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Economic exploitation of lunar resources may be more efficient with a non-rocket approach to launch from the lunar surface. The launch system cost will depend on its design, and on the number of launches from Earth to deliver the system to the Moon. Both of these will depend on the launcher system mass. Properties of an electromagnetic resource launcher are derived from two mature terrestrial electromagnetic launchers. A mass model is derived and used to estimate launch costs for a developmental launch vehicle. A rough manufacturing cost for the system is suggested.

Recent news announcements of corporations formed for the purpose of mining off-Earth resources have received international attention. Both asteroids and the Moon have been cited as locations with valuable, accessible commodities, such as water ice, and raw materials for construction. Compared to asteroids, the Moon has a significant gravity well, thus requiring more energy to reach an off-lunar destination such as a fuel depot. The lack of a lunar atmosphere means that there is no drag heating during ascent.

The idea of using a fixed launcher rather than rocketry to move masses in the solar system has been discussed at least since the work of O’Neill [

The LRL model in this paper is based on the following system concept, which is illustrated schematically in

The LRL location is near one or the other lunar pole, where ice is being mined.

The LRL uses an electromagnetic launch approach chosen from either of two terrestrial electromagnetic systems to be described.

Electric power is provided by photovoltaic panels.

The ice or water is placed into canisters, which may be manufactured on Earth, or manufactured locally from

The canisters are launched to a depot or processing station at L1. The required launch velocity is approximately 2.34 km/s.

Schematic block diagram of lunar resource launcher with segmented design.

Other key factors affecting overall system performance:

The ultimate use of the product is for refueling spacecraft in geosynchronous orbit (GSO). Hence L1 was selected over L2 or low lunar orbit. A vehicle must take the product from the L1 processing plant to GSO.

The canister velocity is assumed to be low at apolune, which is to be in the vicinity of L1.

The launch system will inevitably deliver some variations in launch velocity, although its design should aim to minimize these. Therefore some method must be included to correct their velocity and position L1 for acceptance at the processing station.

It should be noted that there are alternatives to electromagnetic launch, for example, a gas gun [

The cost of the LRL will have two principal contributions: the manufacturing cost and the cost of delivery to the Moon. Both can be assumed to be functions of the system mass. The total mass _{a} + M_{s} + M_{e} + M_{c }+ M_{m }+ M_{p }

_{a}

_{s}

_{e}

_{c}

_{m}

_{p}

In

The goal of this paper is to develop reasonable estimates for each of these components, eliminating variables except for the production rate of the resource. A driving requirement is that the launch packages (of mass _{L}_{c}_{L} / t_{c} > PR

This paper will use two exemplar launch systems that have established the required accelerator mass per unit length to deliver forces in the range of 10^{6} N. The two exemplar systems are:

The Electromagnetic Aircraft Launch System (EMALS) [

The Electromagnetic Mortar (EMM) [

The EMALS system is capable of imparting a maximum energy

EMALS derived quantities:

Force:

Acceleration: assuming a 45,000 kg aircraft, ^{2} = 3.03 g

Mass launched to L1 = 2^{2}^{2} = 44.6 kg

Track mass per unit length: with total track mass of 200T,

Both a coilgun and a railgun version of the EMM were developed. Both versions were required to accelerate a 120 mm mortar projectile, mass 18 kg, to 430 m/s. The railgun barrel was 2.4 m in length and weighed 950 kg. [The coilgun version was probably somewhat heavier, because it required more copper. A solid copper cylinder 2.4 m long and 30 cm in diameter would have a mass of 1,516 kg.]

EMM derived quantities:

Projectile kinetic energy: E = ½ mv^{2} = 0.5 × 1.8E1 × (4.3E2)^{2} = 1.66 MJ

Force: F = E / s = 1.66E6 / 2.4 = 6.93E5 N

Acceleration: a = v^{2} / 2s = (4.3E2)^{2} / (2 × 2.4) = 3.85E4 m/s^{2} = 3930 g

Mass to L1 = 2E / v^{2} = 2 × 1.66E6 / (2.34E3)^{2} = 0.61 kg

Mass per unit length: λ = M / L = 950 / 2.4 = 396 kg/m

EMALS and EMM have very different properties. EMALS is for accelerating very large masses to relatively low velocities with relatively low acceleration. EMM is for accelerating smaller masses to somewhat higher velocities; to keep the barrel length short, the acceleration must be much higher. Interestingly the force applied by each system is about the same, around one million Newtons. In one case,

The EMALS mass per unit length is almost ten times that of EMM. This is probably due to the necessity to restrain large side loads. If the aircraft carrier rolls during launch, or if the aircraft path deviates for any other reason, the large lateral loads must be absorbed by the launcher and transferred to the ship structure, while keeping the aircraft on a straight path. This necessitates a lot of steel in the EMALS launcher construction. The lateral loads in the LRL are anticipated to be much smaller. The EMM lateral loads are primarily caused by the very strong repulsive forces within the rails or electromagnets. The EMM designs included composite bands and members to contain these repulsive forces.

