Sunday, June 26, 2016

What might Musk's MCT look like?

Here is an entirely speculative look at Elon Musk's proposed Mars Colonial Transporter.
There are no details available, so I'll simply be proposing some options for a vehicle that can carry 100+ people to Mars. I will be making plenty of assumptions and treating this like an entry in a high-level design challenge.

For background, Musk's stated goal is to build a colony on Mars that will reach one million people b̶y̶ ̶2̶1̶0̶0̶ at some point, probably 3000.The point of SpaceX is to be a testbed and funding mechanism for this colonization effort. As unlikely as this sounds, I don't see any reason why it can't be accomplished given sufficient cash.

Details after the break.
(This post was updated with a better estimate of booster size and payload)
((I'm not satisfied with the content; this post is a giant blob without enough detail. I plan to break this into several posts with a deeper look and more visibility into how I arrive at these numbers. Thanks for your patience.))

 - The MCT booster (aka the Big Freaking Rocket) is implemented as a single 15 meter diameter core burning methane.
 - S̶a̶i̶d̶ ̶B̶F̶R̶ ̶w̶i̶l̶l̶ ̶a̶c̶h̶i̶e̶v̶e̶ ̶M̶u̶s̶k̶'̶s̶ ̶s̶t̶a̶t̶e̶d̶ ̶g̶o̶a̶l̶ ̶o̶f̶ ̶1̶0̶0̶ ̶t̶o̶n̶s̶ ̶t̶o̶ ̶M̶a̶r̶s̶ ̶s̶u̶r̶f̶a̶c̶e̶,̶ ̶w̶h̶i̶c̶h̶ ̶m̶e̶a̶n̶s̶ ̶a̶t̶ ̶l̶e̶a̶s̶t̶ ̶7̶5̶0̶ ̶t̶o̶n̶s̶ ̶t̶o̶ ̶L̶E̶O̶ ̶b̶e̶f̶o̶r̶e̶ ̶c̶o̶n̶s̶i̶d̶e̶r̶i̶n̶g̶ ̶l̶a̶n̶d̶i̶n̶g̶ ̶f̶u̶e̶l̶.̶ ̶A̶l̶l̶o̶w̶i̶n̶g̶ ̶m̶a̶x̶i̶m̶u̶m̶ ̶d̶r̶a̶g̶ ̶a̶n̶d̶ ̶1̶.̶7̶k̶m̶/̶s̶ ̶p̶r̶o̶p̶u̶l̶s̶i̶v̶e̶ ̶d̶V̶ ̶t̶o̶ ̶l̶a̶n̶d̶,̶ ̶t̶h̶e̶ ̶t̶o̶t̶a̶l̶ ̶L̶E̶O̶ ̶p̶a̶y̶l̶o̶a̶d̶ ̶i̶s̶ ̶r̶i̶g̶h̶t̶ ̶a̶r̶o̶u̶n̶d̶ ̶1̶,̶0̶0̶0̶ ̶t̶o̶n̶s̶.̶
As it turns out, scaling a Falcon 9 full thrust up to 15 meters diameter would yield about 1570 tons of payload to LEO. That's before the 3% boost to Isp by switching to methane. Even a 12-meter diameter version should easily handle 800 tons; if the expandable module can be compressed into a smaller fairing then such a vehicle would be able to handle this project.
 - Near-perfect life support recycling is available.
 - Bigelow / transhab expandable technology is available, with an expansion ratio of at least 3:1 excluding the core.
 - Later trips will use improvements in tech and infrastructure, but the early trips can't rely on anything exotic.
 - Red Dragon missions will develop appropriate EDL systems for Mars.
 - Martian gravity is sufficient for long-term health and for growing crops.
 - Everything is designed to work for normal people, tourist-proof.

 Part 1: Big Freaking Habitats

 Transit habitats are complex and difficult, but this has to be solved very early on. Microgravity is severely debilitating over long periods. Storing enough food and other supplies for an all-Earth-sourced mission is low risk but high cost. Radiation is a major roadblock.

 All of those can be solved with a very large expandable habitat module. Here's a quick bullet-point summary of features which will be explored in greater detail below.

 - 15 meter diameter launch vehicle
 - 20 meter diameter fairing
 - Two expandable habitat sections 8 meters wide
 - Deployed diameter 43.3 meters
 - 22,280 cubic meters of pressurized volume
 - Spin gravity; 4 rpm for Mars equivalent
 - Fully self-sufficient food and life support systems for about 200 people
 - 1 MW solar power at Mars orbit

The BFR's core is 15 meters. An oversized fairing can go about 40% over the core diameter (same ratio as Falcon 9), but we will specify a 20-meter fairing (1.33:1). The rigid core will be 6.4 meters in diameter, with a total folded diameter of 19 meters and a deployed diameter of 43.3 meters. The module hull is 0.45 meters thick when deployed, with an inner radius of 21.2 meters. At this radius a spin of 4 rpm will produce 0.378 g, equal to the gravity on Mars. For a look at the tech behind this, check out the inflatable structures handbook (pdf) on NTRS.

