# Prediction of Theoretical Derailments Caused by Cross-Winds with Frequency
###### Abstract  
In this paper, theoretical derailment equations for cross-wind with frequency were derived to assess running safety. For a KTX (Korean high-speed train) unit, the wheel unloading ratios, which are the criteria for evaluating derailments in UIC (International union of railways) and TSI (Technical Specification for Interoperability) regulations, were calculated through the formula under the driving regulations according to cross-wind speeds, and the theoretical results were compared and evaluated through a multibody dynamics (MBD) simulation. In addition, the wheel unloading ratios were calculated for various frequencies of cross-winds. As a result of the formula and MBD, the wheel unloading ratios were shown to increase rapidly regardless of the dampers in suspension when the cross-wind frequency and the natural frequency of a vehicle were in agreement. Finally, we calculated the changes of wheel unloading ratio for different track gauges and found that these theoretical equations could calculate more accurate results than the existing [PERSON]'s formula. The formula derived in this study has the advantage of considering various variables, such as fluctuant cross-winds, rail irregularities, and derailment behaviors, which were not considered in previous studies or [PERSON]'s formula. It could be used for setting suspensions or railway vehicle specifications in the initial design stage. d 2021 22 March 2021 25 March 2021 25 March 2021 25 2021  
As derailment accidents by strong winds have become serious, the risks of derailment by winds are evaluated by criteria given in standards like EN (European Standard), JIS (Japanese Industrial Standards) at the design stage of railway vehicles. In Europe, the safety of cross-winds by CWC (characteristic wind curves) in EN standard has usually been evaluated [6; 7], and the EN and UIC regulations provide a model for wind forces acting on a vehicle under various conditions such as a wind force of Chinese hat type and wind pressure acting on a vehicle when entering a tunnel, as shown in Figure 2[8; 9]. Since the 1970s in Japan, [PERSON] [10] proposed [PERSON]'s formula to evaluate the risk of derailment by cross-wind because derailment accidents had been frequently caused by strong cross-winds. Since the shape of railway vehicles is a box type which can be severely affected by cross-wind, much research on derailment by cross-wind has been carried out. The studies of cross-winds acting on railway vehicles can be divided into two fields: (1) aerodynamics, which considers the wind flow and force effects on vehicles, and (2) vehicle dynamics, which evaluates the risk of derailments of trains using the force effects derived from aerodynamics. * **Aerodynamics** [PERSON] measured the wind force acting on a train when it passed by a windbreak breach, and studied the effects according to the gap size of the windbreak breach through simulations [11]. [PERSON] carried out simulations on the ICE 2 high-speed train for a range of various yaw angles to compare with wind tunnel test data, and evaluated the changes of wind flows according to the yaw angles through simulation [12]. [PERSON] studied the aerodynamic coefficients through wind tunnel tests on down-scale models, which were on a lightweight train and a high-speed train, and evaluated rollover risks using the CWC based on static equilibrium [13]. Research on aerodynamics has been carried out through tests, using real or down scale models, and CFD (computational fluid dynamics) simulations. The tests using a real vehicle were carried out only in a special case because of cost and test bed problems. In many studies, down-scale tests and CFD simulations were performed in order to obtain wind force acting on a vehicle or aerodynamic characteristics of a vehicle. Whereas down-scale tests yield highly reliable values of the measured forces, CFD simulation reduces the cost of studies on phenomena, such as the pressure field and the wind flow [14].