Monday, May 16, 2016

Massive Topic List with Half-Finished Writings on Gravity Balloons

NOTE: extremely meta post follows.

Several past posts have been a dump of a large set of topics all balled into one. Now, I would like to do something different. I have used a text file as a staging area where I battled ideas against each other (in terms of where they rank in priority) and also just spitball ideas to see what sticks. While I still like to do these things, I'm depreciating the text file as a tool. I would rather keep the extremely premature ideas on the back of a napkin (or email draft), and use the blog itself as a better format for medium-low effort writings.

Even so, I still have that massive backlog of stuff that I never got to finishing. In my personal philosophy, I want to follow the open source model, and just let information free whenever there's no compelling reason not to. So here it is, my newly retired backlog:

If I'm too wordy in my general writings, then there won't be much of interest in there. Nevertheless, not everything is terrible, and I'm always somewhat taken aback when I read my old writings. It might be nice to polish it up and put it in a nicely displayed format (at least with working links). But let me just go through and dig a few things out of the dredges...

Small Gravity Balloons

 I attacked this concept from several different angles. One specific scale I was interested in was 1 km size asteroids, since these get closer to the NEA territory. Air pressure might still be used to resist against self-gravitation or some other uses, but exactly what is an open question.

Stability Topics

Nothing I've posted has come close to an exhaustive accounting of the stability topics which span from the gravity balloon part itself, to the internals, to the friction buffers. Then, multiply some of these by all the different size classes. Every problem you look at, you can probably think of at least five different mathematically simplified cases. Each one of those problems could have an enormous amount of analysis, and even radically different formulations.

Phobos Reference Values

The moon of Mars is just too interesting to give up on. But fairly small, and also close to the Roche Limit, this moon also presents a host of different mathematics that can complicate its scenario. In spite of that, there is still a strong motivation to give definite values for some kind of maximally populated colony.

Space Development Plan

Where does the gravity balloon exist within some kind of space roadmap? There are some efforts to make a detailed space development roadmap (I have one in mind that was on Kickstarter). These can offer an interesting starting place, but may be too near-term to have much connection to gravity balloons. The NSS also has some interesting roadmaps that involve extremely far-reaching development goals. I am interested in making an ordering. What is likely to happen before a gravity balloon is built? What is strictly necessary?

Cross-Structures in Artificial Gravity Tubes

Unlike most artist illustrations and typical guidance from 1970s era concepts, the artificial gravity tubes inside a gravity balloon would be extremely friendly for developers who want to build skyscrapers straight across the tube. In fact, it would be necessary if the mass was not evenly distributed (this is more important for gravity balloons, since the shielding mass isn't integral to the hull, making the livable structures relatively heavier compared to the walls).

Lower-Gravity Tubes and Microgravity Industry

Where would sewage processing happen? Probably in tubes that don't have the burden of friction buffers (accomplished by spinning at very low rates). This seems perfectly fine for algae and other smaller and easy to manage husbandry of animals, etc. What other industry (like shipyards) would happen in the microgravity (but not airless) space? Probably lots.

Procurement and Management of Air

I address "air" in the basic physical sense a lot, but the chemical realities of production of air is more challenging.

Other Agenda Items

These topics aren't in that list, because I've only recently been kicking them around:
  • Looking into the work by Dr. Forward in his 1990s (and hard to obtain) books
  • Of course, actually conducting the scaled experiment
  • Inner solar system asteroid Delta V versus mass map (not perfect math, but good-enough with some help from JPL pre-calculated data)

Sunday, May 15, 2016

Tether Superstructure for Large Space Cities

Given a large number of artificial gravity tubes located near to each other, they all need to fly in formation. A common picture of how to approach this problem is to have many orbital habitats in synchronized orbits. Since their mutual gravity is small, they all essentially trace their own ballistic orbit, and for many orbital locations (like some L4/L5 point) lots of stable non-crossing orbits exist. This does require some station keeping because we can not arrange the orbits with perfect accuracy to begin with.

