A SELF-REPLICATING, GROWING LUNAR FACTORY

This cycle of repeated construction possibly may be largely eliminated by designing the factory as an automated, multi-product, remotely controlled, reprogrammable Lunar Manufacturing Facility (LMF) capable of constructing duplicates of itself which would themselves be capable of replication. Successive new systems need not be exact copies of the original, but rather could, by remote design and control, be improved, reorganized, or enlarged so as to reflect changing human requirements. The benefits of a replicative growing lunar manufacturing facility include:

1. The process of LMF design will lead to the development of highly sophisticated automated processing and assembly technologies. These could be used on Earth to further enhance human productivity and could lead to the emergence of novel forms of large-scale industrial organization and control.
2. The self-replicating LMF can augment global industrial production without adding to the burden on Earth's limited energy and natural resources.
3. An autonomous, growing LMF could, unaided, construct additional production machinery, thus increasing its own output capacity; by replicating, it enlarges these capabilities at an increasing rate since both new production machinery as well as machines to make new machines can be constructed.
4. The initial LMF may be viewed as the first step in a demonstration- development scenario leading to the indefinite continuation of the process of automated exploration and utilization of non-terrestrial resources. Replicating factories should be able to achieve a very general manufacturing capability including such products as space probes, planetary landers, and transportable "seed" factories for siting on the surfaces of other worlds. A major benefit of replicating systems is that they will permit extensive exploration and utilization of space without straining Earth's resources.

The design and construction of a fully self-replicating factory system will be a tremendously complicated and difficult task. it may also be fairly expensive in the near-term. Before embarking upon such an ambitious undertaking it must first be shown that machine self-replication and growth is a fundamentally feasible goal.

The credibility of any replicating system design depends first and foremost upon whether that design is consistent with reasonably foreseeable automation and materials processing technologies. These technologies need not necessarily be well-established or even state-of-the-art, but should at least be conceivable in the context of a dedicated R&D effort spanning the next two decades. It is interesting to note that computer programs capable of self-replication have been written in many different programming languages,^3,4 and that simple physical machines able to replicate in highly specialized environments have already been designed and constructed.^5,6,7

Another major requirement for concept credibility is a plausible system configuration. Proposed designs for self-replicating systems (SRS) must be sufficiently detailed to permit the generation of Work Breakdown Structures, subsystem operational flowcharts, mass and energy throughput calculations, and at least preliminary closure analyses.

A related requirement is plausible mission scenarios. Research and development costs for the proposed design should be many orders of magnitude less than the Gross National Product. The mission must not require launch and support facilities which cannot or will not be available in the next two or three decades. The mission must entail reasonable flight times, system lifetimes, and growth and production rates. The problems of reliability and repair should be addressed.

The final requirement for concept credibility is positive societal impact. A given SRS design must be economically. politically, and socially feasible, or else it may never be translated into reality even if the technology to do so exists.²

Machine Reproduction Theory

The early history of the theory of self-replicating automata is due largely to John von Neumann, who set for himself the goal of showing what the logical organization of a self-reproducing machine might be.⁸ Although he had in mind a full range of reproducing machine models he intended to explore,⁹ ultimately he produced only a very informal description of the model most amenable to engineering applications in a practical sense -- the "kinematic machine." Such a machine, von Neumann concluded, should possess the following characteristics:

1. Logical Universality -- the ability to function as a general-purpose computing machine able to simulate a universal Turing machine.¹⁰ This was necessary because SRS have to be able to read instructions to carry out complex computations.
2. Construction Capability -- to self-replicate a machine must be capable of manipulating information, energy, and materials of the same sort of which it itself is composed.
3. Constructional Universality -- the ability to manufacture any of the finitely-sized machines which can be formed from specific kinds of parts given a finite number of different kinds of parts but an indefinitely large supply of parts of each kind.
4. Self-Reproduction -- the universal constructor must be constructable from the set of manufacturable parts.