LRL must provide an exit velocity of 2.34 km/s, nearly the lunar escape velocity. This is independent of both the mass to be launched, and the acceleration. Requirements influencing the launched mass are:

Lower masses mean less total energy is required per shot.

Higher launch masses mean higher stresses on the LRL structure, and hence more support mass per unit length.

For a given resource recovery rate, the LRL must be able to shoot often enough to keep up with the mining. The longer the cycle time of the launcher, the larger the minimum payload mass must be.

At L1, something must be able to grapple a canister, deliver it to the processing station, and recycle to catch the next canister before it arrives. Again, the longer this cycle, the larger the minimum payload mass must be.

Requirements influencing the acceleration are:

Lower acceleration means smaller forces on the LRL components and structure.

Lower accelerations require greater track length to provide the required exit velocity, as shown in

LRL track lengths for various levels of acceleration.

Acceleration. m/s^{2} |
Track length = v^{2}/2a |
---|---|

196 = 20 g | 13.9 km |

1960 = 200 g | 1.39 km |

9800 = 1000 g | 278 m |

19,600 = 2000 g | 139 m |

Lower forces mean lower mass per unit length, but longer length, for the same payload mass.

If a shuttle is used as does EMALS, a longer track length will result in a longer cycle time, influencing the minimum payload mass (see above). If no shuttle is required, as for EMM, this is not a consideration. Use of a shuttle also increases the total energy required per launch, as some of the energy is imparted to the shuttle and some to the launch package.

The harvested resource, water or ice, must be contained for the launch. Higher acceleration means higher stresses within the canister containing the resource. Therefore the canister mass will increase, and become a larger fraction of the total mass launched.

Schematic of a launch canister with relevant variables.

^{3}). We assign a conservative tensile stress limit ^{2}. The total aftward force on the shell due to the acceleration

Launch canister thicknesses and masses for various levels of acceleration.

Acceleration, g | Min shell thickness, cm | Cylinder mass, kg |
---|---|---|

20 | 0.002 | .0027 |

200 | 0.02 | .027 |

1000 | 0.1 | .13 |

2000 | 0.2 | .27 |

Thus even at 2000 g acceleration, the canister shell, if made of high quality aluminum alloy, adds little to the launch package mass. One might consider making canisters of

The canister will also contain a conducting component that enables the application of electromagnetic force. In the EMM coil-based design, the component was an aluminum ring added to the mortar shell. The eddy current induced in the ring by pulsing the coils generates an opposing magnetic field which results in the launch force. In the EMM rail-gun design, the mortar shell was augmented by a conducting bar that completed the circuit between the launch rails. In the EMM program, these components were fractions of 1 kg and would be no more massive for the LRL. The quality requirements on the conducting components will force their manufacture on Earth.

The launch trajectory is highly elliptical. Launch occurs at the lunar surface, the lunar radius being about 1738 km. L1 is located about 62,700 km from the center of the Moon.

With such highly elliptical trajectories, small errors in launch velocity can result in large errors in the position at apolune. Consider a cross-track velocity variation of 1 m/s, caused for example by vibration of the launching structure. In the several hours’ rise to apolune, this would result in apolune position variations of several kilometers. Along-track velocity errors would result in similar position variations, because apolune height for highly elliptical orbits is very sensitive to launch velocity.

Such errors could be corrected by a placing a retrieval vehicle at L1, which would match position and velocity with each canister, grapple them, and slow down for docking with the processing station at L1. Two considerations argue against this approach. The retrieval vehicle is likely to be much more massive than the canisters; therefore it will expend a considerably greater amount of propellant for its maneuvers. Also, with large position errors, it will have long transit times, and therefore greatly increase the cycle time for the system.

