## 4 Assessment of Safety against Derailment
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter Description** & **Symbol/Equation** & **Value** \\ \hline Total reaction force of the attacking wheel of wheelset 1 & \(Y_{1a}\) 1 & 122.814 kN \\ Total reaction force of the non-attacking wheel of wheelset 1 & \(Y_{1i}\) 1 & \(-\)70.732 kN \\ Minimum deflection of the bogie frame to be reached during tests of the & \(\Delta z_{\text{jk}}^{+}=\text{g}_{\text{lim}}^{+}.2a^{+}\) & 0.0076 m \\ Twist of the bogie frame during test (2a\({}^{+}\) is distance between wheelsets) & \(\text{g}_{\text{lim}}^{+}=7-5/2a^{+}\) & 4.2222\% \\ Minimum deflection of the wagon frame to be reached during tests of the & \(\Delta z*=g_{\text{lim}}^{+}.2a\) & 33.2 mm \\ Twist of the wagon frame during test (2a is the pivot distance) [28] & \(\text{g}_{\text{lim}}^{*}=\frac{15}{2}+2\) & 3.6483\% \\ Load force during torsion test & \(\Delta F_{\text{p}}\) & 10 kN \\ Deflection of the wagon frame under \(\Delta F_{\text{p}}\) & \(\Delta F_{\text{z}*}=\frac{\Delta F_{\text{z}*}}{\Delta F_{\text{z}*}^{*}}\) & 88.22 mm \\ Force needed to achieve \(\Delta z^{*}\) & \(\Delta F_{\text{z}*}=\frac{\Delta F_{\text{z}*}}{\Delta F_{\text{z}*}^{*}}\) & 3.763 kN \\ Maximum force additionally loading bogie frame under \(\Delta F_{\text{z}*}\) & \(\Delta F_{\text{z}*,\text{max}}^{{}^{\prime}}=\frac{\Delta F_{\text{z}*}(F_{ \text{z}*}+b_{\text{z}})}{2b_{\text{z}}}\) & 3.481 kN \\ Minimum force additionally loading bogie frame under \(\Delta F_{\text{z}*}\) & \(\Delta F_{\text{z}*,\text{min}}^{{}^{\prime}}=\Delta F_{\text{z}*}-\Delta F_{ \text{z}*,\text{max}}^{{}^{\prime}}\) & 0.282 kN \\ Maximum force overloading first wheel & \(\Delta F_{\text{z}*,\text{max}}^{{}^{\prime}}=\frac{\Delta F_{\text{z}*,\text{ max}}^{{}^{\prime}}}{2}\) & 1.7405 kN \\ Minimum force overloading first wheel & \(\Delta F_{\text{z}*,\text{min}}^{{}^{\prime}}=\frac{\Delta F_{\text{z}*,\text{ min}}^{{}^{\prime}}}{2}\) & 0.141 kN \\ Additional maximum vertical reaction force in wheels (Equation (25) of [36]) & \(\Delta Q_{\text{1,max}}\) & 2.007 kN \\ Additional minimum vertical reaction force in wheels (Equation (25) of [36]) & \(\Delta Q_{\text{1,min}}\) & \(-\)0.125 kN \\ Nominal vertical force loading the wheels & \(Q_{\text{nom}}=Q/N\) & 93.401 kN \\ Minimum vertical wheel reaction force & \(Q_{\text{jk,min}}=Q_{\text{nom}}+\Delta Q_{\text{1,min}}\) & 93.276 kN \\ Minimum vertical wheel reaction force & \(Q_{\text{jk,max}}=Q_{\text{nom}}+\Delta Q_{\text{1,max}}\) & 95.408 kN \\ \hline \hline \end{tabular}  
* Calculated according to methodology described in [36].  
\end{table} 
Table 4: Results from calculation of parameters used for assessment of safety against derailment of wagon with fixing block. The obtained values of the safety criterion for all wagon types considered are lower than the limit value of 1.08, which means that for specialized train composition for transportation of long rails, the requirement for safety against derailment is fulfilled. 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 criterion. It was found that the friction coefficient has the most serious influence. By increasing its value by only one hundredth from 0.36 to 0.37, the criterion increases from 1.0698 to 1.0874 and exceeds the permissible limits for theoretical evaluation. The remaining parameters have relatively less influence on the change in intensity of the criterion. For example, when reducing the number of rails from 60 (four rows with 15 rails each) to 45 (three rows with 15 rails each) as recommended in [29] (the reduction by 25%), the criterion decreases from 1.0698 to 1.0450, i.e., by only 2.37%, which is within the computational error. This makes it inexpedient to use an approach from [29] with only three layers of long rails in the composition.