On Sickness, Games, and Dyson Spheres

[elfric]

So, after 3 months of being off work and completely unable to concentrate, my liver tests are back to only mildly alarming and I'm going back to work on Monday. I've been bored out of my skull and have played more RPGs/strategy games in the last three months than I think I have my whole life before that.

Morrowind, Oblivion (three times), leveled a prot paladin to 80 in WoW (just in time for Cataclysm rules to totally hose paladins), Ultima (4, 5, 6, and 7), Ultima Underworld I and II, Dungeons and Dragons Online (it's still as bad as I remember it), Elemental: War of Magic (many times), Disciples III, Master of Orion II, The Witcher, Temple of Elemental Evil, Planescape Torment, Might and Magic (6 (twice), 7 (three times), 8, and 9), Daggerfall (WOW, that world is huge!), Dungeon Master (I, II, and Chaos Strikes Back), and Wizardry 7.

Sheesh, just listing them out makes me realize how much time I just wasted. I really hate that I had all that free time and couldn't concentrate enough to get anything useful done. Ah well, what's done is done.

In any case, I'm heading back to work on Monday and they finally are allowing me to take my A.D.D. meds again (though we're trying a new type). Today, after months of feeling like my brain was full of fuzz, I finally was able to concentrate enough. So I picked a fun little problem to work on and test my concentration level. I played around with configurations of Dyson Spheres because I'm bored with game worlds that are like ours. I want to see a game with a horizon that curves UP or something else equally different.



It turns out that a true Dyson Shell is impossible (which makes me sad since I've based my pen-n-paper RPG world inside of one for many years. Ah well). Not only would it take more mass to build than exists in our solar system (unless you use the sun as well (and even then, just barely), but that kind of defeats the point since then there's no sun for the shell to surround!), but because it's a solid shell, gravity would cancel out (leaving the surface at zero-gee) and there would be no way for it to stay in orbit around the star (without some form of stellar engines that would keep it in orbit anyway). Of course, if you added stellar engines to keep the shell around the star and rotated it fast enough to give it 1 gravity, only the equator would have 1g - the rest of the sphere would spin TOO fast and basically everything would pool up at the equator. Might as well just build a ringworld at that point.

Of course, the benefits of a true shell are undeniable. It fully captures ALL stellar output (100% efficiency) and provides a surface area of about 551 million Earths. Any other configuration I can think of has less surface area. Wellllll....not quite true, but there's tradeoffs - see below.

So I tried to think of a Dyson Swarm configuration that maximized both efficiency and surface area. What I came up is something I haven't seen anywhere else, which makes me think I've made a basic mistake about the physics. Maybe one of you can spot a flaw that I can't?

Dyson Sphere Configuration 1A - Dyson Swarm

• Start with a flat plate 10,000km x 10,000km x 1km. The outer surface would be made of carbon nanotube material and would probably be pretty thin (less than a meter).
  
• Surround all four edges with a pyramid 10km wide at the base and 100km tall (to hold in the atmosphere, much like a Bishop Ring).
  
• Then pile up about a kilometer thickness of earth, metals, etc. (one thing that bothers me about most habitats I read is that none of them have any soil, minerals, or thickness to them. The thickness would allow for a much greater chance of self-sustainability as well as good protection against meteors, cosmic radiation, etc. In my case, I just want there to be enough earth to make an Underdark-style cavern system possible - gotta have them Drow and Duergar :) ). The density should be about the same as Earth's - 5515.3 kg/m3.
  
• Put it in orbit around a star at a distance of 1 AU. The livable surface area of the floor plate would ALWAYS face directly towards the sun. Since the mass of the worldlet (including surface, walls, atmosphere, and surrounding cylinder (see below)) is only about 6.29 * 10^20 kg, it only has an innate gravity of 0.00001 of Earth's. Therefore, we'll need to orbit the worldlet about the star at a fast enough rate to give it 9.8m/s^2 of centripetal acceleration. Turns out that to do this, it will need to move at 1,212,044.178 m/s. This is actually a little more than 1/300th of the speed of light, making it quite fast indeed - maybe even fast enough to be noticeably affected by relativity! At that speed, even micrometeorite strikes are quite dangerous. By comparison, the Earth moves along its orbit at a stately 29,785 m/s. Obviously, to get the worldlet moving at that speed we'll need some pretty advanced propulsion tech (or be patient and wait a LONG time with a slow acceleration) as well as some VERY advanced meteor-defense systems. The worldlet would completely orbit the star once every 9 days.
  