Another approach is to tie together several cylinders together to create a larger space station. Like many of these deep-future scenarios I write about on this blog, massive structures would be much better off without needing manufactured steel beams with high compression strength. At a glance, working around the constraints to achieve this ideal might sound impractical, but it's actually entirely reasonable. I will address both scenarios of 1.) the superstructure inside of large gravity balloons and 2.) a generic case for orbital habitats in typical vacuum conditions. These are quite different, but some of the underlying principles are the same.

Purposes of Tethers

Let's get the first things straight - what specifically the engineering role for a superstructure is.

  • Rotation - spinning up and stopping the rotation of the tubes that creates gravity
  • Contingencies - if a tube breaks, there is a space traffic accident, or a host of other scenarios, the tethers must be in place to arrest the motion and avoid a local conflagration from destroying the entire space city in a domino effect
  • Position - must be maintained against tube-to-tube self-gravitation, external gravitational fields, momentum exchanges from transport, and so on
While this blog might have hit on one or two of these roles, I have never faced them all in any capacity. Elsewhere, I have not seen much of any analysis or reference to the superstructure notion to begin with.


For a small gravity balloon, it might be completely reasonable to pull against a tether anchored into asteroid rock to maintain or start up rotation. On any larger scales, however, you would just use force-exchange with the neighbor cylinders for this task.

Also, let me modify and expand on a statement I previously made regarding wall-connected tethers:
These must be anchored deep into the asteroid rock
Larger gravity balloons will see different physics in this respect. The tethers can be (and likely would be) held in place by the air pressure itself. This will demand some curvature of the wall, as I illustrate in the sketch below.

Going further, there are many many more interesting things that need to be taken into account on larger scales. As scale increases, the self-gravitation effect becomes larger and larger and for something like Virga, you might very need to imagine something like carbon nanotubes in order to keep all the habitats from collapsing in on the center.

Tensioners and Enabling Technology

For the superstructure concept to work, we need some form of control input. I have made several references to the generic type of technology whereby a tether can have slack pulled in (thus making it tighter) on command. This is the control machinery side of the equation - we also need good control signals. Simply put, on a large enough scale, the system must have more give than what simple material properties would allow you.

As a counterpoint alternative, think about what the superstructure would be like if it were made of springs. This could accomplish most of what a control system could otherwise do.

Momentum will be fully looked at as a commodity in this system. This implies it can be stored and transferred from one place to another as needed. There are large-scale balance equations that will eventually be satisfied, and a gravity balloon would presumably have an agency that followed these numbers (like the various energy agencies are to us on Earth today).

A Reference Case

Illustrating what I have in mind - tethers extend from the pressure liner into the habitat. These fork into different directions to connect with the different connection points (and have a curve so they can reach closer to the wall) and also with the rotating cylinders themselves. All throughout the middle space you must imagine a vast number of tubes. Each one of these tubes are connected into the tether network - and the tether network will do the work to hold them safely in place, depending on what the particular needs at the time and location are.

I have drawn an empty space between the tethers and the liner. This isn't strictly necessary because you could just have more tethers connected to the liner. I did not go this route because I assume that additional connections would have an additional cost, but this is not strictly true. So you are free to imagine an innumerable number of tethers extending out from the wall and no "dead space" around the edges. Also, I am burdened by the need to illustrate something.

You must also use your imagination to picture a network of ever-thinner tethers that reaches out to each individual habitat in the entire volume, and connects (eventually) to the superstructure.

Comparison to Vacuum Orbital Superstructures

In the cases I've described, air pressure is the "ultimate" tension force. That allows you to pull something away from the center. In an arbitrary orbital location, tidal forces might be one of the easily available options. Even a space elevator could be an extreme version of this.

