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Bending of Sparklers

A new equation is proposed to explain the curvature of spent sparklers. We found the state of a segment of the sparkler to depend strongly on the state of its spent segments. The equation is nearly able to produce the sparkler shape for a range of lengths and for all elevation angles. The method proposed here 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. The equation can produce a very rich spectrum of shapes by varying material parameters (density, temperature-dependent strength), heating temperature, elevation angle, and gravitational acceleration. This might provide new insights into explaining many shapes in nature or man-made structures.