Tuesday, December 1, 2015

Lunar circumferential railway

This is a followup to the last earthside post about arch-lock, looking at longer-term uses for the equipment on the moon. While I think it's more likely that we would build tramways using tensile towers and tether technology, this (relatively) low-tech approach could be started within a few years, without any radical advancements and with fewer leading 't's.

An example late-stage use case would be connecting a Lunar polar base to the equatorial L1 or L2 tether anchor sites. Read on for details.

 The equatorial circumference of the moon is 10,921 km. A polar route would be a few km shorter; the polar radius is 1,736km yielding 10,907.6km, but the route would still cross the equatorial bulge. Connecting one pole to one anchor point requires only one fourth of that distance, or 2,730km. The goal is to build three tracks of maglev train lines on a solid block footing with individual arch tunnels. The entire structure is then buried under roughly 2-3m of regolith for impact and radiation protection. Solar panels would be placed along the top of the heap, providing distributed power. Interconnects will be built at intervals with power storage included. Electrical transmission lines and fiber-optic data lines will run along the tunnels. The train system will be used to shuttle materials between the base and the ever-moving construction site. Raw materials will be harvested along the route, shipped to base for processing, then finished blocks and rail components will be shipped back. Once complete, the system will carry cargo and passengers between the anchor point(s) and base(s) and can also carry bulk material from mining operations anywhere along its length to processing facilities.

 I assumed that the basic physics of a train bed are similar to a highway roadbed. There are several ways for that assumption to go wrong, but at moderate speeds of 100-200kph we should be ok. Using the geometry of the arch lock system (1.5m radius half-circle above a 1.5mx3m rectangle) and 10cm clearances, the maximum mass of a 1-meter car made of solid nickel is 62.3t, or a load of 101kN. I decided to test a block that is 1:2:4 rather than 1:1:2 to see if a half-thickness roadbed would be sufficient, so I used the Portland Cement Association's thickness design manual. I used a k factor of 300 pci (conservative; real lunar soil is probably much higher), modulus of rupture of 600 psi (based on lunarcrete experiments using actual Apollo soil samples) and thickness of 14" (maximum listed in the table; actual thickness is 14-3/4"). That gave me an unlimited load by stress of 108 kips and an unlimited load by erosion of 58 kips. Using one million repetitions the allowable load is 110 kips, so the maximum loads listed from here on out could be multiplied by 1.9 safely and still support one car per hour for 57 years.
These values give a maximum load for a single 1-meter 'bogey' or maglev pad of 132.5 metric tons mass. A 12-meter bulk car with two pads, fully loaded with loose regolith and up to 10 tons of hardware masses 72.4t with a load safety factor of 3.66. Clearly the 0.375m bed thickness will be adequate; we could haul a full load of iron ingots without exceeding the limit.

 Each 'crew' consists of two block-placing vehicles and enough excavators to keep them fed. Also required is a power unit that is connected to the track electrical line and provides conditioned power to other equipment. During daylight hours the block forming factory requires about 60m³ of regolith (about 78t) per hour to support the roadbed construction and 121m³ (157t) per hour to support the arch construction. Excavators need to be able to provide that volume in addition to leveling out the roadway. Excavators could look like this, scaled up appropriately. As an alternative, one drum could be replaced with this blade to allow a broader range of soil moving operations. Higher throughput could be achieved with a series of bucket wheels, where each pair of wheels balances the lateral reaction force and the angle of each wheel provides thrusting force with each cut. Each pair clears a certain volume, with the next pair set wider to make the next cut until the full width of the vehicle is cleared. All of the wheels would dump onto a conveyor and the whole system would not rely on mass for stability. Equipment could be powered by flywheel, by electrical cables or both depending on purpose. Since the range would be very short, beamed microwave power could also be feasible.
 Support is provided by the train cars themselves with onboard manipulator arms, so the train can load and unload itself then move to where it is needed next.


  Let's assume that each block requires one minute to place. That's 2.6 times as long as it takes on Earth. Section width is 12m and blocks are 1.5x0.75x0.375m, so each section contains 16 blocks and requires 8 minutes to assemble with two placers. That's 7.5 sections per hour. The road requires at least 1.82 million sections, but we will round up to 2 million to account for changes in elevation (about 9%). Construction is assumed to be electrically powered and only active for half of each 655.73 hour sol, so we should complete about 2,459 sections (1.64km) per sol. One 'crew' would require 814 sols (22,222 days or 60.8 years) to complete the road segment, racking up 267,000 operating hours. 32 million blocks would be placed, consuming 15.5 million m³ of lunar regolith. Building a full circumference roadway would of course require four times that volume of material and 243 crew-years to complete. Major transit projects on Earth often require 20 years or more to complete; eight crews working out of four bases would complete the job in a bit under 31 years. As construction progresses, the electrical storage capacity of the track will gradually allow more and more operation at night; if applied to this task then the construction period could be shortened somewhat. If the base electrical plant provides enough power (after transmission losses) to run the project at night then construction times should drop by 40-45%.


