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A few years ago, some friends and I went out to a Christmas dinner at a restaurant. The restaurant had a high ceiling, and over the course of the meal, we found out that it takes 23 helium filled balloons to lift a half-full salt cellar to the ceiling fan. We weren't allowed back in the restaurant.
However! With new fangled maths, we can work this out. Helium provides about 9.8 newtons of lift per cubic meter, at sea level and room temperature. That's enough to lift 1kg. So let's assume, to make the calculations easier, that we remain at sea level and room temperature.
5 stone is 31.75 kg, so we need over 31.75 cubic meters of helium. Let's say 31.8 cubic meters.
Now, according to a party supply website I found, big party balloons are 12" across. They're not a uniform shape, but to make the maths easier, let's assume they are - we'll end up with a rough figure. 12" is 0.3048 meters, so the radius is 0.1524m. The volume of a sphere is 4/3 * pi * r cubed, so the volume is 0.014827 metres cubed.
So we want 31.8 m3, and a balloon gives 0.014827 m3. The number of balloons in 31.8 would be 31.8/0.014827, which is about 2212.
Since we've approximated lift, ignored the mass of the balloon's material, and approximated its volume, there's likely to be a large variation in the answer, and indeed an easier job using larger balloons, but 2200 is a good ballpark figure to start a project with.
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