How fast could we build a Dyson Swarm?

Question

I'm in a rush to colonize the Solar System. Thankfully, the latest Space Race, a commercial one between SpaceX, Blue Origin, Rocket Lab and other less known market entrants, is set to dramatically lower the cost of sending a kilogram to space, from >\$20,000/kg to <\$1,500/kg with Falcon Heavy and potentially as low as \$100/kg with SpaceX's Starship currently in prototype stage, but meant to be fully reusable hundreds of times. Elon Musk outrageously claimed a future cost as low as $10/kg, but in my limited vision as of April 2021, that seems wildly optimistic. The progress has been tremendous, as shown below in a LOG scale for current flight-proven systems:

This will likely remain important until we can develop the technology for what they call in-situ utilization. This is to say building space infrastructure using materials harvested in space.

It is fair to assume that, even optimistically, it might take a decade or two to perfect. After all, the challenges of doing so are not trivial, plus while the delta-v cost is lower than from Earth, you have less infrastructure in place so every defect and accident is a lot more impactful at first.

However, once the initial space infrastructure is in place and sufficient automation and self repair capabilities are built up and hardened, more energy can be had for the small marginal cost of building one more solar array. More energy mean you can do more stuff, including build more solar arrays, more smelters, more launch infrastructure. That remains true even if the more complex technologies still need to be sent out from Earth (say microchips). That sounds an awful lot like a virtuous cycle, in which a trend keeps building on itself on and on.

Given that the sun outputs a lot of Watts, and that most of that is currently wasted into empty space, it seems obvious that even a rather primitive space-faring civilization will want to start building solar capture structures. As long as the value of electric power is larger than the marginal cost of building, deploying and maintaining/replacing epsilon more solar capture arrays, these installations will keep on growing. This power can be used on site (imagine running a large data center) or could be transmitted long distance, by microwave or tightbeam laser. Off-earth, the only concern is maintaining line of sight and beam diffusion. Some of the losses can be avoided using good targeting, very large receivers and repeaters along the way.

So, on to the question. Assuming we develop the ability to build infrastructure using space resources using robotic technologies, and assuming (correctly?) that there is economic value in producing vast amounts of power in space, how fast could we get to a point where our Swarm will capture a significant amount of the radiation emitted by our Sun, let's say 0.01% of the 3.846 x 10^26 W. Folks are bad with big numbers so for context, that's about 4 x 10^22 W. A Kardashev I civ has a power output of 1 x 10^16 W (Sagan notation), so 0.01% of solar output is about 1 million times a Kardashev I).

A great answer would provide a number in years (or a range), as well as go as deep as possible into the logistics, the logic of exponential growth. Bonus points if you can spare time to handle questions like how much mass would be required & how quickly can we scale out our mining/processing infrastructure in space to get there.

Answer 1

it depends on ERoEI (energy returned on energy invested) of the technological ecosystem which is used to make the system or average effective ERoEI

ERoEI

mechanical electrical

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:

Heat2Mechanical

• 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 motors/generators

• 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

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

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

efficiency

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.

ERoEI, total

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.

Bottleneck's

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.

P.S.

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.

Answer 2

I think going for 0.01% of solar output is way too ambitious, given where we are now. Let's settle for Kardashev I status and work on that first.

Mankind's yearly energy consumption early 21st century was around $5\times10^{20}J$ Each year, while the sun outputs about $1.2×10^{34}J$ per year, which means we use about 10 femto-suns of power. To Nikolai Kardashev reaching out to the sun seemed like an obvious thing to do. Think about it: you have this immense amount of free energy streaming out into space, and essentially every Joule of it is wasted. You don't have to build a nuclear reactor, you don't have to worry about fuel. All you have to do is reach out and harness it. Since the intensity of the irradiance decreases with the square of the distance, you can maximize your capture and minimize the surface area needed for a particular amount of power generation by placing your generators closer to the source.