The machine continues following the instructions to make something, without really understanding what it is doing. When it finishes it has produced a physical duplicate of itself. Still, the second machine does not have any instructions so the parent machine copies its own memory tape onto the blank of its offspring. The last instruction on the parent machine's tape is to activate the tape of its progeny.

Von Neumann's logical organization for a kinematic machine is not the only one possible, but is perhaps the simplest way to achieve machine self-replication. In its logic it is very close to the way living organisms reproduce themselves.¹³ But work has continued apace in this field. One example of a modern approach is given by Laing,^14,15 who has investigated machine reproduction schemes involving complete self-inspection. In these models the automata is envisioned as having two separate parts each capable of examining and reconstructing the other, thus achieving replication of the pair.

Current Factory Automation Technology

Automation for replication will require extensive application of state-of-the-art computer science and robotics. At the initial stage of development, and during repair or reconstruction operations, computers can be used in many ways to aid in both design and manufacturing processes (e.g., CAD/CAM, ICAM). Today the most advanced numerical-controlled (N/C) machine tools (especially in the aerospace industry) are connected directly to a high-speed digital computer able to generate and store instructions in electronic memory. Ultimately the capability will exist for a human to carry on a dialog with a computer system in which the user merely defines the functional specifications of the desired product and the computer determines the remaining design details autonomously.

The next logical developmental step is the design of a completely computer-managed integrated parts manufacturing system. Cook¹⁶ describes such a system developed and built by Sunstrand Corporation. One version in operation at the Ingersoll-Rand Company is used primarily for fabricating hoists and winches, while another at the Caterpillar Tractor Company is used for making heavy transmission casing parts.¹⁷ As of 1975 there were about ten similar systems in operation in the U.S., Japan, Germany, and the U.S.S.R.¹⁸

The Ingersoll-Rand system consists of six N/C tools -- two 5-axis milling machines, two 4-axis milling machines, and two 4-axis drills -arranged around a looped transfer system. Machining operations include milling, turning, boring, tapping, and drilling, all under the control of an IBM 360/30 central computer. At any given time about 200 tools are in automatic tool-changing carousels, available for selection by the computer, although about 500 are generally available in the system. The computer can simultaneously direct the fabrication of as many as 16 different kinds of parts of totally different design which are either being machined, waiting in queue to be machined, or are in the transfer loop. The entire system is capable of manufacturing about 500 completely different parts. During each 12-hour shift the system is run by three human operators and one supervisor. It is calculated that to achieve the same output using manual labor would require about 30 machines and 30 operators.

Merchant¹⁹ suggests that a fully automatic factory capable of. producing and assembling machined parts will consist of modular manufacturing subsystems, each controlled by a hierarchy of micro- and mini-computers interfaced with a larger central computer. The modular subsystems must perform seven specific manufacturing functions:

1. Product design by an advanced "expert system" software package or by humans remotely or interactively, using a computer design system that stores data on models, computes optimal designs for different options, displays results for approval, and allows efficient process iteration.
2. Production planning, an optimized plan for the manufacturing processes generated by a computer on the basis of product-design outputs, scheduling, and line-balance algorithms, and varying conditions of ore-feedstock deliveries, available robot resources, product mix and priorities. Planning includes routing, timing, work stations, and operating steps and conditions.
3. Parts forming at work stations, each controlled by a small computer able to load and unload workpieces, make parts and employ adaptive control (in-process operation sensing and corrective feedback), and incorporate diagnostic devices such as tool-wear and tool breakage sensors.
4. Materials handling by different computer-controlled devices such as lifts, warehouse stacking cranes, carts, conveyors, and industrial robots with or without sensors that handle (store, retrieve, find, acquire, transport, load, unload) parts, tools, fixtures and other materials throughout the factory.
5. Assembly of parts and subassemblies at computer- controlled work stations, each of which may include a table, jigs, industrial robots with or without sensors, and other devices.
6. Inspection of parts, subassemblies and assemblies by computer- controlled sensor systems during and at the end of the manufacturing process.
7. Organization of production information, a large overseeing computer system that stores, processes, and interprets all manufacturing data including orders; inventories of materials, tools, parts, and products; manufacturing planning and monitoring; plant maintenance; and other factory activities.²⁰