 The habitat will be built in two separate sections, each 8 meters in width. The two sections will spin in opposite directions so the habitat can spin up or down without burning fuel and to minimize gyroscopic precession during maneuvers. The service core (rigid aluminum and composites) will form the central axis and storm shelter. Expanding outward are six decks each three meters tall in the form of concentric cylinders. Deck surfaces will be made of composite planks anchored to rings in the hab walls and reinforced with fiber webbing; these are designed to collapse during folding and expand during deployment much like a rope and plank bridge. Decks are not individually airtight. The outer edge and spaceward wall will include 20cm of water as radiation shielding and reserves, providing enough shielding to allow for 2 to 4 round trips before a person's lifetime exposure limit is reached. (1/e attenuation of 0.33 from water plus additional protection from the hull is sufficient to limit exposure to <500mSv per year.)

 Passenger cabins are roughly the size of a family cruise ship cabin, 17m² of floor space (3 by 5-2/3 meters) and about 47.4m³ of volume. That's around 180 square feet, in the range of tiny house sizes. The spinward walls slope inward a few degrees but not oppressively so. This would hold two to four people; it's not clear if children would be allowed on early flights but at some point they will be. 40 cabins fit on each section, 80 cabins or 160 to 320 people for a full habitat. I'll assume an average of 200 people (half couples and half triples). This deck is at 32.5% gravity. This function requires about 152 tons of equipment (beds, toilets, etc.) at 60kg/m³.

 Hydroponics take up the whole outer deck, which is at Mars gravity. Each person requires 40m³ for their food supply, so the ~2750m³ available on deck 1 isn't quite enough. The remaining demand is met on deck 3 (27% gravity), with about 60% of the space devoted to the other 1250m³ required. This function requires about 300 tons of equipment at 75kg/m³.

 Public spaces (meeting areas, recreation, exercise space and education) take up the remaining 40% of deck 3, with some microgravity activities in the service core. This function requires about 49 tons of equipment at 60kg/m³.

Engineering is housed on deck 4, with 1613m³ of space at 21.8% gravity. This section includes batteries, power conversion gear, computers, water and air purification, humidity and temperature management, a machine shop with 3d printing equipment and any other tools needed to maintain the habitat. This function requires about 194 tons at 120kg/m³.

 Bulk storage is on decks 5 and 6, a total of  1870m³. This holds personal possessions, extra food, emergency supplies and spares. This function requires about 75 tons of equipment at 40kg/m³.

 The rigid service core holds the gear necessary to expand the section and to spin up, plus connections to the other section and the remainder of the spacecraft. This also provides storm shelter area for the occupants in the event of a solar particle event or other high radiation situation. This section is assumed to mass 10 tons, equal to the expandable hull mass.

 A very large solar panel array and an equally enormous radiator array are required. These are assumed to mass 3 tons each based on commercially-available solar panel performance and by assuming the radiator mass is equal to the PV panel mass.

Part 2: Deployment

Each section would be launched compressed, in a stack with tanks of water and other supplies. The largest single item on the manifest is 450 tons of water for radiation shielding and life support. The hull, core, hydroponics gear, fuel tanks, engineering equipment and other furnishings come to around 890 tons. This pushes the 'empty' mass of one module to 1372 tons, s̶o̶ ̶m̶o̶s̶t̶ ̶o̶f̶ ̶t̶h̶e̶ ̶s̶h̶i̶e̶l̶d̶i̶n̶g̶ ̶w̶a̶t̶e̶r̶ ̶n̶e̶e̶d̶s̶ ̶t̶o̶ ̶b̶e̶ ̶d̶e̶l̶i̶v̶e̶r̶e̶d̶ ̶p̶o̶s̶t̶-̶l̶a̶u̶n̶c̶h̶. This is possible with the 15-meter rocket in a single launch, but would need to be broken into two launches for the 12-meter rocket (perhaps including water, PV, radiators, fuel tanks and some fuel in the second launch). Significant savings can be achieved down the road by using lunar water delivered to EML2; this alone would save 700 tons of fuel and 450 tons of water in LEO.

