So four days agoor there abouts, I put a
poll up on Google+ with a selection of spacecraft I was thinking
about making isometric cutaways of. The frontrunner is the
IntraFleet Space Tug. That means, RocketFans,
that we’ve got
ourselves a
project!
This is not the tug. 
The
context for this particular spacecraft, like the Cygnus
capsule I also put in the poll, is
the care and feeding of the distributednetwork fortification that is
a deployed UN Constellation in the Conjunctionsetting. In summary, the fleet’s configuration is a tetrahedron in
space with a single control ship at the apex, patrol craft making up
the other three vertices, and edges three hundred thousand
kilometers long. Just how do
you supply ships that are as far out as the Moon is from LEO?
Cygnus docking with a Class A Patrol Craft 
To
put the problem into perspective, a Cygnus
stack is a rough cylinder 4.5 meters in diameter and about ten meters
long. The propellant tanks on a Type A Patrol Cutter are 8 meters in
diameter and total thirty meters long. And there are two stacks.
Clearly, to refuel a patrol ship, we need a real tanker.
I’ve
said it before RocketFans, and I’ll surely say it again: AtomicRockets is an invaluable
resource for the budding rocketeer. The “Realistic Designs” sections are a
veritable clearinghouse of
old NASA designs that were pretty good but never got a decent budget.
These oldies make for a great library of inspiration when designing
any spacecraft that is meant to work with realworld physics. For
our IntraFleet Tug, I was inspired by the Johnson Space Center’sTug study, who’s image I used in the Poll. This beauty is a
twostage ferry to get from LEO to GEO where NASA was going to build
a solar power station.
Yeah, we could have had that... 
Anyway,
a lightsecond is good deal further than the LEO/ GEO distance,
right? In kilometers, yes,
but in DeltaV, not
even close. It takes
a whopping 4.33 km/s to
go from LEO to GEO, but a paltry 2.74 km/s to get from LEO to Lunar
orbit...a little over
a lightsecond away.
Gravity is funny like that.
So
our tug only needs about 75% the range of the JSC version. Since
that design was staged and the first staged carried the spacecraft
85% of the way to GEO we could
just lop of Stage I and call it a day. But where’s the fun in
that?
The
problem with just ripping of the JSC design is that it isn’t a
tanker. We need to be able to deliver a large amount of propellant,
so we’re going to need a large spacecraft. Something that could
haul at least a quarter or half of the DeltaV needed
to completely refuel a Patrol craft. What follows is an experiment:
I’m thinking of just taking an entire rocket stack from a Patrol
craft and slapping a command module on the front for our Tug. Let’s
see how that would work, shall we?
First
of all, we need to dust off our rocketry equations so we know what
variables we need to consider. We’re going to need to know the
Tugs dry mass, wet mass, and engine details such as propellant flow,
thrust, and exhaust
velocity. Since we’re using the dimensions of the propellant tanks
from the Class A Patrol Craft, and possibly one of its main engines,
that gives us a great place to start. In fact, lets crunch the
numbers for the Patrol rocket’s main engine and an alternate, say
something along the lines of the J2
from
the Saturn V’s SIVB stage.
First,
let’s establish the tonnage for the Tug without
it’s engines. We’ll want a decent sized crew module, because
gaming, and also so we can have cadets aboard during all flights. In
Conjunction,
like in Heinlein’s Space
Cadet,
every UN convoy and spacecraft has a group of peacekeeper candidates
learning how to work in space by working in space. I
see an actual crew of about four: a
Flight Commander (FCom), Guidance Procedures Officer (GPO),
Maintenance,
Mechanical Arms, and Crew Systems Officer
(MACS), and a Payload Officer (Payload). Add
as many again of CandyCruisers,
and you’ve got eight people in the command module. That’s a bit
crowded for a Tug, but we can use hotbunking with to limit the
sleeping berths to four. The
CM must also have at least a pair of robotic arms, and a sturdy
docking module for carrying passenger capsules and cargo pods.
Behind
the CM will sit a flaredout service module, with avionics, life
support, and computer systems. The SM will be mated to a 30 x 10
meter saddle truss, which is what will actually hold our propellant
tanks and provide a mount for the rocket stack. But
in addition to all of that, we will also need
a passenger module and cargo pods, so we need to know the mass for
all of those as well.
Here’s
how it breaks down:
System

Mass (kg)

