Trains on the Moon
The US government is contracting defense contractor Northrop Grumman to develop a concept for passenger and freight rail on the Moon, the idea being to use this to transport resources and perhaps build rockets for travel to the rest of the Solar System. Upon seeing this, I immediately set to try figuring out design standards, and it looks like such a railway would have a much harder time developing an alignment than on Earth, because of the impact of low gravity.
The issue is that lunar gravity is 1.6 m/s^2, and not 9.8 as on Earth. This turns out to affect how vehicles can round corners. The formula connecting speed, lateral acceleration, and the curve radius is the same everywhere:
The value of a is measured in the horizontal plane; curves are normally banked (canted/superelevated), so that gravity countermands centrifugal force, but normally, trains are run faster than the perfect balancing speed, since some lateral acceleration in the plane of the body of the train is acceptable. For much more detail, see old of posts of mine here and here.
In rail engineering, lateral acceleration is usually measured not in units of acceleration, but in units of distance, corresponding to how far the track is canted vertically (cant), and to how much the track would need to be canted further to achieve perfect balancing speed (cant deficiency). These units follow the formula
Here, e is total equivalent cant (cant plus cant deficiency), k is the track gauge from the middle of the rail to middle of the rail (around 60 mm more than the usual value of track gauge, which is measured from inner rail to inner rail), and g is gravitational acceleration. On Earth, on standard-gauge railways, this reduces to the formula that 1 m/s^2 of lateral acceleration is equal to 150 mm of total equivalent cant.
The issue with all of this is that the safety limits of both cant and cant deficiency are better expressed in units of distance rather than acceleration, as gravitational acceleration changes; equivalently, the limit value of a is proportional to g. The reason is that cant deficiency is limited by the ability of the train to round the curve safely, without toppling; if the combined force vector of weight and centrifugal force points too far off-center, then the swaying of the train can lead to derailment and catastrophic damage, including deaths. Thus, the limit value of acceleration in the plane of the tracks is best expressed as a proportion of gravitational acceleration, rather than in absolute units. The limit value of cant, in turn, is related to the safety limit of the ability of the train to stand still on canted track in an emergency.
This analysis can be seen in two distinct places in existing rail design standards and speed limits:
- When the train rounds a vertical curve, there is a minimum curve radius too, governed by both safety and passenger comfort. The minimum curve radius is higher on a crest than on a sag, because on a crest the train’s vertical acceleration slightly countermands gravity, and thus the train does not grip the tracks so well, whereas on a sag the vertical acceleration adds to gravity.
- The maximum values of cant and cant deficiency are usually fairly close for a given train. Two notable exceptions are high-speed rail, and tilting trains. High-speed rail has higher maximum cant than cant deficiency – German standards are 180 and 130 mm respectively – because cant deficiency is a limiting factor when the train is moving at 300 km/h (and thus potentially sways more) whereas cant is a limiting factor when the train sits still. Tilting trains are the exact opposite: the maximum cant deficiency is very high, reaching 270 mm on some high-maintenance Pendolino sets designed to be light enough and have low enough center of mass to be able to round corners safely, because when the train sits still on canted track the tilt system is assumed not to be working.
The upshot is that a standard-gauge railway on the Moon can expect to have a maximum total equivalent cant of 300 mm or somewhat more, same as on Earth – but that is compatible with a value of a of 0.33 m/s^2. In effect, curve radii have to be six times wider, assuming equal technology. The viaducts required to build such a straight right-of-way are easier to build on the Moon, since they don’t need to support as much weight for a given mass, but more and taller viaducts are still needed, and going around obstacles is not easy.
Pedestrian Observations 
Would this noticeably change if you did it as a suspended train hanging from a track elevated on pylons? That might make it easier to avoid abrasive dust getting on the track.
Yeah, building anything with moving parts on the moon is super hard due to the ultra sharp statically charged dust that is everywhere. There’s a reason Mars rovers have been able to remain mobile for years but, Yutu, the lunar record holder, only lasted 42 days.
Mars dust can be pretty bad news as well, although it’s nothing on lunar dust.
In general, the low gravity makes suspending the train below the rail more attractive. And you can cover the suspended track rail to protect it from dust, significant heating/cooling changes from the long lunar days and nights, and from micro-meteoroid impacts.
Waiting for the first NIMBLY* objections to lunar rail right-of-way takings…
*”NIMBLY” = “Not In My Back Lunar Yard”
lol… 😀
I see no reason to build viaducts on the Moon, since the absence of atmosphere makes the option for tunnels even more attractive. And if DARPA decides to resurrect the “subterrene” concept, the downsides would be much less challenging than implementing such concept on Earth.