At a Tokyo conference on robotics in September of last year, Fujitsu FANUC Ltd., a leading international manufacturer of N/C machining equipment, announced its plans to open an historic robot-making factory near Lake Yamanaka in Yamanashi Prefecture in November. In this plant industrial robots controlled by minicomputers will manufacture other industrial robots virtually without human intervention. The plant, which is the first "unmanned" factory in the machinery industry, is expected to produce robots and other electronic equipment worth about $70 million in the first year of operation with only 100 supervisory personnel. In five years the plant is expected to expand, perhaps using some of its own manufactured robots, to a $300 million annual output with a workforce of only 200 people -- less than a tenth of the number required in ordinary machine factories of equivalent output. A spokesman said that FANUC's fully automated system is suitable not only for mass production of a single product line, but also for limited production of divergent products. The methods envisioned for MUM presently are being pursued vigorously by three Japanese government research institutes and twenty private companies, and is being managed by the Agency of Industrial Science and Technology of MITI.²⁴

SRS may be capable of at least five broad classes of machine behavior:

Production -- Generation of useful output from useful input. The unit machine remains unchanged in the process. This is a "primitive" behavior exhibited by all working machines including replicating systems.

Replication -- Complete manufacture of a physical copy of the original unit machine, by the unit machine.

Growth -- Increase in mass of the original unit machine by its own actions, retaining the physical integrity of the original design.

Evolution -- Increase in complexity of structure or function of the unit machine, by adding to, subtracting from, or changing the character of existing system subunits.

Repair -- Any operation performed by a unit machine upon itself. which does not result in an increase of unit population, designed unit mass, or unit complexity. Includes reconstruction, reconfiguration, or replacement of existing subunits.

Replicating systems in principle may be designed to exhibit any or all of these machine behaviors. In actual practice it is likely that a given SRS format will emphasize one or more kinds of behaviors even if capable of displaying all of them. One such "unit replication" system has been described elsewhere;²⁵ a "unit growth" system^2,26 is outlined below. The emphasis is on fully autonomous or "unmanned" SRS because these are more challenging from a technical standpoint than either manned or teleoperated systems.

The replicating LMF design encompasses eight fundamental subsystems. Three subsystems are external to the main factory (Transponder Network, Paving and Mining Robots). The LMF Platform is divided into two identical halves, each comprised of three major production subsystems: The Chemical Processing Sector accepts raw lunar materials, extracts needed elements and prepares process chemicals and refractories for factory use; the Fabrication Sector converts these substances into manufactured parts, tools, and electronics components; and the Assembly Sector assembles fabricated parts into complex working machines or useful products of any conceivable design. (Each Sector must grow at the same relative rate for uniform and efficient perimeter expansion.) Computer facilities and the energy plant are the two remaining major subsystems.

Transponder Network

A Transponder Network operating in the gigahertz range assists mobile LMF robots in accurately fixing their position relative to the main factory complex while they are away from it. The Network is comprised of a number of navigation and communication relay stations set up in a well-defined regular grid pattern around the initial Seed and the growing LMF complex.

Paving Robots

In order to secure a firm foundation upon which to erect Seed (and later LMF) machinery, a Platform of adjoining flat cast basalt slabs is required in the baseline design. A team of five Paving Robots lays down this foundation in a regular checkerboard pattern, using focused solar energy to melt pre-graded lunar soil in situ.

