Analytical Solutions for Bending Of Fireworks and Similarities with the Solution of Electromagnetic Wave Diffraction

TL;DR

This paper derives analytic equations describing the bending of rod-shaped fireworks, revealing their patterns are similar to electromagnetic wave diffraction phenomena, and suggests broader applications in natural evolving systems.

Contribution

It introduces new analytic solutions for firework bending, linking them to Fresnel integrals and electromagnetic diffraction, a novel approach in understanding such phenomena.

Findings

Bending patterns resemble cornu spiral

Positions are described by Fresnel integrals

Method applicable to other natural phenomena involving evolving stiffness

Abstract

In this paper we examine more deeply about the bending mechanism of rod-shaped fireworks which burned from the free end. We derived new analytic equations. Surprisingly, we obtained the bending patterns are similar to the cornu spiral. With a few simple steps we proved that positions of points throughout the fireworks are given by Fresnel integrals, C(x) and S(x), which are generally found in phenomena of electromagnetic wave diffraction. Although we deeply discussed bending of fireworks rods, however the proposed method is likely to explain any phenomena in nature related to an evolving length scale associated with some material that becomes progressively stiff or dry, such as the growth of resin exuded from trees.