The paper presents a new analytical approach to modelling the curvature of a communication route by making use of differential equations. The method makes it possible to identify both linear and nonlinear curvature. It enables us to join curves of the same or opposite signs of curvature. Solutions of problems for linear change of curvature and selected variants of nonlinear curvature in polynomial and trigonometric form were analyzed. A comparison of determined horizontal transition curves was made and examples of negotiating these curves into a geometric system were given.

The article deals with the conception of carrying out investigation work on lateral resistance in the course of geometrical railway track alignment by using a tamping machine. It is a continuation of the experimental work on the application of the tamping machine to the continuous welded rail track diagnosis. In earlier articles, attention was concentrated on the determination of axial forces in rails. An analytical approach to the evaluation of lateral resistances based on a continuous registration of the displacement and the force used by the tamping machine for the displacement of track on a horizontal plane (so-called slewing or shifting) is presented. The obtained results offer a possibility of estimating a phenomenon tested taking into consideration the state of the track ballast (the layer of crushed rock or gravel upon which the railway track is laid) bed stabilization, the distribution of the lateral resistances occurring along the length of railway track sections under tests, and also the effect of the longitudinal forces appear in track sections. The performed experiments have confirmed the thesis about the use of the tamping machine to diagnose the lateral resistance state in railway tracks. Some trends towards further undertakings in this sphere, of development character intended to polish up the measuring system, and the way of archiving and interpreting the measuring results have been formulated.

This paper points to the limited possibilities of improving the existing situation of transition curves used in geometric layouts of the railway track. Difficulties in the practical implementation and maintenance of very small horizontal ordinates of the transition curve and the ordinates of the gradient due to cant in the initial section, appearing on smooth transition curves, were indicated. The main reason for this was the excessive smoothing of the curvature in their initial section. Employing the method of curvature identification by differential equations, a new form of the curve was obtained, referred to as the smoothed transition curve. A definite advantage of this curve was shown, from the implementation point of view, over representing the smooth transition curves of the Bloss curve and the parametric curve. It seems that it could successfully compete with the commonly used clothoid, to which it is similar in the initial section, while it differs significantly along its further length, especially in the final section, where it provides a gentle entry from the transition curve into a circular arc.

In this article a new method of designing railway track geometry is introduced. This method is adapted to the technique of global positioning system (GPS) surveying. In the presented method, the basic data necessary to project railway line modernization (the arterial directions of routes and their intersection angles as well as the coordinates of the existing rail-track axis) are obtained through continuous rail-track satellite measurements using antennas installed on mobile rail vehicle. Because the shaping of straight-line track with satellite measurements does not cause any difficulty, attention was given to designing bending sections. It has been assumed that the geometric track layout will be designed on the basis of an appropriate working system of coordinates. Then, some transformation of the acquired solution will be conveyed to the global system. The whole analysis together with the included theoretical equations is aimed at developing a concept of the rail-track system that will be as friendly i...

The problem of the reproduction of the railway geometric layout in the global spatial system is currently solved in the form of measurements that use geodetic railway networks and also, in recent years, efficient methods of mobile positioning (mainly satellite and inert). The team of authors from the Gdańsk University of Technology and the Maritime University in Gdynia as part of the research project InnoSatTrack is looking for effective and efficient methods for the inventory of railway lines. The research is part of a wider investigation BRIK (Research and Development in Railway Infrastructure, in polish: Badania i Rozwój w Infrastrukturze Kolejowej). This paper presents a comparative analysis of the problem of the reproduction of the trajectory of the measuring system using tacheometry, satellite measurements made using a measurement trolley, and mobile satellite measurements. Algorithms enabling the assessment of the compliance of satellite measurements with classic tacheometric measurements were presented. To this end, the authors held measurement sessions using modern geodetic instruments and satellite navigation on a section of the railway line. The results of the measurements indicate the convergence of the level of accuracy achieved by different measuring techniques.

The article presents a summary of several years (2009-2015) of studies on the application of mobile satellite Global Navigation Satellite Systems (GNSS) measurements in the field of designing and operation of railways. These studies have been conducted by an interdisciplinary research team from the Gdansk University of Technology and the Gdynia Maritime University. Mobile satellite GNSS measurements are taken during a ride (through the railroad) by the measuring train consist of motor car with a trailed double axles platform bogies on which the GNSS receivers were installed. The authors described the adopted methodology of the carried out measurements of the rail and tram tracks. The problem of an accuracy of satellite positioning measurements has been discussed. The authors proposed a method that makes it possible to assess quantitatively the accuracy of the research implemented over years. New concepts were introduced, such as: GNSS positioning networking service availability, reliability and continuity based on the theory of reliability. Using a developed mathematical model they recounted the results of four archival measurement campaigns of years: 2009-2015. The studies have shown that the number of used satellite systems as well as support for GNSS measurements with the inertial system are important from the point of view of the accuracy of the results.