Mdthbs

Ruins of buildings, abandoned cities and suburbs dot the coasts of Earth's landmasses, inhabited by wild animals and the pieces of a once vibrant civilization. The oceans are relatively empty, the soil and dirt sapped of all its nutrients, the vegetation on earth fighting the strong winds clinging to the loose ground. Barren. Humanity seems all but gone, the planet destroyed by ignorance of its most feral inhabitants.

The inhabitants did not leave though; they retreated into their shelters to wait out the storm. The shock and fear that came with the last harvest prompted the citizens of the world for answers. Out of the chaos came Arthur Hawking, a architecture and food scientist from ICBC/Coke/Pepsi. He brought the idea of a self sustaining structure to the masses, the possibility of having everything a human needed in one building. Agriculture would occupy the majority of the structures space, but automated farming would allow a consistent flow of product to the population.

Yuma Arizona was chosen to host the structures, a small town in the south west corner of what was Arizona. This city experience the most sunlight in a year, ideal for the arrays of solar panels that would be used to supplement the nuclear power generators build into the structures. The buildings were originally going to be just for some united states citizens who could afford it, but mass hysteria after "the last harvest" made these structures seem like the only resort for all people in the world so the interest skyrocketed and the world flocked to Yuma, 10 billion people in 2081.

How large would one of these towers have to be to host 1 billion people? My story takes place in 2081 (just read this book), and I am looking to accurately scale the buildings in my head and story. Ideally 10 of these would fit into Yuma, so they would scale vertically more then horizontally. They need to account for agriculture space, living space, and some general use space that would likely be equal to the living space (schools, research facilities, clothing fabricators, restaurants etc.). The plan is to wait out the storm, which likely would be about 1000 years (for a healthy topsoil and native animal population). Once everyone is in the structures, each one will be sealed from outside physical contact to allow nature to develop undisturbed by humans, and to restrict any potential crop blight to a single structure.

EDIT: These structures are too large to fit exclusively in Yuma, so for the sake of future answers I will allow the structures to exist in the entire Yuma County.

Putting a billion people in Yuma, AZ, including food production, industry, and commerce, would require building the entire area to a height of about 2km.

The math:

Based on the answers on this question, we should be able to feed people using about 25 square meters of space, per person, using reasonable near-future assumptions about aeroponic food production. Based on this discussion of living space in modern Japan, the minimum living space allocated per-person is about 25 square meters of additional space. For modern cities, about 50% of city space is residential, with the rest being industrial/commercial. (Proportionally, if we include agricultural allocation in residential areas, this will increase to about 66% of our space.) Additionally, modern cities are around 30% roads. For a megastructure, we'll also need a lot of space to allocate for atmospheric control. Let's assume that's about the same amount of space as roads.

As a per person estimate, we'd then need 50*2*1.6=160 square meters of space to account for transportation, food, housing, industry commerce, and atmospheric infrastructure. A billion people would then need a total of 160 billion square meters of space.

Using the Burj Khalifa as an estimate for floor height, each floor will be about 4 meters. Yuma AZ covers around 300 square kilometers of space. Assuming we stay roughly within its boundaries, we'll need 160 billion square meters/300 million square meters/floor, for a total of around 540 floors, at a total of 2160 m tall buildings.

This, notably, does not include the area you'll need for solar panels, if that's what you're using for power. Solar panels, notably, cannot be stacked. Sunlight provides around 1kW/square meter of energy. Assuming our crops need about the same energy input as the sun provides, and that crop production is about half of our total energy needs, we'll need 50kW/person, for a total of around 50 billion square meters, or 50,000 square kilometers of area for solar panels. That's assuming maximum efficiency: modern solar panels are something like 10%-20% efficient, so you'd need 250-500,000 square km of solar panels. (Cuba, for reference, covers around 100,000 square km.)

