LMF Paving Robot Subsystem

The Platform of the Lunar Manufacturing Facility (LMF) described in section 5.3.4 serves as the physical foundation for both the original deployed Seed and the growing and mature LMF manufacturing complexes. According to Nichols (1976), "pavement is a surfacing for traveled areas, which is intended to provide a long-lasting, smooth, clean, supporting surface; to spread loads sufficiently so that base material can support them; and to protect the base against damage by traffic...." These factors are almost as important on the Moon as in terrestrial applications - a simple graded surface would require frequent maintenance, lack cleanliness, and provide no firm foundation base to anchor SRS factory machines. A small crew of platform-building or paving robots is probably necessary for any fully automated lunar factory.

The best material for construction of the platform ideally should be plentiful, easy to work, and most suitable for the job in terms of structural strength. Native lunar basalt appears to satisfy all three requirements adequately (Rowley and Neudecker, 1980).

Green (1980a, unpublished Summer Study document) has discussed the properties of lunar basalt at length. Raw lunar soil may be fused at about 1550 K, then allowed to cool and solidify into a very, hard, exceptionally strong material. If cooling is virtually immediate - minutes or tens of minutes - the liquid basalt is quickly quenched and becomes a polymeric glassy substance. The material is very strong but also moderately brittle, permitting cracks to propagate rather easily. Using this option, it is necessary to divide the platform into small square-meter-size slabs to help isolate fracture failures and to permit relatively easy maintenance and repair. If the liquid basalt is permitted to cool more slowly - allowing perhaps several hours for the melt to pass from full liquidity at 1570 K to hard solid below about 1370 K - the material anneals into a crystalline form. This method of platform construction takes much longer and requires more energy, but would produce a far less brittle foundation Such a basalt crystal platform could be prepared as one continuous surface, whereas the glassy basalt platform must be made in slab-sized sections.

Green has also pointed out that Moon soil has characteristics necessary to make an excellent basalt casting due to the uncontaminated, unweathered nature of the lunar material and an extraordinarily low viscosity which is necessary for superior basalt castings. Dunning (1980, unpublished Summer Study document) considered the mechanical properties of cast basalt and found them comparable to those of cast iron and many fine steels, and superior to aluminum, brass, bronze, and copper both in compression and shear strengths. Compression strength is important in many construction applications, and shear strength is a necessary requirement for all foundation materials (U.S. Department of the Interior, 1952). A list of the properties of cast basalt is collected and modified from Anderson (1977), Baumeister and Marks (1967), and several other sources in table 5.9.

