Taper-nested With Slightly More Space

Starting out, let's walk though a graph of the style given in a prior post. The question we are asking is "where can we terminate sheet number N", because they don't come to center-line. Somewhat arbitrarily, a relative speed of 3 m/s is allowed, as a seal must be established over that relative speed. The two series of air-relative and tube-relative give the maximum possible radius where the sheet will be at 3 m/s relative to the tube or to air.

In this case I am using a 500 meter radius tube, because I'm also interested in exploring those larger sizes here.

An easy observation is that, on the sides, relatively few sheets are allowed to have a relatively large opening. Because these are relatively few in number, I've draw in a "design" line where I'll simply use less than the maximum for the edges. I believe this will help both sanity (for now) and possibly logistics in practice.

The meaning of taper-nested is that the sheets come in towards center-line as much as needed. This graph means to quantify. Using these specific numbers (with 32 sheets, chosen somewhat arbitrarily), I want to give a better scaled illustration of what a "larger" tube of 500 meter radius might look like in practice, as a cross-section. You should note that the access opening here is more like 20 meters in radius which is somewhat less than the opening for the sheets around the center. For scale:

Going from big to small, with this being an end-on view:

• Grey outer circle: 500 meter radius of actual tube itself
• Green circle: the center opening of the outer-most friction-buffer
• Yellow circle: the center opening of the middle friction-buffer, the smallest center opening of the center openings
• White center: the access opening for moving people, goods, and air, in and out of the tube

This helps to illustrate the R^2 factor, as an increase in linear dimension of 2 is a difference in area of 4. So it certainly seems worth it to use any extra buffer space possible, as opposed to having a long access tube where the access opening is.

Aside: there is a weirdness here, which I need to give in specific terms:

• Sheet 16
• moving +3 m/s relative to the tube
• moving -3 m/s relative to the outside (stationary) air
• The actual hull of the tube itself, buttressed against sheet 16
• moving 3+3 = 6 m/s relative to the stationary outside air

This is a oddball kind of situation. At first look, it seems to me the most reasonable thing would be add 2 additional sheets around the access opening that divide the relative speed between the tube and outside air. This would only cover the distance about 20 meters to 40 meters in radius. Dreamily, I wonder if these might be retractable for cases where traffic is higher or large items have to be moved in or out.

Wrapping up this thought, I want to give an accurate sketch of the 500 meter case, at last.

The somewhat incredible density is why I'm always talking about a 250 meter reference, instead of this, which is twice as large and has twice as many sheets. This is more material-intensive, and less space-efficient. Nonetheless, I must acknowledge value in human factors of slower rotation (thus Coriolis forces) and and more wide-open interior space.

I also needed this to articulate the side view of taper-nested in mostly the standard sense but just adding some very detailed-oriented tweaks.

The Bleed System

The diagram above makes it very hard to believe that the sheets could resist any external force. Again, these will be inflated like a balloon. Each sheet hits either a rotating structure or an externally-connected static structure at an angle near to 90 degrees, maybe 80 or 85 degrees. This means that it lacks any kind of backstop, or buttressing, for the flow dividers as I suggested in another post.

In other posts I have mentioned another design element that I assume is present in basically all my writings. In essentially any case you need a way to put additional air into the sheets to keep and outward pressure to help maintain the shape. The rotation itself does this to some degree, but probably not enough, and not for the entire shape. These prior pictures here mention a small flow of air. Let me redo that same thing, but with the 500 meter reference in mind, and more granularity, and introducing a new thing - soft segmenting of the shape.

Again, return to the fact that there is no surface for the friction-buffers to "push" against to maintain position, at least in the axial direction. What's a way around that? Well you can just puff air into one end of the friction-buffer. Because of the small channel size, this is likely enough on its own. This is a big construction, so we probably going to want at least a handful of these in every sheet, add some sensing, and control systems to respond if needed.

But there's one more way we can do better. I added dotted lines to suggest that we can introduce additional very suggestive flow dividers between two of the sheets. These would not be a tight seal (they have no need to be), but would just lightly reduce the amount of air flow your valving or pumping would need to move to affect the shape at a particular place.

