If you double the radius of the balloon, you raise the volume by eight times (since the volume is proportional to the radius to the cube). But what about the material outside the balloon? Let’s say I want to keep things fair and for a larger balloon I will double the thickness of the material. Since this material only covers the surface of the balloon, its surface area would raise fourfold. If you account for double thickness, the material of the larger balloon will also be eight times the weight of the smaller one.
But at a certain point you no longer need to create thicker and thicker balloon skins. I can get some material (say rubber) that is very forceful and only one millimeter stout. This means that if I raise the radius of the balloon by a factor of 10, the volume increases by 1000, but perhaps the mass of the shell only increases by 100. The volume is critical because that’s where I get my buoyant force.
Now let’s go the other way. Let’s make a balloon for the ants. If I reduce the radius of a regular party balloon by a factor of 100 (in fact it should be even smaller), the thickness of the shell would also have to be reduced by 100. These balloons are already quite slim. Reduce it too much and you won’t have the structure to hold the balloon together. Enhance the thickness a little and the mass becomes too gigantic to float. I’m sorry, but there are no parade balloons for ants.
Larger balloons are more complex
Yes! I have a huge balloon floating in the air. What could be more amazing? Sure, I’ll need a few people to hold it down (along with some vehicles), but it’s still a giant balloon. But wait. Giant balloons still have problems. Larger things may make swimming easier, but they cause other problems.
The first problem is the wind. Sure, that wind in your little handheld balloon is annoying. But what happens when you raise the size of the balloon? The force acting on the balloon is proportional to the cross-sectional area. If you double the radius of a balloon, you quadruple that surface area, which is four times the air force.