How big can the Parachute cities be?

Nobody knows where the big Blue is. Some people say it's a dream. Some people say it's the space between the worlds, where all the things that fall through the cracks end up. The occasional rains of odd socks and pencil sharpeners make me inclined to believe the latter though.

Either way: I know we're falling. Everything, forever, falling through an endless blue sky. The only real stable places are the four Parachute City states: Maelstrom, Charybdis, Freefall and Slip. Four agglomerations of rock and dirt, wooden ships and aluminium planes and some metal parts that nobody left here recognises.

Inside we fall along with whichever city we were born on, protected from the winds below by the lee of the city (though the crosswinds can be brutal). The careful or clever can practically jump from one city to the next, helped along by wing suits or windskiffs.

The cities keep an even keel and can slightly control where they are in relation to each other with strategically placed hot air balloons and vanes around the rim of the city, where the vicious turbulence as they plummet through the endless sky can dash careless airship captains or wing suit swimmers into pieces.

But how large can one of the cities get before they start to tumble or can't hold themselves together any longer? That's what I've been directed to find out.

How large (in terms of flat square meters on the top, assuming it's held steady) can an object falling at its terminal velocity get before the various stresses tear it apart?

Please note the hard science tag: I'm not looking for hard science criticism of the world, just a hard science analysis of the large falling object. If it helps the atmosphere is equivalent to Earth's at sea level and there is 1g of gravity.

Time to break out the fluid flow equations! (Or not. ;-)

A quick note: I don't care if the answer to this question is 'very small', I can work with that. I just want to see some kind of maths or formalised rationale (with citations or equations, preferably) behind the maximum size.

posted about 8 years ago

Joe Bloggs‭

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