Scientists have long understood how snowflakes take shape, but icicles have remained a wintry wonder.

A solution has finally emerged — from a cave.

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In 2005, researchers determined that stalactites, the long, carrot-like structures that hang from ceilings of caves, have a distinctive shape that can be described by a simple mathematical equation.

Oddly, the same math applies to icicles, a new study shows.

Unexpected result

Although stalactites and icicles have similar shapes, they don't have any physics in common.

Icicles grow from heat diffusion and rising warm air, while stalactites rely on the diffusion of carbon dioxide gas.

"We didn't expect to be able to apply the same math, because the physics of the two are so different," said mathematician and physicist Ray Goldstein of the University of Cambridge in England.

"It is really the same shape, apart from the bumps and wiggles," Goldstein added. "It confirms what we know with our eyes."

The findings were published in a recent issue of the journal Physics of Fluids.

Icy ingredients

Icicles typically form on days when the outdoor air temperature is below freezing, but sunshine warms and melts some snow or ice.

As it drips off your roof, a water droplet loses heat to the cold air and eventually refreezes.

An icicle starts with a few frozen droplets. When it reaches a certain size, drops begin to drip down the sides of the structure.

"The water will run down the sides of the formation evenly, in a thin film, and freeze on the way down," said University of Arizona physicist Martin Short, another member of the study team. "This sort of freezing thin film of water is what leads to the eventual icicle shape."

Heat at work

The thin fluid layer on the surface of an icicle gives off heat that warms the air around it through a process called conduction.

As warm air rises, it removes heat from the liquid layer and causes it to freeze.

Here is the main point: The buffer of heated air is widest at the top of the icicle, where conduction is slowest.

"The buoyant air layer is really the most important factor in determining the icicle shape," Short told LiveScience.

Imagine the warm air as a blanket of differing thickness. The thinner part, at the bottom tip, allows more heat to escape than does the thick part of the blanket at the top.

"So the tip grows faster than the base, making the icicle pointy," Short explained.

The research was based on icicle photographs. To test their idea against actual icicles, the team plans to grow icicles in a lab and film their growth.

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