# Mathematical Model for Velocity Calculation of Three Types of Vehicles in the Case of Pedestrian Crash

Open access

## Abstract

This paper treats influencing factors in the determination of vehicles speed on the pedestrian crash moment according to pedestrian throw distance and formulates a mathematical model for vehicle speed determination. Vehicle speed is one of the highest causes of accidents. The mathematical model formulation (as the target of this paper) for velocity calculation, in the case of pedestrian accidents, presents great help and guidance to experts of this field when dealing with accident analysis that through accurate determination of this parameter to find other circumstances as close as possible to the technical process of pedestrian accidents. The target of this paper is to define a mathematical model formulation for vehicle velocity calculation in pedestrian crash moment depending on relevant parameters. For the purpose of model formulating, we have selected three cases of real accidents that involved vehicles (“Peugeot 307”, “VW Golf ” and “Mercedes E 220”) with different geometrical parameters of the front profile and pedestrians with different heights and weights. For regression analysis we used “R” and “SPSS” software, which enables the statistical analysis of the data and mathematical model formulation. Also, for analysis of impact of relevant factors, model formulation and model testing have used “Virtual Crash” and “PC Crash” software, which enables pedestrian-vehicle crash simulation using vehicles with real technical characteristics and various pedestrian characteristics. Inductive, comparative, and deductive methods are part of the research methods in this paper.

[1] Prof. dr. Mia Hubert, Prof. dr. Stefan Van Aelst, Linear Models Regression Analysis, Leuven, 2014 - 2015.

[2] G. Hoxha, R. Likaj, A. Kyçyku. Impact of angle determined by upper bumper ends and the front edge of the engine bonnet of vehicle profile in the throw distance of child. International Journal of Civil Engineering and Technology 2017 (8), No. 11, 42 - 51.

[3] D. Cochrane, G. H. Orcutt. Application of Least Squares Regressions to Relationships Containing Autocorrelation Error Term. Journal of American Statistical Association 1949 (44), No. 245, 32 - 61.

[4] J. Durbin. Estimating of Parameters in Time Series Regression Models, Journal of the Royal Statistics Society 1960 (22), Ser. B, 139 - 153.

[5] G. Hoxha, A. Shala, R. Likaj. Pedestrian crash model for vehicle speed calculation at road accident. International Journal of Civil Engineering and Technology 2017 (8), No. 9, 1093 - 1099.

[6] G. Hoxha, M. Bruçi, A. Shala, R. Likaj. Road friction impact in technical process of vehicle pedestrian crash and pedestrian throwing. 3rd international conference on advances in mechanical engineering from 19 - 21 December 2017, ISBN 978-605-9546- 09-6, Yildiz Technical University, Istanbul, Turkey, 2017.

[7] G. Hoxha, R. Likaj, M. Bruçi. Regression mathematical model application by “r” software in determination of vehicle velocity for truck depend on throw pedestrian distance. 3rd 3rd international conference on advances in mechanical engineering from 19 - 21 December 2017, ISBN 978-605-9546-09-6, Yildiz Technical University, Istanbul, Turkey, 2017.

[8] Virtual-Crash, A Simulation Program for Vehicle Accidents. 2016.

[9] Vehicle vs. Child Pedestrian Collision - Full Scale Crash Tests and Mathematical Simulation, EVU 2010.

[10] Sen, A., Srivastava, Regression Analysis: Theory, Methods and Applications, Springer, New York, 1990.

[11] P. Armitage. Statistical Methods in Medical Research, Oxford, Blackwell Scientific Publications, 1971.

[12] R. Gnandesikan. Methods for Statistical Analysis of Multivariate Observations, Wiley, NY., 1990.

[13] R. A. Johnson, D. W. Wichern. Applied Multivariate Statistical Analysis, Prentice Hall, NJ., 1992.

[14] G. Hoxha, A. Shala, R. Likaj. Vehicle speed determination in case of road accident by software method and comparing of results with the mathematical model, Journal of Mechanical Engineering - Strojnícky časopis 2017 (67), No. 2, 51 - 60.

# Strojnícky casopis – Journal of Mechanical Engineering

### Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 122 122 23