If everyone is to fit in Yuma County, rather than the current city limits of Yuma, the available area increases by about a factor of 50. Under that assumption, you'd cover the entire area to a height of about 50 meters to house a billion people, or 500 meters to house ten billion. 500 meters is about the height of the inhabited portion of the Burj Khalifa, though unlike that building, the megastructure would cover an area of 14000 square kilometers or so. Solar power will require the same area, which will likely be infeasible without either extensive automation to do maintenance or a substantially more dispersed population.

Addendum: I misread the question, and though you were only putting a billion people into Yuma. For 10 billion, these numbers would increase by a factor of 10. Using current or near-future technology, I'm not sure a 20km building is anywhere close to feasible. Also, your solar panels will cover an area close to the size of the EU, so you'll probably want to spread your towers out through an area about that size, anyways.

I can't tell you how big the whole structure is going to need to be but I can give you a couple of figures that will help you get your head around the scale:

• Farmland, you'll need the equivalent of 25000 Hectares (roughly 62500 Acres) of farmland to feed that kind of population, hybrid Aeroponic/Aquaponic systems may reduce the overall volume this requires but that's the land equivalent. Certain fungi or a suggested technology that could assemble basic carbohydrates and proteins from atmospherically sourced oxygen, hydrogen and nitrogen (not sure how viable that is by the way) will get this number down but it's still going to be huge.




• Accommodation, based on tiny houses you'll need at least 50m³ per person to carry out the basics of life; eating, sleeping, and washing. You can probably half that, or better, using communal facilities and assigned shifts but quality of life will suffer badly.

That doesn't cover anything but the absolute bare essentials either, so no luxury foods, i.e. anything that grows on a tree or needs terrestrial living space (so very little fruit and nuts, no red meat, dairy, poultry, or eggs), and no physical recreation space, shared or otherwise. You also need to factor in "migration space", the corridors, elevators, stairwells etc... that people need in order to move around the space you create, and "utility space", the ducting, wiring, and piping to carry the necessaries of air, water, and power. Plus you need to generate the power and source and clean the water and air. Power for farming will need to be sufficient to supply at least 5Wm^-1 of tuned red-infrared lighting for maximum photosynthetic efficiency. Human inhabited spaces will need full spectrum lighting to keep people healthy.

Technical note: a Megastructure is usually at least 1000km in at least one dimension so the current footprint of Yuma is too small to put even one into.

Very. Very. Very large.

Just for some comparison, have a look at a project of this type being proposed for Tokyo bay. Remember, you're not just building a giant apartment block. You need to account for places people work, create food, eat food, most of the stuff you'd have in a regular city.

The structure would house 1,000,000 people. The structure would be 730
meters (2395 feet) high, including five stacked trusses, each with
similar dimensions to that of the Great Pyramid of Giza.

So you'd need something a THOUSAND times larger than this.

Let's try some math here... The greatest density of human occupation right now on a large scale is Manila. 1.6 million people occupying 38.5 square km. It tops out in District 6 with around 70k people per square km. (This is almost three times the population density of Manhattan, btw...).

Now, trying to turn SQUARE meterage into CUBIC meterage is a tricky problem, but I've played with before. I wound up with a rough approximation of ~2.7 cubic km for Manhattan (~1.6MM population) and ~7.75 cubic km (8.6MM population) for all of NYC.

So your starting point is around 10MM people in a cubic building that's about 2km on a side. Manila triples that population density without TOO much trouble, so let's say we can go up by a factor of 5. Now we're up to 50MM in a 2x2x2 cube. Now we get rid of all the roads, all of our transportation of people and goods uses conveyer belts and elevators a la a la Caves of Steel (Asimov, 1953). Let's say that gives us another factor of 2 in terms of space efficiency.

That's 100MM people in a 2km cube. You need at least ten of these.

Oh, the pain...

Bedrock is your first problem. You're not building an itsy-bitsy building like the Burj Khalifa or the Tower of Pisa, your'e building the building, the biggest, honkingest, Oorah-est building on the planet. And you're guaranteed to crack the foundation if we don't go all the way down to bedrock, grind the bedrock flat, drill in a bazillion holes for metal rods, and lay the thickest foundation the world has ever seen ... because you want to build up, not out (in a area that's just begging for more urban sprawl), which is probably a horrible idea, but let's roll with it.

