Space Infrastructure II: How many rockets does you need?

Like this.  Times a hundred.  Everyday.

Space Infrastructure II: How many rockets does you need?

         Welcome back, RocketFans, to part two of this week's discussion on interplanetary trade and all of the infrastructure that it will require.  Today, we are going to take a look at just how many tons of stuff are changing hands, and how many rockets it will take will move it.

         First, some basic assumptions...
          Just as algebra becomes impossible with two or more variables, we cannot start to factor how the brass-tacks questions of how many spacecraft will be boosting into orbit without first deciding what those spacecraft can do.  Obviously, a 2000 ton super-freighter would take less trips to haul cargo than a 100 packet, so we need to establish an average capacity for rockets that we can use as a base-line, as well as decide how far they have to go from point A to B.

         Let's start with the last issue first:  How far must our little transport transport?  In order to understand this question, we need a brief overview of interplanetary travel a la desert noir, in order to find out just where points A and B even are.
          Fast, cramped and cheap, or slow, safe and pricey...
          In The Black Desert, there are two ways to get from Earth to points west:  Cycler and Interplanetary Vehicle.  The Cyclers are tiny Near Earth Objects of a few hundred meters across that have had there orbits changed to match the 2.2 synodic period of Earth/Mars conjunction.  That means if you hitch a ride from Earth heading to the Red Planet, you will get there in 6 months, guaranteed.  You'll need a transfer craft to get to Mars itself, because believe me, a multi-giga-ton rock will not be stopping once it is in motion.  18 months later, you can leave Mars on the same rock and get back to the green hills of Earth in 6 more months.
        An IPV is another animal all together.  These are small(ish) spacecraft with magnetospheric sails that ride the solar wind at a blistering 0.001g acceleration.  While this seems slow as hell, these beauties enjoy constant boost, which means that they can get to Mars in just ten weeks at opposition, the farthest distance the two planets get on average.  These spacecraft are not bound to time or location constraints;  They can take off from any place at any time of year and still reach another planet in a couple months or so.  Because of the shortened travel time, it's actually cheaper for passengers to travel by IPV - the consumables needed for six months travel costs more to transport than the entire trip on the faster spacecraft.

       Both forms of transportation have their restrictions.  The cyclers can't get any closer to their planets than their precise orbits allow.  This won't be any closer than the orbit of Luna, about three hundred thousand kilometers.  The same goes for IPVs, which are so slow that it would take as much time as the entire Trans-Martian Injection, ten weeks, just to go from Low-Earth Orbit to Earth Departure.  These spacecraft won't get any further into Terra's gravity well than a lunar diameter either.

       What does all this mean?  In order to move the mail, we'll need a series of stations at lunar orbital distances (probably at the La Grange Points) for the cyclers and IPVs to off-load at, and a second series of stations in LEO for orbital rockets to take the goods down to the surface and back again.  This will take a fleet of SSTO rockets, as well as a second fleet of tankers to fuel up the transports with propellant. In addition, another fleet of Intra-Orbital Transports will be needed to move the cargo and propellant from low orbit to lunar orbit.
What kind of rockets?
       The next question we have to answer is how many rockets will it take to move the cargo, which requires us to actually give our rockets some stats.  I took a good bit of thinking and a lot of calculations, which without the help of Winchell Chung's Atomic Rockets website, I would never have been able to do.  Specifically, I used his Rocket Equations TiddlyWiki, which is so darn useful I printed it out so I can design spacecraft whenever the mood strikes me.

Here are the basic, generic rockets I used to calculate the traffic data you'll see further down:

Typical Spacecraft Statistics used in Tables

Spacecraft	SSTO	I-OV
Structure Mass	150	300
Cargo Capacity	250	1000
Dry Mass	400	1300
Wet Mass	820	2160
Thrust (Engine)	6,180,000 N (L-Drive)	1,002,183 N (3x NTR-Solid)
Mass Ratio	1.05 (4.2)*	1
Acceleration	10 m/s	0.19 m/s
Mass Flow	1132.4 kg/s	41.3 kg/s
Exhaust Velocity	5457 m/s	8085 m/s
Specific Impulse	556.2 s	824 s
Burn Duration	770 seconds	10,169 seconds
Flight Time	≈2hrs.	43 hrs
∆-V	7842 m/s	4100 m/s
Flights/day	4 (Tanker) 2 (Cargo)	0.5

         I chose such low cargo tonnage for my SSTOs in order to keep the science fiction nice and hard.  This is about twice as much as a cargo airplane carries today, which is as about as far as I want to go for a class of rocket that hasn't been invented yet.  Incidentally, the above table sheds light on the actual capabilities of the L-Drive.  Basically, it's twice as efficient as an scram-jet, and uses only an eigth of the propellant that is currently possible for a chemical rocket.  Because it is an air-breathing engine, I had to calculate the Mass Ratio twice - once for the actual propellant/mass ratio, and again for the propellant and atmosphere it burns while lifting off.  This second number was necessary to calculate the delta-v, because normal rocketry equations don't account for air-breathing engines.

          

But I digress.

          

How much Traffic?

