A control-orientated analytical model for a cyclorotor wave energy device with N hydrofoils

We present a new analytical model from which a model-based controller can be derived for a cyclorotor-based wave energy converter (WEC). Few cyclorotor-based WEC concepts and models have previously been studied and only one control strategy for the entire wave cancellation has been tested. Our model is derived for a horizontal cyclorotor with N hydrofoils and is suitable for the application of various control algorithms and the calculation of various performance metrics. The mechanical model is based on Newton’s second law for rotation. The cyclorotor operates in two dimensional potential flow. This paper modeled the velocity field in detail around the turbine with N hydrofoils by explaining each velocity term and estimated the generated torque using two methods (point source method and thin-chord method). The developed model is very convenient for control design, using the power take off torque and hydrofoil pitch angles as control inputs. The authors of this work have derived new, exact analytic functions for the free surface perturbation and induced fluid velocity field caused by hydrofoil rotation. These new formulae significantly decrease the model calculation time and increase the accuracy of the results. The new equations also provide useful insight into the nature of the associated variables, and are successfully validated against the results of physical experiments and numerical calculations previously published by two independent research groups. Representation of hydrofoils as both a point source and a thin chord were analysed, with both models cross-validated for the case of free rotation in monochromatic waves.

Analysis of Moving Chord Inclination Angles when Determining Curvature of Track Axis

The analysis presented in the paper explains computational issues related to the use of a new method of determining the curvature of the track axis – the so-called moving chord method. It indicates the versatility of this method – it may be used both in a horizontal and vertical plane. It also draws attention to its very high precision, as evidenced by the exemplary geometric cases under consideration. The focus here is on the computational foundations of the discussed method regarding the angles of inclination of the moving chord. It was found that for a circular arc in the horizontal plane, the inclination angles of the moving chord depend on the track turning angle, while the difference in inclination angles depends only on the radius of the arc. In the case of a circular arc in the vertical plane, the moving chord inclination angles are much smaller than in the horizontal plane, which is connected with the range of the applied radii of the arcs. As in the horizontal plane, the radius of the vertical curve is the only factor that determines the discrepancy in the inclination angles of the moving chord.

Analysis of the Effectiveness of Determining the Horizontal Curvature of a Track Axis Using a Moving Chord

The paper addresses the issue of determining the horizontal curvature of a railway track, noting that it is most often done indirectly – on the basis of measured sags from a chord stretched along the track. Further use of this method would not be justified if there were a direct method for determining the curvature. Therefore, the assumptions of the method for deter-mining the horizontal curvature from “Archives of Civil Engineering”, iss. 4/2020, are presented. This method is based on changes in the slope angles of the moving chord in the Cartesian coordinate system. Two important details are examined: the influence of the length of the chord on the obtained values of curvature and the possibility of determining the location of border points between particular geometrical elements. The analysed variants resulted from the type of transition curves used. It has been found that the length of the chord does not play a significant role in determining the curvature and does not limit the application of this method. At the same time, attention is drawn to the precision of determining the nature of the curvature and its compliance with the theoretical course on transition curves. The analysis shows that, in the moving chord method, it is possible to determine the location of the border points between the individual geometrical elements, but the required chord length must be adapted to the type of transition curve. Keywords: railway, horizontal curvature, moving chord, analysis methodology

NUMERICAL SOLUTION OF NONLINEAR EQUATIONS IN ELECTRONIC TABLES AND VISUAL BASIC FOR APPLICATIONS

The article discusses some methods for numerically finding the roots of nonlinear equations, which are determined by numerical methods using the construction of a spreadsheet Microsoft Excel and an application in the Visual Basic for Applications environment. The simplest methods are used: the binary division method and the chord method. The article presents the construction of spreadsheets, the algorithm, the method of creation the VBA application, and the text of the corresponding procedures. The material of the article can be used in informatics courses, both at school and at university, for the development of interdisciplinary connections between informatics and mathematics and expanding ideas about the possibilities of spreadsheets. The problems presented in the article were successfully solved by 10th grade students (profile "Mathematics. Informatics") and first-year students of pedagogical university of the profiles "Physics. Mathematics", "Physics. Informatics". The article reflects the author's personal experience of teaching the course "Informatics" at South Ural State University of Humanities and Education and at school.

Iterative rational least squares fitting

A progressive iterative approximation technique for rational least squares fitting curves is developed. The format is interesting in CAGD (Computer Aided Geometric Design) and improves the recent algorithms. An improved chord method for the root finding based on rational operators is also presented.

Methods for Transformation of Rectangular Spatial Coordinates to Geodetic Coordinates

The article gives a brief analysis of methods and algorithms for the transformation of spatial rectangular coordinates to curvilinear coordinates - geodetic latitude, geodetic longitude, geodetic height. Two algorithms for solving the equation for determining longitude are considered. Three formulas used to calculate the height are analyzed, with an estimate of their errors due to the approximate latitude. The shortcomings of mathematical solutions to these problems are revealed. A study of different approaches and methods for solving the transcendental equation for determining the latitude, based on the theory of separation of the root of the equation, is performed. Using this technique, iterative processes were performed to calculate the reduced latitude , using trigonometric identities, by introducing an auxiliary angle and transforming it to an algebraic quartic equation, which Borkowski solves by the Ferrari's method. The determination of the root isolation interval allowed using the chord method (proportional parts) to determine the latitude. In all cases, estimates of the convergence of the iterative processes that facilitate the comparative analysis of the proposed solutions are obtained. By further decreasing the separation interval of the root, the accuracy of the non-iterative determination of the latitude is improved by the Newton method.