This was originally written as a university physics assignment. As such, it is longer and contains more technical detail than most of my other writing.
The 2009 film ‘Up’ featured the fantastical idea of flying a house by means of a large number of helium balloons. This plays off the common comedic idea of helium balloons being able to lift large objects, such as people. While we know this isn’t achievable with a single balloon (citation – I can hold a balloon), in theory it’s completely possible – hot-air balloons work off the exact same principle of a low-density gas carrying objects through the atmosphere. So how many balloons are needed to actually fly a house?
I’m ignoring the logistics of how you could tie balloons to a house with enough stability that it wouldn’t just fall apart – I’m assuming that the house has been specially built with a frame that allows balloons to be attached, and holds the whole building together. After all, if you’re going to take your house for a fly, you should be prepared.
House Sizes
Obviously, the size of the house that you’re planning to move is the key variable in this whole idea – a tin shack is going to need hardly any balloons compared to a mansion. However, house weights are quite difficult to find. After all, houses aren’t meant to be picked up and moved… most of the time. Sometimes houses are placed on objects other than the ground – specifically, trucks. It isn’t uncommon for people to relocate houses on trucks these days, often in several pieces. Using information about truck load limits, we can roughly determine the weight of a typical house.
According to Australian law, the maximum weight to be carried on a truck is twenty tonnes (for a quad-axle group with double tyres). Trucks can carry larger loads with a special exemption, but this is a good estimation for how much a house-transporting truck is carrying. I’m going to assume that an average house would take three trucks to transport it – many that you see on the road have only been halved, but they are also often smaller and made of lighter materials than the actual average house, so I feel three trucks is a good estimation. This means that a house weighs about sixty tonnes. I’m going to round this up to 100 tonnes (10 kg), which is the same to an order of magnitude, to account for underestimation, as well as make calculations easier. (Yes this is lazy, no I don’t care. You shouldn’t be taking this as serious advice anyway.)
Buoyancy of Helium
Helium is quite a buoyant gas – being the second element in the periodic table, it has an incredibly low molecular mass. As such, it is often used to inflate balloons so that they float aesthetically, as opposed to just lying on the floor. The density of helium is 0.164 kg/m3, compared to an average atmospheric density of 1.161 kg/m3. This means that, every cubic metre of helium can lift a mass of approximately one kilogram (1.161-0.164=0.97 kg/m3). As such, to lift our house, we need 100,000 cubic metres of helium. If this helium was placed in one massive balloon, it would have a radius of about 30 metres. However, it’s pretty hard to find a balloon that size. Regular party balloons, on the hand, are pretty common, so let’s use them.
Balloon Size
The average party balloon has a radius of between ten and fifteen centimetres. This equates to approximately 0.1 metres for the radius of a balloon, with a spherical volume of 0.004 m3. However, I’ll double that to 0.008 m3, because balloons are about twice as tall as they are round, and so have double the volume than was calculated. (Pretty sure this was me correcting for earlier calculations which said helium in a balloon couldn’t even lift that balloon, let alone a house. We know that’s wrong because helium balloons float.)
Dividing the volume of helium to lift the house by the volume per balloon, we need a total of 12.5 million balloons. This is assuming no balloons pop and no helium leaks out. We could try using hydrogen, which is less dense than helium, but it won’t make much of a difference – it still lifts about a kilogram per cubic metre, and so we would need approximately the same number of balloons.
Additionally, there’s the weight of the balloons themselves to account for. I initially discounted this as being insignificant compared to the weight of a house, but given the sheer number of balloons now being used, this will add up. Using a balloon mass of about five grams, and multiplying by 12.5 million, the total balloon mass is found to be 62 million grams, or sixty-two tonnes. This is like lifting another small house, and so is actually quite a significant factor. The equation for the mass of the house plus balloons, in kilograms, will be 100,000+0.005b (where b represents the number of balloons). This equation must equal the total lifting power of the balloons, which is given by 0.008b (since each balloon can lift 0.008 kg). As such, the total number of balloons required can be determined by 100,000+0.005b=0.008b. Solving this equation gives a result of approximately 33 million balloons.
This is an incredibly large number. To fill these balloons, 132,000 m3 of helium would be needed. This is equivalent to almost fifteen thousand large helium bottles, and is, needless to say, incredibly impractical, not to mention incredibly wasteful of our dwindling supplies of helium. This is probably good, because if it were actually easy to fly your house around, with no real way of controlling speed or direction, huge amounts of damage would surely occur as people sought to recreate their Disney dreams.
Lachlan Writes Science 