Bleed System Design Space

Similar to the previous pictures I've drawn on this, the above illustration implies that the air bleed system is a network of valves. These are passive devices that let air flow from an inside sheet to the next out-most stage depending on how far they open. Going all the way to the tube itself, pressure is always higher in the more inward stages, because they are rotating faster.

Even if the valves are passive, they may or may not have any controls applied to them. Without computer control, they are simply holes in the sheet... probably holes of carefully selected areas. These would simply be holes that let some air through, taking advantage of the pumping that is already happening by the main rotor. This air can is then used to maintain the inflation of the sheets, and the air ultimately leaks out the sides. The reason this has started to interest me is that I've realized that this could be relevant for early experiments. As those experiments are mainly going to be concerned with wedge effect and wobble, shape-keeping is likely to play into that. Sacrificing a teensy tiny amount of efficiency could mitigate potentially larger problems of contact and failure.

For extremely large tubes, these are extremely large operations, and if we can do better we would. The problem with passive valving is that it puts the air in a free-jet condition where it loses a LOT of its energy, because it's more than what's needed. The alternative is that you could have pumps go from the outside in, as opposed to inside out. The pressure difference you need to deal with is relatively small, and these are technology-level of computer case fans. But again, this could feed into the control system to prevent sheet-to-sheet contact which could be a very big deal.

The (lack of) Prior Art on Annular (Cylindrical) Flow Dividers

Myself, using old Google Scholar, I previously struggled to find any literature that might hint at the fluid dynamics mechanism I've proposed on this blog, which I tend to call the "friction-buffers". Let me be super clear what this describes:

• Layman:
• A tube in air is rotating, and it is surrounded by cylinders of increasing size. The cylinders rotate at slower speeds, because they are dragged by air movements caused by the tube. The cylinders allow us to spin the tube more easily than if they were not there.
• Kind of fancy:
• Multi-Annulus Taylor–Couette system with freely-moving intermediate cylinders
• Another:
• Segmented annular flow with passive staggered rotation enabled by flow dividers that suppress Taylor Vortices

I want to be abundantly clear about this - I do not want this to be my original idea. That just makes it harder to defend. Over and over again I tell myself that somebody must have come up with this idea before. But if I search I come back empty handed.

Gemini Research Output

That hasn't changed. But what has changed is that we have AI now, so at least I can prove that the AI can't find comparable background literature either. In case anyone was going to ask, although I am a major AI power-user, absolutely none of what's written here is from AI. Here's output from the latest Gemini:

https://gemini.google.com/share/0c90b978750a

Let me highlight the 2 key conclusions

1. It agrees with me. It didn't even take convincing by follow-up prompts, which other AIs have.
2. It can't find background literature either

On the first point, here's an evidentiary quote

The investigation into using intermediate, free-floating concentric cylinders to reduce viscous drag and suppress turbulence in high-speed annular centrifuges confirms the viability of this hydrodynamic control technique as a compelling alternative to vacuum operation.

I want to call out the bold, and really emphasize that this goes way further with the claims than I ever would have. This is probably not useful for Uranium enrichment or any other lab centrifuge applications. If drag matters, you can probably solve it by pulling a vacuum, and if you can reasonably pull a vacuum, that is obviously superior to the method I've proposed. I wouldn't call that "compelling", but if I was in academic I would probably write that anyway... but that's just an academia thing.

In any case, if this could be useful and practical for centrifuges, it's almost guaranteed to work for the much larger and slower case of free-floating tubes in microgravity. This is a full-throated endorsement. All the AIs agree, for whatever that's worth, which isn't much.

And as for (2), I'll just have to show you what it did find.

Rotating Half-Discs Drag Reduction

The best reference by far is:

2021

Reduction of turbulent skin-friction drag by passively rotating discs

https://eprints.whiterose.ac.uk/id/eprint/209042/1/2106.12824v1.pdf

This is abundantly clear that it proposes to have discs on a surface with a fluid moving over it, where half of the disc is kept under a divider. This allows the disc surface to be closer to the velocity of the fluid as opposed to the surface. It is very intuitive how this could work with the discs being rotated passively by the fluid, just like it is intuitive that you could reduce drag by putting a treadmill on it. These are just slightly more practical variations of a passive treadmill (if I am to tell it).

