# Balloons!

When I was a kid, I heard about the buoyant force. Specifically, I heard that the more air/water/fluid something displaces, the more force there is pushing it upward, and if that’s more than the weight of the thing then it’ll float up. Sound right so far? Well, I interpreted that to mean that if you drop a rock off a really high cliff, it’ll eventually move enough air to make it stop falling. And the reason why there aren’t a bunch of rocks that have displaced enough air to float around must be because there isn’t a tall enough cliff on Earth. I may have tried to impart that knowledge to some impressionable younger siblings, and I may have been shot down by their inexplicable common sense in the face of revealed scientific truth. Well, that’s my embarrassing backstory for the day; on to the present.

Someone asked me how many balloons it would take to lift a house. Obviously it’s a lot more than Pixar says, but how much more? As you might expect the answer is “more balloons than you’ve ever seen,” and in fact it takes tons of balloons. Like, literal tons.

According to the masters of internal capital letters and empiricism known as the MythBusters, 3500 balloons lifts a 44-pound three-year-old. That means one balloon can lift about an eightieth of a pound, which is…not a lot. But it’s more or less right. Helium weighs 0.1785 kg/m^3, air weighs 1.225 kg/m^3, so a balloon can pull hard enough to lift 1.225-0.1785= 1.0465 kg per cubic meter of balloon.

If a normal party balloon has a diameter of ten inches, it takes up 8.58*10^-3 m^3 and can lift a 8.98*10^-3 kg mass. (That’s an order-of-magnitude estimate assuming a spherical balloon, just to see what a reasonable number looks like. It’s not supposed to be right, just close.) So one balloon would lift 0.0198 lbs, which is reasonably close to the actual number. So, balloons don’t lift very hard and it’ll take a lot of them.

It’s easy to overestimate the strength of buoyancy. Try this: If gravity were to suddenly stop affecting you, would you float away or would your clothes be heavy enough to hold you down? I tested this,* and it’s not even close. It’d be perfectly safe, except maybe in strong winds. Point is, being pushed upward by air displacement is really weak. But you knew that already because you paid close attention to those numbers.

For some reason, the Internet doesn’t always say how much fictional characters weigh. But guesses are still allowed. Carl Fredricksen is 78 years old, the median weight for men that age is about 170 lbs, so it would take over 13,500 balloons to lift him. That’s a lot more than is remotely likely, and that’s just to lift him.

Now I’m going to go out on a limb and say that his house weighs more than he does. Number: 80,000 lbs. That’s another 6.4 million balloons. Since the ratio of lifting power of the helium to mass of the helium is 1.0465 to 0.1785, that means that the balloons lifting 80,000 pounds would themselves weigh 13.6 thousand pounds. That gives them a mass of over six and three quarters tons. (Things I did not know: The ton, the 2000 lb one, is a unit of mass not weight.) To lift that house, you’d need enough helium to be two or three times heavier than your car. Good luck with that.

Google tells me that the balloons themselves also weigh a few grams, meaning it would take some extra helium to lift all that rubber. And that party balloons are often filled with a mixture of air and helium, meaning it’d take even more of them to get the same amount of lift. I’ll ignore those and just stick with the 6,400,000 number; it’s already too big.

Let’s say Carl Fredricksen’s balloon-blowing powers allow him to inflate and tie off one balloon per second. And that it takes him no time at all to set them all up to come out the chimney in perfect formation. Then that many balloons would take him six point four million seconds to prepare, otherwise known as two and a half months.

Which leads to the next question: When they dramatically came out the chimney, where were the balloons coming from? Inside the house. So when they, being balloons, were pushing upward, what stopped them? The house. If they could pull hard enough to lift the house, they should have done that as soon as he inflated them. Besides which, there obviously isn’t enough space for all those balloons in the house. The obvious answer (in case the implausible conveyance, younger sidekick, treating physics as optional, tweed, and bow tie didn’t tip you off) is that Carl is a Time Lord and the balloons were stored somewhere bigger on the inside. But that’s a bad idea both for intellectual property reasons and also because I should stop using that as the explanation for everything. More likely it’s just a suspension of disbelief thing. In this case, those balloons can apparently suspend both that and the house.

There are a few reasons why this is even harder than the 6.4 million balloons. For one thing, that represents the number it’d take to support the weight of the (empty) house. It’s not enough to both pull it upward and break it off the foundation. So he’d need a lot more balloons, and I can’t say how much of a lot more.

The other reason is that party balloons are not a good method for long-distance travel. When a balloon goes upward, it expands as the pressure around it decreases. Eventually, the pressure gets low enough that the balloon expands enough that it pops. The balloons Carl used are full even at the start, and they’re not made of anything unusually strong, so they’ll do that at a pretty low altitude. And they’re close enough together that they don’t have much room to expand. This is why actual balloonists don’t use those even though it’d be cool.**

The moral of the story is to always do the math first before doing anything like that, just in case physics decides to pay attention that day.

*This was a Noodle Incident that I will not explain except to say that in the course of testing the hypothetical question I lost my only key ring but not the keys on it. Empiricism may have unexpected side effects. Consider sticking with math, which has less.

**There is at least one person who built a replica of the house and lifted it with balloons. The main differences were that he used bigger, less tightly filled balloons than his fictional counterpart did and it was a much smaller and lighter house that was basically just a box and so it would be much less impossible and I’m just jealous.