1. Introduction
Rail transport occupies a significant position in Europe, offering the diversity of the infrastructure network. It provides a cheap, long-term sustainable and especially ecological way of transporting passengers and goods practically over various long distances. Railways often become the main artery for the flow of freight and passenger traffic at the national and international levels with gradual electrification, modernization, and construction. However, within international transport, railways become less flexible, and carriers have to overcome operational problems in the form of national interlocking systems for individual national railway infrastructure managers.
From the viewpoint of safety on the railway network, the most dangerous place is a rail crossing for the railway track and road (railway-crossing or level-crossing) as practically the only place of direct physical contact between otherwise relatively isolated transport modes. This is also documented by accident statistics. Promoting the reduction in unsecured railways is one of the national priorities of national governments and the European Union [
1].
From a safety point of view, level crossings (LCs) are critical points in the safe conduct of rail and road traffic. Due to the different characteristics of rail and road vehicles (size, speed, stopping distance, maneuvering capabilities, etc.) level crossings are often places with frequent accidents and in most cases result in human fatalities and big material damages, even though, all of them are secured with an appropriate level of technical protection. Accident statistics have shown that the main cause for all accidents (more than 95%) is the human factor of road users (drivers, cyclists and pedestrians) who did not follow and obey traffic safety regulations at level crossings. These ideas and outputs are mentioned in the study [
2]. Safety measures for preventing or diminishing rail crossing accidents are presented and proposed in the study. The mentioned study is very important because it serves as an inspiration for the further development of the rail crossing issue. It offers a certain point of view on the safety assessment of railway crossings and creates space for the creation of new methodological procedures. Very useful professional and scientific information, including practical applications related to perspective ratios, are contained in the publications [
3]. It is a very instructive and beneficial publication for this research because the aim of this article is to analyze the perspective ratios at selected railway crossings with the traffic light securing device and to assess whether these ratios are safe for passage in the case of the traffic light securing device failure or in the case of non-compliance with the determined rules by the driver.
The Railway Infrastructure Manager in the Slovak Republic (ŽSR) adopts measures that, to a certain extent, eliminate accidents at rail crossings. Reversing the accidents trend at rail crossings is the result of a reduction in the number of rail crossings, as well as a targeted effort by the Transport Ministries of individual countries to take measures to eliminate the possible train collision with a road motor vehicle. The approved Crossing Security Enhancement Project set priorities in this area and categorized measures to eliminate cross-border accidents. It is primarily a legislative definition of the issue. For example, it can be a clear and transparent definition of public authorities’ rights and obligations in matters relating to the establishment, cancellation and management of rail crossings, the management and maintenance of road markings on roads and so on. It should also be appropriate to implement the principle that the costs of constructing and extending the rail crossing, as well as securing it, are borne by the person in whose interest it is established. For quick orientation of accident participants and rescue services within the Integrated Rescue System 112, it is also necessary to introduce a unique rail crossing number assigned to each rail to identify the rail crossing immediately.
However, from the scientific point of view in the field of transport processes in railway transport, it is necessary to look for other scientific and professional solutions to increase safety at rail crossings. Therefore, this contribution based on the available statistics and literature reviews deals with the assessment of the perspective ratios as an important part of the potential evaluation of the rail crossings and tries to find suitable solutions. The research also includes a practical application [
4].
There are many interesting and useful publications, studies and contributions that deal with the issue of rail transport and especially railway infrastructure. Railway infrastructure can be examined from several angles. There are lots of facts that need to be constantly observed and analyzed and subsequently developed in order to make some progress in this area as well.
Many areas are also necessary to address and explore in the rail crossing issues. Several famous foreign authors have dealt with this topic in the recent past. For example, the study [
5] compares accidents at passive and active railway rail crossings and both immediate and background risk factors are considered. In this study, passive railway rail crossings have no warning devices, although there might be a static warning sign. Active rail crossings are equipped with automatic devices warning road users of approaching trains. The paper [
6] describes the basic design principles for the rail crossings where rail vehicles reach speeds up to 200 km/h, as well as the review of the necessary measures to increase the safety level. Another paper [
7] focuses on the results of studies that cover irregularities occurring on rail crossings and pedestrian crossings.
Very interesting outputs are in the article [
8], which described the methods to reduce the time waiting for public transport and vehicles before the railway rail crossing. One of the proposed methods is the optimization of the rail crossing algorithm. A useful and quality publication [
9] presents a methodological development proposed for railway rail crossing safety systems which is applied in the South Australia region. Rail crossing safety performance is also a very important factor. The most significant publication on the topic is the paper [
10] where data envelopment analysis was performed on the accident data occurring on five types of rail crossings in Turkey and measurement of safety performances of rail crossings in Turkey was provided.
Further, study [
11] examines relationships among attitudes toward traffic rules, impulsiveness, and behavioral intentions at rail crossings. Specific professional and scientific ideas and outputs are mentioned in the publication [
12]. Although it is not a new contribution, the mathematical principles proposed in it are still very beneficial because the rail crossing density estimation method is proposed.