You see half of the discs because the other half is covered

Ok but this is still a bit abstract without a use case. I like this sketch, because it looks like an airplane wing.

Airplane wing maybe, my own interpretation

Could this method improve the fuel economy of an airplane? Yeah, that's totally physically possible. This idea does share many properties of the friction-buffers proposed in this blog.

• Introduce a flow divider (in my case) or a skin friction attacher (their case), which is a "sheet" in all cases
• Allow that sheet to move passively, meaning, it is moved by the flow itself
• There is an expectation that the flow becomes less turbulent, and the energy lost due to viscous forces decreases

So almost-check, check, and check. The other difference we might point out is the entire geometry is different - a surface vs. annular flow.

It looks like this paper also covered the same thing

2013

Turbulent drag reduction through oscillating discs

https://www.researchgate.net/publication/258796176_Turbulent_drag_reduction_through_rotating_discs

However, that was much harder to follow because none of the pictures made it entirely clear what it was showing.

Other Close Misses

This paper describes a passive mechanism for drag reduction in Taylor-Couette flow. Seems promising!

2024

Research on the Sealing Performance of Segmented Annular Seals Based on Fluid–Solid–Thermal Coupling Model

https://discovery.researcher.life/article/research-on-the-sealing-performance-of-segmented-annular-seals-based-on-fluid-solid-thermal-coupling-model/aabc017bc11133f9a41c1f81a3ec4b33

However, that is very clear that it optimized using a groove design. And looking at the pictures further, it might not even be talking about the general topic at all.

Looking further into papers on Taylor-Couette flow is an exercise in madness. One takes two cylinders (tubes) and places them next to each other and has them spin.

I'm tempted to believe that somebody wouldn't write a paper on this friction-divider concept. Let me explain why in 2 scenarios:

• Do not include the effect of oscillations with movement of the cylinders (global stability problem), you've effectively made an undergrad-level problem, not worthy of CFD or of a paper. It's too easy and the effect is obvious
• Include the movement of cylinders, you've added mechanical boundary movement to your CFD at which point you've made a problem that's too hard and give up

So basically, to get progress, I, or you (the reader) need to do it ourselves.

CFD or Experiment

Experiment.

This brings me back to my prior dichotomy. It's either "CFD is useless" or "CFD is impossible". Also, looking towards the specific application, the predictable objection should be a tiny bit more nuanced than "you can't divide the flow in half". Problems you're most likely to hit probably won't occur until you're at a high number of sheets. Not just 1. I'm thinking 4+ sheets to really get some value out of it.

I have some material to write on global oscillations, and maybe it's correct in its approach. But there's no natural confidence in it. Actually doing the experiment, showing the friction-buffers stay in place, and demonstrating a performance gain, would get miles and miles further confirmation that eigenvalues from the coefficients that you came up with on your own. Garbage in, garbage out.

Numbers on Staggering, and new Buttressing Idea

 Qualitative drawings of the friction-buffers sometimes miss an important details, and I believe this is true of the final illustration of my last post. Here, I hope to simply drive this train to thought to its final conclusion in broad terms.

Specific Numerical Methods for the "Ruler" Shape

Doing this took a spreadsheet (intent is that it is publicly visible).

Let's start out writing down some criteria. I was inconsistently using an incorrect criteria that "radius of sheet termination is where its velocity is within +/- 3 m/s from its neighbor". This is not correct, so I'll write the correct criteria in a bullet point:

• constraint: All sheets at all point must move +/- 3 m/s relative to all its neighbors, at all points.
• consequence: As you widen the opening of one sheet, the relative velocity of its revealed neighbors must be +/- 3 m/s
• for some sheets: this is the same as being within 3 m/s of its neighbor
• for other sheets: they must divide up the flow between sheet numbers far away from its position

These are stranger than they look, and give the reason for the "ruler" shape I outlined before. However, I only did that qualitatively so I'll just do the same in a quantitative since here. You can refer to the spreadsheet for numbers, but for completeness I need to give the algorithm because it's not as simple as an equation. Start with the scenarios of interest:

• 125 meter radius, 8 sheets
• 250 meter radius, 16 sheets
• 500 meter radius, 32 sheets

These are chosen because they satisfy the 2^N number, and also because they're close enough to previously published numbers such as to be presumed acceptable in terms of power consumption. Now, for each scenario, for each sheet:

