Determination of Straight-Line Characteristics of Oval-Shaped Geophysical and Waterworks Objects

• Published in: Power technology and engineering 2023-03, Vol.56 (6), p.823-825
• Main Authors: Anakhaev, K. N., Tsicanov, H. A.
• Format: Article
• Language: English
• Subjects: Caves; Electrical Machines and Networks; Elliptic functions; Energy; Energy Systems; Foundations; Geoengineering; Geophysics; Glaciers; Hydraulics; Lakes; Mudflows; Power Electronics; Renewable and Green Energy; Water management; Water utilities; Waterworks
• ISSN: 1570-145X; 1570-1468
• DOI: 10.1007/s10749-023-01593-x

Cross profiles and planned outlines of different natural, geophysical, engineering, water management objects, and constructions in many cases have an oval shape, in particular, very close to an outline of the limacon of Pascal. At the same time, there is quite often a need to identify straight-line features of such objects, including coastlines of water reservoirs and periglacial lakes, sections of rock rills, caves, glaciers, mudflow channels, tunnels, whirlpool zones of water outlets (in the plan), etc. The exact determination of the length of an arch of limacon of Pascal is expressed by the dependence based on “untaken” elliptic integrals of the second kind that complicates analytical transformations and calculations of applied problems. The study presents the elementary dependencies providing a rather close approach (%-2%) to precise values and those suggested for theoretical and applied research in various fields. The suggested equations match the known exact dependencies for cardioids, a specific example of a limacon of Pascal.