Night on the lunar railroad
by Sam Dinkin
|$1/kg to 10 km/sec: perhaps we should add some shipping and handling costs to that—it just does not seem high enough.|
Well, the Moon has no atmosphere. Perhaps better than developing and building a maglev track on the Moon would be to build a spinning tower that can slowly spin a couple of cables, one with payload and one with ballast. With carbon nanotube (CNT) cables, we could get going pretty fast. With a pair of 150-kilometer cables that get reeled out as things get spinning, we could get people up to 3 g.
v2/r = 3g
v2/150 km = 3 × 9.8 m/sec2
v = 2.1 km/sec
With 3,000-km cable arms, we are up to nearly 10 km/sec. That cable needs to hold 18 times as much weight as a space elevator cable in one-sixth g so instead of 60,000 kilometers’ worth of cable let’s make it 20 times as short as the elevator. The catapult cable can be tapered because out toward the end since its own weight won’t be tugging on it.
To get to the ecliptic of the solar system, the place to site the center of the cable is probably one of the poles. The good news is there are some great solar power sites up there. The bad news is that if the catapult messes up, there are probably going to be people around.
For cargo where we don’t care about force so much, just velocity, we can spin things up really fast with a short thick cable. As r gets little, force goes up as 1/r. But if you take the cable and bunch it up, you get a wider cross section. Since the amount of force the CNT can handle is proportional to the cross section, which is the volume of the cable divided by the length, your cross section also goes up as 1/r. Thus a thick cable for cargo that can take 300g can have r down to 300 km for 10 km/sec or 15 km for 2 km/sec.
So if we can get the cost of lunar power down to the cost of terrestrial power, maybe we can get things headed to the outer solar system on a speedy trip for $1/kg to 10 km/sec. Perhaps we should add some shipping and handling costs to that—it just does not seem high enough. Plus Ultra thinks the capital will be about 5 times the cost of electricity so let’s bump it up to $5/kg.
|What should we use as ballast shooting out the other end? How about oxygen?|
How are we doing on the nanotubes? At a theoretical loading of 1,300 gigapascals or 1.3 × 108 N/cm2 , a 1 cm2 thick cable at the end lets us keep about 40,000 kg on the end at 300g. Since we probably want to economize on the nanotubes—and they are probably not going to have that maximum theoretical strength for some time, if ever—maybe we should plan for a smaller payload.
I am not sure what the density of CNT is, but carbon’s density is about 3500 kg/m3 so, ignoring taper, we would need 100,000 kg of carbon nanotubes per arm. I guess we shouldn’t ignore taper. Make that 1% thicker every kilometer for 300 km or 600,000 kg per arm. The taper will tail off as we get closer to the center: at the halfway point the taper only needs to be .5% per km because the force is down to 1.5g, so make it 300,000 kg.
Perhaps we don’t want a separate cargo version of these spinning cables—just the people one. Same weight of the cable but a smaller cross section because it’s only 3g. We probably want to keep that thing spinning and let the cargo ride on down. That’s also less centripetal force if you are not staying put at the end, but sliding outward.
What should we use as ballast shooting out the other end? We should have plenty of oxygen to use if we can crack rocks. It also won’t clobber someone if it runs into them: a nice toast in the sun and it should disperse pretty good.
How about gravity? At 300,000 kilograms we are talking a pretty good droop at one-sixth g. I guess we want to build it spinning. We have 3g pulling out at horizontal. Am I right that we are only 3 degrees off horizontal? Arcsin of 1/18? Since 3,000 km is nearly twice the radius of the Moon, the catapult ends will extend far into space.
Planning to go slower than 10 km/sec? No problem, just get off before the end of the cable. We can also increase our throw weight if we don’t head all the way to the end. A slow boat to Earth takes about 2.4 km/sec. Mars? 3.8 km/sec. Alpha Centauri? Add 10 km/sec to Earth’s orbital velocity of 30 km/sec and rocket 2 km/sec more to hit solar escape velocity. (Personally, I would rather go faster. At 100 km/sec two counter-rotating supertethers can lob cans filled with deuterium and helium-3 at each other and they would fuse without any A-bomb if the 200 km/sec number in Centauri Dreams is to be believed. I think the tethers fly apart though—check my calculations.)
|It’s a cost race: the cost per kilometer of maglev vs. the cost per kilogram of carbon nanotubes will likely determine which gets built when the time comes.|
If carbon nanotubes are too expensive, how about that maglev? My vote would be to put it around the equator and have people ride on the underside of an elevated track. At first, down would be toward the Moon. Later, as things spun up, down would be toward the stars. Our radius is about 1,700 km. Three g’s of outward force would get us a little better than 10 km/sec because the one-sixth g lunar gravity would be counteracting it. It’s not quite as high tech and hip as a CNT spinner, but it could double as a solar train track, a lunar tram system, a power grid, and more. We would need about 12,000 kilometers of track.
We would be trading material science development for propulsion or lunar industry development since a train track would be more mass than a cable, but much of it would be made of in situ materials. If lunar industry gets to terrestrial levels so it only costs $40 million per kilometer (skills and imports may be dear, but real estate is likely to be cheap for a while), that’s an investment of $500 billion to get our marginal cost down $1/kg to 10 km/sec (36,000 km/hr or 3 times around the Moon per hour)—more than twice the speed we need to get to Mars. The train track also does not have the huge investment in spinning up the cable, and there is no huge kinetic whirly-gig hurtling around the Moon like a propeller hat.
It’s a cost race: the cost per kilometer of maglev vs. the cost per kilogram of carbon nanotubes will likely determine which gets built when the time comes. If we can get the delivered, installed cost of nanotubes down to about $800,000 per kilogram, the cable stays ahead even if Moon costs drop to Earth costs. That is, at least until we want our throw weight to be more than what the tensile strength of the CNT can handle. If we want to send a full-size train to the stars, we should probably stick to the train track.