Abstract
The paper deals with a novelty related to the design of a region for an alternative railway track direction adequate for mobile satellite measurements. The new approach may become particularly useful in the design of the existing track axis control when the determination of both the main track directions becomes impossible. The only solution in that case is to apply to the geometrical system two circular arcs of a different radius, namely, to take advantage of compound curves. In the presented method the design of a new system is carried out by the use of the local system of coordinates. The solution of the design problem is aided by mathematical recording and is based on the determination of some universal equations describing the entire geometrical system. This procedure takes place sequentially involving consecutive parts of the system. The method has been illustrated by an appropriate calculation example.
Highlights
The global positioning system GPS (Specht, 2007) opens up possibilities for determining the coordinates of points in a uniform 3-D system of coordinates WGS 84 the outset of which is in the centre of the Earth’s mass
Determination of Coordinates of the Missing Characteristic Points. At this stage of procedure aimed at a complete solution of the problem it is necessary to search for the coordinates of two characteristic points occurring in local systems of coordinates (LCS): K3 xK3, yK3 − of the end of circular arc CA2 and transition curve TC3, and
Owing to the above it is possible to determine the coordinates of the starting point of LCS in the system 2000
Summary
The global positioning system GPS (Specht, 2007) opens up possibilities for determining the coordinates of points in a uniform 3-D system of coordinates WGS 84 the outset of which is in the centre of the Earth’s mass. In the situation of a region to be subject to route direction change the design will most often be based on such a correction of the circular arc radius and type and lengths of the transition curves that the new geometric system can be most advantageous from the point of view of rail vehicle motion kinematics (i.e. the generation of transverse acceleration is as little as possible and changing smoothly), and that at the same time its position in the horizontal plane does not divert too much from the current one. 4), but a precise position of point O3 is still unknown at this stage (it is only obvious that it lies on the other direction of the main route) Using this system it is possible to model the transition curve itself and to find out its basic data necessary for the determination of coordinates of point K3 , i. One can determine the value of tangent sK3 at point K3
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