Wednesday, January 18, 2012

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
Structure Mass
Cargo Capacity
Dry Mass
Wet Mass
Thrust (Engine)
6,180,000 N (L-Drive)
1,002,183 N (3x NTR-Solid)
Mass Ratio
1.05 (4.2)*
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
43 hrs
7842 m/s
4100 m/s
4 (Tanker) 2 (Cargo)

         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
Annual Tonnage
116 million
Transport trips
No. I-O Transports
(= to 3866 at peak season)

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
STO Flights/day
Intra-Orbital Flights/day
Interplanetary Flights/day
Number of Orbital Hubs
No. STO Transports
No. I-O Transports
Propellant use/day
651,620 tonnes
No. Tankers

    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
Dry Mass
50,000 tonnes
250,000 tonnes
Off-Duty personnel
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!

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