Going in another direction, an orbital ring can be used to pull in another direction. Combining tidal and the orbital ring tug, you could arrange habitats in a 2D plane which is essentially a disk around a planet. This structure could hold all the constituent colonies in place. But let me stress that in the radial directions, "anchors" are needed in order to get a good tug on the tether, while operating on habitats that have relatively small micro-g accelerations acting on them.

These could also be very useful for other mega-structure projects, like solar power arrays, or electromagnetic launchers and catchers. These projects might need precise alignment, and you need something with which to act on in order for them to be viable. The disc-type megastructure might be the ideal option for that.

Another option also presents itself (which I have sometimes briefly hit upon), you could have a large bag of low-pressure air that envelops a large space of orbital habitats just for the purpose of holding the tethers in place and keeping tension on them. This would enable massive 3D habitats, but would not allow free-air access to the different habitats. Since the latter (a full gravity balloon) requires access to a large mass source (a large asteroid), many locations would not have that option and may possibly find a space city of this type the best available option.

Thursday, April 28, 2016

Scaled Experiment Metrics and Development Pathway

Stability remains an issue - it is one of the core weaknesses of the proposition for the gravity balloon concept. The issue isn't whether the fundamental principle of laminarization will work, or even necessarily that the channel flow physics are suitable for this problem, but the behavior of a complex and fairly high-energy system.

If you took a simplistic picture of the wedge effect, the prediction would be a slight restorative force for each layer of the friction buffers. The exact directionality of this force gets complicated. It gets even more complicated by the non-rigid nature of the buffers. What we should really raise our eyebrows at, however, is what happens when you consider all the numerous sheets in tandem. Loosely connected dynamic systems can be prone to failure, and this situation seems like a candidate for that. But then again, maybe not. The solution becomes fairly non-trivial.

Due to the complexity of the problem, our only best option left is to perform scaled experiments. Ideally, we would like to use a fluid that is more convenient, in that the same flow patterns can be produced at a smaller scale. To do this, we will look at the Reynold's number.

Re = rho v d / mu

We would like something with a high density and a low viscosity (in particular, relative to air). It becomes fairly obvious that water is our best option for this. Also, you can see that we have 2 dimensions over which to flex our abilities - that is the velocity and the distance metric. Now it seems pretty clear that we want the smallest structure that we can spin at workable speeds.

These 2 degrees of freedom would still dictate a massive scale of experiment, if taken to apply to the entire system all at once. By that, you can say that d is the diameter of the outer-most friction buffer (for example), and that the system will be a scaled model in terms of all geometric dimensions. The enormous cost of this nudges us to seek cheaper solutions that might go 80% of the way with 20% of the effort. In a more accurate accounting, I'm looking for something more like 10% of the ultimate discoveries with 0.001% of the effort.

Obviously, we might instead take d to measure the distance between sheets, while also relaxing the requirement for strict geometric similarity. This might be nice in order to make something testable by reducing the number of sheets compared to the gravity balloon reference design. Thus, the overall scale and velocities will be dramatically less, while still demonstrating channel-to-channel interactions with the same flow patterns.

This still won't be sufficient to make an immediately tenable experiment. We'll need to relax something related to the channel flow pattern itself. The obvious candidate is to change the channel width relative to the overall tube diameter. However, I will not count this as an independent variable, because I think that (for most cases) it will fall out of the selection of the number of sheets. In any format you choose, it's likely that the ratio of the overall thickness of the friction buffer region will be about 50% of the tube radius. So greater channel width will follow with fewer sheets.

Our hypothetical experiment has been cut-and-slashed a lot by this point, but we're not finished yet! What is truly the really important point? What would we want to learn from this? I would argue that it is the interaction of multiple friction buffers in a (generally sufficiently) turbulent flow regime. Even if you cut that out, there's still some value because it answers some questions about this broader notion of friction buffers (which can even have other applications). However, we do want to answer questions about the friction buffers used in a gravity balloon regarding their stability. We basically know that the answer will be different for laminar and turbulent (or at least somewhat independent). Let me illustrate my thinking in a sketch.

