# 3.0 - Design Concepts

## Contents

Engineering as a whole is the application of knowledge to design, build, and operate systems which meet specified goals. Self-expanding production systems, including seed factories and the mature factories they grow to become, have the goal of useful outputs to improve the quality of life and satisfy human needs. So they fit within the scope of a system whose design can be engineered. The design process uses concepts and methods drawn from existing science and technology fields, with the addition of concepts particular to self-expanding systems. In this section (pages 3.0 to 3.4) we will introduce some of the relevant concepts. In the next major section, 4.0 Design Process, we will link them with other engineering methods into an integrated sequence.

The most relevant concept, of course, is that of a self-expanding system. The previous sections have already introduced it in general, but self-expansion should be recognized as one of the main concepts being used in the design process.

## System Measures

In engineering, and the sciences and mathematics it is based on, we use quantities and equations to better understand and design things. A simple object, like a masonry brick, can be measured by physical quantities like size and weight. Those measurements can then be used to calculate how many are needed to make a wall, or how heavy it will be. Similarly, for a complex system like a self-expanding factory, we want to have some useful measurements to make calculations from or compare one design to another. A size measurement, such as 25 cm for a brick, consists of two parts, a quantity (25) and a unit of measure (centimeter). Our factory measurements will also have a quantity and relevant units.

### Self-Expansion

A key difference between a seed factory and other production systems is self-expansion through replication, diversification, and scaling. So one group of useful measurements are for how much it can grow.

• Closure

An ideal self-replicating factory would be able to copy all its own parts, plus make useful products. Human-built systems are less than ideal, so we would like a way to measure a factory which can only copy some of its parts. In mathematics, a Closed Set is "a set that includes all the values obtained by application of a given operation to its members". Past discussions of replicating systems have used the term Closure to mean the outputs of the factory include all the parts which are required for it's own operation. Closure is also related to the idea of "closing the loop", where the output from a process loops back on a flow diagram to become a production input, namely the equipment to operate the process. For replication, closure only counts the factory itself. We can generalize it to include the factory and the products it makes. A Closure Ratio, CR, is then the quantity of outputs the factory can make, divided by the total quantity of that item used in the system itself. For example, using parts count of the factory as the item to measure:

${\displaystyle CR(parts)={\frac {N(produced)}{N(total)}}}$,

where N(total) is the total number of parts from which the factory is made, and N(produced) is how many of those parts it can make itself as outputs. You can measure closure ratios by mass, cost, parts count, quantity of design data, and other variables. So CR(mass) = 0.98 means the system can produce 98% of it's own parts by mass, and the remaining 2% must be supplied from elsewhere to make a complete copy. We can also measure the closure for end products other than the factory, CRep. This is the fraction of the end products made internally by the factory vs. parts and materials supplied from elsewhere. For example, a local computer shop which assembles them for customers, but does not make any of the parts themselves, would have 0% product closure. Finally, we can measure the closure ratio for a factory and all its products combined, CRall. Both end product and combined factory + product ratios can be measured by mass, cost, and the other variables noted previously.

Calculating closure ratios for existing factories and products is a straightforward counting or measuring process. Analyzing potential closure ratios for a future self-expanding system is more complex. This follows a step-wise process working backwards from the end products to whatever equipment you start with. For a completely new seed factory, you start with no equipment - the starter set is supplied from elsewhere.

The first step is to identify which machines and processes you need to make the end products. From that you can identify which equipment you do not already have in place. For the missing ones you can further determine how much of them you can make internally with current equipment. Eventually you trace everything back to parts and materials you can make, or to those you can't. The ratio of internal make to end output is then your closure ratio for those products. In doing such an analysis, what would otherwise be a waste product from one process should be considered for recycling into another process. When you consider the factory itself as the end product, then the closure ratio measures the ability of the factory to replicate itself.

If you try to reach 100% closure in a self expanding system, in theory you can reach some set of starting machines that can make all the later ones plus copies of themselves. We know our entire industrial civilization can do this. All our current equipment traces back to previous generations of equipment and raw materials, and we can still make copies of the oldest and simplest tools. In principle a smaller set than all of civilization, consisting of at least one machine of each type, should also be able to fully copy itself. In practice, a few processes, like making computer chips, are difficult and expensive to do in small quantities. Others processes require rare materials, or are done so infrequently, that it does not make economic sense to have your own equipment to do them. The few previous studies on this kind of closed loop production found around 1-2% of the total items were not practical to self-make, or in other words 98-99% closure. Still, having to buy or import 1-2% of your parts and materials is a great improvement over the levels found in current factories.

• Output Range

A useful factory is able to make other outputs besides copies of itself. An Output Range, OR, for any factory can be defined by the range of possible outputs relative to the same parameter for the factory itself. So a 200% output range by mass means the list of possible outputs has twice the mass of the factory. This is calculated by counting one copy of each output. Most factories are intended to produce many copies of the product, but that is a measure of total output, and not the range in terms of variety of products. In the case of continuously produced materials, like coils of steel sheet, one copy is a deliverable load. Like closure, output range can be measured in terms of mass, cost, parts count, design data, and other parameters.