           Anyway, using the cargo, wet mass, and flights/day statistics on the table above, we only need to calculate how many tons of cargo is moving a day from the IPVs and the Cyclers.  Even though the cyclers only arrive once every 2.2 years, they carry so much stuff that it takes literally hundreds of flights a day to move it into LEO, even at a thousand tons a pop.  Let's check it out:

Table 3: Asteroid Trade Traffic by Planet

Asteroid Imports	Terra/Luna
Annual Tonnage	116 million
Transport trips	116,000
No. I-O Transports	232 (= to 3866 at peak season)
Independent	45

So there we go:  It takes 232 Intra-Orbital Transports boosting from the La Grange points to LEO every day just to move the annual tonnage from the asteroid cyclers to Terra.  The "peak season" number is for modular, temporary transports that are only used during the two month period that the cyclers are within a light-second of Earth, because all of that stuff has to be moved before the cyclers are out of range, but doesn't have to be moved to Terra right away.  A cycler is only economical to use for cargo if that cargo is non-perishable, such as ore and the like.

         Any way, this stuff gets moved to the Intra-orbital commercial hubs, which is a short range trip, then it's all carried, one thousand-ton transport at a time, to the Orbital hubs in LEO.  These hubs will be busy, busy, busy, as they must not only handle the traffic from the I-OTs, but the surface-to-orbit rockets that will carry it down to the ground.  How much all together?  Let's see:

Table 4: Orbital Traffic by Planet

Orbital Stations	Terra/Luna
STO Flights/day	557
Intra-Orbital Flights/day	232
Interplanetary Flights/day	1
Number of Orbital Hubs	5
No. STO Transports	279
No. I-O Transports	232
Propellant use/day	651,620 tonnes
No. Tankers	339
Independent	16

    You'll see that by far the highest number in the column is the amount of propellant all of these rockets use a day.  In order to keep the numbers this low, It is assumed that the tankers themselves require no fuel to go from orbit to the ground.  This is reasonable; the tankers go back empty.  At less than a quarter of their take-off mass the ambient atmosphere should be sufficient to slow them down for landing.   Alas, the Cargo SSTOs and I-OTs must be re-fueled, because they carry as much on the trip back as they did on the trip out.

        All this means that these stations will need lots of docking facilities, cargo-handling equipment, propellant depots and their associated pumps.  These stations will also have to host off-duty pilots by the hundreds, and the few passengers and colonists that are making their way out into the Black Desert with either a few meger possesions, or an outfitted Conestoga and all the fixin's.   I'll save you the headache inducing math with the next table:

Table 5: Orbital Station Statistics

Orbital Space Stations Statistics	Terra
Dry Mass	50,000 tonnes
Cargo/Propellant	250,000 tonnes
Crew	84
Off-Duty personnel	≈500
Passengers	≈24
Orbital Flights/day	186 (≈62 unique craft)
Tanker Flights/day	113 (≈28 unique craft)
Intra-Orbital Flights/day	47 (all unique craft)

 It doesn't take a professional game designer to see that these five commercial orbital hubs are where it's at, in terms of adventuring ideas.  While you won't see many tourists (passengers staying in orbit will not be using these stations; purely orbital traffic requires even more stations and rockets), there will be scads of spacers, traders and other professional astronauts for PCs to interact with, and even be a part of if they want to ply the interplanetary trade.

         Tomorrow, we'll continue this series by adressing the IPVs themselves and how much traffic they produce.  I'll also be going into how many military IPVs their are, and who has what ships.  Should be lots of fun, so see you then, RocketFans!

Space Infrastructure: How Much Stuff is Moving?

Just pretend they're friendly.

Space Infrastructure:  How Much Stuff is Moving?
 
         Greetings, RocketFans!  I wasn't sure if I would get the CASSTOR published on time, seeing as we had some nasty weather and use satellite Internet.  Fortunately, a reboot of, well, everything, fixed our issues and the CASSTOR is available for you right now!

         This week, I'm going to be talking about something I worked on this weekend:  Infrastructure.  I multi-planet trading network isn't something that can just be thrown together, after all, I takes all sorts of supplies and logistics to launch even one spacecraft.  How much then, does one need to launch a dozen, or a hundred?  How many cargo craft, tankers, and space stations are necessary to support an interplanetary vehicle, or a fleet of them?  The Black Desert is a setting that features over two hundred years of permanent presence in orbit and colonies on Luna, Mars, and scattered across dozens of asteroids in between.  This begs the question: just how much stuff is moving up there?

         In this pursuit, I was once again aided by the meticulous work of author and blogger Rick Robinson.  His essay on Interstellar Trade, which is easily convertible to interplanetary trade, provided both inspiration and a springboard for me to calculate all of the information you'll see posted this week.  So, without further ado, let's get to it!

The most important factor:  Money

         The first thing that must be considered is just how much money is changing hands.  Every other factor, from the number of tons of goods that move between planets to the number of flights an average space station sees a day is dictated by money.  The money spent on trade, in turn, is dictated by population.  Below is a table that shows the population of most of the major settlements and their Gross Planetary Product (GPP), as well as the amount of trade that translates into.  Let's take a look, shall we?

