If you double the length of a balloon, you increase the volume by eight (since volume is proportional to the radius cubed). But what about the things outside the balloon? Let’s say that I want to make everything fair and increase the size of the material by two parts for the larger balloon. Since these things only cover the top of the balloon, its area can be increased by four. If you combine the two sizes, the contents of the larger balloon will also weigh five times the smaller one.
But sometimes, you don’t have to keep making bigger and bigger skins. I can find materials (let’s say rubber) that are very strong at 1 millimeter thickness. This means that if I increase the height of the balloon by a factor of 10, the volume will increase by 1,000 but otherwise the weight of the balloon will only increase by 100. This volume is important because that is where I get my speed.
Now let’s go the other way. Let’s make an ant balloon. If I decrease the height of the standard party balloon by 100 (actually it should be smaller than that), the thickness of the shell should also decrease by 100. These balloons are already too thin. Reduce it too much and you won’t have enough structure to hold the balloon together. Increase the thickness a little and the mass becomes too high to float. Sorry, no ant balloons.
Larger Balloons Are More Difficult
There! I have a big balloon and it floats. What could be more surprising? Sure, I’ll need a bunch of people to handle it (along with a few trucks), but it’s still a big balloon. But wait. Large balloons still have problems. Making things bigger can make it easier to float but adds more complexity.
The first problem is the wind. Sure, the breeze of your little hand-held balloon is making you angry. But what happens when you increase the size of the balloon? The buoyant force on the balloon is equal to the area around it. If you double the height of your balloon, you quadruple the area, which quadruples the force of the air.
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