of losing the directional stability of vehicles and shifting them to the oncoming lane or curb as a result of collision.

A comparison of the results of the numerical calculation with the results of software modeling of accidents and the circumstances that were established in the process of studying a real accident was carried out. It was concluded that the results obtained are consistent and make it possible to more accurately assess the parameters of the movement of vehicles after their lateral tangential collision. In general, this produces more objective results of the reconstruction of TA mechanism in cases where there are no traces of slipping and braking on the road surface.

The proposed mathematical model could be used in collisions accompanied by minor deformations or damage to vehicles

## Author Biographies

### Oleksii Saraiev, Kharkiv National Automobile and Highway University

Doctor of Technical Sciences, Professor, Dean

### Alexey Voropay, Kharkiv National Automobile and Highway University

Doctor of Technical Sciences, Professor, Head of Department

Department of Machine Components and Theory of Machines and Mechanisms

### Oleksandr Koriak, Kharkiv National Automobile and Highway University

PhD, Associate Professor

Department of Machine Components and Theory of Machines and Mechanisms

### Serhii Povaliaiev, Kharkiv National Automobile and Highway University

PhD, Associate Professor

Department of Machine Components and Theory of Machines and Mechanisms

### Andrey Sharapata, Kharkiv National Automobile and Highway University

PhD, Associate Professor

Department of Machine Components and Theory of Machines and Mechanisms

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2022-12-30

## How to Cite

Saraiev, O., Voropay, A., Koriak, O., Povaliaiev, S., & Sharapata, A. (2022). Construction of a mathematical model of vehicles tangent collision during reconstruction of the circumstances of a road accident . Eastern-European Journal of Enterprise Technologies, 6(3 (120), 44–50. https://doi.org/10.15587/1729-4061.2022.267800

## Section

Control processes