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Buoyancy: What Goes Up Must Come Down to Density

A hot-air-balloon ride is a magical experience, but it works because of the same principle that makes ice float. Strap in as Groupon explores the basics of buoyancy.

The Greek philosopher Archimedes is famous for coining the term, “Eureka!” in his bathtub when he noticed that the water level rose as he lowered himself in. Among his other revelations, Archimedes discovered the following principle: an object immersed in a fluid experiences an upward force equal to the weight of the liquid it displaces. This concept is known as buoyancy, and it explains why, for example, an ice cube floats in a glass of water. Ice is less dense than water, but it still displaces the same volume of water as its own volume (another Archimedes principle). Thanks to buoyancy, the upward force is equal to the weight of the displaced water, not the ice, and the lighter cube ends up floating.

The same principle explains why a massive hot-air balloon floats as effortlessly as an astronaut evading his chores. As the air inside the balloon is heated, it expands and becomes less dense—each cubic foot of 300-degree air, for instance, weighs about half an ounce less than the same volume of colder air. According to Archimedes, the object (balloon) immersed in a gas (the sky) experiences an upward force equal to the weight of the gas it displaces (the outside air). So as long as the lift generated by the hot air is greater than the balloon, its basket, and its passengers combined, it lifts off into the sky. To bring the vessel back to earth, the pilot simply lets the hot air escape through a vent, increasing the density of the air inside and tipping buoyancy’s scales back toward gravity.