## 1 Introduction
This effort to clarify the mechanism of the process is undeniably positive for two main reasons: first, although the wagons commissioned into operation meet the requirements of the regulatory documents, in practice, railway accidents caused by derailments often occur; and second, it could lead to an adjustment of national or international standards, which would reduce the likelihood of derailment. * Although the proposed criteria are generally valid for the cases of examination of railway vehicles in a loaded or empty state, the safety assessment against derailment is carried out on an unloaded wagon. The reasons for this are logical--with a full wagon, the vertical force \(Q\) increases significantly (especially for freight wagons up to 3-4 times), while the lateral force \(Y\) increases less or in the same order under the influence of centrifugal forces. * Currently, there are regulatory documents that, regardless of their shortcomings, should be respected to reduce the likelihood of derailment. * In most analyzed publications and in all normative documents related to the derailment process, the evaluation is reduced to the application of [PERSON]'s criterion [21]. The limit value of the ratio (\(Y\)/\(Q\)) at a coefficient of friction equal to 0.36 was determined via [PERSON]'s criterion using Equation (1):  
\[\left(\frac{Y}{Q}\right)_{lim}=\frac{\tan\gamma-0.36}{1+0.36\,\tan\,\gamma} \tag{1}\]  
where \(\gamma\) is the angle of inclination of the wheel flange. Based on the third conclusion, a theoretical method for evaluating the safety against derailment of a specialized rolling stock for the transport of long rails is proposed in the present study. In this regard, the second conclusion has relevance to the problem: when transporting long rails, the load is placed not on one wagon, but on a whole specialized train composition (Figure 1). When passing through a curved section of the track, the elastic rails are deformed and describe a complex curved line, the shape of which depends on the radius of the curve, the number of rails, the type of rails, the method of fixing the rails, the number of vertical columns limiting the lateral displacements inside the gauge of the wagon, etc. As a result of the interaction of the elastic rails with the vertical columns of the wagon, enormous lateral forces arise between them, which are transmitted through the vehicle structure and balanced on the rail track. This leads to an increase in the lateral forces \(Y\). The mechanism described above necessitates an assessment of safety against derailment not only in a single empty wagon (the case when a new wagon is commissioned into service), but also in the whole train composition, which is loaded to the permissible values. There is a very small number of studies dealing with this issue. One of them is [22], which uses a multibody dynamics simulation for the assessment of safety against derailment when transporting long rails. In this case, rails are \"only\" 50 m long, loaded in one layer, using four wagons. This is not a common case according to European standards, where longer rails (mostly 120 m long) in three layers are transported in one train composition, which dramatically increases the efficiency of transport work. Based on the above considerations, the study of the safety criterion against derailment should be carried out through two distinct stages:  
* Determination of the lateral forces acting on the central bearings of the bogies, obtained because of the elastic deformations of the long rails transported. Figure 1: Train composition for the transport of long rails in a curve: (**a**) middle view; (**b**) front view (source: personal archive). * Application of the method for theoretical assessment of safety against derailment, considering the permissible vertical load and the total values of lateral forces resulting from the movement of the train composition in a curved section of the track and from the elastic deformation of the transported rails. The first stage takes place in the following sequence: 1.