Wednesday, August 21, 2013

Fantasia and Fugue on Mars settlement transport technology

To my usual readers, this is a highly technical blog post. You have been warned.

Over the last few years I've had the opportunity to visit the SpaceX factory a few times, and each visit has been highly thought provoking. To those that don't know, here is a short history of SpaceX.

Formed 2002. Founder Elon Musk wants to develop technology and put people on Mars. Lots of people. Key to doing this is to develop reusable rocket technology so that, like a commercial airliner, the passenger only pays for fuel instead of the rocket, which is typically a thousand times more expensive. Indeed, airliners and rockets are usually similar in price, of order $100m.

SpaceX has won a contract to deliver cargo to the ISS, and has done so now 3 times. They have a rocket called the Falcon 9 (after the Millenium Falcon, of course), which is currently going through a series of upgrades to become partially re-usable. By 2015 it will transport astronauts to the ISS.

Meanwhile, hints have been dropped from time to time regarding the development of the technology necessary to take humans to Mars. For numbery reasons I'll get onto soon, doing this requires a lot more rocket than going to low earth orbit. However, the flow of hints is very slow. More to the point, engineers I've asked at the factory are downright cagey about what it going on.

In mathematics there is a technique called sparse sampling that allows a reasonably good guess to be made, by simply assuming that most of the signal is nothing. I have loosely applied this methodology to pull together all the hints I can find. I have combined this with various elements of common knowledge, best practise, a bunch of generic published data, and a basic knowledge of rocket science to try and deduce what the mission would look like. The remainder of this blog is elaboration of the architecture I have arrived at.

First, the demands of early exploration missions and later colonization missions are different. That said, they will require a lot of common technology, so an approach that serves both stands to benefit. The approach I outline is the mature, airliner level of the technology. Earlier versions or approaches will be described as I go along.

The Mars rocket is composed of two parts. The first is a large booster rocket, colloquially known as the 'BFR', or (I assume) Big Falcon Rocket. Ideally, it is reusable, though earlier launches will probably be expendable, possibly unintentionally. The second is the MCT, or Mars Colonial Transporter. The BFR will launch it at Mars. It will land, and after a while, take off again to fly back to Earth, where it will re-enter and land. It too will be reusable, though probably the sink would need a wipe-down after three years in space.

Three years! I hear you cry. Indeed. Due to the relative orbits of Earth and Mars, launch windows open for a few months roughly every two years. The usual mission profile would entail a flight from Earth to Mars taking 180 days, 540 days on the surface being awesome and waiting for the next launch window, then a 190 day flight back (with or without passengers).

A quick note about ∆v. Since being in space entails moving really quickly, distances are somewhat meaningless. A more useful measure of how far away something is is ∆v. ∆v is the change in velocity necessary to get from one orbit to another, such as from an orbit around the Earth to an orbit around the Sun that goes to Mars, and then back again. It turns out that the total ∆v needed for a Mars mission is about 22km/s. If that sounds like a lot, it is! The ∆v needed to get to the ISS (International Space Station) is about 9.3km/s. Okay, we have rockets that can do that, 22 isn't that much bigger than 9.3. Unfortunately the Tsiolkovsky rocket equation demands a mass fraction that increases exponentially with ∆v. For a reasonably good rocket, a ∆v of 22km/s implies a mass fraction of 382. Even an egg has a worse mass fraction that this. Even a hot air balloon. It is basically impossible to build any structure that can carry 382 times its own weight in fuel. There are two ways to get around this. One is to use mythical rockets that have much higher exhaust velocities, like some sort of nuclear rocket. Unfortunately, no-one (except engineers) likes nuclear rockets. The other way is staging. You get to throw away the mass of the spent stage, and so you can get by with 3 stages each with a mass fraction of say 10 instead. Even then, there is no way to get enough fuel to the surface of Mars to fly you home again, but there is a workaround.

First, however, I'm going to describe the BFR. My methodology here was simple. Extrapolate the existing SpaceX rockets, then double check the numbers in more detail. In particular, the speculative design named Falcon X seems to compete with the Falcon Heavy launch market, and thus seems unlikely to me. Each new core tends to be about an order of magnitude better, before allowing for advances in rocket technology. The order of magnitude is split by the 3-cored Falcon Heavy. The following table summarizes my findings.

SpaceX rockets progression

Falcon 1e
Falcon 9v1.1R
Falcon Heavy
Height (m)
Core diam. (m)
Init. thrust (kN)
Init. mass (T)
LEO (kg)
GTO (kg)
Price ($m)

* As a rocket engine can only develop a certain amount of thrust per area, it turns out there is a practical ceiling to the height of a cylindrical rocket, of about 100m. This disrupts the trend.