Mining Robots

LMF Mining Robots perform six distinct functions in normal operation: (1) Strip mining, (2) hauling, (3) landfilling, (4) grading, (5) cellar-digging, and (6) towing. Lunar soil is strip-mined in a circular pit surrounding the growing LMF. This material is hauled back to the factory for processing, after which the unused slag is returned to the inside edge of the annular pit and used for landfill which may later be paved over to permit additional LMF radial expansion. Paving operations require a well-graded surface, and cellar-digging is necessary so that part of the LMF Computer may be partially buried a short distance beneath the surface to afford better protection from potentially disabling radiation and particle impacts. Towing is needed for general surface transport and rescue operations to be performed by the Mining Robots. The robot design selected is a modified front loader with combination roll-back bucket/dozer blade and a capacity for aft attachments including a grading blade, towing platform, and a tow bar.

Chemical Processing Sector

Mining Robots deliver raw lunar soil strip-mined at the pit into large input hoppers arranged along the edge of entry corridors leading into the Chemical Processing Sectors in either half of the LMF. This material is electrophoretically separated²⁷ into pure minerals or workable mixtures of minerals, then processed using the HF acid leach method²⁸ and other specialized techniques² to recover volatiles, refractories, metals and nonmetallic elements. Useless residue and wastes are collected in large output hoppers for landfill. Buffer storage of materials output is on-site.

Fabrication Sector

The LMF Fabrication Sector is an integrated system for the production of finished aluminum or magnesium parts, wire stock, cast basalt parts, iron or steel parts, refractories, and electronics parts. Excepting electronics,²⁹ there are two major subsystems: (1) The casting subsystem, consisting of a casting robot to make molds, mixing and alloying furnaces for basalt and metals, and automatic molding machines to manufacture parts to low tolerance using the molds and alloys prepared; and (2) the laser machining and finishing subsystem, which performs final cutting and machining of various complex or very-close-tolerance parts.

Assembly Sector

Finished parts flow into the automated Assembly Sector warehouse to be stored and retrieved by warehouse robots as required. This subsystem provides a buffer against system slowdowns or temporary interruptions in service during unforeseen circumstances. The automated assembly subsystem requisitions necessary parts from the warehouse and fits them together to make subassemblies which are inspected for structural and functional integrity. Subassemblies may be returned to the warehouse for storage, or passed to the Mobile Assembly and Repair Robots (MARR) for transport to the LMF perimeter, either for internal repairs or to be incorporated into working machines and automated subsystems which themselves may contribute to further growth.

Computer Control and Communications

Seed computers must be capable of deploying and operating a highly complex, completely autonomous factory system. The original computer must erect an automated production facility, and must be expandable in order to retain control as the LMF grows to its full "adult" size. The Computer Control subsystem coordinates all aspects of production, scheduling, operations, repairs, inspections, maintenance, and reporting, and must stand ready to respond instantly to emergencies and other unexpected events. Computer Control is nominally located at the hub of the expanding LMF disk, and commands in hierarchical fashion a distributed information processing system with Sector computers at each node and Sector subsystems at the next hierarchical level of control. Communications channels include the Transponder Network, direct data bus links, and E²ROM messenger chips (firmware) for large data block transfers.

Using ideas borrowed from current industrial practice, top-down structures programming, and biology, Cliff³⁰ has devised a system architecture which could perform automated design, fabrication, and repair of complex systems. This architecture is amenable to straightforward mathematical analysis and should be a highly useful component of the proposed lunar SRS. Further work in this area probably should include a survey of the theory of control and analysis of large-scale systems.³¹

In a practical sense, it is quite possible to imagine the lunar SRS operating non-autonomously. For instance, the in situ computer could be used simply as a teleoperation-management system for operations controlled directly by Earth-based workers. Material factory replication would proceed, but information necessary to accomplish this would be supplied from without. An intermediate alternative would permit the on-site computer to handle mundane tasks and normal functions with humans retaining a higher-level supervisory role. Yet another possibility is that human beings might actually inhabit the machine factory and help it reproduce -- manned machine economies can also self-replicate.

Solar Canopy

The Solar Canopy is a "roof" of photovoltaic solar cells, suspended on a relatively flimsy support web of wires, crossbeams and columns perhaps 3-4 meters above ground level. The Canopy covers the entire LMF Platform area and expands outward as the rest of the facility grows. The Solar Canopy and power grid provide all electrical power for LMF systems. Canopy components may be stationary or may track solar motions using heliostats if greater efficiency is required.

