If you double the radius of a balloon, you increase the volume by a factor of eight (since the volume is proportional to the radius cubed). But what about the material on the outside of the balloon? Let’s say I want to get everything right and I increase the thickness of the material by a factor of two for the larger balloon. Since this material only covers the surface of the balloon, its area would increase by a factor of four. If you include the double thickness, even the larger balloon material has eight times the mass of the smaller one.
But at some point it will no longer be necessary to keep making thicker and thicker balloon skins. I can get some material (let’s say rubber) that is very strong with a thickness of just a millimeter. This means that if I increase the radius of a balloon by a factor of 10, the volume will increase by 1,000 but perhaps the mass of the shell only increases by 100. The volume is important because that’s where I get my buoyancy.
Now let’s go to the other side. Let’s make a balloon for the ants. If you decreased the radius of a regular party balloon by a factor of 100 (it should actually be even smaller than that), the thickness of the shell would also need to decrease by 100. These balloons are already pretty thin. Decrease too much and you wouldn’t have a structure capable of holding the balloon together. By increasing the thickness slightly, the mass will become too tall to float. Sorry, no parade balloons for the ants.
Larger balloons are more difficult
Yes! I have a giant balloon and it floats. What could be more fantastic? Oh sure, I’ll 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 floating easier, but it adds more problems.
The first problem is the wind. Sure, that breeze on your portable balloon is annoying. But what happens when you increase the size of the balloon? This force pushing on the balloon is proportional to the cross-sectional area. If you double the radius of your balloon, you will increase this area by a factor of four, which gives four times the air force.