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.
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