CM

12671

SM

3000

Saddle Truss

24119

Propellant
tanks

24119

Passenger
Module

7540

Crew Avg.
Mass

2400

Cargo/consumables

392883

Total Dry
Mass

466732

LH₂

71204

LOX

305788

Propellant
Mass

376992

Total Wet
Mass

843724

I
arrived at some of these number dubiously, so take them with a grain
of salt. The CM mass is from the Trans Hab Calculator on the AR
website, the SM is from the JSC Tug, the truss is simply repeating
the mass of the propellant tanks, since I couldn’t find any
reliable numbers for that. The
Passenger module is also from the JSC tug, while the consumables and
cargo masses are calculated for the tugs trip out and
back, as well as 30 days of supplies for the 20person crew
of
a Patrol craft. And of course, we can’t forget the mass of the crew
and passengers themselves, plus what ever possessions they can carry
inside their regulation 100 kg masslimit. Finally, the
propellant
tank
mass is 6% of the propellant mass, as per Dr. Rob Zubrin, and the
propellant masses came from the Useful Tables appendix from Atomic
Rockets. But the most important thing to remember is that we have no
engine yet.
The
Class A Patrol craft uses an easy to maintain in freefall analog of
the SSME so I could simply steal copy the vital statistics. Engine
List on Atomic Rockets has these
available. Just below that entry is the stats for the Tug engine we
will also use.
These
are not exactly the J2 stats, but they are for a NASA tug, and they
have the information I need to calculate with, whereas sources on the
J2 did not.
What
we want to know is, assuming a 100hour flight time, is how much
propellant will be left in the big tanks at the end? We need to have
spend no more than 1/3 of our propellant mass in transit. That way,
we can refuel with another third (plus a bit extra) and use the
remaining lessthanathird to take our much less massive tug home.
This
means math. So, so much math.
Well,
not so much, perhaps. We know all the vital statistics for our
engines, our mass numbers, our DeltaV budget, and our distances. By
establishing an arbitrary travel time of 100 hours, we also provided
a muchneeded value for equations, and more important, the mass of
needed consumables.
An
IntraFleet Tug that uses a “F2b” SSMEanalog will have a wet
mass of 846,901 kg, or 847 tons. Let’s see if we can get from
point A to B while only burning through 125,664 kg of propellant.
Simple,
right?
If
only using 125.6 tons of our propellant, we will be operating with a
mass ratio of only 1.8 By using the DeltaV equation of DeltaV
= Exhaust Velocity x ln(Mass Ratio).
This results in a DeltaV of 2621.96 m/s, or 2.62 km/s. We need 2.74
km/s to get to our destination, so it’s close, but no cigar.
If
we attempt the same thing with our J2 analog, we have a wet
mass of
845,512
kg. This gives us a mass ratio of 1.8 again. However, the exhaust
velocity is 4159.4 (I had to calculate it using the specific impulse,
but that’s why we have algerbra in the first place). With the mass
ratio and a lover exhaust velocity, the DeltaV is 2.45
km/s. Both engines are pretty comparable,
but neither will get us out a light second and back.
Or
will they?
The
moon
averages
384,000 kilometers from Earth. A lightsecond is only 300,000
kilometers. We actually have less distance to travel, and hopefully
less DeltaV, than the 2.74 km/s we’ve been using. Possibly
a lot less.
I
forgot that moving around a fleet formation like this is not remotely
the same as moving around orbits. Moving from LEO to Luna is a
Hohmann trajectory, which is a change between orbits from around one
body moving at one speed to another body moving at a very different
speed. When deployed, our constellation is all moving at a constant
speed along a constant orbit/vector. This means that all spacecraft
in the formation are at rest relative to one another. So we need to
go from a starting velocity of (relatively) zero to a certain speed,
coast, flip, and then decelerate back to zero. This is just a simple
physics problem.
This
is also where our arbitrary 100hour travel time comes in. With time
and distance known, as well as acceleration (Thanks to the engine
stats) we can solve for velocity and begin to figure out what we need
to know.
Solving
the displacement equation gives us an average velocity of 833.333 m/s
to travel a lightsecond in four days and change. This means we need
a final velocity of 1666.666 m/s. Our SSME engine will take only
721 seconds to boost our monster tug to speed, and the same to
decelerate at the other end. Now for the biggie – mileage. By
which I mean, just how much propellant did we use up in those 1442
seconds?
Turns
out that’s an easy one, because we know the mass flow. A single
SSME tosses 409 kilos out the back every second, so our Tug will have
to burn 589,778 kg. This is more than the entire wet mass of the
tug, so say nothing of the “onethird” we wanted to get by with.
As
for the J2, we need to redo our acceleration calculation so we can
figure our burn duration. Unfortunately,
with a
burn duration of 1282 seconds one
way, the
performance is even worse.
What
went wrong? This tug has half the power or a patrol rocket – it
should have at least comparable performance.
*
* *
Its right there in black and white. Literally. 
I
designed the Patrol Craft to take into account the likely progression
of materials science toward ever lighter and stronger materials. It
was built out something that has the same strength of titanium, and
half the mass. Add
to that it’s outer skin is mostly carbon and aerogel – literally
the least dence substance there is – and its easy to see that
simply cribbing numbers from a design made when aluminum was the
lightest thing you could build spacecraft of is a problem.
Let’s
try this again shall we?
System

Mass (kg)

Total
Structure Mass

24119

Crew Avg.
Mass

2400

Cargo/consumables

4245

Total Dry
Mass

30764

LH₂

71204

LOX

305788

Propellant
Mass

376992

Total Wet
Mass

407756

With SSME

409337

With J2

409544

I
not only went back and
recalculated the structure mass using 22^{nd}
century materials, I also handcalculated the mass of the consumables
and cargo, using NASA rations. Much
better results. With
these stats, the Tug can pull 4.43 m/s, and only has to burn for a
total of 376, instead of 1442. This means we only burn 141,514 kg
of propellant. With less thrust and more mass, I don’t feel a need
to calculate for the J2. 141.5 tons of propellant is 37% of our
propellant mass. For the return trip, we’ll need less propellant,
say, 25%? The
Tug would only mass 126 at that propellant fraction, and accelerate
at a whopping 14.4 m/s, or 1.4 gs.
It will only have to accelerate for 115 seconds and burn only 43
tons of propellant, while carrying 96 tons. This is over a 100%
reserve, enough that we could add another 20 tons or so to the 124
tons our Tug is pumping into the Patrol craft.
So,
there you have it, RocketFans, a glimpse into the hairtearingout,
thankless job of designing a realistic spacecraft. I’m glad I just
have to make these look good on paper. But the important part is, I
can now draw a spacecraft with all the particulars I wanted to, and
it will not only look realistic, it will be
realistic. It’s capabilities and limitation will suggest numerous
plot points and story ideas, and I can be assured that each and every
one of them will pass the litmus test of plausibility, because I did
the math up front.
Next
time I hope to actually have an image or two of new art to show you...