Mass, Power, and Information Requirements

Seed subsystem masses and power requirements scale according to the total system mass assumed. SRS can be reduced indefinitely in size until its components begin to scale nonlinearly. Once this physical or technological limit is reached for any subsystem component, comprehensive redesign of the entire factory may become necessary.

A Seed mass of 100 tons was selected for a number of reasons. First, 100 tons is a credible system mass in terms of foreseeable NASA launch capabilities to the lunar surface, representing very roughly the lunar payload capacity of four Apollo missions to the Moon. Second, after performing the exercise of specifying Seed components in some detail it is found that many subsystems are already approaching a nonlinear scaling regime for a 100-ton LMF. For instance, according to Criswell³² the minimum feasible size for a linear-scaling benchtop HF acid leach plant for materials processing is about 1000 kg; in the present design, two such plants are required with a mass of 1250 k each. Third, the results of a previous study²⁶ which argued the feasibility of 433-ton Seed in the context of an interstellar mission (inherently far more challenging than a lunar factory mission) were compared with preliminary estimates of 15-107 tons for partially self-replicating lunar factories of several different types,³³ and an intermediate trial value of 100 tons selected. The 100-ton figure has appeared in numerous public statements by former NASA Administrator Dr. Robert A. Frosch^34,35 and by others in prior studies.^36,37 It was decided to use a specific system mass rather than unsealed relative component mass fractions to help develop intuitive understanding of a novel concept which has not been extensively studied before.

The ranges given in Table 1 are estimates of mass and power requirements for an initial Seed system able to manufacture 100 tons of all of its own components per working year -- hence, to self-replicate. A trial replication time of one year was selected for similar reasons. These figures are consistent with the original estimate of a 100-ton circular LMF Seed with an initial deployed diameter of 120 meters, so feasibility has been at least tentatively demonstrated. However, it must be emphasized that the LMF Seed design outlined above is intended primarily as a proof of principle. Numerical values for system components are only crude estimates of what ultimately must become a very complex and exacting design.

Information processing and storage requirements also have been collected and summarized in Table 1, and lie within state-of-the-art or foreseeable computer technologies. These calculations, though only rough approximations, quite likely overestimate real needs significantly because of the conservative nature of the assumptions employed.²

In the most general case of fully autonomous operation, a typical LMF deployment scenario might involve the following initial sequence:

1. The predetermined lunar landing site is mapped from orbit to 1-meter resolution across the entire target ellipse.
2. Seed lands on the Moon, as close to dead center of the mapped target area as possible navigationally.
3. Mobile Assembly and Repair Robots, assisted by Mining Robots, emerge from the landing pod and erect a small provisional solar array to provide interim power until the Solar Canopy is completed.
4. LMF robots, with the Computer, select the precise site where erection of the original Seed will commence. This decision will already largely have been made based on orbital mapping data, but ground truth will help refine the estimate of the situation and adjust for unexpected variations.
5. Mobile robots emplace the first three stations of the Transponder Network (the minimum necessary for triangulation), calibrate them carefully, and verify that the system is in good working order.
6. Mining Robots equipped with grading tools proceed to the construction site and level the local surface.,
7. Five Paving Robots disembark and begin laying down the Seed Platform in square grids. This requires one working year for completion.
8. When a sufficiently large Platform section has been completed, Seed mobile robots transfer the main computer to a place prepared for it at the center of the expanding Platform disk.
9. Erection of the Solar Canopy begins, followed by each of the Seed Sectors in turn, starting with the Chemistry Sector. Total time to unpack the landing pod after moonfall is one working year. conducted in parallel with paving and other activities. The completed Seed factory unit, unfurled on the surface of the Moon one year after landing, might appear much as shown in Figure 1.