• Calculate the statically-obvious values for each sheet (1-8, 1-16, 1-32)
• The radius of the sheet in the middle cross section
• The angular velocity of the sheet
• For the 0th and Nth entry you can enter in the tube's angular velocity and 0 angular velocity
• Go to the N/2th sheet
• This sheet will have the 0th and Nth sheet as it's revealed neighbors, so those are entered as the 2 relevant neighbor angular velocities
• Divide each remaining numerical segment into 2, and fill in revealed neighbors for its apparent neighbor
• Example: the N/4th sheet has 0th and N/2th neighbor as neighbors
• Repeat this process to fill in the rest of all the neighbor angular velocities
• From those revealed neighbor angular velocities, find the point that the neighbors are moving 3 m/s relative to each other, and that's how wide the sheet's hole can be 

This is very weird, but it still produces the same "ruler" shape. Here, I report the height from the floor which corresponds well to the illustrations from my last post.

R=125 meter scenario

R=250 meter scenario

R=500 meter scenario

In all these cases you still get the "ruler" shape... however, even for the smallest "ticks" on the ruler, there is still significant height from the floor, about half-way. This just seems to be how the math falls out, you can reason out why if you try hard.

Material Reduction from Staggering

Comparing to the taper-nested reference, we use less material, because the only real observation here is that some openings for some sheets can be made larger (thus, using less material). So let's slap an improvement number on those.

		Sheet area
R	sheets	no staggering (km3)	staggering (km3)	improvement
125	8	2.850	2.916	2.25%
250	16	21.213	21.707	2.27%
500	32	162.888	166.682	2.28%

It's as well-established prior observation on this blog (almost from the first post) that you have to use more dividers (and thus divider area) as you go to bigger radii. I didn't adjust for this, meaning that 500 meters gives bigger livable area in addition to needing more supporting material, so keep that in mind.

The "no staggering" case presumes that all sheets have a hole which matches the size of the access hole exactly. Then there are a number of route geometry work to sum up all the areas of all the sheets, and that's what I did for both the "no staggering" case and with the data shown in the plots.

It is kind of interesting that there is more improvement for larger sizes, but in absolute terms it is marginal in all cases. This will bring me into the economic argument later.

Decent Illustrations of Staggering with Curvature

With this, I can try again with the prior paradigm to draw the friction buffers. I still don't aim for exact numbers, but wanted to get something representative. As you might have guessed, doing anything other than the N=8 scenario would be tedious, so all drawings would map to the R=125 meter scenario.

This gives us a couple of things we were looking for, with some drawbacks.

• Good:
• Friction buffer sheets legitimately have outward curvature everywhere, without any dramatic conceit like a rigid floor integrated (last post)
• The access window is acceptably small-looking, it's an single circle as opposed to a long tunnel, should flow air & people & goods well
• Bad:
• Space inefficient, as you can see big open spaces inside some sheets, mostly an artifact of striving for an exactly circular shape for the inward curve
• The connection angles are terrible at several connection points... I can barely tell what's happening in some places

How can we clean this up? Look back at the plots, you see that sheets 0 (the hull), 4, and 8 all have to come in almost exactly up to the access window. We have not yet taken advantage of the taper-nested idea, so we will do that. However, we want to do it in a way that maintains the direction of outward curvature and gives nice nearly-right connection angles which is important for the air ingress management system.

But visually, this is the thing that didn't work because of the circles. So we will only partially relax that. We will make the mentioned sheet number, 4 (the hull is already straight), and like the hull, straighten it out. This will have a partially-straight segment (might have to be rigid) but the rest of those layers outside of this area will still work like the other dividers.

Doing this, with an eye to connection angle, we'll also return to the slanted hull shape. Here we go:

This is fanciful. To allow the new straight segment we had to re-introduce a long access tunnel. Tradeoffs:

• Good:
• Compared to last, we have good solid connection angles
• Bad (mostly everything else):
• Re-introduced a long access tunnel
• Even less space-efficient

Practical Considerations Leading to Buttressing Design

At this point, we will lean into rigidity, but with a more clear-eyed vision of where we'll go. But first let's better formalize a requirement instead of the hand-waving "connection angle" mention.

