Lifing A House With Balloons

Looks like the scenario as depicted in Disney/Pixar's "Up" continues to get quite a mileage for discussion.

This is Physics World blog, several interesting topics were discussed and linked to. This includes the topic that we had discussed before, which is the scene from "Up" where huge amount of balloons were used to lift Carl's house.

If you enjoyed the film Up, you might want to peruse the paper that asked how many helium balloons would actually be required to lift a small wooden house – like the one in the film – as well as a common brick house found in the UK. The authors found that it would take almost 10 million helium balloons to lift the small wooden house and 400 million helium balloons to lift a typical UK house! They note the downfalls of this particular method of relocation though, by concluding that the balloons would “deflate very quickly at high altitudes” and that the “foundations and drainage of the house would be removed, making the structure very unstable, if by some miracle the journey is possible.” Pity, balloons would make moving so much easier!

Hum... I think they might have missed something. I went and look at the paper (freely available in that blog article if you follow one of the links). This is what the authors said in the discussion:

Since the air density decreases with altitude this would not be enough to let it climb indefinitely, even assuming that no helium can escape from the balloons. This is because the air density (and therefore the buoyancy force) is inversely proportional to N. This means that N would have to be even higher to reach an altitude of normal aeroplanes (37000 ft or 11277m [5]).

At an altitude of 11277m the air density is approximately 0.3471kgm-3 [6] which is more than 3 times smaller than at sea level. This means that N would have to be more than 3 times greater than that calculated previously at this altitude than at sea level.

The balloons will also deflate over time which will also be exacerbated by altitude, even at different altitudes close to sea level [7]. This is due to the diffusion in the balloons [8] to a space of much lower pressure, which at an altitude of 11277m is going to be a massive effect.

Hum... As the balloons rises to higher altitude, it is true that the air density surrounding the balloon becomes less. However, because of that, one can also argue thatm, for ordinary balloon that has elastic skin, the VOLUME of the balloon is also expanding. So in this case, the displaced volume gets bigger, which will add to the buoyancy. Whether the additional buoyancy can compensate for the decrease in air density, that I haven't calculated. I'm sure that depends on the elasticity of the balloon, etc.

When balloon detectors are sent very high up into the upper atmosphere, if you look at the launch on earth, you'll see that the balloons were not completely inflated because of this reason. If you sent things up already fully deflated, the drop in air density (pressure) will cause the balloon to want to expand even further and will eventually cause a rupture in the balloon.

Zz.