The LMF has two primary operational phases, growth and production. The optimal program would probably be to "bootstrap" (grow) up to a production capacity matching current demand, then reconfigure for production until demand increases -- thus necessitating yet further growth.³³ Growth and production of useful output may proceed sequentially, cyclically. or simultaneously. though the former is preferred if large subsystems of the lunar factory must be reconfigured to accommodate the change. (See Figure 2.)

The LMF also may exhibit replicative behavior if and when necessary. Replicas of the original Seed could be constructed much like regular products and dispatched to remote areas, either to increase the total area easily subject to utilization or to avoid mortality due to depletion of local resources or physical catastrophes. The scheduling of factory operational phases is very flexible and should be optimized for each mission and each intended use.

In a finite environment exponential growth cannot continue indefinitely. Geometrical arguments by Taneja and Walsh³⁸ suggest that planar packing of triangular, cubic, or hexagonal units can expand exponentially only for as many generations as each unit has sides, assuming that once all sides are used up no further doubling can occur by the enclosed unit. Growth is quadratic from that time on.

However, real physical systems such as the developing LMF enclosure need not preclude material communication with exterior units. Selected ramification of communication, control, and materials transportation channels or internal component rearrangement, reconfiguration or specialization can prevent "starvation" in the inner regions of the expanding system. Hence SRS exponential growth may continue until limited either by purposeful design or by the specific configuration of the external environment. Assuming that a 100-ton Seed produces 100 tons/year of the same materials of which it is composed, then if T is elapsed time and N is number of Seed units or Seed mass-equivalents generated during this time, T = 1 + log₂N for simple exponential "doubling" growth. (There is no replication in the first year, the time required for initial setup.) If P is productivity in tons/year, then P =100*log₂N.

However, the above is valid only if each unit works only on its own replica. If two or more units cooperate in the construction of a single replica, still more rapid "fast exponential" growth is possible. This is because new complete replicas or LMF subsystems are brought on-line sooner, and hence may begin contributing to the exponentiation earlier than before. Using the above notation, the "fast-exponential" growth rate is given by T = 1 + 1/2 + ... + 1/N in the optimum case where all available machines contribute directly to the production of the next unit. In just ten years the output of such a facility could grow to approximately one million tons per year. if allowed to expand for 18 years without diversion to production, the factory output could exponentiate to more than 4 billion tons per year, roughly the entire annual industrial output of all human civilization.

Useful SRS products may include lunar soil thrown into orbit by mass drivers for orbital processing, construction projects, reaction mass for deep space missions, or as radiation shielding; processed chemicals and elements, such as oxygen to be used in space habitats, as fuel for interorbital vehicles, and as reaction mass for ion thrusters and mass drivers; metals and other feedstock ready-made for space construction or large orbital facilities for human occupation (scientific, commercial, recreational, and medical); components for large deep-space research vessels, radio telescopes, and large high-power satellites; complex devices such as machine shop equipment, integrated circuits, sophisticated electronics gear, or even autonomous robots, teleoperators, or any of their subassemblies; and solar cells, rocket fuels, solar sails, and mass driver subassemblies. Also, a 100-ton Seed which has undergone thousand-fold growth or replication represents a 2 GW power generating capacity, plus a computer facility with a 16,000 gigabit processing capability and a total memory capacity of 272,000 gigabits. These should have many useful applications in both terrestrial and space industry.

In an arbitrary system there are three basic requirements to achieve closure:

1. Matter Closure -- can the system manipulate matter in all ways necessary for complete self-construction?
2. Energy Closure -- can the system generate sufficient energy and in the proper format to power the processes of self-construction?
3. Information Closure -- can the system successfully command and control all processes required for complete self-construction?

It has been pointed out that if a system is "truly isolated in the thermodynamic sense and also perhaps in a more absolute sense (no exchange of information with the environment) then it cannot be self-replicating without violating the laws of thermodynamics."⁴¹ While this is true, it should be noted that a system which achieves complete "closure" is not "closed" or "isolated" in the classical sense. Materials, energy. and information still flow into the system -- it is thermodynamically "open" -- but these flows are of indigenous origin and may be managed autonomously by the SRS itself without need for direct human intervention.

