Saturday, January 23, 2021

HOW MUCH DOES A SPACE STATION COST ANYWAY?

 I was curious  so I did some more napkin math.  I'm pleased that my numbers lined up with APOF's.  This should be useful if you want to see who'd build a large space station and how they'd pay for it.  We'll use the Dream as an example because it's the most accessible example.  We're using my setting assumptions which are probably more conservative than yours -- so a space station in your own setting is likely cheaper.


THE BASICS

The question of cost is really reducible to three separate questions: (1) how much does a space station cost per unit weight, (2) how much does living space weigh, (3) how much does financing cost.  We can figure out some upper and lower bounds on all of those values.

As before I shall assume that one credit is worth $4 USD.  

COST PER TON?

At worst, the cost to launch stuff into orbit provides an upper bound for the cost of a station.  Obviously, launching that much of anything from a deep gravity well is really dumb.  I assume launch costs of $5/kg (about $500 to send a person to orbit).  That's $5,000/ton (oof!).  At these prices labor and fabrication are negligible.  

Using some assumptions about orbital launch and propulsion that aren't really worth elaborating on unless someone is really interested, I assume it takes about 4x less energy to move stuff from the asteroid belt to geosynchronous orbit around an Earthlike world.  Because the energy of extracting stuff is probably equal to the cost of moving it, let's say it's half as much or $2,500/ton.  Again, ignore labor costs. Everything except finishing is probably automated anyway.

Now, if you're located somewhere where power or energy is cheap (asteroid belt, Mercury), you can probably ignore one value.  So 4x cheaper ($1,250/ton).  This is probably the right value.  If you're building a station in a low-orbit asteroid belt or using especially efficient propulsion to get asteroids from A to B it's even cheaper! 

For what it's worth, a regular ordinary American house costs somewhere between $1,000 and $3,000 per ton depending on where the house is located and the style.  Not really very relevant but interesting all the same. 


HOW MUCH DOES IT WEIGH?

An O'Neil Cylinder weighs about 7.5 tons per square meter assuming half is windows and a relatively inefficient design (oof!).

The ISS weighs about 120kg/cubic meter (not much empty space!).

A house weighs about 33kg/cubic meter (plenty of empty space!)

Let's go with 50kg/cubic meter.  A space station has a lot more empty space than the ISS (and also more than a house) but it's also a center of industry etc. and saving weight isn't cost effective (making the ISS as light as it is costs a lot of money which is justifiable when you pay $3,000 to $12,000 dollars per kilogram to launch something into orbit).   

If you look at the Dream, you get between 500 and 1,000 cubic meters per person including space that's not used for living and the Choke.  Maybe a bit more.  We'll assume 1,000 cubic meters.  This comes to about 50 tons per person. Obviously not all of this space is for living.  


FINANCING?

Interest rates vary depending on how secure an investment like a space station is.  It's somewhere between 1% and 10%.  Depending on the size of the station and the length of the loan, high interest rates may make a project nonviable.  I shall assume 2%; lenders will expect that whoever is running the station will be able to charge rent, collect taxes, etc. This is probably too low in the Rim but we want space stations to exist.

Obviously, equity financing is probably preferable here, but better to stick to the pessimistic alternative for the purposes of this article.


WORKED EXAMPLE: THE DREAM

Population of 8.7 million.  Let's round up to 500 million tons.  That's about 625 BILLION dollars.  Sounds like a lot.  It actually isn't.  Manhattan has a population of about 1.6 million.  And the value of all land in Manhattan is about 1.4 trillion dollars.  If you have the energy and population, making a station like the Dream actually looks like a pretty solid investment if you disregard interest rates.

If you do include interest rates it costs about 2.5x more (50 year bonds with 2% yield).  About as much as Manhattan ($1.562 trillion)!  Only you can distribute the cost to about 4x as many people.

In any case, Yandee, Tempest, and every other stakeholder need to bring in about 32 billion dollars per year to pay the down the bonds financing the Dream.  Not actually very much money but obviously the Dream also has to provide other services and infrastructure.  The "oxygen tax" (10cr/day) on the dream is equivalent to about $15,000 per year (oof).  Counting only the people who are paying, that alone brings in $84 BILLION DOLLARS.  Should cover the station, security, and whatever services the Golyano Il Bratva deems essential (trial by combat is essential).  

In other words, Prospero's Dream is a moneymaking machine.  It's a superb investment in a setting where there's enough infrastructure to make projects like this feasible.


CONCLUSIONS

Bigger stations cost less per ton.  An O'Neil cylinder costs about $5.625 trillion.  It's a lot but the type of people undertaking that project can probably get a very good interest rate.  It's certainly within the realm of possibility for a large megacorporation or a joint venture.  

However, most stations are likely to be smaller unless they're located in places where building a large structure is a lot cheaper.   




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