PLACEMENT OPTIMIZATION OF THE POINTS OF THE CONDITIONAL REPER NETWORK FOR RAILWAY CURVES

Railway facilities are responsible and complex structures related to the safety ofpassenger traffic and cargo transportation. To ensure the reliability of all systems, the railway trackneeds continual control of its geometric parameters. Railways require high accuracy of survey andmonitoring both at the construction stage and at the operation stage. Such control can be carried outusing control points of the geodetic benchmark network. These control points must be located nearthe railway track to provide it in the design position and in proper working condition. That is whythe development of "own" railways benchmark network is topical.The purpose of this article is to create a mathematical basis for calculating the locations ofown repers near the railway. These benchmarks will be control points that will be used by track-operation stations, track machine stations, engineering and geodetic departments, track-surveyingstations, services and departments, as well as project and construction organizations duringresearch, design, operation, repair, reconstruction, or new construction. This will keep the track ingood condition and be used for leveling the track during repair work. The paper considers thecalculation method for the placement of control points of the conditional benchmark network on thecurved section of the railway. The novelty is the usage of the mean-value theorem of integral calculusto calculate the coordinates of the curve independently of the national geodetic network. The creationof "own" conditional benchmark network allows railways to perform the pegging of lines and curvesregardless of the presence or remoteness of control points of the local or state geodetic network. Afterchoosing a conditional benchmark, the coordinates of the railway curve, which is divided into 5 parts,were calculated. It is shown that the number of points does not affect the accuracy of determining thecoordinates. Thus, fewer rappers can be dispensed, and the speed of the pegging will increase. Thepolar coordinates for the two polar distances from the conventional benchmark have been determined. It is established that the use of the mean-value theorem of the integral calculus to findthe coordinates of a point gives more accurate data, since this method does not involve replacing thearc with a chord. The described method of determining polar coordinates from any point of one'sown network of conditional benchmarks is of practical importance. After deviating the axis of thetrack from the movement of trains, maintenance workers can put it back without additionalcalculation.