# 3.0 - Design Concepts

Engineering as a whole is the application of knowledge to design, build, and operate systems which meet specified goals. A seed factory, and the mature factory it will expand into, is a production system with the goal of useful outputs to improve the quality of life and satisfy human needs. So it fits within the definition of a system whose design can be engineered. The design process will use concepts and methods drawn from existing engineering fields, with the addition of some new ideas particular to self-expanding systems. In the pages of this section (3.0 to 3.4) we will introduce the new ideas. In the next major section, **4.0 Design Process**, we will link them with existing ones into an integrated sequence.

The most important concept, of course, is that of a self-expanding system. The previous sections have already introduced it in general, so we will not repeat the discussion here. But self-expansion should be recognized as one of the concepts being combined with other existing and new ones.

**System Measures**[edit]

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 clay 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 Measures**[edit]

**Self-Expansion Measures**

A key difference between a seed factory and other production systems is self-expansion through replication, diversification, and scaling. So one set of useful measurements are about 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 of 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:

- ,

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, and quantity of design data, and perhaps 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, CR(end products). This is the fraction of the end products made internally by the factory vs. parts and materials purchased ready-made. 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, CR(all).

Calculating closure ratios for existing factories and products is a straightforward counting or measuring process. Analyzing potential closure ratios for new designs is more complex, using a stepwise process working backwards from the end products. You first 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. Eventually you trace everything back to a 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 include 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 theory you can reach some limit of starting machines that can make all the others including themselves. We know our entire industrial civilization can do this, so some smaller subset of at least one machine of each type should also be able to also. In practice, a few processes, like making computer chips, are difficult and expensive to do in small quantity. Others would require rare materials or are done so seldom it does not make economic sense to make your own. The few previous studies on this kind of closed loop production found around 2% of the total items were not practical to self-make, or in other words 98% closure. Still, having to buy or import 2% of your parts and materials is a great improvement over the typical levels in a factory.

**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. Note this is calculated by using one copy of each output. In the case of continuous materials like coils of steel sheet, one copy is a deliverable load. Total factory output over its life should be many copies, but that is a different measure than the range of outputs. When the output range includes some parts of the factory itself, then OR by mass can be expressed as

- ,

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 UR(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 a n electronics factory typically uses some electronics in its own operation. Seed factories are just intentionally designed to have much higher closure levels.

**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 processes, 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

- ,

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.

Civilization as a whole has CR > 100%, and ER significantly > 0%. Every existing production machine was made somewhere, and can therefore be copied simply by making another one the same way. 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 challenge for a seed factory is to reach high levels of these measures with a much smaller set of equipment than all of civilization.

**Production Measures**[edit]

**Production Measures**

Like any factory, we want a seed factory to produce useful amounts of outputs. So another set of measures is based on the quantity and rates of output. If a given factory element produces 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 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 in shipping, accounting, and profit margins where tasks are combined at one location

Costs, of course, will not be reduced to zero. Land, raw materials, some labor to operate and manage the factory, 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 Measures**[edit]

**Growth Measures**

**Growth Rate**

A rate which people often 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 as follows 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 includes 10 cm of gravel, 20 cm of concrete foundation and floor, and the equivalent of 30 cm of steel in factory equipment and the building that contains them. The actual equipment 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. The embodied energies of these materials are 0.083, 1.14, and 10 MJ/kg respectively. Multiplying, we get 11.6 + 547.2 + 23,400 = 23,958.6, which we round up to 24,000 MJ/m^{2} of energy required to produce the factory.

Assume we have a 50/50 mix of solar collectors in an average climate. Half of them provide 4 hours/day of thermal energy @ 850 W/m^{2} and the other half supply electrical power @ 160 W/m^{2}. If they have 3 times the total floor area of the factory they will produce 21.82 MJ/m^{2} of factory/day. It then takes 1,100 days to generate sufficient energy to build the factory. To this we need to add 175 days to account for the energy to make the solar collectors. This gives 3.5 years combined time to produce sufficient energy to copy the factory. 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. It is evident that since the solar collectors take less time to produce their embodied energy, 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.

**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 Measures**[edit]

**Efficiency Measures**

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 factory 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 energy delivered to outside users as energy, plus embodied energy in products. The invested energy is that supplied from outside sources plus the embodied energy of parts and material inputs, 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 **Non-renewable Efficiency**, NRE, because sustainability of production is of interest. This measure is non-renewable energy and materials used divided by the useful output. If no renewable sources are used, then NRE = 0%. In theory all the energy could be from renewable sources, and all materials recycled, giving an NRE of 100%, but in practice it will be less than this in a real system.