The developments of the scientific and pedagogical staff of the Department of Engineering Geodesy of the Lviv Polytechnic National University in the direction of increasing the accuracy of geodetic measurements in the construction, operation and repair of unique buildings, structures or separate technological equipment, which is particularly important for their safe operation, are considered. Auxiliary equipment (improved light-reflecting mark, device for linear-angular measurements, spherical reflector with a stand, two-prism transducer-vector) has been developed to increase the accuracy of measurements of parameters of engineering structures by electronic total stations. On the basis of theoretical calculations, an optimal image of the geodetic mark for viewing at different distances is proposed, and a three-dimensional holder is developed to compensate for the non-perpendicular error. A technique was developed and implemented in a device for linear-angular measurements, which made it possible to determine the length of segments from 1 to 30 meters with an accuracy of 0.1-0.3 mm. In order to transfer the coordinates of the geodetic base from the reference network to the measurement points of building structures, a spherical reflector and a stand were developed, in the process of using which errors in centering, reduction and height measurement are compensated. The application of the developed spherical reflector was tested during the restoration of the design position of the large-sized equipment of the power complex facility with an accuracy of 0.5 mm. To determine the dimensions of irregularly shaped structures in order to minimize the angles of the prism (to directly determine the coordinates of the prism tip), a two-prism encoder vector was theoretically justified and developed. The accuracy of determining the spatial coordinates by the vector encoder was investigated using the final measure as a reference value. According to the results of research, the deviation of the distances determined with the help of the vector transducer from the reference value is 0.3 mm.
In applied geodesy tasks, it may be necessary to determine spatial angles. When bringing a 3D design of buildings and structures to the field with the help of an electronic total station (ES), it is important to verify the spatial angles between different elements of building structures such as roof overlaps, inclined anchors, and more, using the characteristic points' spatial coordinates. Modern geodetic instruments provide sufficiently high measurement accuracy (up to 1" and 1 mm, respectively). However, measuring the required angles with surveying instruments is not always possible for various reasons. First of all, it is impossible to place the device at the vertex of an angle if the location is not accessible. This paper develops a method for determining a spatial angle whose vertex is not available for measurement. Methods and results. To achieve this goal, we consider one of the options for its determination through the application of the cosine theorem with preliminary measurement or calculation of adjacent sides and vertical angles. This article also presents an algorithm for solving the problem with an estimation of the accuracy of establishing the required parameters. The basic formulas for determining the angles of a spatial triangle with an estimate of their accuracy are proposed. The paper studies the influence of the linear measurement values of the lengths of the sides on the values of the angles of a spatial triangle with the corresponding accuracy assessment. In particular, the root mean square errors of angle calculation were determined based on these calculations and mathematical modeling, namely, the ratio of the sides of the triangle. Through indirect measurements of the tower crane boom and roof spire, the spatial angle values were determined. The inclination of the crane boom to the base resulted in α=910.712±51", while the angle of the roof spire was α=150.109±35". Scientific novelty and practical significance. On the basis of the proposed methodology and numerical experiments, spatial angles were determined and their a priori accuracy was analyzed. This confirms the influence of linear measurements of side lengths on the values of spatial angles. The obtained results make it possible to apply the proposed method in engineering and geodetic works using BIM technologies in 3D space. This method can be used in the application software of electronic total station manufacturers to determine spatial angles in space when solving engineering problems.
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