Plausible design/size of flying cities?
Setting
The setting was a tropical, Mars-sized, ocean-covered world that has completely frozen over. Over the span of several years, the mean global temperature had dropped to below 200 Kelvin. Ice sheets had expanded out from the polar landmasses, as well as from the coastlines of the many chain islands that had peppered the seas, sealing the world in bleakness. Many dozens of millions of humans died in the sudden climate shift, unable to grow food and provide adequate shelter.
"Icefall" lead to the manifestation of great storms that plague the most of the planetary surface. Geothermal activities at previous volcanic island locations drive an engine of jet streams that continuously recycle and resurface the planet of ice and snow. Windspeeds for these storms can occasionally exceed 350 kph, and the rate of fresh snowfall can reach several meters inside a week. Due to the lower gravity, hailstones can rise to greater altitudes and remain airborne for greater durations, increasing hailstone sizes. Inside active storm regions, hail bombards the landscape with stones sometimes large enough to crush a man. On the relatively flat plain of the previous world-spanning ocean, storm structures are allowed to travel far with little topological obstructions and benefit from many geological "hotspots", before whirring off in some polar direction.
All in all, due to constant tempestuous winds/explosive blizzards, heavy snowfall, and destructive hail, it is essentially impossible to settle the surface at almost any latitude above or below the equator.
The poles, however, provide some safety. Both poles are home to the planet's greatest mountains. Storms that meander their way far north or south break and dissipate against the rougher terrain. Most humans who survived Icefall had done so in these polar "safe-havens".
Special circumstances
To go any further, I have to explain a piece of Clarketech. Without going into much detail: after the onset of Icefall, a kind of biannual meteor shower takes place. 922
Hundreds of thousands of tons of metal and slag enters the atmosphere and impacts around the globe. Among the debris are objects called "spinners". Spinners are two identical, long, bar-like rectangular prisms adjoined by a common face, counter-rotating w.r.t each other, typically at rates of rotation no greater than a few RPM. They're made from a metal that is, for all intents, indestructible, and no amount of ungodly force can slow their rate of counter-rotation, betraying a near-infinite torque and tappable work.
I should also note that for reasons mostly unimportant to the question, the human civilization is technologically suppressed by some unworldly force. Transistors and diodes fail erratically, and anything more advanced just does not function. The planet is also extremely metal-poor. The pre-Icefallen civilization was stuck firmly in a sailing ship era and could not leave the planet when hell broke loose.
Why flying cities?
The survivors of Icefall colonized the polar mountains and eventually re-established contact with one another via planes powered by "spinner engines"--simply engines capable of gearing up the slow yet inexhaustible rotation of spinners for more useful applications. They shared what technologies and methodologies they developed to thrive in the new climate and bootstrapped themselves up to an industrial civilization to rival the former of the sailing ship era.
Although the poles harbor many of the world's storm "shadows", there is a hard limit to how many people may be sustained by the crops, cattle, and timber grown there. A limit that encroached. Many city Lords recognized this, as well as how indefensible their territories were given the mountainous obstructions, the irregular and sometimes isolated arrangement of vital infrastructure, and the various angles of attack possible by neighboring states--the proverbial eggs in one basket.
Storms typically occupy the atmosphere up until around a couple dozen kilometers above the surface. (Due to the lower gravity, the atmosphere is much taller at around 160 km.) The environment above the storms reduces to a kind of trade winds; bands of steadily moving air connecting north and south, adjoined to the low-pressure equatorial belt.
As expansion across land halted, expansion into the skies began. It is often easier and cheaper to build airborne superstructures than it is to fight a war with a neighboring city. It is also easier, as a city Lord, to keep your power and influence consolidated if your flying "cities" are large and indivisible. A flotilla of small flying craft for example could succumb to a political division, and it's no good pouring money into expanding your feudal Lordship if half of it could fly away at the drop of a hat. 302