Penumbra Station

[AlanSE]

I want to put out there an artificial mega-structure concept. Specifically, a design that would be an attractive option for civilizations between around 1.0 and 0.75 on the Kardashev scale, who get energy from solar power around a single star. My thinking for this centers around the following goals:

• Optimization of energy production
  
• Maximization of civilization density
  
• lesser goal: minimization of materials to build structure
  

These are conflicting goals with trade-offs between them. Solar power is a diffuse energy source, and that's another reason for this fairly fundamental concept. You could say that even Earth faces that conflict, since people are pushed toward high-density cities for economic reasons, yet resources are dispersed throughout the world. Even in the extreme of an alien race that is just computronium, there is a computational penalty for greater parallelization (versus single-threaded) processing.

If you're building anything short of a Dyson Sphere (consider the satellites in a Dyson Swarm), then there's a certain natural shape that you would likely use, and that is a conical shape that is formed by the shadow of a circle facing the sun. This shape maximizes the heat rejection radiator area relative to the area receiving direct sunlight. Designs of various proposed solar probes reflect this shape. Here is a gallery of some old work of mine, along with an old NASA sketch of such a probe.

http://imgur.com/a/J0qnj

For some specifics, let's start with the heat radiator. Human technology is going to work best in the range of room temperature (an assumption you are free to relax for your own versions of this). Thus, I will peg the radiator temperature at 293 Kelvin. If the radiator is a well-designed perfect blackbody, it will radiate at a power of about 420 W/m^2. Our constraint is that our radiator can't reject heat any faster than this, so that limits the maximum incoming sunlight can be, and thus, the minimum radius we can orbit the sun at. I find this to be about 0.25 AU, slightly inside of the orbit of Mercury. In our own solar system, it might make the most sense to build the station in some stable orbital location relative to Mercury.

Let's consider the implications of this. The solar flux incident on the station would be 4^2=16 times what we get on Earth. One way to rephrase this is that you would have to build 16 times fewer solar panels to get the same energy output, compared to Earth orbit. The habitat could be logically situated near the tip of the radiator cone (facing away from the sun), and receive power through ordinary power transmission lines with ruthless efficiency. As far as I can see, this is the only way (short of fusion power) to deliver such a high throughput of power to such a small space. That could be the exact thing that an advanced civilization wants. Picture all of the sunlight energy incident on Earth, collected in an area with 1/4th the diameter. Then, the electricity produced from that sunlight is delivered to an area much smaller than that.

On to some fine tuning... since I first looked into this, I have strayed away from a dual-cone approach, to preferring a single cone. The solar panels could be on the inside surface of the cone (but still oriented toward the sun). This incurs a penalty factor of 2, which means you'll have to either build twice as many solar panels, or build their equivalent area in reflectors. My rationale for this setup is that the energy collectors can be located right next to the energy sink. This way, you could avoid any long-range heat transfer to cool the solar panels, and even conduction through normal metals may suffice. This will cause the panels to be arranged in a "stair step" pattern along the cone's inner surface, with the stairs being limited in size to around a meter or less.

The habitat, on the other hand, will have its own unique issues for heat rejection. It might make more sense for it to have its own radiator. There is a possibility to connect it by a tether to the cone (which also contains the power cables) in order to give it space for its own radiator, while also keeping the structure tidally stabilized.

Thanks for entertaining my brain-dump on this topic.

[stevebowers]

Welcome back, Alan! I assume these conic habitats are tidally locked to the sun somehow, so that the cone always points towards it. Any thoughts on how to maintain the orientation?

In some respects the O'Neill Island 3 design is a kind of partial cone, with mirrors on the internal face to collect sunlight. These cylinders would be coupled in pairs to allow the cylinders to maintain their orientation mechanically.

[selden]

If an orbiting body has a mass distribution sufficiently non-spherical that tidal forces are significant and isn't rotating otherwise, then over a long period of time it'll naturally tend to go into tidal lock with the long axis pointing toward the central body.

[stevebowers]

In a circular orbit, this is true; but what about a satellite in an eccentric orbit? The Jenkins swarm configuration consists of objects in orbits with a quite high eccentricity, around 0.6; much of the time a cone in such an orbit would be pointing towards the empty locus.

[selden]

In that case, "obviously" some kind of active control would be needed (momentum wheels? coupling to an external magnetic field?). I'd be concerned that the energy needed for that might, in some cases (depending, for example, on the mass of the satellite, its distance from the primary, etc), exceed the external energy supply.