Table 1: Population, GPP and Trade

Planet	Population	Gross Planetary Product	Trade	Total import Tonnage	IPV Transpot Tonnage	% of IPV Transport
Terra/Luna	5 billion	1 quadrillion	3.75 trillion	116 million	1 million	(97%)
Hektor Node	2,000	200 million	100 million	3,000	1,000	(0.1%)
Paris Node	1,250	125 million	71 million	2,200	2,200	(0.21%)
Mars	120,000	60 billion	30 billion	923,000	9,000	(0.88%)
Agamemnon Node	1,750	175 million	76 million	2,300	2,300	(0.21%)
Achilles Node	1,125	112 million	56 million	1,700	1,700	(0.17%)
Aldrin Node	6,000	600 million	300 million	2,200	920	(0.09%)
Odysseus Node	?	?	?	?	?	?
Totals	5,000,132,125	15,013,420,000,000	3,780,603,000,000	116,941,400	1,022,520	(100%)

        There are quite a few assumptions built into this model which need some explanation before we move on.  You'll notice that the different planets must have different average wages per person for me to arrive at the numbers I've chosen for the GPP of the different settlements on the list.  Terra/Luna (from an interplanetary perspective, the two are a matched set.) with a fantastic GPP of one quadrillion, has the lowest annual earnings per person, at 20,000.  Despite this, with a population 3 billion lower than we have currently, the GPP is at least five times higher than 2012 estimates.  Then when you factor in the fact that 99% of the GPP has historically been held by only about 1%....sad, ain't it?
        Anyway, it would also seem that Mars has a GPP of a half-million per person, which seem far fetched until you realize that a 120,000 people living in an area half the size of all the land-masses on Earth means really large pieces of pie for everyone.  According to Bob Zubrin (and he should know, right?), there will be a chronic labor shortage on Mars that drives up the wages and will continue well into the late twenty-third century at the very least.

How much to import?
          This is another place where there is significant inequity between the numbers.  Terra imports less than 4% of its GPP in goods from space (It's only that high because of Luna's need for stuff that's cheaper to ship from Mars) while some of the asteroid node import over half their GPP in goods.  These colonies, especially the ones that support Nav Lasers, are not self-sufficiant and will starve without high imports.  Even Mars has a 50% import rate, due to the difficulty of making quantum computers and QOOR processors, which is the AI equivalent of biomass, from a certain point of view.

Why are the IPV numbers so low?
      The amount of tonnage IPVs carry is so a lot less than the total amount of tonnage.  The tonnage itself is calculated by factoring in the cost to boost to orbit ($20.00/kg)  and the cost of intra-orbital transport and other back-of-the-envelope factors.  The amount that IPVs actually ship is so low because most of the tonnage and all of the bulk cargo is carried via the asteroid cyclers of the Aldrin node.  IPVs only came into service at the start of the Great War, and while they are the fastest way to travel between worlds, they are also expensive compared to the cyclers.  The only exception to this is personnel transport; the difference between the consumables for a ten-week trip compared to a six-month cycler journey makes IPVs cheaper for passengers.

Table 2: Consumables and how they factor in
       In space, imports are not just a luxury, they are literally the stuff of life.  It takes air, water and food to just survive, and in many places most of these supplies must be imported.  Below is a table that explains how much of the import tonnage is just food and the like:

Table 2: Consumables Trade Percentage by Planet

Planet	Population	Consumable imports (%)	Annual Tonnage (Cost)
Terra/Luna	5 billion	-	-
Hektor Node	2,000	33%	1679 (53,720,000)
Paris Node	1,250	33%	1058 (33,856,000)
Mars	120,000	1%	3066 (98,112,000)
Agamemnon Node	1,750	33%	1450 (46,400,000)
Achilles Node	1,125	33%	949 (30,368,000)
Aldrin Node	6,000	10%	1533 (49,056,000)

      You'll notice that even for the Nav Laser installations, the consumables imports account for only a third of the total consumables needed.  This is based on the assumption that most if not all of the air and water is recycled.  This is a practical consideration, not a meta- one; IPV transport, the only kind that can reach the Navigation Nodes, is too costly to import water and air in addition to groceries.  The only reason these stations import even this much is that you don't want the hard SF analog of a Death Star to be self-sufficient.  It breeds insubordination.

What next?
         Now that we have some idea of the tonnage and costs of importing to the different locals in The Black Desert, we can start to figure how many ships we need to move the stuff and how big they have to be.  We'll pick up tomorrow with the cargo and propellant requirements to ship to the different planets, which will give us an idea of how much traffic they see on a routine basis.

         See you then, RocketFans!
  

CASSTOR Prieview 2: Now with Optional Second Stage!

Not an Ares.

"The Optional Second-Stage (OSS) upgrade, which has become standard on modern CASSTORs, allowed the spacecraft to achieve trans-lunar injection speeds while carrying everything from habitats to fusion plants for the new ships. This increased cargo capacity, when combined with the L-Drive propulsion system gave the American aerospace industry an advantage it lacked with the older Marquisa Gras transport, which used chemical rockets and were unarmed."