Engines need to provide at least 0.1 g of thrust when fully fueled, about 9.6MN. Assuming a thrust to weight ratio of 180 that's about another 6 tons of engines. O̶n̶e̶ ̶o̶f̶ ̶t̶h̶e̶ ̶t̶w̶o̶ ̶s̶t̶r̶u̶c̶t̶u̶r̶a̶l̶ ̶l̶a̶u̶n̶c̶h̶e̶s̶ ̶w̶o̶u̶l̶d̶ ̶c̶o̶n̶t̶a̶i̶n̶ ̶e̶n̶g̶i̶n̶e̶s̶ ̶w̶h̶i̶l̶e̶ ̶t̶h̶e̶ ̶o̶t̶h̶e̶r̶ ̶w̶o̶u̶l̶d̶ ̶c̶o̶n̶t̶a̶i̶n̶ ̶t̶h̶e̶ ̶r̶e̶m̶a̶i̶n̶i̶n̶g̶ ̶n̶o̶n̶r̶o̶t̶a̶t̶i̶n̶g̶ ̶s̶t̶r̶u̶c̶t̶u̶r̶e̶.̶ ̶A̶ ̶f̶u̶r̶t̶h̶e̶r̶ ̶s̶i̶x̶ ̶l̶a̶u̶n̶c̶h̶e̶s̶ ̶w̶o̶u̶l̶d̶ ̶b̶e̶ ̶n̶e̶e̶d̶e̶d̶ ̶t̶o̶ ̶f̶i̶l̶l̶ ̶u̶p̶ ̶t̶h̶e̶ ̶w̶a̶t̶e̶r̶ ̶a̶n̶d̶ ̶f̶u̶e̶l̶ ̶t̶a̶n̶k̶s̶ ̶t̶o̶ ̶g̶e̶t̶ ̶t̶h̶e̶ ̶c̶r̶a̶f̶t̶ ̶t̶o̶ ̶E̶M̶L̶2̶,̶ The 15-meter rocket can deliver both habitat sections and all necessary fuel for the journey to EML2 in five launches, with a LEO departure mass of just under 7,200 tons.
 At EML2 the assembly would be completed, with internal furnishings in place and all systems operational. From this point on the whole vehicle would travel back and forth between EML2 and Mars orbit. Fueled mass at EML2 would be up to 7640 tons (including 16.4 tons of colonists and 5̶0̶ ̶t̶o̶n̶s̶ ̶o̶f̶ ̶p̶e̶r̶s̶o̶n̶a̶l̶ ̶p̶o̶s̶s̶e̶s̶s̶i̶o̶n̶s̶ up to 600 tons of cargo including personal possessions). 4,346 tons of that is fuel; at an oxidizer-fuel ratio of 2.77 that's 1,153 tons of methane and 3,193 tons of oxygen. Passengers and cargo could be delivered to EML2 via Falcon Heavy launches, using a passenger container and upper stage designed for powered re-entry.

 ̶A̶ ̶d̶i̶r̶e̶c̶t̶ ̶o̶p̶t̶i̶o̶n̶ ̶l̶e̶a̶v̶i̶n̶g̶ ̶s̶t̶r̶a̶i̶g̶h̶t̶ ̶f̶r̶o̶m̶ ̶L̶E̶O̶ ̶t̶o̶ ̶M̶a̶r̶s̶ ̶w̶o̶u̶l̶d̶ ̶r̶e̶q̶u̶i̶r̶e̶ ̶v̶a̶s̶t̶l̶y̶ ̶m̶o̶r̶e̶ ̶f̶u̶e̶l̶.̶ ̶F̶u̶l̶l̶y̶ ̶1̶8̶ ̶l̶a̶u̶n̶c̶h̶e̶s̶ ̶w̶o̶u̶l̶d̶ ̶b̶e̶ ̶r̶e̶q̶u̶i̶r̶e̶d̶ ̶w̶i̶t̶h̶ ̶f̶u̶e̶l̶e̶d̶ ̶m̶a̶s̶s̶ ̶a̶ ̶b̶i̶t̶ ̶u̶n̶d̶e̶r̶ ̶1̶7̶ ̶t̶h̶o̶u̶s̶a̶n̶d̶ ̶t̶o̶n̶s̶.̶ ̶P̶e̶r̶h̶a̶p̶s̶ ̶t̶h̶e̶ ̶f̶i̶r̶s̶t̶ ̶t̶r̶i̶p̶ ̶w̶o̶u̶l̶d̶ ̶b̶e̶ ̶d̶o̶n̶e̶ ̶l̶i̶k̶e̶ ̶t̶h̶i̶s̶,̶ ̶b̶u̶t̶ ̶i̶t̶ ̶w̶o̶u̶l̶d̶ ̶b̶e̶ ̶o̶u̶t̶r̶a̶g̶e̶o̶u̶s̶l̶y̶ ̶e̶x̶p̶e̶n̶s̶i̶v̶e̶.̶ (no good reason to do this unless there is just no possibility of lunar fuel.)