So, let's examine a geological map of Yuma County, AZ. We'd need someone like Arkenstein XII to give us the low-down, but I'm betting the word "Granite" is good (My thanks to Ash for pointing this out), which is a good thing, because there's more of it than basalt. Unfortunately, what you'll quickly discover looking at that map is that while you'll have good sun coverage for your solar panels, it's pretty much the worst possible place on the planet for a foundation the size of what you're looking for. The situation isn't as bad as I feared, but it's still inconvenient. But, there's spots out there we can make this work because we're about to calculate our footprint size.

If I remember my geology classes in high school correctly, the areas of the world that would be best for a honking huge foundation are pretty much the worst for solar panels. I could be wrong, though. High school was sometime during the Cretaceous Period. But it's worth thinking about.

Water is your second problem. You want to be self-sufficient for a billion people. This is actually a really ugly calculation. People need to drink, dispose of waste, experience hygiene (in a sealed system w/1B people... oh, yeah), then there's crops, industry, humidity control, yada-yada-yada. I'm going to take a complete pull-it-out-of-the-air guess and suggest calculated per-person you need something like 100 gallons of water per day. Let's pretend we have 100% efficient recycling and that the recycling is capable of processing every drop of water each day (an oversimplification that literally will make angels weep). That's 100 billion gallons of water or a storage tank 13.4 billion cubic feet in size. If it's just half the height of the aforementioned Burj Khalifa (1,358 feet) it covers a little over a third of a square mile. Let's call it a third for convenience and just build a little higher.

So, a third of a square mile, doesn't sound too bad, and we should be able to find a nice, big chunk of basalt even near Yuma we can work with. Let's pour that sucker a solid 30 feet deep, fully reinforced and tensioned, of course, and another 2,000 feet (easy) of honeycombed water tank so we can build a support structure on top of it. It's the honeycombs needed to support the rest of the building that causes the height (which is a round guess) because they consume volume not previously accounted for.

And it's worth noting that if you didn't have a crisis driving this process before, the diversion of water to fill that tank will cause it. OK, maybe not really, but the resulting fight between California and Arizona over water rights would likely start a second civil war in the U.S.

Food is your next problem. This fascinating article boils the issue down to a simple number: one acre per person if you do it the "natural" way (growing crops, grazing cows, etc.). That's (*cough*) one billion acres under your roof. To give you a sense of size, The United States is 2.3 billion acres. To make things interesting,
just over 1 billion of those acres are devoted to crops and grazing. Considering the potential for U.S. food production, that casts a shadow on that previous article's conclusion that 1-acre-per-person was needed, but we'll roll with it. So, you need to build a building (now it has to be vertical) that houses the entire food-production land usage of the United States. That third-of-a-square-mile is looking a bit small, as is my 100-gallon-per-person estimate.

And something must be wrong with my sources at this point. But not too wrong. People have been complaining about too-many-people vs. too-little-arable-land for a long time now. This might simply be drawing a huge underline below the problem. In other words, unless you can compress food production something awful, your premise isn't believable as you need a planet to feed a planet worth of people.

Let's assume that you've improved food production technologically such that, somehow, you need only 1/1,000^th the space to feed a person. Thus, one billion becomes one million ... acres (sigh). A third of a square mile is about 211 acres, so you need 4,740 floors for food production at about ten feet per floor (which is incredibly unrealistic) so now your building is working on 50,000 feet of altitude (which is well above the 35,000 foot average cruising altitude of a Boeing 737) and we haven't even begun to address industry and infrastructure — much less housing.

I did say building up, not out, was a horrible idea....

And it's time to stop

Yes, you can lower the height of the building by spreading out the foundation, but that causes problems with a believable foundation (remember that geological map of Yuma County). Obviously we can't conceive of a believable way to do this today. So I'm going to go out on a limb and suggest...

Your building's foundation is the size of Connecticut and the building is approximately 20,000 feet (6,100 meters) tall.

And we won't talk about what the weather around this sucker would be like.