When the output range includes some parts of the factory itself, then OR by mass can be expressed as

${\displaystyle OR(mass)=CR(mass)+EP(mass)}$,

where OR(mass) is the mass of the total range of outputs, CR(mass) is the closure ratio by mass, i.e. the mass of its own parts it can output, and EP(mass) is the mass of all the other end products it can make. Traditional factories which make none of their own parts would have CR(mass) = 0, and EP(mass) > 0. While traditional factories tend to have low closure ratios they are often not zero. For example, cement and steel plants both typically use some cement and steel in their construction, and an electronics factory typically uses some electronics in its own operation. Seed factories are just intentionally designed to have much higher levels of closure. The output range of a traditional factory may be quite low. For example, the mass of an automobile is small compared to the mass of the auto assembly plant where it is made. A semiconductor foundry is quite large compared to the chips it produces. This is often the result of high levels of specialization and mass production at the expense of product flexibility. Self-expanding factories with programmable smart tools are more able to vary their outputs, by changing the software files for what parts to make, and then what products to assemble them into. So they can reach high output ranges.

• Expansion Range

Output range refers to all the outputs the factory can make. Expansion Range, ER, refers to the set of outputs which can be used to expand the factory, relative to the set of which it is made. So if a factory uses 8 production processes, and can produce parts for 4 new ones, it would have a 50% expansion range in process count. Measures for expansion range can use mass, parts count, number of materials used, or other quantities, in addition to process count. For example, we can write the formula

${\displaystyle ER(parts)={\frac {N(expansion\ parts)}{N(factory\ parts)}}}$,

where ER(parts) is the expansion range in parts count, N(expansion parts) is the number of new parts to expand the factory, and N(factory parts) is the number of parts in the current factory. A factory which can copy all it's own parts, but not make any new parts for different equipment, would then have CR(parts) = 100% and ER(parts) = 0%. This is actually an unlikely situation in the real world, but for now we are just trying to explain the types of measures.

The expansion range can vary with the growth of a self-expanding factory. It may be low at the seed stage, where only a few starter set machines area available, and can only produce a few types of new items. It may then increase as the factory grows and can make more types of materials and parts, and decrease again as it reaches practical limits in the types of materials and processes it can use. How the expansion range varies in a growing factory is a new area of study, and not well understood at present.

Civilization as a whole has a CR > 100%, and an ER significantly > 0%. Every existing production machine was made somewhere, and can therefore be copied simply by making another one the same way. So civilization can copy all its parts. The constantly growing range of products across time shows that existing equipment can make new equipment that didn't exist before. This proves by example that high levels of closure and expansion are possible. The design challenge for a seed factory is to reach high levels of these measures with a much smaller starter set than what all of civilization uses.

### Production

• Absolute, Ratio, and Rate Measures

Like any factory, we want a self-expanding seed factory to produce useful amounts of outputs. So another set of measures are based on the quantity and rates of output. If a given factory element can produce 50 kg of outputs, then 50 kg is a production quantity in absolute units, designated P in formulas. A Production Ratio, PR, is a measure of the outputs divided by the same measure for the factory element itself. So the total mass of outputs divided by the mass of the factory elements gives the Production Mass Ratio, PR(mass). Many such ratios can be measured depending on what features of the system are important. Ratios are simple numbers or fractions. Dividing an absolute unit by time gives a Production Rate, P/t, such as 50 kg/hour. By adding a time unit to a production ratio, it also becomes a rate. So if the system produces three times its own mass in outputs per year, the Output Mass Rate, PR(mass)/t, is 3.0/year.

• Relative Measures

Relative production ratios can be defined by comparing a self-expanding design to non-expanding and non-automated factories. For example, if a conventional factory needs to purchase all the parts and prepared materials, and our mature automated one only needs to purchase 2% and makes 98% internally from raw materials and energy, then the Relative Production Ratio is 100%/2% = 50 times higher relative to purchasing all the items. The Relative Cost Ratio is the total cost of production for a self-expanding design vs a conventional design. This includes the effect of:

- Lower capital cost, because the factory partly builds itself,
- Lower cost of parts and materials because fewer finished parts are purchased, and materials are obtained closer to the less expensive raw state,
- Reduced labor cost from increased automation and automated transfer between production steps, and
- Reduced overhead where tasks are combined at one location. This comes from eliminating intermediate stages of the production chain, and their levels of shipping, accounting, and profit margins.

Costs, of course, will not be reduced to zero. Land, raw materials, some labor to operate and manage the factory and for product design, and other costs will still exist. If the above cost reduction factors are large enough, though, that provides a major justification to pursue self-expanding designs over conventional ones.