[AlanSE]

This doesn't work well with less-than-perfect orbits, because the angle of the penumbra is on the order of 1 degrees (although it depends on where you are). So I lack any idea of how a non-circular orbit could keep it aligned well enough to make sense. Even in a tidally-locked configuration, it would need to be kept free of much oscillation, but for a true megastructure I don't expect this would be much of a problem. In our solar system, gravitational interference from planets could be a problem.

[stevebowers]

Why is a 1 degree angle optimal for a Penumbra Station? I'm not disagreeing, just curious.

[stevebowers]

If your design needs a perfectly circular orbit, then maybe a snailshell configuration might be best. This consists of numerous objects sharing a single orbit, (basically an 'orbital band' in OA terminology) surrounded by several similar bands in larger and gradually tilting orbits. Here's an illustration of one by Anders Sandberg;

Early in the construction process, only a few bands are filled


later in the process the bands form an almost complete shell


I used the 'snailshell' configuration for the Black Acropolis in OA, incidentally.
Unfortunately the snailshell suffers quite a bit from self-shadowing, and the mass distribution looks a bit asymmetric- which might make maintaining a perfect alignment a bit tricky.

[Drashner1]

A few random thoughts here:

1) Are perfectly circular orbits actually stable in nature? My understanding was that pretty much every orbit we find is an ellipse, not a perfect circle. Not sure if our satellites fit into this or not.

2) If the cone stations need to be stabilized, perhaps you could do one of these options:

a) Link them in counter-rotating pairs just like an O'Neill hab so that they stabilize each other. If the linking mechanism is of sufficient size, there shouldn't be issues of shading or the like.

b) Instead of putting them in orbit around the star, suspend each station using statite technology. Actively controlled solar sails hold the station stationary in relation to the star rather than being in orbit. Of course you'd lose a certain amount of area to light sail instead of collector stations, but perhaps you could use the sail as a power sources as well, either by making it operate as a solar cell or by reflecting light onto some kind of thermal power station.

Just some thoughts,

Todd

[AlanSE]

Reading the last batch of comments here, I see some very valuable feedback. First, let me cover some of the sun-shading physics, as per stevebowers comments.

Why 1 degree? Because that's roughly the angle that the sun occupies in our field of vision. That's the entire point. The "dark" portions of the station, which radiate heat, will see absolutely no light from the sun. That means that your radiator is exposed to a perfectly cold vacuum, as if it were in the middle of space.

Get closer to the sun, and this angle increases (and the penumbra cone becomes a fatter shape). Go to a larger radius, and the angle decreases. At every given radius, the taper angle of the penumbra station is proportional to the angle that the sun occupies in the field of vision at that radius. A penumbra station is also the coldest possible temperature that something can be at that radius, given a constant efficiency of their energy conversion systems from the sun-facing side. The maximum energy the station can consume is limited by the Carnot efficiency, which is hyper-sensitive to the temperature of their heat reservoir.

If your design needs a perfectly circular orbit, then maybe a snailshell configuration might be best. This consists of numerous objects sharing a single orbit, (basically an 'orbital band' in OA terminology)

Limiting the discussion to a single orbital band of formation flying, there's a problem with the energy-efficiency. Picture a cone right next to another cone. The surfaces of both of them are acting as radiators, giving off the station's heat into space. But being right next to its neighbor, a lot of the radiated heat will hit the neighbor's surface, thereby warming it and hurting its effectiveness (limiting the energy the station has access to). Because of this, "crowding" the orbital neighborhood defeats the point of penumbra stations. So as you approach a 2 on the Kardashev scale, it makes less and less sense.

But an orbital band leads to a fascinating revision of the concept. Instead of individual cone-shaped stations, it would be more efficient to make it a fully continuous ring with a cross-section which is a skinny isosceles triangle. It would be a wedge-shape that continues in a full circle around the sun. I believe this have slightly worse energy economics than a single penumbra station, but it would have other advantages.

As for the orientation issues...

The reason I see it as an issue is because I keep thinking of an Earth-sized station. For any small station (like the ISS size), fine-tuning attitude a few fractions of a degree over the course of a year is completely trivial. For a large station, I don't think you even need gyroscopes per-se (like Island Three, that's a big gyroscope after all). You just need a superstructure that is tidally-locked, and then some counterweights that can move in the opposite direction of what you need. Gyroscopes (momentum wheels) would still work, and so would a number of technologies, so it's just hard to say what would be best.