Intra-Fleet Tugs and why Rocket Science is as hard as Rocket Science

     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 Intra-Fleet 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 distributed-network 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

   In the article about how fleets work, I stated that the crews on the patrol craft could be swapped out by ferrying fresh people out via the Cygnus. While this would certainly work for crew transfers, you’d also have to detail additional craft for cargo transfers, of consumables and (if armed with rail guns) ammunition. As versatile as the Cygnus is, it cannot not re-supply that most important consumable resource in terms of tactical movement, propellant.

     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 real-world physics. For our Intra-Fleet Tug, I was inspired by the Johnson Space Center’sTug study, who’s image I used in the Poll. This beauty is a two-stage 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 light-second is good deal further than the LEO/ GEO distance, right? In kilometers, yes, but in Delta-V, 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 light-second 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 Delta-V 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 J-2 from the Saturn V’s SIV-B 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 (F-Com), Guidance Procedures Officer (GPO), Maintenance, Mechanical Arms, and Crew Systems Officer (MACS), and a Payload Officer (Payload). Add as many again of Candy-Cruisers, and you’ve got eight people in the command module. That’s a bit crowded for a Tug, but we can use hot-bunking 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 flared-out 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 20-person 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 mass-limit. 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 J-2 stats, but they are for a NASA tug, and they have the information I need to calculate with, whereas sources on the J-2 did not.

     What we want to know is, assuming a 100-hour 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 less-than-a-third 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 Delta-V budget, and our distances. By establishing an arbitrary travel time of 100 hours, we also provided a much-needed value for equations, and more important, the mass of needed consumables.

   An Intra-Fleet Tug that uses a “F-2b” SSME-analog 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 Delta-V equation of Delta-V = Exhaust Velocity x ln(Mass Ratio). This results in a Delta-V 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 J-2 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 Delta-V 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 light-second is only 300,000 kilometers. We actually have less distance to travel, and hopefully less Delta-V, 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 100-hour 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 light-second 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 “one-third” we wanted to get by with.

     As for the J-2, we need to re-do 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.

   Having gone back over my notes I discovered my problem, and it’s an embarrassing one. The Class A Patrol Craft I just mentioned, the one that’s over twice as large as this tug? It has a dead weight tonnage of 70 tons. That’s it. The Tug has a dry massof 466 tons. Well, there’s our problem!

     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 J-2	409544

     I not only went back and recalculated the structure mass using 22^nd century materials, I also hand-calculated 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 J-2. 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 hair-tearing-out, 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...