Therefore it will be assumed that each launch canister has a small propulsion system, including a radio receiver to enable control by signals sent from the L1 processing station. Correction of 5 m/sec total velocity error (much larger than, e.g. the design velocity variation of EMM which was 1.5 m/s) with a specific impulse of 200 s would add a propellant mass fraction of

This would be 0.025 kg for a 10 kg package. Using solid state digital thruster technology, digital radio and patch antennas, the overall control system should add less than 1 kg to package weight. Such a controllable thrust package should ensure accurate delivery to a depot at L1 and minimize the impact of launch velocity errors.

It is likely that the feasible length of the launcher will be constrained, not merely by performance considerations, but by irregularities in the lunar topography. Therefore a relatively short design, 278 m, will be used. This fixes the required acceleration, ^{2}/2s^{2} or 1000 g.

The package canister will be 5% of the total launch weight. However, the package mass will be increased by 1 kg for the propulsion package. This should represent a small fraction of the total launch weight for efficiency. Therefore a 10 kg launch mass is specified, which fixes the launch force at 98,000N, well within the capability of EMM as tested.

A closed-bore, fixed payload EMM-like design will be assumed. This is to limit the energy required per cycle, and the total force. With a shuttle, the energy is provided both to the launch package and the shuttle. With EMM, all energy goes into the launch package. This also avoids the need for a shuttle energy dissipation mechanism, and removes the impact on cycle time of shuttle retrieval. The disadvantage is the loss of adaptability; an open design, EMALS-like launcher would be able to launch packages of widely varying geometry, whereas the closed-bore design is restricted to canisters fitting the launcher bore.

Scaling the EMM down linearly to the lower launch force of 98,000N, the mass per unit length would be 56 kg/m. The resulting total mass for the 278 m accelerator is 15,600 kg.

The function of the LRL structure is to transfer launch loads to the lunar surface. The difference in mass per unit length of EMALS and EMM shows that structural mass can be a significant contributor to the total launch system mass. The breech and yoke assembly of EMM barrel weight were probably several hundred kg. These transferred the EMM launch force to the baseplate.

Schematic of accelerator subsection with support structure and anchors.

It is assumed that a support structure effective density of 5 kg/m^{3} will withstand 10,000N. This is much lighter than terrestrial structures, but a lunar structure does not need to withstand wind, ice or seismic forces. The structure to withstand 98,000N would therefore have a density of 50 kg/m^{3}.The support structure volume is assumed to be 0.01 times the cube of the subsection length. Then the support structure mass per subsection is 50 × 0.01 × L_{s}^{3}, and the total structure mass (including anchors) is (278 / L_{s}) × (200 + 0.5 × L_{s}^{3}). Minimizing this function with respect to L_{s} gives a subsection length of 5.85m. 48 subsections are needed, and the total support structure mass with anchors is 14,300 kg.

Some of the structural mass could be obtained

The ability to use _{s}_{IS})_{IS}

Photovoltaic panels for space applications of very high performance are being produced. The panels being installed on the JUNO spacecraft have efficiency of over 40%. Panels with energy density of 200 watts per kilogram are available. There are some cost implications for using the highest performance panels available, but these will be insignificant compared to overall LRL cost.

Assume a photovoltaic power source for the system, with area _{p}^{2}. Define the energy efficiency of the launch system as _{L}_{e}_{L}_{p}

The required cycle time _{c}_{c}_{c}

At 42% efficiency, the required solar panel area is 1.8 square meters times the number of launches per day. At 2.87 kg per square meter, this contributes a mass to the system of only 5.2 kg times the number of launches per day.

High density energy storage is available today using lithium-ion batteries. Storage densities of 100 watt-hours per kilogram, or 0.36 MJ/kg, are standard. However, lithium ion batteries have limited discharge rates. A rapid-discharge energy storage solution, such as supercapacitors, must be included in the LRL design. Today’s supercapacitor energy storage densities are no more than 5 W·hr/kg (0.018 MJ/kg).

A 10 kg launch mass (which delivers 8.6 kg of resource) requires a kinetic energy at launcher exit of ½ × 10 × (2340)^{2} = 27.4 MJ. Assuming 30% launcher efficiency, the required mass of supercapacitors for rapid discharge energy storage is 1520 kg.