Solar Irradiance at the Planets
Planet Solar Irradiance, W/m-2

             Mean       Perihelion        Aphelion

Mercury      9116.4      14447.5            6271.1 
Venus        2611.0       2646.4            2575.7 
Earth        1366.1       1412.5            1321.7 

There is a vast, vast amount of matter in the Solar system, some of it conveniently outside of the massive gravity wells of the rocky and giant planets, so it's not an insane guess to expect that we'd use Asteroid Belt matter first, then the even larger Oort cloud resources. However, bringing material inwards towards the sun tends to speed it up (dancer closing arms stuff), so you need to actually spend delta V to do it anyway.

So it might actually be cost-effective to build mass drivers on Mercury itself, folks have floated the idea of an equatorial rail line that has a city on it, keeping in the pleasant twilight.

So, let's see what we need to do to reach Type I, defined roughly as making use of the resources of a home planet. If we take the Yearly solar irradiance of Earth, at $5.5×10^{24}J$, we still have a ten-thousand fold growth curve to ascend to even reach Type I. To do a Fermi simplification, let's assume 100% capture efficiency, so if you built solar panels at the Mercury perihelion (where irradiation is 10x Earth levels), to reach Type I via solar you'd "only" need 12 million sq. km. of panels, which is in the same order of magnitude as the area of Europe. Might seem like a lot, and it would doubtlessly require far more resources than we can currently even dream about harnessing, but the area of a sphere at the orbit of Mercury's perihelion is about 6.6e15 sq. km, so you've only built about 2 billionths of a Dyson sphere.

Let that sink in for a second. A Kardashev I civ, fully 10,000 times more energetic than we currently are, is 2 billionths of a Type II. So you can see why the 0.01% coverage (1/10,000 of a Dyson sphere) would be equivalent to 100,000 Type I civs. Nuts.

So, yeah, space is BIG. Moreover, you can see from that that you can go a long way towards a Dyson sphere before anything at all would be noticeable to unaided vision on Earth, and with some level of planning, you can ensure that even a near-complete Dyson sphere does not shade Earth (or the other planets) at all.

We got a long way to go.

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Ok, let's talk mass requirements, at a conservative 840 tons / sq. km, (See their data sheets: ~ 70.6 mg/cm^2) the structure required to bring us up to Kardashev I would weigh about 1E13 kg. That's 10 billion tons. Obviously with our best launch system of today (SpaceX prototype Starship lift capability of 100 tons) this would be exorbitant (100M launches), but with a mass driver on Mercury (3.7m/s^2 surface gravity) (essentially a big railgun), you could send 1 ton of payload every few seconds. Scaling up the industrial capability will likely take some time, so let's assume once we have the capability to build these railguns, and one can naturally build more and more of them every year. We can probably also bank of some improvements in the technology thru praxis, so both the quantity and the quality of our stock will improve. Here's one (highly optimistic) scenario. You can increase the time scales by a factor of 10 if you think I'm too optimistic:

So a relatively heavy buildout of industrial infrastructure culminating in over 1000 launchers each of which could send 1 ton up every ten seconds would be able to send that much mass up in about 15 years, with most of the actual mass being sent up in the last 2 years (if you dislike "years" and find it unrealistic, just replace it in your mind with "doubling periods").

So the answer is that once we have the tech to start building mass drivers capable of launching 1 ton payload from the surface of a planet like Mercury, if you're serious about scaling up and work on perfecting the launch tech: The optimistic forecast above has all that mass launched into space in about 15 years. A more pessimistic view would have it at about 150 years. How soon will we have advanced enough Space-based industry to build a 1 ton mass launcher on Mercury? Good question. Technically, this is within our reach, it's "just" a matter of good automation, potentially setting up local or orbital habitats for technicians, and maximizing self-repair capabilities in the the associated extraction and refining infrastructure.

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So it becomes a question of a) How quickly we develop this magical-seeming automation levels and b) How quickly we can send enough mass (and potentially supervisor/repair tech habitats in orbit or on planet) to make it go brrr.

a) automation levels -- A present day Tesla can already drive itself from point a to point b for >$30k in retail cost, most of which is raw materials (i.e. battery), with the remainder being labor, opex and capital. You can cut down human-friendly amenities, allow for 3-4 decades of decrease in battery costs and scale up 3d printing and automated manufacturing, and while haulers might not exactly drop to "disposable" cost levels, you could probably deploy a whole fleet for the current cost of a single commercial truck (+ driver) of today on Earth.

