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Real World Physics Problems Newsletter - Lead Balloons, Issue #30
May 02, 2016

Lead Balloons

There's a myth that a balloon made out of lead can't float. This myth was actually tested on Mythbusters once, and they determined that yes, a balloon made out of very thin lead foil can float when filled with helium, provided it's big enough. The Mythbusters built a balloon that was roughly a cube shape, with each side measuring 3 meters. Given how interesting this myth is, I decided to work out for myself how big a helium-filled lead balloon would have to be, based on the lead foil thickness, in order to float. In my model I make the balloon a perfect cube shape, with 1 mm thick steel wire used to build the cube frame with. Each edge of the cube consists of a single steel wire which makes up the frame (there are 12 edges in total). The wire frame is then covered all around with thin lead foil, 0.02 mm thick. Lastly, the balloon is filled with helium to a pressure equal to atmospheric pressure (101.3 kPa). The helium temperature is 20 degrees Celsius. By filling the balloon with helium at atmospheric pressure, it will neither expand or contract, which is ideal for not tearing the very thin lead foil constituting the envelope of the balloon.

So after working it out, I find that for lead foil of thickness 0.02 mm, the minimum side length of the cube-shaped balloon is 1.4 meters, in order to float. By the way, my calculation is based on Archimedes' principle, which is the same principle that is responsible for hot air balloons floating. Now, for a lead foil thickness of 0.2 mm, the minimum side length of the cube-shaped balloon is about 14 meters - which is much bigger! And it's also very heavy, weighing about 3 tons. This far exceeds the weight of a regular hot air balloon of comparable size, giving good evidence that, although a lead balloon can float, it's not at all practical!

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