## 5 Conclusions  
The present study proposes a theoretical method for assessment of safety against derailment of a specialized train composition for the transportation of long rails. For this purpose, a method was developed to determine the horizontal forces in the vertical stanchions of the wagon, occurring when they contact the transported rails in a curved section of the track. The forces are used in the computational model for the study of safety against derailment and an evaluation is made according to [PERSON]'s criterion.  
* Four different types of train composition wagons were considered: a wagon with fixing blocks, front wagon, intermediate wagon, and an empty wagon. The analysis of the results shows that the wagon with fixing blocks is most at risk of derailment. The obtained value (Table 4) fully corresponds to the requirements of the normative documents not only for real tests (<1.2), but also for theoretical studies (<1.08).
* The front and intermediate wagons have criterion values very close to that of the empty wagon. This shows that the emerging horizontal elastic forces do not significantly influence the derailment process.
* The developed model allows us to evaluate the influence of individual factors like pivot distance, own weight, number of rails, movement speed, overhang of the outer rail of the track, friction coefficient, etc., on the safety against derailment criterion.
* The transportation of long rails can be carried out with wagons that have different parameters (length, base, width, own weight, load capacity, etc.). After analyzing the mentioned parameters, the authors propose the most efficient version of the specialized train composition for 120 m long rails. When using another modification in the wagons or another rail length, the mentioned efficiency cannot be guaranteed.
* The obtained results show that the transportation of long rails with specialized train composition can be realized on four levels. This will significantly increase the efficiency of operators when delivering long new rails.  
The transportation of rails on more than three levels is not new in global practice and is widely used in India (a record was set there for the transportation of rails with a length of 260 m, in five rows with 12 rails each), the USA, Russia, etc. (in four rows with 12-15 rails each).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criterion** & **Wagon with** & **Fixing Block** & **Front Wagon** & **Intermediate** & **Empty Wagon** \\ \hline \(\left(\frac{\chi}{\zeta}\right)_{\mu}\leq\) 1.08 & 1.0698 & 0.8024 & 0.8295 & 0.8268 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Safety criterion for different wagon types.  
For future research, it would be necessary to conduct a physical validation of the model. This will certainly be carried out if there is a proposal from companies carrying out the transportation of long rails.  
Conceptualization, V.S. and P.S.; methodology, V.S. and P.S.; software, S.S., P.S. and V.M.; validation, V.S. and S.P.; formal analysis, P.S., S.S. and V.M.; investigation, P.S. and S.S.; resources, S.S. and S.P.; data curation, S.S. and V.M.; writing--original draft preparation, V.S., P.S. and S.P.; writing--review and editing, V.S., P.S. and S.P.; visualization, S.S. and V.M.; supervision, V.S.; project administration, V.S.; funding acquisition, V.S. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the European Regional Development Fund within the Operational Programme \"Science and Education for Smart Growth 2014-2020\" under the Project CoE \"National center of mechtronics and clean technologies\" under Grant BC05M2 OP001\(-\)1.001\(-\)0008-C01.  
Not applicable.  
Data Availability Statement: Data are contained within this article.  
The authors would like to thank the Research and Development Sector at the Technical University of Sofia for the financial and technical support.  
The authors declare no conflicts of interest.