Your material haulers (can you even call it ore in space?) have to function basically independently, be able to drive back and forth, dump things in the right places, not run into things, and they occasionally need someone or something to perform maintenance. Alternatively if engines, batteries, wheels, onboard AI/vision/decision system and structural elements can be made cheaply enough in space, as soon as it drops below a given effectiveness level, you just park it and build another one. There's plenty of space.

We don't yet have a fully automated factory, so hard to say exactly how far away we are from something with (ideally) 0 or (otherwise) minimal human telepresence. With IOT costs dropping like a rock, everything is going to be intelligent and potential problems identified and adressed long before they materialize. This will likely require decades of practice to work the kinks out of, so expect the amount of human (tele- and direct) presence to be high initially, then gradually decrease towards 0 as we accumulate decades of experience working with such systems in space.

Depending on how good the robotic process automation is at the point where we want to start building this megastructure, you can scale up or down the required level of human presence. Even with very good automation, I would expect that by the time the industrial launch capability reaches the high levels mentioned above, there would be thousands of humans and millions of mostly autonomous drones either directly on or within telepresence distance of Mercury.

b) Looking at the speed with which the likes of SpaceX are moving, I would guess about 3-4 decades. So we could have Kardashev I energy levels by 2080 (optimistically) or 2200 (pesimistically). This all assumed that space-based energy has economic value (as I cannot imagine why it would not, as for instance running giant amounts of computation in space using marginally free energy would be nice and valuable)

This is ignoring ancillary structures for energy storage, transmission, repair, etc, -- you can quadruple my estimate if you want, and then triple it again if you want to assume 30% efficiency, which still leaves you within an order of magnitude of the first estimate anyway). For a full Dyson statite swarm (let's call it a Dyson Enveloping Haze) you'd need at least 5.5E21 kg of mass, which puts you around the combined mass of the asteroid belt, or about 1% of the mass of Mercury. So doable without really dismantling planets. We might need to to some transmutation of materials, but with so much free power, shouldn't be a major issue.

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Now, to the question of whether a genuine Type II civ would actually build a Dyson swarm, we can't really know. Perhaps a civilization so advanced has found far less crude methods to extract energy than from the wiggle of electrons on a slab facing a natural fusion reactor, from burning complex carbon molecules in a tin can, or from using atomic decay to boil water and using the vapor to make some brushes spin.

I recall reading once that there is enough zero-point energy is the volume contained by a regular mug to boil all of Earth's oceans away. And that's the stuff we know about. Who knows what wondrous tricks the descendants of Humankind will come up with in the future?

Answer 3

The limiting factor isn't energy, space launch capacity, or anything else yet mentioned. While there is potential for the virtuous cycle to emerge as you note, in which we could convert incredible amounts of matter into machinery, our population is simply too low (and Earthbound) for humans themselves to be the logistical administrators of this endeavor. And yet, there are no other substitutes at the moment. If AI is invented, it would be much more agreeable to working in situ and would make this possible (even plausible). Alternatively, if Von Neumann machines are invented this too could possibly be the solution to the logistical issues.

The AI solution is pretty much a "magic" solution in that humans don't have to figure out any of the hard answers themselves, they just let the AI do it instead. So let's talk about the VN solution instead. They wouldn't have to be truly intelligent, just able to self-replicate and be capable of externally commanded tasks. Once a population of a few dozen/hundred exists, some fraction would be told to built a smelter and to operate it while the others continue to replicate. This continues until there are millions of those facilities out in the far solar system. In turn, they build all these facilities and operate them. Excess units could even be recycled if needed. They'd obey simple rules like insect colonies for coordination, even if this isn't optimal efficiency. High level orchestration would come from Earth. While Earth's 10 billion couldn't hope to manually-and-remotely administer each of the billions of facilities doing low-level ore extraction, smelting, and fabrication, they will maybe be sufficient to coordinate the output of that system and administer final construction.

Until one or the other of these (possibly related) technologies are invented, the timeline can't even start.