question for science/engineers guys (bioshock related)

There's no technology available that could create something seen in the game with massive floating structures. Something like that could only be achieved with some form of levitation as you couldn't float something so heavy in light, highly turbulent air and still keep it stable. Hell, I doubt we could even build something like it on the sea which would be a lot easier in comparison.
 
Speaking as an actual engineer, no. It's not possible with modern technology, let alone the century old technology of the game. If you actually take a look at the balloons which are holding these buildings up, they are far too tiny to lift such a weight, even if they were filled with hydrogen instead of helium. A big enough balloon could lift it, but:

1) it would have to go above the buildings, not below, to maintain stability, which would block out all that lovely sunlight.

2) the buildings would not look like that - their structure would have to be completely different to account for being supported from above instead of by foundations from below. Doing that to a normal pre-depression era building would make it fall to pieces.

Also, hydrogen and helium would leak out of the balloons, so there's no way the city could survive like that for very long without replenishing its lifting gases.

So yeah, it's not realistic. But it's still a pretty awesome setting for a game.
 
There is someone that lives on a man made island, from bottles keeping his land afloat. Cannot remember where I saw this though, it was part of a documentary I believe.

Edit: Here he is:

 
Just ask the architects of Cloud City on the planet of Bespin - featured in that historical documentary "The Empire Strikes Back"...
 
A pseudo floating city, held up by massive pillars like Midgar in Final Fantasy VII would be cool enough.
 
Idea 1: expanding on uncle_rufus's space elevator style idea, you could tether the city to many very heavy weights in space. For large adjustments in height you could use a winch to allow the weight to go further into space or to haul it closer to earth. for finer adjustments some powerful turbines could be used

Idea 2: use 8923746590283745 of the things shown at the start of this video:
 
Just strip away the earth to around a hundredth of its mass, then you could easily do it with a few desk fans. Or create two objects of relative masses that create a sweet spot where such a city is pulled in both directions equally.
 
[..]
this is basing it on the following:

we had unlimited budget & resources
no real reason not to.

basically I'm asking if it was technically possible.

we could use rocket fuel but it be a bit dangerous :p

With those conditions, it would be technically possible with today's technology. The conditions nullify each other though, because with today's technology you couldn't possibly have unlimited budget and resources. Also, while it would be technically possible to have massive rockets all over the place to provide enough force to counter the force of mavity on a city and enough rock under it to keep it together, it wouldn't really be possible. Also, that much thrust would be wildly dangerous even without the danger of countless billions of tonnes of rocket fuel. You'd be causing huge changes. For example, the air under the city would be displaced extremely forcefully by the vast amount of thrust from the rockets holding the city up. You'd be creating winds that would make hurricanes look like a fart from a small mouse. It might change weather patterns globally. It would certainly create a big uninhabitable zone of destruction.

EDIT: I'm reconsidering - would there be enough space under the city to fit the number of rockets required to produce enough thrust? I don't know. It might not be even theoretically possible with today's technology even with those unobtainable conditions.
 
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