(let me volunteer that I know I illustrated the transition region poorly)

Basically, we want to probe on the minimum edge of turbulent flow regimes with a multi-sheet friction buffer system. Just opt for an outright change of Reynolds number according to the abilities available for experimentation. This would be the 10% of ultimate knowledge I'm interested in. This would set the stage for everything that may (or may not) come in the future.

The good news - all this slashing of the metrics gets our experiment size way down (the scale is highly sensitive to Reynolds number). And that gives us some wiggle room. With lower Reynolds number, we can play around with more sheets (even up to 10 or 16 as I'm dreamed about), while staying at least in the turbulent regime. With the same general equipment, dial the numbers the other direction, and see about higher Reynolds number channels with fewer sheets.

Once you start chewing on this, something new starts to take form - a general format of the development path. Because as these numbers are dialed back up to the full scale (with more resources), its possible to speculate when many different components of the design will be proven in principle. After that, you can image at what point those components will mature into a representative suite of technologies. For instance, at certain numbers, the intra-sheet flow management will become testable. At another point later on, active controls for maintaining the seals could be strapped on.

So now we've covered 4 (mostly) independent factors. I think this is probably the right way to look at scaling of real, physical, experiments. These can start on a household scale.

Wednesday, April 27, 2016

Illustrations of the Friction Buffer Tapers

This is a fairly simple illustration of the problem that we start out with. The friction buffer concept was conceived of essentially within a cross-section of a gravity tube and the surrounding sheets. As the ends of the tube's hull is pinched, so must the friction buffer sheets as well. The problem comes down to how we manage the geometry of the sheets in this area, as well as how we make the moving connection.

Two solutions have presented themselves as relatively strong candidates for an ultimate solution. They both have a similar pattern to them. The sheets pinch in with both ideas, but in the "zero" solution they terminate against the next-inner-most sheet, while in the "nested" solution they terminate against the hull itself.

Here is a quick sketch of the taper-zero solution. Keep in mind that this is 1 quadrant of what is illustrated in the above problem sketch.

Here is a quick sketch of the taper-nested solution. The calculation for the connection points is different from the taper-zero, and this causes the connections to happen at small radii, and possibly face higher velocities at the connection points. An advantage is that connecting to the hull is probably easier, since it is a hard surface.

For the connections themselves, I envision a tensile tensioner acting at the end of the sheet in order to control the clearance and positioning of the sheet. This applies for both of the concepts.

Hope these were fun to look at. I'm not much of an artist, but since the hand-drawn sketch is a popular style these days, I figure "why not" and avoid the tedium of creating these on a computer.

Friday, April 22, 2016

Introduction of "Taper-Nested" Friction Buffer Connection Scheme

Suffice it to say that a minimum viable case has been made for the engineering of the friction buffer connection points. However, the very day after I claim to have "solved" that problem, I noticed that another scheme is possible, and possibly even better. I will make this post as a brief introduction, and I apologize for the painful lack of illustrations this leads to.

Let me clarify the naming - the names refer to whatever kind of logic sets the pressure around the (moving) connection points (seals). You can see that this, combined with the velocity constraint, forces all of the other parameters to follow suit. That's why this taxonomy makes sense. In the taper-zero scheme, all seals were approximately at ambient atmosphere pressure. Note that all friction buffer sheets are at a slightly positive pressure in order to maintain their shape with a controlled leakage, and this extra positive pressure is not accounted for directly in the math (partly because there is no lower-bound, and partly because it may be small enough to neglect).

Imagine, instead, that the seals connect to the tube itself. It's irresistible to call this the "hull" of the artificial gravity tube. The interior is obviously where people live, but the exterior may be just a metal wall. Picture connection points all along the sloped part of the hull. There are 2 options for how to determine the spacing between those connection points:
  1. Constant distance between each connection
  2. Setting connection location based on a invariant relative velocity limit
Once I ran a few numbers, it quickly became clear that option #2 leaves the majority of the connection points clustered very close to the end opening (at small radii to minimize the velocity difference between the sheet material and the faster rotating tube). After chewing on this a bit, I find that this sets the stage for the central engineering tradeoffs for the friction buffer connection engineering.