Part 3: Operations

 Launch windows to and from Mars arrive every 26 months. Round-trip travel times are 32 months and up depending on how much extra fuel is used, so a minimum fleet of two transit habitats are required to deliver colonists at every opportunity. Each habitat spends around 17 months in orbit around either Earth or Mars between trips.

 The vessels are operated by trained crewmembers assisted by colonists. Crew can only handle 2 to 4 round trips before their lifetime radiation exposure limit grounds them permanently, so many of them will simply be colonists paying part of their way with skilled labor.

 The Earth phase is spent at EML2 accumulating fuel, spares and other supplies. Near the end of the stay, passengers and cargo are sent from Earth. Once everyone is aboard the vessel departs for Mars, using a close Earth pass for maximum Oberth boost.

 On arrival at Mars orbit the passengers are transferred to a fleet of Mars landers. These are reusable SSTO vehicles that deliver fuel to the habitat and take passengers and cargo to the surface. Offloading may take a few weeks.

 The Mars phase is spent in low Mars orbit initially, then later spent docked at Phobos port. Fuel is transferred from the surface (and possibly from Phobos). In addition, CO2 is delivered to the habitat to be split into O2 and carbon blocks; a supply of storable carbon is needed to balance the life support systems during periods of overproduction and can double as an emergency reserve of fuel (with conversion to methane, sacrificing some of the water supply for hydrogen). As the launch window approaches, any returning passengers and Earth-bound cargo make the trip to the habitat. Departure is straightforward, no complex maneuvers.

 On arrival at Earth a Lunar gravity assist is used to help match speed and deliver the craft to EML2. Earth-bound passengers transfer to crew landing craft for return to the surface. The cycle of maintenance, cargo and fuel is repeated.

 While in orbit the habitats are not idle; hydroponics are run at full capacity with a focus on storable crops like grains and legumes plus low-yield spices and herbs. This helps build up emergency food supplies and allows the available space to be used primarily for fresh vegetables and greens while transporting passengers. The hydroponics systems are sized for 200 people, so this 'crop rotation' approach allows some extra margin. Further, the habitat's output can supplement food supplies for crews on Luna, Phobos or any occupied stations.

Part 4: long term

 The goal is one million people on Mars. If the first flight leaves in 2035 then we have only 30 windows in this century. If a new transit habitat is launched at each window and each habitat only lasts 20 years, only 28,000 colonists will be delivered by 2100. At steady state, 630 tons of fuel per month would be delivered to Phobos and 1,670 tons per month to EML2 to allow an ongoing delivery of one thousand colonists per window. Going beyond a thousand people per window would mean launching more than one transit habitat per window.

 A more realistic option would be to transition into electric propulsion. Most likely that will be solar electric using argon as propellant. Each trip would consume a bit under 180 tons of argon one way. At 430 MJ/kg of propellant and 75% efficiency the power system needs to deliver 108 TJ of energy. For a 'burn' time of 90 days we need about 15 MW of total power (77,500 m² and 39 tons, perhaps as a pair of 112 meter radius round panel arrays at 33% eff.). The travel time is still the same as the chemical option, but we coast a bit over half the time. Adding more fuel would shorten the trip time a bit without needing more power. This represents an immense power output and would surely be useful for industrial purposes while docked at EML2 or Phobos. The SEP version would need a bit more radiation shielding since there won't be large methane and LOX tanks.

 Importantly, a network of SEP cargo haulers would allow for the cheap exchange of materials and products between LEO, EML1/2 and Phobos/Deimos. With chemical systems from Earth and Mars plus either chemical or tether systems from Luna the infrastructure is complete. Only those things that are absolutely necessary would come from Earth, mostly people, seeds and very high-end technology. Water, oxygen, carbon, salts, nitrogen and argon would come from Mars. Water, oxygen and metals would come from Luna. Continued improvements in solar power and electric propulsion technology would increase the available payload capacity of transit habitats, while the ability to construct new vessels using in-space materials would greatly accelerate the pace of colonization.

An alternative to traditional transfer orbits would be to use a low-fuel cycler orbit for the transit habitats. This would require vastly less fuel at the cost of requiring four habitats for each set of passengers to be transferred at each window. This might be an intermediate step before converting fully to SEP, though the main benefit is that each vessel can operate as a deep-space laboratory (with massive hydroponics overcapacity) between passenger runs. Another downside is that all passengers and cargo need to be delivered during a very short timeframe, only a few days at the most.

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