Mass Drivers

There have been many suggestions for mass drivers on Luna for the exportation of raw materials and other purposes, notably by Gerard K. O'Neill (God rest his soul) and the Space Studies Institute. Plans for early designs can keep the power requirement low by using low payload sizes. Higher acceleration rates allow shorter tracks. High firing rates keep the investment actively earning its return.

Mass driver design

E=1/2*m*v2 We can use 2000 m/s as a good orbital speed(v), although not quite enough to leave the Moon's orbit.

For each kg launched, E = 2000*2000/2= 2 MJ (0,55 kWh) plus the energy losses. Let's put these at 20%, for a launch requirement of 2,4 MJ/kg (0,66 kWh/kg)

The track length depends on the acceleration used, that in turn depends on the type of payload and the power than can be delivered. With an acceleration of 2g, or 20 km/s the time required is 2000/20 = 100 seconds The power would then be 2,4 MJ/100s = 24 KW/kg.

The track length is then: length=1/2*a*t^2 = 20*100*100/2 = 100 000m = 100 km.

Comparison with rocket launching

Rocket carry their own energy in the form of fuel or propellant, and therefore extra mass, and follow the rocket equation. V=ve*ln(Mo/Mf) For the same velocity of 2000 m/s, a rocket using, for example, aluminum-oxygen engines with an exhaust velocity (ve) of 2800 m/s (reference) will require 1 kg of propellant per kg launched, or a mass ratio (Mo/Mf) of two. The kinetic energy of the propellant is 1/2*m*ve^2= 2800*2800/2 = 3,92 MJ/kg compared to 2,4 MJ/kg for a mass driver.

However, industrial processes are far from 100% energy efficient. The embodied energy of aluminum is about 210 MJ/kg. the chemical reaction of the aluminum oxygen rocket Al2+O3 has a ratio of 52(Al) to 48(O) so 1 kg of propellant includes 520 grams of aluminum. The energy required to produce this aluminum is 110 MJ, or about 28 times the exhaust energy of the propellant. Therefore an oxygen-aluminum rocket will require 1100 MJ per kg launched and a mass driver 2,4 MJ/kg launched, so 45 times more energy required for a rocket.

Limitations

Mass drivers cannot send an object into orbit on their own. Any item launched at lower than escape velocity will return to the launch point following orbital mechanics and hit the surface. So they require either mass catchers in orbit, or payloads equipped with engines to circularize their orbits. However, they can send objets at over escape velocity.
Tracks need to be very well built in order to avoid unwanted accelerations and oscillations during launch.
Although the energy use is among the lowest possible, the power required is high, since the launch period is short, and most designs require energy storage systems to operate.
Launching on different orbits require different tracks.

Proposals

Linear mass driver

Circular Mass Driver

Consider here a circular mass driver or mass accelerator which would keep power requirements low by spreading the acceleration out over many laps of a circular track. The payload could be about 200 kilograms. If there are passengers or cargo available every 110 minutes for rendezvous with a catcher satelite, it can keep constantly busy. Suitability for passenger service requires a low radial acceleration, 30 meters per second squared (about 3 g's) will do. This in turn requires a large diameter (about 120 miles). The shape of the device is like a very regular volcanic mountain peak with gently sloping sides and a circular crater on top. The accelerator track would run along the vertical wall of the circular crater. When the payload and carrier reach orbital velocity (1680 meters per second), the payload is dropped tangentially outward over the top of the wall. A counter weight may be required on the carrier near the base of the wall to ballance the carrier. Since the diameter of the track is 120 miles, there is about one and two thirds miles bulge of the curvature of Luna interfering with line of sight communication from one side of the track to the other. The plane of the circular track makes a 3.2 degree angle with the surface of Luna. (It's like a slice off of the top of Luna one and two thirds miles thick at the Pole.) Payloads launched tangentialy from the track, however, deviate from that plane by curving downward toward Luna in an orbital path. This makes it more likely than otherwise that a payload would smash into a mountain peak. So the accelerator track should be built up on fill as high as practical and care should be taken in choosing the exact dirrection of launch. The circular accelerator should be centered at the North pole while the catcher satelite would orbit about once per 110 minutes at an inclination of about 86.8 degrees. So it would pass over one or another spot on the circular track with every orbit as Luna rotates under the orbit. It could catch a payload whenever a mountain peak did not interfere. Troublesome peaks could be razed.

