## Monday, April 11, 2016

### Small Balloon-Tubes Systems, a Gauntlet of Wires, and Sucking Sheet Pinches

This is a fairly general brain dump of a collection of topics. I could see them all being posts, but not all of them are likely to become posts, so I want to get them out while the concepts are fresh in my mind.

## People-Units

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.

## Scaled Experiments

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.

1. Hi Alan,

I've been keeping up with your blog for a while and I'm glad to see some update RE: the friction buffers! They're one of the parts of your design that I'm most intensely curious about, as I'm writing a science fiction story featuring open-air centrifugal habitats and your project has been a very useful resource, which I will definitely credit you for!

If it's not too much to ask about, though, I have been somewhat stumped in one area trying to figure out how your colonies work. I know you have acknowledged previously that the friction buffers are very much a work in progress, so I'm not questioning those so much, with my limited fluid physics background.

But I've read through (I think) all the posts on your blog about open-air rotating habitat design and I can't seem to find anywhere where you explicitly specify how the innermost centrifuge (the 1g cylinder) is supposed to maintain its spin.

You've mentioned attitude control fans, if I recall correctly, for each whole colony; but I remain unclear on how the inhabited cylinder itself is supposed to spin up in the first place. I can't imagine that the innermost cylinder has some propulsive engines attached to itself which impart torque -- the only way I can imagine engines/fans being mounted to the innermost cylinder is via placement somewhere around the circumferences of the end seals, in order to blast air out of the colony; which I would imagine may interfere severely with inter-colony transport, if nothing else.

So where - and how - is the thrust generated to spin up the innermost, 1g, cylinder, and to maintain that spin? Is the inhabited cylinder supposed to push against the buffers/sheets somehow? Then the outermost sheet has some kind of engines mounted on it, to counteract this force and keep the outer sheet stationary relative to the air?

Hope that's not too much.

1. Awesome! Thanks for your comment. You have a good question which I have glossed over (and when I have hit it, I think it was in a tangential and confusing way). I believe I have a good answer, and it can mostly be summarized by two mechanisms: tethers and motors.

You are 100% correct to imagine that the torque must be transmitted through the openings on either end. In fact, this will factor into the design for commodity transport that I've been writing about lately. It is impractical to either spin the tube up before installing the friction buffers, or have some force action through the multiple layers (keep them passive). By restricting the action to the end openings, we are magnifying the gross force that must be applied by something like a factor of 10 (but this is not a problem).

When running some calcs before, I came up with a torque similar to a large construction truck's axle that is necessary to keep the tube rotating in steady-state. I have not looked into the times and power levels needed for the initial spin-up. However, it should compare favorably to colonies inside of vacuum because the floor contains less mass. Larger radius tubes take longer to get spinning as a law of nature. Obviously you power the motors by electric power from PV panels on the outside of the asteroid or a nuclear reactor.

How do we transmit these forces, and where do we transmit them to? For small constructions, you connect tethers to the wall, and pull on those. These must be anchored deep into the asteroid rock (because the asteroid material is weak, maybe even squishy). The force transmitted through the tether will be large, but not crazy. For a single colony, perhaps it is similar to the breaking strength of a common seat belt - or the force needed to lift a decent size truck on Earth. These are small potatoes compared to the immense scale of the colony.

For larger constructions, every tube must have a partner tube that spins in the opposite direction. To obtain rotation, they must push & pull against each other. O'Neil wrote about this (Island Three, I think). When you use anchors in the wall, you only need tension, while the buddy system needs a limited compressed member (slightly more expensive). Both buddy tubes spin up at the same time, and both spin down at the same time.

