I couldn't sleep last night, so I took to trying to do some mental maths. I tried to work out how many 100mm diameter balls would fit in a sphere 700mm in diameter. I failed.
I have had another go at it this morning, because it was annoying me, and I came up with a figure of 286. Please feel free to tell me I'm wrong!
If each of these balls was made of 1mm thick carbon fiber, they would weigh about 55.4 grammes. Anyone remember those "
holy holey" plastic balls you used to get, which meant cricket in the garden didn't threaten your window panes? Anyway, imagine removing half the shell of the carbon fibre balls by moulding some sizeable holes. Your ball now weighs 27.7 grammes, and 286 of them weigh 7.92kg.
These balls, in my mind, represent the most efficient way of re-inforcing our sphere such that it would take the pressure of being totally evacuated
(OK, I know that isn't poss.)
Stuff this lot of holy balls into your 700mm diameter sphere, again made of 1mm thick carbon fibre (which itself weighs 2.76kg), and the total weight of carbon fibre is now 10.69kg. Extract all the air.
The weight of the air that the sphere is displacing is, I reckon, about 0.2155kg.
Therefore, the evacuated spheroid, presuming it survived the evacuation, is some 49 times heavier than it needs to be before it would float off into the sky.
Even if you made the material 0.2mm thick, it would still be nearly 10 times heavier than it needs to be to fly.
Even just the outer shell alone, 1mm thick carbon fiber, is some 12.8 times heavier than the air it displaces. To fly, it would have to be .078mm thick max, and there is no way on this planet that this would be strong enough to cope with a perfect vacuum inside.
I'd be happy for anyone to check my figures, which are bound to be wrong......but they aren't going to be 50 times too high, and that illustrates the huge issues required to be overcome before any vacuum zeppelin would fly.
Mike (ducking for cover, for fear of having my maths shredded!)