• Requirement: we are able to hold the friction-dividers in place
• Radially:
• wobble can be partially dampened by contact near the end cap
• non-periodic bulk forces, like air currents, micro-gravity forces, can be resisted by the edge of the friction-buffer pushing against something
• Axially:
• here too, bulk forces must be resisted by giving it something to push against

If you look at past sketches, it seems clear that taper-zero could have a problem, since it's balloons pushing against balloons. The case of taper-nested seems like this requirement isn't a problem, but you have to pull up the numbers to see that most sheets have to terminate very near to the access window... which isn't necessarily a problem for radial stabilization, but axially there's nothing to push against. It's not obvious that this is a problem but it could be a problem.

To accomplish the ideal for all the stated goals, I'll double-down on the rigid segments for certain flag-leader sheets, and further sacrifice the circular shape. I'll mark the rigid parts with a bold line. This still uses smooth circular curvature in places, but also demands a custom shape.

Instead of a long access tunnel, we will simply angle the sheet N=4 inward. By keeping it at an angle, we still satisfy both the radial & axial push requirement.

Trade-offs here:

• Good:
• Minimal clutter around access window
• Vastly more space efficient, with the theoretical "triangle" wedge shape starting to emerge
• Able to buttress the friction buffers against movement in all directions
• Bad:
• The rigid segment (only for N=4) must now move at a different speed, this requires a stronger direct mechanical coupling over this moving joint for the mechanical forces involved

On the bad, I want to be clear this isn't just a different speed for the outside air (which is stationary), but is between the inner tube and the outside air. So it is offering a "checkpoint" kind of speed so that the slower sheets can push against it and the faster sheets can push against the hull.

If you refer back to the graphs, you can logically predict that very large sizes will have more checkpoint friction-buffers, all requiring mechanical connection and rigid parts. For extreme sizes, you might require not only several checkpoint sheets, but a tree-like network of these extending out at +45 degree and -45 degree angles, every one at a unique speed.

I'll end it here, but want to add one more claim that the benefits of de-cluttering the access window are likely to be greater at greater sizes. Because at those sizes you are managing more sheets with roughly the same spacing between them. So balancing mechanical thrust on those sheets precisely becomes a much bigger deal. In short, when you get big enough you will want buttressing for the friction-buffer sheets. That seems reasonable and intuitive.

My sketch here is awful, they would all be smooth surfaces in practice. 3-D printed, I'm sure. That's likely overkill for small tubes, but this is at least a path to a scalable design that I can endorse, and that's important.

Wide-Mouth Taper and Group-Based Termination (Staggering)

Here, we will entertain an alternative to the tiny access center-hole at the ends of a rotating tube in a gravity balloon (or generally, artificial gravity integrated into atmosphere). Return to our reference design:

• Radius of ground: 250 meters
• Access hold radius: 15 meters

The 15 meters could be pushed, of course. Because it's not that large to begin with, we may be able to accept a larger relative velocity to get, say, 20 meters radius for this access opening at the cost of slightly faster edge speed. That is 40 meters wide. While, to me, this seems sufficient to supply such a tube, it's not the only option and I want to give proper treatment to the alternative.

To start our goal - this is asking for a greater area at which the tube can interface with the surrounding atmosphere. Similar to cans going from the traditional opening to the "wide mouth" opening.

Wide-Mouth Can

Unlike the cans, however, we will go as big as we can, up to occupying the entire cross-section of the tube. Erase everything I've written about the termination of the friction buffers. We have a tube (like the tube of a toilet paper roll), and we know we need the friction buffers around them, and we know that the tube will be moving too fast relative to the atmosphere if we leave it as-is.

Making the Floor Itself Move

To make this work, we will move the ground itself. Similar to how (in any rotating artificial gravity habitat), you can get lower gravity by climbing a ladder, in our new innovation here, you will get lower gravity by walking onto another segment of the tube that rotates more slowly. Yes, this will require some kind of mechanical, moving, coupling between the floor moving at different speeds.