The BFR can launch 170T to low earth orbit. Three launches would be necessary to more than equal the mass of the ISS. It outclasses the SLS system (70T-130T) being developed as a replacement for the shuttle.

In more detail, the BFR first stage would comprise about 80% of the mass of the rocket, or 4600T, of which perhaps 220T would be structural (tanks, engines, pipes, legs, etc). There is some freedom in how the propulsion is developed, but my best guess is that it uses an octoweb structure like the F9R. This structure allows throttling of the central engine to partially counteract overexpansion in the high atmosphere and increase efficiency. Each engine develops a peak thrust of 7.6MN, which is somewhat more than the 6.77MN F-1 behemoths that flew the Saturn-V to the moon. I anticipate they will be similar in size, though will employ methane oxygen fuel and hopefully staged combustion for an Isp of around 340s at sea level. This could be the shadowy raptor engine under development, though the earlier mooted gas-generator Merlin 2 could do equally well. The second stage will employ a single engine equivalent to the first stage engines, except with a larger expansion nozzle of around 250:1 to function more efficiently in a vacuum, with an Isp of around 380s. Each BFR would use 10 units of the same motor, which is a good tradeoff between commonality of parts, mass production, and the complexity of having too many engines. The second stage would be fitted with a heat shield to enable re-entry, and a subsidiary set of motors based on the super draco engine (67kN of thrust) to land at the launch pad after a few orbits.

Edit: Oct 24 2013. It seems Raptor's targeted thrust is 705T (840T vac), or 6.9MN (8.2MN vac), with a vacuum Isp of 380s. This makes a three-core structure, each with octoweb, much more likely for the BFR. This configuration is easier to re-use, but the single-core version overlaps with Falcon Heavy's capabilities in an already slim market.

Both the first and second stage will ultimately be re-usable on a timescale of hours. In the discussed mission profile to follow, both stages would be sub-orbital, though allowing the second stage to complete a single orbit (depending on launch site/inclination) might be the easiest way to get it back. Given that each launch window is open for a few months, many more MCTs than BFRs will be required. Each BFR could launch hundreds of MCTs every two years, followed by an off-season for maintenance, low-earth orbit work, and bombarding other hapless planets with a few brave humans.

Highly technical sketch of the BFR:

Second stage with retractable interstage, landing legs and rockets:

This rocket is capable of hurling its empty second stage plus 44T to Mars. However, ideally we'd like to get the second stage back, and not creating a crater on impact would also be super cool. This is where the MCT comes in.

What is the MCT? It's a self contained spaceship. It has a single stage, so all of it comes back. It is capable of carrying cargo (including people with one way tickets). It is capable of bringing people and itself back. In order to avoid carrying all the fuel to fly back with it, it is capable of making new fuel on Mars out of the Martian atmosphere (CO2). Eventually, a Mars base will be capable of refuelling an MCT and allowing an immediate unmanned return via Venus conjunction, permitting reuse for every launch window. Initially, however, it will have to bring its own feedstocks and power, and spend a considerable portion of time on the surface making new fuel. Flying back after the usual mission duration will permit a period of time for refitting on Earth before sending it back again, 4 years after the original launch. Alternatively, it could aerocapture into LEO, and be refitted and refuelled with humans there.

Happily, there are plenty of constraints on what the various component masses could be. Without going into all the detail, the masses can be broken into three broad groups; mC for cargo that stays on Mars, mS for structural components that make the round trip, and mF for fuel that has to be made on Mars. In order to fly mS back to Earth, mF = 7ms. This is not impossible, especially if you use the life support system to help hold the roof on. Also, you can fuel the MCT on Earth, and use mF to help fly to Mars, arriving with only enough fuel to land. Then the BFR and the onboard fuel combined must be enough to fire mS + mC to Mars. Obviously there's a tradeoff here. It turns out that the most cargo possible is mC = 2.8mS. This is absurdly high, even for a truck or a train, let alone a plane. Taking into account the reduced gravity on Mars, an even ratio is more likely. Also, the tradeoff is pretty flat near the top. With mC = mS, you can bring 80% the cargo and 300% the structure, which is probably a good thing. My calculation presumes this ratio, though small variations around this ideal are possible, and will probably be employed in the construction of different types of MCTs tailored to different needs.