I recall seeing a crayonish Chinese proposal of underground maglevs on the moon…
America struggles to build railroads on Earth, so why not shoot for the Moon? 😀 lol… Still, an interesting idea I’ve thought about since a child, railways on other planets. Moon Base might have a Meter Gauge system for internal transport, like mines or the Capitol Subway, for true long-distance, perhaps a 2 Meter Gauge utilizing linear motors?
A lunar base should probably be using road rather than rail transport. Road transport scales down more efficiently whereas rail transport scales up, and the population of a lunar base is going to be low. (For the same reason, there’s no rail transport in Antarctica.) There is no environment for cars to destroy, and no air to pollute (and internal combustion is not viable anyway).
On Mastodon, people are proposing an aerial gondola, pointing out that the limiting factor to it on Earth is stability in the wind, which is not relevant to the Moon.
Yeah, I would agree with you that the need for a Lunar rail system seems pretty far off, and that road transport would come first and be what is needed for a long time, unless there is sudden rapid development of the Moon.
I could however imagine that in a few decades time perhaps, for a large Moon Base (like Clavius in ‘2001: A Space Odyssey’) of several thousand people, to see a “urban” narrow gauge rail system similar to the US Capitol Subway, the Chicago Tunnel Company, and the London Post Office Railway. I’ve been in a terra cotta factory that used a two-foot railway of carts to move material around the complex, including the terra cotta into the kelms. A lot of coastal military forts had light railways, including the Maginot Line.
For a light railway, the diminutive locomotives and power equipment could be imported for Earth (SpaceX Starship, Blue Orgin’s Blue Moon) with the iron rails, wheels, and other basic equipment manufactured locally out of in-situ resources.
Due to radiation and micro-meteorites a Lunar Base should be under ground, likely cut and cover, and it could be spread out over a great distance between separate habitat, commercial, research, industrial, energy, port, and shipyard complexes, so connecting them with a cut-an-cover subway containing a light railway and pedestrian walkway would make sense. Perhaps a Lunar city might start out build along one long subway.
Of course on Earth a automated light railway would make so much more sense than Teslas in a Tunnel! 😀
I so much want to hire Disney to show Elon Musk how to do the Las Vegas Convention Center Loop the right way!
Las Vegas had a monorail that failed spectacularly. It borrowed $650 million which it never paid back because its ridership estimates were hugely inflated. It went bankrupt — twice. It didn’t connect with the airport because cab drivers successfully argued that it would drive them out of business.
I’m excited about the potential for some incredibly tight curves on Jupiter
Read a book in which one nation’s moon base had enough air, but was starving. The competition had enough food but was suffocating from cracks in their dome.
Tell me, how do you run a jackhammer or a TBM, without the vibrations undermining the integrity of the nearby built environment?
As a child I waited for those beautiful crayon maps to come true, a one mile stretch of the -6- train to Co-op City. Not gonna hold my breath for the Luna Express.
Well, it depends on how bad the vibrations are. Evidently cities do run TBMs without disturbing the built environment, by going deep – I never remember if the required depth for a TBM is that the top of the bore’s depth needs to be twice the bore diameter or if the bottom is.
Then there’s the question of what vibrations are acceptable. There are different building settlement regulations depending on site sensitivity. Normally, the regulation is that 3 cm of subsidence are allowed for a residential or commercial building, but in the most sensitive historic areas, this is still too destructive, so the regulation in Italy near historic monuments is 3 mm, requiring the use of different (and much more expensive) techniques for station construction.
According to this study, using the simplified methodology, the minimum overburden depth to tunnel diameter ratio ranges from 0.9 to 1.2 for tunnel lining thickness of 0.3m and from 0.8 to 1.1 for tunnel lining thickness of 0.4m. Using optimized methodology results in less overburden.
Since the model does take the earths gravity for the overburden soil into consideration within the calculations, the overburden ratio for tunnels on the moon would be much higher than on earth. I don’t know by how much as I haven’t done the calculations using the moon’s gravity. Maybe 6X if we simplistically use the ratio of the earth’s gravity to the moon’s gravity.
Cut & cover would not need such high overburden though.
Even without curves, in extremely low gravity, wouldn’t there be an issue with traction? In the limit of no gravity, there is no normal force to produce friction between the wheels and the track and the wheels would just slip. Any idea if that would be an issue at moon levels of gravity?
I think the propulsion system would be Linear Motor for just the reason you mentioned. And then there’s braking. LIM’s do both very well.
I expect that any rail system there would use Linear Induction Motors. LIM’s are great both for acceleration and braking, the things that require friction.
How much impact does the track gauge affect the minimum curve radius for any given speed?
It doesn’t; track gauge affects the minimum curve radius if you’re willing to take a bigger penalty to speed, from the perspective of rail wear, squeal, etc.
Thanks, is there a formula to show this? That would be very helpful.
I don’t know.
Driving that train, high on the moon
Casey Jones you better, watch your speed. Trouble ahead, trouble behind
And you know that gravity isn’t holding the line.