**Table 5.9.- Properties Of Cast Basalt**

Physical properties | Average numerical value, MKS units |
---|---|

Density of magma @ 1473 K | 2600-2700 kg/m^{3} |

Density of solid | 2900-2960 kg/m^{3} |

Hygroscopicity | 0.1% |

Tensile strength | 3.5X10^{7} N/m^{2} |

Compressive strength | 5.4X10^{8} N/m^{2} |

Bending strength | 4.5X10^{7} N/m^{2} |

Modulus of elasticity (Young's modulus) | 1.1X10^{11} N/m^{2} |

Moh's hardness | 8.5 |

Grinding hardness | 2.2X10^{5} m^{2}/m^{3} |

Specific heat | 840 J/kg K |

Melting point | 1400-1600 K |

Heat of fusion | 4.2X10^{5} J/kg(+/-30%) |

Thermal conductivity | 0.8 W/m K |

Linear thermal expansion coefficient | |

... 273-373 K | 7.7X10^{-6} m/m K |

... 273-473 K | 8.6X10^{-6} m/m K |

Thermal shock resistance | 150 K |

Surface resistivity | 1.0X10^{10} ohm-m |

Internal resistivity | 1.0X10^{9} ohm-m |

Basalt magma viscosity | 10^{2}-10^{5} N-sec/m^{2} |

Magma surface tension | 0.27-0.35 N/m |

Velocity of sound, in melt @ 1500 K | 2300 m/sec (compression wave) |

Velocity of sound, solid @ 1000 K | 5700 m/sec (compression wave) |

Resistivity of melt @ 1500 K | 1.0X10^{-4} ohm-m |

Thermal conductivity, | |

... melt @ 1500 K | 0.4-1.3 W/m K |

... solid @ STP | 1.7-2.5 W/m K |

Magnetic susceptibility | 0.1-4.0X10^{-8} V/kg |

Crystal growth rate | 0.02-6X10^{-9} m/sec |

Shear strength | ~10^{8} N/m^{2} |

Having chosen the foundation material, the team next considered the physical configuration. According to Nichols, concrete pavements for highways are generally about 15-25-cm thick, 30 cm and higher for airport runways. Adjusting for the 0.17-g lunar gravity and the attendant reduced forces to be sustained, the equivalent load bearing strength on the Moon would require a thickness of perhaps 2.6-4.3 cm for highways. Both highways and encounter heavier use than the LMF platform is expected to receive in normal use, so a choice near the lower end of this range appears justified especially since basalt appears to be stronger than concrete in compression and shear (Baumeister and Marks, 1967; Zwikker, 1954). Consequently, a thickness of 3 cm (Green, 1980b, private communication) was tentatively selected. The square-meter size of individual slabs represents a compromise between limiting possible structural damage caused by fracture propagation and the minimum reasonable size from a practical construction standpoint.

Individual slabs comprising the platform should be formed with a 5-cm margin around the edge (slab separation 0.1 m). Rather than a second sintering pass by the paving robots, slabs are placed close enough so that overheating beyond the nominal square-meter target area for a brief period during each production cycle is sufficient to sinter neighboring blocks. (Some backfilling may be required as about 1-cm horizontal shrinkage is anticipated upon cooling.) A simple diagram of the slab pattern is shown in figure 5.34. Calculations suggest that the baseline design for paving robots should permit each device to prepare about six slabs per day in continuous operation.

**Figure 5.34. - Slab pattern of LMF cast basalt platform.**

To obtain a baseline design for LMF paving robots a rough estimate of the power required to fuse the basalt slabs required (in a reasonable amount of time) must be made. For this crude model, basalt platform slabs were taken as square plates with horizontal dimension x and vertical dimension y, with a sintering margin of width s (2s between slabs). A platform of radius R must be constructed within a time r, so a total of πR^{2}/(x + s)^{2} slabs must be produced in 7 sec, a rate of t^{-1} = πR^{2}/r(x + s)^{2} slab/sec.

The total input power to each square meter of lunar regolith for slab production is given by:

P = P_{h} + P_{m} + P_{r} + P_{c}

where P is total power required, P_{h} is the power needed to heat the basalt material to its melting point, P_{m} is the power necessary to melt the slab at the melting point, P_{r} is the rate at which energy is lost due to radiation from the top surface of the slab, and P_{c} is the rate of energy loss by conduction into the lunar subsurface (modified from Davies and Simpson, 1979). Radiation losses through the thin slab side walls are ignored.

To a first approximation it is sufficient to simply calculate the total energy which must be supplied and divide this by the length of time spent on each slab, hence:

P_{h} = H_{s}(T_{m} - T_{L})x^{2}yp/t

P_{m} = H_{f}x^{2}yp/t

where H_{s} and H_{f} are the specific heat and heat of fusion of lunar regolith,respectively, T_{m} is the melting point of lunar basalt, T_{L} is the mean daylight temperature of the lunar surface under direct sunlight at the LMF site, and p is the mean density of lunar basalt.

Assuming that heating time is long compared to melting time so that the latter may be neglected, the mean radiative power loss through the exposed face of the slab is given by:

P_{r}~(E_{L}ax^{2}&integral;_{0}^{t}T^{4}dt')/t

where E_{L} is the emissivity of lunar regolith, a is the Stephan-Boltzmann constant, and T is temperature at elapsed time t'. If heat is applied such that temperature rises at a linear rate, then:

P_{r}~(1/5)E_{L}ax^{2}(T_{m}-T_{L})^{4}

P_{c}~(1/2)(T_{m}+T_{L})Cx^{2}/d

where C is thermal conductivity of lunar soil and d is the depth at which regolith temperature returns approximately to T_{L}.

