If you double the radius of the balloon, you increase the volume by one-eighth (since the volume is equal to the radius cubed). But what about the cargo outside the balloon? Let’s say I want to make everything fit and double the thickness of the object with a large balloon. Since this object covers only the surface of the balloon, its area will increase by a factor of four. If you include twice the thickness, the material of the large balloon is also eight times as thick as the small one.
But sometimes, you don’t need to keep making thick and thick balloon skins. I can get something (let’s say rubber) very hard about one millimeter thick. This means that if I increase the radius of the balloon by a factor of 10, the volume will increase by a factor of 1,000 but the volume of the shell may only increase by a factor of 100.
Now let’s go the other way. Let’s make an ant balloon. If I reduce the radius of a regular party balloon by a factor of 100 (actually it should be smaller than that), the thickness of the shell will also have to decrease by 100. These balloons are already very thin. Reduce it too much and you wouldn’t have a structure that could hold the balloon together. Increase the thickness a bit and the weight becomes too high to float. Sorry, no balloons for the ant show.
Yes! I have a big balloon and it floats. What would be amazing? Sure, I’ll need a bunch of people to hold it down (and a few cars), but it’s still a big balloon. But wait. Larger balloons still have problems. Making things bigger can make it easier to float but adds more problems.
The first problem is the wind. Sure, that wind blowing your little hand-held balloon is annoying. But what happens when you increase the size of the balloon? This force pushing the balloon is proportional to the cross-sectional area. If you double the radius of your balloon, you increase this area by four, which gives you four times the force of the wind.