Engineering Showdown between Solutions

Taper-zero connects sheet-to-sheet. This taper-nested scheme connects sheet-to-hull. Making the connections to the hull will give better predictability and stability, because the other sheets and highly deformable. The advantage of the taper-zero approach is that the relative velocities at the connection points are very slow and consistent, while at the same time they are evenly spaced and open to atmosphere for maintenance.

Now compare to the taper-nested approach. This scheme puts each friction buffer sheet fully inside of the next outer-most one. Getting to that connection to do service work on it will be much more complicated. Also, they will require awkward clustering toward the end if the relative velocity is kept constant. Alternatively, we can assume the constant distance spacing, and we find that the connection points have variable, and often quite high, relative velocities. This is riskier (but might be preferable with the advantage of the stationary hull), and it also imposes a meaningful air drag penalty. The additional air drag may be partially compensated for by increased spacing between sheets compared to the radially symmetric portion.

We're not done yet. Recall the central concession of the taper-zero approach - that the friction buffer sheets must have substantial material strength. This is partly to compensate for the radial acceleration of the air in its region, but mostly as a design tweak to keep the seal at close to ambient pressure (thus the "zero"). For the taper-nested approach, leakage air is recycled from one stage to the next. That means that the sheets connect at a pressure which is already higher than ambient due to a non-zero radius. In taper-nested, you wouldn't strictly need holes in each sheet to allow ingress into the next stage, because the loss from one stage is also the loss for the next-most stage.

My initial hope was the the material strength of the sheets would be lowered in the taper-nested scheme, but so far I have not been able to nail this feature down, and it could go either way. Jury is out on that topic. It is also not obvious that one is simply better than the other, and I may be hedging my bets between the two for quite some time to come.

Thursday, April 21, 2016

Artificial Gravity Tubes with of the Mashveya World with Friction Buffers

There are now honest-to-god friction buffers being utilized in fiction and world-building. Check it out at:

This author illustrated the tethers used to spin up a tube, as well as a buddy system for spin maintenance. For future reference, here is one post that contains both pieces of content. This has a great deal of technical accuracy. You can see in the axle mount system (buddy system) that there are trusses necessary to handle the varying compression / tension action with changing the direction of angular acceleration.

The world these designs exist in is called Mashveya, and uses transportable fuels (like hydrocarbons) for their energy economy, so these are free floating and exist in a smoke-ring type world with a fairly low density of habitation. I find this image with additional world context quite stunning. Calling this a catamaran system makes a lot of sense.

Quite a few possibilities jump right out at me. Many different methods of navigation would be possible. You could use some flow control to direct air out one end to power flight in the axial direction. It would even be possible to fly perpendicular by allowing the outer-most sheet to spin freely, and blocking flow around the middle portion or on the two sides. I might diagram some of these later. These are extremely cool. Seeing these brings an entirely new perspective to some of the underlying concepts.

Wednesday, April 20, 2016

The "Taper-Zero" Design for Friction Buffer Tapering and Pressurizing

Gravity balloons, with friction buffers to allow artificial gravity inside them, have so-far had one major design aspect missing. There are a few reasons for this. Partly, it was an non-intuitive problem, and every time I returned to it, I started out going down the wrong track with a careless sign error somewhere in there. Another reason is that it's genuinely a hard problem. But the main reason it has taken me so long to present a full solution is because I didn't want to accept what the math was telling me. Up until this point, I have always wanted to imagine the friction buffer sheets as something with a zero-thickness limit - something that could be literal paper, aluminum foil, or some other absurdly thin material. This was unrealistic and didn't fit with the other basic realities of the turbulent reference design parameters. I also resisted a 2nd obvious design decision, which was to have the moving seals connect sheet-to-sheet as opposed to sheet-to-center-line-structure. I may go into those trains of thought, but in this post I mainly want to communicate the bare minimum to lay out this design.

