**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. It therefore fits within the definition of a system whose design can be engineered. The design process uses concepts and methods drawn from existing fields, with the addition of some new ideas particular to self-expanding systems. In this section (3.0) we will introduce the concepts and ideas. In the next section, **4.0 Design Process**, we will link them 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 new concepts being combined with other existing and new ones.

**System Measures**[edit]

In engineering, and the science 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 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]

A key difference between a Seed Factory and other production systems is self-expansion through replication, diversification, and scaling. So useful measurements for a Seed Factory are how good it is at self-expanding.

**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". Discussion of replicating systems thus applies 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 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. Useful closure ratios include mass, cost, parts count, and quantity of design data. Thus CR(mass) = 0.98 means the system can produce 98% of it's own parts by mass, and the remaining 2% by mass must be supplied from elsewhere to make a complete copy. We can measure the closure for end products other than the factory. 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 combined closure for a factory and its products combined.

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 those 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. Thus 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. 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 it 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 UR(mass) is the mass of all the other useful 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 computer factory typically uses computers in its own operation. Seed Factories are just specially designed to have much higher closure levels.

**Expansion Range**

Output range refers to all the outputs the factory can make. **Expansion Range** refers to the set of new outputs which can be used to expand the factory, relative to the set of which it is made. Thus if a factory uses 8 production processes, and can additionally produce parts for 4 new processes, it would have a 50% expansion range in process count. Expansion range measures can also use mass, parts count, number of materials used, or other quantities. 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 increase 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 reaching high levels of these measures with a much smaller set of equipment.

__Production Measures__[edit]

Like any factory, we want it to produce useful 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 quantity in absolute units. A **Production Ratio** is a measure of the outputs divided by the same measure for the factory element itself. Thus the mass of outputs divided by the mass of the factory elements gives the **Production Mass Ratio**. 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**, such as 50 kg/hour. By adding a time unit to a production ratio, it also becomes a rate. Thus if the system produces three times its own mass in outputs per year, the **Output Mass Rate** 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 is 100%/2% = 50 times higher relative to purchased 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 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 Rates__[edit]

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/year. An alternate way to express the growth rate is **Doubling Time** - how long it would take the factory operations to double its size. Growth rates are limited by the slowest process within the factory. Thus 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:

**Embodied Energy** is the total energy used in making an item, starting from raw materials until production is complete. For our simplified factory, 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 factory equipment. 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 gravel, 480 kg concrete, and 2340 kg steel. The embodied energies (in MJ/kg) of these materials are 0.083, 1.14, and 10 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 solar collectors which provide 2 hours/day of thermal energy and 2 hours/day electrical generation. If they have 2.5 times the floor area of the factory they will produce 18 MJ/m^{2} of factory/day, and it then takes 1,333 days to generate sufficient energy to build the factory. To this we need to add 175 days of energy to make the solar collectors, giving 4.13 years combined time to produce sufficient energy to build the factory. This is a 24% 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.

__Efficiency__[edit]

The conventional measure of engineering efficiency is useful output divided by 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. Besides the conventional engineering efficiency that looks at total inputs, we can look at **Non-renewable Efficiency**. This is the useful output divided by the non-renewable energy and materials used. In theory the non-renewable inputs can be reduced to zero, and so the non-renewable efficiency value can be unlimited. The higher this measure gets, the more sustainable a factory is.