• EDIT: As hallerlake rightly pointed out, the orbital velocity is actually the main flaw for this configuration. Since the escape velocity of a "normal" sun at 1 AU is around 30,000 m/s, anything with a higher orbital velocity would not be able to have a stable orbit without adding (in this case, a LOT of) constant acceleration towards the star. Even if we could find a way to apply this acceleration, I suspect it would require far more energy than we'd have available. Ah well, at least now I know why I've never seen anything like this configuration elsewhere. Gravity is, indeed, a real bitch.
  
• At this point, we could be almost done. But personally, I want my worlds to have day/night cycles, seasons, tides (some theorize that life could not have happened without tides churning up the oceans!), etc. Currently, the worldlet would always be in daylight and have no weather, seasons, tides, etc. To solve this, I added a cylinder made up of carbon nanotubes about 1m thick with a radius of 6,000 km and a height of 12,000 km. Basically, just big enough to surround the plate and spin. Connect it to the plate by two "rods" from 2 sides of the plate to the top and bottom of the cylinder. The top and bottom of the cylinder are not solid, but simply made of a few sets of crossed "girders" that connect in the middle (where the rod from the plate is attached).
  
• Spin the surrounding cylinder at about 1 rotation/day. Coat the outer surface with photovoltaic cells (or some other high-tech energy capturing material) and the inner surface with an energy radiator material. Approximately half the cylinder is essentially transparent while the other half is opaque. As it spins, it emulates a day/night cycle. In addition, by controlling the amount of the cylinder that's opaque over the course of a year, you also give the worldlet seasons. During the night cycle, the inner surface of the cylinder can be made to show a simulation of a night sky or whatever else is desired. Finally, tides can be simulated by moving plates at the bottom of any large bodies of water (like a wave pool at a water park ... on a gigantic scale). The only thing I can't figure out how to reasonably simulate is tectonic movement and earthquakes. Of course, I'm not sure they're really beneficial, so I'm not too worried about it.
  
• EDIT: of course, after posting this, I realized there's a much simpler and more efficient solution that doesn't require an awkward surrounding cylinder. See Version 1B below.
  
• As an added benefit, because the surface area exposed to sunlight at any point in time of the cylinder is slightly larger than the livable surface area of the worldlet, meaning that we can potentially get about 144% efficiency. By comparison, Earth has about a 50% efficiency at capturing solar energy because only half the surface area is visible at any one time (Of course, if we covered the Earth with energy-absorbing material and shared the energy between the day and night side, we could get 100% efficiency). But having a absorbent surface area larger than the livable surface area means that we can actually get BETTER efficiency per square meter than we could on a normal planet.
  
• Now, add 67,139 more of them side by side with your first worldlet with a gap of about 2,000 km between each one. You now have the equivalent of a non-rigid Ringworld. Since each worldlet has a livable surface area of 1x10^14 m^2, this would give you a total usable surface area of 6.7 x 10^18 m^2 (approximately 13,163 Earths). Not quite as good as a rigid ring made of one piece, but it's close.
  
• Finally, the tricky bit. We make many rings like this, enough to completely surround the star. The reason it's tricky is that we can't just make a globe of parallel strips because only the equatorial strip would be stable. Gravity acts like a point source, not a cylinder and thus each strip needs to form a ring at the "widest" point of the star (this is why Dr. Michio Kaku's Dyson Sphere configuration he talks about here is impossible). So we make the strips at slightly varying distances (some less than 1 AU, some greater, but overall equalling an average distance of 1 AU from the star). Think of a ring, then place another ring JUST inside it, skewed slightly, then another, etc, until the entire surface of the sphere is covered. Of course, this also means that every 4 1/2 days or so, each worldlet (except the innermost ring) will have an eclipse as it encounters the ring inside it. Some small energy loss, but fairly negligible. Of course, this is an extremely complex set of orbitals and it wouldn't take much at all to cause a devastatingly destructive chain reaction of collisions, but that's what high tech is there to prevent - either through powerful stellar propulsion station-keeping engines or advanced matter-disintegration defense systems.
  
• All this together gives us a non-rigid Dyson Sphere with a surface area of about 328,190,747 Earths. Not as good as a rigid shell, but unlike the shell, it's theoretically possible and gives 144% energy efficiency. It probably doesn't capture quite 100% of the star's output as there will likely be small gaps here and there, especially between the worldlets in each ring, but it will be close. As a final downside, though, the total mass needed to construct this Dyson Swarm is 1.05 * 10^30 kg (about 2/3 of that needed for a rigid shell) - again, more than the total mass of all the planets, asteroids, comets, and dust in the solar system by a wide margin. Matter would have to be "imported" to construct this shell.
  