The problem is how to "terminate" the friction buffer sheets. For the bulk of an artificial gravity tube, there is radial symmetry, so the problem is relatively easy to envision. The fluid flow between sheets is very nearly approximately a parallel sheet flow problem. The basic mechanism to reduce friction is flushed out in the radially symmetric form. Intuitively, it seems "messy" to picture how the sheets pinch at the end, similar to the tube itself. No matter what specifics you opt for, this also introduces a moving seal, at which point an engineer may think "yuck", but still accept that there's no choice but to deal with some seals. We take comfort in the fact that, while the seal length is large, it is at low speeds and low pressures. The problem that really blows down the house of cards is the realization that, as the sheet pinches to the contact point, the air pressure in its volume decreases - and that different layers decrease at different gradients.

I've summed up some details of this problem space in the last post and at other times in this blog. So here I want to jump right into the solution space.

The Solution Space

A design solution starts by holding something specific constant, and then fills in the rest of the values from there. I will name the different solutions according to that assumption. The first intuition I had was to terminate all friction buffer sheets very close to the tube's end opening, which I will call the taper-center design. This is still a possible solution, but I believe it's inferior due to the complications of making the seal act between the flexible sheet and the stationary connection point around the tube ending.

As I came to better understand that the pressure distribution within the friction buffer region would be a problem (at all), my natural intuition was to imagine that there is no pressure difference over the radially symmetric part of any of the friction buffers. I would call this the sheet-isobaric solution method. This start with the assumption that we will preserve the "no strength" requirement for the sheets, and figures out where to go from there. The problem comes when you pinch in toward the end opening - even the slightest bit. The pressure drops as you decrease radius, but the real kicker is the fact that pressure drops (a) below micro-gravity ambient and (b) faster for the innermost sheets. This means that in the taper region the sheets will be "sucked" in towards the tubes. Combating this would require complex, rigid, and moving parts. I hate all 3 of those adjectives! The fact that the sheets can't passively maintain their shape if they don't have a positive pressure is what I will call the convexity-constraint. How often do you see a balloon with sharply convex shapes? Never, exactly. Now, the balloon notion here is different from that of the overall gravity balloon. But for simplicity of operation, we all but demand that the friction buffers act sort-of like a balloon so that they don't need rigid members. Moving on, why does this constraint create any problems? Why do we need to taper (pinch at the end) the sheets at all? Why can't we just terminate them against a rigid structure at the radius they start out at? Because that would demand a moving seal at > 100 mph, and defeat most of the purpose of the friction buffers in the first place. This is what I will call the velocity-constraint.

Maybe we can come to something of a compromise here, and now we arrive in a design space that I found to be a large bit of a pitfall myself. I imagined the sheets terminating against a rigid structure that fanned out from the end opening. This increases the radius in a graded system, and thus largely avoids the velocity-constraint. I might call this the center-graded deign, and it has some neat properties, but those properties wound up being largely irrelevant to the problem. These configurations just couldn't save us from the convexity-constraint. By connecting to a seal with a rigid structure at low radius / low velocity, you are still going to run into that sucking problem and have to use a massively expensive system to partially pin the moving sheet to the rigid structure. I struggled in this logical knot, trying to somehow make the pressure gradient turn around in my mind. Alas, when you rotate stuff, it wants to fling outward. Fighting that is a fool's errand, and tension is better than compression by 10x factor or greater.

So let's move on to accept taper-zero hypothesis and design. The cold logical facts are telling us that the friction buffer sheets (1) are concave geometries (2) must have positive pressure compared to ambient and (3) must have positive pressure relative to the next outer-most sheet. This is a mouthful, it is weird, and it sacrifices some of the most beloved assumptions up until this point. I believe there is a logical train of thought directly from these principles (hard-fought conclusions from the previous failed design spaces), and I will probably not do that train of thought justice here, and I will be skipping some. But the final insight is pretty cool.

