Mathematics of Floating 3D Printed Objects

TL;DR

This paper combines mathematical modeling, computational analysis, and 3D printing experiments to study the stability of various floating shapes, providing tools and insights for designing stable floating objects.

Contribution

It introduces a comprehensive framework for analyzing floating stability of 3D printed shapes using energy landscapes and offers open-source code for testing new designs.

Findings

Identified stable and unstable floating orientations for various shapes.

Validated models with experimental 3D printed objects.

Provided computational tools for shape stability analysis.

Abstract

We explore the stability of floating objects through mathematical modeling and experimentation. Our models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes' Principle. We investigate a variety of floating shapes with two-dimensional cross sections and identify analytically and/or computationally a potential energy landscape that helps identify stable and unstable floating orientations. We compare our analyses and computations to experiments on floating objects designed and created through 3D printing. In addition to our results, we provide code for testing the floating configurations for new shapes, as well as giving details of the methods for 3D printing the objects. The paper includes conjectures and open problems for further study.