• Note that to figure out how many habitats "fit", I'm basically covering the surface of a sphere with rectangles (or squares in Version 1B). This is not an easily solvable problem, so far as I can tell, and there's no magical formula I can find that tells me the best percentage of space that will be usable (unlike packing circles onto a sphere in Version 2). To deal with this, I decided that the 1km gap on each side of the worldlet would not have to be strictly maintained. Thus, some habitats would have less of a gap than others. This allowed me, with better confidence, to give a good estimate of the number of worldlets that would fit. As a side benefit, it also allows a slightly greater percentage of the star's total energy to be captured, but with a downside that the orbital mechanics become even more prone to devastating chain reactions from a collision that knocks a habitat from it's orbit.
  
• Visually, standing on the surface of one of these worldlets, the view would probably look fairly familiar - except for the high mountains completely surrounding you. The good news is that a square surface area surrounded by a barrier is EXTREMELY easy to program as well as visualize in a game. The only interesting thing would be the occasional eclipse and possible sightings of rings inside your own. However, at the distance scales involved, it's highly unlikely the human eye would be able to see anything in the sky. Unfortunately, this is exactly the opposite of what I was going for, so ... on to idea number 2.
  

Dyson Sphere Configuration 1B - Dyson Swarm with Cubes

Almost exactly like Version 1, except that instead of having a cylinder surround the plate/walls structure, just put a ceiling on it. This makes a number of things more efficient and the overall size of the worldlet smaller, meaning that more can be crammed onto the sphere, meaning more livable surface area. In addition, while the walls would keep the atmosphere in 99.99% of the time, there would still be leakage over time - a ceiling prevents even that problem. There is, however, one drawback, but I think it's livable - more below.

• Place a 1m thick carbon nanotube ceiling over the structure. The ceiling will ALWAYS face directly at the sun. To gather energy, we could go low-tech and just make the ceiling transparent all the time, but use mirrors in front of the ceiling to gather energy and then a series of mirrors to bounce the light around and shine onto the worldlet surface at specific times and strengths to emulate day/night and seasons. This is much the same idea as the McKendree cylinders in Configuration 2. Alternately, we could go high-tech and make the outer surface of the ceiling coated with an energy-absorbent material and the inner surface with a programmably energy-radiant material (like the surrounding cylinder in Version 1A).
  
• The drawback to this method is that because the ceiling is only as big as the worldlet and doesn't surround it, the sunlight-exposed surface area is less. We still have an efficiency of 100%, but that's not quite as good as 144% as in Version 1A. We COULD make the ceiling larger than the floor to give it more energy-gathering surface area, but that gets a bit awkward. If greater than 100% efficiency is desired, it's a viable option.
  
• Make walls into flat 1m thick panels instead of 10km x 90km pyramids. I only had them as pyramids to increase structural strength because there was no supporting ceiling. Now that there is a ceiling, the walls can be made into 1m thick carbon nanotube panels, just like the ceiling.
  
• Because we don't have a surrounding cylinder, the "footprint" on the 1 AU solar sphere is smaller and thus we can fit more habitats into solar orbit. In this case, while still leaving a 1000 km gap on each side, we can now fit approximately 1,952,981,800 worldlet habitats into orbit, giving us a total livable surface area of approximately 382,889,205 Earths. Better than Version 1A, but still not as good as Version 2. Unfortunately, even though we're now using less mass per habitat, we have even more habitats, so we end up needing even more total mass (1.09828 x 10^30 kg).
  
• The view from the surface would still be mostly the same as Version 1A, with one notable exception. If we made the walls transparent, then standing on the edge of the world really WOULD look like you could step off and fall into the void. Something which I'm sure would give lots of material to play with to primitive or fantasy-based religions. However, due to the size of the worldlets, this view would only be visible from very limited regions, so overall, it's still not that much fun.
  
• Of course, we could always coat the inner surfaces of the walls (and possibly ceiling) with a programmable LED-type material and show anything we want. World as holodeck. Fun.
  

Dyson Sphere Configuration 2 - Dyson Bubble

The second idea is a bit more mundane and has fewer problems, but still requires tech much advanced than we have now.

• Create a McKendree Cylinder with any desired radius from 4km to 1000km (about the theoretical limit of what carbon nanotubes will support) and a length of 3.8 times the radius and a thickness of 1/1000th of the radius (like the swarm above, the outer surface is covered in a thin layer of carbon nanotube material and the rest of the thickness is standard rock, soil, etc.)
  
• Spin the cylinder around its length-wise axis at a rate that would give an internal centripetal acceleration of 1 gravity.
  
• Place the cylinder so that it's top is facing directly toward the star.
  
• Place many more cylinders in the same relative configuration around the star - leaving a gap equal to the cylinder's radius between each neighboring cylinder. What you'll end up with is basically like a spherical pin cushion with needles poked into the cushion and covering 100% of it's surface area.
  
