# Method for Theoretical Assessment of Safety against Derailment of New Freight Wagons
## 1 Introduction  
The methods for assessing safety against derailment for new vehicle acceptance are mostly performed using some combination of testing and theoretical mathematical calculations or simulations. Most methods are based on dynamic tests, which can be performed as controlled tests in a laboratory or as long runs under representative service conditions or under the described test conditions, using exactly defined track characteristics and statistical assessment methods. All three test types have their advantages and disadvantages, as described in [1]. There are many methods used for evaluating safety against derailments worldwide. A good overview of these methods is given in [1]. Theoretical mathematical calculations have a long tradition since the first attempts from [PERSON] [2], [PERSON] [3], and [PERSON] [4] to mathematically describe the processes occurring in the wheel-rail interface. In particular, the Nadal criterion [4] sets the basics for further developing theoretical methods to assess safety against derailment [5; 6; 7; 8]. Today, it is applied in different international and European normative documents [9; 10]. On the other hand, the experimental measurement of certain parameters relevant to derailment safety is still a standard procedure for approving new freight wagons for operational commissioning. The measured values of these parameters are then used to calculate the safety criterion; if the limit values are not exceeded, the new wagon is approved. The performance of these tests is strictly regulated by international and European authorities in standards and regulatory works [9; 10]. Even if these test procedures and conditions are strictly described, some new approaches and methods for measuring forces and displacements are used nowadays [11; 12]. However, the practical implementationof the tests is accompanied by many difficulties: finding a track with a proper radius, ensuring free access to the railway infrastructure for a long period of time, waiting for suitable metrological conditions, preparing the curve and the test wagon, etc. For the wagon manufacturers, these difficulties mean long-term approval procedures and higher expenses. This is why most wagon manufacturers attempt to avoid dynamic tests since this is possible according to EN 14363:2019 [9]. The required evidence and procedure for acceptance are well defined in this European standard, and, thus, it is possible to compare the resulting parameters from the theoretical calculations or simulations of safety against derailment with parameters of reference wagons that have undergone real tests. This approach is allowed according to clause 6.1.5.2.6 of EN 14363:2019 [9] when using Method 2 for the assessment. This method is described in detail in Section 2 of this paper. When using Method 2 of EN 14363:2019 [9], it is necessary to determine the vertical and transversal forces acting in wheel-rail contact. In tests, these parameters are measured directly. It is not explicitly pointed out which theoretical method or type of simulation should be used. The only condition is that the method used for calculation or simulation delivers sufficiently reliable results that are close enough to the results from dynamic tests. Depending on the mechanism that causes derailment of wagons, many methods that determine forces and displacements exist. As mentioned above, a very good overview of these methods is given in [1]. Many methods are based on the flange climb in the wheel-rail contact [13; 14; 15; 16], which is the most frequent reason for derailment. Many researchers in this field deal with geometrical properties of wheel-rail contact on straight tracks or in curves [13; 15], including dynamic properties of suspension, while others propose methods to control these processes [14; 16]. Some researchers deal with derailment caused by other mechanisms: passing through an S-shaped curve [17], passing through turnouts and switches [18], or due to track failure [19].