Functions and Analysis

Simple Formulas for the Horizontal Span of a Catenary Curve

Authors: Yuhei Ando
Comments: 15 Pages.

This study derives formulas for the horizontal span of a catenary curve, formed by a string fixed at two points. Given the heights h_1 and h_2 at the endpoints and the curve length l, we calculate the horizontal span s. We consider two cases based on the position of the minimum point, proving corresponding formulas. Theorems 1 and 2 provide complex logarithmic expressions, while Theorems 3 and 4 offer concise forms using hyperbolic functions. These results enhance the understanding of catenary curves and support applications in engineering and physics, where precise calculations of such curves are essential.
Category: Functions and Analysis