TO THE CALCULATION OF LENGTH OF GEOPHYSICAL OBJECTS OF HYPERBOLIC OUTLINE

Abstract

Hyperbolic curves are used in various theoretical and practical studies, including in the field of water management and environmental construction when calculating various geophysical objects with hyperbolic outlines (surfaces of coastal slopes, sliding lines of landslide massifs, directing dams, spillway surfaces of watersheds, water free fall trajectories, etc.). The exact determination of the length of the hyperbola arc is represented by a rather complex dependence based on “unbreakable” incomplete elliptic integrals, which makes it difficult to carry out analytical calculations and involves the use of tabular data with a time-consuming cross and non-linear interpolation of them, etc. Elementary dependencies are proposed to determine the length of the hyperbola arc, which give a very close approximation (up to 1%) to exact values. The obtained calculated analytical dependencies for determining the length of the hyperbola arc are recommended for practical use in theoretical and applied research in various fields of science and technology.