 Building a three-track 100kph maglev monorail into this roadbed would be done just behind the roadbed crew. Three tracks allow for one track to fail without blocking two-way traffic and simplifies some maintenance and equipment operations. It also allows human passengers to take the inner track for maximum protection from the environment while cargo shipments travel in either direction. Along with the tracks come several electrical conductors to carry power from the line's solar panels and flywheel backups. Track interchanges will be built every so often; this is mostly a maintenance concern, but if each quarter contains eight switching stations then they will be 273km from each other and from each base. If some maximum distance is required, the number of stations is (2730 / distance) - 2. Switching stations would include access to the surface for maintenance, mining and exploration.
 I do not know how to design a maglev track, so all I can do is provide some constraints. Lunar soil is expected to contain iron in significant concentrations, in some areas more than 12%. I will assume a 5% iron content on average across the surface. Each meter of the system requires 13.83m³ of material in block form. That material is post-processed regolith; if we assume processing removes 15% of the mass then each meter requires an intake of 15.9m³ of regolith at perhaps 1.3t/m³, or 20.68t. 5% of that is 1,034kg or 345kg per meter of track. That's 436 cm² of iron in cross-section, more than 20x20cm. That should be adequate if not downright excessive. Similar quantities of aluminum should be available; this will make adequate conductors for carrying power through the system. Six conductors (two per arch) are placed into slots in the road pavers and covered with an insulator to prevent arcing (even if it's just some processed regolith gravel). Along with power cables, one fiber-optic data cable will be laid in each tunnel. This allows redundant high-speed communication with power and monitoring equipment, trains and between destinations on the line.
 During the construction phase, every sol each crew requires 59,344m³ of material to be excavated and shipped for processing. Using 12m cars with 48m³ capacity that's 1,237 carloads or 3.77 carloads per hour of daylight. A 15-car train every four hours would handle the load; using 16-car trains allows for the track itself plus some extra margin for travel between switches and other issues. Efficient excavation requires that the train is in place to be filled, then immediately replaced with an empty train as the full one departs. If each car is equipped with a manipulator arm and each carload contains about 99 blocks then the car can unload itself in about an hour and 40 minutes. As long as the block-carrying train is emptied and moved into position just before the excavators fill theirs, four trainsets can handle the work for one-way trips up to four hours. Each additional four hours of travel require two additional trainsets. At 100kph and with only one crew working on a quarter section, 16 trainsets or 256 cars are required to keep materials flowing. Allowing for 10% of cars to require maintenance at any given time that means a fleet of 285 cars is required in order to complete the work. If the entire project is built from four established bases using eight teams then work starts with 32 trainsets and an additional 48 are required at completion, for a total of 1,422 cars (including 10% maintenance). Once construction is complete each trainset could carry about a thousand tons of bulk cargo (possibly up to 3000 tons of dense metals); the quarter-section system could see 16,000 tons of cargo in transit at one time and the full system could see 80,000 tons. Daily throughput would be 14,000 to 70,000 tons unless more cars were placed in service; with a ten-minute separation between trains the maximum throughput would be 144,000 tons per day in each direction.


 The next step is covering the roadbed with three 3m arches for radiation and meteor protection. Each course of the arch is composed of 13 blocks; the bottom two on each side are identical to the roadbed blocks (1.125m²), while the upper nine blocks form a 1.5x3m ID semicircular arch with a solid cross-sectional area of 2m². The entire block volume is about 4.7m³ per 1.5m section, or 14m³ per section for all three arches. A full circuit of arches would require 128.8 million m³, compared to 62.1 million m³ for the roadbed. The volume required for switching stations is close to that required for three arches, plus stations represent only a tiny fraction of the overall length.
 Arches can be constructed using train-mounted equipment or independent equipment. There are 39 blocks per segment, so keeping pace with the roadbed requires at least five block placers or some way to optimize placement. The bottom two blocks on each side can be placed in advance of the arch pieces, but the arch requires that all blocks are in place before moving on. Ideally this work would be done with a track switch between arch construction and roadbed construction, since a zipper truck is required to hold the arch in place and the track will not be available for use. Two arches can go up at a time, each with two block placers handling arch pieces and another one or two  placers handling the bottom or stemwall section.
 After the arches are formed they are buried under 2-3 meters of regolith. This is to protect against radiation and meteorite strikes, and should avoid damage from impacts that make craters less than a meter deep. It also provides a compressive load so the structure can resist a bit of uplift from quakes and to maintain stiffness. Power cables are run periodically for solar panel attachments, and flat beds are built to hold the panels at the proper angle for that latitude. Switching stations and other service access points are protected with a berm of soil that completely blocks any view of space from the inner opening, maintaining full protection even with the door (if any) open.


