Two-dimensional body of maximum mean resistance

TL;DR

This paper identifies a two-dimensional shape that nearly maximizes resistance in a rarefied medium, advancing previous research and revealing potential applications beyond Newtonian resistance.

Contribution

It presents a new optimal shape for maximum resistance, derived through numerical and analytical methods, improving upon prior nonconvex body designs.

Findings

Shape achieves resistance close to theoretical maximum

Analytical properties explain shape's effectiveness

Potential applications beyond classical resistance problems

Abstract

A two-dimensional body, exhibiting a slight rotational movement, moves in a rarefied medium of particles which collide with it in a perfectly elastic way. In previously realized investigations by the first two authors, Plakhov & Gouveia (2007, Nonlinearity, 20), shapes of nonconvex bodies were sought which would maximize the braking force of the medium on their movement. Giving continuity to this study, new investigations have been undertaken which culminate in an outcome which represents a large qualitative advance relative to that which was achieved earlier. This result, now presented, consists of a two-dimensional shape which confers on the body a resistance which is very close to its theoretical supremum value. But its interest does not lie solely in the maximization of Newtonian resistance; on regarding its characteristics, other areas of application are seen to begin to appear which are thought to be capable of having great utility. The optimal shape which has been encountered resulted from numerical studies, thus it is the object of additional study of an analytical nature, where it proves some important properties which explain in great part its effectiveness.