Accidents at rail crossings are a very important but unpopular topic. The development of accidents at rail crossings is closely followed by the phenomenon in the Slovak Republic. When reconstructing railway corridors to 160 km/h, rail crossings are canceled, leading to a reduction in their number. This issue is addressed in detail in the publication [
13]. The aim of the paper is to propose actions to reduce the number of occurrences of these accidents on road and railway transport system crossings based on the analysis of incidents at rail crossings in the example of the Slovak Republic. There are analyses of the development of rail crossing accidents between 2000 and 2021 in Slovakia in the paper. A special graph was also created showing a trend exponential curve for rail crossing development and for the number of accidents, as shown in
Figure 1.
Other publications that address similar issues and offer interesting ideas and modern progressive solutions, including an analysis of the various factors related to rail crossings are, for example, contributions [
14,
15,
16]. There are also many scientific methods of optimization that can be used in transport processes and railway transport rationalization and optimization. For example, the employment of the Monte Carlo optimization method is described in the article [
17]. This method can be used to optimize the railway infrastructure and its capacity. The railway infrastructure improvement is also necessary in order to improve the transport service of the area. Public passenger transport rationalization and timetabling are mentioned in the publications [
18,
19]. This issue is seamlessly followed by other outputs related to rail transport operations [
20] and other infrastructure measures [
21], as well as economic measures [
22].
Last but not least, it is necessary to mention the publications [
23,
24,
25,
26,
27,
28,
29], which also serve as inspiration in achieving the stated goal and the proposed methodology.
All this information shows that several scientists and experts have dealt with the issue of rail crossings. However, the factors influencing the potential of the rail crossing and the factors influencing the restrictive elements of the rail crossing have not yet been specified. The methodology of the perspective ratios of the rail crossing determination has also not been proposed. Therefore, this paper focuses on this part of the research in the field of rail crossings.
4. Discussion
The contribution was primarily focused on the perspective ratios determination on the rail crossings. The basic goal is primarily to increase safety and reduce accidents at rail crossings at this potentially dangerous point. However, achieving increased safety and quality also depends on other important factors. The possibility of avoiding a collision of vehicles at the rail crossing by the train driver depends on the early observation of the obstacle on the rail crossing and the stopping of the rail vehicle before this obstacle. Whether the train driver can stop the vehicle in time depends mainly on the driver’s perspective ratios and the braking distance of the rail vehicle. In terms of the rail crossings, the train driver’s perspective ratios are determined by the length of his or her clear view of the rail crossing. These ratios are not precisely specified, but the line speed can be adjusted with respect to these ratios at the crossing point). The stopping distance of the rail vehicle is the distance that the rail vehicle covers from the moment when the obstacle is noticed at the rail crossing until the vehicle stops [
42].
The length of this distance is significantly influenced by the low coefficient of usable adhesion on the braking of rail vehicle, which is due to the low rolling resistance during the movement of the steel wheel on the rail. The adhesion coefficient values of rail vehicles may vary from 0.05 to 0.15 depending on the condition of the track surface. The fundamental influence on adhesion value is the speed of the vehicle and the contact surfaces of the wheel and rail. Apart from usable adhesion, the stopping distance depends on the starting speed of the rail vehicle, gravity acceleration, train driver reaction time, and rise time of braking effect.
The level of securing a rail crossing is within the competence of ŽSR, but it also falls within the competence of state administration and traffic police. The increase in the security level shall be assessed according to local conditions, the road and rail transport frequency, whether it is a major or minor road, a major or minor line, sighting conditions, and the occurrence of rail crossing accidents are also taken into account.
Several interesting facts were identified in this research. For example, when analyzing the possibility of avoiding a collision by the engine (car) driver, it was found out that even undisturbed perspective ratios do not have to be sufficient to prevent a collision of the rail vehicle with an obstacle at the rail crossing at high line speeds and the low coefficient of useful adhesion. In such cases, the distance needed for stopping the vehicle is too long for the car driver to be able to identify the obstacle at the crossing and start braking. The lower the line speed is and the higher the coefficient of the useful adhesion is, the more influential perspective ratios are on possibly avoiding a collision by the car driver at the rail crossing. However, considering high speeds and low coefficient of useful adhesion, perspective ratios still play a very important role. The sooner the car driver identifies the obstacle, the lower the speed of the vehicle will be and thereby the consequences of the collision will be less fatal.
Based on the above information, it can be stated that there are several ways to increase safety at rail crossings by improving the visibility conditions and perspective ratios. Based on the above information, it can be concluded that there are several ways to increase safety at rail crossings by improving visibility conditions. This paper presents a scientific way of solving this problem, which consists of the design of a methodological (heuristic) procedure, using certain scientific methods. Within this procedure, individual steps are defined, which are based on standard physical and mathematical methods. The article offers one possible way to solve this problem, but it is not the only possible way. The benefit of the article for the readers is to get to know new scientific procedures and outputs in the field of transport process science. The practical application of this methodology is also a very important and useful output [
43].