it depends on ERoEI (energy returned on energy invested) of the technological ecosystem which is used to make the system or average effective ERoEI
what are some energy expenses in technologies which can be useful here:
- glass production, 4600 kWh per tonne, or around 16.6 GJ per tonne
- melting scrap steel, about 900 kWh per tonne, for batches of few+ tonnes
what are some energy investments, for technological production, there is some Power-to-weight ratio wiki page, let's pick some in not shabby in middle to the low side of power production ones:
- piston, 1L, 4 stroke, 74.5 kW, 100 hp, 0.44 kW/kg
- turboshaft engine, 9 kW 12 hp 3.67 kW/kg
- pneumatic motors, 0.74 kW 0.99 hp 0.44 kW/kg, range 0.3-0.7 kW/kg, for small power ones
- Photovoltaics, 9.64 W/kg
- electric car middle grade, 120 kW 160 hp 4.8 kW/kg
- power plant, 660 MW 890,000 hp 0.49 kW/kg
- range in general from 0.29 kW/kg to 11.56 kW/kg
overall we can count on some 0.5 kW/kg for converting heat energy to mechanical work, so a similar number for converting it to electricity, as one of the convenient energy forms for local consumption, but some processes can use mechanical energy directly without conversion.
total for material usage about 4 kg per 1 kW generation, for mechanical part
efficiency, radiators, concentrators
concentrators for solar energy can be made out of different material, metal, glass, ceramic, anything coated with a reflective material(usually metals)
it useful for heat to electricity conversion, so as for photovoltaics.
The advantages of using glass, or basalt, or other mineral composition is that it does not need to be reduced, and when making transparent glass is quite expensive, 4600 kWh per tonne, melting basalt is on pair with melting metal scrap, there is not much chemical reaction involved.
thanks to the microgravity construction of reflectors do not have to be particularly robust, it easy to see how strength equivalent to a 0.5mm sheet of soft iron can be enough if it has a reflective coating, to serve as reflectors of significant size. A cell may be hundreds by hundred meters - there is no real wind and such. it can be made out of small pieces 1x1m with some additional means scattered across for different needs.
total can be 1.5kg per 1300W solar, or about 1.2kg/kW of solar energy, some stone/mineral-based concentrators with mineral fiber for brittle resistance.
radiators we need, as well, to discard waste heat and make a cold end for our heat machines. So it needs some working fluid, heat exchanger fluid.
concentrators can serve as a base for radiators as well, with similar mass 2 walls, some piping, heat exchange fluid, let's say 4x of concentrator mass
let's take the number from the wall, and consider just a few things
- Sodium melting point 370K (97°C, 208°F), available in moon regolith
- 1000K hot end
- 500K cold end
- 70% reflector efficiency
- solar flux 1300W/m2
- electric generators 80% efficiency
- mechanical efficiency 70%
So overall from 1300 we can hope for making 254W/m2 or about 19% efficiency, so round it up to 20%
Not a superior efficiency and a better optimization could easily bring us to 30-40% territory which is typical for power plants and even better numbers are in reality, but let's play with that 20% as a potential start for cure setups and not to be overly optimistic and some room other unforeseeable losses - repair, remelt, recycle, production tools, etc. So we have some ample reserves here for all sorts of bells and whistles
with radiator masse, and working temperatures, and energy expenses - there is a need to optimize those numbers, as smaller radiators may mean fewer expenses and even if reduces efficiency it may be better. So there is an optimum for a given mass of radiators which temperatures it needs to be and which efficiency it will be - but as it is just a very crude illustration of the principle and potential numbers - that work isn't done here.
let's sum up and see which number we can hope for.
bill of materials per 1kW electric or 5kW solar, or 3.84m2:
- melted minerals (stone, regolith, basalt, diabase) for concentrators radiators - 23kg
- metals - iron, aluminum - 4kg
- tools - metals, cast stone - 0.2kg (quite a random number, playing from the feel, just to state that tools are a fraction of total)
total 27kg of materials, round it up and add materials for tools, electrics, chips, and stuff - 30kg.
Arbitrarily devide it for 85% needs mostly melting casting rolling (1000kW/t), 15% needs melting and reduction to metals, let's take Al2O3 as one of the most expensive as energy gauge, 8.6kW/kg for ideal process, in practice as industrial processes it is 17kW/kg, let's round it to 20kW.
Sooooo, what do we get as result, for production of 1kW we spend about 25+100=125kWh per 1kW electrical power production or per each 5kW solar energy.
So there is a potential for double the power generation every 125 hours, or about 5.2 days.
in a year it is a multiplication of initial power 1.247906641633902×10²¹ times
Sooo, starting with an initial power of 100kW, we potentially can finish a full-powered Dyson swarm in 373 days. If we start with an initial setup of 1GW, then we finish it in 304 days.
- direct heating melting of materials increases the efficiency of that process from 20% to about the efficiency of reflectors, in this case, I took 70%. And in microgravity, you do not need complex material demanding furnace construction - all melting heating can be done for the price of that reflector - you heat some blob in space and it will melt. In some processes, like recycling, is a drastic improvement of ERoEI, so as when in our case were 23kg is basically melting, no need to spend electricity for that or belters can value that aspect that they need just some flimsy sheet of reflective something(foil) to make heavy lifting of melting of a bunch of material at 2-3 a.u.