What else do we need? The moving floor segments will be connected to a friction buffer at the matching angular velocity. This connection happens under the floor, so would not be observable to residents. Now we have a tube that rotates fast in the center, and then rotates at decreasing speed as you go to the edge. For less obvious fluid mechanics reasons, this will not be sufficient either. There is quite considerable pumping you will get from this unless the length over which this happens is really really long. That would be possible, but wouldn't be practical. So to smooth out this flow, just like in the other friction buffer termination design, we have to add dividers and this time it goes into the interior of the tube in a very obvious way to the residents. We have enough to sketch now. This starts from the cross-section perspective I've used in prior posts and illustrates the described setup.

Wide-Mouth Tube with Variable Speed Floors

You need a lot of imagination for human-scale stories happening here. The diameter of the large tube is 500 meters, and a human is less than 2 meters. The relative speed between each segment of floor is the same as the existing reference design, 2.9 m/s, 10.5 kph, or 6.5 mph. Speaking personally, my running speed is 7.5 mph, so physical able humans can physically jump from one to the next (assuming no "video game platformer" gap). Moveable walkways travel at more gentle speeds of 2 mph, but the internet informs me that some go up to 9 mph. So real-world movable walkways could cover this, and one on both sides could easily cover it.

Because of these factors, I assume some minor assistance would be added if the gaps were to be traversed on foot, specifically one or two literal moving walkways. What happens after stepping onto the next segment? You are faced with the flow divider. Could a hole just put be in that? Maybe. There is expected to be some pressure gap between one stage and the next, so if there is a door I expect some door-opening resistance, and if it is left open, I expect some notable airflow that contributes to losses. To avoid travel delays, you would need doors along virtually the entire radius so I could see this being a problem. Reminder - if the pressure difference is too great, you can do the good-old 2-doors and a room in-between trick. This is similar to an airlock, but... just ordinary doors.

How would a vehicle travel from the tube interior to the edge? I'm at a loss. You wouldn't use a railed vehicle (how do you match the tracks on the next shell?). A rotating mechanical device to pick up the vehicle and place it at zero velocity on the next shell sounds expensive, but trivially possible. I think my favorite idea is that each shell has ramps built into it, and the vehicle goes in the circumferential direction and jumps to the next shell? Sounds fun.

I frankly have no idea how truly practical it would be to travel this way, it is an exercise left up to the reader. All I have to offer is the observation that it is an additional option. The above-illustrated design does not lose any utility compared to the other designs seen in taper-nested or others throughout this blog. You can ride a lift to the center-line, and then ride a gondola through the center hole into the microgravity space. This checks all of the boxes of being physical, economical, and practical. I just have no idea whether it is useful. If I'm maintaining a list of canonical ideas, things I accept as being in the real design space, count wide-mouth in!

Reducing Clutter, Group-Based (Staggered) Termination

While I'm iffy about the usefulness or need for this, it is academically useful to me to clarify the remaining work we need to optimize the termination of the friction buffers. As you can see in the diagram, this really is the same thing as the other designs, just with a different curvature to the geometry of each sheet (and a floor added, not relevant here).

Let me describe the obvious issue - at the edge of the access space, the sheets are moving at a relative velocity of 0.3 m/s, or less than 1 mph, all while assumed to have the same spacing between sheets as the rest of the geometry (it must, due to the velocity at the floors). This is much less speed reduction than what we need. We can pull that back for some sheets (make the center hole bigger)... but which sheets specifically?

Re-stating our constraint - the relative speed of each sheet must not be more than about 3 m/s relative to its neighbor. But if you reduced the inner radius of all expect the 1st and last, then the relative speed of the 1st and last becomes too high... as they kind of become neighbors. This leads me a form of grouping, like the markers on a ruler.

Center Opening Widened, Relative Velocity Still OK

This is a strange outcome, but I believe it to be legitimate. This also lifts the concern about traffic jams due to a very long and relatively skinny access tunnel. Yes, we still retain a single choke point, but it's not a choke tube. It opens up the atmosphere in the transition region... somewhat.

Implications of Group-Based (Staggered) Termination for Other Designs

This also helps clarify what the actual minimum clutter is in all designs. Through this sketching, I have learned something new about what is possible with almost all friction buffer termination solutions. For taper-nested, a brief sketch:

Taper-zero with Staggered Termination

For years, I have had a gut feeling that something was still off in how I was drawing these, and I believe this is it. The reason it was hard to find was that it was so non-obvious how to state the maximum relative velocity constraint, because it applies to the revealed neighbor sheet, not just the N+1 sheet. It also makes sheet numbers of 2^N desirable.

