40 Billion is literally NOTHING when Trantor canonically is covered in a mile deep layer of skyscrapers that forms a near solider layer of metal. Like compared to Trantor, new York city uses almost none of its airspace.
For reference an ecumenopolis covering earth's surface area of 509.6 million square kilometers with a population density comparable to the following regions would have a total population of:
France=52 billion (higher than Trantor!)
Houston=707 billion (and this is a city infamous for sprawling suburbs)
Singapore=4 trillion
New York City=15 trillion
Kowloon Walled City=968 trillion (KWC maxed out at 14 stories. Mile high city with half a thousand stories could fit that density without being as cramped)
The numbers get pretty crazy. By the time you hit 326 billion people you are exceeding the biomass of all animals on modern day earth combined. By 82 trillion people you are exceeding all living biomass combined. At KWC levels you need 3.6 Lake Michigans a day just for drinking water. At KWC levels you can fit nearly the entire population of the USA into DC.
So just going to do some napkin math on this, and I COULD be wrong.
Dividing USA's annual
electricity consumption by population gives 12,916 kilowatt hours per person per year, or 35 kilowatt hours a day. Electricity consumption is only about a 1/3rd of total power grid
energy consumption though, so make that 100 kilowatt hours a day.
Ergo at 100% efficiency you need 12.2 square meters to support an average American's energy consumption. 33% is a hard limit for conventional panels though, and 20% a more realistic nameplate capacity, which would put at more 61 square meters. Given that there are 1 million square meters per square kilometer, that puts a ceiling of around 16,393 per square kilometer. NYC is about 11,313 people per square kilometer, so it'd pass, but that's just energy consumption from powerplants we're talking about here. Returning to the food example:
1: Humans need 2000 calories a day translates into 2.32 kwh a day.
2: If humans were robots plugged in to 20% efficient solar panels would translate into 11.6 kwh a day. The thing is humans aren't robots.
3: Our food chain starts at planets, for whom photosynthesis is about 1-2% efficient, putting things at 116-232 kwh a day.
4: Of course that's "energy to feed" not "feed to edible calories" as a lot of energy goes to upkeep or inedible parts. Assuming soil->plant is comparable to plant->chicken, we're up to 464-928 kwh.
5: For modern farm animals the '
feed to edible calories' ratio is somewhere between 4 and 25, so assuming you include meat in your diet it will be even worse.
Taking that into account and combining it with the machine energy consumption figure, the average American probably depends on 1000+ kilowatt hours a day, which would set a ceiling of 1,000 people per square kilometer, less than a tenth the density of NYC. Now to be fair I suspect there is tremendous room for improvement, but my point is that present-day cities are already exceeding their usable solar budget per square meter. Let alone some insane Coruscant style ecumenopolis that is as dense per square meter as KWC that has to deal with the 'feed people' and 'power machines' but also has exciting new issues like 'how do stop waste heat from literally cooking the population?' or 'I emptied the world's oceans into my plumbing system to make room for more 500 story condos is that gonna be a problem?'