Closure Theory

For replicating machine systems, complete closure is theoretically quite plausible -- no fundamental or logical impossibilities have yet been identified. Indeed, in many areas automata theory already provides relatively unambiguous conclusions. For example, the theoretical capability of machines to perform "universal computation" and "universal construction" can be demonstrated with mathematical rigor,^8,10 so parts assembly closure is theoretically possible.

An approach to the problem of closure in real engineering systems is to begin with the issue of parts closure by asking the question: Can a set of machines produce all of its own elements? If the manufacture of each part requires, on average, the addition of ³  l new parts to produce it, then an infinite number of parts are required in the initial system and closure cannot be achieved. On the other hand, if the mean number of new parts per original part is < 1, then the design sequence converges to some finite ensemble of elements and bounded replication becomes possible.

The central theoretical issue is: Can a real machine system itself produce and assemble all the kinds of parts of which it is comprised? In our generalized terrestrial industrial economy the answer clearly is yes, since "the set of machines which make all other machines is a subset of the set of all machines."⁴² In space a few percent of total system mass could feasibly be supplied from Earth-based manufacturers as "vitamin parts." Alternatively, the system could be designed with components of very limited complexity.⁴¹ The minimum size of a self-sufficient "machine economy" remains unknown.

In actual practice, the achievement of full closure will be a highly complicated, iterative engineering design process. Every factory system, subsystem, component structure and input requirement must be carefully matched against known factory output capabilities. Any gaps in the manufacturing flow must be filled by the introduction of additional machines, whose own construction and operation may create new gaps requiring the introduction of still more machines. Any procedure for generating designs for engineering self-replicating systems must take account of three additional dimensions of closure: (1) Qualitative Closure -- can all parts be made? (2) Quantitative Closure -- can enough parts be made? and (3) Throughput Closure -- can all parts be made fast enough?

Quantitative Materials Closure

In the context of materials processing, "closure" is a relationship between a given machine design and a given particular substrate from which the machine's elemental chemical constituents are to be drawn. Hence the numerical demonstration of closure requires a knowledge of the precise composition both of the intended base-substrate to be utilized and of the products which the SRS must manufacture from that substrate. Following a method suggested by the work of Freitas,² a modified "extraction ratio" R_n, is defined as the mass of raw substrate material which must be processed (input stream) to obtain a unit mass of useful system output having the desired mass fraction of element n (output stream).

Consider the significance of the extraction ratio to the problem of materials closure. Assume that the final product is to be composed of elements x, y, and z. An R_x = 1 means that a kilogram of lunar soil contains exactly the mass of element x needed in the manufacture of a kilogram of the desired output product. R_y = 10, on the other hand, means that 10 kg of lunar regolith must be processed to extract all of element y required in one kilogram of final product. The difference between R_x and R_y may signify that y is more rare in lunar soil than x, or that the two elements are equally abundant but ten times more y is required (by weight) in the final product than x. When the output stream is identical to the machine processing system itself. then the system is manufacturing more of itself -- self-replicating -and the extraction ratio becomes an index of system materials closure on an element-by-element basis.

The Total Net Extraction Ratio R is some function of the individual extraction ratios R_n, and depends upon the methods of materials processing employed. At worst, if only one element is recovered from a given mass of input stream ("parallel processing"), then R is the sum of all R_n. At best, if the input stream is processed sequentially to extract all desired elements in the necessary amounts ("serial processing"), then R is driven solely by the R_n of the element most difficult to extract, say, element z. That is, R = (R_n)max = R_z, which is always smaller than the sum of all R_n. As serial processing should dominate in the lunar factory the latter formula is assumed for ,purposes of the present calculations. Note that Rn can be less than 1 for individual elements, but for an entire machine system R must always be greater than or equal to 1.