 PV panels distributed along the roadbed would provide power year-round. Unfortunately the entire system experiences dawn/dusk at the same time, so there is still a monthly cycle of high and low output. This will be balanced with flywheel storage capacity throughout the system, and could be further offset by laying an equatorial line of panels.
 Each quarter-section intercepts 1,736km of sunlight. A one-meter wide strip of panels would cover over 1.7 million square meters; at 15% efficiency this strip would produce 355.7 megawatts of power. Extending to 8 meters wide and 22% efficient the peak power production rises to 4.17 gigawatts, or 8.35GW for the full system. Without a means of pointing, the panels are lit for 327 hours per sol and receive the equivalent of 208 hours of full sun. 15% efficient panels would yield 42.6 kWh per m² each sol, while 22% efficient panels would yield 62.5 kWh per m² per sol. 35% efficient concentrating panels would yield 99.4 kWh per m² per sol. An 8-meter 22% array along the quarter-section would generate 108.5 gigawatt-hours each sol.
 Actually placing panels would require offloading them at a station or past the current arch construction point, hauling offroad to the current panel point, then positioning them on their beds on top of the regolith blanket over the arches. Panels would then be connected into strings and attached to the pre-placed power cables. Each cable would run to a power management unit built into a tunnel wall. Each PMU consists of power conditioning equipment to convert the DC power from PV panels into high-voltage AC for transmission, plus a flywheel energy storage device for load leveling. The FES provides surge capacity to handle the load of a train in its section of track and also functions as distributed storage. A commercial system stores 1900 J for 590 kg, though a fair amount of that mass is the cabinet and disintegration shielding; another problem is that it uses carbon fiber for the rotor and carbon is exceedingly scarce on the moon. Bulk aluminum devices could be built with available materials at somewhat reduced mass efficiency. Overall efficiency of these systems should be about 85%, much better than battery systems. Maintenance likewise is rare due to the use of magnetic bearings and a sealed vacuum environment for the rotor. They do consume power; the commercial system I linked eats 300W to maintain itself but can provide 190 kW for 10 seconds. Utility-scale systems like this one can store 25 kWh / 90 MJ per unit and can discharge in as little as 15 minutes.


 Constructing a single quarter-section of this system would involve mining and shipping 47.7 million cubic meters of regolith, about 62 million tons of material taken from the upper 2-3 meters of the lunar surface and almost exactly one million 12-meter traincar loads. This is expected to yield about 3 million tons each of iron, aluminum and a mix of oxygen and embedded volatiles like hydrogen and helium from the solar wind. If even 1% of the harvested metal can be used for other purposes that leaves 60,000 tons of the stuff for building satellites, space ships, habitats and heavy equipment.
 Trace elements start to look abundant when you're pulling them out of tens of millions of tons of raw material. Much of the iron in the upper regolith is shattered pieces of nickel-iron meteorites. For every ton of free iron extracted we should see 100-120kg nickel, 5-6kg cobalt, 100 grams germanium, 30 grams gallium, 7 grams iridium and 6 grams platinum. These and various related PGMs and rare earths could also be extracted economically from free metal grains. Assuming free iron grains make up 10% of the total iron in the regolith that's 33,000 tons of nickel, 1,650 tons of cobalt, 30 tons germanium, 9 tons gallium and 1.8 tons platinum after the first quarter-section is complete. Free iron grains almost certainly make up more than that for the upper few cm of soil, so the final yields will depend strongly on what material is harvested.
 These values are rough estimates across the set of iron meteorites without population weighting. The only way to know for sure what we can get is to get out there and mine some dirt.

