A Design of an Axisymmetric Roof With a Horizontal Rotation Axis

ABSTRACT This research proposes a novel roof design whose shape follows the mathematical model of an ideal hanging surface. The resulting roof is a surface of revolution, but its rotation axis is horizontal, which challenges conventional intuition because the axis is perpendicular to the direction of gravity. Similar to the catenary, inverting a solution of this equation yields the shape of an ideal roof where the internal forces are purely tangential at every point. By investigating the possible solutions under specific geometric assumptions, we demonstrate the existence of ideal roof shapes that are axisymmetric with respect to a horizontal axis. This paper presents the properties of this axisymmetric horizontal roof, along with graphical visualizations and numerical approximations of the generating curve derived using simple methods.