*Article* **Obsolete or Viable? Revision of Lane-Change Manoeuvre Duration Empirical Calculation**

**Roman Mikulec \*, Marek Semela, Albert Bradác, Stanislav Tokaˇ ˇ r, Martin Bilík, Michal Kˇrižák, Michal Belák, Robert Kledus, Andrej Haring and Vlastimil Rábek**

> Institute of Forensic Engineering, Brno University of Technology, Purkynova 464/118, 612 00 Brno, Czech Republic; marek.semela@vut.cz (M.S.); albert.bradac@vut.cz (A.B.); stanislav.tokar@usi.vutbr.cz (S.T.); martin.bilik@vut.cz (M.B.); michal.krizak@vut.cz (M.K.); michal.belak@vut.cz (M.B.); robert.kledus@vut.cz (R.K.); andrej.haring@usi.vutbr.cz (A.H.); v.rabek@volny.cz (V.R.)

**\*** Correspondence: roman.mikulec@vut.cz

**Abstract:** This study presents a calculation of the time required to execute a lane-change manoeuvre. Compared with other (and older) calculation methods, an analysis was conducted to determine which approach could yield the most reliable results. This study aimed to present a universal calculation method for different road surfaces, surface conditions (dry and wet road surface), and vehicle types (i.e., from small vehicles to SUVs). A total of 108 comparable manoeuvres with modern vehicles were used as a basis for statistical analysis. A new mathematical constant was found based on a regression analysis, adjusting one of the older calculation methods (so-called Kovaˇrík equation), providing the best match between real and calculated manoeuvre duration.

**Keywords:** lane change; manoeuvre duration; empirical calculation; vehicle stability; lateral acceleration

### **1. Introduction**

A lane-change manoeuvre is part of a day-to-day commute. However, if the manoeuvre is part of a crash scenario (either in the form of crash avoidance or if the crash happened during or before the manoeuvre execution), it is necessary to determine when and where the manoeuvre began to place it in the crash scenario timeline.

Although the pre-crash analysis could be done using EDR data currently, older vehicle models usually do not possess these data, which can be problematic considering the average age of personal vehicles in the Czech Republic exceeds 15 years. Furthermore, vehicle manufacturers in Europe are not yet required to provide access to EDR data. Therefore, a calculation of the time needed to execute the avoidance manoeuvre by other methods is necessary.

Analysis of vehicle lateral movement during lane change, overtaking, or crash avoidance presents a problem in traffic accident reconstruction. The lane-change manoeuvre is not used as often as braking for crash avoidance [1,2] (the mechanism of the manoeuvre is more complex compared to braking), and there is usually less evidence left by the vehicle used to identify the vehicle's trajectory (such as yaw or skid marks). If a vehicle crash occurs on a wet road surface, a crash investigator must consider lowered adhesion while analyzing vehicle dynamics. Lane-change alteration by vehicle's adaptive cruise control was explored in [3]. As for the driving conditions, weather is one of the most common factors changing road surface conditions, especially rain, lowering tyre traction (adhesion) due to wet road surface [4].

While modern accident reconstruction methods utilize various simulation programs with integrated mathematical models, there is no guarantee that the result reflects reality. There are several unknown input parameters (delay of the steering mechanism, steering speed, driver model, and others). Therefore, using an empirical calculation based on actual manoeuvre analysis data or the simulation basis seems to be a prudent approach.

**Citation:** Mikulec, R.; Semela, M.; Bradáˇc, A.; Tokaˇr, S.; Bilík, M.; Kˇrižák, M.; Belák, M.; Kledus, R.; Haring, A.; Rábek, V. Obsolete or Viable? Revision of Lane-Change Manoeuvre Duration Empirical Calculation. *Energies* **2021**, *14*, 8439. https:// doi.org/10.3390/en14248439

Academic Editors: Guzek Marek, Rafał Jurecki and Wojciech Wach

Received: 7 November 2021 Accepted: 10 December 2021 Published: 14 December 2021

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