Taking the parameters listed in table 5.10 as typical, then for a team of five paving robots each capable of processing two slabs at once:

t = 10r(x + s)^{2}/πR^{2} = 30,600 sec

and

P = 20,530 W

**Table 5.10. Typical Values For LMF Paving Robot Parameters**

R = 60 m | T_{m} = 1573 K |

r = 1 yr = 3.14X10^{7} sec |
T_{L} = 503 K |

x = 1 m | p = 2700 kg/m^{3} (for melt) |

s = 0.05 m | H_{f}=4X10^{5} J/kg |

H_{s}= 840 J/kg |
a = 5.67X10^{-8} W/m^{2}-K^{4} |

E_{L} = 0.80 (typical for silica brick and fire brick) |
C = 1 W/m K |

y = 0.03 m | d ~ 0.2 m |

For the given platform layout there are many possible different modes of operation for paving robots. For instance, each robot might scoop out a hole of the appropriate dimensions, "ingest" the soil and melt it in an internal furnace, then drain the basalt magma back into the hole, neatly filling the depression. Alternative heating techniques may be readily imagined - resistance heating, controlled oxyhydrogen combustion torch with hydrogen recovery, are furnaces (molten basalt is surprisingly electrically conductive), or induction/dielectric heating using vertical-parallel plates, finger electrodes or "stray field heating" (Cable, 1954; Curtis, 1950; Davies and Simpson, 1979). However. from a pragmatic standpoint, direct solar energy is preferred both for practical convenience and to reduce total external demand on the main LMF power grid.

The solar option for paving robots also has many degrees of design freedom, but for illustrative purposes a comparatively simple model was selected. The basic paving power module consists of a large, spherical polished aluminum mirror, constructed with easily manufactured small planar segments and affixed to a single-axis equatorial-drive turntable with a 90° sweep. This large dish is mounted on the north side of paving robots working in the lunar northern hemisphere. The robots travel east-west to maintain near-constant directional orientation at all times (except when beginning or completing a row of slabs). A planar rectangular mirror is mounted low in front of the dish, leaning forward at about 45° to direct the focus of the solar rays downward onto the carefully graded lunar surface. This second mirror may require three degrees of freedom for tracking and to permit it to project a proper square beam. Assuming accurate dish and plate mirror servo gearing, mirror positions are at all times accurately known. If the position of the robot vehicle is precisely fixed by the transponder network (see app. 5B), and an updated monthly lunar solar ephemeris is provided each robot by the seed central computer when work begins each lunar dawn, then the entire mirror pointing task can be fully automated and sun-tracking sensor apparatus eliminated. The basic optical geometry is shown in figure 5.35.

**Figure 5.35. - LMF paving robot optical geometry.**

Main dish size is given by:

D = 2(P/πk^{2}aI cos q)^{1/2}

where D is mirror diameter, k is the reflectivity of either of the two polished mirror surfaces (which may range up to 0.86 for aluminized glass, Weast, 1969), a is the coefficient of absorption of solar radiation for lunar basalt (taken as 0.93 for lunar albedo of 7%), I is solar insolation (1400 W/m^{2}), and q is the angle between the mirror pointing axis and the Sun. In a worst case of q = 20° error, D = 5.4 m.

The planar mirror is roughly rectangular, long end pointing downward, of approximate dimensions 2m X 4m. The heat absorbed by this mirror is at most P(1 - k)/8 + I or 1710 W/m^{2}, corresponding to a blackbody radiation temperature of 417 K which seems manageable. Mirrors should require resurfacing only rarely, since oxidation and meteorite pitting are not expected to be major problems.

