Derivation of the radius of gyration and aspect ratio of a circular, constant thickness patch on a spherical surface
Year: 2025
Type: article
Abstract: In this technical note, we present a direct derivation of closed-form expressions for the following parameters for a circular, constant thickness patch on a spherical substrate, where the patch thickness and coverage can be varied independently: The moment of inertia of a patch about its symmetry axis. The radius of gyration of the patch. The aspect ratio of the patch, defined as the ratio of an effective “diameter” (twice the radius of gyration) to the patch thickness. The relationship between patch volume, coverage, and aspect ratio. These analytical expressions not only fill a crucial gap in the technical literature but also provide a quantitative basis for assessing how variations in patch morphology influence mechanical, dynamic, and optical properties, thereby offering valuable guidance for both theoretical analysis and experimental design.
Authors: Klupp Taylor, Robin, Seifert, Julia
Institution: Friedrich-Alexander-Universität Erlangen-Nürnberg
Language: English
Subfield: Civil and Structural Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W6912078530