If we double the radius of a balloon, we multiply its volume by eight (since the volume is proportional to the radius cubed). But what happens to the material on the outside of the balloon? Let’s say I want everything to be just right and I increase the thickness of the material by a factor of two for the largest balloon. Since this material only covers the surface of the balloon, its area would be multiplied by four. If we include twice the thickness, the material in the largest balloon also has eight times the mass of the smallest.
Now, there comes a time when it is not necessary to continue making thicker and thicker balloon skins. I can get some material (let’s say rubber) that is very strong with only a 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 the mass of the shell may only increase by 100. Volume is important because that’s where I get the buoyancy force from.
Now let’s think the opposite. Let’s make an ant balloon. If I reduce the radius of a normal party balloon by a factor of 100 (actually it should be even less than that), the thickness of the shell would also have to decrease by 100. These balloons are already quite thin. If it were reduced too much, we would not have a structure capable of holding the globe together. Increase the thickness a little and the dough will be too tall to float. Sorry, you can’t make parade balloons for ants.
Bigger balloons are more difficult
Super! I have a giant balloon and it floats. What could be more incredible? Sure, I’m going to need a lot of people to hold it down (plus a couple vehicles), but it’s still a giant balloon. Oh wait. Giant balloons continue to have problems. Making things bigger may make them easier to float, but it adds other problems.
The first is the wind. Sure, that breeze in your little handheld balloon is annoying. But what happens when you increase the size of the balloon? The force pushing on the balloon is proportional to its cross-sectional area. If you double the radius of your balloon, you multiply this area by four, which multiplies the force of the air by four.
How about a quick estimate? If we take a balloon like the one from Dora the Explorer, it measures about 16 by 13 meters (viewed from the side). If it were a perfect sphere with a radius of only 6.5 meters, we can estimate the air force assuming a typical model for air resistance. With a wind of 4.5 m/s, the horizontal force of the air would be about 760 newtons. Not bad for a group of 30 to 50 adults. But if you double the wind speed, the air resistance would multiply by 4 to reach 3,000 newtons. Now it’s out of control.
And here is the second problem. A balloon out of control is bad. You might think that since it’s floating it’s harmless, but these balloons still have mass. If a balloon uses 12,000 cubic feet of helium, that’s about 55 kilograms of mass. If you add the mass of the balloon, it easily exceeds 200 kilograms. When a 200 kilo balloon collides with a light pole it can easily tip over, causing injuries (as has indeed happened in the past).
If these balloons are dangerous, how can we make them parade safely? There is always some risk, but it is minimized by training the pilots (yes, balloons have pilots) and leaving them on the ground in adverse weather conditions.
Article originally published in WIRED. Adapted by Andrea Baranenko.
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