Let's start with what isn't a bottleneck, or in this case what isn't that drags us or slows us down - the energy required to deliver materials from Moon, as an example. Escape velocity for the Moon is 2.38 km/s, or if we do it via massdriver launch system something like 23.4kWh/kW(30x0.78kWh), so it around 20% of the energy we spend on shaping all the materials to be able to produce that 1kW, and if we recalculate the difference then 304 days become 360 days.
So with rockets, it can be different, but with that massdriver thing, we do not need to worry that much, if we can build it. But rockets are no-go immediately anyway, as we do need about many many kg's of materials.
real bottlenecks start at technologies that are used to deliver materials to space, in my case I suggest Moon and mass drivers, and it not necessarily sufficient for a full Dyson swarm or 0.01% of it - there is no difference.
We need 2.304×10²⁴ kg of materials(half of a planet) for full-fledged Dyson for that type of engineering design, which requires a supply of 73 trillion(e12) tonnes of material per second to be processed and all that, but in the first place to be dug and pushed in space, closer to the end of the process, in a second, I repeat, in a second, in average, I repeat, in average - meaning it is a number for the process in the middle of intensity, aka 3.1e-6% of total Dyson. In the end, it will look like blasting a planet in space for a full Dyson swarm.
If you like the speed, that 5 days to double the production, as I do, then 0.01% does not make a difference, and technology and setups used to deliver materials will be a bottleneck, not the energy required for that, but the process itself.
Do not be greedy, make 1-10x of K1 and chill a bit, it still a lo-o-ot, compared to what we have today, and use that to get a firm footing in space and propel technologies to the next level. There are ways to make Venus be useful for this purpose, so as potential technologies for that, it just needs simulations to understand how to make them.
From K1 and upwards it needs to calculate the bottleneck to say some number in years or whatever, and that depends on a lot of things, but let's do some
Material delivery, Moon case, massdriver
Let's say we launch 100t packages, with good 1g acceleration, then we need a track 283km in length. Not so much, so as 1g is doable, nothing super fantastic here.
one can launch as a stream of those, let's say one per second, it a matter of energy provided and system design.
expanding the launch system to increase the output also has its ERoEI for power production and corresponding launch track which uses the energy, and it harder to calculate and is specific for the design. But principle the same.
Let's go with the same efficiency, 20% for electricity generation and 50% for launch then 10% total, for the launch system and electricity generation, then for the case, launch track consumes 283 GW electricity and occupies 7.3km x 283km area.
a ring around moon 100km wide, can launch half of the max, due day-night cycles, can be solved(or be twice wide), and we get something like 500 such segments and 50'000 tons per second.
And the materials can be spewed in a direction of some of the Lagrangian points namely L1 and L2 of earth-sun
- yes, I know they are not stable in long term but there are ways to handle that without losing mass if we talk about big installation.
Then we can finish and installation for K1 electricity production (5.7789×10¹⁵ kg in space) in 3.7 years. Let's say few years for ring expansion, not an unreasonable number, and then around 5-6 years can be enough for K1
there are all sorts of orbital position problems, which have all sorts of solutions, but focusing on what pops in mind instantly - catching those payloads and here Lagrange points are good because orbiting speed there, around the earth, is quite slow, relatively, around 130m/s, and raw materials do provide reactive mass if it is one of the means to catch stuff at the beginning, cold trusters can squeeze 800m/s. So as it all takes time, so ion engines and variations can work there as well on catching job, on corrections, proper insertions into catchers etc. So there all sorts of options at those speeds.
the speed number isn't a hard one, it just crude approximation, orbital processes, in this case, are quite hard ones, and will depend on a number of factors.
So K1 is relatively easy, K2 is harder, but I see that you digging the topic and then you may dive into that answer as well, it lengthy and a bit too old and can be improved as I see it now, but still it touches some technologies you may need for 0.01-100% of K2 - so as well as where and why you get the materials.
why that mechanical approach and not fancy Photovoltaics and other great technologies.
The main reason is simple, there two of them.
The first one is that it is easier to calculate ERoEI, simpler the system simpler the calculations, so there may be some better ways or fancier technologies that are even more simple and efficient, but where do you get the numbers for them.
The second is - simpler the processes, less of them involved in making things happen simpler automatization of those processes. And if brains for the process is easier to make on vacuum tubes, you do make them on vacuum tubes, and once you finish with the expansive part of the expansion/building the system, you can use the materials to shape them in more intricate and sophisticated and efficient ways. Mass efficiency and perfection of technologies are not that important for the thing compared to ERoEI of the process.
So if your photovoltaics using 10times fewer materials, is 2 times more efficient, serves 30 years, but needs 10-100 times more energy(which is easy to be 100 times, and it is a good trade-off on the planet, maybe) but compared to a thing that is crude and works a year - you go with that crude thing first, as recycling it costs almost nothing compared to photovoltaics, and it has better ERoEI from the get-go.
reading current answers, another reason pops up - we can envision process step by step, we do not have to handwave things, we can have a quite a good detailed understanding of how things are done. what is automated, how it is automated, what do we need, in which quantities do we need it etc.
it is a quantifiable problem that can be described in current, this day, technologies.
if I forgot something to mention or need to add something, write in comments, may add it.
Disclaimer if one decides to make a business plan on all that, give Mr.X a beer and do check the numbers.