# Prediction of Theoretical Derailments Caused by Cross-Winds with Frequency
###### Abstract
* **Vehicle dynamics** [PERSON] [15] used MBD (multibody dynamics) simulation to obtain the derailment coefficient for all wheels when cross-wind was applied in a curved track. In addition,  
Figure 2: Tunnel pressure profile at a position just behind the nose of a train. the derailment coefficients according to vehicle speeds and wind speeds were analyzed. [PERSON] [16] performed down-scale tests and CFD simulations to obtain the aerodynamic coefficients of a passenger car and a freight car. The wind forces were calculated based on the results and applied to the MBD simulation. The risk of derailment was assessed under various conditions reflecting wind forces and actual track conditions. [PERSON] studied the rollover derailment that could be caused by cross-wind and/or centrifugal force using physical parameters such as the center of gravity, aerodynamic coefficient, and the center of wind force on a vehicle body [10]. It was confirmed that the theoretical results obtained through the formula and the statical experimental ones obtained through the full-scale real tests were in good agreement [17]. The formula has been used in Japan to theoretically predict a rollover derailment by cross-winds until now [18]. [PERSON] researched the rollover derailment safety of the KTX based on [PERSON]'s formula, considering the wind forces generated by a train running from the opposite direction and the cross-wind on a curved track [19]. Research on derailments is carried out using MBD simulations and theoretical calculations. By the way, it is difficult to obtain accurate results through theoretical calculation because the behavior of a railway vehicle could be obtained through various variables and nonlinear equations. So, in many studies, the running safety has been evaluated using MBD simulation to obtain results similar to real situations. However, a theoretical derailment analysis is necessary to derive good estimations on suspensions at the initial design stage, because every detail of information on a vehicle must be prepared for MBD simulations, which give a better result. Although a lot of studies on derailments by cross-wind were conducted, the derailment study on cross-winds with frequencies generated by geographical features or wayside structures is insufficient. A cross-wind with exciting frequency can act on vehicles due to railside structures that are repeatedly placed, as in Figure 3, when running on a bridge. However, the theoretical derailment equations due to cross-wind in the previous studies could only statically evaluate the derailment risk under a constant wind speed condition [10; 19], and the fluctuant wind or gust conditions have been evaluated using a multibody dynamics simulation [15; 16; 20]. In this paper, a theoretical formula on the risk of derailment was derived considering cross-winds with varying wind forces generated by structures displaced at regular intervals on the trackside. Then, the relationship of the cross-wind frequency to the natural frequency of a vehicle was evaluated. The main content in this study is to predict the behavior of a railway vehicle using theoretical calculations, and the aerodynamic coefficients and cross-wind condition were referred to in previous studies [21; 22; 23] and the regulation [24] on driving conditions of high-speed trains in Korea. Figure 3: Structures installed with regular intervals. To consider the dynamic effects of cyclic cross-winds and wheelsets running on tracks with irregularities, we combined this formulation with the single wheelset derailment formula derived by [PERSON] and others in previous studies [25; 26; 27]. So, this derailment formula was improved for running train derailments, which is different from [PERSON]'s formula or previous derailment theories for statically standing train derailments.