The politics and purpose of your arco would significantly impact the number of residents that would be packed into it.
In my mind, the default picture for an arcology is the hippie utopian 1970s Arcosanti, and I immediately imagined a clean city with apartment balconies over a lake. Any untidy industry gets tucked away inside the structure and the residential population is limited only by air/light exposure… Ahhhh.
No, wait. That’s just an architect’s pipedream…. Those web things are the apartments. I don’t actually know what’s going on with that Swiss cheese slice, is that a walkway? In the top-down view (top right in the drawing) we see this isn’t actually a working dam so much as an crazy facade apartment building in front of a dam…. Or maybe I’m reading it wrong. Those web apartments are actually horizontal compression supports. The dam really is that thin, the structure is like a bridge on its side…
Simcity2000 pushed arcologies into pop culture, but shortened it to the hip arco. Their populations ranged from 30,000 – 55,000 but were pollution neutral. A secret easter egg involved building over 300 Launch Arcos that colonized space. Many considered it “winning” the game.
Decide WHY the arco exists.
- Accommodate a dense population.
- Self-contained ecology
- Keep labor close to work
Decide WHO built it
- An egalitarian society that appreciates nature
- a crowded city pressing the limits of its resources
- a mining company, the government, or space aliens.
An actual arco is constructed for a purpose. It’s a machine with a built-in power source. Industry would need the outside wall for venting CO2 or whatever byproduct it produces. It probably has a large industrial conveyor lift to bridge cargo from the lake above to the river below. The population might be limited to only the necessary workers, managers, and their families. The people serve the machine, like an oil rig. The costs to provide for them will push the number of residents to a minimum.
But arcos are eco-friendly, right? What if you take the fragile ecology scenario to opposite extremes. What if the environment can no longer sustain your population? If the goal is to gather all the people into one building there would be pressure to pack as many people as physically possible into every cubic meter of the structure. Workers live in crowded dorms. Only the elite would have private apartments, but even those would be tiny. If the purpose of the arco is to keep as many people as possible alive in one concentrated space, I think we have not seen the limits of where we can go.
Even in a utopian/socialist future where a residential megastructure also serves a utilitarian function, there is a negotiated balance between space devoted to industry and space devoted to community housing. Those needs might change over time leading to overcrowding or reclaiming of industrial space. Was the arco financed by luxury condos, or is this a low-income housing project in exchange for pollution credits?
It’s not the volume or surface area that defines the population, but the purpose of the arco, and the politics of the society who built it. In reality humans are not like logs that can be stacked into a defined volume. Humans will adapt to overcrowding, and “personal space” is based on income and real estate values.
**Zone your arco’s industrial areas and subtract them from the volume.** The space left over is available for residents and public areas. Depending on where in the world your dam is, it will have different legal definitions of [Overcrowding]. If your goal is maximum number of dwellers start with existing overcrowding/zoning regulations and make it more dense. [Kowloon City] for example was unregulated but obv not designed as an efficient arco. [Cruise ships can be very dense] and still comfortable, but they are almost the opposite spectrum of a self-sustainable arcology. Also look at Chungking Mansions and Mirador Mansions budget hotels in HK for examples of very small private living quarters. After that you have [SRO hotels] with shared bathrooms, and then hostels and dormitories. Your arco might have any mix of these with the ability to reconfigure as housing needs fluctuate.
Without some idea of what you consider suitable space for your population there isn’t a hard answer. Social and legal pressures would decide the limits, not architects.