### Growth

• Growth Rates

A rate which people often will care about is how fast a factory can grow or copy itself. Usually this is expressed as the amount of growth divided by the original size, over a time interval, in percent per year. An alternate way to express the growth rate is Doubling Time - how long it would take the factory operations to double in size. Growth rates are limited by the slowest process within the factory. So a well-designed factory will balance the size and speed of its parts so that no part is excessively slow relative to the others. Since factories require energy to operate, this is one of the factors that often limit growth rates. As an example, we can estimate the amount of energy needed and growth rate for a simplified factory model:

 Embodied Energy is the total energy used in making an item, starting from raw materials until production is complete. That energy is said to be "embodied" in the final product, although much of it is physically dissipated elsewhere. For our simplified factory model, we will assume an average square meter of factory area includes 10 cm of gravel, 20 cm of concrete foundation and slab, and the equivalent of 30 cm of steel in factory equipment and the building that contains them. The actual equipment and building will take up more height than this, but for the purpose of calculating embodied energy we can treat it as a solid slab of metal with a given thickness. From the material densities, we then get 140 kg of gravel, 480 kg of concrete, and 2340 kg of steel. Embodied energies for these materials are 0.083, 1.14, and 10 MJ/kg respectively, which can be found from reference sources like the Inventory of Carbon and Energy (spreadsheet, v2.0, 2011). Multiplying the mass/area by energy/mass for each material, then adding, we get 11.6 + 547.2 + 23,400 = 23,958.6 MJ for each square meter. We round this up to 24,000 MJ/m2 as the energy required to produce our simple model factory. Assume we have a 50/50 mix of thermal and photovoltaic solar collectors in an average climate. Half of them provide 4 hours/day of thermal energy @ 850 W/m2 and the other half supply 4 hours/day of electrical power @ 160 W/m2. If their total collection area is 3 times the floor area of the factory, then they will produce 21.82 MJ/m2 of factory floor per day. Dividing the energy to produce the model factory by this number gives 1,100 days to generate sufficient energy to copy the factory. To this we need to add 175 days to account for the energy to make the solar collectors. This gives 1275 days = 3.5 years combined time to produce sufficient energy to copy the factory plus power supply. This is a 22% annual growth rate in theory. In practice, our factory will be more complex than our simple three layer example, and other factors than energy may limit the growth rates.

The solar collectors take less time per area to produce their own embodied energy. This is because they require much less than the ~3,000 kg/m2 of materials to build the factory. Therefore a higher ratio of power supply to the rest of the factory will shorten the doubling time, up to the point that something else limits the growth rate. Faster operation of the factory machines, and higher Duty Cycles can also shorten the doubling times and increase growth rates. However this also will increase equipment wear, and likely require more sturdy and therefore more massive equipment.

There is likely to be some practical limit to future growth rates on Earth. Locations on Earth vary in available renewable energy. Less location-dependent, non-fossil sources, like nuclear power, may not have high output relative to the embodied energy in their construction. Fossil sources are fairly high energy output, but are undesirable for their side effects. There is also a limit to how fast and how intensively you can run factory equipment. Beyond Earth, in orbits that avoid the shadows of large bodies, sunlight is available 100% of the time. It is also 36% more intense from lack of atmospheric absorption. So available energy is 4-10 times higher in space compared to locations on the ground. Production processes are potentially faster or lower mass, since equipment does not have to withstand gravity, vacuum is a good insulator, and deep space is an infinite heat sink. Therefore growth rates are potentially very high. A lot more work is needed to investigate this potential.

• Growth Ratios

We can describe various ratios of a mature factory to the starter set as Growth Ratios, GR. The simplest of these are ratios of physical size. The final factory can be measured in mass or floor area relative to the starter factory. So a mature factory that is 10 times the floor area of the starter set would have a GR(area) = 10. Measures of complexity can count the number of processes or equipment types in the final vs starter sets, or look at the relative data for their design in terms of computer files, number of drawings, or number of production steps to build the equipment. Obviously a starter set needs GR > 1.0 in order to grow.

### Efficiency

The conventional measure of engineering Efficiency is useful output divided by total energy input. This is suitable for looking at a particular process or device in isolation. For an integrated factory that uses wastes from one process as input to anther, and recycles materials, we want to look at total system efficiency for the factory as a whole. When a production system produces some or all of its own energy, the ratio of Energy Returned on Energy Invested (EROEI) can be a useful measure. The returned energy includes the energy delivered to outside users as energy, plus the embodied energy in products. The invested energy is that supplied from outside sources plus the embodied energy from inputs of equipment, parts, and materials, where both inputs are used to build and operate the factory.

Conventional engineering efficiency and return ratios look at total inputs. We can also look at Renewable Efficiency, Reff, because we are interested in sustainability of production. This measure is renewable energy, as inputs in both direct energy and embodied form, divided by total outputs in both forms. If no renewable sources are used, then Reff = 0%. In theory, all the energy could be from renewable sources, and all materials recycled or from renewable sources, giving an Reff = 100%. In practice this measure will be less than 100% in a real system. No energy source is truly renewable - entropy is a one-way process. When we use the term, we mean the source is refilled on human and civilization time scales. For example, a wind turbine absorbs some of the energy in the wind and converts it to electricity, but there will be more wind tomorrow. Geothermal energy originates from radioactive decay inside the Earth. A particular plant may deplete the heat in a given location, but eventually more will migrate from deeper ground.