Shape Optimization of Symmetric Cylinder Shape on Buoyancy Using Fourier Series Approximation

Abstract

The hydrophobicity of water striders and fisher spiders shows the geometrical property of microsetae with elaborate nanogrooves. Studying such geometrical morphology naturally leads to the question: what is an optimal shape for buoyancy? In this paper, we present a methodology to find suboptimal shapes for star-shaped cross-sectional rods, which maximizes the buoyant force by modeling the cross-sectional shapes with Fourier series representation in the polar coordinate. We provide four suboptimal cross-sectional shapes and their experimental results. Our results support the importance of the geometrical shape for buoyant force and might be helpful in designing water repelling devices.