So, I was sitting in my algebra based college physics class and we were talking about buoyancy. According to Archimedes' Principal, "an object that is completely or partially submerged in a fluid experiences and upward force equal to the weight of the fluid displaced.":
Fb = mg
It got me to thinking, why not just make a balloon with nothing inside of it? Wouldn't that float a lot better than a balloon filled with helium, or even hydrogen? The problem is that without anything inside of the balloon to counteract the force of the atmosphere, the balloon will collapse.
A quick google search shows that I'm not the first person to ask this question. One person said:
"build it LARGE. This makes for the greatest amount of interior space as opposed to the structure that contains it."
Makes enough sense. The surface area/volume ratio actually gets smaller as the balloon gets bigger. The surface area gets smaller relative to the volume as the balloon gets larger. Intuitively, this doesn't make sense to me though. The rigid balloon material would need to be thicker for a larger balloon, would it not?
The Attempt at a Solution
I got nothing. Somehow you need to account for all of the unknowns: mass, thickness, and density of the material, as well as the size of the balloon.