If you double the radius of a balloon, you increase the volume by a factor of eight (since volume is proportional to the radius cubed). But what about the material on the outside of the balloon? Let’s say I want to make everything fair and I increase the thickness of the material by a factor of two for the larger balloon. Since this material only covers the surface area of the balloon, its area would increase by a factor of four. If you include the double thickness, the material of the larger balloon also has eight times the mass of the smaller one.
But at some point, you don’t need to keep making thicker and thicker balloon skins. I can get some material (let’s say rubber) that is very strong at just one millimeter thick. This means that if I increase the radius of a balloon by a factor of 10, the volume will increase by 1,000 but maybe the mass of the shell only increases by 100. The volume is important because that’s where I get my buoyancy force from.
Now let’s go the other way. Let’s make a balloon for ants. If I decrease the radius of a regular party balloon by a factor of 100 (really it should even be smaller than that), the thickness of the shell would have to also decrease by 100. These balloons are already pretty thin. Decrease too much and you just wouldn’t have a structure capable of holding the balloon together. Increase the thickness a little bit and the mass gets too high to float. Sorry, no parade balloons for ants.
Bigger Balloons Are More Difficult
Yay! I have a giant balloon and it floats. What could be more awesome? Oh sure, I am going to need a bunch of people to hold it down (along with a couple of vehicles), but it’s still a giant balloon. But wait. Giant balloons still have problems. Making things bigger might make it easier to float but it adds other issues.
The first problem is wind. Sure, that breeze on your little hand-held balloon is annoying. But what happens when you increase the balloon size? This force pushing on the balloon is proportional to the cross-sectional area. If you double the radius of your balloon, you increase this area by a factor of four, which gives four times the air force.