The tentative design for the LMF paving robot is shown in figure 5.36. Each machine has a pair of dish and rectangular mirrors. Two small navigational receivers are at either end of the flatbed, permitting the onboard computer to calculate its rotational orientation with respect to the transponder network as well as its position, and a two-axis level sensor measures tipping angle. Simple retractable IR sensors extend down near the slab working area to monitor energy flux and temperature, and a steerable low-resolution camera with two degrees of freedom (vertical and horizontal rotation) is installed between the two main dish mirrors to check slab placement as construction proceeds. Tires are made of soft woven basalt fibers (see sec. 4.2.2), and the vehicle is driven by four low-power electric motors fore and aft geared to steerable front and rear wheel pairs. Energy requirements for mobility and onboard computing are expected to be modest, so a few square meters of exterior solar cell paneling augmented by a rechargeable fuel cell should suffice.

**Figure 5.36. - Tentative LMF paving robot design.**

A 5.4 m spherical dish made of aluminum 1-cm thick will have , mass of about 620 kg, or 1240 kg for a pair. Similarly , the total for both planar mirrors is 440 kg. Assuming 2X10^{-2} kg computer/kg serviced (Freitas, 1980), each robot computer is about 50 kg. Camera, sensors, and navigational equipment add another estimated 50 kg. Solar panels and fuel cells may total 100 kg. The aluminum vehicle frame should be able to support its own weight (1700 kg) on Earth, so in low lunar gravity only 280 kg are required to obtain equivalent support. Each tire and drive assembly is about 40 kg, a total of 240 kg for all six wheels. Hence, the mass of each paving robot is about 2400 kg. The fleet of five included with the original seed totals 12,000 kg.

Paving robot computers must serve a number of functions, including autopilot, dish mirror guidance and control, planar mirror guidance and control, executive operating program execution, operational "timesheet" memory for the run in progress, traffic pattern coordination with other robots, neighbor machine avoidance, self-diagnostic routines for simple malfunctions, pattern recognition for slab working area imaging, sensor control and data processing, energy system maintenance, lunar solar ephemeris memory and calculation of solar pointing angles, navigation and drive wheel control, and various routines for recognition and verification of task completion. The computation capacity needed to handle these functions probably is in the range 10^{6}-10^{7} bits (about 64 K-512 K bytes). The information necessary to completely describe the machine for purposes of replication is probably about an order of magnitude greater, roughly 10^{7}-10^{8} bits.

Anderson, Alfred T., Jr.: Basalt. in Encyclopedia of Science and Technology, vol. 2, McGraw-Hill, New York, 1977, pp.110-110D.

Baumeister, Theodore; and Marks, Lionel S., eds.: Standard Handbook for Mechanical Engineering. 7th Ed. McGraw-Hill, New York, 1967.

Cable, J. Wesley: Induction and Dielectric Heating. Reinhold Publishing Corp., New York, 1954.

Curtis, Frank W.: High-Frequency Induction Heating. 2nd ed., McGraw-Hill Book Company, Inc., New York, 1950.

Davies, John; and Simpson, Peter: Induction Heating Handbook. McCraw-Hill Book Company, Ltd., London, 1979.

Freitas, Robert A., Jr.: A Self-Reproducing Interstellar Probe. J. of the British Interplanetary Sec., vol. 33, July 1980, pp.251-264.

Nichols, Herbert L., Jr.: Moving the Earth: The Workbook of Excavation. 3rd ed. North Castle Books, Greenwich, Conn., 1976.

Rowley, J. C.; and Neudecker, J.W.: Melted In-Place Lunar Soil for Construction of Primary Lunar Surface Structures. In Extraterrestrial Materials Processing and Construction, David R. Criswell, ed. Final Report, NSR 09-051-001 Mod. No. 24, Lunar and Planetary Institute, Houston, Texas, 31 January 1980, pp. 215-219. (Also published as NASA CR-158870.)

U.S. Department of the Interior: Earth Manual: A Manual on the Use of Earth Materials for Foundation and Construction Purposes. Reprinted by Bureau of Reclamation, with revisions, February 1952.

Weast, Robert C.: Handbook of Chemistry and Physics. 49th ed. CRC Company, Cleveland, Ohio, 1968.

Zwikker, C.: Physical Properties of Solid Materials. Interscience, New York, 1954.