The above specifications would require 43 kilowatts average power put constantly into payloads plus power to accelerate the carrier and allow for the losses in magnetic levitation. Unfortunately, the carrier can not constantly accelerate because it must come to a stop to be ready to pick up the next payload. Two tracks, the second with 10 meters less radius and 2 meters more altitude than the first would allow one track to accelerate while the other uses regenerative braking.

As long as we consider developments that must be many years in the future, there is a capability of adding carriers in a train as there is increased available power and need for cargo tonnage. The whole 370 mile circumference of the accelerator could be filled with one train of carriers. The payloads could be connected by rope and the whole train of payloads launched from one point on the circumference into one orbit as 5 minutes and 53 seconds go by.

The First Lunar Mass Driver

Catching one kilogram loads of sintered soils at L2 (a Lagrangian point ) one a second or one every few seconds by having them smash into a grid and having the bits go through to fill up a cone is unacceptable. A continuing rain of dust and grit would be produced at L2 from whence it would fill up the plane of the Earth Luna system and trail a cloud into independent orbit around the sun. ^[1] The dust from thousands of tons of stuff splashed into a catcher would sandblast every satelite in orbit.

What Will Work

Instead a mass driver should launch 10 kilogram loads as fast as can be managed. This should be once a minute or better. The payloads should go into equatorial orbit about Luna. Each payload should be about a 10.2 kilogram spaceship containing a supposed 120 gram pressurized oxygen flash bulb rocket. The payload is spin stabilized and the rocket is fired by a timer at apolune to circularize the orbit. The payloads orbit at a 111 minute orbit at 30 kilometers altitude. The catcher satelite orbits at 127 kilometers altitude once every 120 minutes. A set of nets is attached to computer controlled radar guided arms. These operate from a structure depended by tether from the main body of the catcher satellite and sweep up the entire payload orbit once in twenty-four hours, sending the payloads by conveyor up the tether. For launch to a 30 kilometer orbit launch velocity is about 7.2 meters per second more than circular orbit velocity at the surface which combined is about 1685.7 meters per second.(The launch velocity requirement was worked out as an example in Orbital Dynamics.) The circularizing impulse at 30 kilometers altitude is about 7.1 meters per second. So the work to be done by the flash bulb rocket is rather small. An alternative rocket would use magnesium and/or aluminum powder as fuel and sodium superoxide (NaO₂) as an oxidizer. 4Mg + 8NaO₂ ==> 4MgO + 4Na₂O + 4O₂ The reaction yields heat and excess oxygen with the performance characteristics to be determined by experimentation. The planned reaction mass is hot oxygen.

If the design of any obit circularization rocket results in dust ejected from the rocket nozzle, it would be ejected in the direction opposite orbital motion and the dust would crash into the lunar surface and be of no further concern. The problem will be in choosing the cargo launching techniques that are most economical.

Worth Waiting

Previous schemes called for a mass driver built as prefabricated sections on Earth for shipping raw materials into orbit for processing. This scheme calls for the mass driver to be built from lunar materials by remote controled devices. So there will be the infrastructure for manufacturing many things by the time the mass driver comes on line. The same things that went into building the mass driver will be shipped out as export. We will let a full engineering team calculate which scheme requires more stuff shipped from earth by the time of first exports.

Developments

The United States Navy has developed electromagnetic acceleration for carrier launched aircraft to replace steam catapults in the newest generation of carriers now being built. ^[2]
Magnetically suspended rail cars have reached velocities of xxx