Given the BFR's characteristics above, the resulting MCT has mS = 21T, mC = 21T, and mF = 147T. Combined they have a mass of 189T, which is more than the BFR's 170T to LEO, which is why the second stage is (barely) sub-orbital. The MCT depends on its own rockets to even enter LEO, let alone go to Mars. Since the MCT's own rockets are not powerful enough to enable its escape from Earth when fully loaded, astronauts would either fly in a man-rated Dragon on this or a separate flight, where they would meet in orbit. Additionally, the BFR is not a precondition to MCT flight. An almost unfueled MCT could be launched by a Falcon Heavy, then gradually increased by an electric ion drive to an escape orbit. A second Falcon Heavy launch provides a load of fuel, and at the last moment (after several months of climbing out of Earth's gravity well) astronauts would be delivered by a final launch for the shot to Mars.

The MCT is powered by 12 super draco engines, grouped in 4 pods of 3. They will also run on (probably catalytically ignited) methane-oxygen fuel, unlike the current super draco, which uses a dinitrogen tetroxide and monomethyl hydrazine hypergolic mixture. They will be partially steerable, independently operable, throttleable, and have engine-out tolerance for all stages of the mission. For landing on Earth, they will employ expansion bell bypasses or some other method to compensate for atmospheric pressure. It is not capable of launch abort, so if desired astronauts can be ferried to orbit in a dragon. Indeed, in campaign settlement, sequences of MCTs could be launched into LEO continuously, then each manned only during the appropriate launch window.

The MCT has landing legs, a heat shield, and is a truncated cone with similar proportions to Dragon. In this discussion it is 10m wide and 7m high, though other geometries could work just as well. The structure is divided into thirds. The lowest third consists of engines, fuel tanks, landing legs, various plumbing components, and the fuel generator, including the power source. The middle third is a storage area, containing rovers, equipment, and other cargo. The top third is living quarters, with space for initially four or five astronauts, though later missions could add more living space on the middle level.

Edit: Constraints on the ballistic coefficient (mass to heat shield ratio) render a wider, longer, thinner lifting body much more viable. A central living space flanked by two partitioned tanks with a heat shield area of ~200m^2 for the same mass has both a higher L/D ratio and a ballistic coefficient comparable to MSL. Landing configuration on rockets would place the heat shield on top to avoid holes for legs or rocks, and a close-to-the-ground, single level hab design. Launching from Mars in this configuration is okay, as the Martian atmosphere is thin enough that drag isn't a huge concern. Effectively it enters the atmosphere on its back. An identical airframe structure could serve as a TMI injection stage and tether counter balance, returning to Earth after a flyby. Both could be launched by individual Falcon Heavy launches. The lifting body design could land on the moon or Mars or Earth, and can launch from Mars or the moon. It would nominally lack control surfaces, using RCS for control instead. The same design can be leveraged as a Mars orbital shuttle for movement of larger amounts of cargo and humans in conjunction with a large cycler or orbital-only spaceship, at the cost of on-board ISRU or substantial LSS capability.

Fuel generation on Mars is carried out using the Sabatier reaction combined with the Reverse Water Gas Shift reaction.

3CO2 + 6H2 → CH4 + 4H2O + 2CO (with a ruthenium catalyst)

The water is electrolysed to create oxygen for propellant and hydrogen, which is run through the reactor again. The CO is kept for all sorts of nefarious purposes, including carbonyl metallurgy and ethene/ethanol synthesis. Ethanol is liquid at (low) Mars temperatures and pressures as well as human conditions and therefore is a easily handled fuel to use to power rovers and spacesuits, via either fuel cells or internal combustion.

Highly technical sketch of possible MCT geometry.
To generate 147T of fuel to fly to Earth, 8.5T of hydrogen has to be brought from Earth as feedstock. This consumes rather a lot of the cargo capacity; a base would be able to generate hydrogen or even all the necessary fuel, thus enabling more cargo to be brought.

Power is generated by a space-optimized fission reactor, such as the Safe Affordable Fission Engine (SAFE). This reactor produces 100kW and weighs 500kg. Additionally, a number of Stirling cycle RTGs could be used for auxiliary purposes. The reactor would be deployed on landing and left behind on the surface. Depending on the efficiency of the unit, around 100kW is needed to run the fuel production. On the flight out, the reactor shielding forms part of the solar radiation shield for the people on board. Being modular in nature, a base can use discarded RTGs to power all sorts of interesting site specific stuff, like drill rigs, observatories, remote landing areas, outposts, etc.

Landing on Mars and Earth is performed via aerocapture. On Earth, the nearly empty spacecraft has a terminal velocity of about 60m/s, and lands propulsively under rockets. On Mars, the thin atmosphere is not compensated adequately by gravity, and terminal velocity is about 740m/s, nearly 3 times the local speed of sound. Here, the rockets are used in earnest to slow and land the craft on the ground, expending 16T of fuel brought from Earth. As the rockets are mounted in pods on the side of the vehicle and heat shield, they are ideally placed to minimize disruptions to the supersonic shock. It is hoped this approach is relatively stable.

