Icicles hanging from the roof on a winter's day look like glittering stalactites suspended from the roofs of hidden caves. It wasn't until 2005 that scientists figured out the mathematical formula that described the shape of stalactites. In 2006 those same University of Arizona scientists discovered that the formula also described the spiky shape of icicles.

Stalactites and icicles, however, are formed by different processes. Stalactites grow - very slowly, over many years - from the minerals left behind when dripping water evaporates. Icicles, on the other hand, are made of water itself, frozen in the shape of an icy sword.

How do icicles form? A snow-covered roof on a sunny, frigid day makes a perfect icicle incubator. Sunlight heats the rooftop snow, which is also warmed by heat radiating from the attic. As the snow melts, water trickles down the roof to the icy-cold edges and metal gutters. Since metal is such a good conductor of thermal energy, the water quickly loses heat to the gutter. And so it refreezes, forming an icy ridge.

As water continues to run down the roof, pulled by gravity, it collects where its fellow molecules have already frozen. (Water molecules are attracted to other water molecules.) Ice adds to ice, drip by drip. And slowly, an icicle grows toward the ground.

(Ever notice an icicle's bumpy ridges? Scientists say the bumps start out as small bulges. Since they jut out into the air, these bulges lose heat more quickly than other areas of the icicle. So trickling-down water refreezes on the bumps first, making them thicken into ridges.)

But it's not just dripping water that fuels the growth of an icy spike. The temperature of the liquid water dripping off the roof is higher than that of the freezing air. Heat energy flows from warmer objects to cooler objects. So heat diffuses from the thin film of water coating the icicle's surface into the cooler air around it.

As it loses some of its heat, the water film freezes, piling on another layer of ice to the growing icicle. The icicle's growth is amplified by a peculiar feature of water: Liquid water actually expands as it freezes (think ice cubes bulging out of a tray). This process of melting, dripping and refreezing makes icicles grow into long, glittering spikes. Icicles can grow 5 feet long or more before their own weight causes them to crash to the ground.

The secret to an icicle's sharp point is the surrounding air. How does it work? As water flows down the ice, loses heat to the air and refreezes, a mini-updraft of warmed air whooshes up the icicle. This warmer air surrounds the top of the icicle like a blanket.

Since the top of the icicle is warmer than the bottom, its growth slows. Meanwhile, as long as water continues to drip, the tip grows more. The result: a long, tapering, spiky icicle - with a very pointy tip.

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