Even with the briefest visual survey of the taper-zero-staggered sketch, you intuitively see less clutter going towards the center. This concept of staggering the circular opening of each sheet is going to be assumed in most designs going forward.

Putting Some Numbers on the Taper Options

 See the prior post for the definitions here:

Illustrations of the Friction Buffer Tapers

Here, I just want to give more elaboration on the specific connection points because they were only drawn in the abstract before. To do this, I have a simple spreadsheet which I'll just leave a shared link for. To explain what I'm looking for, we'll go by the designs introduced in the prior post.

• taper-nested:
• The connection points can connect to a point along the triangular ramp which is at the end of the rotating cylinder. There is a constraint of a maximum radius where we can connect it, because connecting at a larger radius would leave us with a large relative velocity. The reason for existence of the sheets is to minimize drag, so we can't do that.
• taper-zero:
• Each connection point (confusingly) has to of a small enough radius so that it shields the sheet inside of it. This, again, results in a maximum radius value, beyond which the sheet inside of it will make contact at the air at too high of velocity.
• Note, however, that the design calls for the innermost sheet to envelope basically the entire ramp. This this brings the connection further in, to a smaller radius, it does not violate the maximum radius constraint.

This note on taper-zero is going to cause some trouble communicating, so I'm not going to plot its numbers directly (because they don't apply to all sheets), so I'll instead have a series "air-acceptable R" which is the radius at which any given sheet is moving slow enough relative to the static air so that it can be exposed directly to the outside micogravity.

One item not exposed here is that the access opening is assumed to be at a radius of 15 meters. That is largely set by the arguments around acceptable speed (the 3 m/s thing), so it shouldn't be surprising that no point in the graph dips below this radius.

The biggest thing I want to observe here is that the points are clustered fairly heavily towards the center (low values of R). This does quite a lot to change one's visual image, which were poorly represented by the earlier hand drawings.

Let's take taper-nested as an example. Start with the first sheet, and it can connect about 3/4ths the way along the ramp, next, maybe 1/3rd. But then numbers 6 through 17 are super close together. The sheets at their full cylinder radius should be a large distance apart, like 10 meters, and you won't have this automatically with the triangle shape. Thus, a key takeaway is that you would have to elongate the access tunnel to increase spacing. Because decreasing spacing increases drag, just like increasing relative velocity does.

So my revised mental image of the taper-nested looks more like this.

I've added an additional detail which is compartmentalization in the tapering region. This would be a leaky flow divider, and to be honest I arrived at this addition after a conversation with ChatGPT, where it was concerned about "pumping" being caused in the tapering region. I think it is still small, because the tapering region keeps velocities as low or lower than what they are at the full radius... but I still see the point that we have 2 axes of eddy creation, and a dumb divider is a cheap solution. We already have some controlled air ingress through the channels, so they would bend in the direction of the access tunnel.

Onto the elephant in the room - that seems inconvenient. This would make it harder to transport goods and people in and out. Yes, but it's an obtuse academic over-simplification. Given this reference design (17 sheets), there is clear advantage to having the first 3 or so sheets hug the tube, but beyond that, spending the material to wrap all the way to the access point is pure waste. The direct solution basically winds up being what I've already named taper-zero.

I do have many more thoughts on taper-zero, and I need to mature the numerical constraints for that design (angles get "weird", but this isn't... a technical statement). I almost might start over from scratch with a new approach that helps conceptualize the overall design space better. However...

Rejection of Hybrid Taper Solutions

I speculated in another design direction before.

Very Preliminary Thoughts on a Hybrid Taper Solution

I now believe this was an unproductive dead end. It does not solve any problem that mattered. Total quantity of material strength needed for the sheets will simply never be an issue, ever. You spend more on the ground itself. Sheet positioning is a much bigger issue. Keeping the fully or mostly tensile constructions (balloons) also has a big economic impact. Control systems for the air ingress mater, means of maintaining the seals matter. I think what that design direction was offering was just worthless. In the end, with new designs I'm still working on there might some some non-uniformity between different sheets, but nothing like different material composition from one to the next.