The mass budget of the MCT is as follows*.

Cargo mass (T)
Structural mass (T)

Life support system

1.9/person/2 years
0.4/person/half a year
Solar array (cruise)

Reaction control system


Science (telescopes, greenhouse, etc)
EVA suit


Open rover
0.8 (two rovers)

Pressurized rover

Hydrogen feedstock

SAFE-400 (120kW)
Engines (12 super draco)

Propellant tanks

Propellant chemical reactor

Heat shield (PICA-X)


Spares/margin (16%)
* With heavy credit to The Case For Mars, Table 4.5

Detailed ∆v budget

∆v (km/s)
Earth surface to LEO
LEO to escape
LEO to TMI (180 days with free return)
Mars aerocapture to surface
Margin/course corrections
Total Earth to Mars

Mars surface to LMO
LMO to TEI (190 days)
Earth aerocapture to surface
Margin/course corrections
Total Mars to Earth

A note on breathing gas. Earth at sea level has atmospheric pressure of 1 bar, 101.3kPa, 760mmHg, or 14.7psi, depending on preference. I'm going to stick with bar for now. The partial pressure of oxygen is about 210mbar, but anyone who's lived in Lhasa can tell you that that's more than you need. I think an atmosphere of 140mbar oxygen, 200mbar nitrogen is a good compromise. As an added bonus, oxygen paucity makes your face less likely to catch fire. For pressurised rover and spacesuit operations, leave out the nitrogen to avoid the bends. There is no shortage of oxygen generated by the propellant generator, so it's possible to sacrifice a lot of oxygen for the sake of simplicity and reliability of design. Alternatively, ambient temperature on Mars makes thermal cycling CO2 scrubbing relatively straightforward.

A note on radiation. Space is filled with radiation. Astronauts do not have the benefit of atmosphere, dirt, and a large magnetic field to shield them. That said, it's not as scary as it might seem. About half the ambient radiation is cosmic rays, GeV energy particles from outside the galaxy. You can't block them without being surrounded on all sides by many metres of stuff. The corollary of that is that most cosmic rays go right through people without causing serious harm. Indeed, thin dense shielding causes showers of secondary particles which are far more harmful. In space you get cosmic rays, but on Mars, most are blocked either by the ground or the atmosphere.

The other half is radiation from the sun, which is mostly harmless most of the time. Every now and then a solar flare pumps out an earth mass or so of particles in the MeV range. Unshielded sentient goo in space will receive up to 5 grays in a few hours, which is universally fatal. Fortunately, MeV scale radiation is easily blocked by some lead and/or a 10cm column of water between the people and the local direction of solar magnetic fields, along which energetic charged particles flow. There is plenty of water on board in food, water, and their products, plus hydrogen feedstock, plus reactor shielding. The few places on board not shielded can be avoided for a few hours. The MCT will utilise these elements in combination to minimise unnecessary exposure.

A two year mission will deliver roughly half a gray, in a very gradual fashion. Statistically, this corresponds to about a 1% increase in lifetime cancer risk. Smoking is a 20% lifetime cancer risk. Living in a polluted city is somewhere in between. Most of the radiation dose is incurred in space. If you send people one way, you halve the risk.

Artificial gravity. Some proposals call for spinning a hab around on a tether or giant space wheels to provide gravity and prevent wasting due to a lack of load bearing exercise. The MCT is a single spacecraft. While it could be spun about its axis at some speed, the gravity thus obtained would be outwards, perpendicular to the sense on Mars, complicating interior design. The advantage of microgravity in transit is greater surface utilization. Alternatively, 2 or more MCTs could be spun from each other, providing apparent gravity in the design direction.

Glossary for TLAs.
TLA: Three letter acronym
CO2: Carbon dioxide
LMO: Low Mars orbit
LEO: Low Earth orbit
TMI: Trans-Mars injection. In this case, we choose an orbit with a period of 2 years, so that the landing can be aborted and the spaceship eventually return to Earth, instead of drifting in space forever.
TEI: Trans-Earth injection
EVA: Extra-vehicular activity. SPACEWALKING! Or Mars-walking as the case may be.
ISS: International Space Station
BFR: Big 'Falcon' Rocket
MCT: Mars Colonial Transporter
∆v: 'delta-v', or the change in velocity needed to get from one orbit to another.
MeV: mega electron Volt. The energy gained by accelerating one electron across 10^6 volts. Typical of nuclear energies, radioactive gamma rays, etc.
GeV: giga electron Volt. The energy gained by accelerating one electron across 10^9 volts. Typical of cosmic rays. For perspective, the Large Hadron Collider (LHC) operates at 14 TeV, or tera-electron volts (1.4x10^13 eV).