As a general rule, a low value for R implies that the system is designed for low mass throughput rates and is built from relatively few different chemical elements. A high value of R implies that many more elements are necessary and that a higher mass throughput rate will be accommodated to obtain them.

The "closure" of a given output stream (product) relative to a specified input stream (substrate) is computed by treating R as an independent variable. If I_n is the concentration of element n in mineral form in the input stream of lunar soil(kg/kg), E_n is the efficiency of chemical extraction of pure element n from its mineral form which is present in lunar soil (kg/kg), and O_n is the concentration of element n in the desired factory output stream (kg/kg), then R_n = O_n/E_nI_n. Closure C_n for each element is defined as the mass of pure element n available in a system with a Total Net Extraction Ratio R, per unit mass of output stream. For any given element, if R³ R_n then all pure element n needed is already available within the system. In this case, C_n = O_n. On the other hand, if R<R_n then the choice of R is too low -- all the pure element n needed cannot be recovered, and more lunar soil must be processed to make up the difference if 100% closure is to be achieved. In this case, C_n = O_n(R/R_n), since the closure deficit is measured by the ratio of the chosen R to the actual Rn of the given element (i.e., how much the factory has, divided by how much the factory actually needs). Total Net System Closure C is simply the sum of all C_n for all elements n required in the output stream of the SRS factory.

To estimate the quantitative materials closure for the unit growth factory described earlier, three different approaches were taken in an attempt to converge on a useful estimate of the composition of the output stream necessary for LMF self-replication. First, the "Seed" element distribution given by Freitas²⁶ in the context of a self-reproducing exploratory spaceprobe was adopted. These figures are derived from published data on the material consumption of the United States (the world's largest factory) during the years 1972-1976.^43,44 A second but less comprehensive measure called "demandite" is based on 1968 U.S. consumption data.⁴⁵ A molecule of "nonfuel demandite" is the average nonrenewable resource used by humans, less fuel resources.²⁸ Third, a direct estimate of LMF elemental composition² was used to obtain additional trial values for O_n. In all cases the input stream was assumed to consist of lunar maria regolith, with values for In averaged from published data.⁴⁶ Following earlier work, for simplicity all efficiencies E_n were taken to be 0.93.^47,48

The closures calculated from these data are plotted against extraction ratio in Figure 3. (Data for the human body are included for purposes of comparison.) Note that 100% closure (C=1) is achieved for the "U.S. Industrial" estimate (84 elements of the spaceprobe "Seed") at R = 2984; for "Demandite" (28 elements) at R = 1631; and for the "LMF" (18 elements) at R = 45. This suggests that the fewer the number of different elements, and the more common and more efficiently extractable are the elements the factory system needs for replication to occur, the lower will be the total mass of raw materials which must be processed by the LMF.

Note also that in all three cases, virtually complete (>90%) closure is achieved for extraction ratios of 2-14. The incremental gains in closure after 90% are purchased only at great price -- from 1-4 orders of magnitude more raw materials mass must be processed to achieve the last bit of full materials autonomy. Two conclusions may be drawn from this observation. First, for any given SRS design it may well be more economical to settle for 90-95% system closure and then import the remaining 5-10% as "vitamins" from Earth. Second, in those applications where 100% closure (full materials autonomy) is desirable or required, great care must be taken to engineer the self-replicating system to match the expected input substrate as closely as possible. In the case of quantitative materials closure, this demands a design which minimizes the value of R, thus optimizing the use of abundantly available, easily extractable elements.

• The basic concept of physical machine systems capable of self-replication appears credible both from a theoretical and a practical engineering standpoint.
• It is reasonable to begin designing replicating systems based on current knowledge and state-of-the-art technology, although final design definition will require significant further research.
• Complete systems closure is achievable in principle, though partial closure may be more feasible in terms of economic and pragmatic engineering considerations in the near term.
• It is feasible to consider beginning immediate work on the development of a simple demonstration SRS on a laboratory scale, with phased steps to more sophisticated levels as the technology is proven and matures.

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