Two essential functions will require heavy machinery: hoisting and anchoring,

Terrestrial cranes tend to weigh about two thirds of their lifting capacity. For example, the Liebherr LTM 1030-2.1 crane weighs 24T and can lift 35T. Roughly the same proportion should pertain on the Moon. A mass of 4T is assigned for the LRL assembly crane. This should permit lifting the 6m accelerator sections, with masses of 330 kg, without difficulty.

Compacted regolith must be removed by a process such as those being investigated by L. Bernhold. The equipment consists of pipes, blowers, separators and chambers. These must be mounted on a vehicle. A mass of 3T is assigned for the anchoring machinery.

Structural members might be fabricated by processes such as electric resistance heating, selective laser sintering, and 3D printing. A mass of 1T is assigned for structural member fabrication equipment.

With the above assumptions, the system mass, equation (1), becomes

The mass delivered to the Moon is
_{IS}

Clearly, the mass of the LRL is not very sensitive to the production rate. At 240 kg per day production rate (1 launch per hour), the energy harvesting mass of solar panels is only 130 kg.

A scenario for delivery of the LRL components to the lunar surface will now be constructed, assuming the use of SpaceX Corporation’s Falcon Heavy vehicle now in development [

The Apollo stack of the Saturn V rocket [

With a Falcon Heavy-based transportation system, the mass of equation (4), delivered in 5050 kg payloads, requires nine launches with all material delivered from Earth (_{IS}_{IS}

This delivery scenario would require two development projects: (1) upper stages for the Falcon Heavy, with performance equivalent to the S-II and S-IVB upper stages of the Saturn V; and (2) a LEM-like lander to deliver the LRL to the lunar surface. An underlying assumption of this paper is that assembly is performed by human construction workers on the Moon. These workers would require two-way transportation, habitats, consumables replenishment,

Mass delivered to Moon by Falcon Heavy derived from Saturn V Apollo stack.

Parameter | Apollo Saturn V | Falcon Heavy + 1-way lunar |
---|---|---|

Mass to LEO | 127,000 kg | 53,000 kg |

Mass to trans-lunar injection | 45,400 kg | 19,900 kg |

Lunar Excursion Module mass | 14,454 kg | |

Ascent stage fraction of LEM | 30.9% | 30.9% |

P/L for 1-way lunar descent | 6310 kg | |

LRL mass delivered (80%) | 5050 kg |

Anecdotally, the budget for the DARPA EMM program from 2004 to 2008 was about US$ 13M, which resulted in the development of both the coil and rail versions, as well as some advanced capacitor work. Each launcher had a 2.4 m barrel. Taking $ 5M as the cost of one 2.4 m coil segment with energy storage, and scaling up to the 278 m length of the LRL, the accelerator cost would be $ 580M. Other components of the system would add fractionally to this cost.

However, this could be an overestimate. The Australian Synchrotron is a machine similar in size and complexity to the LRL, and like the LRL its design includes multiple high strength magnets. Constructed contemporaneously with the EMM program, it cost AU$ 206.3M to build [

As with any complex electromechanical system, maintenance will be required. Presumably this would be done by humans on the lunar surface. The cost of transporting these workers, and providing life support, will be considerable. Launches for their support could also supply the canisters (constructed on Earth), as well as any components requiring replacement. An example of finite-life components would be the rails if a rail-gun approach is used. Terrestrial experience is that rails wear quickly due to arcing; the absence of a lunar atmosphere might mitigate that problem. A coil-gun approach is likely to experience less degradation due to wear.

A lunar resource launcher concept, based on tested electromagnetic launch systems developed for terrestrial applications, has been described. The resultant mass model has been used to estimate the number of launches required to deliver the system from Earth to the Moon. A rough estimate of the manufacturing cost was made. No estimates were made for research and development costs, development of delivery vehicles, or operation and sustainment costs.

Properties estimated for electromagnetic lunar resource launcher.

Property | Value (no |
Value (maximal use of |
---|---|---|

Resource rate supported | 240 kg/da | 240 kg/da |

System mass delivered to Moon | 40,550 kg | 26,250 kg |

Accelerator cost | US$ 580M | US$ 580M |

No. Falcon Heavy launches | 9 | 6 |

Launch cost | US$ 1,152M | US$ 768M |

(Accelerator + launch) cost sum | US$ 1.732B | US$ 1.348B |

No assessment has been made of the merit of constructing such a system. That would depend completely on the market for the resource.

The author acknowledges the support of the Australian Centre for Space Engineering Research during the preparation of this paper.

The author declares no conflict of interest.