While working on the math for this stuff, I keep coming back to notions of "magic" numbers. There are very defined numerical parameters that we can spin our own abstract tapestry. What's most unique about this project is what defines those bounding parameters - they almost all come down to human biology. Why is a gravity balloon a certain size? Because humans need a certain pressure, and this combines with the _fundamental_ gravitational constant to produce a tangible number.
All this reminds me of the notion of "god" units, or Planck units. The fundamental units span the full range of physical values. Because of this, you can measure practically any complex quantity as a combination of the fundamental ones - like volume.
People units constitute a rougher and more gray set of fundamental constants. Combining the gravity people need with the air properties they need, you can get the characteristic height of Earth's atmosphere, but there are lots of other ways you can come up with different length units.
Minimum Size for Friction Buffers
Lately on NASA Spaceflight forms, I've seen artificial gravity inside of balloon envelopes come up. This has a rather strange similarity to what I've talked about in this blog. The motivations given for this design are predictable - space stations can continue to be thought of as a nice inertial frame of reference, like the ISS, while adding centrifuges in a limited domain. The basic idea is to take a large Bigelow module and put 2 counter-rotating centrifuges. The two can be spun up at the same time so they have minimal effect on the rest of the station.
The minimal effect principle is an objective very much worth pursuing. For near-term space stations, we will expect many roles to be fulfilled by the station, and external operations can not be compromised for the logistics of a spinning module. In this context, it's hard to imagine that anything other than a fully enclosed centrifuge can make sense.
But where does this lead us? Operationally, I can paint somewhat of a picture. If you moved around in such a centrifuge, vomiting seems inevitable. However, limited time spent for the purpose of maintaining health seems possible if you limit people's activities (and compare to the fact that they'll be feeling sick anyway). But what about drag? For something just a few 10s of meters, it's likely that you would leave the annular space alone between the centrifuge and the balloon wall. But at what size will it make sense to add any friction-reducing buffers? It depends on how much energy you're willing to put in, but it seems simple to compare this to the energy expenditure of other station systems.
That sounds like some pretty low-hanging fruit for developing a practical case for more investigation into this tech. Importantly, some push into this area would raise some obvious experimental pathways to establish the friction buffer sheet stability.
Stability of the friction buffers is a tough topic, so it makes sense to give up on the analysis and defer to experimental evidence at some point. Fortunately for us, the available fluids helps to make the problem easier for us. Air is a low density and low viscosity fluid. Water an extremely obvious stand-in for scaling based on similar Reynolds numbers.
I have two types of things in mind:
sheet Reynolds number
true scale model
You could scale the entire system of an artificial gravity tube by selecting an experiment geometry that is exactly similar to it but on a tabletop scale. In practice, however, this leads to sizes or speeds and torque that are just not workable. This could not be a tabletop scale experiment.
Instead, it will make more sense to emulate the separation distance and speed of the friction buffer layers, and see how the multi-sheet stability looks with different kinds of configurations.
Problem with all Center Connections
I misspoke somewhat in my previous post introducing transport of commodities. I had presumed that some commodities could be sent through connections that existed exactly on the axial line. This can not possibly be the case.
It is an easy mistake to mistake. You can simply imagine that cargo moving through the center can move slightly to the side of the axial line itself. The rotation speeds will not be substantial for a great distance beyond this, and the weight itself would not be overly burdensome. The problem comes when you realize that the rotating part... well... rotates. You can't simply move cargo to the size of the connection and move it along, because the line (pipe, wire, etc.) going to the colony rotates. If the cargo stalled inside of the plane that this line rotated in, then it would collide with the line.
This seems impractical in my vision of the economy. It would be far better to keep the center-line of artificial gravity tubes completely empty aside from rails which which cargo is moved along with. The challenges for connecting at a larger radius for power, water, information, etc. are completely solvable. Transit of bulk materials is much trickier, so the center line would need to be reserved for these activities.
Relative Movement of Tubes and Balloon
I must take some time to argue with myself on the subject of how the artificial gravity tubes move relative to the balloon "wall". The most simple solution is that they don't move. Actually, this is quite practical in terms of the inflation physics. Halting the rotation of an asteroid in general isn't a hard problem. With a strong tether, you can dangle a large rock from the equator, slowly releasing it to a large radius, pulled by the rotation of the asteroid. This is a cheap way to expel a great amount of the asteroid's rotation. You may still keep a small amount of rotation to stay sun-synchronous. The inflation process itself also reduces the rotation speed. The only cases where this is not practical are small asteroids. Those will be easier to manage in general, and will probably have rotating joints for electric connections.
So I envision artificial gravity tubes fully tethered to the wall. This will help to keep them suspended in-place inside of colonies with insanely huge scaling. It will also develop a hard electrical connection between the tubes and solar panels that may lie out the surface of the asteroid (or slightly off). Things can be balanced by a tether at the asteroid-sun L2 and L1 points (these are not impractically far away either).
Because of this, I will personally have to abandon the idea of the geosynchronous washer-shaped radiator. It's better to not rotate and tie the tubes to the walls (if sufficiently large).
Pressure Management and End Seals
Friction buffers are not rigid. I mean, they're monstrously huge. Instead, they would maintain their shape by having some positive pressure inside of them. Note that this positive pressure is relative to the next outer-most friction buffer sheet. This constitutes some fluid management constraints. Keep in mind that air pressure changes with the rotational acceleration (like a gravity gradient). Because of this, we can draw a graph of the pressure over an outward line from the axis to somewhere on the surface of the outermost friction buffer.
Are there any complications with this scheme? Of course there are. The ends are pinched, remember? As you get closer to the end-cap, the friction buffer sheets pinch in as well. This means that the acceleration gradient will be more gentle. In the limit case, consider that the outer-most sheet is almost stationary, but the 2nd outermost sheet is rotating very slowly. Going from the outside to the pinch point will be a small change in pressure. On the other end of the spectrum, the air pressure changes a great deal from surface to axial line inside the tube itself.
We would like to equalize all the different pressures around the end seals (this would make it easier to seal, clearly), but this isn't possible due to the pressure demands of the friction buffer layers at their full radial position. The real problem comes at both ends of the tube where we should maintain a negative pressure inside the spaces between the friction buffers. Positive pressures are easy, negative pressures are tricky. I'm not sure exactly how this problem would be solved, but I think there are a lot of tricks to mitigate the challenge.
To be clear, I think this is one of the biggest problems for the viability overall. It probably comes somewhere close to the stability of the buffers in general.