# Method for Theoretical Assessment of Safety against Derailment of New Freight Wagons
## 4 Discussion  
The partial results from the experimental study are given in [11; 30]. In [11], as well as in this paper, only an excerpt of the results is presented due to the sensitivity and confi  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Remark** \\ \hline \(v_{1}\) & 58.3 km/h & Methodology from Section 2.1. \\ \(Y_{1}=Y_{1a}\) & 24.718 kN & Methodology from Section 2.1. \\ \(Y_{1i}\) & \(-14.024\) kN & Methodology from Section 2.2. \\ \(g^{*}\) & 3.251\% & Equation (19) \\ \(\Delta z^{*}\) & 39 mm & Equation (18) \\ \(\Delta F_{p}\) & 50 kN & The selected load value for the torsional stiffness test [30] \\ \(\Delta z_{p}\) & 0.08265 mm & Deflection of the frame under the Load, \(\Delta F_{p}\), determined in [31] \\ \(\Delta F_{z^{*}}\) & 23.59 kN & Equation (20) \\ \(\Delta F_{z^{*},max}\) & 21.82 kN & Equation (21) \\ \(\Delta F_{z^{*},min}\) & 1.769 kN & Equation (22) \\ \(\Delta F_{z^{*},max}\) & 10.909 kN & Equation (23) \\ \(\Delta F_{z^{*},min}\) & 0.885 kN & Equation (24) \\ \(\Delta Q_{1,max}\) & 12.58 kN & Equation (25) \\ \(\Delta Q_{1,min}\) & \(-0.7862\) kN & Equation (26) \\ \(Q_{nom}\) & 22.48 kN & Equation (17) \\ \(Q_{jk,min}\) & 21.695 kN & Equation (27) \\ \(Q_{jk,max}\) & 35.061 kN & Equation (28) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results from the calculation needed for determination of safety against derailment.  
dentiality of the data contained in the report [30], as requested by the wagon manufacturer. For the final assessment in tests, not all parameters from Table 2 were determined, but only a few of them, which are necessary for the assessment and measured directly or indirectly. These parameters are Y1i, \(\Delta z^{*}\), Q\({}_{nom}\), and Q\({}_{jk\_min}\). A comparison of the results from tests and calculations is given in Table 3.  
The values for the lateral force, \(Y_{1i}\), were measured in the test on the flat track with a radius of 150 m, while forces \(Q_{nom}\) and \(Q_{jk\_min}\) were measured on the twist test rig, as well as \(\Delta z^{*}\)[11; 30]. It should be noted that all values of parameters measured in the tests are the average values from different numbers of tests (seven tests on twist rig and three on flat track) conducted. In [30], the measurement uncertainty was determined at 1.4% for vertical forces and 1.2% for displacements and twists. This, along with wagon imperfections caused by production, welding, and other influential factors, explains the deviation from the theoretical assumptions.  
The results from the tests also confirm that the safety against derailment for this wagon fulfills the requirements. The value obtained in the tests is equal to 1.03 (Table 1 in [11]). It should be mentioned that the limit value in this case is set to 1.2, as stated in Equation (1) and Reference [9].  
Table 3 shows that the values of measured and calculated parameters are close enough (in order of \(\pm 10\%\)). This gives reason to claim that the proposed theoretical safety assessment method delivers very good results and can be used for the safety assessment of similar wagons.  
The advantages of our method compared to similar methods are mainly the use of fewer input parameters, simplicity, and no need for complex simulations. On the other hand, the proposed method uses some initial parameters for which assumptions are made (the value of the coefficient of friction, \(\mu\)) or for which their values are determined in tests (additional tracks widening in a curved section (\(\delta\)) or wind pressure (\(W\))). With other values for these parameters, safety against derailment would have values other than the calculated values, and the final fulfillment could be questionable. This is the reason why it would be necessary to conduct more assessments using the proposed method and on different wagon series for future research. This would help to additionally verify the results from calculations.