 The complete system would span the entire moon; a trip of 27 hours 18 minutes would get you from point to point, 54 hours and 36 minutes to the opposite point or 109 hours and 12 minutes to travel the entire track. If four and a half days to circle the moon seems excessive then the track could just as easily be built to 500kph to drop the travel time below a day; there is no wind resistance, no weather and no turns, so the two main restrictions are rate of change of elevation and the straightness of the rail. The current maglev speed record exceeds 600kph in air on Earth, with the commercial Chūō Shinkansen line expected to operate at 500kph with grades up to 4%. Also worth noting: no atmosphere means the system's lifespan is subject only to actual wear and significant meteor impacts. Once built, the system could conceivably operate for hundreds of years with minimal maintenance. After the construction phase track switching would be minimal, so the few moving parts required would move only rarely. The structural components are precast and dropped in place, so sections of track can easily be uncovered, track and bed removed, subsoil compacted, bed and track replaced and recovered using the same equipment that built the line in the first place. Electrical components will be modular, mass-produced and easy to replace.
 Each switching station marks a logical expansion point, with access to the power, data and cargo networks plus easy access outside. These could grow into mining yards or even populated habitats, taking advantage of the industrial capacity built up in the process of building the rail system to build equipment and ship anywhere along the line. The process would look much like the growth produced by the first railroads crossing the American great plains; an area that was considered mostly uninhabitable developed small towns about every seven miles along the track around each station. Fast cargo plus the telegraph led to a connected society that was geographically separated, where each physical community made use of their unique local resources to participate in trade throughout the system.


  1. Since you're talking about maglev this would only be the starting point of what you could do with a circumlunar train. Build those arches much beefier and put another track on the bottom. Put a second maglev rig on the top of your train--now it can exceed orbital velocity. The train goes round and round, faster and faster. When it's going as fast as you want it to go a cargo capsule separates and is ejected--on anything from a sungrazer to solar escape orbit trajectory (with human-tolerable accelerations.) Mega engineering but what it will save you in rockets over the years...

    1. Right. The polar loop allows you to fine-tune your inclination on departure, while the equatorial loop allows slightly better efficiency. The equatorial loop would produce electricity grossly in excess of the amount required.

      The basic maglev concept could be done with existing technology and a lot of cash, potentially cheaper with advances in automation and additive manufacturing. I suspect a launch track sized for Lagrange destinations could be done with modest tech advances at nearly the same cost. This probably deserves its own post. More aggressive destinations may require significant advances in maglev technology.

      A full-scale launch loop would be a significantly bigger project. Lunar escape speed is 2.38km/s; accelerating at 1 g would take only four minutes and cover 290km of track for a C3=0 launch (Lagrange points). That's only about 2.7% of the full circumference, so you would need a compelling argument for why the entire track should be upgraded for orbital launch. Throughput and the lack of launch windows would be compelling arguments if the system needs to move a large enough mass of cargo.
      The peak centripetal acceleration for this launch would be 3.26m/s² minus the 1.62m/s² surface gravity for a net upward acceleration of 1.64m/s². This is very reasonable; a 10-ton payload would generate 16.4kN of force on the upper arch (equal to the resting weight of a 1.7-ton object on Earth). In fact, a properly-designed lower track should easily handle this load without the need to change the upper structure or use a second track at all. This system could be expected to last centuries provided adequate maintenance of the electrical systems, though the open areas for payload release would be at higher risk of damage from meteorites and radiation.

      Higher energies require longer tracks and/or higher acceleration. A Jupiter mission direct from the Moon would require C3~80km²/s², or a departure velocity from the Lunar surface of roughly 11.4km/s (2.4km/s to escape plus 9km/s to transfer). A 3 g launch (30m/s²) would take 6 minutes 20 seconds and cover 2,166km of track (about 10.4%). Travel time would be about 2 years 9 months and orbital insertion would require about 5.7km/s (high-thrust).
      The peak centripetal acceleration for this launch would be 74.86m/s², or a net acceleration of 73.22m/s². The same 10-ton payload would now be generating 732kN of vertical force. This sort of profile would likely require an upper rail, with release accomplished by simply ending the upper rail at an opening in the arch. (Such a design would use a sled or sabot for the lower track with rods to carry launch force to the payload, while the centripetal force would be resisted entirely by the upper track; the payload module would slide right off the rods with no complex release mechanisms.) The payload itself would experience a peak net acceleration of 80.65m/s² (8.22 g, via pythagorean theorem combining the centripetal acceleration with the launch acceleration). Note that this launch profile is near the limit for eyeballs-in human endurance.

      For an unusual twist, consider a mobile habitat that travels full-time on the track at speeds high enough to experience a stable 1 g acceleration. That would be 4.454km/s. The hab would circle the moon about every 41 minutes. Mechanical failure would be promptly fatal, so this is probably too risky to actually do. Still, it would be possible to reach any desired acceleration between 0.165 g and several g.