To picture the motor and connection, I think of the motor as existing somewhere in the clutter of systems right around the end openings. Ideally you want to connect the tethers at large radii, so the supporting structure will either be as large as the end opening itself, or will connect to a stationary steel scaffolding that surrounds the friction buffers. Inside of the tube, there will also be some strong steal beam scaffolding that transmits force through a cylindrical pattern in the middle with the same radius as the end opening. From there, there may be multiple tethers that connect to the ground at a slightly oblique angle in order to minimize the forces involved. These tethers and structures inside the tube should double-up in their purpose with transportation systems, skyscrapers, and elevators. The forces for dealing with rotation will be small relative to the forces due to centrifugal acceleration. For the contact point, you could imagine wheels making contact on a track connected to the steel scaffolding that goes through the middle of the tube.

2. Thank you very much for the detailed response! I am drafting a (web)comic so I want to be certain of the details as I want to visualize these structures in depth. To that end I've come up with some sketches - would you say these accurately capture the basic idea of what you're describing? I see in retrospect I probably should have extended the scaffolding further into the cylinder and added some interior tethers, for minimization of force as you specify, but hopefully I'm getting the gist of it right.

1. Partner Cylinders
2. Tethered Cylinder

Should you wish to entertain it, I'm also curious to hear your thoughts on a related worldbuilding question. Although my setting will likely feature gravity balloons as well, one of the locales I focus on in the story is a habitable gas torus a la The Integral Trees (the long-term stability of which raises a plethora of questions on its own, I'm aware, although I lack the knowledge to work out any non-handwaving solutions). In this story, the gas torus is located at the Roche limit of a warm Jovian planet rather than a neutron star, formed from the breakup of a volatile-rich moon; the inhabitants of one of the Jovian's intact moons then make use of the available microgravity air to build open habitats.

Setting aside any discrepancies of the setting itself (although input on those is certainly welcome, if the thought interests): might it be physically feasible, if economically non-preferable, for the stationary outermost friction buffer to be rigid?

I ask because the setting is meant to allow various free-flying "station-states" to engage each other in aerial combat. I presume some desire for armor to protect the other, thinner friction buffers, and perhaps to keep natural debris from impacting the sheets, carried by the wind. These stations will be built in partner pairs, of course.

3. Holy moley, those are incredible! That illustrates the notion extremely well. The only comment I could make is that the "tether type" looks like it's geared to rotate either way, because the angle of connection would give it traction to rotate in either - clockwise or counterclockwise directions.

For the outer layer (kind of like a shell), there are several possibilities and I have a few distinct functions in mind. These may or may not be relevant for your own design. Firstly, I envision a stationary outer structure that is basically a wire-frame steel structure (which can be used to attach to other things, or as an anchor for micro-gravity travel around it). The friction buffers are solid sheets. For managing global air circulation, I have imagined the outer-most friction buffer rotating at some small speed - probably around 2 m/s. This motion of the outer sheet lets use transport air to the walls so it can reject heat. A stationary steel wireframe is helpful for navigation in that case (because otherwise there is no stationary frame of reference). In a dual or quad system with additional sails, you could even use that motion to move the colonies around the balloon. Take that for what you will, because letting them move untethered obvious makes it difficult to maintain wired electric connections or whatever else it needs to share with other tubes.

Of course, the most simple concept is to tether the outermost sheet itself in place. This lets the air stagnate, which has good points and bad.

4. One more thing - could I post those images? Do you have some links to what you're working on?

5. Sure - feel free to repost the above linked images. Thank you! I hadn't realized about the gearing of the tether connections - I'll keep that in mind in the future.

I maintain a blog at Accelerando on tumblr for my content; my primary project is called the Alsiverse, and the gas torus is called The Mashveya. I'll keep the steel wireframe in mind for sure, as well as tethering the outer sheets together - I'd visualized the latter in an earlier concept sketch already (along with compressive members, which I assumed might be useful as a safety precaution).

For clarity if you read further: a "gimmick" of the Mashveyan setting (as well as the broader star system it resides in, Alsifer) is that very little if any electrical technology is in use, something which I've been wrestling to make plausible for a spacefaring society. I may ultimately end up giving up the idea, but it's a concept that captures my imagination nonetheless, hence my cylinders' diesel-fueled rotation mechanisms among other things.

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