A combination of two, and somewhat a 3rd one, factors suggests that we don't connect the sheets (moving joint) to a rigid structure, but instead to each other. Those are the convexity-constraint and the velocity-constraint together. We want the outer sheet to connect at large radius (velocity, combined subtly with a desire to keep strength requirements low), but we also want to keep the friction buffers "puffy". We wind up with a vision of one puff puffed out on the outside of another puff. Now, for pressure, this suggests that the connection between the puffs is just a little bit higher than ambient. This directly suggests what the pressure of each stage will be like (assuming you have values of radii for connection points, which you can just get directly from the velocity constraint).

Taper-Zero Design Specifics

Each sheet connects at a different radius - smaller radius for the innermost sheet, and large radius for the outermost sheet. The exact picking of connection points can be engineered to your own desire. Here, I'm going to be using the velocity constraint to have all sheets move at the end-opening speed at their connection point. I'm using 10 sheets in this reference design, because 16 (a previous benchmark) is just too labor intensive to illustrate.

These sheets will actually have a pressure at some minuscule value over ambient at the seals, and they will be constantly leaking air (I'll talk more about this later). Additionally, there will be no complicated system maintaining the pressure and position. Instead, the 2 ends of the friction buffer sheet will have a simple remote-controlled tensioner unit which can increase or decrease the clearance distance (thus impacting the leak rate and the pressure).

Start from the seal, and move outward toward the center of the channel in the radially symmetric portion of its geometry. The pressure increases, depending on how fast that stage is rotating. The ultimate pressure in the channel is almost entirely a consequence of the rotation speed of the stage. Next, observe that inside of the channel there is some radial pressure gradient, but the sheet is also holding back some amount of air pressure as well.

I don't know if this fully illustrates it, but it is an attempt. This graph is telling the story for each stage, going from the connecting point (venting air to atmosphere) to the channel interior.

Next, let's look at the profile as you increase radius from the center-line in the center of the tube. You can't literally traverse this path, and this is just an illustration. The tube itself has a pressure increase from ambient, dictated by its rotation. The innermost friction buffers mostly inherit these same numbers.

The big point I want to make here is that the friction buffer sheets are fighting the radial gradient of air pressure. In the 2nd graph, you can also make note that the saw-tooth looks different. The "step" part of it has a slope to it that the outer layers don't share. This is because the inner layers are rotating faster. That shows the presence of a strong radial air pressure gradient toward the inner-most layers compared to the outer layers that are most stationary.

Air Flow

The floor of the artificial gravity tube, and the sheets themselves, would have holes in them. Not a huge number - there is no obvious lower limit. The inner layers would have more holes than the outer layers, because air must flow through them all to get to the outer layer while ever layer loses about the same amount to leakage.

In this scheme, while the air flow percolating through the layers can be actively controlled, it is not necessary. It would be more simple and still effective to just operate the tensions that control the leak rate along the seals, and these would be tremendously simple seals.

In retrospect, abandoning the dream of zero-strength requirement sheets bought us a lot. It's that simplicity that I see coalescing the design where someone can put their foot down and say "yes, this all is consistent and coherent now". I still see possible improvements to this, but the important thing to note is that I see them all starting from this design as a template.

What's left to do? I need to revisit the impact of elasticity. It was never really an issue before now, but with the sheets holding back some quantity of air pressure, it will be relevant again. Trickier - it may change as the rotation rate changes. That demands some extra engineering of the seal actuation during spin-up and spin-down. Nothing crazy, I can already mentally picture a lot of the specifics. It's likely that the tube would have auxiliary compressors that will intentionally inflate the friction buffers while the tube is not yet rotating. Predictable movements in this phase of spin-up will give confidence to begin rotating the entire tube.