• Now give each cylinder a way of station-keeping movement (either engines or tractor beams or what-have-you) and program them to behave very similar to Boids so that each one keeps it's distance from all neighbors and keeps within a set distance (1 AU) of the star. This is the tricky part of this configuration. The current bubble configuration listed on the wikipedia page requires a light-sail with a MUCH larger radius surrounding each cylinder that would perform this function. The problem with that is that it places pretty severe limitations on the size of the habitats, drastically reduces the number of habitats that would "fit" and would use most of the star's energy simply to keep the habitats in place (in fact, the best light-sail Dyson Bubble configuration I could come up with only had the surface area of 39,207 Earths - abysmally low for the effort required. Though on the bright side, the total mass needed is well within reason (2.14843 x 10^20 kg)). In essence, without the tractor-beam tech, the Dyson Bubble is extremely inefficient and not a very viable option. With it, however, it becomes one of the best configurations.
  
• EDIT: After some more thought, I suspect this need for constant station-keeping acceleration may end up being the primary flaw for this configuration. Even if we could find a way of propulsion that didn't use up internal mass (or could possibly recapture and re-use it), it seems likely that it would still require energy. The amount of energy needed to keep the cylinder in place around the star may be more than is gathered by the habitat. Since we don't currently have such a propulsion system any notions about how much energy our theoretical propulsion system would use are also..theoretical. Thus it seems likely that with this configuration, we would end up having to give up livable surface area to dedicate to energy-gathering nodes that would gather power for the propulsion systems to keep things in place. The original light-sail configuration is suddenly starting to make more sense. Of course, for the purposes of the game, this is irrelevant, but it's still frustrating.
  
• Even with half of each cylinder's internal surface area unusable, this still gives a total usable surface area of 475,027,190 Earths - pretty close to the ideal of a Dyson Shell (551 million). The only reason we don't get full 100% coverage is because we are basically packing circles onto the surface of a sphere and that leaves gaps. The best we can get is about 90% coverage (see here for more details).
  
• Of course, we COULD make each cylinder longer and that could increase the available surface area far beyond a Dyson Sphere. The only problem with this is energy efficiency. Because the surface area on the top of the cylinder is the only place where sunlight hits, the energy absorbed here has to be spread out over the internal (livable) surface area of the cylinder. A length of 3.8 times the radius gives us an energy efficiency of approximately 100%. If we make the length equal to 8 times the radius, we would also increase the available surface area (to a whopping 1 BILLION Earths!), but would go down to 47.5% efficiency (although that may not be so bad as that's almost as good as Earth's).
  
• Weather inside each cylinder would be nonexistent unless we intervene, but I'm assuming we can do so to simulate seasons. Also, like the Swarm, we could create giant wave pools to simulate tides. Day/night cycles are a bit trickier and we would have to use mirrors to bounce the light into the lengthwise sides of the cylinder - but it's possible.
  
• Of course, another thing that makes Dyson Shells interesting is that you could theoretically travel all the way around it without encountering space. In both the swarm and bubble configurations, this is not possible. The solution of course is to have each habitat have 1 or more stargates. I figure that with 1 stargate per 100 km^2, you'll need somewhere between 1.67 x 10^31 (for the swarm) to 2.42 x 10^31 (for the bubble) gates. The good news is that the total number of DTD codes possible would JUST fit into a 32-bit integer for a swarm, so your codes would only be 8 Hexadecimal numbers. However, for the bubble configuration, you'd need 33 bits, which would likely mean that you'd end up with a 64-bit integer and thus 16-digit hexadecimal stargate DTD codes. Yuck.
  
• Interestingly, no matter what radius you choose for your cylinders, the total surface area around the star is the same (which surprised me). However, the smaller the radius, the smaller each world becomes (making for less interesting politics, etc), but conversely, the less mass overall is used. For example, if each cylinder has a radius of 4km, the livable surface area inside each cylinder is only 191 km^2 (and it would take 1.27 x 10^15 habitats to make the full bubble), but the TOTAL mass needed would "only" be 1.1846 x 10^28 kg (still more than the mass available, but it's at least a couple orders of magnitude less than the worldlet configuration). Of course, Oblivion's game world only has a surface of area of 41 km^2, and that seemed pretty huge, so in the context of a game world, small cylinders may be perfect. However, if we increase the radius to 1000km, we get a usable surface area of 11.9 million square kilometers (almost the size of Eurasia) and "only" need 2.03 x 10^10 habitats, but would need 2.96 x 10^30 kg of mass (almost double the entire solar system, INCLUDING the sun!)
  
• Standing on the inner surface of a McKendree Cylinder would give you an interesting view. In fact, it's one of the more unique views I've ever seen and well worth putting into a game. Mission successful!
  

Anyway, it seems my brain is back, which makes me very happy.